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\n \n \n\n \n \n \n \n \n Understanding gambling behaviour and risk attitudes using cryptocurrency-based casino blockchain data: Gambling behavior and risk attitudes.\n \n \n \n\n\n \n Meng, J.; and Fu, F.\n\n\n \n\n\n\n Royal Society Open Science, 7(10). 2020.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Understanding gambling behaviour and risk attitudes using cryptocurrency-based casino blockchain data: Gambling behavior and risk attitudes},\n type = {article},\n year = {2020},\n keywords = {betting strategies,irrationality,optimal stopping,risk preferences},\n volume = {7},\n id = {a8d29724-32ab-39fc-a8b4-05952f78f2f0},\n created = {2020-12-03T14:18:56.339Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.339Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2020 The Authors. The statistical concept of gambler's ruin suggests that gambling has a large amount of risk. Nevertheless, gambling at casinos and gambling on the Internet are both hugely popular activities. In recent years, both prospect theory and laboratory-controlled experiments have been used to improve our understanding of risk attitudes associated with gambling. Despite theoretical progress, collecting real-life gambling data, which is essential to validate predictions and experimental findings, remains a challenge. To address this issue, we collect publicly available betting data from a DApp (decentralized application) on the Ethereum blockchain, which instantly publishes the outcome of every single bet (consisting of each bet's timestamp, wager, probability of winning, userID and profit). This online casino is a simple dice game that allows gamblers to tune their own winning probabilities. Thus the dataset is well suited for studying gambling strategies and the complex dynamic of risk attitudes involved in betting decisions. We analyse the dataset through the lens of current probability-theoretic models and discover empirical examples of gambling systems. Our results shed light on understanding the role of risk preferences in human financial behaviour and decision-makings beyond gambling.},\n bibtype = {article},\n author = {Meng, J. and Fu, F.},\n doi = {10.1098/rsos.201446},\n journal = {Royal Society Open Science},\n number = {10}\n}\n\n © 2020 The Authors. The statistical concept of gambler's ruin suggests that gambling has a large amount of risk. Nevertheless, gambling at casinos and gambling on the Internet are both hugely popular activities. In recent years, both prospect theory and laboratory-controlled experiments have been used to improve our understanding of risk attitudes associated with gambling. Despite theoretical progress, collecting real-life gambling data, which is essential to validate predictions and experimental findings, remains a challenge. To address this issue, we collect publicly available betting data from a DApp (decentralized application) on the Ethereum blockchain, which instantly publishes the outcome of every single bet (consisting of each bet's timestamp, wager, probability of winning, userID and profit). This online casino is a simple dice game that allows gamblers to tune their own winning probabilities. Thus the dataset is well suited for studying gambling strategies and the complex dynamic of risk attitudes involved in betting decisions. We analyse the dataset through the lens of current probability-theoretic models and discover empirical examples of gambling systems. Our results shed light on understanding the role of risk preferences in human financial behaviour and decision-makings beyond gambling.\n
\n\n\n\n \n\n \n \n \n \n \n Understanding gambling behavior and risk attitudes using cryptocurrency-based casino blockchain data.\n \n \n \n\n\n \n Meng, J.; and Fu, F.\n\n\n \n\n\n\n 2020.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Understanding gambling behavior and risk attitudes using cryptocurrency-based casino blockchain data},\n type = {misc},\n year = {2020},\n source = {arXiv},\n keywords = {Betting strategies,Irrationality,Optimal stopping,Risk preferences},\n id = {3e227898-7c7a-3d09-94f4-a82a15221ec8},\n created = {2020-12-03T14:18:56.381Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.381Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2020, arXiv, All rights reserved. The statistical concept of Gambler’s Ruin suggests that gambling has a large amount of risk. Nevertheless, gambling at casinos and gambling on the Internet are both hugely popular activities. In recent years, both prospect theory and lab-controlled experiments have been used to improve our understanding of risk attitudes associated with gambling. Despite theoretical progress, collecting real-life gambling data, which is essential to validate predictions and experimental findings, remains a challenge. To address this issue, we collect publicly available betting data from a DApp (decentralized application) on the Ethereum Blockchain, which instantly publishes the outcome of every single bet (consisting of each bet’s timestamp, wager, probability of winning, userID, and profit). This online casino is a simple dice game that allows gamblers to tune their own winning probabilities. Thus the dataset is well suited for studying gambling strategies and the complex dynamic of risk attitudes involved in betting decisions. We analyze the dataset through the lens of current probability-theoretic models and discover empirical examples of gambling systems. Our results shed light on understanding the role of risk preferences in human financial behavior and decision-makings beyond gambling.},\n bibtype = {misc},\n author = {Meng, J. and Fu, F.}\n}\n\n Copyright © 2020, arXiv, All rights reserved. The statistical concept of Gambler’s Ruin suggests that gambling has a large amount of risk. Nevertheless, gambling at casinos and gambling on the Internet are both hugely popular activities. In recent years, both prospect theory and lab-controlled experiments have been used to improve our understanding of risk attitudes associated with gambling. Despite theoretical progress, collecting real-life gambling data, which is essential to validate predictions and experimental findings, remains a challenge. To address this issue, we collect publicly available betting data from a DApp (decentralized application) on the Ethereum Blockchain, which instantly publishes the outcome of every single bet (consisting of each bet’s timestamp, wager, probability of winning, userID, and profit). This online casino is a simple dice game that allows gamblers to tune their own winning probabilities. Thus the dataset is well suited for studying gambling strategies and the complex dynamic of risk attitudes involved in betting decisions. We analyze the dataset through the lens of current probability-theoretic models and discover empirical examples of gambling systems. Our results shed light on understanding the role of risk preferences in human financial behavior and decision-makings beyond gambling.\n
\n\n\n\n \n\n \n \n \n \n \n Eco-evolutionary dynamics with environmental feedback: Cooperation in a changing world.\n \n \n \n\n\n \n Wang, X.; and Fu, F.\n\n\n \n\n\n\n 2020.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Eco-evolutionary dynamics with environmental feedback: Cooperation in a changing world},\n type = {misc},\n year = {2020},\n source = {arXiv},\n id = {ca95ef7a-b851-3764-85e4-a3c47aa6d15b},\n created = {2020-12-03T14:18:56.384Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.384Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2020, arXiv, All rights reserved. Eco-evolutionary game dynamics which characterizes the mutual interactions and the coupled evolutions of strategies and environments has been of growing interests in very recent years. Since such feedback loops widely exist in a range of coevolutionary systems, such as microbial systems, social-ecological system and psychologicaleconomic system, recent modeling frameworks that unveil the oscillating dynamics of social dilemmas have great potential for practical applications. In this perspective article, we overview the latest progress of evolutionary game theory in this direction. We describe both mathematical methods and interdisciplinary applications across different fields. The ideas worthy of further consideration are discussed in prospects, with the central role of promoting cooperations in a changing world.},\n bibtype = {misc},\n author = {Wang, X. and Fu, F.}\n}\n\n Copyright © 2020, arXiv, All rights reserved. Eco-evolutionary game dynamics which characterizes the mutual interactions and the coupled evolutions of strategies and environments has been of growing interests in very recent years. Since such feedback loops widely exist in a range of coevolutionary systems, such as microbial systems, social-ecological system and psychologicaleconomic system, recent modeling frameworks that unveil the oscillating dynamics of social dilemmas have great potential for practical applications. In this perspective article, we overview the latest progress of evolutionary game theory in this direction. We describe both mathematical methods and interdisciplinary applications across different fields. The ideas worthy of further consideration are discussed in prospects, with the central role of promoting cooperations in a changing world.\n
\n\n\n\n \n\n \n \n \n \n \n Asymmetric partisan voter turnout games.\n \n \n \n\n\n \n Guage, C.; and Fu, F.\n\n\n \n\n\n\n 2020.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Asymmetric partisan voter turnout games},\n type = {misc},\n year = {2020},\n source = {arXiv},\n keywords = {Downs’ paradox,Evolutionary game dynamics,Social learning},\n id = {b6401173-55b2-3ca5-9865-3c869762f660},\n created = {2020-12-03T14:18:56.478Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.478Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2020, arXiv, All rights reserved. Since Downs proposed that the act of voting is irrational in 1957, myriad models have been proposed to explain voting and account for observed turnout patterns. We propose a model in which partisans consider both the instrumental and expressive benefits of their vote when deciding whether or not to abstain in an election, introducing an asymmetry that most other models do not consider. Allowing learning processes within our electorate, we analyze what turnout states are rationalizable under various conditions. Our model predicts comparative statics that are consistent with voter behavior. Furthermore, relaxing some of our preliminary assumptions eliminates some of the discrepancies between our model and empirical voter behavior.},\n bibtype = {misc},\n author = {Guage, C. and Fu, F.}\n}\n\n Copyright © 2020, arXiv, All rights reserved. Since Downs proposed that the act of voting is irrational in 1957, myriad models have been proposed to explain voting and account for observed turnout patterns. We propose a model in which partisans consider both the instrumental and expressive benefits of their vote when deciding whether or not to abstain in an election, introducing an asymmetry that most other models do not consider. Allowing learning processes within our electorate, we analyze what turnout states are rationalizable under various conditions. Our model predicts comparative statics that are consistent with voter behavior. Furthermore, relaxing some of our preliminary assumptions eliminates some of the discrepancies between our model and empirical voter behavior.\n
\n\n\n\n \n\n \n \n \n \n \n Evolutionary Kuramoto Dynamics.\n \n \n \n\n\n \n Tripp, E.; Fu, F.; and Pauls, S.\n\n\n \n\n\n\n 2020.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Evolutionary Kuramoto Dynamics},\n type = {misc},\n year = {2020},\n source = {arXiv},\n keywords = {Cooperation,Evolutionary game theory,Kuramoto dilemma,Neuroscience,Synchronization},\n id = {4b64ef31-e409-3e19-afd6-1ea5d4c0aa8f},\n created = {2020-12-03T14:18:56.984Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.984Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2020, arXiv, All rights reserved. Common models of synchronizable oscillatory systems consist of a collection of coupled oscillators governed by a collection of differential equations. The ubiquitous Kuramoto models rely on an a priori fixed connectivity pattern facilitates mutual communication and influence between oscillators. In biological synchronizable systems, like the mammalian suprachaismatic nucleus, enabling communication comes at a cost — the organism expends energy creating and maintaining the system — linking their development to evolutionary selection. Here, we introduce and analyze a new evolutionary game theoretic framework modeling the behavior and evolution of systems of coupled oscillators. Each oscillator in our model is characterized by a pair of dynamic behavioral traits: an oscillatory phase and whether they connect and communicate to other oscillators or not. Evolution of the system occurs along these dimensions, allowing oscillators to change their phases and/or their communication strategies. We measure success of mutations by comparing the benefit of phase synchronization to the organism balanced against the cost of creating and maintaining connections between the oscillators. Despite such a simple setup, this system exhibits a wealth of nontrivial behaviors, mimicking different classical games – the Prisoner’s Dilemma, the snowdrift game, and coordination games – as the landscape of the oscillators changes over time. Despite such complexity, we find a surprisingly simple characterization of synchronization through connectivity and communication: if the benefit of synchronization B(0) is greater than twice the cost c, B(0) > 2c, the organism will evolve towards complete communication and phase synchronization. Taken together, our model demonstrates possible evolutionary constraints on both the existence of a synchronized oscillatory system and its overall connectivity.},\n bibtype = {misc},\n author = {Tripp, E.A. and Fu, F. and Pauls, S.D.}\n}\n\n Copyright © 2020, arXiv, All rights reserved. Common models of synchronizable oscillatory systems consist of a collection of coupled oscillators governed by a collection of differential equations. The ubiquitous Kuramoto models rely on an a priori fixed connectivity pattern facilitates mutual communication and influence between oscillators. In biological synchronizable systems, like the mammalian suprachaismatic nucleus, enabling communication comes at a cost — the organism expends energy creating and maintaining the system — linking their development to evolutionary selection. Here, we introduce and analyze a new evolutionary game theoretic framework modeling the behavior and evolution of systems of coupled oscillators. Each oscillator in our model is characterized by a pair of dynamic behavioral traits: an oscillatory phase and whether they connect and communicate to other oscillators or not. Evolution of the system occurs along these dimensions, allowing oscillators to change their phases and/or their communication strategies. We measure success of mutations by comparing the benefit of phase synchronization to the organism balanced against the cost of creating and maintaining connections between the oscillators. Despite such a simple setup, this system exhibits a wealth of nontrivial behaviors, mimicking different classical games – the Prisoner’s Dilemma, the snowdrift game, and coordination games – as the landscape of the oscillators changes over time. Despite such complexity, we find a surprisingly simple characterization of synchronization through connectivity and communication: if the benefit of synchronization B(0) is greater than twice the cost c, B(0) > 2c, the organism will evolve towards complete communication and phase synchronization. Taken together, our model demonstrates possible evolutionary constraints on both the existence of a synchronized oscillatory system and its overall connectivity.\n
\n\n\n\n \n\n \n \n \n \n \n Cancer-induced immunosuppression can enable effectiveness of immunotherapy through bistability generation: A mathematical and computational examination.\n \n \n \n\n\n \n Garcia, V.; Bonhoeffer, S.; and Fu, F.\n\n\n \n\n\n\n Journal of Theoretical Biology, 492. 2020.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Cancer-induced immunosuppression can enable effectiveness of immunotherapy through bistability generation: A mathematical and computational examination},\n type = {article},\n year = {2020},\n keywords = {Cancer,Cancer-immune system interactions,Immunotherapy,Mathematical modeling},\n volume = {492},\n id = {feeda735-dde3-33db-894c-91108bdbd133},\n created = {2020-12-03T14:18:57.308Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.308Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2020 The Authors Cancer immunotherapies rely on how interactions between cancer and immune system cells are constituted. The more essential to the emergence of the dynamical behavior of cancer growth these interactions are, the more effectively they may be used as mechanisms for interventions. Mathematical modeling can help unearth such connections, and help explain how they shape the dynamics of cancer growth. Here, we explored whether there exist simple, consistent properties of cancer-immune system interaction (CISI) models that might be harnessed to devise effective immunotherapy approaches. We did this for a family of three related models of increasing complexity. To this end, we developed a base model of CISI, which captures some essential features of the more complex models built on it. We find that the base model and its derivates can plausibly reproduce biological behavior that is consistent with the notion of an immunological barrier. This behavior is also in accord with situations in which the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects. Under these circumstances, the model family may display a pattern of bistability, where two distinct, stable states (a cancer-free, and a full-grown cancer state) are possible. Increasing the effectiveness of immune-caused cancer cell killing may remove the basis for bistability, and abruptly tip the dynamics of the system into a cancer-free state. Additionally, in combination with the administration of immune effector cells, modifications in cancer cell killing may be harnessed for immunotherapy without the need for resolving the bistability. We use these ideas to test immunotherapeutic interventions in silico in a stochastic version of the base model. This bistability-reliant approach to cancer interventions might offer advantages over those that comprise gradual declines in cancer cell numbers.},\n bibtype = {article},\n author = {Garcia, V. and Bonhoeffer, S. and Fu, F.},\n doi = {10.1016/j.jtbi.2020.110185},\n journal = {Journal of Theoretical Biology}\n}\n\n © 2020 The Authors Cancer immunotherapies rely on how interactions between cancer and immune system cells are constituted. The more essential to the emergence of the dynamical behavior of cancer growth these interactions are, the more effectively they may be used as mechanisms for interventions. Mathematical modeling can help unearth such connections, and help explain how they shape the dynamics of cancer growth. Here, we explored whether there exist simple, consistent properties of cancer-immune system interaction (CISI) models that might be harnessed to devise effective immunotherapy approaches. We did this for a family of three related models of increasing complexity. To this end, we developed a base model of CISI, which captures some essential features of the more complex models built on it. We find that the base model and its derivates can plausibly reproduce biological behavior that is consistent with the notion of an immunological barrier. This behavior is also in accord with situations in which the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects. Under these circumstances, the model family may display a pattern of bistability, where two distinct, stable states (a cancer-free, and a full-grown cancer state) are possible. Increasing the effectiveness of immune-caused cancer cell killing may remove the basis for bistability, and abruptly tip the dynamics of the system into a cancer-free state. Additionally, in combination with the administration of immune effector cells, modifications in cancer cell killing may be harnessed for immunotherapy without the need for resolving the bistability. We use these ideas to test immunotherapeutic interventions in silico in a stochastic version of the base model. This bistability-reliant approach to cancer interventions might offer advantages over those that comprise gradual declines in cancer cell numbers.\n
\n\n\n\n \n\n \n \n \n \n \n Steering eco-evolutionary game dynamics with manifold control.\n \n \n \n\n\n \n Wang, X.; Zheng, Z.; and Fu, F.\n\n\n \n\n\n\n Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2233). 2020.\n \n\n\n\n
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\n\n\n@article{\n title = {Steering eco-evolutionary game dynamics with manifold control},\n type = {article},\n year = {2020},\n keywords = {Cooperation,Ecological public goods,Environmental feedback,Social dilemma,Switching control},\n volume = {476},\n id = {a8498cfd-3ff5-31e8-9ad2-401eac49a265},\n created = {2020-12-03T14:18:57.325Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.325Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2020 The Author(s) Published by the Royal Society. All rights reserved. Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature and have shown profound effects on the resulting eco-evolutionary dynamics. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centred on cooperators not only accelerates the convergence of stable manifolds but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population state. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.},\n bibtype = {article},\n author = {Wang, X. and Zheng, Z. and Fu, F.},\n doi = {10.1098/rspa.2019.0643},\n journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},\n number = {2233}\n}\n\n © 2020 The Author(s) Published by the Royal Society. All rights reserved. Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature and have shown profound effects on the resulting eco-evolutionary dynamics. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centred on cooperators not only accelerates the convergence of stable manifolds but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population state. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.\n
\n\n\n\n \n\n \n \n \n \n \n \n Evolutionary Kuramoto Dynamics.\n \n \n \n \n\n\n \n Tripp, E., A.; Fu, F.; and Pauls, S., D.\n\n\n \n\n\n\n Technical Report 2020.\n \n\n\n\n
\n\n\n\n \n \n![\"Evolutionary](\"//bibbase.org/img/filetypes/pdf.svg\"\n\t "\\"Paper\\"\n")
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\n\n\n@techreport{\n title = {Evolutionary Kuramoto Dynamics},\n type = {techreport},\n year = {2020},\n id = {ae064e3c-162a-3ba4-9009-dd0d8384e60a},\n created = {2020-12-03T14:25:20.946Z},\n file_attached = {true},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:35:32.981Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Biological systems have a variety of time-keeping mechanisms ranging from molecular clocks within a single cell to complex interconnected unit across an entire organism. Mammals have a centralized "master-clock" within the brain, the suprachiasmatic nucleus (SCN), comprising a large collection of interconnected oscillatory neurons. The ubiquity of such systems points to an evolutionary benefit to time-keeping outweighing the cost of establishing and maintaining them. But little is known about how these systems develop in the presence of evolutionary constraints. For systems like the SCN, mathematical models such as the commonly used Kuramoto framework allow analysis of the outcomes of the system but do not address its development. To begin to deal with this shortfall, we introduce and analyze a new evolutionary game theoretic framework modeling the behavior and evolution of systems of coupled oscillators. Each oscillator in our model is characterized by a pair of dynamic behavioral traits: an oscillatory phase and whether they connect and communicate to other oscillators or not. Evolution of the system occurs along these dimensions, allowing oscillators to change their phases and/or their communication strategies. We measure success of mutations by comparing the benefit of phase synchronization to the organism balanced against the cost of creating and maintaining connections between the oscillators. Despite such a simple setup, this system exhibits a wealth of nontrivial behaviors, mimicking different classical games-the Prisoner's Dilemma, the snowdrift game, and coordination games-as the landscape of the oscillators changes over time. Across many different situations, we find a surprisingly simple characterization of synchronization through connectivity and communication: if the benefit of synchronization is greater than twice the cost, the system will evolve towards complete communication and phase synchronization. And, in the case of strong selection pressure, we see outcomes that have mixtures of communication and non-communication which are coarsely reflective of what is known about neural connectivity within the SCN. Taken together, our model demonstrates possible evolutionary constraints on both the existence of a synchronized oscillatory system and its overall connectivity. Author Summary Collective dynamics of neurons modulated by their underlying connectivity patterns are essential to help maintain brain function. One of the remarkable capacities of these neuronal systems is the synchronization of internal biological rhythms. For example, the suprachiasmatic nucleus (SCN), which is mammalian circadian system, acts as a central "master clock". Why do individual neurons have to maintain communication and PLOS 1/22 Mannscripp Click heee acceee/ddddllad;Maaaacciii;kkkaaaaagaaee..df synchronize with others despite the cost? To address this question, here we analyze the long time behavior and dynamics of systems of coupled Kuramoto oscillators through the lens of evolutionary game theory. Each oscillator models a neuron via two traits: an oscillatory phase and whether they connect and communicate to other oscillators or not. Our work provides rigorous mathematical results that are consequences of the common concepts of benefit and cost of neural interactions. We fully characterize evolutionary dynamics of communicative vs. noncommunicative neurons in biologically plausible scenarios encompassing a wide range of evolutionary games: from snowdrift games to the Prisoner's Dilemma to coordination games to mutualism. We find a surprisingly simple condition that only requires a moderate level of synergy of mutual communication and synchronization, B(0), in order to overcome the barrier imposed by the cost, c, that is, B(0) > 2c. Our results may help shed new insights into the ubiquitous synchronization behavior in neuronal populations.},\n bibtype = {techreport},\n author = {Tripp, Elizabeth A and Fu, Feng and Pauls, Scott D}\n}\n\n Biological systems have a variety of time-keeping mechanisms ranging from molecular clocks within a single cell to complex interconnected unit across an entire organism. Mammals have a centralized \"master-clock\" within the brain, the suprachiasmatic nucleus (SCN), comprising a large collection of interconnected oscillatory neurons. The ubiquity of such systems points to an evolutionary benefit to time-keeping outweighing the cost of establishing and maintaining them. But little is known about how these systems develop in the presence of evolutionary constraints. For systems like the SCN, mathematical models such as the commonly used Kuramoto framework allow analysis of the outcomes of the system but do not address its development. To begin to deal with this shortfall, we introduce and analyze a new evolutionary game theoretic framework modeling the behavior and evolution of systems of coupled oscillators. Each oscillator in our model is characterized by a pair of dynamic behavioral traits: an oscillatory phase and whether they connect and communicate to other oscillators or not. Evolution of the system occurs along these dimensions, allowing oscillators to change their phases and/or their communication strategies. We measure success of mutations by comparing the benefit of phase synchronization to the organism balanced against the cost of creating and maintaining connections between the oscillators. Despite such a simple setup, this system exhibits a wealth of nontrivial behaviors, mimicking different classical games-the Prisoner's Dilemma, the snowdrift game, and coordination games-as the landscape of the oscillators changes over time. Across many different situations, we find a surprisingly simple characterization of synchronization through connectivity and communication: if the benefit of synchronization is greater than twice the cost, the system will evolve towards complete communication and phase synchronization. And, in the case of strong selection pressure, we see outcomes that have mixtures of communication and non-communication which are coarsely reflective of what is known about neural connectivity within the SCN. Taken together, our model demonstrates possible evolutionary constraints on both the existence of a synchronized oscillatory system and its overall connectivity. Author Summary Collective dynamics of neurons modulated by their underlying connectivity patterns are essential to help maintain brain function. One of the remarkable capacities of these neuronal systems is the synchronization of internal biological rhythms. For example, the suprachiasmatic nucleus (SCN), which is mammalian circadian system, acts as a central \"master clock\". Why do individual neurons have to maintain communication and PLOS 1/22 Mannscripp Click heee acceee/ddddllad;Maaaacciii;kkkaaaaagaaee..df synchronize with others despite the cost? To address this question, here we analyze the long time behavior and dynamics of systems of coupled Kuramoto oscillators through the lens of evolutionary game theory. Each oscillator models a neuron via two traits: an oscillatory phase and whether they connect and communicate to other oscillators or not. Our work provides rigorous mathematical results that are consequences of the common concepts of benefit and cost of neural interactions. We fully characterize evolutionary dynamics of communicative vs. noncommunicative neurons in biologically plausible scenarios encompassing a wide range of evolutionary games: from snowdrift games to the Prisoner's Dilemma to coordination games to mutualism. We find a surprisingly simple condition that only requires a moderate level of synergy of mutual communication and synchronization, B(0), in order to overcome the barrier imposed by the cost, c, that is, B(0) > 2c. Our results may help shed new insights into the ubiquitous synchronization behavior in neuronal populations.\n
\n\n\n\n \n\n \n \n \n \n \n \n Elitism in Mathematics and Inequality.\n \n \n \n \n\n\n \n Chang, H., H.; and Fu, F.\n\n\n \n\n\n\n . 2 2020.\n \n\n\n\n
\n\n\n\n \n \nPaper\n \n \n \n ![\"Elitism](\"//bibbase.org/img/filetypes/link.svg\"\n\t "\\"Website\\"\n")
Website\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Elitism in Mathematics and Inequality},\n type = {article},\n year = {2020},\n websites = {http://arxiv.org/abs/2002.07789},\n month = {2},\n day = {18},\n id = {22b4f76e-4a71-3aee-9d92-fefd5e3af205},\n created = {2020-12-03T14:25:42.242Z},\n file_attached = {true},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:25:43.574Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {The Fields Medal, often referred as the Nobel Prize of mathematics, is awarded to no more than four mathematician under the age of 40, every four years. In recent years, its conferral has come under scrutiny of math historians, for rewarding the existing elite rather than its original goal of elevating mathematicians from under-represented communities. Prior studies of elitism focus on citational practices and sub-fields; the structural forces that prevent equitable access remain unclear. Here we show the flow of elite mathematicians between countries and lingo-ethnic identity, using network analysis and natural language processing on 240,000 mathematicians and their advisor-advisee relationships. We found that the Fields Medal helped integrate Japan after WWII, through analysis of the elite circle formed around Fields Medalists. Arabic, African, and East Asian identities remain under-represented at the elite level. Through analysis of inflow and outflow, we rebuts the myth that minority communities create their own barriers to entry. Our results demonstrate concerted efforts by international academic committees, such as prize-giving, are a powerful force to give equal access. We anticipate our methodology of academic genealogical analysis can serve as a useful diagnostic for equality within academic fields.},\n bibtype = {article},\n author = {Chang, Ho-Chun Herbert and Fu, Feng}\n}\n\n The Fields Medal, often referred as the Nobel Prize of mathematics, is awarded to no more than four mathematician under the age of 40, every four years. In recent years, its conferral has come under scrutiny of math historians, for rewarding the existing elite rather than its original goal of elevating mathematicians from under-represented communities. Prior studies of elitism focus on citational practices and sub-fields; the structural forces that prevent equitable access remain unclear. Here we show the flow of elite mathematicians between countries and lingo-ethnic identity, using network analysis and natural language processing on 240,000 mathematicians and their advisor-advisee relationships. We found that the Fields Medal helped integrate Japan after WWII, through analysis of the elite circle formed around Fields Medalists. Arabic, African, and East Asian identities remain under-represented at the elite level. Through analysis of inflow and outflow, we rebuts the myth that minority communities create their own barriers to entry. Our results demonstrate concerted efforts by international academic committees, such as prize-giving, are a powerful force to give equal access. We anticipate our methodology of academic genealogical analysis can serve as a useful diagnostic for equality within academic fields.\n
\n\n\n\n \n\n \n \n \n \n \n \n Public Discourse and Social Network Echo Chambers Driven by Socio-Cognitive Biases.\n \n \n \n \n\n\n \n Wang, X.; Sirianni, A., D.; Tang, S.; Zheng, Z.; and Fu, F.\n\n\n \n\n\n\n Technical Report 2020.\n \n\n\n\n
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\n\n\n@techreport{\n title = {Public Discourse and Social Network Echo Chambers Driven by Socio-Cognitive Biases},\n type = {techreport},\n year = {2020},\n keywords = {23 Interdisciplinary Physics,Complex Systems,DOI,Subject Areas},\n websites = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.041042},\n id = {ba905208-3fd0-3b7f-8fc7-10ef90503729},\n created = {2020-12-03T14:26:22.950Z},\n accessed = {2020-12-03},\n file_attached = {true},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:35:22.220Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {In recent years, social media has become an important platform for political discourse, being a site of 11 both political conversations between voters and political advertisements from campaigns. While their 12 individual influences on public discourse are well documented, the interplay between individual-level 13 cognitive biases, social influence processes, dueling campaign efforts, and social media platforms remains 14 unexamined. We introduce an agent-based model that integrates these dynamics and illustrates how their 15 combination can lead to the formation of echo chambers. We find that the range of political viewpoints that 16 individuals are willing to consider is a key determinant in the formation of polarized networks and the 17 emergence of echo chambers and show that aggressive political campaigns can have counterproductive 18 outcomes by radicalizing supporters and alienating moderates. Our model results demonstrate how certain 19 elements of public discourse and political polarization can be understood as the result of an interactive 20 process of shifting individual opinions, evolving social networks, and political campaigns. We also 21 introduce a dynamic empirical case, retweet networks from the final stage of the 2016 U.S. presidential 22 election, to show how our proposed model can be calibrated with real-world behavior.},\n bibtype = {techreport},\n author = {Wang, Xin and Sirianni, Antonio D and Tang, Shaoting and Zheng, Zhiming and Fu, Feng}\n}\n\n In recent years, social media has become an important platform for political discourse, being a site of 11 both political conversations between voters and political advertisements from campaigns. While their 12 individual influences on public discourse are well documented, the interplay between individual-level 13 cognitive biases, social influence processes, dueling campaign efforts, and social media platforms remains 14 unexamined. We introduce an agent-based model that integrates these dynamics and illustrates how their 15 combination can lead to the formation of echo chambers. We find that the range of political viewpoints that 16 individuals are willing to consider is a key determinant in the formation of polarized networks and the 17 emergence of echo chambers and show that aggressive political campaigns can have counterproductive 18 outcomes by radicalizing supporters and alienating moderates. Our model results demonstrate how certain 19 elements of public discourse and political polarization can be understood as the result of an interactive 20 process of shifting individual opinions, evolving social networks, and political campaigns. We also 21 introduce a dynamic empirical case, retweet networks from the final stage of the 2016 U.S. presidential 22 election, to show how our proposed model can be calibrated with real-world behavior.\n
\n\n\n\n \n\n \n \n \n \n \n \n Eco-evolutionary dynamics with environmental feedback: cooperation in a changing world.\n \n \n \n \n\n\n \n Wang, X.; and Fu, F.\n\n\n \n\n\n\n . 8 2020.\n \n\n\n\n
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\n\n\n@article{\n title = {Eco-evolutionary dynamics with environmental feedback: cooperation in a changing world},\n type = {article},\n year = {2020},\n websites = {http://arxiv.org/abs/2008.07671},\n month = {8},\n day = {17},\n id = {0b634899-6486-38f3-8e2f-a4d10a0f4f06},\n created = {2020-12-03T14:26:42.276Z},\n file_attached = {true},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:26:43.107Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Eco-evolutionary game dynamics which characterizes the mutual interactions and the coupled evolutions of strategies and environments has been of growing interests in very recent years. Since such feedback loops widely exist in a range of coevolutionary systems, such as microbial systems, social-ecological system and psychological-economic system, recent modeling frameworks that unveil the oscillating dynamics of social dilemmas have great potential for practical applications. In this perspective article, we overview the latest progress of evolutionary game theory in this direction. We describe both mathematical methods and interdisciplinary applications across different fields. The ideas worthy of further consideration are discussed in prospects, with the central role of promoting cooperations in a changing world.},\n bibtype = {article},\n author = {Wang, Xin and Fu, Feng}\n}\n\n Eco-evolutionary game dynamics which characterizes the mutual interactions and the coupled evolutions of strategies and environments has been of growing interests in very recent years. Since such feedback loops widely exist in a range of coevolutionary systems, such as microbial systems, social-ecological system and psychological-economic system, recent modeling frameworks that unveil the oscillating dynamics of social dilemmas have great potential for practical applications. In this perspective article, we overview the latest progress of evolutionary game theory in this direction. We describe both mathematical methods and interdisciplinary applications across different fields. The ideas worthy of further consideration are discussed in prospects, with the central role of promoting cooperations in a changing world.\n
\n\n\n\n \n\n \n \n \n \n \n \n Mathematically modeling spillovers of an emerging infectious zoonosis with an intermediate host.\n \n \n \n \n\n\n \n Royce, K.; and Fu, F.\n\n\n \n\n\n\n PLoS ONE, 15(8 August). 8 2020.\n \n\n\n\n
