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\n  \n 2018\n \n \n (6)\n \n \n
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\n \n\n \n \n \n \n Fibonacci-type sequences in rings and Banach algebras, Binet-type formulas, and polynomials in $x+1/x$.\n \n\n\n \n Eckman, D.; and Lennard, C.\n \n\n\n \n\n\n\n 2018.\n Under revision.\n\n\n\n
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@unpublished{EckmanLennard2018,\r\n  abstract={We consider Fibonacci-type sequences in rings and Banach algebras.\r\nWe show that Binet-type formulas can be derived under quite general\r\ncircumstances. We also show that in certain rings and Banach algebras\r\nBinet-type formulas may not exist; e.g., in the Banach algebra $L^1(R)$,\r\nwhere the product is convolution\r\nWe consider the fact that in rings with identity, for every invertible $x$,\r\nand for all positive integers $n$,\r\n$x^n +1/x^n$  is a monic polynomial in $x + 1/x$; and related identities.\r\nWe prove theorems concerning the Banach algebra of\r\nall continuous linear operators on a Hilbert space. For example,\r\nwe show that if $x$ is invertible and $x - 1/x$ is positive definite,\r\n  then\r\n  $x^{\\nu} + (-1)^{\\nu}/x^{\\nu}$ is positive definite, for all $\\nu$ in $N$.\r\nWe also derive some\r\nwell-known and less common results for Fibonacci-type sequences of integers.},\r\n  title={Fibonacci-type sequences in rings and Banach algebras, Binet-type formulas, and polynomials in $x+1/x$},\r\n  author={David Eckman and Chris Lennard},\r\n  year={2018},\r\n  note={Under revision.}\r\n  %url_Paper={},\r\n}\r\n\r\n
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\n We consider Fibonacci-type sequences in rings and Banach algebras. We show that Binet-type formulas can be derived under quite general circumstances. We also show that in certain rings and Banach algebras Binet-type formulas may not exist; e.g., in the Banach algebra $L^1(R)$, where the product is convolution We consider the fact that in rings with identity, for every invertible $x$, and for all positive integers $n$, $x^n +1/x^n$ is a monic polynomial in $x + 1/x$; and related identities. We prove theorems concerning the Banach algebra of all continuous linear operators on a Hilbert space. For example, we show that if $x$ is invertible and $x - 1/x$ is positive definite, then $x^{\\nu} + (-1)^{\\nu}/x^{\\nu}$ is positive definite, for all $\\nu$ in $N$. We also derive some well-known and less common results for Fibonacci-type sequences of integers.\n
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\n \n\n \n \n \n \n Reusing search data in ranking and selection: What could possibly go wrong?.\n \n\n\n \n Eckman, D. J.; and Henderson, S. G.\n \n\n\n \n\n\n\n ACM Transactions on Modeling and Computer Simulation (TOMACS), 28(3): 18:1-18:15. 2018.\n \n\n\n\n
\n\n\n \n \n \n \"Reusing paper\n  \n \n \n \"Reusing slides\n  \n \n \n \"Reusing poster\n  \n \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
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@article{EckmanHenderson2018a,\r\n  abstract={It is tempting to reuse replications taken during a simulation optimization search as input to a ranking-and-selection procedure.\r\nHowever, even when the random inputs used to generate replications are i.i.d. and independent across systems, we show that for searches that use the observed performance of explored systems to identify new systems, the replications are conditionally dependent given the sequence of returned systems.\r\nThrough simulation experiments, we demonstrate that reusing the replications taken during search in selection and subset-selection procedures can result in probabilities of correct and good selection well below the guaranteed levels.\r\nBased on these negative findings, we call into question the guarantees of established ranking-and-selection procedures that reuse search data.\r\nWe also rigorously define guarantees for ranking-and-selection procedures after search and discuss how procedures that only provide guarantees in the preference zone are ill-suited to this setting.},\r\n  title={Reusing search data in ranking and selection: What could possibly go wrong?},  \r\n  author={David J. Eckman and Shane G. Henderson},\r\n  year={2018},\r\n  journal={ACM Transactions on Modeling and Computer Simulation (TOMACS)},\r\n  volume={28},\r\n  number={3},\r\n  pages={18:1-18:15},\r\n  %url_Paper={mypdfs/RS-after-search-paper.pdf},\r\n  url_Paper={https://dl.acm.org/authorize?N665104},\r\n  url_Slides={mypdfs/RS-after-search-slides.pdf},\r\n  url_Poster={mypdfs/RS-after-search-poster.pdf},\r\n%<!-- ACM DL Article: Reusing Search Data in Ranking and Selection: What Could Possibly Go Wrong? -->\r\n%<div class="acmdlitem" id="item3170503"><img src="//dl.acm.org/images/oa.gif" width="25" height="25" border="0" alt="ACM DL Author-ize service" style="vertical-align:middle"/><a href="https://dl.acm.org/authorize?N665104" title="Reusing Search Data in Ranking and Selection: What Could Possibly Go Wrong?">Reusing Search Data in Ranking and Selection: What Could Possibly Go Wrong?</a><div style="margin-left:25px"><a href="http://dl.acm.org/author_page.cfm?id=81553190756" >David J. Eckman</a>, <a href="http://dl.acm.org/author_page.cfm?id=81100433315" >Shane G. Henderson</a><br />ACM Transactions on Modeling and Computer Simulation (TOMACS), 2018</div></div>\r\n}\r\n\r\n
