Bruno Buonomo, Alessandra D'Alise, Rossella Della Marca, Francesco Sannino
Recent pandemics triggered the development of a number of mathematical models and computational tools apt at curbing the socio-economic impact of these and future pandemics. The need to acquire solid estimates from the data led to the introduction of effective approaches such as the emph{epidemiological Renormalization Group} (eRG). A recognized relevant factor impacting the evolution of pandemics is the feedback stemming from individuals' choices. The latter can be taken into account via the textit{information index} which accommodates the information--induced perception regarding the status of the disease and the memory of past spread. We, therefore, show how to augment the eRG by means of the information index. We first develop the {it behavioural} version of the eRG and then test it against the US vaccination campaign for COVID-19. We find that the behavioural augmented eRG improves the description of the pandemic dynamics of the US divisions for which the epidemic peak occurs after the start of the vaccination campaign. Our results strengthen the relevance of taking into account the human behaviour component when modelling pandemic evolution. To inform public health policies, the model can be readily employed to investigate the socio-epidemiological dynamics, including vaccination campaigns, for other regions of the world.
{"title":"Information index augmented eRG to model vaccination behaviour: A case study of COVID-19 in the US","authors":"Bruno Buonomo, Alessandra D'Alise, Rossella Della Marca, Francesco Sannino","doi":"arxiv-2407.20711","DOIUrl":"https://doi.org/arxiv-2407.20711","url":null,"abstract":"Recent pandemics triggered the development of a number of mathematical models\u0000and computational tools apt at curbing the socio-economic impact of these and\u0000future pandemics. The need to acquire solid estimates from the data led to the\u0000introduction of effective approaches such as the emph{epidemiological\u0000Renormalization Group} (eRG). A recognized relevant factor impacting the\u0000evolution of pandemics is the feedback stemming from individuals' choices. The\u0000latter can be taken into account via the textit{information index} which\u0000accommodates the information--induced perception regarding the status of the\u0000disease and the memory of past spread. We, therefore, show how to augment the\u0000eRG by means of the information index. We first develop the {it behavioural}\u0000version of the eRG and then test it against the US vaccination campaign for\u0000COVID-19. We find that the behavioural augmented eRG improves the description\u0000of the pandemic dynamics of the US divisions for which the epidemic peak occurs\u0000after the start of the vaccination campaign. Our results strengthen the\u0000relevance of taking into account the human behaviour component when modelling\u0000pandemic evolution. To inform public health policies, the model can be readily\u0000employed to investigate the socio-epidemiological dynamics, including\u0000vaccination campaigns, for other regions of the world.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"363 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The inherent huge complexities in human beings show a remarkable diversity in response to complex surroundings, enabling us to tackle problems from different perspectives. In the realm of cooperation studies, however, existing work assumes that individuals get access to the same kind of information to make their decisions, in contrast to the facts that individuals often perceive differently. Here, within the reinforcement learning framework, we investigate the impact of information perception on the evolution of cooperation in a 2-person scenario when playing the prisoner's dilemma game. We demonstrate that distinctly different evolution processes are observed in three information perception scenarios, revealing that the structure of information significantly affects the emergence of cooperation. Notably, the asymmetric information scenario exhibits a rich dynamical process, including the cooperation emergence, breakdown, and reconstruction, akin to psychological changes in humans. Our findings indicate that the information structure is vital to the emergence of cooperation, shedding new light on establishing mutually stable cooperative relationships and understanding human behavioral complexities in general.