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\n\n\n@article{\n title = {Mathematically modeling spillovers of an emerging infectious zoonosis with an intermediate host},\n type = {article},\n year = {2020},\n volume = {15},\n month = {8},\n publisher = {Public Library of Science},\n day = {1},\n id = {e4cee779-688b-32d2-b7c2-f74e11645088},\n created = {2020-12-03T14:27:03.409Z},\n file_attached = {true},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:27:06.439Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Modeling the behavior of zoonotic pandemic threats is a key component of their control. Many emerging zoonoses, such as SARS, Nipah, and Hendra, mutated from their wild type while circulating in an intermediate host population, usually a domestic species, to become more transmissible among humans, and this transmission route will only become more likely as agriculture and trade intensifies around the world. Passage through an intermediate host enables many otherwise rare diseases to become better adapted to humans, and so understanding this process with accurate mathematical models is necessary to prevent epidemics of emerging zoonoses, guide policy interventions in public health, and predict the behavior of an epidemic. In this paper, we account for a zoonotic disease mutating in an intermediate host by introducing a new mathematical model for disease transmission among three species. We present a model of these disease dynamics, including the equilibria of the system and the basic reproductive number of the pathogen, finding that in the presence of biologically realistic interspecies transmission parameters, a zoonotic disease with the capacity to mutate in an intermediate host population can establish itself in humans even if its R0 in humans is less than 1. This result and model can be used to predict the behavior of any zoonosis with an intermediate host and assist efforts to protect public health.},\n bibtype = {article},\n author = {Royce, Katherine and Fu, Feng},\n doi = {10.1371/journal.pone.0237780},\n journal = {PLoS ONE},\n number = {8 August}\n}\n\n Modeling the behavior of zoonotic pandemic threats is a key component of their control. Many emerging zoonoses, such as SARS, Nipah, and Hendra, mutated from their wild type while circulating in an intermediate host population, usually a domestic species, to become more transmissible among humans, and this transmission route will only become more likely as agriculture and trade intensifies around the world. Passage through an intermediate host enables many otherwise rare diseases to become better adapted to humans, and so understanding this process with accurate mathematical models is necessary to prevent epidemics of emerging zoonoses, guide policy interventions in public health, and predict the behavior of an epidemic. In this paper, we account for a zoonotic disease mutating in an intermediate host by introducing a new mathematical model for disease transmission among three species. We present a model of these disease dynamics, including the equilibria of the system and the basic reproductive number of the pathogen, finding that in the presence of biologically realistic interspecies transmission parameters, a zoonotic disease with the capacity to mutate in an intermediate host population can establish itself in humans even if its R0 in humans is less than 1. This result and model can be used to predict the behavior of any zoonosis with an intermediate host and assist efforts to protect public health.\n
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\n \n \n\n \n \n \n \n \n Co-contagion diffusion on multilayer networks.\n \n \n \n\n\n \n Chang, H.; and Fu, F.\n\n\n \n\n\n\n 2019.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Co-contagion diffusion on multilayer networks},\n type = {misc},\n year = {2019},\n source = {arXiv},\n keywords = {Complex contagions,Network diffusion,Stochastic modeling},\n id = {deea9b0a-54c8-3589-a79f-655c43e06b6c},\n created = {2020-12-03T14:18:56.423Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.423Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2019, arXiv, All rights reserved. This study examines the interface of three elements during co-contagion diffusion: The synergy between contagions, the dormancy rate of each individual contagion, and the multiplex network topology. Dormancy is defined as a weaker form of "immunity," where dormant nodes no longer actively participate in diffusion, but are still susceptible to infection. The proposed model extends the literature on threshold models, and demonstrates intricate interdependencies between different graph structures. Our simulations show that first, the faster contagion induces branching on the slower contagion; second, shorter characteristic path lengths diminish the impact of dormancy in lowering diffusion. Third, when two long-range graphs are paired, the faster contagion depends on both dormancy rates, whereas the slower contagion depends only on its own; fourth, synergistic contagions are less sensitive to dormancy, and have a wider window to diffuse. Furthermore, when long-range and spatially constrained graphs are paired, ring vaccination occurs on the spatial graph and produces partial diffusion, due to dormant, surrounding nodes. The spatial contagion depends on both dormancy rates whereas the long-range contagion depends on only its own.},\n bibtype = {misc},\n author = {Chang, H.-C.H. and Fu, F.}\n}\n\n Copyright © 2019, arXiv, All rights reserved. This study examines the interface of three elements during co-contagion diffusion: The synergy between contagions, the dormancy rate of each individual contagion, and the multiplex network topology. Dormancy is defined as a weaker form of \"immunity,\" where dormant nodes no longer actively participate in diffusion, but are still susceptible to infection. The proposed model extends the literature on threshold models, and demonstrates intricate interdependencies between different graph structures. Our simulations show that first, the faster contagion induces branching on the slower contagion; second, shorter characteristic path lengths diminish the impact of dormancy in lowering diffusion. Third, when two long-range graphs are paired, the faster contagion depends on both dormancy rates, whereas the slower contagion depends only on its own; fourth, synergistic contagions are less sensitive to dormancy, and have a wider window to diffuse. Furthermore, when long-range and spatially constrained graphs are paired, ring vaccination occurs on the spatial graph and produces partial diffusion, due to dormant, surrounding nodes. The spatial contagion depends on both dormancy rates whereas the long-range contagion depends on only its own.\n
\n\n\n\n \n\n \n \n \n \n \n Mathematically modeling spillover dynamics of emerging zoonoses with intermediate hosts.\n \n \n \n\n\n \n Royce, K.; and Fu, F.\n\n\n \n\n\n\n 2019.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Mathematically modeling spillover dynamics of emerging zoonoses with intermediate hosts},\n type = {misc},\n year = {2019},\n source = {arXiv},\n id = {8801ffa3-2ede-37fd-a2c1-22ffc56ce43b},\n created = {2020-12-03T14:18:56.531Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.531Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2019, arXiv, All rights reserved. The World Health Organization describes zoonotic diseases as a major pandemic threat, and modeling the behavior of such diseases is a key component of their control. Many emerging zoonoses, such as SARS, Nipah, and Hendra, mutated from their wild type while circulating in an intermediate host population, usually a domestic species, to become more transmissible among humans, and moreover, this transmission route will only become more likely as agriculture and trade intensifies around the world. Passage through an intermediate host enables many otherwise rare diseases to become better adapted to humans, and so understanding this process with mathematical epidemiological models is necessary to prevent epidemics of emerging zoonoses, guide policy interventions in public health, and predict the behavior of an epidemic. In this paper, we account for spillovers of a zoonotic disease mutating in an intermediate host by means of modeling transmission dynamics within and between three host species, namely, wild reservoir, intermediate domestic animals, and humans. We calculate the basic reproductive number of the pathogen, present critical conditions for the emergence dynamics of zoonosis, and perform stability analysis of admissible disease equilibria. Our analytical results agree well with long-term simulations of the system. We find that in the presence of biologically realistic interspecies transmission parameters, a zoonotic disease can establish itself in humans even if it fails to persist in its reservoir},\n bibtype = {misc},\n author = {Royce, K.P. and Fu, F.}\n}\n\n Copyright © 2019, arXiv, All rights reserved. The World Health Organization describes zoonotic diseases as a major pandemic threat, and modeling the behavior of such diseases is a key component of their control. Many emerging zoonoses, such as SARS, Nipah, and Hendra, mutated from their wild type while circulating in an intermediate host population, usually a domestic species, to become more transmissible among humans, and moreover, this transmission route will only become more likely as agriculture and trade intensifies around the world. Passage through an intermediate host enables many otherwise rare diseases to become better adapted to humans, and so understanding this process with mathematical epidemiological models is necessary to prevent epidemics of emerging zoonoses, guide policy interventions in public health, and predict the behavior of an epidemic. In this paper, we account for spillovers of a zoonotic disease mutating in an intermediate host by means of modeling transmission dynamics within and between three host species, namely, wild reservoir, intermediate domestic animals, and humans. We calculate the basic reproductive number of the pathogen, present critical conditions for the emergence dynamics of zoonosis, and perform stability analysis of admissible disease equilibria. Our analytical results agree well with long-term simulations of the system. We find that in the presence of biologically realistic interspecies transmission parameters, a zoonotic disease can establish itself in humans even if it fails to persist in its reservoir\n
\n\n\n\n \n\n \n \n \n \n \n Co-contagion diffusion on multilayer networks.\n \n \n \n\n\n \n Chang, H.; and Fu, F.\n\n\n \n\n\n\n Applied Network Science, 4(1). 2019.\n \n\n\n\n
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\n\n\n@article{\n title = {Co-contagion diffusion on multilayer networks},\n type = {article},\n year = {2019},\n keywords = {Complex contagions,Network diffusion,Stochastic modeling},\n volume = {4},\n id = {67274942-d2b9-33cf-8ca1-7e51dcb978d1},\n created = {2020-12-03T14:18:56.594Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.594Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2019, The Author(s). This study examines the interface of three elements during co-contagion diffusion: the synergy between contagions, the dormancy rate of each individual contagion, and the multiplex network topology. Dormancy is defined as a weaker form of “immunity,” where dormant nodes no longer actively participate in diffusion, but are still susceptible to infection. The proposed model extends the literature on threshold models, and demonstrates intricate interdependencies between different graph structures. Our simulations show that first, the faster contagion induces branching on the slower contagion; second, shorter characteristic path lengths diminish the impact of dormancy in lowering diffusion. Third, when two long-range graphs are paired, the faster contagion depends on both dormancy rates, whereas the slower contagion depends only on its own; fourth, synergistic contagions are less sensitive to dormancy, and have a wider window to diffuse. Furthermore, when long-range and spatially constrained graphs are paired, ring vaccination occurs on the spatial graph and produces partial diffusion, due to dormant, surrounding nodes. The spatial contagion depends on both dormancy rates whereas the long-range contagion depends on only its own.},\n bibtype = {article},\n author = {Chang, H.-C.H. and Fu, F.},\n doi = {10.1007/s41109-019-0176-6},\n journal = {Applied Network Science},\n number = {1}\n}\n\n © 2019, The Author(s). This study examines the interface of three elements during co-contagion diffusion: the synergy between contagions, the dormancy rate of each individual contagion, and the multiplex network topology. Dormancy is defined as a weaker form of “immunity,” where dormant nodes no longer actively participate in diffusion, but are still susceptible to infection. The proposed model extends the literature on threshold models, and demonstrates intricate interdependencies between different graph structures. Our simulations show that first, the faster contagion induces branching on the slower contagion; second, shorter characteristic path lengths diminish the impact of dormancy in lowering diffusion. Third, when two long-range graphs are paired, the faster contagion depends on both dormancy rates, whereas the slower contagion depends only on its own; fourth, synergistic contagions are less sensitive to dormancy, and have a wider window to diffuse. Furthermore, when long-range and spatially constrained graphs are paired, ring vaccination occurs on the spatial graph and produces partial diffusion, due to dormant, surrounding nodes. The spatial contagion depends on both dormancy rates whereas the long-range contagion depends on only its own.\n
\n\n\n\n \n\n \n \n \n \n \n Imperfect vaccine and hysteresis.\n \n \n \n\n\n \n Chen, X.; and Fu, F.\n\n\n \n\n\n\n Proceedings of the Royal Society B: Biological Sciences, 286(1894). 2019.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Imperfect vaccine and hysteresis},\n type = {article},\n year = {2019},\n keywords = {Evolutionary dynamics,Hysteresis loop,Social imitation,Vaccine efficacy},\n volume = {286},\n id = {60578d64-ed25-3804-8b6e-42c77cbf527b},\n created = {2020-12-03T14:18:56.616Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.616Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2019 The Author(s) Published by the Royal Society. All rights reserved. Addressing vaccine compliance problems is of particular relevance and significance to public health. Despite resurgence of vaccine-preventable diseases and public awareness of vaccine importance, why is it so challenging to boost population vaccination coverage to desired levels especially in the wake of declining vaccine uptake? To understand this puzzling phenomenon, here we study how social imitation dynamics of vaccination can be impacted by the presence of imperfect vaccine, which only confers partial protection against the disease. Besides weighing the perceived cost of vaccination with the risk of infection, the effectiveness of vaccination is also an important factor driving vaccination decisions. We discover that there can exist multiple stable vaccination equilibria if vaccine efficacy is below a certain threshold. Furthermore, our bifurcation analysis reveals the occurrence of hysteresis loops of vaccination rate with respect to changes in the perceived vaccination cost as well as in the vaccination effectiveness. Moreover, we find that hysteresis is more likely to arise in spatial populations than in well-mixed populations, even for parameter choices that do not allow for bifurcation in the latter. Our work shows that hysteresis can appear as an unprecedented roadblock for the recovery of vaccination uptake, thereby helping explain the persistence of vaccine compliance problem.},\n bibtype = {article},\n author = {Chen, X. and Fu, F.},\n doi = {10.1098/rspb.2018.2406},\n journal = {Proceedings of the Royal Society B: Biological Sciences},\n number = {1894}\n}\n\n © 2019 The Author(s) Published by the Royal Society. All rights reserved. Addressing vaccine compliance problems is of particular relevance and significance to public health. Despite resurgence of vaccine-preventable diseases and public awareness of vaccine importance, why is it so challenging to boost population vaccination coverage to desired levels especially in the wake of declining vaccine uptake? To understand this puzzling phenomenon, here we study how social imitation dynamics of vaccination can be impacted by the presence of imperfect vaccine, which only confers partial protection against the disease. Besides weighing the perceived cost of vaccination with the risk of infection, the effectiveness of vaccination is also an important factor driving vaccination decisions. We discover that there can exist multiple stable vaccination equilibria if vaccine efficacy is below a certain threshold. Furthermore, our bifurcation analysis reveals the occurrence of hysteresis loops of vaccination rate with respect to changes in the perceived vaccination cost as well as in the vaccination effectiveness. Moreover, we find that hysteresis is more likely to arise in spatial populations than in well-mixed populations, even for parameter choices that do not allow for bifurcation in the latter. Our work shows that hysteresis can appear as an unprecedented roadblock for the recovery of vaccination uptake, thereby helping explain the persistence of vaccine compliance problem.\n
\n\n\n\n \n\n \n \n \n \n \n Evolution of cooperation in public goods games with stochastic opting-out.\n \n \n \n\n\n \n Ginsberg, A.; and Fu, F.\n\n\n \n\n\n\n Games, 10(1). 2019.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Evolution of cooperation in public goods games with stochastic opting-out},\n type = {article},\n year = {2019},\n keywords = {Adaptive dynamics,Evolutionary dynamics,Finite populations,Mathematical biology,Social dilemmas},\n volume = {10},\n id = {bf3f6770-fe18-3a14-b53d-a0dbe2fb57ad},\n created = {2020-12-03T14:18:56.642Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.642Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2018 by the authors. Licensee MDPI, Basel, Switzerland. We study the evolution of cooperation in group interactions where players are randomly drawn from well-mixed populations of finite size to participate in a public goods game. However, due to the possibility of unforeseen circumstances, each player has a fixed probability of being unable to participate in the game, unlike previous models which assume voluntary participation. We first study how prescribed stochastic opting-out affects cooperation in finite populations, and then generalize for the limiting case of large populations. Because we use a pairwise comparison updating rule, our results apply to both genetic and behavioral evolution mechanisms. Moreover, in the model, cooperation is favored by natural selection over both neutral drift and defection if the return on investment exceeds a threshold value depending on the population size, the game size, and a player’s probability of opting-out. Our analysis further shows that, due to the stochastic nature of the opting-out in finite populations, the threshold of return on investment needed for natural selection to favor cooperation is actually greater than the one corresponding to compulsory games with the equal expected game size. We also use adaptive dynamics to study the co-evolution of cooperation and opting-out behavior. Indeed, given rare mutations minutely different from the resident population, an analysis based on adaptive dynamics suggests that over time the population will tend towards complete defection and non-participation, and subsequently cooperators abstaining from the public goods game will stand a chance to emerge by neutral drift, thereby paving the way for the rise of participating cooperators. Nevertheless, increasing the probability of non-participation decreases the rate at which the population tends towards defection when participating. Our work sheds light on understanding how stochastic opting-out emerges in the first place and on its role in the evolution of cooperation.},\n bibtype = {article},\n author = {Ginsberg, A.G. and Fu, F.},\n doi = {10.3390/g10010001},\n journal = {Games},\n number = {1}\n}\n\n © 2018 by the authors. Licensee MDPI, Basel, Switzerland. We study the evolution of cooperation in group interactions where players are randomly drawn from well-mixed populations of finite size to participate in a public goods game. However, due to the possibility of unforeseen circumstances, each player has a fixed probability of being unable to participate in the game, unlike previous models which assume voluntary participation. We first study how prescribed stochastic opting-out affects cooperation in finite populations, and then generalize for the limiting case of large populations. Because we use a pairwise comparison updating rule, our results apply to both genetic and behavioral evolution mechanisms. Moreover, in the model, cooperation is favored by natural selection over both neutral drift and defection if the return on investment exceeds a threshold value depending on the population size, the game size, and a player’s probability of opting-out. Our analysis further shows that, due to the stochastic nature of the opting-out in finite populations, the threshold of return on investment needed for natural selection to favor cooperation is actually greater than the one corresponding to compulsory games with the equal expected game size. We also use adaptive dynamics to study the co-evolution of cooperation and opting-out behavior. Indeed, given rare mutations minutely different from the resident population, an analysis based on adaptive dynamics suggests that over time the population will tend towards complete defection and non-participation, and subsequently cooperators abstaining from the public goods game will stand a chance to emerge by neutral drift, thereby paving the way for the rise of participating cooperators. Nevertheless, increasing the probability of non-participation decreases the rate at which the population tends towards defection when participating. Our work sheds light on understanding how stochastic opting-out emerges in the first place and on its role in the evolution of cooperation.\n
\n\n\n\n \n\n \n \n \n \n \n Steering eco-evolutionary games dynamics with manifold control.\n \n \n \n\n\n \n Wang, X.; Zheng, Z.; and Fu, F.\n\n\n \n\n\n\n 2019.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Steering eco-evolutionary games dynamics with manifold control},\n type = {misc},\n year = {2019},\n source = {arXiv},\n id = {571c709a-1611-3f1b-9739-705b36ebbf06},\n created = {2020-12-03T14:18:57.031Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.031Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2019, arXiv, All rights reserved. Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature, and have shown profound effects on the resulting eco-evolutionary dynamics. Incorporating linear environmental feedback law into replicator dynamics of two-player games, recent theoretical studies shed light on understanding the oscillating dynamics of social dilemma. However, detailed effects of more general nonlinear feedback loops in multi-player games, which is more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centered on cooperators not only accelerates the convergence of stable manifolds, but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population states. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.},\n bibtype = {misc},\n author = {Wang, X. and Zheng, Z. and Fu, F.}\n}\n\n Copyright © 2019, arXiv, All rights reserved. Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature, and have shown profound effects on the resulting eco-evolutionary dynamics. Incorporating linear environmental feedback law into replicator dynamics of two-player games, recent theoretical studies shed light on understanding the oscillating dynamics of social dilemma. However, detailed effects of more general nonlinear feedback loops in multi-player games, which is more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centered on cooperators not only accelerates the convergence of stable manifolds, but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population states. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.\n
\n\n\n\n \n\n \n \n \n \n \n Evolutionary dynamics of group cooperation with asymmetrical environmental feedback.\n \n \n \n\n\n \n Shao, Y.; Wang, X.; and Fu, F.\n\n\n \n\n\n\n 2019.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Evolutionary dynamics of group cooperation with asymmetrical environmental feedback},\n type = {misc},\n year = {2019},\n source = {arXiv},\n id = {e5671019-5737-3b1c-974f-e2fbba4c31e1},\n created = {2020-12-03T14:18:57.073Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.073Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2019, arXiv, All rights reserved. In recent years, there has been growing interest in studying evolutionary games with environmental feedback. Previous studies exclusively focus on two-player games. However, extension to multi-player game is needed to study problems such as microbial cooperation and crowdsourcing collaborations. Here, we study coevolutionary public goods games where strategies coevolve with the multiplication factors of group cooperation. Asymmetry can arise in such environmental feedback, where games organized by focal cooperators may have a different efficiency than the ones by defectors. Our analysis shows that coevolutionary dynamics with asymmetrical environmental feedback can yield oscillatory convergence to persistent cooperation, if the relative changing speed of cooperators’ multiplication factor is above a certain threshold. Our work provides useful insights into sustaining group cooperation in a changing world.},\n bibtype = {misc},\n author = {Shao, Y. and Wang, X. and Fu, F.}\n}\n\n Copyright © 2019, arXiv, All rights reserved. In recent years, there has been growing interest in studying evolutionary games with environmental feedback. Previous studies exclusively focus on two-player games. However, extension to multi-player game is needed to study problems such as microbial cooperation and crowdsourcing collaborations. Here, we study coevolutionary public goods games where strategies coevolve with the multiplication factors of group cooperation. Asymmetry can arise in such environmental feedback, where games organized by focal cooperators may have a different efficiency than the ones by defectors. Our analysis shows that coevolutionary dynamics with asymmetrical environmental feedback can yield oscillatory convergence to persistent cooperation, if the relative changing speed of cooperators’ multiplication factor is above a certain threshold. Our work provides useful insights into sustaining group cooperation in a changing world.\n
\n\n\n\n \n\n \n \n \n \n \n Evolutionary dynamics of group cooperation with asymmetrical environmental feedback.\n \n \n \n\n\n \n Shao, Y.; Wang, X.; and Fu, F.\n\n\n \n\n\n\n EPL, 126(4). 2019.\n \n\n\n\n
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\n\n\n@article{\n title = {Evolutionary dynamics of group cooperation with asymmetrical environmental feedback},\n type = {article},\n year = {2019},\n volume = {126},\n id = {52d856e0-1bfe-3195-8838-abd30d265879},\n created = {2020-12-03T14:18:57.393Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.393Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© CopyrightEPLA, 2019. In recent years, there has been growing interest in studying evolutionary games with environmental feedback. Previous studies exclusively focus on two-player games. However, extension to multi-player game is needed to study problems such as microbial cooperation and crowdsourcing collaborations. Here, we study coevolutionary public goods games where strategies coevolve with the multiplication factors of group cooperation. Asymmetry can arise in such environmental feedback, where games organized by focal cooperators may have a different efficiency than the ones by defectors. Our analysis shows that coevolutionary dynamics with asymmetrical environmental feedback can yield oscillatory convergence to persistent cooperation, if the relative changing speed of cooperators' multiplication factor is above a certain threshold. Our work provides useful insights into sustaining group cooperation in a changing world.},\n bibtype = {article},\n author = {Shao, Y. and Wang, X. and Fu, F.},\n doi = {10.1209/0295-5075/126/40005},\n journal = {EPL},\n number = {4}\n}\n\n © CopyrightEPLA, 2019. In recent years, there has been growing interest in studying evolutionary games with environmental feedback. Previous studies exclusively focus on two-player games. However, extension to multi-player game is needed to study problems such as microbial cooperation and crowdsourcing collaborations. Here, we study coevolutionary public goods games where strategies coevolve with the multiplication factors of group cooperation. Asymmetry can arise in such environmental feedback, where games organized by focal cooperators may have a different efficiency than the ones by defectors. Our analysis shows that coevolutionary dynamics with asymmetrical environmental feedback can yield oscillatory convergence to persistent cooperation, if the relative changing speed of cooperators' multiplication factor is above a certain threshold. Our work provides useful insights into sustaining group cooperation in a changing world.\n
\n\n\n\n \n\n \n \n \n \n \n Phenotype affinity mediated interactions can facilitate the evolution of cooperation.\n \n \n \n\n\n \n Wu, T.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n Journal of Theoretical Biology, 462. 2019.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Phenotype affinity mediated interactions can facilitate the evolution of cooperation},\n type = {article},\n year = {2019},\n keywords = {Interaction diversity,Phenotype,Population dynamics},\n volume = {462},\n id = {c857bd3b-808e-3040-89cb-e9e4e8786e1e},\n created = {2020-12-03T14:18:57.407Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.407Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2018 Elsevier Ltd We study the coevolutionary dynamics of the diversity of phenotype and the evolution of cooperation in the Prisoner's Dilemma. Rather than pre-assigning zero-or-one interaction rate, we diversify the rate of interaction by associating it with phenotypes. Individuals each carry a set of potentially expressible traits and expresses a number of such traits at a cost proportional to the number. The set of traits expressed constitutes phenotype. Phenotypes and thus the rate of interaction are evolvable over time. Our results show that nonnegligible cost of expressing traits restrains phenotype diversity, and the evolutionary race mainly proceeds on between cooperative strains and defective strains who express a very few traits. It pays for cooperative strains to express a very few traits. Though such a low level of expression weakens reciprocity between cooperative strains, it decelerates the rate of interaction between cooperative strains and defective strains to a larger degree, leading to the predominance of cooperative strains over defective strains. We also find that evolved diversity of phenotype can occasionally destabilize due to the invasion of defective mutants, implying that cooperation and diversity of phenotype can mutually reinforce each other. Our results may help better understand the coevolution of cooperation and the diversity of phenotype.},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Wang, L.},\n doi = {10.1016/j.jtbi.2018.11.026},\n journal = {Journal of Theoretical Biology}\n}\n\n © 2018 Elsevier Ltd We study the coevolutionary dynamics of the diversity of phenotype and the evolution of cooperation in the Prisoner's Dilemma. Rather than pre-assigning zero-or-one interaction rate, we diversify the rate of interaction by associating it with phenotypes. Individuals each carry a set of potentially expressible traits and expresses a number of such traits at a cost proportional to the number. The set of traits expressed constitutes phenotype. Phenotypes and thus the rate of interaction are evolvable over time. Our results show that nonnegligible cost of expressing traits restrains phenotype diversity, and the evolutionary race mainly proceeds on between cooperative strains and defective strains who express a very few traits. It pays for cooperative strains to express a very few traits. Though such a low level of expression weakens reciprocity between cooperative strains, it decelerates the rate of interaction between cooperative strains and defective strains to a larger degree, leading to the predominance of cooperative strains over defective strains. We also find that evolved diversity of phenotype can occasionally destabilize due to the invasion of defective mutants, implying that cooperation and diversity of phenotype can mutually reinforce each other. Our results may help better understand the coevolution of cooperation and the diversity of phenotype.\n
\n\n\n\n \n\n \n \n \n \n \n Sentiment-based prediction of alternative cryptocurrency price fluctuations using gradient boosting tree model.\n \n \n \n\n\n \n Li, T.; Chamrajnagar, A.; Fong, X.; Rizik, N.; and Fu, F.\n\n\n \n\n\n\n Frontiers in Physics, 7(JULY). 2019.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Sentiment-based prediction of alternative cryptocurrency price fluctuations using gradient boosting tree model},\n type = {article},\n year = {2019},\n keywords = {Cryptocurrency,Data integration and computational methods,Data science,Social dynamics,Tree-model,Twitter sentiment},\n volume = {7},\n id = {2bb48ab7-8205-3e71-8601-a354c633d53d},\n created = {2020-12-03T14:18:58.695Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.695Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2019 Li, Chamrajnagar, Fong, Rizik and Fu. In this paper, we analyze Twitter signals as a medium for user sentiment to predict the price fluctuations of a small-cap alternative cryptocurrency called ZClassic. We extracted tweets on an hourly basis for a period of 3.5 weeks, classifying each tweet as positive, neutral, or negative. We then compiled these tweets into an hourly sentiment index, creating an unweighted and weighted index, with the latter giving larger weight to retweets. These two indices, alongside the raw summations of positive, negative, and neutral sentiment were juxtaposed to ~400 data points of hourly pricing data to train an Extreme Gradient Boosting Regression Tree Model. Price predictions produced from this model were compared to historical price data, with the resulting predictions having a 0.81 correlation with the testing data. Our model's predictive data yielded statistical significance at the p < 0.0001 level. Our model is the first academic proof of concept that social media platforms such as Twitter can serve as powerful social signals for predicting price movements in the highly speculative alternative cryptocurrency, or "alt-coin," market.},\n bibtype = {article},\n author = {Li, T.R. and Chamrajnagar, A.S. and Fong, X.R. and Rizik, N.R. and Fu, F.},\n doi = {10.3389/fphy.2019.00112},\n journal = {Frontiers in Physics},\n number = {JULY}\n}\n\n © 2019 Li, Chamrajnagar, Fong, Rizik and Fu. In this paper, we analyze Twitter signals as a medium for user sentiment to predict the price fluctuations of a small-cap alternative cryptocurrency called ZClassic. We extracted tweets on an hourly basis for a period of 3.5 weeks, classifying each tweet as positive, neutral, or negative. We then compiled these tweets into an hourly sentiment index, creating an unweighted and weighted index, with the latter giving larger weight to retweets. These two indices, alongside the raw summations of positive, negative, and neutral sentiment were juxtaposed to ~400 data points of hourly pricing data to train an Extreme Gradient Boosting Regression Tree Model. Price predictions produced from this model were compared to historical price data, with the resulting predictions having a 0.81 correlation with the testing data. Our model's predictive data yielded statistical significance at the p < 0.0001 level. Our model is the first academic proof of concept that social media platforms such as Twitter can serve as powerful social signals for predicting price movements in the highly speculative alternative cryptocurrency, or \"alt-coin,\" market.\n
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\n\n \n \n 2018\n \n \n (12)\n \n \n
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\n \n \n\n \n \n \n \n \n Co-Diffusion of social contagions.\n \n \n \n\n\n \n Chang, H.; and Fu, F.\n\n\n \n\n\n\n 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Co-Diffusion of social contagions},\n type = {misc},\n year = {2018},\n source = {arXiv},\n keywords = {Co-diffusion,Complex contagions,Multiplex networks modeling,Synergy},\n id = {813a64b8-92ec-3424-9dd4-266dc86f7f88},\n created = {2020-12-03T14:18:56.470Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.470Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2018, arXiv, All rights reserved. Prior social contagion models consider the spread of either one contagion at a time on interdependent networks or multiple contagions on single layer networks or under assumptions of pure competition. We propose a new threshold model for the diffusion of multiple contagions. Individuals are placed on a multiplex network with a periodic lattice and a random-regular-graph layer. On these population structures, we study the interface between two key aspects of the diffusion process: the level of synergy between two contagions, and the rate at which individuals become dormant after adoption. Dormancy is defined as a looser form of immunity that models the ability to spread without resistance. Monte Carlo simulations reveal lower synergy makes contagions more susceptible to percolation, especially those that diffuse on lattices. Faster diffusion of one contagion with dormancy probabilistically blocks the diffusion of the other, in a way similar to ring vaccination. We show that within a band of synergy, contagions on the lattices undergo bimodal or trimodal branching if they are the slower diffusing contagion.},\n bibtype = {misc},\n author = {Chang, H.-C.H. and Fu, F.}\n}\n\n Copyright © 2018, arXiv, All rights reserved. Prior social contagion models consider the spread of either one contagion at a time on interdependent networks or multiple contagions on single layer networks or under assumptions of pure competition. We propose a new threshold model for the diffusion of multiple contagions. Individuals are placed on a multiplex network with a periodic lattice and a random-regular-graph layer. On these population structures, we study the interface between two key aspects of the diffusion process: the level of synergy between two contagions, and the rate at which individuals become dormant after adoption. Dormancy is defined as a looser form of immunity that models the ability to spread without resistance. Monte Carlo simulations reveal lower synergy makes contagions more susceptible to percolation, especially those that diffuse on lattices. Faster diffusion of one contagion with dormancy probabilistically blocks the diffusion of the other, in a way similar to ring vaccination. We show that within a band of synergy, contagions on the lattices undergo bimodal or trimodal branching if they are the slower diffusing contagion.\n
\n\n\n\n \n\n \n \n \n \n \n Social learning of prescribing behavior can promote population optimum of antibiotic use.\n \n \n \n\n\n \n Chen, X.; and Fu, F.\n\n\n \n\n\n\n 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Social learning of prescribing behavior can promote population optimum of antibiotic use},\n type = {misc},\n year = {2018},\n source = {arXiv},\n keywords = {Antibiotic resistance,Evolutionary dynamics,Game theory,Public health},\n id = {1d0f9abc-a3fc-3403-81ae-9d481eb37338},\n created = {2020-12-03T14:18:56.554Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.554Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2018, arXiv, All rights reserved. The rise and spread of antibiotic resistance causes worsening medical cost and mortality especially for life-threatening bacteria infections, thereby posing a major threat to global health. Prescribing behavior of physicians is one of the important factors impacting the underlying dynamics of resistance evolution. It remains unclear when individual prescribing decisions can lead to the overuse of antibiotics on the population level, and whether population optimum of antibiotic use can be reached through an adaptive social learning process that governs the evolution of prescribing norm. Here we study a behavior-disease interaction model, specifically incorporating a feedback loop between prescription behavior and resistance evolution. We identify the conditions under which antibiotic resistance can evolve as a result of the tragedy of the commons in antibiotic overuse. Furthermore, we show that fast social learning that adjusts prescribing behavior in prompt response to resistance evolution can steer out cyclic oscillations of antibiotic usage quickly towards the stable population optimum of prescribing. Our work demonstrates that provision of prompt feedback to prescribing behavior with the collective consequences of treatment decisions and costs that are associated with resistance helps curb the overuse of antibiotics.},\n bibtype = {misc},\n author = {Chen, X. and Fu, F.}\n}\n\n Copyright © 2018, arXiv, All rights reserved. The rise and spread of antibiotic resistance causes worsening medical cost and mortality especially for life-threatening bacteria infections, thereby posing a major threat to global health. Prescribing behavior of physicians is one of the important factors impacting the underlying dynamics of resistance evolution. It remains unclear when individual prescribing decisions can lead to the overuse of antibiotics on the population level, and whether population optimum of antibiotic use can be reached through an adaptive social learning process that governs the evolution of prescribing norm. Here we study a behavior-disease interaction model, specifically incorporating a feedback loop between prescription behavior and resistance evolution. We identify the conditions under which antibiotic resistance can evolve as a result of the tragedy of the commons in antibiotic overuse. Furthermore, we show that fast social learning that adjusts prescribing behavior in prompt response to resistance evolution can steer out cyclic oscillations of antibiotic usage quickly towards the stable population optimum of prescribing. Our work demonstrates that provision of prompt feedback to prescribing behavior with the collective consequences of treatment decisions and costs that are associated with resistance helps curb the overuse of antibiotics.\n
