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\n  \n 2023\n \n \n (3)\n \n \n
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\n \n\n \n \n \n \n \n Genotype-Phenotype Landscapes for Immune-Pathogen Coevolution.\n \n \n \n\n\n \n Moulana, A.; Dupic, T.; Phillips, A.; and Desai, M.\n\n\n \n\n\n\n Trends in immunology, 44(5). May 2023.\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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@article{moulanaGenotypephenotypeLandscapesImmunepathogen2023,\n  title = {Genotype-Phenotype Landscapes for Immune-Pathogen Coevolution},\n  author = {Moulana, Alief and Dupic, Thomas and Phillips, Angela and Desai, Michael},\n  year = {2023},\n  month = may,\n  journal = {Trends in immunology},\n  volume = {44},\n  number = {5},\n  publisher = {{Trends Immunol}},\n  issn = {1471-4981},\n  doi = {10.1016/j.it.2023.03.006},\n  urldate = {2023-06-29},\n  abstract = {Our immune systems constantly coevolve with the pathogens that challenge them, as pathogens adapt to evade our defense responses, with our immune repertoires shifting in turn. These coevolutionary dynamics take place across a vast and high-dimensional landscape of potential pathogen and immune recep \\ldots},\n  langid = {english},\n  pmid = {37024340},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/P44FM6S5/A et al. - 2023 - Genotype-phenotype landscapes for immune-pathogen .pdf;/home/thomas/snap/zotero-snap/common/Zotero/storage/6SXBA4V7/37024340.html}\n}\n\n
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\n Our immune systems constantly coevolve with the pathogens that challenge them, as pathogens adapt to evade our defense responses, with our immune repertoires shifting in turn. These coevolutionary dynamics take place across a vast and high-dimensional landscape of potential pathogen and immune recep …\n
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\n \n\n \n \n \n \n \n The Landscape of Antibody Binding Affinity in SARS-CoV-2 Omicron BA.1 Evolution.\n \n \n \n\n\n \n Moulana, A.; Dupic, T.; Phillips, A. M; Chang, J.; Roffler, A. A; Greaney, A. J; Starr, T. N; Bloom, J. D; and Desai, M. M\n\n\n \n\n\n\n eLife, 12: e83442. February 2023.\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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@article{moulanaLandscapeAntibodyBinding2023,\n  title = {The Landscape of Antibody Binding Affinity in {{SARS-CoV-2 Omicron BA}}.1 Evolution},\n  author = {Moulana, Alief and Dupic, Thomas and Phillips, Angela M and Chang, Jeffrey and Roffler, Anne A and Greaney, Allison J and Starr, Tyler N and Bloom, Jesse D and Desai, Michael M},\n  editor = {{van der Meer}, Jos W},\n  year = {2023},\n  month = feb,\n  journal = {eLife},\n  volume = {12},\n  pages = {e83442},\n  publisher = {{eLife Sciences Publications, Ltd}},\n  issn = {2050-084X},\n  doi = {10.7554/eLife.83442},\n  urldate = {2023-06-28},\n  abstract = {The Omicron BA.1 variant of SARS-CoV-2 escapes convalescent sera and monoclonal antibodies that are effective against earlier strains of the virus. This immune evasion is largely a consequence of mutations in the BA.1 receptor binding domain (RBD), the major antigenic target of SARS-CoV-2. Previous studies have identified several key RBD mutations leading to escape from most antibodies. However, little is known about how these escape mutations interact with each other and with other mutations in the RBD. Here, we systematically map these interactions by measuring the binding affinity of all possible combinations of these 15 RBD mutations (215=32,768 genotypes) to 4 monoclonal antibodies (LY-CoV016, LY-CoV555, REGN10987, and S309) with distinct epitopes. We find that BA.1 can lose affinity to diverse antibodies by acquiring a few large-effect mutations and can reduce affinity to others through several small-effect mutations. However, our results also reveal alternative pathways to antibody escape that does not include every large-effect mutation. Moreover, epistatic interactions are shown to constrain affinity decline in S309 but only modestly shape the affinity landscapes of other antibodies. Together with previous work on the ACE2 affinity landscape, our results suggest that the escape of each antibody is mediated by distinct groups of mutations, whose deleterious effects on ACE2 affinity are compensated by another distinct group of mutations (most notably Q498R and N501Y).},\n  keywords = {antibody escape,fitness landscape,immune evasion,omicron variant,SARS-CoV-2},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/4DEEP2HA/Moulana et al. - 2023 - The landscape of antibody binding affinity in SARS.pdf}\n}\n\n
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\n The Omicron BA.1 variant of SARS-CoV-2 escapes convalescent sera and monoclonal antibodies that are effective against earlier strains of the virus. This immune evasion is largely a consequence of mutations in the BA.1 receptor binding domain (RBD), the major antigenic target of SARS-CoV-2. Previous studies have identified several key RBD mutations leading to escape from most antibodies. However, little is known about how these escape mutations interact with each other and with other mutations in the RBD. Here, we systematically map these interactions by measuring the binding affinity of all possible combinations of these 15 RBD mutations (215=32,768 genotypes) to 4 monoclonal antibodies (LY-CoV016, LY-CoV555, REGN10987, and S309) with distinct epitopes. We find that BA.1 can lose affinity to diverse antibodies by acquiring a few large-effect mutations and can reduce affinity to others through several small-effect mutations. However, our results also reveal alternative pathways to antibody escape that does not include every large-effect mutation. Moreover, epistatic interactions are shown to constrain affinity decline in S309 but only modestly shape the affinity landscapes of other antibodies. Together with previous work on the ACE2 affinity landscape, our results suggest that the escape of each antibody is mediated by distinct groups of mutations, whose deleterious effects on ACE2 affinity are compensated by another distinct group of mutations (most notably Q498R and N501Y).\n
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\n \n\n \n \n \n \n \n Hierarchical Sequence-Affinity Landscapes Shape the Evolution of Breadth in an Anti-Influenza Receptor Binding Site Antibody.\n \n \n \n\n\n \n Phillips, A. M; Maurer, D. P; Brooks, C.; Dupic, T.; Schmidt, A. G; and Desai, M. M\n\n\n \n\n\n\n eLife, 12: e83628. January 2023.\n \n\n\n\n