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\n It is tempting to reuse replications taken during a simulation optimization search as input to a ranking-and-selection procedure. However, even when the random inputs used to generate replications are i.i.d. and independent across systems, we show that for searches that use the observed performance of explored systems to identify new systems, the replications are conditionally dependent given the sequence of returned systems. Through simulation experiments, we demonstrate that reusing the replications taken during search in selection and subset-selection procedures can result in probabilities of correct and good selection well below the guaranteed levels. Based on these negative findings, we call into question the guarantees of established ranking-and-selection procedures that reuse search data. We also rigorously define guarantees for ranking-and-selection procedures after search and discuss how procedures that only provide guarantees in the preference zone are ill-suited to this setting.\n
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\n \n\n \n \n \n \n Green simulation optimization using likelihood ratio estimators.\n \n\n\n \n Eckman, D. J.; and Feng, M. B.\n \n\n\n \n\n\n\n 2018.\n Accepted for the 2018 Winter Simulation Conference.\n\n\n\n
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@unpublished{EckmanFeng2018,\r\n  abstract={Green simulation is the reuse of past simulation outputs to enhance the efficiency of current and future simulation experiments. One natural application of green simulation is in the context of simulation optimization, wherein outputs from past iterations in a search can be reused in subsequent iterations. In this article, we draw attention to challenges that arise when green simulation likelihood ratio estimators are naively employed in simulation optimization. In particular, we show that for searches that identify new designs based on past outputs, outputs in different iterations are conditionally dependent, violating one of the assumptions for the validity of the likelihood ratio estimator. As a result, green simulation likelihood ratio estimators of the objective and gradient can become biased. We demonstrate how this conditional dependence and bias can adversely affect the behavior of gradient-based optimization algorithms.},\r\n  title={Green simulation optimization using likelihood ratio estimators},\r\n  author={David J. Eckman and M. Ben Feng},\r\n  year={2018},\r\n  note={Accepted for the 2018 Winter Simulation Conference.}\r\n  %url_Paper={},\r\n}\r\n\r\n
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\n Green simulation is the reuse of past simulation outputs to enhance the efficiency of current and future simulation experiments. One natural application of green simulation is in the context of simulation optimization, wherein outputs from past iterations in a search can be reused in subsequent iterations. In this article, we draw attention to challenges that arise when green simulation likelihood ratio estimators are naively employed in simulation optimization. In particular, we show that for searches that identify new designs based on past outputs, outputs in different iterations are conditionally dependent, violating one of the assumptions for the validity of the likelihood ratio estimator. As a result, green simulation likelihood ratio estimators of the objective and gradient can become biased. We demonstrate how this conditional dependence and bias can adversely affect the behavior of gradient-based optimization algorithms.\n
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\n \n\n \n \n \n \n Guarantees on the probability of good selection.\n \n\n\n \n Eckman, D. J.; and Henderson, S. G.\n \n\n\n \n\n\n\n 2018.\n Accepted for the 2018 Winter Simulation Conference.\n\n\n\n
\n\n\n \n \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