\n\n\n\n \n\n \n \n \n \n \n Opinion formation on dynamic networks: Identifying conditions for the emergence of partisan echo chambers.\n \n \n \n\n\n \n Evans, T.; and Fu, F.\n\n\n \n\n\n\n 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Opinion formation on dynamic networks: Identifying conditions for the emergence of partisan echo chambers},\n type = {misc},\n year = {2018},\n source = {arXiv},\n keywords = {Consensus,Polarization,Social dynamics},\n id = {1b9cde46-09fb-336f-923a-57c6696fdb0b},\n created = {2020-12-03T14:18:56.573Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.573Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2018, arXiv, All rights reserved. Modern political interaction is characterized by strong partisanship and a lack of interest in information sharing and agreement across party lines. It remains largely unclear how such partisan echo chambers arise and how they coevolve with opinion formation. Here we explore the emergence of these structures through the lens of coevolutionary games. In our model, the payoff of an individual is determined jointly by the magnitude of their opinion, their degree of conformity with their social neighbors, and the benefit of having social connections. Each individual can simultaneously adjust their opinion as well as the weights of their social connections. We present and validate the conditions for the emergence of partisan echo chambers, characterizing the transition from cohesive communities with consensus to divisive networks with splitting opinions. Moreover, we apply our model to voting records of the United States House of Representatives over a timespan of decades in order to understand the influence of underlying psychological and social factors on increasing partisanship in recent years. Our work helps elucidate how the division of today has come to be and how cohesion and unity could otherwise be attained on a variety of political and social issues.},\n bibtype = {misc},\n author = {Evans, T. and Fu, F.}\n}\n\n Copyright © 2018, arXiv, All rights reserved. Modern political interaction is characterized by strong partisanship and a lack of interest in information sharing and agreement across party lines. It remains largely unclear how such partisan echo chambers arise and how they coevolve with opinion formation. Here we explore the emergence of these structures through the lens of coevolutionary games. In our model, the payoff of an individual is determined jointly by the magnitude of their opinion, their degree of conformity with their social neighbors, and the benefit of having social connections. Each individual can simultaneously adjust their opinion as well as the weights of their social connections. We present and validate the conditions for the emergence of partisan echo chambers, characterizing the transition from cohesive communities with consensus to divisive networks with splitting opinions. Moreover, we apply our model to voting records of the United States House of Representatives over a timespan of decades in order to understand the influence of underlying psychological and social factors on increasing partisanship in recent years. Our work helps elucidate how the division of today has come to be and how cohesion and unity could otherwise be attained on a variety of political and social issues.\n
\n\n\n\n \n\n \n \n \n \n \n Social learning of prescribing behavior can promote population optimum of antibiotic use.\n \n \n \n\n\n \n Chen, X.; and Fu, F.\n\n\n \n\n\n\n Frontiers in Physics, 6(DEC). 2018.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Social learning of prescribing behavior can promote population optimum of antibiotic use},\n type = {article},\n year = {2018},\n keywords = {Antibiotic resistance,Cooperation,Evolutionary dynamics,Game theory,Public health},\n volume = {6},\n id = {3a0dfc32-731b-3c44-9817-d065dfcb4608},\n created = {2020-12-03T14:18:56.673Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.673Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2018 Chen and Fu. The rise and spread of antibiotic resistance causes worsening medical cost and mortality especially for life-threatening bacteria infections, thereby posing a major threat to global health. Prescribing behavior of physicians is one of the important factors impacting the underlying dynamics of resistance evolution. It remains unclear when individual prescribing decisions can lead to the overuse of antibiotics on the population level, and whether population optimum of antibiotic use can be reached through an adaptive social learning process that governs the evolution of prescribing norm. Here we study a behavior-disease interaction model, specifically incorporating a feedback loop between prescription behavior and resistance evolution. We identify the conditions under which antibiotic resistance can evolve as a result of the tragedy of the commons in antibiotic overuse. Furthermore, we show that fast social learning that adjusts prescribing behavior in prompt response to resistance evolution can steer out cyclic oscillations of antibiotic usage quickly toward the stable population optimum of prescribing. Our work demonstrates that provision of prompt feedback to prescribing behavior with the collective consequences of treatment decisions and costs that are associated with resistance helps curb the overuse of antibiotics.},\n bibtype = {article},\n author = {Chen, X. and Fu, F.},\n doi = {10.3389/fphy.2018.00139},\n journal = {Frontiers in Physics},\n number = {DEC}\n}\n\n © 2018 Chen and Fu. The rise and spread of antibiotic resistance causes worsening medical cost and mortality especially for life-threatening bacteria infections, thereby posing a major threat to global health. Prescribing behavior of physicians is one of the important factors impacting the underlying dynamics of resistance evolution. It remains unclear when individual prescribing decisions can lead to the overuse of antibiotics on the population level, and whether population optimum of antibiotic use can be reached through an adaptive social learning process that governs the evolution of prescribing norm. Here we study a behavior-disease interaction model, specifically incorporating a feedback loop between prescription behavior and resistance evolution. We identify the conditions under which antibiotic resistance can evolve as a result of the tragedy of the commons in antibiotic overuse. Furthermore, we show that fast social learning that adjusts prescribing behavior in prompt response to resistance evolution can steer out cyclic oscillations of antibiotic usage quickly toward the stable population optimum of prescribing. Our work demonstrates that provision of prompt feedback to prescribing behavior with the collective consequences of treatment decisions and costs that are associated with resistance helps curb the overuse of antibiotics.\n
\n\n\n\n \n\n \n \n \n \n \n Opinion formation on dynamic networks: Identifying conditions for the emergence of partisan echo chambers.\n \n \n \n\n\n \n Evans, T.; and Fu, F.\n\n\n \n\n\n\n Royal Society Open Science, 5(10). 2018.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Opinion formation on dynamic networks: Identifying conditions for the emergence of partisan echo chambers},\n type = {article},\n year = {2018},\n keywords = {Consensus,Polarization,Social dynamics},\n volume = {5},\n id = {272ac1a9-4c31-3592-9331-f54c274ceece},\n created = {2020-12-03T14:18:56.703Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.703Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2018 The Authors. Modern political interaction is characterized by strong partisanship and a lack of interest in information sharing and agreement across party lines. It remains largely unclear how such partisan echo chambers arise and how they coevolve with opinion formation. Here, we explore the emergence of these structures through the lens of coevolutionary games. In our model, the payoff of an individual is determined jointly by the magnitude of their opinion, their degree of conformity with their social neighbours and the benefit of having social connections. Each individual can simultaneously adjust their opinion and the weights of their social connections. We present and validate the conditions for the emergence of partisan echo chambers, characterizing the transition from cohesive communities with a consensus to divisive networks with splitting opinions. Moreover, we apply our model to voting records of the US House of Representatives over a timespan of decades to understand the influence of underlying psychological and social factors on increasing partisanship in recent years. Our work helps elucidate how the division of today has come to be and how cohesion and unity could otherwise be attained on a variety of political and social issues.},\n bibtype = {article},\n author = {Evans, T. and Fu, F.},\n doi = {10.1098/rsos.181122},\n journal = {Royal Society Open Science},\n number = {10}\n}\n\n © 2018 The Authors. Modern political interaction is characterized by strong partisanship and a lack of interest in information sharing and agreement across party lines. It remains largely unclear how such partisan echo chambers arise and how they coevolve with opinion formation. Here, we explore the emergence of these structures through the lens of coevolutionary games. In our model, the payoff of an individual is determined jointly by the magnitude of their opinion, their degree of conformity with their social neighbours and the benefit of having social connections. Each individual can simultaneously adjust their opinion and the weights of their social connections. We present and validate the conditions for the emergence of partisan echo chambers, characterizing the transition from cohesive communities with a consensus to divisive networks with splitting opinions. Moreover, we apply our model to voting records of the US House of Representatives over a timespan of decades to understand the influence of underlying psychological and social factors on increasing partisanship in recent years. Our work helps elucidate how the division of today has come to be and how cohesion and unity could otherwise be attained on a variety of political and social issues.\n
\n\n\n\n \n\n \n \n \n \n \n Co-diffusion of social contagions.\n \n \n \n\n\n \n Chang, H.; and Fu, F.\n\n\n \n\n\n\n New Journal of Physics, 20(9). 2018.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Co-diffusion of social contagions},\n type = {article},\n year = {2018},\n keywords = {complex contagion,diffusion,multilayer networks,stochastic modeling,synergy},\n volume = {20},\n id = {f0bd06c8-266b-396b-b5e7-5de7092912a0},\n created = {2020-12-03T14:18:56.721Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.721Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. Prior social contagion models consider the spread of either one contagion on interdependent networks or multiple contagions on single layer networks, usually under assumptions of competition. We propose a new threshold model for the diffusion of multiple contagions. Individuals are placed on a multiplex network with a periodic lattice layer and a random-regular-graph layer. On these population structures, we study the interface between two key aspects of the diffusion process: the level of synergy between two contagions, and the rate at which individuals become dormant after adoption. Dormancy is defined as a looser form of immunity that limits active spreading but without conferring resistance. Monte Carlo simulations reveal lower synergy makes contagions more susceptible to percolation, especially those that diffuse on lattices. Faster diffusion of one contagion with dormancy probabilistically blocks the diffusion of the other, in a way similar to ring vaccination. We show that within a band of synergy, bimodal or trimodal branchings occur on the slower contagion on the lattice. We also show complimentary contagions can provide a synergistic boost to help spread contagions that have almost gone dormant.},\n bibtype = {article},\n author = {Chang, H.-C.H. and Fu, F.},\n doi = {10.1088/1367-2630/aadce7},\n journal = {New Journal of Physics},\n number = {9}\n}\n\n © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. Prior social contagion models consider the spread of either one contagion on interdependent networks or multiple contagions on single layer networks, usually under assumptions of competition. We propose a new threshold model for the diffusion of multiple contagions. Individuals are placed on a multiplex network with a periodic lattice layer and a random-regular-graph layer. On these population structures, we study the interface between two key aspects of the diffusion process: the level of synergy between two contagions, and the rate at which individuals become dormant after adoption. Dormancy is defined as a looser form of immunity that limits active spreading but without conferring resistance. Monte Carlo simulations reveal lower synergy makes contagions more susceptible to percolation, especially those that diffuse on lattices. Faster diffusion of one contagion with dormancy probabilistically blocks the diffusion of the other, in a way similar to ring vaccination. We show that within a band of synergy, bimodal or trimodal branchings occur on the slower contagion on the lattice. We also show complimentary contagions can provide a synergistic boost to help spread contagions that have almost gone dormant.\n
\n\n\n\n \n\n \n \n \n \n \n Strategy intervention for the evolution of fairness.\n \n \n \n\n\n \n Zhang, Y.; and Fu, F.\n\n\n \n\n\n\n PLoS ONE, 13(5). 2018.\n \n\n\n\n
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\n\n\n@article{\n title = {Strategy intervention for the evolution of fairness},\n type = {article},\n year = {2018},\n volume = {13},\n id = {ff8e919a-5ea9-3b57-981d-64add8ee5e4a},\n created = {2020-12-03T14:18:56.755Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.755Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2018 Zhang, Fu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The ‘irrational’ preference for fairness has attracted increasing attention. Although previous studies have focused on the effects of spitefulness on the evolution of fairness, they did not consider non-monotonic rejections shown in behavioral experiments. In this paper, we introduce a non-monotonic rejection in an evolutionary model of the Ultimatum Game. We propose strategy intervention to study the evolution of fairness in general structured populations. By sequentially adding five strategies into the competition between a fair strategy and a selfish strategy, we arrive at the following conclusions. First, the evolution of fairness is inhibited by altruism, but it is promoted by spitefulness. Second, the non-monotonic rejection helps fairness overcome selfishness. Particularly for group-structured populations, we analytically investigate how fairness, selfishness, altruism, and spitefulness are affected by population size, mutation, and migration in the competition among seven strategies. Our results may provide important insights into understanding the evolutionary origin of fairness.},\n bibtype = {article},\n author = {Zhang, Y. and Fu, F.},\n doi = {10.1371/journal.pone.0196524},\n journal = {PLoS ONE},\n number = {5}\n}\n\n © 2018 Zhang, Fu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The ‘irrational’ preference for fairness has attracted increasing attention. Although previous studies have focused on the effects of spitefulness on the evolution of fairness, they did not consider non-monotonic rejections shown in behavioral experiments. In this paper, we introduce a non-monotonic rejection in an evolutionary model of the Ultimatum Game. We propose strategy intervention to study the evolution of fairness in general structured populations. By sequentially adding five strategies into the competition between a fair strategy and a selfish strategy, we arrive at the following conclusions. First, the evolution of fairness is inhibited by altruism, but it is promoted by spitefulness. Second, the non-monotonic rejection helps fairness overcome selfishness. Particularly for group-structured populations, we analytically investigate how fairness, selfishness, altruism, and spitefulness are affected by population size, mutation, and migration in the competition among seven strategies. Our results may provide important insights into understanding the evolutionary origin of fairness.\n
\n\n\n\n \n\n \n \n \n \n \n Cancer-induced immunosuppression can enable effectiveness of immunotherapy through bistability generation: A mathematical and computational Examination.\n \n \n \n\n\n \n Garcia, V.; Bonhoeffer, S.; and Fu, F.\n\n\n \n\n\n\n 2018.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Cancer-induced immunosuppression can enable effectiveness of immunotherapy through bistability generation: A mathematical and computational Examination},\n type = {misc},\n year = {2018},\n source = {bioRxiv},\n id = {df5cf0de-7006-352e-928b-b0b7db7b53dc},\n created = {2020-12-03T14:18:56.956Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.956Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license. Cancer immunotherapies rely on how interactions between cancer and immune system cells are constituted. The more essential to the emergence of the dynamical behavior of cancer growth these are, the more effectively they may be used as mechanisms for interventions. Mathematical modeling can help unearth such connections, and help explain how they shape the dynamics of cancer growth. Here, we explored whether there exist simple, consistent properties of cancer-immune system interaction (CISI) models that might be harnessed to devise effective immunotherapy approaches. We did this for a family of three related models of increasing complexity. To this end, we developed a base model of CISI, which captures some essential features of the more complex models built on it. We find that the base model and its derivates can plausibly reproduce biological behavior that is consistent with the notion of an immunological barrier. This behavior is also in accord with situations in which the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects. Under these circumstances, the model family may display a pattern of bistability, where two distinct, stable states (a cancer-free, and a full-grown cancer state) are possible. Increasing the effectiveness of immune-caused cancer cell killing may remove the basis for bistability, and abruptly tip the dynamics of the system into a cancer-free state. Additionally, in combination with the administration of immune effector cells, modifications in cancer cell killing may be harnessed for immunotherapy without the need for resolving the bistability. We use these ideas to test immunotherapeutic interventions in silico in a stochastic version of the base model. This bistability-reliant approach to cancer interventions might offer advantages over those that comprise gradual declines in cancer cell numbers.},\n bibtype = {misc},\n author = {Garcia, V. and Bonhoeffer, S. and Fu, F.},\n doi = {10.1101/498741}\n}\n\n The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license. Cancer immunotherapies rely on how interactions between cancer and immune system cells are constituted. The more essential to the emergence of the dynamical behavior of cancer growth these are, the more effectively they may be used as mechanisms for interventions. Mathematical modeling can help unearth such connections, and help explain how they shape the dynamics of cancer growth. Here, we explored whether there exist simple, consistent properties of cancer-immune system interaction (CISI) models that might be harnessed to devise effective immunotherapy approaches. We did this for a family of three related models of increasing complexity. To this end, we developed a base model of CISI, which captures some essential features of the more complex models built on it. We find that the base model and its derivates can plausibly reproduce biological behavior that is consistent with the notion of an immunological barrier. This behavior is also in accord with situations in which the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects. Under these circumstances, the model family may display a pattern of bistability, where two distinct, stable states (a cancer-free, and a full-grown cancer state) are possible. Increasing the effectiveness of immune-caused cancer cell killing may remove the basis for bistability, and abruptly tip the dynamics of the system into a cancer-free state. Additionally, in combination with the administration of immune effector cells, modifications in cancer cell killing may be harnessed for immunotherapy without the need for resolving the bistability. We use these ideas to test immunotherapeutic interventions in silico in a stochastic version of the base model. This bistability-reliant approach to cancer interventions might offer advantages over those that comprise gradual declines in cancer cell numbers.\n
\n\n\n\n \n\n \n \n \n \n \n Phenotype affinity mediated interactions can facilitate the evolution of cooperation.\n \n \n \n\n\n \n Wu, T.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n 2018.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Phenotype affinity mediated interactions can facilitate the evolution of cooperation},\n type = {misc},\n year = {2018},\n source = {arXiv},\n keywords = {Interaction diversity,Phenotype,Population dynamics},\n id = {dff3020a-2aa5-3d28-9dc1-f055fc64c4d3},\n created = {2020-12-03T14:18:57.096Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.096Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2018, arXiv, All rights reserved. We study the coevolutionary dynamics of the diversity of phenotype expression and the evolution of cooperation in the Prisoner's Dilemma game. Rather than pre-assigning zero-or-one interaction rate, we diversify the rate of interaction by associating it with the phenotypes shared in common. Individuals each carry a set of potentially expressible phenotypes and expresses a certain number of phenotypes at a cost proportional to the number. The number of expressed phenotypes and thus the rate of interaction is an evolvable trait. Our results show that nonnegligible cost of expressing phenotypes restrains phenotype expression, and the evolutionary race mainly proceeds on between cooperative strains and defective strains who express a very few phenotypes. It pays for cooperative strains to express a very few phenotypes. Though such a low level of expression weakens reciprocity between cooperative strains, it decelerates rate of interaction between cooperative strains and defective strains to a larger degree, leading to the predominance of cooperative strains over defective strains. We also find that evolved diversity of phenotype expression can occasionally destabilize due to the invasion of defective mutants, implying that cooperation and diversity of phenotype expression can mutually reinforce each other. Therefore, our results provide new insights into better understanding the coevolution of cooperation and the diversity of phenotype expression.},\n bibtype = {misc},\n author = {Wu, T. and Fu, F. and Wang, L.}\n}\n\n Copyright © 2018, arXiv, All rights reserved. We study the coevolutionary dynamics of the diversity of phenotype expression and the evolution of cooperation in the Prisoner's Dilemma game. Rather than pre-assigning zero-or-one interaction rate, we diversify the rate of interaction by associating it with the phenotypes shared in common. Individuals each carry a set of potentially expressible phenotypes and expresses a certain number of phenotypes at a cost proportional to the number. The number of expressed phenotypes and thus the rate of interaction is an evolvable trait. Our results show that nonnegligible cost of expressing phenotypes restrains phenotype expression, and the evolutionary race mainly proceeds on between cooperative strains and defective strains who express a very few phenotypes. It pays for cooperative strains to express a very few phenotypes. Though such a low level of expression weakens reciprocity between cooperative strains, it decelerates rate of interaction between cooperative strains and defective strains to a larger degree, leading to the predominance of cooperative strains over defective strains. We also find that evolved diversity of phenotype expression can occasionally destabilize due to the invasion of defective mutants, implying that cooperation and diversity of phenotype expression can mutually reinforce each other. Therefore, our results provide new insights into better understanding the coevolution of cooperation and the diversity of phenotype expression.\n
\n\n\n\n \n\n \n \n \n \n \n Coevolutionary dynamics of aspiration and strategy in spatial repeated public goods games.\n \n \n \n\n\n \n Wu, T.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n New Journal of Physics, 20(6). 2018.\n \n\n\n\n
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\n\n\n@article{\n title = {Coevolutionary dynamics of aspiration and strategy in spatial repeated public goods games},\n type = {article},\n year = {2018},\n keywords = {aspiration,coevolutionary dynamics,cyclical dominance,optimal aspiration level,repeated public goods games},\n volume = {20},\n id = {174be7ef-1dab-3aff-90e6-3d31852e7b02},\n created = {2020-12-03T14:18:57.439Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.439Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. The evolutionary dynamics remain largely unknown for spatial populations where individuals are more likely to interact repeatedly. Under this settings, individuals can make their decisions to cooperate or not based on the decisions previously adopted by others in their neighborhoods. Using repeated public goods game, we construct a spatial model and use a statistical physics approach to study the coevolutionary dynamics of aspiration and strategy. Individuals each have an aspiration towards the groups they are involved. According to the outcome of each group, individuals have assessment of whether their aspirations are satisfied. If satisfied, they cooperate next round. Otherwise, they switch to defecting. Results show threshold phenomenon for harsh collective dilemma: cooperators sticking to high levels of aspiration can prevail over defectors, while cooperators with other levels are invariably wiped out. When the collective dilemma is relaxed, cooperation is greatly facilitated by inducing a high level of diversity of aspiration. Snapshots further show the spatial patterns of how this coevolutionary process leads to the emergence of an optimal solution associated with aspiration level, whose corresponding strategy are most prevalent. This optimal solution lies in one and the highest aspiration level allowed, and depends on the intensity of the social dilemma. By removing the memory effect, our results also confirm that repeated interactions can promote cooperation, but to a limited degree.},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Wang, L.},\n doi = {10.1088/1367-2630/aac687},\n journal = {New Journal of Physics},\n number = {6}\n}\n\n © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. The evolutionary dynamics remain largely unknown for spatial populations where individuals are more likely to interact repeatedly. Under this settings, individuals can make their decisions to cooperate or not based on the decisions previously adopted by others in their neighborhoods. Using repeated public goods game, we construct a spatial model and use a statistical physics approach to study the coevolutionary dynamics of aspiration and strategy. Individuals each have an aspiration towards the groups they are involved. According to the outcome of each group, individuals have assessment of whether their aspirations are satisfied. If satisfied, they cooperate next round. Otherwise, they switch to defecting. Results show threshold phenomenon for harsh collective dilemma: cooperators sticking to high levels of aspiration can prevail over defectors, while cooperators with other levels are invariably wiped out. When the collective dilemma is relaxed, cooperation is greatly facilitated by inducing a high level of diversity of aspiration. Snapshots further show the spatial patterns of how this coevolutionary process leads to the emergence of an optimal solution associated with aspiration level, whose corresponding strategy are most prevalent. This optimal solution lies in one and the highest aspiration level allowed, and depends on the intensity of the social dilemma. By removing the memory effect, our results also confirm that repeated interactions can promote cooperation, but to a limited degree.\n
\n\n\n\n \n\n \n \n \n \n \n Spillover modes in multiplex games: Double-edged effects on cooperation and their coevolution.\n \n \n \n\n\n \n Khoo, T.; Fu, F.; and Pauls, S.\n\n\n \n\n\n\n Scientific Reports, 8(1). 2018.\n \n\n\n\n
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\n\n\n@article{\n title = {Spillover modes in multiplex games: Double-edged effects on cooperation and their coevolution},\n type = {article},\n year = {2018},\n volume = {8},\n id = {bbe1d908-0b5a-361d-b247-4a35ee2daf6d},\n created = {2020-12-03T14:18:57.455Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.455Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2018 The Author(s). In recent years, there has been growing interest in studying games on multiplex networks that account for interactions across linked social contexts. However, little is known about how potential cross-context interference, or spillover, of individual behavioural strategy impact overall cooperation. We consider three plausible spillover modes, quantifying and comparing their effects on the evolution of cooperation. In our model, social interactions take place on two network layers: repeated interactions with close neighbours in a lattice, and one-shot interactions with random individuals. Spillover can occur during the learning process with accidental cross-layer strategy transfer, or during social interactions with errors in implementation. Our analytical results, using extended pair approximation, are in good agreement with extensive simulations. We find double-edged effects of spillover: increasing the intensity of spillover can promote cooperation provided cooperation is favoured in one layer, but too much spillover is detrimental. We also discover a bistability phenomenon: spillover hinders or promotes cooperation depending on initial frequencies of cooperation in each layer. Furthermore, comparing strategy combinations emerging in each spillover mode provides good indication of their co-evolutionary dynamics with cooperation. Our results make testable predictions that inspire future research, and sheds light on human cooperation across social domains.},\n bibtype = {article},\n author = {Khoo, T. and Fu, F. and Pauls, S.},\n doi = {10.1038/s41598-018-25025-3},\n journal = {Scientific Reports},\n number = {1}\n}\n\n © 2018 The Author(s). In recent years, there has been growing interest in studying games on multiplex networks that account for interactions across linked social contexts. However, little is known about how potential cross-context interference, or spillover, of individual behavioural strategy impact overall cooperation. We consider three plausible spillover modes, quantifying and comparing their effects on the evolution of cooperation. In our model, social interactions take place on two network layers: repeated interactions with close neighbours in a lattice, and one-shot interactions with random individuals. Spillover can occur during the learning process with accidental cross-layer strategy transfer, or during social interactions with errors in implementation. Our analytical results, using extended pair approximation, are in good agreement with extensive simulations. We find double-edged effects of spillover: increasing the intensity of spillover can promote cooperation provided cooperation is favoured in one layer, but too much spillover is detrimental. We also discover a bistability phenomenon: spillover hinders or promotes cooperation depending on initial frequencies of cooperation in each layer. Furthermore, comparing strategy combinations emerging in each spillover mode provides good indication of their co-evolutionary dynamics with cooperation. Our results make testable predictions that inspire future research, and sheds light on human cooperation across social domains.\n
\n\n\n\n \n\n \n \n \n \n \n Sentiment-based prediction of alternative cryptocurrency price fluctuations using gradient boosting tree model.\n \n \n \n\n\n \n Li, T.; Chamrajnagar, A.; Fong, X.; Rizik, N.; and Fu, F.\n\n\n \n\n\n\n 2018.\n \n\n\n\n
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\n\n\n@misc{\n title = {Sentiment-based prediction of alternative cryptocurrency price fluctuations using gradient boosting tree model},\n type = {misc},\n year = {2018},\n source = {arXiv},\n keywords = {Cryptocurrency,Data Science,Speculation,Tree-Model,Twitter Sentiment,ZClassic},\n id = {054d8fb4-0d7f-389a-ba5b-e6096eeafc04},\n created = {2020-12-03T14:18:58.690Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.690Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2018, arXiv, All rights reserved. In this paper, we analyze Twitter signals as a medium for user sentiment to predict the price fluctuations of a small-cap alternative cryptocurrency called ZClassic. We extracted tweets on an hourly basis for a period of 3.5 weeks, classifying each tweet as positive, neutral, or negative. We then compiled these tweets into an hourly sentiment index, creating an unweighted and weighted index, with the latter giving larger weight to retweets. These two indices, alongside the raw summations of positive, negative, and neutral sentiment were juxtaposed to ∼ 400 data points of hourly pricing data to train an Extreme Gradient Boosting Regression Tree Model. Price predictions produced from this model were compared to historical price data, with the resulting predictions having a 0.81 correlation with the testing data. Our model’s predictive data yielded statistical significance at the p < 0.0001 level. Our model is the first academic proof of concept that social media platforms such as Twitter can serve as powerful social signals for predicting price movements in the highly speculative alternative cryptocurrency, or “alt-coin”, market.},\n bibtype = {misc},\n author = {Li, T.R. and Chamrajnagar, A.S. and Fong, X.R. and Rizik, N.R. and Fu, F.}\n}\n\n Copyright © 2018, arXiv, All rights reserved. In this paper, we analyze Twitter signals as a medium for user sentiment to predict the price fluctuations of a small-cap alternative cryptocurrency called ZClassic. We extracted tweets on an hourly basis for a period of 3.5 weeks, classifying each tweet as positive, neutral, or negative. We then compiled these tweets into an hourly sentiment index, creating an unweighted and weighted index, with the latter giving larger weight to retweets. These two indices, alongside the raw summations of positive, negative, and neutral sentiment were juxtaposed to ∼ 400 data points of hourly pricing data to train an Extreme Gradient Boosting Regression Tree Model. Price predictions produced from this model were compared to historical price data, with the resulting predictions having a 0.81 correlation with the testing data. Our model’s predictive data yielded statistical significance at the p < 0.0001 level. Our model is the first academic proof of concept that social media platforms such as Twitter can serve as powerful social signals for predicting price movements in the highly speculative alternative cryptocurrency, or “alt-coin”, market.\n
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\n \n \n\n \n \n \n \n \n Risk-aware multi-armed bandit problem with application to portfolio selection.\n \n \n \n\n\n \n Huo, X.; and Fu, F.\n\n\n \n\n\n\n 2017.\n \n\n\n\n
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\n\n\n@misc{\n title = {Risk-aware multi-armed bandit problem with application to portfolio selection},\n type = {misc},\n year = {2017},\n source = {arXiv},\n keywords = {Conditional value-at-risk,Graph theory,Multi-armed bandit,Online learning,Portfolio selection,Risk-awareness},\n id = {0e782de0-cce0-3a25-bfec-53177b1cc4cf},\n created = {2020-12-03T14:18:56.438Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.438Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2017, arXiv, All rights reserved. Sequential portfolio selection has attracted increasing interests in the machine learning and quantitative finance communities in recent years. As a mathematical framework for reinforcement learning policies, the stochastic multi-armed bandit problem addresses the primary difficulty in sequential decision making under uncertainty, namely the exploration versus exploitation dilemma, and therefore provides a natural connection to portfolio selection. In this paper, we incorporate risk-awareness into the classic multiarmed bandit setting and introduce an algorithm to construct portfolio. Through filtering assets based on the topological structure of financial market and combining the optimal multi-armed bandit policy with the minimization of a coherent risk measure, we achieve a balance between risk and return.},\n bibtype = {misc},\n author = {Huo, X. and Fu, F.}\n}\n\n Copyright © 2017, arXiv, All rights reserved. Sequential portfolio selection has attracted increasing interests in the machine learning and quantitative finance communities in recent years. As a mathematical framework for reinforcement learning policies, the stochastic multi-armed bandit problem addresses the primary difficulty in sequential decision making under uncertainty, namely the exploration versus exploitation dilemma, and therefore provides a natural connection to portfolio selection. In this paper, we incorporate risk-awareness into the classic multiarmed bandit setting and introduce an algorithm to construct portfolio. Through filtering assets based on the topological structure of financial market and combining the optimal multi-armed bandit policy with the minimization of a coherent risk measure, we achieve a balance between risk and return.\n