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@article{phillipsHierarchicalSequenceaffinityLandscapes2023a,\n  title = {Hierarchical Sequence-Affinity Landscapes Shape the Evolution of Breadth in an Anti-Influenza Receptor Binding Site Antibody},\n  author = {Phillips, Angela M and Maurer, Daniel P and Brooks, Caelan and Dupic, Thomas and Schmidt, Aaron G and Desai, Michael M},\n  editor = {Kurosaki, Tomohiro and Diamond, Betty},\n  year = {2023},\n  month = jan,\n  journal = {eLife},\n  volume = {12},\n  pages = {e83628},\n  publisher = {{eLife Sciences Publications, Ltd}},\n  issn = {2050-084X},\n  doi = {10.7554/eLife.83628},\n  urldate = {2023-06-29},\n  abstract = {Broadly neutralizing antibodies (bnAbs) that neutralize diverse variants of a particular virus are of considerable therapeutic interest. Recent advances have enabled us to isolate and engineer these antibodies as therapeutics, but eliciting them through vaccination remains challenging, in part due to our limited understanding of how antibodies evolve breadth. Here, we analyze the landscape by which an anti-influenza receptor binding site (RBS) bnAb, CH65, evolved broad affinity to diverse H1 influenza strains. We do this by generating an antibody library of all possible evolutionary intermediates between the unmutated common ancestor (UCA) and the affinity-matured CH65 antibody and measure the affinity of each intermediate to three distinct H1 antigens. We find that affinity to each antigen requires a specific set of mutations \\textendash{} distributed across the variable light and heavy chains \\textendash{} that interact non-additively (i.e., epistatically). These sets of mutations form a hierarchical pattern across the antigens, with increasingly divergent antigens requiring additional epistatic mutations beyond those required to bind less divergent antigens. We investigate the underlying biochemical and structural basis for these hierarchical sets of epistatic mutations and find that epistasis between heavy chain mutations and a mutation in the light chain at the VH-VL interface is essential for binding a divergent H1. Collectively, this is the first work to comprehensively characterize epistasis between heavy and light chain mutations and shows that such interactions are both strong and widespread. Together with our previous study analyzing a different class of anti-influenza antibodies, our results implicate epistasis as a general feature of antibody sequence-affinity landscapes that can potentiate and constrain the evolution of breadth.},\n  keywords = {antibody,breadth,epistasis,evolution,influenza},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/JEP5F2P5/Phillips et al. - 2023 - Hierarchical sequence-affinity landscapes shape th.pdf}\n}\n\n
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\n Broadly neutralizing antibodies (bnAbs) that neutralize diverse variants of a particular virus are of considerable therapeutic interest. Recent advances have enabled us to isolate and engineer these antibodies as therapeutics, but eliciting them through vaccination remains challenging, in part due to our limited understanding of how antibodies evolve breadth. Here, we analyze the landscape by which an anti-influenza receptor binding site (RBS) bnAb, CH65, evolved broad affinity to diverse H1 influenza strains. We do this by generating an antibody library of all possible evolutionary intermediates between the unmutated common ancestor (UCA) and the affinity-matured CH65 antibody and measure the affinity of each intermediate to three distinct H1 antigens. We find that affinity to each antigen requires a specific set of mutations – distributed across the variable light and heavy chains – that interact non-additively (i.e., epistatically). These sets of mutations form a hierarchical pattern across the antigens, with increasingly divergent antigens requiring additional epistatic mutations beyond those required to bind less divergent antigens. We investigate the underlying biochemical and structural basis for these hierarchical sets of epistatic mutations and find that epistasis between heavy chain mutations and a mutation in the light chain at the VH-VL interface is essential for binding a divergent H1. Collectively, this is the first work to comprehensively characterize epistasis between heavy and light chain mutations and shows that such interactions are both strong and widespread. Together with our previous study analyzing a different class of anti-influenza antibodies, our results implicate epistasis as a general feature of antibody sequence-affinity landscapes that can potentiate and constrain the evolution of breadth.\n
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\n  \n 2022\n \n \n (2)\n \n \n
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\n \n\n \n \n \n \n \n Compensatory Epistasis Maintains ACE2 Affinity in SARS-CoV-2 Omicron BA.1.\n \n \n \n\n\n \n Moulana, A.; Dupic, T.; Phillips, A. M.; Chang, J.; Nieves, S.; Roffler, A. A.; Greaney, A. J.; Starr, T. N.; Bloom, J. D.; and Desai, M. M.\n\n\n \n\n\n\n Nature Communications, 13(1): 7011. November 2022.\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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@article{moulanaCompensatoryEpistasisMaintains2022,\n  title = {Compensatory Epistasis Maintains {{ACE2}} Affinity in {{SARS-CoV-2 Omicron BA}}.1},\n  author = {Moulana, Alief and Dupic, Thomas and Phillips, Angela M. and Chang, Jeffrey and Nieves, Serafina and Roffler, Anne A. and Greaney, Allison J. and Starr, Tyler N. and Bloom, Jesse D. and Desai, Michael M.