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@unpublished{EckmanHenderson2018b,\r\n  abstract={This tutorial provides an overview of guarantees on the probability of good selection (PGS), i.e., statistical guarantees on selecting---with high probability---an alternative whose expected performance is within a given tolerance of the best. We discuss why PGS guarantees are superior to more popular, related guarantees on the probability of correct selection (PCS) under the indifference-zone formulation. We review existing procedures that deliver PGS guarantees and assess several direct and indirect methods of proof. We compare the frequentist and Bayesian interpretations of PGS and highlight the differences in how procedures are designed to deliver PGS guarantees under the two frameworks.},\r\n  title={Guarantees on the probability of good selection},\r\n  author={David J. Eckman and Shane G. Henderson},\r\n  year={2018},\r\n  note={Accepted for the 2018 Winter Simulation Conference.}\r\n  %url_Paper={},\r\n}\r\n\r\n
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\n This tutorial provides an overview of guarantees on the probability of good selection (PGS), i.e., statistical guarantees on selecting–-with high probability–-an alternative whose expected performance is within a given tolerance of the best. We discuss why PGS guarantees are superior to more popular, related guarantees on the probability of correct selection (PCS) under the indifference-zone formulation. We review existing procedures that deliver PGS guarantees and assess several direct and indirect methods of proof. We compare the frequentist and Bayesian interpretations of PGS and highlight the differences in how procedures are designed to deliver PGS guarantees under the two frameworks.\n
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\n \n\n \n \n \n \n Fixed-confidence, fixed tolerance guarantees for selection-of-the-best procedures.\n \n\n\n \n Eckman, D. J.; and Henderson, S. G.\n \n\n\n \n\n\n\n 2018.\n Submitted.\n\n\n\n
\n\n\n \n \n \n \"Fixed-confidence, paper\n  \n \n \n \"Fixed-confidence, slides\n  \n \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
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@unpublished{EckmanHenderson2018c,\r\n  abstract={Selection-of-the-best procedures designed under the indifference-zone (IZ) formulation provide a guarantee on the probability of correct selection (PCS) whenever the performance of the best system exceeds that of the second-best system by a specified amount. We discuss the shortcomings of this guarantee and argue that providing a guarantee on the probability of good selection (PGS)---selecting a system whose performance is within a specified tolerance of the best---is a more justifiable goal. Although this form of fixed-confidence, fixed-tolerance guarantee has been well studied in the multi-armed-bandit community, it has received far less attention in the simulation community. We examine numerous techniques for proving the PGS guarantee, including sufficient conditions under which selection and subset-selection procedures that deliver the IZ-inspired PCS guarantee also deliver the PGS guarantee. We also compare the frequentist PGS guarantee to its Bayesian counterpart and discuss the differences in how procedures are designed for these two goals.},\r\n  title={Fixed-confidence, fixed tolerance guarantees for selection-of-the-best procedures},\r\n  author={David J. Eckman and Shane G. Henderson},\r\n  year={2018},\r\n  note={Submitted.},\r\n  url_Paper={mypdfs/PGS-overview-paper.pdf},\r\n  url_Slides={mypdfs/PGS-overview-slides.pdf}\r\n}\r\n\r\n
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\n Selection-of-the-best procedures designed under the indifference-zone (IZ) formulation provide a guarantee on the probability of correct selection (PCS) whenever the performance of the best system exceeds that of the second-best system by a specified amount. We discuss the shortcomings of this guarantee and argue that providing a guarantee on the probability of good selection (PGS)–-selecting a system whose performance is within a specified tolerance of the best–-is a more justifiable goal. Although this form of fixed-confidence, fixed-tolerance guarantee has been well studied in the multi-armed-bandit community, it has received far less attention in the simulation community. We examine numerous techniques for proving the PGS guarantee, including sufficient conditions under which selection and subset-selection procedures that deliver the IZ-inspired PCS guarantee also deliver the PGS guarantee. We also compare the frequentist PGS guarantee to its Bayesian counterpart and discuss the differences in how procedures are designed for these two goals.\n
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\n \n\n \n \n \n \n Posterior-based stopping rules for Bayesian sequential selection procedures.\n \n\n\n \n Eckman, D. J.; and Henderson, S. G.\n \n\n\n \n\n\n\n 2018.\n Working paper.\n\n\n\n