\n\n\n\n \n\n \n \n \n \n \n Strategy intervention for the evolution of fairness.\n \n \n \n\n\n \n Zhang, Y.; and Fu, F.\n\n\n \n\n\n\n 2017.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Strategy intervention for the evolution of fairness},\n type = {misc},\n year = {2017},\n source = {arXiv},\n id = {e41d5a1f-d1c7-3ba8-b09e-72d8e45f1127},\n created = {2020-12-03T14:18:56.517Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.517Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2017, arXiv, All rights reserved. Masses of experiments have shown individual preference for fairness which seems irrational. The reason behind it remains a focus for research. The effect of spite (individuals are only concerned with their own relative standing) on the evolution of fairness has attracted increasing attention from experiments, but only has been implicitly studied in one evolutionary model. The model did not involve high-offer rejections, which have been found in the form of non-monotonic rejections (rejecting offers that are too high or too low) in experiments. Here, we introduce a high offer and a non-monotonic rejection in structured populations of finite size, and use strategy intervention to explicitly study how spite influences the evolution of fairness: five strategies are in sequence added into the competition of a fair strategy and a selfish strategy. We find that spite promotes fairness, altruism inhibits fairness, and the non-monotonic rejection can cause fairness to overcome selfishness, which cannot happen without high-offer rejections. Particularly for the group-structured population with seven discrete strategies, we analytically study the effect of population size, mutation, and migration on fairness, selfishness, altruism, and spite. A larger population size cannot change the dominance of fairness, but it promotes altruism and inhibits selfishness and spite. Intermediate mutation maximizes selfishness and fairness, and minimizes spite; intermediate mutation maximizes altruism for intermediate migration and minimizes altruism otherwise. The existence of migration inhibits selfishness and fairness, and promotes altruism; sufficient migration promotes spite. Our study may provide important insights into the evolutionary origin of fairness.},\n bibtype = {misc},\n author = {Zhang, Y. and Fu, F.}\n}\n\n Copyright © 2017, arXiv, All rights reserved. Masses of experiments have shown individual preference for fairness which seems irrational. The reason behind it remains a focus for research. The effect of spite (individuals are only concerned with their own relative standing) on the evolution of fairness has attracted increasing attention from experiments, but only has been implicitly studied in one evolutionary model. The model did not involve high-offer rejections, which have been found in the form of non-monotonic rejections (rejecting offers that are too high or too low) in experiments. Here, we introduce a high offer and a non-monotonic rejection in structured populations of finite size, and use strategy intervention to explicitly study how spite influences the evolution of fairness: five strategies are in sequence added into the competition of a fair strategy and a selfish strategy. We find that spite promotes fairness, altruism inhibits fairness, and the non-monotonic rejection can cause fairness to overcome selfishness, which cannot happen without high-offer rejections. Particularly for the group-structured population with seven discrete strategies, we analytically study the effect of population size, mutation, and migration on fairness, selfishness, altruism, and spite. A larger population size cannot change the dominance of fairness, but it promotes altruism and inhibits selfishness and spite. Intermediate mutation maximizes selfishness and fairness, and minimizes spite; intermediate mutation maximizes altruism for intermediate migration and minimizes altruism otherwise. The existence of migration inhibits selfishness and fairness, and promotes altruism; sufficient migration promotes spite. Our study may provide important insights into the evolutionary origin of fairness.\n
\n\n\n\n \n\n \n \n \n \n \n Risk-aware multi-armed bandit problem with application to portfolio selection.\n \n \n \n\n\n \n Huo, X.; and Fu, F.\n\n\n \n\n\n\n Royal Society Open Science, 4(11). 2017.\n \n\n\n\n
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\n\n\n@article{\n title = {Risk-aware multi-armed bandit problem with application to portfolio selection},\n type = {article},\n year = {2017},\n keywords = {Conditional value-at-risk,Graph theory,Multi-armed bandit,Online learning,Portfolio selection,Risk-awareness},\n volume = {4},\n id = {c825118b-323b-3cfd-b8b9-9160b0dc0b77},\n created = {2020-12-03T14:18:56.769Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.769Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2017 The Authors. Sequential portfolio selection has attracted increasing interest in the machine learning and quantitative finance communities in recent years. As amathematical framework for reinforcement learning policies, the stochastic multi-armed bandit problem addresses the primary difficulty in sequential decision-making under uncertainty, namely the exploration versus exploitation dilemma, and therefore provides a natural connection to portfolio selection. In this paper, we incorporate risk awareness into the classic multi-armed bandit setting and introduce an algorithm to construct portfolio. Through filtering assets based on the topological structure of the financial market and combining the optimal multi-armed bandit policy with the minimization of a coherent risk measure, we achieve a balance between risk and return.},\n bibtype = {article},\n author = {Huo, X. and Fu, F.},\n doi = {10.1098/rsos.171377},\n journal = {Royal Society Open Science},\n number = {11}\n}\n\n © 2017 The Authors. Sequential portfolio selection has attracted increasing interest in the machine learning and quantitative finance communities in recent years. As amathematical framework for reinforcement learning policies, the stochastic multi-armed bandit problem addresses the primary difficulty in sequential decision-making under uncertainty, namely the exploration versus exploitation dilemma, and therefore provides a natural connection to portfolio selection. In this paper, we incorporate risk awareness into the classic multi-armed bandit setting and introduce an algorithm to construct portfolio. Through filtering assets based on the topological structure of the financial market and combining the optimal multi-armed bandit policy with the minimization of a coherent risk measure, we achieve a balance between risk and return.\n
\n\n\n\n \n\n \n \n \n \n \n Leveraging statistical physics to improve understanding of cooperation in multiplex networks.\n \n \n \n\n\n \n Fu, F.; and Chen, X.\n\n\n \n\n\n\n New Journal of Physics, 19(7). 2017.\n \n\n\n\n
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\n\n\n@article{\n title = {Leveraging statistical physics to improve understanding of cooperation in multiplex networks},\n type = {article},\n year = {2017},\n keywords = {cooperation,evolutionary games,multiplex networks},\n volume = {19},\n id = {887e7fa1-bee7-3c0f-aba4-f473f401bef5},\n created = {2020-12-03T14:18:56.801Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.801Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {A study conducted by Battiston and other researchers improves the understanding of the role of multiplexity in cooperation, revealing that a significant edge overlap across network layers along with benign conditions for cooperation in at least one of the layers is needed to facilitate the emergence of cooperation in the multiplex. The study unveils that enhanced resilience of cooperation owing to the presence of multiplexity requires significant edge overlap ω across network layers, in combination with at least one layer being able to sustain cooperation by means of a sufficiently high enhancement factor r. These results shed light on the complexity of cooperation in the multiplex through the lens of statistical physics. Their findings can have practical implications for promoting prosocial behavior in multiple, interdependent social domains.},\n bibtype = {article},\n author = {Fu, F. and Chen, X.},\n doi = {10.1088/1367-2630/aa78c1},\n journal = {New Journal of Physics},\n number = {7}\n}\n\n A study conducted by Battiston and other researchers improves the understanding of the role of multiplexity in cooperation, revealing that a significant edge overlap across network layers along with benign conditions for cooperation in at least one of the layers is needed to facilitate the emergence of cooperation in the multiplex. The study unveils that enhanced resilience of cooperation owing to the presence of multiplexity requires significant edge overlap ω across network layers, in combination with at least one layer being able to sustain cooperation by means of a sufficiently high enhancement factor r. These results shed light on the complexity of cooperation in the multiplex through the lens of statistical physics. Their findings can have practical implications for promoting prosocial behavior in multiple, interdependent social domains.\n
\n\n\n\n \n\n \n \n \n \n \n Evolution of cooperation in public goods games with stochastic opting-out.\n \n \n \n\n\n \n Ginsberg, A.; Fu, F.; and Ginsberg, A.\n\n\n \n\n\n\n 2017.\n \n\n\n\n
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\n\n\n@misc{\n title = {Evolution of cooperation in public goods games with stochastic opting-out},\n type = {misc},\n year = {2017},\n source = {arXiv},\n keywords = {Adaptive dynamics,Evolutionary dynamics,Finite populations,Pairwise comparison,Social dilemmas},\n id = {4a593638-b730-34af-ba5e-17d28c074349},\n created = {2020-12-03T14:18:57.005Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.005Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2017, arXiv, All rights reserved. This paper investigates the evolution of strategic play where players drawn from a finite well-mixed population are offered the opportunity to play in a public goods game. All players accept the offer. However, due to the possibility of unforeseen circumstances, each player has a fixed probability of being unable to participate in the game, unlike similar models which assume voluntary participation. We first study how prescribed stochastic opting-out affects cooperation in finite populations. Moreover, in the model, cooperation is favored by natural selection over both neutral drift and defection if return on investment exceeds a threshold value defined solely by the population size, game size, and a player's probability of opting-out. Ultimately, increasing the probability that each player is unable to fulfill her promise of participating in the public goods game facilitates natural selection of cooperators. We also use adaptive dynamics to study the coevolution of cooperation and opting-out behavior. However, given rare mutations minutely different from the original population, an analysis based on adaptive dynamics suggests that the over time the population will tend towards complete defection and non-participation, and subsequently, from there, participating cooperators will stand a chance to emerge by neutral drift. Nevertheless, increasing the probability of non-participation decreases the rate at which the population tends towards defection when participating. Our work sheds light on understanding how stochastic opting-out emerges in the first place and its role in the evolution of cooperation.},\n bibtype = {misc},\n author = {Ginsberg, A.G. and Fu, F. and Ginsberg, A.G.}\n}\n\n Copyright © 2017, arXiv, All rights reserved. This paper investigates the evolution of strategic play where players drawn from a finite well-mixed population are offered the opportunity to play in a public goods game. All players accept the offer. However, due to the possibility of unforeseen circumstances, each player has a fixed probability of being unable to participate in the game, unlike similar models which assume voluntary participation. We first study how prescribed stochastic opting-out affects cooperation in finite populations. Moreover, in the model, cooperation is favored by natural selection over both neutral drift and defection if return on investment exceeds a threshold value defined solely by the population size, game size, and a player's probability of opting-out. Ultimately, increasing the probability that each player is unable to fulfill her promise of participating in the public goods game facilitates natural selection of cooperators. We also use adaptive dynamics to study the coevolution of cooperation and opting-out behavior. However, given rare mutations minutely different from the original population, an analysis based on adaptive dynamics suggests that the over time the population will tend towards complete defection and non-participation, and subsequently, from there, participating cooperators will stand a chance to emerge by neutral drift. Nevertheless, increasing the probability of non-participation decreases the rate at which the population tends towards defection when participating. Our work sheds light on understanding how stochastic opting-out emerges in the first place and its role in the evolution of cooperation.\n
\n\n\n\n \n\n \n \n \n \n \n Spillover modes in multiplex games: Double-edged effects on cooperation, and their coevolution.\n \n \n \n\n\n \n Khoo, T.; Fu, F.; and Pauls, S.\n\n\n \n\n\n\n 2017.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@misc{\n title = {Spillover modes in multiplex games: Double-edged effects on cooperation, and their coevolution},\n type = {misc},\n year = {2017},\n source = {arXiv},\n id = {ff5fd6e5-b14c-30dc-8cf7-e143e1a36432},\n created = {2020-12-03T14:18:57.058Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.058Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Copyright © 2017, arXiv, All rights reserved. In recent years, there has been growing interest in studying games on multiplex networks that account for interactions across linked social contexts. However, little is known about how potential crosscontext interference, or spillover, of individual behavioural strategy impact overall cooperation. We consider three plausible spillover modes, quantifying and comparing their effects on the evolution of cooperation. In our model, social interactions take place on two network layers: one represents repeated interactions with close neighbours in a lattice, the other represents one-shot interactions with random individuals across the same population. Spillover can occur during the social learning process with accidental cross-layer strategy transfer, or during social interactions with errors in implementation due to contextual interference. Our analytical results, using extended pair approximation, are in good agreement with extensive simulations. We find double-edged effects of spillover on cooperation: increasing the intensity of spillover can promote cooperation provided cooperation is favoured in one layer, but too much spillover is detrimental. We also discover a bistability phenomenon of cooperation: spillover hinders or promotes cooperation depending on initial frequencies of cooperation in each layer. Furthermore, comparing strategy combinations that emerge in each spillover mode provides a good indication of their co-evolutionary dynamics with cooperation. Our results make testable predictions that inspire future research, and sheds light on human cooperation across social domains and their interference with one another.},\n bibtype = {misc},\n author = {Khoo, T. and Fu, F. and Pauls, S.}\n}\n\n Copyright © 2017, arXiv, All rights reserved. In recent years, there has been growing interest in studying games on multiplex networks that account for interactions across linked social contexts. However, little is known about how potential crosscontext interference, or spillover, of individual behavioural strategy impact overall cooperation. We consider three plausible spillover modes, quantifying and comparing their effects on the evolution of cooperation. In our model, social interactions take place on two network layers: one represents repeated interactions with close neighbours in a lattice, the other represents one-shot interactions with random individuals across the same population. Spillover can occur during the social learning process with accidental cross-layer strategy transfer, or during social interactions with errors in implementation due to contextual interference. Our analytical results, using extended pair approximation, are in good agreement with extensive simulations. We find double-edged effects of spillover on cooperation: increasing the intensity of spillover can promote cooperation provided cooperation is favoured in one layer, but too much spillover is detrimental. We also discover a bistability phenomenon of cooperation: spillover hinders or promotes cooperation depending on initial frequencies of cooperation in each layer. Furthermore, comparing strategy combinations that emerge in each spillover mode provides a good indication of their co-evolutionary dynamics with cooperation. Our results make testable predictions that inspire future research, and sheds light on human cooperation across social domains and their interference with one another.\n
\n\n\n\n \n\n \n \n \n \n \n Dueling biological and social contagions.\n \n \n \n\n\n \n Fu, F.; Christakis, N.; and Fowler, J.\n\n\n \n\n\n\n Scientific Reports, 7. 2017.\n \n\n\n\n
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\n\n\n@article{\n title = {Dueling biological and social contagions},\n type = {article},\n year = {2017},\n volume = {7},\n id = {f695bdca-39f8-32d3-8cf1-3fc0ee62b1bc},\n created = {2020-12-03T14:18:57.492Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.492Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2017 The Author(s). Numerous models explore how a wide variety of biological and social phenomena spread in social networks. However, these models implicitly assume that the spread of one phenomenon is not affected by the spread of another. Here, we develop a model of "dueling contagions", with a particular illustration of a situation where one is biological (influenza) and the other is social (flu vaccination). We apply the model to unique time series data collected during the 2009 H1N1 epidemic that includes information about vaccination, flu, and face-to-face social networks. The results show that well-connected individuals are more likely to get vaccinated, as are people who are exposed to friends who get vaccinated or are exposed to friends who get the flu. Our dueling contagion model suggests that other epidemiological models may be dramatically underestimating the R 0 of contagions. It also suggests that the rate of vaccination contagion may be even more important than the biological contagion in determining the course of the disease. These results suggest that real world and online platforms that make it easier to see when friends have been vaccinated (personalized vaccination campaigns) and when they get the flu (personalized flu warnings) could have a large impact on reducing the severity of epidemics. They also suggest possible benefits from understanding the coevolution of many kinds of dueling contagions.},\n bibtype = {article},\n author = {Fu, F. and Christakis, N.A. and Fowler, J.H.},\n doi = {10.1038/srep43634},\n journal = {Scientific Reports}\n}\n\n © 2017 The Author(s). Numerous models explore how a wide variety of biological and social phenomena spread in social networks. However, these models implicitly assume that the spread of one phenomenon is not affected by the spread of another. Here, we develop a model of \"dueling contagions\", with a particular illustration of a situation where one is biological (influenza) and the other is social (flu vaccination). We apply the model to unique time series data collected during the 2009 H1N1 epidemic that includes information about vaccination, flu, and face-to-face social networks. The results show that well-connected individuals are more likely to get vaccinated, as are people who are exposed to friends who get vaccinated or are exposed to friends who get the flu. Our dueling contagion model suggests that other epidemiological models may be dramatically underestimating the R 0 of contagions. It also suggests that the rate of vaccination contagion may be even more important than the biological contagion in determining the course of the disease. These results suggest that real world and online platforms that make it easier to see when friends have been vaccinated (personalized vaccination campaigns) and when they get the flu (personalized flu warnings) could have a large impact on reducing the severity of epidemics. They also suggest possible benefits from understanding the coevolution of many kinds of dueling contagions.\n
\n\n\n\n \n\n \n \n \n \n \n Coevolutionary dynamics of phenotypic diversity and contingent cooperation.\n \n \n \n\n\n \n Wu, T.; Wang, L.; and Fu, F.\n\n\n \n\n\n\n PLoS Computational Biology, 13(1). 2017.\n \n\n\n\n
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\n\n\n@article{\n title = {Coevolutionary dynamics of phenotypic diversity and contingent cooperation},\n type = {article},\n year = {2017},\n volume = {13},\n id = {8e5e4ba3-838c-3708-a26b-b3f4673e08e0},\n created = {2020-12-03T14:18:57.506Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.506Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2017 Wu et al. Phenotypic diversity is considered beneficial to the evolution of contingent cooperation, in which cooperators channel their help preferentially towards others of similar phenotypes. However, it remains largely unclear how phenotypic variation arises in the first place and thus leads to the construction of phenotypic complexity. Here we propose a mathematical model to study the coevolutionary dynamics of phenotypic diversity and contingent cooperation. Unlike previous models, our model does not assume any prescribed level of phenotypic diversity, but rather lets it be an evolvable trait. Each individual expresses one phenotype at a time and only the phenotypes expressed are visible to others. Moreover, individuals can differ in their potential of phenotypic variation, which is characterized by the number of distinct phenotypes they can randomly switch to. Each individual incurs a cost proportional to the number of potentially expressible phenotypes so as to retain phenotypic variation and expression. Our results show that phenotypic diversity coevolves with contingent cooperation under a wide range of conditions and that there exists an optimal level of phenotypic diversity best promoting contingent cooperation. It pays for contingent cooperators to elevate their potential of phenotypic variation, thereby increasing their opportunities of establishing cooperation via novel phenotypes, as these new phenotypes serve as secret tags that are difficult for defector to discover and chase after. We also find that evolved high levels of phenotypic diversity can occasionally collapse due to the invasion of defector mutants, suggesting that cooperation and phenotypic diversity can mutually reinforce each other. Thus, our results provide new insights into better understanding the coevolution of cooperation and phenotypic diversity.},\n bibtype = {article},\n author = {Wu, T. and Wang, L. and Fu, F.},\n doi = {10.1371/journal.pcbi.1005363},\n journal = {PLoS Computational Biology},\n number = {1}\n}\n\n © 2017 Wu et al. Phenotypic diversity is considered beneficial to the evolution of contingent cooperation, in which cooperators channel their help preferentially towards others of similar phenotypes. However, it remains largely unclear how phenotypic variation arises in the first place and thus leads to the construction of phenotypic complexity. Here we propose a mathematical model to study the coevolutionary dynamics of phenotypic diversity and contingent cooperation. Unlike previous models, our model does not assume any prescribed level of phenotypic diversity, but rather lets it be an evolvable trait. Each individual expresses one phenotype at a time and only the phenotypes expressed are visible to others. Moreover, individuals can differ in their potential of phenotypic variation, which is characterized by the number of distinct phenotypes they can randomly switch to. Each individual incurs a cost proportional to the number of potentially expressible phenotypes so as to retain phenotypic variation and expression. Our results show that phenotypic diversity coevolves with contingent cooperation under a wide range of conditions and that there exists an optimal level of phenotypic diversity best promoting contingent cooperation. It pays for contingent cooperators to elevate their potential of phenotypic variation, thereby increasing their opportunities of establishing cooperation via novel phenotypes, as these new phenotypes serve as secret tags that are difficult for defector to discover and chase after. We also find that evolved high levels of phenotypic diversity can occasionally collapse due to the invasion of defector mutants, suggesting that cooperation and phenotypic diversity can mutually reinforce each other. Thus, our results provide new insights into better understanding the coevolution of cooperation and phenotypic diversity.\n
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\n\n \n \n 2016\n \n \n (1)\n \n \n
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\n \n \n\n \n \n \n \n \n Coevolution of Cooperation and Partner Rewiring Range in Spatial Social Networks.\n \n \n \n\n\n \n Khoo, T.; Fu, F.; and Pauls, S.\n\n\n \n\n\n\n Scientific Reports, 6. 2016.\n \n\n\n\n
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\n\n\n\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Coevolution of Cooperation and Partner Rewiring Range in Spatial Social Networks},\n type = {article},\n year = {2016},\n volume = {6},\n id = {f20a0b70-e5e0-3f95-9d46-d0e76f9af51c},\n created = {2020-12-03T14:18:57.542Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.542Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© The Author(s) 2016. In recent years, there has been growing interest in the study of coevolutionary games on networks. Despite much progress, little attention has been paid to spatially embedded networks, where the underlying geographic distance, rather than the graph distance, is an important and relevant aspect of the partner rewiring process. It thus remains largely unclear how individual partner rewiring range preference, local vs. global, emerges and affects cooperation. Here we explicitly address this issue using a coevolutionary model of cooperation and partner rewiring range preference in spatially embedded social networks. In contrast to local rewiring, global rewiring has no distance restriction but incurs a one-time cost upon establishing any long range link. We find that under a wide range of model parameters, global partner switching preference can coevolve with cooperation. Moreover, the resulting partner network is highly degree-heterogeneous with small average shortest path length while maintaining high clustering, thereby possessing small-world properties. We also discover an optimum availability of reputation information for the emergence of global cooperators, who form distant partnerships at a cost to themselves. From the coevolutionary perspective, our work may help explain the ubiquity of small-world topologies arising alongside cooperation in the real world.},\n bibtype = {article},\n author = {Khoo, T. and Fu, F. and Pauls, S.},\n doi = {10.1038/srep36293},\n journal = {Scientific Reports}\n}\n\n © The Author(s) 2016. In recent years, there has been growing interest in the study of coevolutionary games on networks. Despite much progress, little attention has been paid to spatially embedded networks, where the underlying geographic distance, rather than the graph distance, is an important and relevant aspect of the partner rewiring process. It thus remains largely unclear how individual partner rewiring range preference, local vs. global, emerges and affects cooperation. Here we explicitly address this issue using a coevolutionary model of cooperation and partner rewiring range preference in spatially embedded social networks. In contrast to local rewiring, global rewiring has no distance restriction but incurs a one-time cost upon establishing any long range link. We find that under a wide range of model parameters, global partner switching preference can coevolve with cooperation. Moreover, the resulting partner network is highly degree-heterogeneous with small average shortest path length while maintaining high clustering, thereby possessing small-world properties. We also discover an optimum availability of reputation information for the emergence of global cooperators, who form distant partnerships at a cost to themselves. From the coevolutionary perspective, our work may help explain the ubiquity of small-world topologies arising alongside cooperation in the real world.\n
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\n \n \n\n \n \n \n \n \n Evolutionary models of in-group favoritism.\n \n \n \n\n\n \n Masuda, N.; and Fu, F.\n\n\n \n\n\n\n F1000Prime Reports, 7. 2015.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Evolutionary models of in-group favoritism},\n type = {article},\n year = {2015},\n volume = {7},\n id = {32cd2378-517a-316f-89ab-c14d3bec9434},\n created = {2020-12-03T14:18:56.816Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.816Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2015 Faculty of 1000 Ltd. In-group favoritism is the tendency for individuals to cooperate with in-group members more strongly than with out-group members. Similar concepts have been described across different domains, including in-group bias, tag-based cooperation, parochial altruism, and ethnocentrism. Both humans and other animals show this behavior. Here, we review evolutionary mechanisms for explaining this phenomenon by covering recently developed mathematical models. In fact, in-group favoritism is not easily realized on its own in theory, although it can evolve under some conditions.We also discuss the implications of these modeling results in future empirical and theoretical research.},\n bibtype = {article},\n author = {Masuda, N. and Fu, F.},\n doi = {10.12703/P7-27},\n journal = {F1000Prime Reports}\n}\n\n © 2015 Faculty of 1000 Ltd. In-group favoritism is the tendency for individuals to cooperate with in-group members more strongly than with out-group members. Similar concepts have been described across different domains, including in-group bias, tag-based cooperation, parochial altruism, and ethnocentrism. Both humans and other animals show this behavior. Here, we review evolutionary mechanisms for explaining this phenomenon by covering recently developed mathematical models. In fact, in-group favoritism is not easily realized on its own in theory, although it can evolve under some conditions.We also discuss the implications of these modeling results in future empirical and theoretical research.\n
\n\n\n\n \n\n \n \n \n \n \n Spatial Heterogeneity in Drug Concentrations Can Facilitate the Emergence of Resistance to Cancer Therapy.\n \n \n \n\n\n \n Fu, F.; Nowak, M.; and Bonhoeffer, S.\n\n\n \n\n\n\n PLoS Computational Biology, 11(3). 2015.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Spatial Heterogeneity in Drug Concentrations Can Facilitate the Emergence of Resistance to Cancer Therapy},\n type = {article},\n year = {2015},\n volume = {11},\n id = {e0c71a60-5485-3c3f-8bb7-251e0182dff8},\n created = {2020-12-03T14:18:57.558Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.558Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2015 Fu et al. Acquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on the microscopic level within solid tumors as well as on the macroscopic level across metastases may also contribute to acquired drug resistance. Here we use mathematical models to investigate the effect of drug heterogeneity on the probability of escape from treatment and the time to resistance. Specifically we address scenarios with sufficiently potent therapies that suppress growth of all preexisting genetic variants in the compartment with the highest possible drug concentration. To study the joint effect of drug heterogeneity, growth rate, and evolution of resistance, we analyze a multi-type stochastic branching process describing growth of cancer cells in multiple compartments with different drug concentrations and limited migration between compartments. We show that resistance is likely to arise first in the sanctuary compartment with poor drug penetrations and from there populate non-sanctuary compartments with high drug concentrations. Moreover, we show that only below a threshold rate of cell migration does spatial heterogeneity accelerate resistance evolution, otherwise deterring drug resistance with excessively high migration rates. Our results provide new insights into understanding why cancers tend to quickly become resistant, and that cell migration and the presence of sanctuary sites with little drug exposure are essential to this end.},\n bibtype = {article},\n author = {Fu, F. and Nowak, M.A. and Bonhoeffer, S.},\n doi = {10.1371/journal.pcbi.1004142},\n journal = {PLoS Computational Biology},\n number = {3}\n}\n\n © 2015 Fu et al. Acquired resistance is one of the major barriers to successful cancer therapy. The development of resistance is commonly attributed to genetic heterogeneity. However, heterogeneity of drug penetration of the tumor microenvironment both on the microscopic level within solid tumors as well as on the macroscopic level across metastases may also contribute to acquired drug resistance. Here we use mathematical models to investigate the effect of drug heterogeneity on the probability of escape from treatment and the time to resistance. Specifically we address scenarios with sufficiently potent therapies that suppress growth of all preexisting genetic variants in the compartment with the highest possible drug concentration. To study the joint effect of drug heterogeneity, growth rate, and evolution of resistance, we analyze a multi-type stochastic branching process describing growth of cancer cells in multiple compartments with different drug concentrations and limited migration between compartments. We show that resistance is likely to arise first in the sanctuary compartment with poor drug penetrations and from there populate non-sanctuary compartments with high drug concentrations. Moreover, we show that only below a threshold rate of cell migration does spatial heterogeneity accelerate resistance evolution, otherwise deterring drug resistance with excessively high migration rates. Our results provide new insights into understanding why cancers tend to quickly become resistant, and that cell migration and the presence of sanctuary sites with little drug exposure are essential to this end.\n
\n\n\n\n \n\n \n \n \n \n \n The risk-return trade-off between solitary and eusocial reproduction.\n \n \n \n\n\n \n Fu, F.; Kocher, S.; and Nowak, M.\n\n\n \n\n\n\n Ecology Letters, 18(1). 2015.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {The risk-return trade-off between solitary and eusocial reproduction},\n type = {article},\n year = {2015},\n keywords = {Ecology and evolution,Eusociality,Evolutionary dynamics,Mathematical biology,Social insects,Stochastic process},\n volume = {18},\n id = {53168005-5686-386d-b6aa-d0c445da14a9},\n created = {2020-12-03T14:18:57.591Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.591Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {© 2014 John Wiley & Sons Ltd/CNRS. Social insect colonies can be seen as a distinct form of biological organisation because they function as superorganisms. Understanding how natural selection acts on the emergence and maintenance of these colonies remains a major question in evolutionary biology and ecology. Here, we explore this by using multi-type branching processes to calculate the basic reproductive ratios and the extinction probabilities for solitary vs. eusocial reproductive strategies. We find that eusociality, albeit being hugely successful once established, is generally less stable than solitary reproduction unless large demographic advantages of eusociality arise for small colony sizes. We also demonstrate how such demographic constraints can be overcome by the presence of ecological niches that strongly favour eusociality. Our results characterise the risk-return trade-offs between solitary and eusocial reproduction, and help to explain why eusociality is taxonomically rare: eusociality is a high-risk, high-reward strategy, whereas solitary reproduction is more conservative.},\n bibtype = {article},\n author = {Fu, F. and Kocher, S.D. and Nowak, M.A.},\n doi = {10.1111/ele.12392},\n journal = {Ecology Letters},\n number = {1}\n}\n\n © 2014 John Wiley & Sons Ltd/CNRS. Social insect colonies can be seen as a distinct form of biological organisation because they function as superorganisms. Understanding how natural selection acts on the emergence and maintenance of these colonies remains a major question in evolutionary biology and ecology. Here, we explore this by using multi-type branching processes to calculate the basic reproductive ratios and the extinction probabilities for solitary vs. eusocial reproductive strategies. We find that eusociality, albeit being hugely successful once established, is generally less stable than solitary reproduction unless large demographic advantages of eusociality arise for small colony sizes. We also demonstrate how such demographic constraints can be overcome by the presence of ecological niches that strongly favour eusociality. Our results characterise the risk-return trade-offs between solitary and eusocial reproduction, and help to explain why eusociality is taxonomically rare: eusociality is a high-risk, high-reward strategy, whereas solitary reproduction is more conservative.\n
\n\n\n\n \n\n \n \n \n \n \n Cooperation in group-structured populations with two layers of interactions.\n \n \n \n\n\n \n Zhang, Y.; Fu, F.; Chen, X.; Xie, G.; and Wang, L.\n\n\n \n\n\n\n Scientific Reports, 5. 2015.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Cooperation in group-structured populations with two layers of interactions},\n type = {article},\n year = {2015},\n volume = {5},\n id = {9f015b76-191e-3ec9-a9d3-5f8eebab17d2},\n created = {2020-12-03T14:18:58.741Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.741Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Recently there has been a growing interest in studying multiplex networks where individuals are structured in multiple network layers. Previous agent-based simulations of games on multiplex networks reveal rich dynamics arising from interdependency of interactions along each network layer, yet there is little known about analytical conditions for cooperation to evolve thereof. Here we aim to tackle this issue by calculating the evolutionary dynamics of cooperation in group-structured populations with two layers of interactions. In our model, an individual is engaged in two layers of group interactions simultaneously and uses unrelated strategies across layers. Evolutionary competition of individuals is determined by the total payoffs accrued from two layers of interactions. We also consider migration which allows individuals to move to a new group within each layer. An approach combining the coalescence theory with the theory of random walks is established to overcome the analytical difficulty upon local migration. We obtain the exact results for all " isotropic" migration patterns, particularly for migration tuned with varying ranges. When the two layers use one game, the optimal migration ranges are proved identical across layers and become smaller as the migration probability grows.},\n bibtype = {article},\n author = {Zhang, Y. and Fu, F. and Chen, X. and Xie, G. and Wang, L.},\n doi = {10.1038/srep17446},\n journal = {Scientific Reports}\n}\n\n Recently there has been a growing interest in studying multiplex networks where individuals are structured in multiple network layers. Previous agent-based simulations of games on multiplex networks reveal rich dynamics arising from interdependency of interactions along each network layer, yet there is little known about analytical conditions for cooperation to evolve thereof. Here we aim to tackle this issue by calculating the evolutionary dynamics of cooperation in group-structured populations with two layers of interactions. In our model, an individual is engaged in two layers of group interactions simultaneously and uses unrelated strategies across layers. Evolutionary competition of individuals is determined by the total payoffs accrued from two layers of interactions. We also consider migration which allows individuals to move to a new group within each layer. An approach combining the coalescence theory with the theory of random walks is established to overcome the analytical difficulty upon local migration. We obtain the exact results for all \" isotropic\" migration patterns, particularly for migration tuned with varying ranges. When the two layers use one game, the optimal migration ranges are proved identical across layers and become smaller as the migration probability grows.\n
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\n \n \n\n \n \n \n \n \n Evolutionary Game Dynamics in Populations with Heterogenous Structures.\n \n \n \n\n\n \n Maciejewski, W.; Fu, F.; and Hauert, C.\n\n\n \n\n\n\n PLoS Computational Biology, 10(4). 2014.\n \n\n\n\n