},\n  year = {2022},\n  month = nov,\n  journal = {Nature Communications},\n  volume = {13},\n  number = {1},\n  pages = {7011},\n  publisher = {{Nature Publishing Group}},\n  issn = {2041-1723},\n  doi = {10.1038/s41467-022-34506-z},\n  urldate = {2023-06-28},\n  abstract = {The Omicron BA.1 variant emerged in late 2021 and quickly spread across the world. Compared to the earlier SARS-CoV-2 variants, BA.1 has many mutations, some of which are known to enable antibody escape. Many of these antibody-escape mutations individually decrease the spike receptor-binding domain (RBD) affinity for ACE2, but BA.1 still binds ACE2 with high affinity. The fitness and evolution of the BA.1 lineage is therefore driven by the combined effects of numerous mutations. Here, we systematically map the epistatic interactions between the 15 mutations in the RBD of BA.1 relative to the Wuhan Hu-1 strain. Specifically, we measure the ACE2 affinity of all possible combinations of these 15 mutations (215\\,=\\,32,768 genotypes), spanning all possible evolutionary intermediates from the ancestral Wuhan Hu-1 strain to BA.1. We find that immune escape mutations in BA.1 individually reduce ACE2 affinity but are compensated by epistatic interactions with other affinity-enhancing mutations, including Q498R and N501Y. Thus, the ability of BA.1 to evade immunity while maintaining ACE2 affinity is contingent on acquiring multiple interacting mutations. Our results implicate compensatory epistasis as a key factor driving substantial evolutionary change for SARS-CoV-2 and are consistent with Omicron BA.1 arising from a chronic infection.},\n  copyright = {2022 The Author(s)},\n  langid = {english},\n  keywords = {Evolutionary biology,SARS-CoV-2,Viral evolution,Virus\\textendash host interactions},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/QJ3N4CIY/Moulana et al. - 2022 - Compensatory epistasis maintains ACE2 affinity in .pdf}\n}\n\n
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\n The Omicron BA.1 variant emerged in late 2021 and quickly spread across the world. Compared to the earlier SARS-CoV-2 variants, BA.1 has many mutations, some of which are known to enable antibody escape. Many of these antibody-escape mutations individually decrease the spike receptor-binding domain (RBD) affinity for ACE2, but BA.1 still binds ACE2 with high affinity. The fitness and evolution of the BA.1 lineage is therefore driven by the combined effects of numerous mutations. Here, we systematically map the epistatic interactions between the 15 mutations in the RBD of BA.1 relative to the Wuhan Hu-1 strain. Specifically, we measure the ACE2 affinity of all possible combinations of these 15 mutations (215\\,=\\,32,768 genotypes), spanning all possible evolutionary intermediates from the ancestral Wuhan Hu-1 strain to BA.1. We find that immune escape mutations in BA.1 individually reduce ACE2 affinity but are compensated by epistatic interactions with other affinity-enhancing mutations, including Q498R and N501Y. Thus, the ability of BA.1 to evade immunity while maintaining ACE2 affinity is contingent on acquiring multiple interacting mutations. Our results implicate compensatory epistasis as a key factor driving substantial evolutionary change for SARS-CoV-2 and are consistent with Omicron BA.1 arising from a chronic infection.\n
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\n \n\n \n \n \n \n \n Combining Mutation and Recombination Statistics to Infer Clonal Families in Antibody Repertoires.\n \n \n \n\n\n \n Spisak, N.; Dupic, T.; Mora, T.; and Walczak, A. M.\n\n\n \n\n\n\n December 2022.\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
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@misc{spisakCombiningMutationRecombination2022,\n  title = {Combining Mutation and Recombination Statistics to Infer Clonal Families in Antibody Repertoires},\n  author = {Spisak, Natanael and Dupic, Thomas and Mora, Thierry and Walczak, Aleksandra M.},\n  year = 2022,\n  month = dec,\n  number = {arXiv:2212.11997},\n  eprint = {2212.11997},\n  primaryclass = {q-bio},\n  publisher = {{arXiv}},\n  doi = {10.48550/arXiv.2212.11997},\n  urldate = {2023-06-29},\n  abstract = {B-cell repertoires are characterized by a diverse set of receptors of distinct specificities generated through two processes of somatic diversification: V(D)J recombination and somatic hypermutations. B cell clonal families stem from the same V(D)J recombination event, but differ in their hypermutations. Clonal families identification is key to understanding B-cell repertoire function, evolution and dynamics. We present HILARy (High-precision Inference of Lineages in Antibody Repertoires), an efficient, fast and precise method to identify clonal families from high-throughput sequencing datasets. HILARy combines probabilistic models that capture the receptor generation and selection statistics with adapted clustering methods to achieve consistently high inference accuracy. It automatically leverages the phylogenetic signal of shared mutations in difficult repertoire subsets. Exploiting the high sensitivity of the method, we find the statistics of evolutionary properties such as the site frequency spectrum and dN/dS ratio do not depend on the junction length. We also identify a broad range of selection pressures scanning two orders of magnitude.},\n  archiveprefix = {arxiv},\n  keywords = {Quantitative Biology - Genomics,Quantitative Biology - Populations and Evolution},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/NJFWR4XN/Spisak et al. - 2022 - Combining mutation and recombination statistics to.pdf;/home/thomas/snap/zotero-snap/common/Zotero/storage/PPF7ZQYF/2212.html}\n}\n
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\n B-cell repertoires are characterized by a diverse set of receptors of distinct specificities generated through two processes of somatic diversification: V(D)J recombination and somatic hypermutations. B cell clonal families stem from the same V(D)J recombination event, but differ in their hypermutations. Clonal families identification is key to understanding B-cell repertoire function, evolution and dynamics. We present HILARy (High-precision Inference of Lineages in Antibody Repertoires), an efficient, fast and precise method to identify clonal families from high-throughput sequencing datasets. HILARy combines probabilistic models that capture the receptor generation and selection statistics with adapted clustering methods to achieve consistently high inference accuracy. It automatically leverages the phylogenetic signal of shared mutations in difficult repertoire subsets. Exploiting the high sensitivity of the method, we find the statistics of evolutionary properties such as the site frequency spectrum and dN/dS ratio do not depend on the junction length. We also identify a broad range of selection pressures scanning two orders of magnitude.\n
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\n \n\n \n \n \n \n \n Immune Fingerprinting through Repertoire Similarity.\n \n \n \n\n\n \n Dupic, T.; Bensouda Koraichi, M.; Minervina, A. A.; Pogorelyy, M. V.; Mora, T.; and Walczak, A. M.\n\n\n \n\n\n\n PLoS genetics, 17(1): e1009301. January 2021.\n \n\n\n\n