\n\n\n \n \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
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@unpublished{EckmanHenderson2018d,\r\n  abstract={The problem of selecting the best from among a finite number of simulated alternatives has been studied under the contrasting frequentist and Bayesian interpretations of probability. We emphasize the conceptual differences in fixed-confidence guarantees under the two frameworks and examine practical implications of this distinction. We also discuss how frequentist selection procedures are inherently conservative and Bayesian selection procedures are relatively easier to design. Through simulation experiments, we compare the performance of selection procedures designed under each framework with respect to the other type of guarantee.},\r\n  title={Posterior-based stopping rules for Bayesian sequential selection procedures},\r\n  author={David J. Eckman and Shane G. Henderson},\r\n  year={2018},\r\n  note={Working paper.}\r\n  %url_Paper={},\r\n}
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\n The problem of selecting the best from among a finite number of simulated alternatives has been studied under the contrasting frequentist and Bayesian interpretations of probability. We emphasize the conceptual differences in fixed-confidence guarantees under the two frameworks and examine practical implications of this distinction. We also discuss how frequentist selection procedures are inherently conservative and Bayesian selection procedures are relatively easier to design. Through simulation experiments, we compare the performance of selection procedures designed under each framework with respect to the other type of guarantee.\n
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\n  \n 2017\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n Empirically comparing the finite-time performance of simulation-optimization algorithms.\n \n\n\n \n Dong, N.; Eckman, D.; Poloczek, M.; Zhao, X.; and Henderson, S.\n \n\n\n \n\n\n\n In V. Chan, A. D.; and Mustafee, N., editor(s), Proceedings of the 2017 Winter Simulation Conference, pages 2206-2217, 2017. IEEE\n \n\n\n\n
\n\n\n \n \n \n \"Empirically paper\n  \n \n \n \"Empirically slides\n  \n \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
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@inproceedings{DongEtal2017,\r\n  abstract={We empirically evaluate the finite-time performance of several simulation-optimization algorithms on a testbed of problems with the goal of motivating further development of algorithms with strong finite-time performance.\r\nWe investigate if the observed performance of the algorithms can be explained by properties of the problems, e.g., the number of decision variables, the topology of the objective function, or the magnitude of the simulation error.},\r\n  title={Empirically comparing the finite-time performance of simulation-optimization algorithms},\r\n  author={Naijia Dong and David Eckman and Matthias Poloczek and Xueqi Zhao and Shane Henderson},\r\n  booktitle={Proceedings of the 2017 Winter Simulation Conference},\r\n  pages={2206-2217},\r\n  editor={V. Chan, A. D'Ambrogio, G. Zacharewicz, and N. Mustafee},\r\n  year={2017},\r\n  organization={IEEE},\r\n  url_Paper={mypdfs/Dong-etal-2017.pdf},\r\n  url_Slides={mypdfs/SimOpt-comp-slides.pdf}\r\n}\r\n\r\n
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\n We empirically evaluate the finite-time performance of several simulation-optimization algorithms on a testbed of problems with the goal of motivating further development of algorithms with strong finite-time performance. We investigate if the observed performance of the algorithms can be explained by properties of the problems, e.g., the number of decision variables, the topology of the objective function, or the magnitude of the simulation error.\n
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\n  \n 2016\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n Optimal pinging frequencies in the search for an immobile beacon.\n \n\n\n \n Eckman, D.; Maillart, L.; and Schaefer, A.\n \n\n\n \n\n\n\n IIE Transactions, 48(6): 489-500. 2016.\n \n\n\n\n
\n\n\n \n \n \n \"Optimal paper\n  \n \n \n \"Optimal slides\n  \n \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