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\n\n\n@article{\n title = {Evolutionary Game Dynamics in Populations with Heterogenous Structures},\n type = {article},\n year = {2014},\n volume = {10},\n id = {a19d1e7c-3ea4-39f0-a1b3-9f0e9aa1a5b8},\n created = {2020-12-03T14:18:57.603Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.603Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place. In particular, averaging payoffs garnered through game interactions rather than accumulating the payoffs can altogether remove the cooperative advantage of heterogeneous graphs while such a difference does not affect the outcome on homogeneous structures. In addition, the rate at which game interactions occur can alter the evolutionary outcome. Less interactions allow heterogeneous graphs to support more cooperation than homogeneous graphs, while higher rates of interactions make homogeneous and heterogeneous graphs virtually indistinguishable in their ability to support cooperation. Most importantly, we show that common measures of evolutionary advantage used in homogeneous populations, such as a comparison of the fixation probability of a rare mutant to that of the resident type, are no longer valid in heterogeneous populations. Heterogeneity causes a bias in where mutations occur in the population which affects the mutant's fixation probability. We derive the appropriate measures for heterogeneous populations that account for this bias. © 2014 Maciejewski et al.},\n bibtype = {article},\n author = {Maciejewski, W. and Fu, F. and Hauert, C.},\n doi = {10.1371/journal.pcbi.1003567},\n journal = {PLoS Computational Biology},\n number = {4}\n}\n\n Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place. In particular, averaging payoffs garnered through game interactions rather than accumulating the payoffs can altogether remove the cooperative advantage of heterogeneous graphs while such a difference does not affect the outcome on homogeneous structures. In addition, the rate at which game interactions occur can alter the evolutionary outcome. Less interactions allow heterogeneous graphs to support more cooperation than homogeneous graphs, while higher rates of interactions make homogeneous and heterogeneous graphs virtually indistinguishable in their ability to support cooperation. Most importantly, we show that common measures of evolutionary advantage used in homogeneous populations, such as a comparison of the fixation probability of a rare mutant to that of the resident type, are no longer valid in heterogeneous populations. Heterogeneity causes a bias in where mutations occur in the population which affects the mutant's fixation probability. We derive the appropriate measures for heterogeneous populations that account for this bias. © 2014 Maciejewski et al.\n
\n\n\n\n \n\n \n \n \n \n \n Social influence promotes cooperation in the public goods game.\n \n \n \n\n\n \n Wu, T.; Fu, F.; Dou, P.; and Wang, L.\n\n\n \n\n\n\n Physica A: Statistical Mechanics and its Applications, 413. 2014.\n \n\n\n\n
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\n\n\n@article{\n title = {Social influence promotes cooperation in the public goods game},\n type = {article},\n year = {2014},\n keywords = {Evolution of cooperation,Preferential selection rule,Public goods game,Social influence},\n volume = {413},\n id = {a83edde9-002c-3499-ae2a-548c43102fd4},\n created = {2020-12-03T14:18:58.278Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.278Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Previous studies mainly consider the random selection pattern in which individuals randomly choose reference models from their neighbors for strategy updating. However, the random selection pattern is unable to capture all real world circumstances. We institute a spatial model to investigate the effects of influence-based reference selection pattern on the evolution of cooperation in the context of public goods games. Whenever experiencing strategy updating, all the individuals each choose one of its neighbors as a reference with the probability proportional to this neighbor's influence. Levels of individuals' influence are dynamical. When an individual is imitated, the level of its influence increases, thus constituting a positive feedback between the frequencies of individuals being imitated and the likelihood for them to be reference models. We find that the level of collective cooperation can be enhanced whenever the influence-based reference selection pattern is integrated into the strategy updating process. Results also show that the evolution of cooperation can be promoted when the increase in individuals' frequency of being imitated upholds their influence in large magnitude. Our work may improve the understanding of how influence-based selection patterns promote cooperative behavior. © 2014 Elsevier B.V. All rights reserved..},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Dou, P. and Wang, L.},\n doi = {10.1016/j.physa.2014.06.040},\n journal = {Physica A: Statistical Mechanics and its Applications}\n}\n\n Previous studies mainly consider the random selection pattern in which individuals randomly choose reference models from their neighbors for strategy updating. However, the random selection pattern is unable to capture all real world circumstances. We institute a spatial model to investigate the effects of influence-based reference selection pattern on the evolution of cooperation in the context of public goods games. Whenever experiencing strategy updating, all the individuals each choose one of its neighbors as a reference with the probability proportional to this neighbor's influence. Levels of individuals' influence are dynamical. When an individual is imitated, the level of its influence increases, thus constituting a positive feedback between the frequencies of individuals being imitated and the likelihood for them to be reference models. We find that the level of collective cooperation can be enhanced whenever the influence-based reference selection pattern is integrated into the strategy updating process. Results also show that the evolution of cooperation can be promoted when the increase in individuals' frequency of being imitated upholds their influence in large magnitude. Our work may improve the understanding of how influence-based selection patterns promote cooperative behavior. © 2014 Elsevier B.V. All rights reserved..\n
\n\n\n\n \n\n \n \n \n \n \n Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1.\n \n \n \n\n\n \n Hill, A.; Rosenbloom, D.; Fu, F.; Nowak, M.; and Siliciano, R.\n\n\n \n\n\n\n Proceedings of the National Academy of Sciences of the United States of America, 111(37). 2014.\n \n\n\n\n
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\n\n\n@article{\n title = {Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1},\n type = {article},\n year = {2014},\n volume = {111},\n id = {94d01f20-7d5d-3aac-a50a-550005f2843c},\n created = {2020-12-03T14:18:58.746Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.746Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Massive research efforts are now underway to develop a cure for HIV infection, allowing patients to discontinue lifelong combination antiretroviral therapy (ART). New latency-reversing agents (LRAs) may be able to purge the persistent reservoir of latent virus in resting memory CD4+ T cells, but the degree of reservoir reduction needed for cure remains unknown. Here we use a stochastic model of infection dynamics to estimate the efficacy of LRA needed to prevent viral rebound after ART interruption. We incorporate clinical data to estimate population-level parameter distributions and outcomes. Our findings suggest that ?2,000-fold reductions are required to permit a majority of patients to interrupt ART for 1 y without rebound and that rebound may occur suddenly after multiple years. Greater than 10,000-fold reductions may be required to prevent rebound altogether. Our results predict large variation in rebound times following LRA therapy, which will complicate clinical management. This model provides benchmarks for moving LRAs from the laboratory to the clinic and can aid in the design and interpretation of clinical trials. These results also apply to other interventions to reduce the latent reservoir and can explain the observed return of viremia after months of apparent cure in recent bone marrow transplant recipients and an immediately-treated neonate.},\n bibtype = {article},\n author = {Hill, A.L. and Rosenbloom, D.I.S. and Fu, F. and Nowak, M.A. and Siliciano, R.F.},\n doi = {10.1073/pnas.1406663111},\n journal = {Proceedings of the National Academy of Sciences of the United States of America},\n number = {37}\n}\n\n Massive research efforts are now underway to develop a cure for HIV infection, allowing patients to discontinue lifelong combination antiretroviral therapy (ART). New latency-reversing agents (LRAs) may be able to purge the persistent reservoir of latent virus in resting memory CD4+ T cells, but the degree of reservoir reduction needed for cure remains unknown. Here we use a stochastic model of infection dynamics to estimate the efficacy of LRA needed to prevent viral rebound after ART interruption. We incorporate clinical data to estimate population-level parameter distributions and outcomes. Our findings suggest that ?2,000-fold reductions are required to permit a majority of patients to interrupt ART for 1 y without rebound and that rebound may occur suddenly after multiple years. Greater than 10,000-fold reductions may be required to prevent rebound altogether. Our results predict large variation in rebound times following LRA therapy, which will complicate clinical management. This model provides benchmarks for moving LRAs from the laboratory to the clinic and can aid in the design and interpretation of clinical trials. These results also apply to other interventions to reduce the latent reservoir and can explain the observed return of viremia after months of apparent cure in recent bone marrow transplant recipients and an immediately-treated neonate.\n
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\n \n \n\n \n \n \n \n \n Quantifying the impact of noise on macroscopic organization of cooperation in spatial games.\n \n \n \n\n\n \n Du, F.; and Fu, F.\n\n\n \n\n\n\n Chaos, Solitons and Fractals, 56. 2013.\n \n\n\n\n
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\n\n\n@article{\n title = {Quantifying the impact of noise on macroscopic organization of cooperation in spatial games},\n type = {article},\n year = {2013},\n volume = {56},\n id = {0a388988-74e2-339b-896d-1c8d44d8ad60},\n created = {2020-12-03T14:18:56.849Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.849Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Spatial games have been extensively studied in recent years. It is known that spatial structure could have a differing role in promoting cooperation, if comparing prisoner's dilemma to snowdrift game. Less is known about whether there also exists qualitative difference of the emerging macroscopic spatial pattern of cooperation in the two respective games, in particular when noise is present in individual strategy learning. To address this issue, we quantify and compare the impact of noise on spatial organization of cooperation in the two games. In our simulations, individuals are located in a spatial lattice with the von Neumann neighbourhood. They play games with their immediate neighbors and update their strategies based on a Fermi function-like rule, 1/[1+exp(ΔP)/K], where ΔP is the payoff difference between the focal individual and one randomly chosen neighbour, and K represents the noise level (temperature) in strategy learning. Small K values represent the tendency of imitating better performing individuals while high K values increase the likelihood that individuals adopt worse performing strategies. Our results reveal striking differences between the two types of games in regard to the resulting macroscopic pattern of cooperation. Assortment between cooperators is much weaker in the snowdrift game than in the prisoner's dilemma. Intermediate levels of noise maximize the local assortment in the prisoner's dilemma while most weakening assortment in the snowdrift game. The cluster size of cooperators has a peak in the prisoner's dilemma but shows a valley in the snowdrift game for varying level of noise. With increasing the noise level cooperators break into small clusters in the prisoner's dilemma while cooperators tend to be clustered into larger lumps in the snowdrift game. These quantitative results highlight the underlying microscopic interaction, whether being the prisoner's dilemma or the snowdrift type, nontrivially determines how noise affects the spatial pattern of cooperation. © 2013 Elsevier Ltd. All rights reserved.},\n bibtype = {article},\n author = {Du, F. and Fu, F.},\n doi = {10.1016/j.chaos.2013.06.008},\n journal = {Chaos, Solitons and Fractals}\n}\n\n Spatial games have been extensively studied in recent years. It is known that spatial structure could have a differing role in promoting cooperation, if comparing prisoner's dilemma to snowdrift game. Less is known about whether there also exists qualitative difference of the emerging macroscopic spatial pattern of cooperation in the two respective games, in particular when noise is present in individual strategy learning. To address this issue, we quantify and compare the impact of noise on spatial organization of cooperation in the two games. In our simulations, individuals are located in a spatial lattice with the von Neumann neighbourhood. They play games with their immediate neighbors and update their strategies based on a Fermi function-like rule, 1/[1+exp(ΔP)/K], where ΔP is the payoff difference between the focal individual and one randomly chosen neighbour, and K represents the noise level (temperature) in strategy learning. Small K values represent the tendency of imitating better performing individuals while high K values increase the likelihood that individuals adopt worse performing strategies. Our results reveal striking differences between the two types of games in regard to the resulting macroscopic pattern of cooperation. Assortment between cooperators is much weaker in the snowdrift game than in the prisoner's dilemma. Intermediate levels of noise maximize the local assortment in the prisoner's dilemma while most weakening assortment in the snowdrift game. The cluster size of cooperators has a peak in the prisoner's dilemma but shows a valley in the snowdrift game for varying level of noise. With increasing the noise level cooperators break into small clusters in the prisoner's dilemma while cooperators tend to be clustered into larger lumps in the snowdrift game. These quantitative results highlight the underlying microscopic interaction, whether being the prisoner's dilemma or the snowdrift type, nontrivially determines how noise affects the spatial pattern of cooperation. © 2013 Elsevier Ltd. All rights reserved.\n
\n\n\n\n \n\n \n \n \n \n \n Global Migration Can Lead to Stronger Spatial Selection than Local Migration.\n \n \n \n\n\n \n Fu, F.; and Nowak, M.\n\n\n \n\n\n\n Journal of Statistical Physics, 151(3-4). 2013.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Global Migration Can Lead to Stronger Spatial Selection than Local Migration},\n type = {article},\n year = {2013},\n keywords = {Evolutionary dynamics,Evolutionary game theory,Mathematical biology,Population structure},\n volume = {151},\n id = {86f16810-7060-3fba-9a2a-efa3868fdc24},\n created = {2020-12-03T14:18:56.867Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.867Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {The outcome of evolutionary processes depends on population structure. It is well known that mobility plays an important role in affecting evolutionary dynamics in group structured populations. But it is largely unknown whether global or local migration leads to stronger spatial selection and would therefore favor to a larger extent the evolution of cooperation. To address this issue, we quantify the impacts of these two migration patterns on the evolutionary competition of two strategies in a finite island model. Global migration means that individuals can migrate from any one island to any other island. Local migration means that individuals can only migrate between islands that are nearest neighbors; we study a simple geometry where islands are arranged on a one-dimensional, regular cycle. We derive general results for weak selection and large population size. Our key parameters are: the number of islands, the migration rate and the mutation rate. Surprisingly, our comparative analysis reveals that global migration can lead to stronger spatial selection than local migration for a wide range of parameter conditions. Our work provides useful insights into understanding how different mobility patterns affect evolutionary processes. © 2012 Springer Science+Business Media New York.},\n bibtype = {article},\n author = {Fu, F. and Nowak, M.A.},\n doi = {10.1007/s10955-012-0631-6},\n journal = {Journal of Statistical Physics},\n number = {3-4}\n}\n\n The outcome of evolutionary processes depends on population structure. It is well known that mobility plays an important role in affecting evolutionary dynamics in group structured populations. But it is largely unknown whether global or local migration leads to stronger spatial selection and would therefore favor to a larger extent the evolution of cooperation. To address this issue, we quantify the impacts of these two migration patterns on the evolutionary competition of two strategies in a finite island model. Global migration means that individuals can migrate from any one island to any other island. Local migration means that individuals can only migrate between islands that are nearest neighbors; we study a simple geometry where islands are arranged on a one-dimensional, regular cycle. We derive general results for weak selection and large population size. Our key parameters are: the number of islands, the migration rate and the mutation rate. Surprisingly, our comparative analysis reveals that global migration can lead to stronger spatial selection than local migration for a wide range of parameter conditions. Our work provides useful insights into understanding how different mobility patterns affect evolutionary processes. © 2012 Springer Science+Business Media New York.\n
\n\n\n\n \n\n \n \n \n \n \n Spatial prisoner's dilemma with stochastic reaction strategies.\n \n \n \n\n\n \n Yang, M.; Fu, F.; Cao, Z.; and Yang, X.\n\n\n \n\n\n\n In Chinese Control Conference, CCC, 2013. \n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@inproceedings{\n title = {Spatial prisoner's dilemma with stochastic reaction strategies},\n type = {inproceedings},\n year = {2013},\n keywords = {Complex network,Evolutionary Dynamics,Prisoner's Dilemma,Spatial Game},\n id = {056155ec-f84c-321e-8691-e0450103ebf5},\n created = {2020-12-03T14:18:58.291Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.291Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We extend the spatial game proposed by Nowak in 1992. In Nowak's original model, agents can only choose two strategies: AllC(unconditional cooperation) and AllD(unconditional defection). In our model, agents are allowed to adopt stochastic reaction strategies, and can learn from neighbors' according to payoff differences. Only the lattice network was considered in Nowak's model, while both homogenous(lattice, small-world) and non-homogenous(scale-free) networks are investigated in our paper. On the lattice networks, we found that the evolving process of the population's strategies is quite similar to that in the replicator dynamics model [13]. On the small-world networks, we investigated the effect of randomness of the topology to the evolving result, and found that a more clustering topology tends to sustain a more cooperative world. On the scale-free networks, we investigate how the hub nodes' initial states affect the evolving result. © 2013 TCCT, CAA.},\n bibtype = {inproceedings},\n author = {Yang, M. and Fu, F. and Cao, Z. and Yang, X.},\n booktitle = {Chinese Control Conference, CCC}\n}\n\n We extend the spatial game proposed by Nowak in 1992. In Nowak's original model, agents can only choose two strategies: AllC(unconditional cooperation) and AllD(unconditional defection). In our model, agents are allowed to adopt stochastic reaction strategies, and can learn from neighbors' according to payoff differences. Only the lattice network was considered in Nowak's model, while both homogenous(lattice, small-world) and non-homogenous(scale-free) networks are investigated in our paper. On the lattice networks, we found that the evolving process of the population's strategies is quite similar to that in the replicator dynamics model [13]. On the small-world networks, we investigated the effect of randomness of the topology to the evolving result, and found that a more clustering topology tends to sustain a more cooperative world. On the scale-free networks, we investigate how the hub nodes' initial states affect the evolving result. © 2013 TCCT, CAA.\n
\n\n\n\n \n\n \n \n \n \n \n Quality versus quantity of social ties in experimental cooperative networks.\n \n \n \n\n\n \n Shirado, H.; Fu, F.; Fowler, J.; and Christakis, N.\n\n\n \n\n\n\n Nature Communications, 4. 2013.\n \n\n\n\n
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\n\n\n@article{\n title = {Quality versus quantity of social ties in experimental cooperative networks},\n type = {article},\n year = {2013},\n volume = {4},\n id = {a33dad36-3518-33e5-95c7-e2360e0ea42f},\n created = {2020-12-03T14:18:58.352Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.352Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Recent studies suggest that allowing individuals to choose their partners can help to maintain cooperation in human social networks; this behaviour can supplement behavioural reciprocity, whereby humans are influenced to cooperate by peer pressure. However, it is unknown how the rate of forming and breaking social ties affects our capacity to cooperate. Here we use a series of online experiments involving 1,529 unique participants embedded in 90 experimental networks, to show that there is a 'Goldilocks' effect of network dynamism on cooperation. When the rate of change in social ties is too low, subjects choose to have many ties, even if they attach to defectors. When the rate is too high, cooperators cannot detach from defectors as much as defectors re-attach and, hence, subjects resort to behavioural reciprocity and switch their behaviour to defection. Optimal levels of cooperation are achieved at intermediate levels of change in social ties. © 2013 Macmillan Publishers Limited. All rights reserved.},\n bibtype = {article},\n author = {Shirado, H. and Fu, F. and Fowler, J.H. and Christakis, N.A.},\n doi = {10.1038/ncomms3814},\n journal = {Nature Communications}\n}\n\n Recent studies suggest that allowing individuals to choose their partners can help to maintain cooperation in human social networks; this behaviour can supplement behavioural reciprocity, whereby humans are influenced to cooperate by peer pressure. However, it is unknown how the rate of forming and breaking social ties affects our capacity to cooperate. Here we use a series of online experiments involving 1,529 unique participants embedded in 90 experimental networks, to show that there is a 'Goldilocks' effect of network dynamism on cooperation. When the rate of change in social ties is too low, subjects choose to have many ties, even if they attach to defectors. When the rate is too high, cooperators cannot detach from defectors as much as defectors re-attach and, hence, subjects resort to behavioural reciprocity and switch their behaviour to defection. Optimal levels of cooperation are achieved at intermediate levels of change in social ties. © 2013 Macmillan Publishers Limited. All rights reserved.\n
\n\n\n\n \n\n \n \n \n \n \n The Increased Risk of Joint Venture Promotes Social Cooperation.\n \n \n \n\n\n \n Wu, T.; Fu, F.; Zhang, Y.; and Wang, L.\n\n\n \n\n\n\n PLoS ONE, 8(6). 2013.\n \n\n\n\n
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\n\n\n@article{\n title = {The Increased Risk of Joint Venture Promotes Social Cooperation},\n type = {article},\n year = {2013},\n volume = {8},\n id = {3bf5e717-28a3-3c26-a40e-bcbcaae24af7},\n created = {2020-12-03T14:18:58.355Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.355Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {The joint venture of many members is common both in animal world and human society. In these public enterprizes, highly cooperative groups are more likely to while low cooperative groups are still possible but not probable to succeed. Existent literature mostly focuses on the traditional public goods game, in which cooperators create public wealth unconditionally and benefit all group members unbiasedly. We here institute a model addressing this public goods dilemma with incorporating the public resource foraging failure risk. Risk-averse individuals tend to lead a autarkic life, while risk-preferential ones tend to participate in the risky public goods game. For participants, group's success relies on its cooperativeness, with increasing contribution leading to increasing success likelihood. We introduce a function with one tunable parameter to describe the risk removal pattern and study in detail three representative classes. Analytical results show that the widely replicated population dynamics of cyclical dominance of loner, cooperator and defector disappear, while most of the time loners act as savors while eventually they also disappear. Depending on the way that group's success relies on its cooperativeness, either cooperators pervade the entire population or they coexist with defectors. Even in the later case, cooperators still hold salient superiority in number as some defectors also survive by parasitizing. The harder the joint venture succeeds, the higher level of cooperation once cooperators can win the evolutionary race. Our work may enrich the literature concerning the risky public goods games. © 2013 Wu et al.},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Zhang, Y. and Wang, L.},\n doi = {10.1371/journal.pone.0063801},\n journal = {PLoS ONE},\n number = {6}\n}\n\n The joint venture of many members is common both in animal world and human society. In these public enterprizes, highly cooperative groups are more likely to while low cooperative groups are still possible but not probable to succeed. Existent literature mostly focuses on the traditional public goods game, in which cooperators create public wealth unconditionally and benefit all group members unbiasedly. We here institute a model addressing this public goods dilemma with incorporating the public resource foraging failure risk. Risk-averse individuals tend to lead a autarkic life, while risk-preferential ones tend to participate in the risky public goods game. For participants, group's success relies on its cooperativeness, with increasing contribution leading to increasing success likelihood. We introduce a function with one tunable parameter to describe the risk removal pattern and study in detail three representative classes. Analytical results show that the widely replicated population dynamics of cyclical dominance of loner, cooperator and defector disappear, while most of the time loners act as savors while eventually they also disappear. Depending on the way that group's success relies on its cooperativeness, either cooperators pervade the entire population or they coexist with defectors. Even in the later case, cooperators still hold salient superiority in number as some defectors also survive by parasitizing. The harder the joint venture succeeds, the higher level of cooperation once cooperators can win the evolutionary race. Our work may enrich the literature concerning the risky public goods games. © 2013 Wu et al.\n
\n\n\n\n \n\n \n \n \n \n \n Adaptive tag switching reinforces the coevolution of contingent cooperation and tag diversity.\n \n \n \n\n\n \n Wu, T.; Fu, F.; Zhang, Y.; and Wang, L.\n\n\n \n\n\n\n Journal of Theoretical Biology, 330. 2013.\n \n\n\n\n
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\n\n\n@article{\n title = {Adaptive tag switching reinforces the coevolution of contingent cooperation and tag diversity},\n type = {article},\n year = {2013},\n keywords = {Evolutionary game theory,Population dynamics,Prisoner's dilemma game,Time scale},\n volume = {330},\n id = {7588dd5b-7d8b-3887-814d-88435b9fa64c},\n created = {2020-12-03T14:18:58.392Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.392Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Most of the previous studies concerning the similarity-based interaction have assumed that the change of tags just happens in the imitation stage. Individuals actually can adjust their tags whenever the environments related to these tags grow nasty. We institute a spatial model to investigate the effect of the coevolution of tag and strategy on the evolution of cooperation in the context of the Prisoner's Dilemma game. Interactions just happen between tag-identical neighbors. Individuals exploited by defectors change their current tags at a certain cost. The time-scale ratio controls how fast interaction happens relatively to selection. Results show that whenever individuals have enough chance to adapt to the environment, cooperation is greatly improved even for quite large temptation to defect. Intensive exploration reveals that both little and large costs of tag switching can further favor the establishment of cooperation. Our work may add more into the literature concerning games on adaptive networks. © 2013 Elsevier Ltd.},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Zhang, Y. and Wang, L.},\n doi = {10.1016/j.jtbi.2013.04.007},\n journal = {Journal of Theoretical Biology}\n}\n\n Most of the previous studies concerning the similarity-based interaction have assumed that the change of tags just happens in the imitation stage. Individuals actually can adjust their tags whenever the environments related to these tags grow nasty. We institute a spatial model to investigate the effect of the coevolution of tag and strategy on the evolution of cooperation in the context of the Prisoner's Dilemma game. Interactions just happen between tag-identical neighbors. Individuals exploited by defectors change their current tags at a certain cost. The time-scale ratio controls how fast interaction happens relatively to selection. Results show that whenever individuals have enough chance to adapt to the environment, cooperation is greatly improved even for quite large temptation to defect. Intensive exploration reveals that both little and large costs of tag switching can further favor the establishment of cooperation. Our work may add more into the literature concerning games on adaptive networks. © 2013 Elsevier Ltd.\n
\n\n\n\n \n\n \n \n \n \n \n Adaptive role switching promotes fairness in networked ultimatum game.\n \n \n \n\n\n \n Wu, T.; Fu, F.; Zhang, Y.; and Wang, L.\n\n\n \n\n\n\n Scientific Reports, 3. 2013.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Adaptive role switching promotes fairness in networked ultimatum game},\n type = {article},\n year = {2013},\n volume = {3},\n id = {f2a5d545-9806-39a6-a1aa-3c7d2cea4fd2},\n created = {2020-12-03T14:18:58.401Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.401Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {In recent years, mechanisms favoring fair split in the ultimatum game have attracted growing interests because of its practical implications for international bargains. In this game, two players are randomly assigned two different roles respectively to split an offer: the proposer suggests how to split and the responder decides whether or not to accept it. Only when both agree is the offer successfully split; otherwise both get nothing. It is of importance and interest to break the symmetry in role assignment especially when the game is repeatedly played in a heterogeneous population. Here we consider an adaptive role assignment: whenever the split fails, the two players switch their roles probabilistically. The results show that this simple feedback mechanism proves much more effective at promoting fairness than other alternatives (where, for example, the role assignment is based on the number of neighbors).},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Zhang, Y. and Wang, L.},\n doi = {10.1038/srep01550},\n journal = {Scientific Reports}\n}\n\n In recent years, mechanisms favoring fair split in the ultimatum game have attracted growing interests because of its practical implications for international bargains. In this game, two players are randomly assigned two different roles respectively to split an offer: the proposer suggests how to split and the responder decides whether or not to accept it. Only when both agree is the offer successfully split; otherwise both get nothing. It is of importance and interest to break the symmetry in role assignment especially when the game is repeatedly played in a heterogeneous population. Here we consider an adaptive role assignment: whenever the split fails, the two players switch their roles probabilistically. The results show that this simple feedback mechanism proves much more effective at promoting fairness than other alternatives (where, for example, the role assignment is based on the number of neighbors).\n
\n\n\n\n \n\n \n \n \n \n \n A tale of two contribution mechanisms for nonlinear public goods.\n \n \n \n\n\n \n Zhang, Y.; Fu, F.; Wu, T.; Xie, G.; and Wang, L.\n\n\n \n\n\n\n Scientific Reports, 3. 2013.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n\n\n\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {A tale of two contribution mechanisms for nonlinear public goods},\n type = {article},\n year = {2013},\n volume = {3},\n id = {509d2019-b861-3b2f-8127-539815f41460},\n created = {2020-12-03T14:18:58.789Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.789Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Amounts of empirical evidence, ranging from microbial cooperation to collective hunting, suggests public goods produced often nonlinearly depend on the total amount of contribution. The implication of such nonlinear public goods for the evolution of cooperation is not well understood. There is also little attention paid to the divisibility nature of individual contribution amount, divisible vs. non-divisible ones. The corresponding strategy space in the former is described by a continuous investment while in the latter by a continuous probability to contribute all or nothing. Here, we use adaptive dynamics in finite populations to quantify and compare the roles nonlinearity of public-goods production plays in cooperation between these two contribution mechanisms. Although under both contribution mechanisms the population can converge into a coexistence equilibrium with an intermediate cooperation level, the branching phenomenon only occurs in the divisible contribution mechanism. The results shed insight into understanding observed individual difference in cooperative behavior.},\n bibtype = {article},\n author = {Zhang, Y. and Fu, F. and Wu, T. and Xie, G. and Wang, L.},\n doi = {10.1038/srep02021},\n journal = {Scientific Reports}\n}\n\n Amounts of empirical evidence, ranging from microbial cooperation to collective hunting, suggests public goods produced often nonlinearly depend on the total amount of contribution. The implication of such nonlinear public goods for the evolution of cooperation is not well understood. There is also little attention paid to the divisibility nature of individual contribution amount, divisible vs. non-divisible ones. The corresponding strategy space in the former is described by a continuous investment while in the latter by a continuous probability to contribute all or nothing. Here, we use adaptive dynamics in finite populations to quantify and compare the roles nonlinearity of public-goods production plays in cooperation between these two contribution mechanisms. Although under both contribution mechanisms the population can converge into a coexistence equilibrium with an intermediate cooperation level, the branching phenomenon only occurs in the divisible contribution mechanism. The results shed insight into understanding observed individual difference in cooperative behavior.\n
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\n \n \n\n \n \n \n \n \n Rational behavior is a 'double-edged sword' when considering voluntary vaccination.\n \n \n \n\n\n \n Zhang, H.; Fu, F.; Zhang, W.; and Wang, B.\n\n\n \n\n\n\n Physica A: Statistical Mechanics and its Applications, 391(20). 2012.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Rational behavior is a 'double-edged sword' when considering voluntary vaccination},\n type = {article},\n year = {2012},\n keywords = {Dynamics of epidemics,Game theory,Rational behavior,Vaccination dilemma},\n volume = {391},\n id = {86ca41eb-a7c7-302a-8155-d8494beb987a},\n created = {2020-12-03T14:18:56.935Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.935Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Of particular importance for public health is how to understand strategic vaccination behavior in social networks. Social learning is a central aspect of human behavior, and it thus shapes vaccination individuals' decision-making. Here, we study two simple models to address the impact of the more rational decision-making of individuals on voluntary vaccination. In the first model, individuals are endowed with memory capacity for their past experiences of dealing with vaccination. In addition to their current payoffs, they also take account of the historical payoffs that are discounted by a memory-decaying factor. They use such overall payoffs (weighing the current payoffs and historical payoffs) to reassess their vaccination strategies. Those who have higher overall payoffs are more likely imitated by their social neighbors. In the second model, individuals do not blindly learn the strategies of neighbors; they also combine the fraction of infection in the past epidemic season. If the fraction of infection surpasses the perceived risk threshold, individuals will increase the probability of taking vaccination. Otherwise, they will decrease the probability of taking vaccination. Then we use evolutionary game theory to study the vaccination behavior of people during an epidemiological process. To do this, we propose a two-stage model: individuals make vaccination decisions during a yearly vaccination campaign, followed by an epidemic season. This forms a feedback loop between the vaccination decisions of individuals and their health outcomes, and thus payoffs. We find that the two more rational decision-making models have nontrivial impacts on the vaccination behavior of individuals, and, as a result, on the final fraction of infection. Our results highlight that, from an individual's viewpoint, the decisions are optimal and more rational. However, from the social viewpoint, the strategies of individuals can give rise to distinct outcomes. Namely, the rational behavior of individuals plays a 'double-edged-sword' role on the social effects. © 2012 Elsevier B.V. All rights reserved.},\n bibtype = {article},\n author = {Zhang, H. and Fu, F. and Zhang, W. and Wang, B.},\n doi = {10.1016/j.physa.2012.05.009},\n journal = {Physica A: Statistical Mechanics and its Applications},\n number = {20}\n}\n\n Of particular importance for public health is how to understand strategic vaccination behavior in social networks. Social learning is a central aspect of human behavior, and it thus shapes vaccination individuals' decision-making. Here, we study two simple models to address the impact of the more rational decision-making of individuals on voluntary vaccination. In the first model, individuals are endowed with memory capacity for their past experiences of dealing with vaccination. In addition to their current payoffs, they also take account of the historical payoffs that are discounted by a memory-decaying factor. They use such overall payoffs (weighing the current payoffs and historical payoffs) to reassess their vaccination strategies. Those who have higher overall payoffs are more likely imitated by their social neighbors. In the second model, individuals do not blindly learn the strategies of neighbors; they also combine the fraction of infection in the past epidemic season. If the fraction of infection surpasses the perceived risk threshold, individuals will increase the probability of taking vaccination. Otherwise, they will decrease the probability of taking vaccination. Then we use evolutionary game theory to study the vaccination behavior of people during an epidemiological process. To do this, we propose a two-stage model: individuals make vaccination decisions during a yearly vaccination campaign, followed by an epidemic season. This forms a feedback loop between the vaccination decisions of individuals and their health outcomes, and thus payoffs. We find that the two more rational decision-making models have nontrivial impacts on the vaccination behavior of individuals, and, as a result, on the final fraction of infection. Our results highlight that, from an individual's viewpoint, the decisions are optimal and more rational. However, from the social viewpoint, the strategies of individuals can give rise to distinct outcomes. Namely, the rational behavior of individuals plays a 'double-edged-sword' role on the social effects. © 2012 Elsevier B.V. All rights reserved.\n