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@article{dupicImmuneFingerprintingRepertoire2021,\n  title = {Immune Fingerprinting through Repertoire Similarity},\n  author = {Dupic, Thomas and Bensouda Koraichi, Meriem and Minervina, Anastasia A. and Pogorelyy, Mikhail V. and Mora, Thierry and Walczak, Aleksandra M.},\n  year = {2021},\n  month = jan,\n  journal = {PLoS genetics},\n  volume = {17},\n  number = {1},\n  pages = {e1009301},\n  issn = {1553-7404},\n  doi = {10.1371/journal.pgen.1009301},\n  abstract = {Immune repertoires provide a unique fingerprint reflecting the immune history of individuals, with potential applications in precision medicine. However, the question of how personal that information is and how it can be used to identify individuals has not been explored. Here, we show that individuals can be uniquely identified from repertoires of just a few thousands lymphocytes. We present "Immprint," a classifier using an information-theoretic measure of repertoire similarity to distinguish pairs of repertoire samples coming from the same versus different individuals. Using published T-cell receptor repertoires and statistical modeling, we tested its ability to identify individuals with great accuracy, including identical twins, by computing false positive and false negative rates {$<$} 10-6 from samples composed of 10,000 T-cells. We verified through longitudinal datasets that the method is robust to acute infections and that the immune fingerprint is stable for at least three years. These results emphasize the private and personal nature of repertoire data.},\n  langid = {english},\n  pmcid = {PMC7808657},\n  pmid = {33395405},\n  keywords = {CD4-Positive T-Lymphocytes,Humans,Immune System,Lymphocytes,{Models, Statistical},Precision Medicine,{Receptors, Antigen, T-Cell},{Twins, Monozygotic}},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/MYU9I5YF/Dupic et al. - 2021 - Immune fingerprinting through repertoire similarit.pdf}\n}\n\n
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\n Immune repertoires provide a unique fingerprint reflecting the immune history of individuals, with potential applications in precision medicine. However, the question of how personal that information is and how it can be used to identify individuals has not been explored. Here, we show that individuals can be uniquely identified from repertoires of just a few thousands lymphocytes. We present \"Immprint,\" a classifier using an information-theoretic measure of repertoire similarity to distinguish pairs of repertoire samples coming from the same versus different individuals. Using published T-cell receptor repertoires and statistical modeling, we tested its ability to identify individuals with great accuracy, including identical twins, by computing false positive and false negative rates $<$ 10-6 from samples composed of 10,000 T-cells. We verified through longitudinal datasets that the method is robust to acute infections and that the immune fingerprint is stable for at least three years. These results emphasize the private and personal nature of repertoire data.\n
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\n \n\n \n \n \n \n \n Contribution of Resident and Circulating Precursors to Tumor-Infiltrating CD8+ T Cell Populations in Lung Cancer.\n \n \n \n\n\n \n Gueguen, P.; Metoikidou, C.; Dupic, T.; Lawand, M.; Goudot, C.; Baulande, S.; Lameiras, S.; Lantz, O.; Girard, N.; Seguin-Givelet, A.; Lefevre, M.; Mora, T.; Walczak, A. M.; Waterfall, J. J.; and Amigorena, S.\n\n\n \n\n\n\n Science Immunology, 6(55): eabd5778. January 2021.\n \n\n\n\n
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@article{gueguenContributionResidentCirculating2021,\n  title = {Contribution of Resident and Circulating Precursors to Tumor-Infiltrating {{CD8}}+ {{T}} Cell Populations in Lung Cancer},\n  author = {Gueguen, Paul and Metoikidou, Christina and Dupic, Thomas and Lawand, Myriam and Goudot, Christel and Baulande, Sylvain and Lameiras, Sonia and Lantz, Olivier and Girard, Nicolas and {Seguin-Givelet}, Agathe and Lefevre, Marine and Mora, Thierry and Walczak, Aleksandra M. and Waterfall, Joshua J. and Amigorena, Sebastian},\n  year = {2021},\n  month = jan,\n  journal = {Science Immunology},\n  volume = {6},\n  number = {55},\n  pages = {eabd5778},\n  issn = {2470-9468},\n  doi = {10.1126/sciimmunol.abd5778},\n  abstract = {Tumor-infiltrating lymphocytes (TILs), in general, and especially CD8+ TILs, represent a favorable prognostic factor in non-small cell lung cancer (NSCLC). The tissue origin, regenerative capacities, and differentiation pathways of TIL subpopulations remain poorly understood. Using a combination of single-cell RNA and T cell receptor (TCR) sequencing, we investigate the functional organization of TIL populations in primary NSCLC. We identify two CD8+ TIL subpopulations expressing memory-like gene modules: one is also present in blood (circulating precursors) and the other one in juxtatumor tissue (tissue-resident precursors). In tumors, these two precursor populations converge through a unique transitional state into terminally differentiated cells, often referred to as dysfunctional or exhausted. Differentiation is associated with TCR expansion, and transition from precursor to late-differentiated states correlates with intratumor T cell cycling. These results provide a coherent working model for TIL origin, ontogeny, and functional organization in primary NSCLC.},\n  langid = {english},\n  pmid = {33514641},\n  keywords = {{Carcinoma, Non-Small-Cell Lung},CD8-Positive T-Lymphocytes,Cell Differentiation,Female,Humans,Lung,Lung Neoplasms,{Lymphocytes, Tumor-Infiltrating},Male,Pneumonectomy,Tumor Microenvironment},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/6DY7NCDE/Gueguen et al. - 2021 - Contribution of resident and circulating precursor.pdf}\n}\n\n
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\n Tumor-infiltrating lymphocytes (TILs), in general, and especially CD8+ TILs, represent a favorable prognostic factor in non-small cell lung cancer (NSCLC). The tissue origin, regenerative capacities, and differentiation pathways of TIL subpopulations remain poorly understood. Using a combination of single-cell RNA and T cell receptor (TCR) sequencing, we investigate the functional organization of TIL populations in primary NSCLC. We identify two CD8+ TIL subpopulations expressing memory-like gene modules: one is also present in blood (circulating precursors) and the other one in juxtatumor tissue (tissue-resident precursors). In tumors, these two precursor populations converge through a unique transitional state into terminally differentiated cells, often referred to as dysfunctional or exhausted. Differentiation is associated with TCR expansion, and transition from precursor to late-differentiated states correlates with intratumor T cell cycling. These results provide a coherent working model for TIL origin, ontogeny, and functional organization in primary NSCLC.\n