{"title":"The evolution of cooperation with Q-learning: the impact of information perception","authors":"Guozhong Zheng, Zhenwei Ding, Jiqiang Zhang, Shengfeng Deng, Weiran Cai, Li Chen","doi":"arxiv-2407.19634","DOIUrl":"https://doi.org/arxiv-2407.19634","url":null,"abstract":"The inherent huge complexities in human beings show a remarkable diversity in\u0000response to complex surroundings, enabling us to tackle problems from different\u0000perspectives. In the realm of cooperation studies, however, existing work\u0000assumes that individuals get access to the same kind of information to make\u0000their decisions, in contrast to the facts that individuals often perceive\u0000differently. Here, within the reinforcement learning framework, we investigate\u0000the impact of information perception on the evolution of cooperation in a\u00002-person scenario when playing the prisoner's dilemma game. We demonstrate that\u0000distinctly different evolution processes are observed in three information\u0000perception scenarios, revealing that the structure of information significantly\u0000affects the emergence of cooperation. Notably, the asymmetric information\u0000scenario exhibits a rich dynamical process, including the cooperation\u0000emergence, breakdown, and reconstruction, akin to psychological changes in\u0000humans. Our findings indicate that the information structure is vital to the\u0000emergence of cooperation, shedding new light on establishing mutually stable\u0000cooperative relationships and understanding human behavioral complexities in\u0000general.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"176 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guozhong Zheng, Jiqiang Zhang, Shengfeng Deng, Weiran Cai, Li Chen
Recent paradigm shifts from imitation learning to reinforcement learning (RL) is shown to be productive in understanding human behaviors. In the RL paradigm, individuals search for optimal strategies through interaction with the environment to make decisions. This implies that gathering, processing, and utilizing information from their surroundings are crucial. However, existing studies typically study pairwise games such as the prisoners' dilemma and employ a self-regarding setup, where individuals play against one opponent based solely on their own strategies, neglecting the environmental information. In this work, we investigate the evolution of cooperation with the multiplayer game -- the public goods game using the Q-learning algorithm by leveraging the environmental information. Specifically, the decision-making of players is based upon the cooperation information in their neighborhood. Our results show that cooperation is more likely to emerge compared to the case of imitation learning by using Fermi rule. Of particular interest is the observation of an anomalous non-monotonic dependence which is revealed when voluntary participation is further introduced. The analysis of the Q-table explains the mechanisms behind the cooperation evolution. Our findings indicate the fundamental role of environment information in the RL paradigm to understand the evolution of cooperation, and human behaviors in general.
{"title":"Evolution of cooperation in the public goods game with Q-learning","authors":"Guozhong Zheng, Jiqiang Zhang, Shengfeng Deng, Weiran Cai, Li Chen","doi":"arxiv-2407.19851","DOIUrl":"https://doi.org/arxiv-2407.19851","url":null,"abstract":"Recent paradigm shifts from imitation learning to reinforcement learning (RL)\u0000is shown to be productive in understanding human behaviors. In the RL paradigm,\u0000individuals search for optimal strategies through interaction with the\u0000environment to make decisions. This implies that gathering, processing, and\u0000utilizing information from their surroundings are crucial. However, existing\u0000studies typically study pairwise games such as the prisoners' dilemma and\u0000employ a self-regarding setup, where individuals play against one opponent\u0000based solely on their own strategies, neglecting the environmental information.\u0000In this work, we investigate the evolution of cooperation with the multiplayer\u0000game -- the public goods game using the Q-learning algorithm by leveraging the\u0000environmental information. Specifically, the decision-making of players is\u0000based upon the cooperation information in their neighborhood. Our results show\u0000that cooperation is more likely to emerge compared to the case of imitation\u0000learning by using Fermi rule. Of particular interest is the observation of an\u0000anomalous non-monotonic dependence which is revealed when voluntary\u0000participation is further introduced. The analysis of the Q-table explains the\u0000mechanisms behind the cooperation evolution. Our findings indicate the\u0000fundamental role of environment information in the RL paradigm to understand\u0000the evolution of cooperation, and human behaviors in general.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
François Bienvenu, Jean-Jil Duchamps, Michael Fuchs, Tsan-Cheng Yu
In recent years, there has been an effort to extend the classical notion of phylogenetic balance, originally defined in the context of trees, to networks. One of the most natural ways to do this is with the so-called $B_2$ index. In this paper, we study the $B_2$ index for a prominent class of phylogenetic networks: galled trees. We show that the $B_2$ index of a uniform leaf-labeled galled tree converges in distribution as the network becomes large. We characterize the corresponding limiting distribution, and show that its expected value is 2.707911858984... This is the first time that a balance index has been studied to this level of detail for a random phylogenetic network. One specificity of this work is that we use two different and independent approaches, each with its advantages: analytic combinatorics, and local limits. The analytic combinatorics approach is more direct, as it relies on standard tools; but it involves slightly more complex calculations. Because it has not previously been used to study such questions, the local limit approach requires developing an extensive framework beforehand; however, this framework is interesting in itself and can be used to tackle other similar problems.