\n\n\n\n \n\n \n \n \n \n \n The evolution of homophily.\n \n \n \n\n\n \n Fu, F.; Nowak, M.; Christakis, N.; and Fowler, J.\n\n\n \n\n\n\n Scientific Reports, 2. 2012.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {The evolution of homophily},\n type = {article},\n year = {2012},\n volume = {2},\n id = {a766450b-8c2a-3cce-aee2-9fa526b90e4c},\n created = {2020-12-03T14:18:58.446Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.446Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Biologists have devoted much attention to assortative mating or homogamy, the tendency for sexual species to mate with similar others. In contrast, there has been little theoretical work on the broader phenomenon of homophily, the tendency for individuals to interact with similar others. Yet this behaviour is also widely observed in nature. Here, we model how natural selection can give rise to homophily when individuals engage in social interaction in a population with multiple observable phenotypes. Payoffs to interactions depend on whether or not individuals have the same or different phenotypes, and each individual has a preference that determines how likely they are to interact with others of their own phenotype (homophily) or of opposite phenotypes (heterophily). The results show that homophily tends to evolve under a wide variety of conditions, helping to explain its ubiquity in nature.},\n bibtype = {article},\n author = {Fu, F. and Nowak, M.A. and Christakis, N.A. and Fowler, J.H.},\n doi = {10.1038/srep00845},\n journal = {Scientific Reports}\n}\n\n Biologists have devoted much attention to assortative mating or homogamy, the tendency for sexual species to mate with similar others. In contrast, there has been little theoretical work on the broader phenomenon of homophily, the tendency for individuals to interact with similar others. Yet this behaviour is also widely observed in nature. Here, we model how natural selection can give rise to homophily when individuals engage in social interaction in a population with multiple observable phenotypes. Payoffs to interactions depend on whether or not individuals have the same or different phenotypes, and each individual has a preference that determines how likely they are to interact with others of their own phenotype (homophily) or of opposite phenotypes (heterophily). The results show that homophily tends to evolve under a wide variety of conditions, helping to explain its ubiquity in nature.\n
\n\n\n\n \n\n \n \n \n \n \n Expectation-driven migration promotes cooperation by group interactions.\n \n \n \n\n\n \n Wu, T.; Fu, F.; Zhang, Y.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 85(6). 2012.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Expectation-driven migration promotes cooperation by group interactions},\n type = {article},\n year = {2012},\n volume = {85},\n id = {e0b29026-dcf0-3671-8a52-72d6adbf0f52},\n created = {2020-12-03T14:18:58.454Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.454Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {"Voting with feet" describes the prominent social phenomenon that people tend to move away from deteriorating neighborhoods and search for and join prosperous groups. To quantify the role this kind of expectation-driven migration plays in the evolution of cooperation, here we study a simple yet effective model of cooperation based on spatial public goods games. The population structure is characterized by a square lattice with some nodes being left empty. Individuals have expectations toward their current habitats. Dissatisfied players, whose expectation is not met after interacting with all directly connected neighbors, tend to abstain from the groups of low quality by moving away and explore the physical niches of avail. How fast interaction happens relatively to selection is regulated by the time-scale ratio of game interaction to natural selection. Under strong selection, simulation results show that cooperation is greatly improved for either low, moderate, or high expectations compared to whenever the expectation-driven migration is absent. Further explorations reveal that neither too high nor too low but rather a combination of moderate expectations and rapid interaction establishes cooperation for a moderate public goods enhancement factor. There exists an optimal interval of expectation level most favoring the evolution of cooperation as the required time-scale ratio is minimized. © 2012 American Physical Society.},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Zhang, Y. and Wang, L.},\n doi = {10.1103/PhysRevE.85.066104},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {6}\n}\n\n \"Voting with feet\" describes the prominent social phenomenon that people tend to move away from deteriorating neighborhoods and search for and join prosperous groups. To quantify the role this kind of expectation-driven migration plays in the evolution of cooperation, here we study a simple yet effective model of cooperation based on spatial public goods games. The population structure is characterized by a square lattice with some nodes being left empty. Individuals have expectations toward their current habitats. Dissatisfied players, whose expectation is not met after interacting with all directly connected neighbors, tend to abstain from the groups of low quality by moving away and explore the physical niches of avail. How fast interaction happens relatively to selection is regulated by the time-scale ratio of game interaction to natural selection. Under strong selection, simulation results show that cooperation is greatly improved for either low, moderate, or high expectations compared to whenever the expectation-driven migration is absent. Further explorations reveal that neither too high nor too low but rather a combination of moderate expectations and rapid interaction establishes cooperation for a moderate public goods enhancement factor. There exists an optimal interval of expectation level most favoring the evolution of cooperation as the required time-scale ratio is minimized. © 2012 American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Evolution of in-group favoritism.\n \n \n \n\n\n \n Fu, F.; Tarnita, C.; Christakis, N.; Wang, L.; Rand, D.; and Nowak, M.\n\n\n \n\n\n\n Scientific Reports, 2. 2012.\n \n\n\n\n
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\n\n\n\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Evolution of in-group favoritism},\n type = {article},\n year = {2012},\n volume = {2},\n id = {9f818c55-695f-35c7-9a3b-ac47ada69d30},\n created = {2020-12-03T14:18:58.878Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.878Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {In-group favoritism is a central aspect of human behavior. People often help members of their own group more than members of other groups. Here we propose a mathematical framework for the evolution of in-group favoritism from a continuum of strategies. Unlike previous models, we do not pre-suppose that players never cooperate with out-group members. Instead, we determine the conditions under which preferential in-group cooperation emerges, and also explore situations where preferential out-group helping could evolve. Our approach is not based on explicit intergroup conflict, but instead uses evolutionary set theory. People can move between sets. Successful sets attract members, and successful strategies gain imitators. Individuals can employ different strategies when interacting with in-group versus out-group members. Our framework also allows us to implement different games for these two types of interactions. We prove general results and derive specific conditions for the evolution of cooperation based on in-group favoritism.},\n bibtype = {article},\n author = {Fu, F. and Tarnita, C.E. and Christakis, N.A. and Wang, L. and Rand, D.G. and Nowak, M.A.},\n doi = {10.1038/srep00460},\n journal = {Scientific Reports}\n}\n\n In-group favoritism is a central aspect of human behavior. People often help members of their own group more than members of other groups. Here we propose a mathematical framework for the evolution of in-group favoritism from a continuum of strategies. Unlike previous models, we do not pre-suppose that players never cooperate with out-group members. Instead, we determine the conditions under which preferential in-group cooperation emerges, and also explore situations where preferential out-group helping could evolve. Our approach is not based on explicit intergroup conflict, but instead uses evolutionary set theory. People can move between sets. Successful sets attract members, and successful strategies gain imitators. Individuals can employ different strategies when interacting with in-group versus out-group members. Our framework also allows us to implement different games for these two types of interactions. We prove general results and derive specific conditions for the evolution of cooperation based on in-group favoritism.\n
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\n \n \n\n \n \n \n \n \n Partner Selection Shapes the Strategic and Topological Evolution of Cooperation: The Power of Reputation Transitivity.\n \n \n \n\n\n \n Du, F.; and Fu, F.\n\n\n \n\n\n\n Dynamic Games and Applications, 1(3). 2011.\n \n\n\n\n
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\n\n\n@article{\n title = {Partner Selection Shapes the Strategic and Topological Evolution of Cooperation: The Power of Reputation Transitivity},\n type = {article},\n year = {2011},\n keywords = {Coevolutionary games,Partner switching,Reputation,Social networks},\n volume = {1},\n id = {4b6ac4e9-fdb5-3288-a645-fd3d3c03ea25},\n created = {2020-12-03T14:18:56.893Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.893Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Coevolution of individual strategies and social ties, in which individuals not only adjust their strategies by social learning but also switch their adverse partners to search for potential beneficial ones, has attracted increasing attention very recently. It is found that the interplay of strategic updating and partner network adaptation can facilitate the escape from the stalemate of cooperation in social dilemmas. But the question how individual preferential partner choice shapes the dynamical and topological organization of cooperation has yet to be fully answered. Here we propose a simple evolutionary game model to address this problem. In our model, when severing a current disadvantageous partnership, individuals can choose a new partner, either among their friends of friends preferentially according to their reputation scores or randomly from the remaining population. In addition to partner switching, individuals also update their strategies by imitating social neighbors. The interplay between these two processes gives rise to rich evolutionary dynamics. We focus on both strategic and topological evolution. We find that reputation-based partner selection leads to highly heterogeneous and often disassortative partner networks. During the coevolutionary process, a few successful individuals who attain a large number of partners emerge as social hubs and thus directly influence periphery individuals of small degree, forming leader-follower hierarchical structures. Cooperation prevails because of the positive feedback effects: good guys attract more partnerships and "the rich get richer." Our work sheds light on the emergence and maintenance of cooperation on dynamically changing social networks, where reputation plays a decisive role in the formation of social ties. © 2011 Springer Science+Business Media, LLC.},\n bibtype = {article},\n author = {Du, F. and Fu, F.},\n doi = {10.1007/s13235-011-0015-6},\n journal = {Dynamic Games and Applications},\n number = {3}\n}\n\n Coevolution of individual strategies and social ties, in which individuals not only adjust their strategies by social learning but also switch their adverse partners to search for potential beneficial ones, has attracted increasing attention very recently. It is found that the interplay of strategic updating and partner network adaptation can facilitate the escape from the stalemate of cooperation in social dilemmas. But the question how individual preferential partner choice shapes the dynamical and topological organization of cooperation has yet to be fully answered. Here we propose a simple evolutionary game model to address this problem. In our model, when severing a current disadvantageous partnership, individuals can choose a new partner, either among their friends of friends preferentially according to their reputation scores or randomly from the remaining population. In addition to partner switching, individuals also update their strategies by imitating social neighbors. The interplay between these two processes gives rise to rich evolutionary dynamics. We focus on both strategic and topological evolution. We find that reputation-based partner selection leads to highly heterogeneous and often disassortative partner networks. During the coevolutionary process, a few successful individuals who attain a large number of partners emerge as social hubs and thus directly influence periphery individuals of small degree, forming leader-follower hierarchical structures. Cooperation prevails because of the positive feedback effects: good guys attract more partnerships and \"the rich get richer.\" Our work sheds light on the emergence and maintenance of cooperation on dynamically changing social networks, where reputation plays a decisive role in the formation of social ties. © 2011 Springer Science+Business Media, LLC.\n
\n\n\n\n \n\n \n \n \n \n \n Moving away from nasty encounters enhances cooperation in ecological prisoner's dilemma game.\n \n \n \n\n\n \n Wu, T.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n PLoS ONE, 6(11). 2011.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Moving away from nasty encounters enhances cooperation in ecological prisoner's dilemma game},\n type = {article},\n year = {2011},\n volume = {6},\n id = {e5a767a3-a80b-3e97-a67c-b58ac84fccdd},\n created = {2020-12-03T14:18:57.662Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.662Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We study the role of migration in the evolution of cooperation. Individuals spatially located on a square lattice play the prisoner's dilemma game. Dissatisfied players, who have been exploited by defectors, tend to terminate interaction with selfish partners by leaving the current habitats, and explore unknown physical niches available surrounding them. The time scale ratio of game interaction to natural selection governs how many game rounds occur before individuals experience strategy updating. Under local migration and strong selection, simulation results demonstrate that cooperation can be stabilized for a wide range of model parameters, and the slower the natural selection, the more favorable for the emergence of cooperation. Besides, how the selection intensity affects cooperators' evolutionary fate is also investigated. We find that increasing it weakens cooperators' viability at different speeds for different time scale ratios. However, cooperation is greatly improved provided that individuals are offered with enough chance to agglomerate, while cooperation can always establish under weak selection but vanishes under very strong selection whenever individuals have less odds to migrate. Whenever the migration range restriction is removed, the parameter area responsible for the emergence of cooperation is, albeit somewhat compressed, still remarkable, validating the effectiveness of collectively migrating in promoting cooperation. © 2011 Wu et al.},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Wang, L.},\n doi = {10.1371/journal.pone.0027669},\n journal = {PLoS ONE},\n number = {11}\n}\n\n We study the role of migration in the evolution of cooperation. Individuals spatially located on a square lattice play the prisoner's dilemma game. Dissatisfied players, who have been exploited by defectors, tend to terminate interaction with selfish partners by leaving the current habitats, and explore unknown physical niches available surrounding them. The time scale ratio of game interaction to natural selection governs how many game rounds occur before individuals experience strategy updating. Under local migration and strong selection, simulation results demonstrate that cooperation can be stabilized for a wide range of model parameters, and the slower the natural selection, the more favorable for the emergence of cooperation. Besides, how the selection intensity affects cooperators' evolutionary fate is also investigated. We find that increasing it weakens cooperators' viability at different speeds for different time scale ratios. However, cooperation is greatly improved provided that individuals are offered with enough chance to agglomerate, while cooperation can always establish under weak selection but vanishes under very strong selection whenever individuals have less odds to migrate. Whenever the migration range restriction is removed, the parameter area responsible for the emergence of cooperation is, albeit somewhat compressed, still remarkable, validating the effectiveness of collectively migrating in promoting cooperation. © 2011 Wu et al.\n
\n\n\n\n \n\n \n \n \n \n \n Imperfect vaccine aggravates the long-standing dilemma of voluntary vaccination.\n \n \n \n\n\n \n Wu, B.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n PLoS ONE, 6(6). 2011.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Imperfect vaccine aggravates the long-standing dilemma of voluntary vaccination},\n type = {article},\n year = {2011},\n volume = {6},\n id = {3ab410c6-850e-37c6-9754-8ec6f5c85de3},\n created = {2020-12-03T14:18:57.709Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.709Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Achieving widespread population immunity by voluntary vaccination poses a major challenge for public health administration and practice. The situation is complicated even more by imperfect vaccines. How the vaccine efficacy affects individuals' vaccination behavior has yet to be fully answered. To address this issue, we combine a simple yet effective game theoretic model of vaccination behavior with an epidemiological process. Our analysis shows that, in a population of self-interested individuals, there exists an overshooting of vaccine uptake levels as the effectiveness of vaccination increases. Moreover, when the basic reproductive number, R0, exceeds a certain threshold, all individuals opt for vaccination for an intermediate region of vaccine efficacy. We further show that increasing effectiveness of vaccination always increases the number of effectively vaccinated individuals and therefore attenuates the epidemic strain. The results suggest that 'number is traded for efficiency': although increases in vaccination effectiveness lead to uptake drops due to free-riding effects, the impact of the epidemic can be better mitigated. © 2011 Wu et al.},\n bibtype = {article},\n author = {Wu, B. and Fu, F. and Wang, L.},\n doi = {10.1371/journal.pone.0020577},\n journal = {PLoS ONE},\n number = {6}\n}\n\n Achieving widespread population immunity by voluntary vaccination poses a major challenge for public health administration and practice. The situation is complicated even more by imperfect vaccines. How the vaccine efficacy affects individuals' vaccination behavior has yet to be fully answered. To address this issue, we combine a simple yet effective game theoretic model of vaccination behavior with an epidemiological process. Our analysis shows that, in a population of self-interested individuals, there exists an overshooting of vaccine uptake levels as the effectiveness of vaccination increases. Moreover, when the basic reproductive number, R0, exceeds a certain threshold, all individuals opt for vaccination for an intermediate region of vaccine efficacy. We further show that increasing effectiveness of vaccination always increases the number of effectively vaccinated individuals and therefore attenuates the epidemic strain. The results suggest that 'number is traded for efficiency': although increases in vaccination effectiveness lead to uptake drops due to free-riding effects, the impact of the epidemic can be better mitigated. © 2011 Wu et al.\n
\n\n\n\n \n\n \n \n \n \n \n Imitation dynamics of vaccination behaviour on social networks.\n \n \n \n\n\n \n Fu, F.; Rosenbloom, D.; Wang, L.; and Nowak, M.\n\n\n \n\n\n\n Proceedings of the Royal Society B: Biological Sciences, 278(1702). 2011.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Imitation dynamics of vaccination behaviour on social networks},\n type = {article},\n year = {2011},\n keywords = {Epidemiology,Evolutionary dynamics,Mathematical biology,Peer influence,Vaccination dilemma},\n volume = {278},\n id = {6148a0a5-2c03-3778-9db1-879036021924},\n created = {2020-12-03T14:18:58.490Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.490Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {The problem of achieving widespread immunity to infectious diseases by voluntary vaccination is often presented as a public-goods dilemma, as an individual's vaccination contributes to herd immunity, protecting those who forgo vaccination. The temptation to free-ride brings the equilibrium vaccination level below the social optimum. Here, we present an evolutionary game-theoretic approach to this problem, exploring the roles of individual imitation behaviour and population structure in vaccination. To this end, we integrate an epidemiological process into a simple agent-based model of adaptive learning, where individuals use anecdotal evidence to estimate costs and benefits of vaccination. In our simulations, we focus on parameter values that are realistic for a flu-like infection. Paradoxically, as agents become more adept at imitating successful strategies, the equilibrium level of vaccination falls below the rational individual optimum. In structured populations, the picture is only somewhat more optimistic: vaccination is widespread over a range of low vaccination costs, but coverage plummets after cost exceeds a critical threshold. This result suggests parallels to historical scenarios in which vaccination coverage provided herd immunity for some time, but then rapidly dropped. Our work sheds light on how imitation of peers shapes individual vaccination choices in social networks. © 2010 The Royal Society.},\n bibtype = {article},\n author = {Fu, F. and Rosenbloom, D.I. and Wang, L. and Nowak, M.A.},\n doi = {10.1098/rspb.2010.1107},\n journal = {Proceedings of the Royal Society B: Biological Sciences},\n number = {1702}\n}\n\n The problem of achieving widespread immunity to infectious diseases by voluntary vaccination is often presented as a public-goods dilemma, as an individual's vaccination contributes to herd immunity, protecting those who forgo vaccination. The temptation to free-ride brings the equilibrium vaccination level below the social optimum. Here, we present an evolutionary game-theoretic approach to this problem, exploring the roles of individual imitation behaviour and population structure in vaccination. To this end, we integrate an epidemiological process into a simple agent-based model of adaptive learning, where individuals use anecdotal evidence to estimate costs and benefits of vaccination. In our simulations, we focus on parameter values that are realistic for a flu-like infection. Paradoxically, as agents become more adept at imitating successful strategies, the equilibrium level of vaccination falls below the rational individual optimum. In structured populations, the picture is only somewhat more optimistic: vaccination is widespread over a range of low vaccination costs, but coverage plummets after cost exceeds a critical threshold. This result suggests parallels to historical scenarios in which vaccination coverage provided herd immunity for some time, but then rapidly dropped. Our work sheds light on how imitation of peers shapes individual vaccination choices in social networks. © 2010 The Royal Society.\n
\n\n\n\n \n\n \n \n \n \n \n Inertia in strategy switching transforms the strategy evolution.\n \n \n \n\n\n \n Zhang, Y.; Fu, F.; Wu, T.; Xie, G.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 84(6). 2011.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Inertia in strategy switching transforms the strategy evolution},\n type = {article},\n year = {2011},\n volume = {84},\n id = {c85c7c2a-417d-31ef-aa58-84cd361e04f1},\n created = {2020-12-03T14:18:58.793Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.793Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {A recent experimental study shows that human strategy updating involves both direct payoff comparison and the cost of switching strategy, which is equivalent to inertia. However, it remains largely unclear how such a predisposed inertia affects 2Ã-2 games in a well-mixed population of finite size. To address this issue, the âinertia bonusâ(strategy switching cost) is added to the learner payoff in the Fermi process. We find how inertia quantitatively shapes the stationary distribution and that stochastic stability under inertia exhibits three regimes, with each covering seven regions in the plane spanned by two inertia parameters. We also obtain the extended â 1/3â rule with inertia and the speed criterion with inertia; these two findings hold for a population above two. We illustrate the above results in the framework of the Prisoner's Dilemma game. As inertia varies, two intriguing stationary distributions emerge: the probability of coexistence state is maximized, or those of two full states are simultaneously peaked. Our results may provide useful insights into how the inertia of changing status quo acts on the strategy evolution and, in particular, the evolution of cooperation. © 2011 American Physical Society.},\n bibtype = {article},\n author = {Zhang, Y. and Fu, F. and Wu, T. and Xie, G. and Wang, L.},\n doi = {10.1103/PhysRevE.84.066103},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {6}\n}\n\n A recent experimental study shows that human strategy updating involves both direct payoff comparison and the cost of switching strategy, which is equivalent to inertia. However, it remains largely unclear how such a predisposed inertia affects 2Ã-2 games in a well-mixed population of finite size. To address this issue, the âinertia bonusâ(strategy switching cost) is added to the learner payoff in the Fermi process. We find how inertia quantitatively shapes the stationary distribution and that stochastic stability under inertia exhibits three regimes, with each covering seven regions in the plane spanned by two inertia parameters. We also obtain the extended â 1/3â rule with inertia and the speed criterion with inertia; these two findings hold for a population above two. We illustrate the above results in the framework of the Prisoner's Dilemma game. As inertia varies, two intriguing stationary distributions emerge: the probability of coexistence state is maximized, or those of two full states are simultaneously peaked. Our results may provide useful insights into how the inertia of changing status quo acts on the strategy evolution and, in particular, the evolution of cooperation. © 2011 American Physical Society.\n
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\n \n \n\n \n \n \n \n \n Invasion and expansion of cooperators in lattice populations: Prisoner's dilemma vs. snowdrift games.\n \n \n \n\n\n \n Fu, F.; Nowak, M.; and Hauert, C.\n\n\n \n\n\n\n Journal of Theoretical Biology, 266(3). 2010.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Invasion and expansion of cooperators in lattice populations: Prisoner's dilemma vs. snowdrift games},\n type = {article},\n year = {2010},\n keywords = {Cooperation,Invasion pattern,Pair approximation,Spatial games},\n volume = {266},\n id = {304b5879-d885-3ba2-b922-423f7a09c58e},\n created = {2020-12-03T14:18:57.751Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.751Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {The evolution of cooperation is an enduring conundrum in biology and the social sciences. Two social dilemmas, the prisoner's dilemma and the snowdrift game have emerged as the most promising mathematical metaphors to study cooperation. Spatial structure with limited local interactions has long been identified as a potent promoter of cooperation in the prisoner's dilemma but in the spatial snowdrift game, space may actually enhance or inhibit cooperation. Here we investigate and link the microscopic interaction between individuals to the characteristics of the emerging macroscopic patterns generated by the spatial invasion process of cooperators in a world of defectors. In our simulations, individuals are located on a square lattice with Moore neighborhood and update their strategies by probabilistically imitating the strategies of better performing neighbors. Under sufficiently benign conditions, cooperators can survive in both games. After rapid local equilibration, cooperators expand quadratically until global saturation is reached. Under favorable conditions, cooperators expand as a large contiguous cluster in both games with minor differences concerning the shape of embedded defectors. Under less favorable conditions, however, distinct differences arise. In the prisoner's dilemma, cooperators break up into isolated, compact clusters. The compact clustering reduces exploitation and leads to positive assortment, such that cooperators interact more frequently with other cooperators than with defectors. In contrast, in the snowdrift game, cooperators form small, dendritic clusters, which results in negative assortment and cooperators interact more frequently with defectors than with other cooperators. In order to characterize and quantify the emerging spatial patterns, we introduce a measure for the cluster shape and demonstrate that the macroscopic patterns can be used to determine the characteristics of the underlying microscopic interactions. © 2010 Elsevier Ltd.},\n bibtype = {article},\n author = {Fu, F. and Nowak, M.A. and Hauert, C.},\n doi = {10.1016/j.jtbi.2010.06.042},\n journal = {Journal of Theoretical Biology},\n number = {3}\n}\n\n The evolution of cooperation is an enduring conundrum in biology and the social sciences. Two social dilemmas, the prisoner's dilemma and the snowdrift game have emerged as the most promising mathematical metaphors to study cooperation. Spatial structure with limited local interactions has long been identified as a potent promoter of cooperation in the prisoner's dilemma but in the spatial snowdrift game, space may actually enhance or inhibit cooperation. Here we investigate and link the microscopic interaction between individuals to the characteristics of the emerging macroscopic patterns generated by the spatial invasion process of cooperators in a world of defectors. In our simulations, individuals are located on a square lattice with Moore neighborhood and update their strategies by probabilistically imitating the strategies of better performing neighbors. Under sufficiently benign conditions, cooperators can survive in both games. After rapid local equilibration, cooperators expand quadratically until global saturation is reached. Under favorable conditions, cooperators expand as a large contiguous cluster in both games with minor differences concerning the shape of embedded defectors. Under less favorable conditions, however, distinct differences arise. In the prisoner's dilemma, cooperators break up into isolated, compact clusters. The compact clustering reduces exploitation and leads to positive assortment, such that cooperators interact more frequently with other cooperators than with defectors. In contrast, in the snowdrift game, cooperators form small, dendritic clusters, which results in negative assortment and cooperators interact more frequently with defectors than with other cooperators. In order to characterize and quantify the emerging spatial patterns, we introduce a measure for the cluster shape and demonstrate that the macroscopic patterns can be used to determine the characteristics of the underlying microscopic interactions. © 2010 Elsevier Ltd.\n
\n\n\n\n \n\n \n \n \n \n \n Effects of heterogeneous wealth distribution on public cooperation with collective risk.\n \n \n \n\n\n \n Wang, J.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 82(1). 2010.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Effects of heterogeneous wealth distribution on public cooperation with collective risk},\n type = {article},\n year = {2010},\n volume = {82},\n id = {c2da9388-08f4-3eaa-9d7e-0f56e4024559},\n created = {2020-12-03T14:18:57.783Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.783Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {The distribution of wealth among individuals in real society can be well described by the Pareto principle or "80-20 rule." How does such heterogeneity in initial wealth distribution affect the emergence of public cooperation, when individuals, the rich and the poor, engage in a collective-risk enterprise, not to gain a profit but to avoid a potential loss? Here we address this issue by studying a simple but effective model based on threshold public goods games. We analyze the evolutionary dynamics for two distinct scenarios, respectively: one with fair sharers versus defectors and the other with altruists versus defectors. For both scenarios, particularly, we in detail study the dynamics of the population with dichotomic initial wealth-the rich versus the poor. Moreover, we demonstrate the possible steady compositions of the population and provide the conditions for stability of these steady states. We prove that in a population with heterogeneous wealth distribution, richer individuals are more likely to cooperate than poorer ones. Participants with lower initial wealth may choose to cooperate only if all players richer than them are cooperators. The emergence of pubic cooperation largely relies on rich individuals. Furthermore, whenever the wealth gap between the rich and the poor is sufficiently large, cooperation of a few rich individuals can substantially elevate the overall level of social cooperation, which is in line with the well-known Pareto principle. Our work may offer an insight into the emergence of cooperative behavior in real social situations where heterogeneous distribution of wealth among individual is omnipresent. © 2010 The American Physical Society.},\n bibtype = {article},\n author = {Wang, J. and Fu, F. and Wang, L.},\n doi = {10.1103/PhysRevE.82.016102},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {1}\n}\n\n The distribution of wealth among individuals in real society can be well described by the Pareto principle or \"80-20 rule.\" How does such heterogeneity in initial wealth distribution affect the emergence of public cooperation, when individuals, the rich and the poor, engage in a collective-risk enterprise, not to gain a profit but to avoid a potential loss? Here we address this issue by studying a simple but effective model based on threshold public goods games. We analyze the evolutionary dynamics for two distinct scenarios, respectively: one with fair sharers versus defectors and the other with altruists versus defectors. For both scenarios, particularly, we in detail study the dynamics of the population with dichotomic initial wealth-the rich versus the poor. Moreover, we demonstrate the possible steady compositions of the population and provide the conditions for stability of these steady states. We prove that in a population with heterogeneous wealth distribution, richer individuals are more likely to cooperate than poorer ones. Participants with lower initial wealth may choose to cooperate only if all players richer than them are cooperators. The emergence of pubic cooperation largely relies on rich individuals. Furthermore, whenever the wealth gap between the rich and the poor is sufficiently large, cooperation of a few rich individuals can substantially elevate the overall level of social cooperation, which is in line with the well-known Pareto principle. Our work may offer an insight into the emergence of cooperative behavior in real social situations where heterogeneous distribution of wealth among individual is omnipresent. © 2010 The American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Evolution of cooperation on stochastic dynamical networks.\n \n \n \n\n\n \n Wu, B.; Zhou, D.; Fu, F.; Luo, Q.; Wang, L.; and Traulsen, A.\n\n\n \n\n\n\n PLoS ONE, 5(6). 2010.\n \n\n\n\n
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\n\n\n@article{\n title = {Evolution of cooperation on stochastic dynamical networks},\n type = {article},\n year = {2010},\n volume = {5},\n id = {57d460e9-a89f-371b-a7f6-dd1eedb277d6},\n created = {2020-12-03T14:18:58.882Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.882Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Cooperative behavior that increases the fitness of others at a cost to oneself can be promoted by natural selection only in the presence of an additional mechanism. One such mechanism is based on population structure, which can lead to clustering of cooperating agents. Recently, the focus has turned to complex dynamical population structures such as social networks, where the nodes represent individuals and links represent social relationships. We investigate how the dynamics of a social network can change the level of cooperation in the network. Individuals either update their strategies by imitating their partners or adjust their social ties. For the dynamics of the network structure, a random link is selected and breaks with a probability determined by the adjacent individuals. Once it is broken, a new one is established. This linking dynamics can be conveniently characterized by a Markov chain in the configuration space of an ever-changing network of interacting agents. Our model can be analytically solved provided the dynamics of links proceeds much faster than the dynamics of strategies. This leads to a simple rule for the evolution of cooperation: The more fragile links between cooperating players and non-cooperating players are (or the more robust links between cooperators are), the more likely cooperation prevails. Our approach may pave the way for analytically investigating coevolution of strategy and structure. © 2010 Wu et al.},\n bibtype = {article},\n author = {Wu, B. and Zhou, D. and Fu, F. and Luo, Q. and Wang, L. and Traulsen, A.},\n doi = {10.1371/journal.pone.0011187},\n journal = {PLoS ONE},\n number = {6}\n}\n\n Cooperative behavior that increases the fitness of others at a cost to oneself can be promoted by natural selection only in the presence of an additional mechanism. One such mechanism is based on population structure, which can lead to clustering of cooperating agents. Recently, the focus has turned to complex dynamical population structures such as social networks, where the nodes represent individuals and links represent social relationships. We investigate how the dynamics of a social network can change the level of cooperation in the network. Individuals either update their strategies by imitating their partners or adjust their social ties. For the dynamics of the network structure, a random link is selected and breaks with a probability determined by the adjacent individuals. Once it is broken, a new one is established. This linking dynamics can be conveniently characterized by a Markov chain in the configuration space of an ever-changing network of interacting agents. Our model can be analytically solved provided the dynamics of links proceeds much faster than the dynamics of strategies. This leads to a simple rule for the evolution of cooperation: The more fragile links between cooperating players and non-cooperating players are (or the more robust links between cooperators are), the more likely cooperation prevails. Our approach may pave the way for analytically investigating coevolution of strategy and structure. © 2010 Wu et al.\n
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\n \n \n\n \n \n \n \n \n Individual's expulsion to nasty environment promotes cooperation in public goods games.\n \n \n \n\n\n \n Wu, T.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n Europhysics Letters, 88(3). 2009.\n \n\n\n\n