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\n \n\n \n \n \n \n \n Binding Affinity Landscapes Constrain the Evolution of Broadly Neutralizing Anti-Influenza Antibodies.\n \n \n \n\n\n \n Phillips, A. M; Lawrence, K. R; Moulana, A.; Dupic, T.; Chang, J.; Johnson, M. S; Cvijovic, I.; Mora, T.; Walczak, A. M; and Desai, M. M\n\n\n \n\n\n\n eLife, 10: e71393. September 2021.\n \n\n\n\n
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@article{phillipsBindingAffinityLandscapes2021,\n  title = {Binding Affinity Landscapes Constrain the Evolution of Broadly Neutralizing Anti-Influenza Antibodies},\n  author = {Phillips, Angela M and Lawrence, Katherine R and Moulana, Alief and Dupic, Thomas and Chang, Jeffrey and Johnson, Milo S and Cvijovic, Ivana and Mora, Thierry and Walczak, Aleksandra M and Desai, Michael M},\n  editor = {Fleishman, Sarel Jacob and Rath, Satyajit and Bloom, Jesse D and Wu, Nicholas C},\n  year = {2021},\n  month = sep,\n  journal = {eLife},\n  volume = {10},\n  pages = {e71393},\n  publisher = {{eLife Sciences Publications, Ltd}},\n  issn = {2050-084X},\n  doi = {10.7554/eLife.71393},\n  urldate = {2023-06-28},\n  abstract = {Over the past two decades, several broadly neutralizing antibodies (bnAbs) that confer protection against diverse influenza strains have been isolated. Structural and biochemical characterization of these bnAbs has provided molecular insight into how they bind distinct antigens. However, our understanding of the evolutionary pathways leading to bnAbs, and thus how best to elicit them, remains limited. Here, we measure equilibrium dissociation constants of combinatorially complete mutational libraries for two naturally isolated influenza bnAbs (CR9114, 16 heavy-chain mutations; CR6261, 11 heavy-chain mutations), reconstructing all possible evolutionary intermediates back to the unmutated germline sequences. We find that these two libraries exhibit strikingly different patterns of breadth: while many variants of CR6261 display moderate affinity to diverse antigens, those of CR9114 display appreciable affinity only in specific, nested combinations. By examining the extensive pairwise and higher order epistasis between mutations, we find key sites with strong synergistic interactions that are highly similar across antigens for CR6261 and different for CR9114. Together, these features of the binding affinity landscapes strongly favor sequential acquisition of affinity to diverse antigens for CR9114, while the acquisition of breadth to more similar antigens for CR6261 is less constrained. These results, if generalizable to other bnAbs, may explain the molecular basis for the widespread observation that sequential exposure favors greater breadth, and such mechanistic insight will be essential for predicting and eliciting broadly protective immune responses.},\n  keywords = {antibody,breadth,epistasis,evolution,influenza,landscape},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/BWSQVPAS/Phillips et al. - 2021 - Binding affinity landscapes constrain the evolutio.pdf}\n}\n\n
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\n Over the past two decades, several broadly neutralizing antibodies (bnAbs) that confer protection against diverse influenza strains have been isolated. Structural and biochemical characterization of these bnAbs has provided molecular insight into how they bind distinct antigens. However, our understanding of the evolutionary pathways leading to bnAbs, and thus how best to elicit them, remains limited. Here, we measure equilibrium dissociation constants of combinatorially complete mutational libraries for two naturally isolated influenza bnAbs (CR9114, 16 heavy-chain mutations; CR6261, 11 heavy-chain mutations), reconstructing all possible evolutionary intermediates back to the unmutated germline sequences. We find that these two libraries exhibit strikingly different patterns of breadth: while many variants of CR6261 display moderate affinity to diverse antigens, those of CR9114 display appreciable affinity only in specific, nested combinations. By examining the extensive pairwise and higher order epistasis between mutations, we find key sites with strong synergistic interactions that are highly similar across antigens for CR6261 and different for CR9114. Together, these features of the binding affinity landscapes strongly favor sequential acquisition of affinity to diverse antigens for CR9114, while the acquisition of breadth to more similar antigens for CR6261 is less constrained. These results, if generalizable to other bnAbs, may explain the molecular basis for the widespread observation that sequential exposure favors greater breadth, and such mechanistic insight will be essential for predicting and eliciting broadly protective immune responses.\n
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\n  \n 2020\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n Population Variability in the Generation and Selection of T-cell Repertoires.\n \n \n \n\n\n \n Sethna, Z.; Isacchini, G.; Dupic, T.; Mora, T.; Walczak, A. M.; and Elhanati, Y.\n\n\n \n\n\n\n PLoS computational biology, 16(12): e1008394. December 2020.\n \n\n\n\n