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@article{EckmanMaillartSchaefer2016,\r\n  abstract={We consider a search for an immobile object that can only be detected if the searcher is within a\r\ngiven range of the object during one of a finite number of instantaneous detection opportunities, i.e.,\r\n"pings." More specifically, motivated by naval searches for battery-powered \r\nflight data recorders of missing aircraft, we consider the trade-off between the frequency of pings for an underwater locator\r\nbeacon and the duration of the search. First, assuming the search speed is known, we formulate\r\na mathematical model to determine the pinging period that maximizes the probability that the\r\nsearcher detects the beacon before it stops pinging. Next, we consider generalizations to discrete\r\nsearch speed distributions under a uniform beacon location distribution. Lastly, we present a case\r\nstudy based on the search for Malaysia Airlines Flight 370 that suggests the industry-standard\r\nbeacon pinging period---roughly one second between pings---is too short.},\r\n  title={Optimal pinging frequencies in the search for an immobile beacon},\r\n  author={David Eckman and Lisa Maillart and Andrew Schaefer},\r\n  journal={IIE Transactions},\r\n  volume={48},\r\n  number={6},\r\n  pages={489-500},\r\n  year={2016},\r\n  publisher={Taylor \\& Francis},\r\n  url_Paper={mypdfs/Eckman-Maillart-Schaefer-2016.pdf},\r\n  url_Slides={mypdfs/Optimal-pinging-slides.pdf}\r\n}\r\n\r\n
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\n We consider a search for an immobile object that can only be detected if the searcher is within a given range of the object during one of a finite number of instantaneous detection opportunities, i.e., \"pings.\" More specifically, motivated by naval searches for battery-powered flight data recorders of missing aircraft, we consider the trade-off between the frequency of pings for an underwater locator beacon and the duration of the search. First, assuming the search speed is known, we formulate a mathematical model to determine the pinging period that maximizes the probability that the searcher detects the beacon before it stops pinging. Next, we consider generalizations to discrete search speed distributions under a uniform beacon location distribution. Lastly, we present a case study based on the search for Malaysia Airlines Flight 370 that suggests the industry-standard beacon pinging period–-roughly one second between pings–-is too short.\n
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\n \n\n \n \n \n \n Sensitivity analysis of an ICU simulation model.\n \n\n\n \n Bountourelis, T.; Eckman, D.; Luangkesorn, L.; Schaefer, A.; Nabors, S. G.; and Clermont, G.\n \n\n\n \n\n\n\n In C. Laroque, J. H.; and Uhrmacher, A. M., editor(s), Proceedings of the 2012 Winter Simulation Conference, pages 931-942, 2012. IEEE\n \n\n\n\n
\n\n\n \n \n \n \"Sensitivity paper\n  \n \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
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@inproceedings{BountourelisEtal2012,\r\n  abstract={The modeling and simulation of inpatient healthcare systems comprising of multiple interconnected units\r\nof monitored care is a challenging task given the nature of clinical practices and procedures that regulate\r\npatient flow. Therefore, any related study on the properties of patient flow should (i) explicitly consider the\r\nmodeling of patient movement rules in face of congestion, and (ii) examine the sensitivity of simulation\r\noutput, expressed by patient delays and diversions, over different patient movement modeling approaches.\r\nIn this work, we use a high fidelity simulation model of a tertiary facility that can incorporate complex\r\npatient movement rules to investigate the challenges inherent in its employment for resource allocation\r\ntasks.},\r\n  title={Sensitivity analysis of an ICU simulation model},\r\n  author={Theologos Bountourelis and David Eckman and Louis Luangkesorn and Andrew Schaefer and Spencer G. Nabors and Gilles Clermont},\r\n  booktitle={Proceedings of the 2012 Winter Simulation Conference},\r\n  pages={931-942},\r\n  editor={C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher},\r\n  year={2012},\r\n  organization={IEEE},\r\n  url_Paper={mypdfs/Bountourelis-etal-2012.pdf}\r\n}\r\n\r\n
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\n The modeling and simulation of inpatient healthcare systems comprising of multiple interconnected units of monitored care is a challenging task given the nature of clinical practices and procedures that regulate patient flow. Therefore, any related study on the properties of patient flow should (i) explicitly consider the modeling of patient movement rules in face of congestion, and (ii) examine the sensitivity of simulation output, expressed by patient delays and diversions, over different patient movement modeling approaches. In this work, we use a high fidelity simulation model of a tertiary facility that can incorporate complex patient movement rules to investigate the challenges inherent in its employment for resource allocation tasks.\n
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