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\n\n\n@article{\n title = {Individual's expulsion to nasty environment promotes cooperation in public goods games},\n type = {article},\n year = {2009},\n volume = {88},\n id = {8c45339e-7d02-3ea3-beb9-3d914e64fc57},\n created = {2020-12-03T14:18:57.742Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.742Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Previous studies of games on dynamic graphs have almost specified pairwise interactions using the prisoner's dilemma game. We instead here for the first time explore coevolutionary dynamics in the context of interactions being characterized by the public goods game. Individuals are endowed with the capacity to adjust both their strategy and their social ties, occurring exclusively dependent on their payoffs. Under strategy updating, focal individuals are more likely to imitate their neighbors performing better. Meanwhile, they would abstain from engaging in the most defective neighborhoods if the opportunities of adjusting social ties arise, representing trait of individuals that they prefer better but exclude nasty environments. How often strategy dynamics and adaptation of social ties separately progress is governed by a tunable parameter. We experimentally found that opportune tradeoff of these two dynamics peaks cooperation, an observation absent whenever either dynamics is considered. We confirm that the stabilization of cooperation resulting from the partner switching remains effective under some more realistic situation where the maximal number of social ties one can admit is restrained. Copyright © EPLA, 2009.},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Wang, L.},\n doi = {10.1209/0295-5075/88/30011},\n journal = {Europhysics Letters},\n number = {3}\n}\n\n Previous studies of games on dynamic graphs have almost specified pairwise interactions using the prisoner's dilemma game. We instead here for the first time explore coevolutionary dynamics in the context of interactions being characterized by the public goods game. Individuals are endowed with the capacity to adjust both their strategy and their social ties, occurring exclusively dependent on their payoffs. Under strategy updating, focal individuals are more likely to imitate their neighbors performing better. Meanwhile, they would abstain from engaging in the most defective neighborhoods if the opportunities of adjusting social ties arise, representing trait of individuals that they prefer better but exclude nasty environments. How often strategy dynamics and adaptation of social ties separately progress is governed by a tunable parameter. We experimentally found that opportune tradeoff of these two dynamics peaks cooperation, an observation absent whenever either dynamics is considered. We confirm that the stabilization of cooperation resulting from the partner switching remains effective under some more realistic situation where the maximal number of social ties one can admit is restrained. Copyright © EPLA, 2009.\n
\n\n\n\n \n\n \n \n \n \n \n Could feedback-based self-learning help solve networked prisoner's dilemma?.\n \n \n \n\n\n \n Chen, X.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n In Proceedings of the IEEE Conference on Decision and Control, 2009. \n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@inproceedings{\n title = {Could feedback-based self-learning help solve networked prisoner's dilemma?},\n type = {inproceedings},\n year = {2009},\n id = {ffae4957-5673-3982-aa12-5972bce19a35},\n created = {2020-12-03T14:18:57.798Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.798Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We present a self-learning evolutionary Prisoner's Dilemma game model to study the evolution of cooperation in network-structured populations. During the evolutionary process, each agent updates its current strategy with a probability depending on the difference feedback between its actual score and score aspiration. Each agent's score is a weighed mean of its payoff coming from its neighbors (social partners) and the payoff of its social partners obtaining from it. Simulation results show that the cooperation level in the structured populations increases with increasing the weight of partners' obtaining payoff in the score. More interestingly, we find that very similar evolution of cooperation can respectively emerge in lattice, small-world and scale-free networks under the learning-feedback updating rule. Moreover, we provide theoretical analysis and qualitative explanations for these numerical simulations. Our work may provide an effective way to solve the dilemma of cooperation for structured populations. ©2009 IEEE.},\n bibtype = {inproceedings},\n author = {Chen, X. and Fu, F. and Wang, L.},\n doi = {10.1109/CDC.2009.5400154},\n booktitle = {Proceedings of the IEEE Conference on Decision and Control}\n}\n\n We present a self-learning evolutionary Prisoner's Dilemma game model to study the evolution of cooperation in network-structured populations. During the evolutionary process, each agent updates its current strategy with a probability depending on the difference feedback between its actual score and score aspiration. Each agent's score is a weighed mean of its payoff coming from its neighbors (social partners) and the payoff of its social partners obtaining from it. Simulation results show that the cooperation level in the structured populations increases with increasing the weight of partners' obtaining payoff in the score. More interestingly, we find that very similar evolution of cooperation can respectively emerge in lattice, small-world and scale-free networks under the learning-feedback updating rule. Moreover, we provide theoretical analysis and qualitative explanations for these numerical simulations. Our work may provide an effective way to solve the dilemma of cooperation for structured populations. ©2009 IEEE.\n
\n\n\n\n \n\n \n \n \n \n \n Social tolerance allows cooperation to prevail in an adaptive environment.\n \n \n \n\n\n \n Chen, X.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 80(5). 2009.\n \n\n\n\n
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\n\n\n@article{\n title = {Social tolerance allows cooperation to prevail in an adaptive environment},\n type = {article},\n year = {2009},\n volume = {80},\n id = {eadfcb04-226e-3a79-8b3e-ce160fcb558d},\n created = {2020-12-03T14:18:57.821Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.821Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {In real situations, individuals often have moderate tolerance toward ambient cooperative environment in which they tend to avoid unfavorable interactions and search for favorable ones. How such social tolerance affects the evolution of cooperation and the resulting cooperative networks remains to be answered. To address this issue, here we present an effective model of co-evolutionary prisoner's dilemma by introducing cooperative environment and social tolerance for networked players. An individual's level of cooperative environment characterizes the cooperativity and sustainability of its interaction environment centered on itself. In our model, for paired individuals we assume that the one in better cooperative environment has a certain tolerance threshold to the opponent. If the opponent's cooperative environment level is beyond the tolerance threshold, the one in better cooperative environment cuts unilaterally the link, and rewires to others. Otherwise, the link is not severed, and meanwhile an inhomogeneous strategy imitation process between them is considered. Moreover, a player's cooperative environment is adjusted in response to the strategy choices in the neighborhood. Interestingly, we find that there exists a moderate tolerance threshold warranting the best promotion of cooperation. We explain the nontrivial results by investigating the time ratio of strategy (network) updating during the whole process and properties in emerging networks. Furthermore, we investigate the effect of memory-dependent discounting of individuals' cooperative environment on the evolution of cooperation. We also demonstrate the robustness of our results by considering two other modified co-evolutionary rules. Our results highlight the importance of appropriate tolerance threshold for the evolution of cooperation during the entangled co-evolution of strategy and structure. © 2009 The American Physical Society.},\n bibtype = {article},\n author = {Chen, X. and Fu, F. and Wang, L.},\n doi = {10.1103/PhysRevE.80.051104},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {5}\n}\n\n In real situations, individuals often have moderate tolerance toward ambient cooperative environment in which they tend to avoid unfavorable interactions and search for favorable ones. How such social tolerance affects the evolution of cooperation and the resulting cooperative networks remains to be answered. To address this issue, here we present an effective model of co-evolutionary prisoner's dilemma by introducing cooperative environment and social tolerance for networked players. An individual's level of cooperative environment characterizes the cooperativity and sustainability of its interaction environment centered on itself. In our model, for paired individuals we assume that the one in better cooperative environment has a certain tolerance threshold to the opponent. If the opponent's cooperative environment level is beyond the tolerance threshold, the one in better cooperative environment cuts unilaterally the link, and rewires to others. Otherwise, the link is not severed, and meanwhile an inhomogeneous strategy imitation process between them is considered. Moreover, a player's cooperative environment is adjusted in response to the strategy choices in the neighborhood. Interestingly, we find that there exists a moderate tolerance threshold warranting the best promotion of cooperation. We explain the nontrivial results by investigating the time ratio of strategy (network) updating during the whole process and properties in emerging networks. Furthermore, we investigate the effect of memory-dependent discounting of individuals' cooperative environment on the evolution of cooperation. We also demonstrate the robustness of our results by considering two other modified co-evolutionary rules. Our results highlight the importance of appropriate tolerance threshold for the evolution of cooperation during the entangled co-evolution of strategy and structure. © 2009 The American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Partner selections in public goods games with constant group size.\n \n \n \n\n\n \n Wu, T.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 80(2). 2009.\n \n\n\n\n
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\n\n\n@article{\n title = {Partner selections in public goods games with constant group size},\n type = {article},\n year = {2009},\n volume = {80},\n id = {e8dffa1b-db49-3cc1-8797-51c5e9cbe5c1},\n created = {2020-12-03T14:18:57.850Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.850Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Most of previous studies concerning the public goods game assume either participation is unconditional or the number of actual participants in a competitive group changes over time. How the fixed group size, prescribed by social institutions, affects the evolution of cooperation is still unclear. We propose a model where individuals with heterogeneous social ties might well engage in differing numbers of public goods games, yet with each public goods game being constant size during the course of evolution. To do this, we assume that each focal individual unidirectionally selects a constant number of interaction partners from his immediate neighbors with probabilities proportional to the degrees or the reputations of these neighbors, corresponding to degree-based partner selection or reputation-based partner selection, respectively. Because of the stochasticity the group formation is dynamical. In both selection regimes, monotonical dependence of the stationary density of cooperators on the group size was found, the latter over the whole range but the former over a restricted range of the renormalized enhancement factor. Moreover, the reputation-based regime can substantially improve cooperation. To interpret these differences, the microscopic characteristics of individuals are probed. We later extend the degree-based partner selection to general cases where focal individuals have preferences toward their neighbors of varying social ties to form groups. As a comparison, we as well investigate the situation where individuals locating on the degree regular graphs choose their coplayers at random. Our results may give some insights into better understanding the widespread teamwork and cooperation in the real world. © 2009 The American Physical Society.},\n bibtype = {article},\n author = {Wu, T. and Fu, F. and Wang, L.},\n doi = {10.1103/PhysRevE.80.026121},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {2}\n}\n\n Most of previous studies concerning the public goods game assume either participation is unconditional or the number of actual participants in a competitive group changes over time. How the fixed group size, prescribed by social institutions, affects the evolution of cooperation is still unclear. We propose a model where individuals with heterogeneous social ties might well engage in differing numbers of public goods games, yet with each public goods game being constant size during the course of evolution. To do this, we assume that each focal individual unidirectionally selects a constant number of interaction partners from his immediate neighbors with probabilities proportional to the degrees or the reputations of these neighbors, corresponding to degree-based partner selection or reputation-based partner selection, respectively. Because of the stochasticity the group formation is dynamical. In both selection regimes, monotonical dependence of the stationary density of cooperators on the group size was found, the latter over the whole range but the former over a restricted range of the renormalized enhancement factor. Moreover, the reputation-based regime can substantially improve cooperation. To interpret these differences, the microscopic characteristics of individuals are probed. We later extend the degree-based partner selection to general cases where focal individuals have preferences toward their neighbors of varying social ties to form groups. As a comparison, we as well investigate the situation where individuals locating on the degree regular graphs choose their coplayers at random. Our results may give some insights into better understanding the widespread teamwork and cooperation in the real world. © 2009 The American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Partner switching stabilizes cooperation in coevolutionary prisoner's dilemma.\n \n \n \n\n\n \n Fu, F.; Wu, T.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 79(3). 2009.\n \n\n\n\n
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\n\n\n@article{\n title = {Partner switching stabilizes cooperation in coevolutionary prisoner's dilemma},\n type = {article},\n year = {2009},\n volume = {79},\n id = {4722e90b-38a9-3988-9a02-70d5eb80953d},\n created = {2020-12-03T14:18:57.863Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.863Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Previous studies suggest that cooperation prevails when individuals can switch their interaction partners quickly. However, it is still unclear how quickly individuals should switch adverse partners to maximize cooperation. To address this issue, we propose a simple model of coevolutionary prisoner's dilemma in which individuals are allowed to either adjust their strategies or switch their defective partners. Interestingly, we find that, depending on the game parameter, there is an optimal tendency of switching adverse partnerships that maximizes the fraction of cooperators in the population. We confirm that the stabilization of cooperation by partner switching remains effective under some situations, where either normalized or accumulated payoff is used in strategy updating, and where either only cooperators or all individuals are privileged to sever disadvantageous partners. We also provide an extended pair approximation to study the coevolutionary dynamics. Our results may be helpful in understanding the role of partner switching in the stabilization of cooperation in the real world. © 2009 The American Physical Society.},\n bibtype = {article},\n author = {Fu, F. and Wu, T. and Wang, L.},\n doi = {10.1103/PhysRevE.79.036101},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {3}\n}\n\n Previous studies suggest that cooperation prevails when individuals can switch their interaction partners quickly. However, it is still unclear how quickly individuals should switch adverse partners to maximize cooperation. To address this issue, we propose a simple model of coevolutionary prisoner's dilemma in which individuals are allowed to either adjust their strategies or switch their defective partners. Interestingly, we find that, depending on the game parameter, there is an optimal tendency of switching adverse partnerships that maximizes the fraction of cooperators in the population. We confirm that the stabilization of cooperation by partner switching remains effective under some situations, where either normalized or accumulated payoff is used in strategy updating, and where either only cooperators or all individuals are privileged to sever disadvantageous partners. We also provide an extended pair approximation to study the coevolutionary dynamics. Our results may be helpful in understanding the role of partner switching in the stabilization of cooperation in the real world. © 2009 The American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Hamilton-like rule for coevolution of strategy and structure.\n \n \n \n\n\n \n Wu, B.; Wang, L.; Fu, F.; and Chen, X.\n\n\n \n\n\n\n In Proceedings of 2009 7th Asian Control Conference, ASCC 2009, 2009. \n \n\n\n\n
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\n\n\n@inproceedings{\n title = {Hamilton-like rule for coevolution of strategy and structure},\n type = {inproceedings},\n year = {2009},\n id = {4cdbcef5-7f29-3a56-afce-244d4934c926},\n created = {2020-12-03T14:18:58.494Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.494Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {In this paper, we investigate coevolution of strategy and structure in Prisoner's Dilemma. We concentrate on the noise effect in the topological evolution on cooperation. We assume individuals can either update their strategies by imitating their partners or adjust their social ties. At each time in the strategy evolution, pairwise comparison is employed. While at each time in the topological evolution, with some probability, an individual dumps off one of its partner and makes a new social relationship. We show that a Hamilton-like rule is obtained, quantitatively saying the more often dissatisfied links break off than satisfied ones, the more likely cooperation can prevail, provided the linking dynamics proceeds much faster than strategy evolution. Furthermore, by investigating the upper bound of the strategy updating probability, we also show how much faster linking dynamics proceeds than strategy evolution to make the Hamilton-like rule valid. Interestingly, we unveil that the probability is dependent on the frequency of cooperators. Our work may shed light on the ubiquitous cooperation in societies. ©2009 ACA.},\n bibtype = {inproceedings},\n author = {Wu, B. and Wang, L. and Fu, F. and Chen, X.},\n booktitle = {Proceedings of 2009 7th Asian Control Conference, ASCC 2009}\n}\n\n In this paper, we investigate coevolution of strategy and structure in Prisoner's Dilemma. We concentrate on the noise effect in the topological evolution on cooperation. We assume individuals can either update their strategies by imitating their partners or adjust their social ties. At each time in the strategy evolution, pairwise comparison is employed. While at each time in the topological evolution, with some probability, an individual dumps off one of its partner and makes a new social relationship. We show that a Hamilton-like rule is obtained, quantitatively saying the more often dissatisfied links break off than satisfied ones, the more likely cooperation can prevail, provided the linking dynamics proceeds much faster than strategy evolution. Furthermore, by investigating the upper bound of the strategy updating probability, we also show how much faster linking dynamics proceeds than strategy evolution to make the Hamilton-like rule valid. Interestingly, we unveil that the probability is dependent on the frequency of cooperators. Our work may shed light on the ubiquitous cooperation in societies. ©2009 ACA.\n
\n\n\n\n \n\n \n \n \n \n \n Emergence of social cooperation in threshold public goods games with collective risk.\n \n \n \n\n\n \n Wang, J.; Fu, F.; Wu, T.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 80(1). 2009.\n \n\n\n\n
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\n\n\n@article{\n title = {Emergence of social cooperation in threshold public goods games with collective risk},\n type = {article},\n year = {2009},\n volume = {80},\n id = {ee6330bc-8d3e-36d2-83a0-3d2186b95a95},\n created = {2020-12-03T14:18:58.541Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.541Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {In real situations, people are often faced with the option of voluntary contribution to achieve a collective goal, for example, building a dam or a fence, in order to avoid an unfavorable loss. Those who do not donate, however, can free ride on others' sacrifices. As a result, cooperation is difficult to maintain, leading to an enduring collective-risk social dilemma. To address this issue, here we propose a simple yet effective theoretical model of threshold public goods game with collective risk and focus on the effect of risk on the emergence of social cooperation. To do this, we consider the population dynamics represented by replicator equation for two simplifying scenarios, respectively: one with fair sharers, who contribute the minimum average amount versus defectors and the other with altruists contributing more than average versus defectors. For both cases, we find that the dilemma is relieved in high-risk situations where cooperation is likely to persist and dominate defection in the population. Large initial endowment to individuals also encourages the risk-averse action, which means that, as compared to poor players (with small initial endowment), wealthy individuals (with large initial endowment) are more likely to cooperate in order to protect their private accounts. In addition, we show that small donation amount and small threshold (collective target) can encourage and sustain cooperation. Furthermore, for other parameters fixed, the impacts of group size act differently on the two scenarios because of distinct mechanisms: in the former case where the cost of cooperation depends on the group size, large size of group readily results in defection, while easily maintains cooperation in the latter case where the cost of cooperation is fixed irrespective of the group size. Our theoretical results of the replicator dynamics are in excellent agreement with the individual based simulation results. © 2009 The American Physical Society.},\n bibtype = {article},\n author = {Wang, J. and Fu, F. and Wu, T. and Wang, L.},\n doi = {10.1103/PhysRevE.80.016101},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {1}\n}\n\n In real situations, people are often faced with the option of voluntary contribution to achieve a collective goal, for example, building a dam or a fence, in order to avoid an unfavorable loss. Those who do not donate, however, can free ride on others' sacrifices. As a result, cooperation is difficult to maintain, leading to an enduring collective-risk social dilemma. To address this issue, here we propose a simple yet effective theoretical model of threshold public goods game with collective risk and focus on the effect of risk on the emergence of social cooperation. To do this, we consider the population dynamics represented by replicator equation for two simplifying scenarios, respectively: one with fair sharers, who contribute the minimum average amount versus defectors and the other with altruists contributing more than average versus defectors. For both cases, we find that the dilemma is relieved in high-risk situations where cooperation is likely to persist and dominate defection in the population. Large initial endowment to individuals also encourages the risk-averse action, which means that, as compared to poor players (with small initial endowment), wealthy individuals (with large initial endowment) are more likely to cooperate in order to protect their private accounts. In addition, we show that small donation amount and small threshold (collective target) can encourage and sustain cooperation. Furthermore, for other parameters fixed, the impacts of group size act differently on the two scenarios because of distinct mechanisms: in the former case where the cost of cooperation depends on the group size, large size of group readily results in defection, while easily maintains cooperation in the latter case where the cost of cooperation is fixed irrespective of the group size. Our theoretical results of the replicator dynamics are in excellent agreement with the individual based simulation results. © 2009 The American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Evolutionary dynamics on graphs: Efficient method for weak selection.\n \n \n \n\n\n \n Fu, F.; Wang, L.; Nowak, M.; and Hauert, C.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 79(4). 2009.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Evolutionary dynamics on graphs: Efficient method for weak selection},\n type = {article},\n year = {2009},\n volume = {79},\n id = {41351c99-69a5-34d9-8fc2-6a4efe6eb869},\n created = {2020-12-03T14:18:58.553Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.553Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Investigating the evolutionary dynamics of game theoretical interactions in populations where individuals are arranged on a graph can be challenging in terms of computation time. Here, we propose an efficient method to study any type of game on arbitrary graph structures for weak selection. In this limit, evolutionary game dynamics represents a first-order correction to neutral evolution. Spatial correlations can be empirically determined under neutral evolution and provide the basis for formulating the game dynamics as a discrete Markov process by incorporating a detailed description of the microscopic dynamics based on the neutral correlations. This framework is then applied to one of the most intriguing questions in evolutionary biology: the evolution of cooperation. We demonstrate that the degree heterogeneity of a graph impedes cooperation and that the success of tit for tat depends not only on the number of rounds but also on the degree of the graph. Moreover, considering the mutation-selection equilibrium shows that the symmetry of the stationary distribution of states under weak selection is skewed in favor of defectors for larger selection strengths. In particular, degree heterogeneity-a prominent feature of scale-free networks-generally results in a more pronounced increase in the critical benefit-to-cost ratio required for evolution to favor cooperation as compared to regular graphs. This conclusion is corroborated by an analysis of the effects of population structures on the fixation probabilities of strategies in general 2×2 games for different types of graphs. Computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies. © 2009 The American Physical Society.},\n bibtype = {article},\n author = {Fu, F. and Wang, L. and Nowak, M.A. and Hauert, C.},\n doi = {10.1103/PhysRevE.79.046707},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {4}\n}\n\n Investigating the evolutionary dynamics of game theoretical interactions in populations where individuals are arranged on a graph can be challenging in terms of computation time. Here, we propose an efficient method to study any type of game on arbitrary graph structures for weak selection. In this limit, evolutionary game dynamics represents a first-order correction to neutral evolution. Spatial correlations can be empirically determined under neutral evolution and provide the basis for formulating the game dynamics as a discrete Markov process by incorporating a detailed description of the microscopic dynamics based on the neutral correlations. This framework is then applied to one of the most intriguing questions in evolutionary biology: the evolution of cooperation. We demonstrate that the degree heterogeneity of a graph impedes cooperation and that the success of tit for tat depends not only on the number of rounds but also on the degree of the graph. Moreover, considering the mutation-selection equilibrium shows that the symmetry of the stationary distribution of states under weak selection is skewed in favor of defectors for larger selection strengths. In particular, degree heterogeneity-a prominent feature of scale-free networks-generally results in a more pronounced increase in the critical benefit-to-cost ratio required for evolution to favor cooperation as compared to regular graphs. This conclusion is corroborated by an analysis of the effects of population structures on the fixation probabilities of strategies in general 2×2 games for different types of graphs. Computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies. © 2009 The American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Strategy selection in structured populations.\n \n \n \n\n\n \n Tarnita, C.; Ohtsuki, H.; Antal, T.; Fu, F.; and Nowak, M.\n\n\n \n\n\n\n Journal of Theoretical Biology, 259(3). 2009.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Strategy selection in structured populations},\n type = {article},\n year = {2009},\n keywords = {Evolutionary dynamics,Finite populations,Stochastic effects},\n volume = {259},\n id = {b3d7e98b-d393-31ba-88dc-c998b1cfd0c5},\n created = {2020-12-03T14:18:58.833Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.833Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans. Traditionally evolutionary game dynamics are studied in well-mixed populations, where the interaction between any two individuals is equally likely. There have also been several approaches to study evolutionary games in structured populations. In this paper we present a simple result that holds for a large variety of population structures. We consider the game between two strategies, A and B, described by the payoff matrix (frac(a, c) frac(b, d)). We study a mutation and selection process. For weak selection strategy A is favored over B if and only if σ a + b > c + σ d. This means the effect of population structure on strategy selection can be described by a single parameter, σ. We present the values of σ for various examples including the well-mixed population, games on graphs, games in phenotype space and games on sets. We give a proof for the existence of such a σ, which holds for all population structures and update rules that have certain (natural) properties. We assume weak selection, but allow any mutation rate. We discuss the relationship between σ and the critical benefit to cost ratio for the evolution of cooperation. The single parameter, σ, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games. © 2009 Elsevier Ltd. All rights reserved.},\n bibtype = {article},\n author = {Tarnita, C.E. and Ohtsuki, H. and Antal, T. and Fu, F. and Nowak, M.A.},\n doi = {10.1016/j.jtbi.2009.03.035},\n journal = {Journal of Theoretical Biology},\n number = {3}\n}\n\n Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans. Traditionally evolutionary game dynamics are studied in well-mixed populations, where the interaction between any two individuals is equally likely. There have also been several approaches to study evolutionary games in structured populations. In this paper we present a simple result that holds for a large variety of population structures. We consider the game between two strategies, A and B, described by the payoff matrix (frac(a, c) frac(b, d)). We study a mutation and selection process. For weak selection strategy A is favored over B if and only if σ a + b > c + σ d. This means the effect of population structure on strategy selection can be described by a single parameter, σ. We present the values of σ for various examples including the well-mixed population, games on graphs, games in phenotype space and games on sets. We give a proof for the existence of such a σ, which holds for all population structures and update rules that have certain (natural) properties. We assume weak selection, but allow any mutation rate. We discuss the relationship between σ and the critical benefit to cost ratio for the evolution of cooperation. The single parameter, σ, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games. © 2009 Elsevier Ltd. All rights reserved.\n
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\n \n \n\n \n \n \n \n \n Empirical analysis of online social networks in the age of Web 2.0.\n \n \n \n\n\n \n Fu, F.; Liu, L.; and Wang, L.\n\n\n \n\n\n\n Physica A: Statistical Mechanics and its Applications, 387(2-3). 2008.\n \n\n\n\n
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\n\n\n@article{\n title = {Empirical analysis of online social networks in the age of Web 2.0},\n type = {article},\n year = {2008},\n keywords = {(dis)Assortativity,Blogging networks,Social Networking Site,Social networks,Topological analysis},\n volume = {387},\n id = {75a65c52-e376-35eb-a0c9-d94ef07d8957},\n created = {2020-12-03T14:18:56.280Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.280Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Today the World Wide Web is undergoing a subtle but profound shift to Web 2.0, to become more of a social web. The use of collaborative technologies such as blogs and social networking site (SNS) leads to instant online community in which people communicate rapidly and conveniently with each other. Moreover, there are growing interest and concern regarding the topological structure of these new online social networks. In this paper, we present empirical analysis of statistical properties of two important Chinese online social networks-a blogging network and an SNS open to college students. They are both emerging in the age of Web 2.0. We demonstrate that both networks possess small-world and scale-free features already observed in real-world and artificial networks. In addition, we investigate the distribution of topological distance. Furthermore, we study the correlations between degree (in/out) and degree (in/out), clustering coefficient and degree, popularity (in terms of number of page views) and in-degree (for the blogging network), respectively. We find that the blogging network shows disassortative mixing pattern, whereas the SNS network is an assortative one. Our research may help us to elucidate the self-organizing structural characteristics of these online social networks embedded in technical forms. © 2007 Elsevier Ltd. All rights reserved.},\n bibtype = {article},\n author = {Fu, F. and Liu, L. and Wang, L.},\n doi = {10.1016/j.physa.2007.10.006},\n journal = {Physica A: Statistical Mechanics and its Applications},\n number = {2-3}\n}\n\n Today the World Wide Web is undergoing a subtle but profound shift to Web 2.0, to become more of a social web. The use of collaborative technologies such as blogs and social networking site (SNS) leads to instant online community in which people communicate rapidly and conveniently with each other. Moreover, there are growing interest and concern regarding the topological structure of these new online social networks. In this paper, we present empirical analysis of statistical properties of two important Chinese online social networks-a blogging network and an SNS open to college students. They are both emerging in the age of Web 2.0. We demonstrate that both networks possess small-world and scale-free features already observed in real-world and artificial networks. In addition, we investigate the distribution of topological distance. Furthermore, we study the correlations between degree (in/out) and degree (in/out), clustering coefficient and degree, popularity (in terms of number of page views) and in-degree (for the blogging network), respectively. We find that the blogging network shows disassortative mixing pattern, whereas the SNS network is an assortative one. Our research may help us to elucidate the self-organizing structural characteristics of these online social networks embedded in technical forms. © 2007 Elsevier Ltd. All rights reserved.\n
\n\n\n\n \n\n \n \n \n \n \n Coevolutionary dynamics of opinions and networks: From diversity to uniformity.\n \n \n \n\n\n \n Fu, F.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 78(1). 2008.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Coevolutionary dynamics of opinions and networks: From diversity to uniformity},\n type = {article},\n year = {2008},\n volume = {78},\n id = {729a4870-6597-3f5a-9148-ad7f83c3f84b},\n created = {2020-12-03T14:18:56.912Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.912Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We investigate the coevolutionary dynamics of opinions and networks based upon majority-preference (MP) and minority-avoidance (MA) rules. Under MP, individuals adopt the majority opinion among their neighbors; while in MA individuals can break the link to one holding a minority and different opinion, and rewire either to neighbors of their neighbors with the same opinion or to a random one from the whole population except their nearest neighbors. We study opinion formation as a result of combination of these two competing rules, with a parameter tuning the balance between them. We find that the underlying network can be self-organized into connected communities with like-minded individuals belonging to the same group; thus a broad variety of opinions coexist. Diverse opinions disappear in a population in which all individuals share a uniform opinion, when the model parameter exceeds a critical value. Furthermore, we show that an increasing tendency to redirect to neighbors of neighbors is more likely to result in a consensus of opinion. © 2008 The American Physical Society.},\n bibtype = {article},\n author = {Fu, F. and Wang, L.},\n doi = {10.1103/PhysRevE.78.016104},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {1}\n}\n\n We investigate the coevolutionary dynamics of opinions and networks based upon majority-preference (MP) and minority-avoidance (MA) rules. Under MP, individuals adopt the majority opinion among their neighbors; while in MA individuals can break the link to one holding a minority and different opinion, and rewire either to neighbors of their neighbors with the same opinion or to a random one from the whole population except their nearest neighbors. We study opinion formation as a result of combination of these two competing rules, with a parameter tuning the balance between them. We find that the underlying network can be self-organized into connected communities with like-minded individuals belonging to the same group; thus a broad variety of opinions coexist. Diverse opinions disappear in a population in which all individuals share a uniform opinion, when the model parameter exceeds a critical value. Furthermore, we show that an increasing tendency to redirect to neighbors of neighbors is more likely to result in a consensus of opinion. © 2008 The American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Cooperation in networked prisoner's dilemma with individual learning feedback.\n \n \n \n\n\n \n Chen, X.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n In IFAC Proceedings Volumes (IFAC-PapersOnline), volume 17, 2008. \n \n\n\n\n
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\n\n\n@inproceedings{\n title = {Cooperation in networked prisoner's dilemma with individual learning feedback},\n type = {inproceedings},\n year = {2008},\n keywords = {Dynamic games,Models with explicit expectations and learning},\n volume = {17},\n issue = {1 PART 1},\n id = {e4da82cf-2c8a-3ba0-81a4-4766976ece98},\n created = {2020-12-03T14:18:57.668Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.668Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We introduce a modified learning updating mechanism into the evolutionary Prisoner's Dilemma on Newman-Watts (NW) networks. During the evolutionary process, each individual updates its strategy according to individual deterministic switch in combination with a feedback between its score aspiration and actual score. And individual's score is a linear combination of individual's total payoff and local contribution to its neighbors. We study the cooperation level of the system under this learning feedback mechanism, and find that the cooperation level increases as the relative weight of the local contribution to the score increases. In addition, we focus on the influences of learning rate and intensity of deterministic switch in the strategy updating rule on cooperation. Simulations show that for much low intensity of deterministic switch, cooperation is independent of learning rate to a large extent, and full cooperation can be reached when relative weight is not less than 0.5. Otherwise, cooperation depends on the value of learning rate. Besides, the cooperation level is not sensitive to topological parameters of NW networks. To explain these simulation results, we provide corresponding analytical results of mean-field approximation, and find that simulation results are in good agreement with analytical ones. Our work may shed some light on the maintenance of cooperative behavior in social systems with individual learning feedback. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.},\n bibtype = {inproceedings},\n author = {Chen, X. and Fu, F. and Wang, L.},\n doi = {10.3182/20080706-5-KR-1001.3101},\n booktitle = {IFAC Proceedings Volumes (IFAC-PapersOnline)}\n}\n\n We introduce a modified learning updating mechanism into the evolutionary Prisoner's Dilemma on Newman-Watts (NW) networks. During the evolutionary process, each individual updates its strategy according to individual deterministic switch in combination with a feedback between its score aspiration and actual score. And individual's score is a linear combination of individual's total payoff and local contribution to its neighbors. We study the cooperation level of the system under this learning feedback mechanism, and find that the cooperation level increases as the relative weight of the local contribution to the score increases. In addition, we focus on the influences of learning rate and intensity of deterministic switch in the strategy updating rule on cooperation. Simulations show that for much low intensity of deterministic switch, cooperation is independent of learning rate to a large extent, and full cooperation can be reached when relative weight is not less than 0.5. Otherwise, cooperation depends on the value of learning rate. Besides, the cooperation level is not sensitive to topological parameters of NW networks. To explain these simulation results, we provide corresponding analytical results of mean-field approximation, and find that simulation results are in good agreement with analytical ones. Our work may shed some light on the maintenance of cooperative behavior in social systems with individual learning feedback. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.\n