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@article{sethnaPopulationVariabilityGeneration2020a,\n  title = {Population Variability in the Generation and Selection of {{T-cell}} Repertoires},\n  author = {Sethna, Zachary and Isacchini, Giulio and Dupic, Thomas and Mora, Thierry and Walczak, Aleksandra M. and Elhanati, Yuval},\n  year = {2020},\n  month = dec,\n  journal = {PLoS computational biology},\n  volume = {16},\n  number = {12},\n  pages = {e1008394},\n  issn = {1553-7358},\n  doi = {10.1371/journal.pcbi.1008394},\n  abstract = {The diversity of T-cell receptor (TCR) repertoires is achieved by a combination of two intrinsically stochastic steps: random receptor generation by VDJ recombination, and selection based on the recognition of random self-peptides presented on the major histocompatibility complex. These processes lead to a large receptor variability within and between individuals. However, the characterization of the variability is hampered by the limited size of the sampled repertoires. We introduce a new software tool SONIA to facilitate inference of individual-specific computational models for the generation and selection of the TCR beta chain (TRB) from sequenced repertoires of 651 individuals, separating and quantifying the variability of the two processes of generation and selection in the population. We find not only that most of the variability is driven by the VDJ generation process, but there is a large degree of consistency between individuals with the inter-individual variance of repertoires being about {$\\sim$}2\\% of the intra-individual variance. Known viral-specific TCRs follow the same generation and selection statistics as all TCRs.},\n  langid = {english},\n  pmcid = {PMC7725366},\n  pmid = {33296360},\n  keywords = {Adaptive Immunity,Humans,{Receptors, Antigen, T-Cell, alpha-beta},T-Lymphocytes,V(D)J Recombination},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/H7T2C5GY/Sethna et al. - 2020 - Population variability in the generation and selec.pdf}\n}\n\n
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\n The diversity of T-cell receptor (TCR) repertoires is achieved by a combination of two intrinsically stochastic steps: random receptor generation by VDJ recombination, and selection based on the recognition of random self-peptides presented on the major histocompatibility complex. These processes lead to a large receptor variability within and between individuals. However, the characterization of the variability is hampered by the limited size of the sampled repertoires. We introduce a new software tool SONIA to facilitate inference of individual-specific computational models for the generation and selection of the TCR beta chain (TRB) from sequenced repertoires of 651 individuals, separating and quantifying the variability of the two processes of generation and selection in the population. We find not only that most of the variability is driven by the VDJ generation process, but there is a large degree of consistency between individuals with the inter-individual variance of repertoires being about $∼$2% of the intra-individual variance. Known viral-specific TCRs follow the same generation and selection statistics as all TCRs.\n
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\n  \n 2019\n \n \n (3)\n \n \n
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\n \n\n \n \n \n \n \n Genesis of the $αβ$ T-cell Receptor.\n \n \n \n\n\n \n Dupic, T.; Marcou, Q.; Walczak, A. M.; and Mora, T.\n\n\n \n\n\n\n PLOS Computational Biology, 15(3): e1006874. March 2019.\n \n\n\n\n
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@article{dupicGenesisAvTcell2019,\n  title = {Genesis of the {$\\alpha\\beta$} {{T-cell}} Receptor},\n  author = {Dupic, Thomas and Marcou, Quentin and Walczak, Aleksandra M. and Mora, Thierry},\n  year = {2019},\n  month = mar,\n  journal = {PLOS Computational Biology},\n  volume = {15},\n  number = {3},\n  pages = {e1006874},\n  issn = {1553-7358},\n  doi = {10.1371/journal.pcbi.1006874},\n  urldate = {2019-08-08},\n  abstract = {The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called {$\\alpha$} and {$\\beta$}, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human TCR repertoires, we quantitively characterize the {$\\alpha\\beta$} generation process. We estimate the probabilities of a rescue recombination of the {$\\beta$} chain on the second chromosome upon failure or success on the first chromosome. Unlike {$\\beta$} chains, {$\\alpha$} chains recombine simultaneously on both chromosomes, resulting in correlated statistics of the two genes which we predict using a mechanistic model. We find that {$\\sim$}35\\% of cells express both {$\\alpha$} chains. Altogether, our statistical analysis gives a complete quantitative mechanistic picture that results in the observed correlations in the generative process. We learn that the probability to generate any TCR{$\\alpha\\beta$} is lower than 10-12 and estimate the generation diversity and sharing properties of the {$\\alpha\\beta$} TCR repertoire.},\n  langid = {english},\n  keywords = {Chromosome structure and function,Chromosomes,Cloning,DNA sequence analysis,Nucleotide sequencing,Sequence analysis,T cell receptors,T cells},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/KIME36YP/Dupic et al. - 2019 - Genesis of the αβ T-cell receptor.pdf;/home/thomas/snap/zotero-snap/common/Zotero/storage/B2SX53MF/article.html}\n}\n\n
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\n The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called $α$ and $β$, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human TCR repertoires, we quantitively characterize the $αβ$ generation process. We estimate the probabilities of a rescue recombination of the $β$ chain on the second chromosome upon failure or success on the first chromosome. Unlike $β$ chains, $α$ chains recombine simultaneously on both chromosomes, resulting in correlated statistics of the two genes which we predict using a mechanistic model. We find that $∼$35% of cells express both $α$ chains. Altogether, our statistical analysis gives a complete quantitative mechanistic picture that results in the observed correlations in the generative process. We learn that the probability to generate any TCR$αβ$ is lower than 10-12 and estimate the generation diversity and sharing properties of the $αβ$ TCR repertoire.\n
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\n \n\n \n \n \n \n \n The Imaginary Toda Field Theory.\n \n \n \n\n\n \n Dupic, T.; Estienne, B.; and Ikhlef, Y.\n\n\n \n\n\n\n Journal of Physics A: Mathematical and Theoretical, 52(10): 105201. February 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