\n\n\n\n \n\n \n \n \n \n \n Interaction stochasticity supports cooperation in spatial Prisoner's dilemma.\n \n \n \n\n\n \n Chen, X.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 78(5). 2008.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Interaction stochasticity supports cooperation in spatial Prisoner's dilemma},\n type = {article},\n year = {2008},\n volume = {78},\n id = {ee8457e8-0b98-3126-a55a-055bb11e10ee},\n created = {2020-12-03T14:18:57.915Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.915Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Previous studies mostly assume deterministic interactions among neighboring individuals for games on graphs. In this paper, we relax this assumption by introducing stochastic interactions into the spatial Prisoner's dilemma game, and study the effects of interaction stochasticity on the evolution of cooperation. Interestingly, simulation results show that there exists an optimal region of the intensity of interaction resulting in a maximum cooperation level. Moreover, we find good agreement between simulation results and theoretical predictions obtained from an extended pair-approximation method. We also show some typical snapshots of the system and investigate the mean payoffs for cooperators and defectors. Our results may provide some insight into understanding the emergence of cooperation in the real world where the interactions between individuals take place in an intermittent manner. © 2008 The American Physical Society.},\n bibtype = {article},\n author = {Chen, X. and Fu, F. and Wang, L.},\n doi = {10.1103/PhysRevE.78.051120},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {5}\n}\n\n Previous studies mostly assume deterministic interactions among neighboring individuals for games on graphs. In this paper, we relax this assumption by introducing stochastic interactions into the spatial Prisoner's dilemma game, and study the effects of interaction stochasticity on the evolution of cooperation. Interestingly, simulation results show that there exists an optimal region of the intensity of interaction resulting in a maximum cooperation level. Moreover, we find good agreement between simulation results and theoretical predictions obtained from an extended pair-approximation method. We also show some typical snapshots of the system and investigate the mean payoffs for cooperators and defectors. Our results may provide some insight into understanding the emergence of cooperation in the real world where the interactions between individuals take place in an intermittent manner. © 2008 The American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Effects of learning activity on cooperation in evolutionary prisoner's dilemma game.\n \n \n \n\n\n \n Chen, X.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n International Journal of Modern Physics C, 19(9). 2008.\n \n\n\n\n
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\n\n\n@article{\n title = {Effects of learning activity on cooperation in evolutionary prisoner's dilemma game},\n type = {article},\n year = {2008},\n keywords = {Cooperation,Learning activity,Prisoner's dilemma,Social network},\n volume = {19},\n id = {b0816603-5c32-320e-9836-30eedd58b05f},\n created = {2020-12-03T14:18:57.931Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:57.931Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We study the evolutionary Prisoner's Dilemma game under individual learning activity mechanism on small-world and scale-free networks, respectively. Each player updates its strategy with quenched learning rate which characterizes the strength of individual learning activity during the evolutionary process. Simulation results show that the mechanism of learning activity presents nontrivial phenomena on both the two networks: optimal intermediate levels of learning activity can promote or sustain cooperation. Specifically, there exists an interesting resonance-like manner in the evolutionary game when the intermediate level of learning activity promotes cooperation, and there exists a plateau for cooperation in the favorable moderate region of learning activity when the intermediate level of learning activity sustains cooperation. Moreover, these interesting phenomena are not sensitive to the two networks with other topological parameters. Our work can be helpful in reflecting the effects of individual learning mechanism on cooperative behavior in social systems. © 2008 World Scientific Publishing Company.},\n bibtype = {article},\n author = {Chen, X. and Fu, F. and Wang, L.},\n doi = {10.1142/S0129183108012972},\n journal = {International Journal of Modern Physics C},\n number = {9}\n}\n\n We study the evolutionary Prisoner's Dilemma game under individual learning activity mechanism on small-world and scale-free networks, respectively. Each player updates its strategy with quenched learning rate which characterizes the strength of individual learning activity during the evolutionary process. Simulation results show that the mechanism of learning activity presents nontrivial phenomena on both the two networks: optimal intermediate levels of learning activity can promote or sustain cooperation. Specifically, there exists an interesting resonance-like manner in the evolutionary game when the intermediate level of learning activity promotes cooperation, and there exists a plateau for cooperation in the favorable moderate region of learning activity when the intermediate level of learning activity sustains cooperation. Moreover, these interesting phenomena are not sensitive to the two networks with other topological parameters. Our work can be helpful in reflecting the effects of individual learning mechanism on cooperative behavior in social systems. © 2008 World Scientific Publishing Company.\n
\n\n\n\n \n\n \n \n \n \n \n Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism.\n \n \n \n\n\n \n Chen, X.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n Physica A: Statistical Mechanics and its Applications, 387(22). 2008.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism},\n type = {article},\n year = {2008},\n keywords = {Cooperation,Prisoner's Dilemma,Stochastic win-stay-lose-shift (WSLS)},\n volume = {387},\n id = {60c5a662-e781-386d-b196-d8a1bf2129bb},\n created = {2020-12-03T14:18:58.029Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.029Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We introduce a stochastic win-stay-lose-shift (WSLS) mechanism into evolutionary Prisoner's Dilemma on small-world networks. At each time step, after playing with all its immediate neighbors, each individual gets a score to evaluate its performance in the game. The score is a linear combination of an individual's total payoff (i.e., individual gain from the group) and local contribution to its neighbors (i.e., individual donation to the group). If one's actual score is not larger than its desired score aspiration, it switches current strategy to the opposite one with the probability depending on the difference between the two scores. Under this stochastic WSLS regime, we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood, and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation. We also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation. Simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score. For much low intensity of deterministic switch, cooperation is to a large extent independent of learning rate, and full cooperation can be reached when relative weight is not less than 0.5. Otherwise, cooperation level is affected by the value of learning rate. Besides, we find that the cooperation level is not sensitive to the topological parameters. To explain these simulation results, we provide corresponding analytical results based on mean-field approximation, and find out that simulation results are in close agreement with the analytical ones. Our work may be helpful in understanding the cooperative behavior in social systems based on this stochastic WSLS mechanism. © 2008 Elsevier B.V. All rights reserved.},\n bibtype = {article},\n author = {Chen, X. and Fu, F. and Wang, L.},\n doi = {10.1016/j.physa.2008.05.043},\n journal = {Physica A: Statistical Mechanics and its Applications},\n number = {22}\n}\n\n We introduce a stochastic win-stay-lose-shift (WSLS) mechanism into evolutionary Prisoner's Dilemma on small-world networks. At each time step, after playing with all its immediate neighbors, each individual gets a score to evaluate its performance in the game. The score is a linear combination of an individual's total payoff (i.e., individual gain from the group) and local contribution to its neighbors (i.e., individual donation to the group). If one's actual score is not larger than its desired score aspiration, it switches current strategy to the opposite one with the probability depending on the difference between the two scores. Under this stochastic WSLS regime, we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood, and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation. We also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation. Simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score. For much low intensity of deterministic switch, cooperation is to a large extent independent of learning rate, and full cooperation can be reached when relative weight is not less than 0.5. Otherwise, cooperation level is affected by the value of learning rate. Besides, we find that the cooperation level is not sensitive to the topological parameters. To explain these simulation results, we provide corresponding analytical results based on mean-field approximation, and find out that simulation results are in close agreement with the analytical ones. Our work may be helpful in understanding the cooperative behavior in social systems based on this stochastic WSLS mechanism. © 2008 Elsevier B.V. All rights reserved.\n
\n\n\n\n \n\n \n \n \n \n \n Influence of different initial distributions on robust cooperation in scale-free networks: A comparative study.\n \n \n \n\n\n \n Chen, X.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n Physics Letters, Section A: General, Atomic and Solid State Physics, 372(8). 2008.\n \n\n\n\n
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\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Influence of different initial distributions on robust cooperation in scale-free networks: A comparative study},\n type = {article},\n year = {2008},\n keywords = {Initial distribution,Prisoner's dilemma,Robust cooperation,Scale-free networks},\n volume = {372},\n id = {f70c2ddd-cfdb-3577-995d-a7fd75dfe355},\n created = {2020-12-03T14:18:58.042Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.042Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We study the evolutionary Prisoner's dilemma game on scale-free networks, focusing on the influence of different initial distributions for cooperators and defectors on the evolution of cooperation. To address this issue, we consider three types of initial distributions for defectors: uniform distribution at random, occupying the most connected nodes, and occupying the lowest-degree nodes, respectively. It is shown that initial configurations for defectors can crucially influence the cooperation level and the evolution speed of cooperation. Interestingly, the situation where defectors initially occupy the lowest-degree vertices can exhibit the most robust cooperation, compared with two other distributions. That is, the cooperation level is least affected by the initial percentage of defectors. Moreover, in this situation, the whole system evolves fastest to the prevalent cooperation. Besides, we obtain the critical values of initial frequency of defectors above which the extinction of cooperators occurs for the respective initial distributions. Our results might be helpful in explaining the maintenance of high cooperation in scale-free networks. © 2007 Elsevier B.V. All rights reserved.},\n bibtype = {article},\n author = {Chen, X. and Fu, F. and Wang, L.},\n doi = {10.1016/j.physleta.2007.09.044},\n journal = {Physics Letters, Section A: General, Atomic and Solid State Physics},\n number = {8}\n}\n\n We study the evolutionary Prisoner's dilemma game on scale-free networks, focusing on the influence of different initial distributions for cooperators and defectors on the evolution of cooperation. To address this issue, we consider three types of initial distributions for defectors: uniform distribution at random, occupying the most connected nodes, and occupying the lowest-degree nodes, respectively. It is shown that initial configurations for defectors can crucially influence the cooperation level and the evolution speed of cooperation. Interestingly, the situation where defectors initially occupy the lowest-degree vertices can exhibit the most robust cooperation, compared with two other distributions. That is, the cooperation level is least affected by the initial percentage of defectors. Moreover, in this situation, the whole system evolves fastest to the prevalent cooperation. Besides, we obtain the critical values of initial frequency of defectors above which the extinction of cooperators occurs for the respective initial distributions. Our results might be helpful in explaining the maintenance of high cooperation in scale-free networks. © 2007 Elsevier B.V. All rights reserved.\n
\n\n\n\n \n\n \n \n \n \n \n Consensus of population systems with community structures.\n \n \n \n\n\n \n Wang, J.; Wu, B.; Wang, L.; and Fu, F.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 78(5). 2008.\n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@article{\n title = {Consensus of population systems with community structures},\n type = {article},\n year = {2008},\n volume = {78},\n id = {3a9f002f-641d-36bc-82e5-99fa3dacfcaa},\n created = {2020-12-03T14:18:58.591Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.591Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {Multicommunity population systems may reach a consensus state where the fractions of each species in different communities agree on a common value. In this paper, by analyzing the evolutionary dynamics based on an extended replicator equation incorporating community effects, the consensus problem of population systems with n communities is studied. In particular, the simple case of two communities is investigated in detail. In general, for n communities, a sufficient and necessary condition for population systems to reach a consensus of coexistent state is provided. Regarding the population dynamics for the four different types of games, whether the population systems can achieve consensus is determined. The dynamics of community-structured populations shows richer features than nonstructured populations, and some nontrivial phenomena arising from different community-structured population systems are illustrated with concrete numerical examples. © 2008 The American Physical Society.},\n bibtype = {article},\n author = {Wang, J. and Wu, B. and Wang, L. and Fu, F.},\n doi = {10.1103/PhysRevE.78.051923},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {5}\n}\n\n Multicommunity population systems may reach a consensus state where the fractions of each species in different communities agree on a common value. In this paper, by analyzing the evolutionary dynamics based on an extended replicator equation incorporating community effects, the consensus problem of population systems with n communities is studied. In particular, the simple case of two communities is investigated in detail. In general, for n communities, a sufficient and necessary condition for population systems to reach a consensus of coexistent state is provided. Regarding the population dynamics for the four different types of games, whether the population systems can achieve consensus is determined. The dynamics of community-structured populations shows richer features than nonstructured populations, and some nontrivial phenomena arising from different community-structured population systems are illustrated with concrete numerical examples. © 2008 The American Physical Society.\n
\n\n\n\n \n\n \n \n \n \n \n Reputation-based partner choice promotes cooperation in social networks.\n \n \n \n\n\n \n Fu, F.; Hauert, C.; Nowak, M.; and Wang, L.\n\n\n \n\n\n\n Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 78(2). 2008.\n \n\n\n\n
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\n\n\n@article{\n title = {Reputation-based partner choice promotes cooperation in social networks},\n type = {article},\n year = {2008},\n volume = {78},\n id = {46696e3e-3ea1-3ed8-94ae-67ddb4bd2b39},\n created = {2020-12-03T14:18:58.599Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.599Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We investigate the cooperation dynamics attributed to the interplay between the evolution of individual strategies and evolution of individual partnerships. We focus on the effect of reputation on an individual's partner-switching process. We assume that individuals can either change their strategies by imitating their partners or adjust their partnerships based on local information about reputations. We manipulate the partner switching in two ways; that is, individuals can switch from the lowest reputation partners, either to their partners' partners who have the highest reputation (i.e., ordering in partnership) or to others randomly chosen from the entire population (i.e., randomness in partnership). We show that when individuals are able to alter their behavioral strategies and their social interaction partnerships on the basis of reputation, cooperation can prevail. We find that the larger temptation to defect and the denser the partner network, the more frequently individuals need to shift their partnerships in order for cooperation to thrive. Furthermore, an increasing tendency of switching to partners' partners is more likely to lead to a higher level of cooperation. We show that when reputation is absent in such partner-switching processes, cooperation is much less favored than that of the reputation involved. Moreover, we investigate the effect of discounting an individual's reputation on the evolution of cooperation. Our results highlight the importance of the consideration of reputation (indirect reciprocity) on the promotion of cooperation when individuals can adjust their partnerships. © 2008 The American Physical Society.},\n bibtype = {article},\n author = {Fu, F. and Hauert, C. and Nowak, M.A. and Wang, L.},\n doi = {10.1103/PhysRevE.78.026117},\n journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter Physics},\n number = {2}\n}\n\n We investigate the cooperation dynamics attributed to the interplay between the evolution of individual strategies and evolution of individual partnerships. We focus on the effect of reputation on an individual's partner-switching process. We assume that individuals can either change their strategies by imitating their partners or adjust their partnerships based on local information about reputations. We manipulate the partner switching in two ways; that is, individuals can switch from the lowest reputation partners, either to their partners' partners who have the highest reputation (i.e., ordering in partnership) or to others randomly chosen from the entire population (i.e., randomness in partnership). We show that when individuals are able to alter their behavioral strategies and their social interaction partnerships on the basis of reputation, cooperation can prevail. We find that the larger temptation to defect and the denser the partner network, the more frequently individuals need to shift their partnerships in order for cooperation to thrive. Furthermore, an increasing tendency of switching to partners' partners is more likely to lead to a higher level of cooperation. We show that when reputation is absent in such partner-switching processes, cooperation is much less favored than that of the reputation involved. Moreover, we investigate the effect of discounting an individual's reputation on the evolution of cooperation. Our results highlight the importance of the consideration of reputation (indirect reciprocity) on the promotion of cooperation when individuals can adjust their partnerships. © 2008 The American Physical Society.\n
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\n \n \n\n \n \n \n \n \n Information propagation in hierarchical networks.\n \n \n \n\n\n \n Fu, F.; Liu, L.; and Wang, L.\n\n\n \n\n\n\n In Proceedings of the IEEE Conference on Decision and Control, 2007. \n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
\n\n\n \n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n
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\n\n\n@inproceedings{\n title = {Information propagation in hierarchical networks},\n type = {inproceedings},\n year = {2007},\n id = {16e30422-2681-3116-bd4a-6595c9c20dbd},\n created = {2020-12-03T14:18:56.279Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.279Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {A hierarchical network model is proposed, and information propagation process taking place on top of the network is investigated. It is found that the frequency distribution of refractory element number is bimodal and the location of initially chosen seed infection affects the spreading range of the information. Besides, when the initially selected individual belongs to a certain intermediate layer, the maximum spreading range of the information would be achieved. Our results can help optimize and control information spreading on social networks. © 2007 IEEE.},\n bibtype = {inproceedings},\n author = {Fu, F. and Liu, L. and Wang, L.},\n doi = {10.1109/CDC.2007.4434650},\n booktitle = {Proceedings of the IEEE Conference on Decision and Control}\n}\n\n A hierarchical network model is proposed, and information propagation process taking place on top of the network is investigated. It is found that the frequency distribution of refractory element number is bimodal and the location of initially chosen seed infection affects the spreading range of the information. Besides, when the initially selected individual belongs to a certain intermediate layer, the maximum spreading range of the information would be achieved. Our results can help optimize and control information spreading on social networks. © 2007 IEEE.\n
\n\n\n\n \n\n \n \n \n \n \n Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network.\n \n \n \n\n\n \n Fu, F.; Liu, L.; and Wang, L.\n\n\n \n\n\n\n European Physical Journal B, 56(4). 2007.\n \n\n\n\n
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\n\n\n@article{\n title = {Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network},\n type = {article},\n year = {2007},\n volume = {56},\n id = {5a38cbde-1e2a-3f69-b144-4d3853f2f49f},\n created = {2020-12-03T14:18:56.341Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:56.341Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We focus on the heterogeneity of social networks and its role to the emergence of prevailing cooperators and sustainable cooperation. The social networks are representative of the interaction relationships between players and their encounters in each round of games. We study an evolutionary Prisoner's Dilemma game on a variant of Newman-Watts small-world network, whose heterogeneity can be tuned by a parameter. It is found that optimal cooperation level exists at some intermediate topological heterogeneity for different temptations to defect. That is, frequency of cooperators peaks at a certain specific value of degree heterogeneity - neither the most heterogeneous case nor the most homogeneous one would favor the cooperators. Besides, the average degree of networks and the adopted update rule also affect the cooperation level. © EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007.},\n bibtype = {article},\n author = {Fu, F. and Liu, L.-H. and Wang, L.},\n doi = {10.1140/epjb/e2007-00124-5},\n journal = {European Physical Journal B},\n number = {4}\n}\n\n We focus on the heterogeneity of social networks and its role to the emergence of prevailing cooperators and sustainable cooperation. The social networks are representative of the interaction relationships between players and their encounters in each round of games. We study an evolutionary Prisoner's Dilemma game on a variant of Newman-Watts small-world network, whose heterogeneity can be tuned by a parameter. It is found that optimal cooperation level exists at some intermediate topological heterogeneity for different temptations to defect. That is, frequency of cooperators peaks at a certain specific value of degree heterogeneity - neither the most heterogeneous case nor the most homogeneous one would favor the cooperators. Besides, the average degree of networks and the adopted update rule also affect the cooperation level. © EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007.\n
\n\n\n\n \n\n \n \n \n \n \n Prisoner's Dilemma on community networks.\n \n \n \n\n\n \n Chen, X.; Fu, F.; and Wang, L.\n\n\n \n\n\n\n Physica A: Statistical Mechanics and its Applications, 378(2). 2007.\n \n\n\n\n
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\n\n\n@article{\n title = {Prisoner's Dilemma on community networks},\n type = {article},\n year = {2007},\n keywords = {Community networks,Cooperation,Heterogeneity,Prisoner's Dilemma},\n volume = {378},\n id = {d05e6688-15fb-32cb-a0ad-2b75e1fc4ac5},\n created = {2020-12-03T14:18:58.096Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.096Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We introduce a community network model which exhibits scale-free property and study the evolutionary Prisoner's Dilemma game (PDG) on this network model. It is found that the frequency of cooperators decreases with the increment of the average degree over(k, -) from the simulation results. And reducing inter-community links can promote cooperation when we keep the total links (including inner-community and inter-community links) unchanged. It is also shown that the heterogeneity of networks does not always enhance cooperation and the pattern of links among all the vertices under a given degree-distribution plays a crucial role in the dominance of cooperation in the network model. © 2007 Elsevier B.V. All rights reserved.},\n bibtype = {article},\n author = {Chen, X. and Fu, F. and Wang, L.},\n doi = {10.1016/j.physa.2006.12.024},\n journal = {Physica A: Statistical Mechanics and its Applications},\n number = {2}\n}\n\n We introduce a community network model which exhibits scale-free property and study the evolutionary Prisoner's Dilemma game (PDG) on this network model. It is found that the frequency of cooperators decreases with the increment of the average degree over(k, -) from the simulation results. And reducing inter-community links can promote cooperation when we keep the total links (including inner-community and inter-community links) unchanged. It is also shown that the heterogeneity of networks does not always enhance cooperation and the pattern of links among all the vertices under a given degree-distribution plays a crucial role in the dominance of cooperation in the network model. © 2007 Elsevier B.V. All rights reserved.\n
\n\n\n\n \n\n \n \n \n \n \n Flocking of multi-agent systems with a virtual leader.\n \n \n \n\n\n \n Shi, H.; Wang, L.; Chu, T.; Fu, F.; and Xu, M.\n\n\n \n\n\n\n In Proceedings of the 2007 IEEE Symposium on Artificial Life, CI-ALife 2007, 2007. \n \n\n\n\n
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\n\n\n@inproceedings{\n title = {Flocking of multi-agent systems with a virtual leader},\n type = {inproceedings},\n year = {2007},\n id = {efe29057-d368-3bc1-b93d-9e00010ff645},\n created = {2020-12-03T14:18:58.104Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.104Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {This paper considers the flocking problem of a group of autonomous agents moving in the space with a virtual leader. We investigate the dynamic properties of the group for the case where the state of the virtual leader may be time-varying and the topology of the neighboring relations between agents is dynamic. To track such a leader, we introduce a set of switching control laws that enable the entire group to generate the desired stable flocking motion. The control law acting on each agent relies on the state information of its neighboring agents and the external reference signal (or "virtual leader"). Then we prove that, if the acceleration input of the virtual leader is known, then each agent can follow the virtual leader, and moreover, the convergence rate of the center of mass (CoM) can be estimated; if the acceleration input is unknown, then the velocities of all agents asymptotically approach the velocity of the CoM, and thus the flocking motion can be obtained, however in this case, the final velocity of the group may not be equal to the desired velocity. Numerical simulations are worked out to further illustrate our theoretical results. © 2007 IEEE.},\n bibtype = {inproceedings},\n author = {Shi, H. and Wang, L. and Chu, T. and Fu, F. and Xu, M.},\n doi = {10.1109/ALIFE.2007.367808},\n booktitle = {Proceedings of the 2007 IEEE Symposium on Artificial Life, CI-ALife 2007}\n}\n\n This paper considers the flocking problem of a group of autonomous agents moving in the space with a virtual leader. We investigate the dynamic properties of the group for the case where the state of the virtual leader may be time-varying and the topology of the neighboring relations between agents is dynamic. To track such a leader, we introduce a set of switching control laws that enable the entire group to generate the desired stable flocking motion. The control law acting on each agent relies on the state information of its neighboring agents and the external reference signal (or \"virtual leader\"). Then we prove that, if the acceleration input of the virtual leader is known, then each agent can follow the virtual leader, and moreover, the convergence rate of the center of mass (CoM) can be estimated; if the acceleration input is unknown, then the velocities of all agents asymptotically approach the velocity of the CoM, and thus the flocking motion can be obtained, however in this case, the final velocity of the group may not be equal to the desired velocity. Numerical simulations are worked out to further illustrate our theoretical results. © 2007 IEEE.\n
\n\n\n\n \n\n \n \n \n \n \n Social dilemmas in an online social network: The structure and evolution of cooperation.\n \n \n \n\n\n \n Fu, F.; Chen, X.; Liu, L.; and Wang, L.\n\n\n \n\n\n\n Physics Letters, Section A: General, Atomic and Solid State Physics, 371(1-2). 2007.\n \n\n\n\n
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\n\n\n@article{\n title = {Social dilemmas in an online social network: The structure and evolution of cooperation},\n type = {article},\n year = {2007},\n keywords = {Cooperation,Network effects,Prisoner's Dilemma,Snowdrift game,Social networks},\n volume = {371},\n id = {9a7aa560-6a8b-3ec4-9303-30dccf712daa},\n created = {2020-12-03T14:18:58.632Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.632Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We investigate two paradigms for studying the evolution of cooperation-Prisoner's Dilemma and Snowdrift game in an online friendship network, obtained from a social networking site. By structural analysis, it is revealed that the empirical social network has small-world and scale-free properties. Besides, it exhibits assortative mixing pattern. Then, we study the evolutionary version of the two types of games on it. It is found that cooperation is substantially promoted with small values of game matrix parameters in both games. Whereas the competent cooperators induced by the underlying network of contacts will be dramatically inhibited with increasing values of the game parameters. Further, we explore the role of assortativity in evolution of cooperation by random edge rewiring. We find that increasing amount of assortativity will to a certain extent diminish the cooperation level. We also show that connected large hubs are capable of maintaining cooperation. The evolution of cooperation on empirical networks is influenced by various network effects in a combined manner, compared with that on model networks. Our results can help understand the cooperative behaviors in human groups and society. © 2007 Elsevier B.V. All rights reserved.},\n bibtype = {article},\n author = {Fu, F. and Chen, X. and Liu, L. and Wang, L.},\n doi = {10.1016/j.physleta.2007.05.116},\n journal = {Physics Letters, Section A: General, Atomic and Solid State Physics},\n number = {1-2}\n}\n\n We investigate two paradigms for studying the evolution of cooperation-Prisoner's Dilemma and Snowdrift game in an online friendship network, obtained from a social networking site. By structural analysis, it is revealed that the empirical social network has small-world and scale-free properties. Besides, it exhibits assortative mixing pattern. Then, we study the evolutionary version of the two types of games on it. It is found that cooperation is substantially promoted with small values of game matrix parameters in both games. Whereas the competent cooperators induced by the underlying network of contacts will be dramatically inhibited with increasing values of the game parameters. Further, we explore the role of assortativity in evolution of cooperation by random edge rewiring. We find that increasing amount of assortativity will to a certain extent diminish the cooperation level. We also show that connected large hubs are capable of maintaining cooperation. The evolution of cooperation on empirical networks is influenced by various network effects in a combined manner, compared with that on model networks. Our results can help understand the cooperative behaviors in human groups and society. © 2007 Elsevier B.V. All rights reserved.\n
\n\n\n\n \n\n \n \n \n \n \n Promotion of cooperation induced by the interplay between structure and game dynamics.\n \n \n \n\n\n \n Fu, F.; Chen, X.; Liu, L.; and Wang, L.\n\n\n \n\n\n\n Physica A: Statistical Mechanics and its Applications, 383(2). 2007.\n \n\n\n\n
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\n\n\n@article{\n title = {Promotion of cooperation induced by the interplay between structure and game dynamics},\n type = {article},\n year = {2007},\n keywords = {Cooperation,Heterogeneity,Network structure adaption,Prisoner's Dilemma,Social networks},\n volume = {383},\n id = {c4c4f4f0-d0e5-38d6-a31e-f793add788fa},\n created = {2020-12-03T14:18:58.648Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.648Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We consider the coupled dynamics of the adaption of network structure and the evolution of strategies played by individuals occupying the network vertices. We propose a computational model in which each agent plays a n-round Prisoner's Dilemma game with its immediate neighbors, after that, based upon self-interest, partial individuals may punish their defective neighbors by dismissing the social tie to the one who defects the most times, meanwhile seek for a new partner at random from the neighbors of the punished agent. It is found that the promotion of cooperation is attributed to the entangled evolution of individual strategy and network structure. Moreover, we show that the emerging social networks exhibit high heterogeneity and disassortative mixing pattern. For a given average connectivity of the population and the number of rounds, there is a critical value for the fraction of individuals adapting their social interactions, above which cooperators wipe out defectors. Besides, the effects of the average degree, the number of rounds, and the intensity of selection are investigated by extensive numerical simulations. Our results to some extent reflect the underlying mechanism promoting cooperation. © 2007.},\n bibtype = {article},\n author = {Fu, F. and Chen, X. and Liu, L. and Wang, L.},\n doi = {10.1016/j.physa.2007.04.099},\n journal = {Physica A: Statistical Mechanics and its Applications},\n number = {2}\n}\n\n We consider the coupled dynamics of the adaption of network structure and the evolution of strategies played by individuals occupying the network vertices. We propose a computational model in which each agent plays a n-round Prisoner's Dilemma game with its immediate neighbors, after that, based upon self-interest, partial individuals may punish their defective neighbors by dismissing the social tie to the one who defects the most times, meanwhile seek for a new partner at random from the neighbors of the punished agent. It is found that the promotion of cooperation is attributed to the entangled evolution of individual strategy and network structure. Moreover, we show that the emerging social networks exhibit high heterogeneity and disassortative mixing pattern. For a given average connectivity of the population and the number of rounds, there is a critical value for the fraction of individuals adapting their social interactions, above which cooperators wipe out defectors. Besides, the effects of the average degree, the number of rounds, and the intensity of selection are investigated by extensive numerical simulations. Our results to some extent reflect the underlying mechanism promoting cooperation. © 2007.\n
\n\n\n\n \n\n \n \n \n \n \n Collective behaviors and self-organizing cooperation.\n \n \n \n\n\n \n Wang, L.; Fu, F.; Chen, X.; Chu, T.; and Xie, G.\n\n\n \n\n\n\n In Proceedings of the 26th Chinese Control Conference, CCC 2007, 2007. \n \n\n\n\n
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\n\n\n@inproceedings{\n title = {Collective behaviors and self-organizing cooperation},\n type = {inproceedings},\n year = {2007},\n keywords = {Collective behaviors,Complex networks,Cooperation,Dynamics,Evolutionary games,Prisoner's dilemma,Self-organization,Snowdrift game,Topology},\n id = {8fa09be4-ecbd-33fa-9ec4-0bba970aaab6},\n created = {2020-12-03T14:18:58.834Z},\n file_attached = {false},\n profile_id = {739e3ab1-bdc9-3ffe-8c87-1f334ded8d51},\n last_modified = {2020-12-03T14:18:58.834Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {false},\n hidden = {false},\n private_publication = {false},\n abstract = {We investigate evolutionary games on complex networks. First, we investigate the evolutionary Prisoner's Dilemma game on scale-free networks with community structures. Then we explore the heterogeneity's role in the evolution of cooperation on a variant of Newman-Watts small-world networks. We also study the influence of different initial conditions on the evolution of cooperation corresponding to different initial configurations for cooperators and defectors distributing among the vertices of networks. Moreover, we investigate Snowdrift game on an empirical social network. Furthermore, we study the entangled dynamics of the evolution of network structure and strategy. Finally, we present the unresolved open problems, future research directions, and possible application areas of evolutionary games on complex networks.},\n bibtype = {inproceedings},\n author = {Wang, L. and Fu, F. and Chen, X. and Chu, T. and Xie, G.},\n doi = {10.1109/CHICC.2006.4346930},\n booktitle = {Proceedings of the 26th Chinese Control Conference, CCC 2007}\n}\n\n We investigate evolutionary games on complex networks. First, we investigate the evolutionary Prisoner's Dilemma game on scale-free networks with community structures. Then we explore the heterogeneity's role in the evolution of cooperation on a variant of Newman-Watts small-world networks. We also study the influence of different initial conditions on the evolution of cooperation corresponding to different initial configurations for cooperators and defectors distributing among the vertices of networks. Moreover, we investigate Snowdrift game on an empirical social network. Furthermore, we study the entangled dynamics of the evolution of network structure and strategy. Finally, we present the unresolved open problems, future research directions, and possible application areas of evolutionary games on complex networks.\n
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