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@article{dupicImaginaryTodaField2019,\n  title = {The Imaginary {{Toda}} Field Theory},\n  author = {Dupic, T. and Estienne, B. and Ikhlef, Y.},\n  year = {2019},\n  month = feb,\n  journal = {Journal of Physics A: Mathematical and Theoretical},\n  volume = {52},\n  number = {10},\n  pages = {105201},\n  issn = {1751-8121},\n  doi = {10.1088/1751-8121/aafeaa},\n  urldate = {2019-08-08},\n  abstract = {We consider the two-dimensional quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry (W n algebra), a central charge and a continuous spectrum. Using the conformal bootstrap, we compute structure constants involving two arbitrary scalar fields and a semi-degenerate field of Wyllard type. The solution obtained is not the analytic continuation of the usual Toda three-point function. Non-scalar primary fields and their three-point functions are also discussed. Non-scalar primary fields are classified by conjugacy classes of the permutation group , and their structure constants are computed explicitly, up to an overall factor.},\n  langid = {english},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/PTID9HUA/Dupic et al. - 2019 - The imaginary Toda field theory.pdf}\n}\n\n
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\n We consider the two-dimensional quantum Toda field theory with an imaginary background charge. This conformal field theory has a higher spin symmetry (W n algebra), a central charge and a continuous spectrum. Using the conformal bootstrap, we compute structure constants involving two arbitrary scalar fields and a semi-degenerate field of Wyllard type. The solution obtained is not the analytic continuation of the usual Toda three-point function. Non-scalar primary fields and their three-point functions are also discussed. Non-scalar primary fields are classified by conjugacy classes of the permutation group , and their structure constants are computed explicitly, up to an overall factor.\n
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\n \n\n \n \n \n \n \n Three-Point Functions in the Fully Packed Loop Model on the Honeycomb Lattice.\n \n \n \n\n\n \n Dupic, T.; Estienne, B.; and Ikhlef, Y.\n\n\n \n\n\n\n Journal of Physics A: Mathematical and Theoretical, 52(20): 205003. April 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
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@article{dupicThreepointFunctionsFully2019,\n  title = {Three-Point Functions in the Fully Packed Loop Model on the Honeycomb Lattice},\n  author = {Dupic, T. and Estienne, B. and Ikhlef, Y.},\n  year = {2019},\n  month = apr,\n  journal = {Journal of Physics A: Mathematical and Theoretical},\n  volume = {52},\n  number = {20},\n  pages = {205003},\n  issn = {1751-8121},\n  doi = {10.1088/1751-8121/ab1725},\n  urldate = {2019-08-08},\n  abstract = {The fully-packed loop model on the honeycomb lattice is a critical model of non-intersecting polygons covering the full lattice, and was introduced by Reshetikhin (1991 J. Phys. A: Math. Gen. 24 2387). Using the two-component Coulomb-gas approach of Kondev et al (1996 J. Phys. A: Math. Gen. 29 6489), we argue that the scaling limit consists of two degrees of freedom: a field governed by the imaginary Liouville action, and a free boson. We introduce a family of three-point correlation functions which probe the imaginary Liouville component, and we use transfer-matrix numerical diagonalisation to compute finite-size estimates. We obtain good agreement with our analytical predictions for the universal amplitudes and spatial dependence of these correlation functions. Finally we conjecture that this relation between non-intersecting loop models and the imaginary Liouville theory is in fact quite generic. We give numerical evidence that this relation indeed holds for various loop models.},\n  langid = {english},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/MVHCVQU6/Dupic et al. - 2019 - Three-point functions in the fully packed loop mod.pdf}\n}\n\n
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\n The fully-packed loop model on the honeycomb lattice is a critical model of non-intersecting polygons covering the full lattice, and was introduced by Reshetikhin (1991 J. Phys. A: Math. Gen. 24 2387). Using the two-component Coulomb-gas approach of Kondev et al (1996 J. Phys. A: Math. Gen. 29 6489), we argue that the scaling limit consists of two degrees of freedom: a field governed by the imaginary Liouville action, and a free boson. We introduce a family of three-point correlation functions which probe the imaginary Liouville component, and we use transfer-matrix numerical diagonalisation to compute finite-size estimates. We obtain good agreement with our analytical predictions for the universal amplitudes and spatial dependence of these correlation functions. Finally we conjecture that this relation between non-intersecting loop models and the imaginary Liouville theory is in fact quite generic. We give numerical evidence that this relation indeed holds for various loop models.\n
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\n  \n 2018\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n Entanglement Entropies of Minimal Models from Null-Vectors.\n \n \n \n\n\n \n Dupic, T.; Estienne, B.; and Ikhlef, Y.\n\n\n \n\n\n\n SciPost Physics, 4(6): 031. June 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\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{dupicEntanglementEntropiesMinimal2018a,\n  title = {Entanglement Entropies of Minimal Models from Null-Vectors},\n  author = {Dupic, Thomas and Estienne, Benoit and Ikhlef, Yacine},\n  year = {2018},\n  month = jun,\n  journal = {SciPost Physics},\n  volume = {4},\n  number = {6},\n  pages = {031},\n  issn = {2542-4653},\n  doi = {10.21468/SciPostPhys.4.6.031},\n  urldate = {2019-08-08},\n  langid = {english},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/GJLFURSD/Dupic et al. - 2018 - Entanglement entropies of minimal models from null.pdf;/home/thomas/snap/zotero-snap/common/Zotero/storage/7M2KQQUR/SciPostPhys.4.6.html}\n}\n\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 \n The Fully Packed Loop Model as a Non-Rational W3 Conformal Field Theory.\n \n \n \n\n\n \n Dupic, T.; Estienne, B.; and Ikhlef, Y.\n\n\n \n\n\n\n Journal of Physics A: Mathematical and Theoretical, 49. June 2016.\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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@article{dupicFullyPackedLoop2016a,\n  title = {The Fully Packed Loop Model as a Non-Rational {{W3}} Conformal Field Theory},\n  author = {Dupic, Thomas and Estienne, Beno{\\^i}t and Ikhlef, Yacine},\n  year = {2016},\n  month = jun,\n  journal = {Journal of Physics A: Mathematical and Theoretical},\n  volume = {49},\n  doi = {10.1088/1751-8113/49/50/505202},\n  abstract = {The fully packed loop (FPL) model is a statistical model related to the integrable \\$U\\_q(\\textbackslash hat\\{\\textbackslash mathfrak\\{sl\\}\\}\\_3)\\$ vertex model. In this paper we study the continuum limit of the FPL. With the appropriate weight of non-contractible loops, we give evidence of an extended \\$W\\_3\\$ symmetry in the continuum. The partition function on the torus is calculated exactly, yielding new modular invariants of \\$W\\_3\\$ characters. The full CFT spectrum is obtained, and is found to be in excellent agreement with exact diagonalisation.},\n}\n\n
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\n The fully packed loop (FPL) model is a statistical model related to the integrable $U_q(\\ hat\\{\\ mathfrak\\{sl\\}\\}_3)$ vertex model. In this paper we study the continuum limit of the FPL. With the appropriate weight of non-contractible loops, we give evidence of an extended $W_3$ symmetry in the continuum. The partition function on the torus is calculated exactly, yielding new modular invariants of $W_3$ characters. The full CFT spectrum is obtained, and is found to be in excellent agreement with exact diagonalisation.\n
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\n  \n 2014\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n Reunion Probabilities of N One-Dimensional Random Walkers with Mixed Boundary Conditions.\n \n \n \n\n\n \n Castillo, I. P.; and Dupic, T.\n\n\n \n\n\n\n Journal of Statistical Physics, 156(3): 606–616. August 2014.\n \n\n\n\n
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@article{castilloReunionProbabilitiesOneDimensional2014,\n  title = {Reunion {{Probabilities}} of {{N One-Dimensional Random Walkers}} with {{Mixed Boundary Conditions}}},\n  author = {Castillo, Isaac P{\\'e}rez and Dupic, Thomas},\n  year = {2014},\n  month = aug,\n  journal = {Journal of Statistical Physics},\n  volume = {156},\n  number = {3},\n  pages = {606--616},\n  issn = {1572-9613},\n  doi = {10.1007/s10955-014-1017-8},\n  urldate = {2019-08-08},\n  abstract = {In this work we extend the results of the reunion probability of {$\\mathsl{N}$}NN one-dimensional random walkers to include mixed boundary conditions between their trajectories. The level of the mixture is controlled by a parameter {$\\mathsl{c}$}cc, which can be varied from {$\\mathsl{c}$}=0c=0c=0 (independent walkers) to {$\\mathsl{c}\\rightarrow\\infty$}c\\textrightarrow{$\\infty$}c\\textbackslash rightarrow \\textbackslash infty (vicious walkers). The expressions are derived by using Quantum Mechanics formalism (QMf) which allows us to map this problem into a Lieb-Liniger gas (LLg) of {$\\mathsl{N}$}NN one-dimensional particles. We use Bethe ansatz and Gaudin's conjecture to obtain the normalized wave-functions and use this information to construct the propagator. As it is well-known, depending on the boundary conditions imposed at the endpoints of a line segment, the statistics of the maximum heights of the reunited trajectories have some connections with different ensembles in Random Matrix Theory. Here we seek to extend those results and consider four models: absorbing, periodic, reflecting, and mixed. In all four cases, the probability that the maximum height is less or equal than {$\\mathsl{L}$}LL takes the form {$\\mathsl{F}\\mathsl{N}$}({$\\mathsl{L}$})={$\\mathsl{A}\\mathsl{N}\\sum\\mathsl{k}\\mathsl{k}\\in\\Omega$}Be-{$\\sum\\mathsl{N}\\mathsl{j}$}=1{$\\mathsl{k}$}2{$\\mathsl{j}$}{$\\mathsl{N}$}({$\\mathsl{k}\\mathsl{k}$})FN(L)=AN{$\\sum$}kk{$\\in\\Omega$}Be-{$\\sum$}j=1Nkj2VN(kk)F\\_N(L)=A\\_N\\textbackslash sum \\_\\{\\textbackslash varvec\\{k\\}\\textbackslash in \\textbackslash Omega \\_\\{\\textbackslash text \\{B\\}\\}\\} \\textbackslash mathrm\\{e\\}\\^\\{-\\textbackslash sum \\_\\{j=1\\}\\^Nk\\_j\\^2\\}\\textbackslash mathcal \\{V\\}\\_N(\\textbackslash varvec\\{k\\}), where {$\\mathsl{A}\\mathsl{N}$}ANA\\_N is a normalization constant, {$\\mathsl{N}$}({$\\mathsl{k}\\mathsl{k}$})VN(kk)\\textbackslash mathcal \\{V\\}\\_N(\\textbackslash varvec\\{k\\}) contains a deformed and weighted Vandermonde determinant, and {$\\Omega$}B{$\\Omega$}B\\textbackslash Omega \\_\\{\\textbackslash text \\{B\\}\\} is the solution set of quasi-momenta {$\\mathsl{k}\\mathsl{k}$}kk\\textbackslash varvec\\{k\\} obeying the Bethe equations for that particular boundary condition.},\n  langid = {english},\n  keywords = {Bethe ansatz,Random matrices,Random walkers,Vicious walkers},\n  file = {/home/thomas/snap/zotero-snap/common/Zotero/storage/74KJQQAY/Castillo and Dupic - 2014 - Reunion Probabilities of $$N$$NOne-Dimensional Ran.pdf}\n}\n\n
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\n In this work we extend the results of the reunion probability of $\\mathsl{N}$NN one-dimensional random walkers to include mixed boundary conditions between their trajectories. The level of the mixture is controlled by a parameter $\\mathsl{c}$cc, which can be varied from $\\mathsl{c}$=0c=0c=0 (independent walkers) to $\\mathsl{c}→∞$c\\textrightarrow$∞$c\\ rightarrow \\ infty (vicious walkers). The expressions are derived by using Quantum Mechanics formalism (QMf) which allows us to map this problem into a Lieb-Liniger gas (LLg) of $\\mathsl{N}$NN one-dimensional particles. We use Bethe ansatz and Gaudin's conjecture to obtain the normalized wave-functions and use this information to construct the propagator. As it is well-known, depending on the boundary conditions imposed at the endpoints of a line segment, the statistics of the maximum heights of the reunited trajectories have some connections with different ensembles in Random Matrix Theory. Here we seek to extend those results and consider four models: absorbing, periodic, reflecting, and mixed. In all four cases, the probability that the maximum height is less or equal than $\\mathsl{L}$LL takes the form $\\mathsl{F}\\mathsl{N}$($\\mathsl{L}$)=$\\mathsl{A}\\mathsl{N}∑\\mathsl{k}\\mathsl{k}∈Ω$Be-$∑\\mathsl{N}\\mathsl{j}$=1$\\mathsl{k}$2$\\mathsl{j}$$\\mathsl{N}$($\\mathsl{k}\\mathsl{k}$)FN(L)=AN$∑$kk$∈Ω$Be-$∑$j=1Nkj2VN(kk)F_N(L)=A_N\\ sum _\\\\ varvec\\k\\\\ in \\ Omega _\\\\ text \\B\\\\\\ \\ mathrm\\e\\\\̂-\\ sum _\\j=1\\N̂k_j2̂\\\\ mathcal \\V\\_N(\\ varvec\\k\\), where $\\mathsl{A}\\mathsl{N}$ANA_N is a normalization constant, $\\mathsl{N}$($\\mathsl{k}\\mathsl{k}$)VN(kk)\\ mathcal \\V\\_N(\\ varvec\\k\\) contains a deformed and weighted Vandermonde determinant, and $Ω$B$Ω$B\\ Omega _\\\\ text \\B\\\\ is the solution set of quasi-momenta $\\mathsl{k}\\mathsl{k}$kk\\ varvec\\k\\ obeying the Bethe equations for that particular boundary condition.\n
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