{"title":"The $B_2$ index of galled trees","authors":"François Bienvenu, Jean-Jil Duchamps, Michael Fuchs, Tsan-Cheng Yu","doi":"arxiv-2407.19454","DOIUrl":"https://doi.org/arxiv-2407.19454","url":null,"abstract":"In recent years, there has been an effort to extend the classical notion of\u0000phylogenetic balance, originally defined in the context of trees, to networks.\u0000One of the most natural ways to do this is with the so-called $B_2$ index. In\u0000this paper, we study the $B_2$ index for a prominent class of phylogenetic\u0000networks: galled trees. We show that the $B_2$ index of a uniform leaf-labeled\u0000galled tree converges in distribution as the network becomes large. We\u0000characterize the corresponding limiting distribution, and show that its\u0000expected value is 2.707911858984... This is the first time that a balance index\u0000has been studied to this level of detail for a random phylogenetic network. One specificity of this work is that we use two different and independent\u0000approaches, each with its advantages: analytic combinatorics, and local limits.\u0000The analytic combinatorics approach is more direct, as it relies on standard\u0000tools; but it involves slightly more complex calculations. Because it has not\u0000previously been used to study such questions, the local limit approach requires\u0000developing an extensive framework beforehand; however, this framework is\u0000interesting in itself and can be used to tackle other similar problems.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In phylogenetic networks, it is desirable to estimate edge lengths in substitutions per site or calendar time. Yet, there is a lack of scalable methods that provide such estimates. Here we consider the problem of obtaining edge length estimates from genetic distances, in the presence of rate variation across genes and lineages, when the network topology is known. We propose a novel criterion based on least-squares that is both consistent and computationally tractable. The crux of our approach is to decompose the genetic distances into two parts, one of which is invariant across displayed trees of the network. The scaled genetic distances are then fitted to the invariant part, while the average scaled genetic distances are fitted to the non-invariant part. We show that this criterion is consistent provided that there exists a tree path between some pair of tips in the network, and that edge lengths in the network are identifiable from average distances. We also provide a constrained variant of this criterion assuming a molecular clock, which can be used to obtain relative edge lengths in calendar time.
{"title":"A consistent least-squares criterion for calibrating edge lengths in phylogenetic networks","authors":"Jingcheng Xu, Cécile Ané","doi":"arxiv-2407.19343","DOIUrl":"https://doi.org/arxiv-2407.19343","url":null,"abstract":"In phylogenetic networks, it is desirable to estimate edge lengths in\u0000substitutions per site or calendar time. Yet, there is a lack of scalable\u0000methods that provide such estimates. Here we consider the problem of obtaining\u0000edge length estimates from genetic distances, in the presence of rate variation\u0000across genes and lineages, when the network topology is known. We propose a\u0000novel criterion based on least-squares that is both consistent and\u0000computationally tractable. The crux of our approach is to decompose the genetic\u0000distances into two parts, one of which is invariant across displayed trees of\u0000the network. The scaled genetic distances are then fitted to the invariant\u0000part, while the average scaled genetic distances are fitted to the\u0000non-invariant part. We show that this criterion is consistent provided that\u0000there exists a tree path between some pair of tips in the network, and that\u0000edge lengths in the network are identifiable from average distances. We also\u0000provide a constrained variant of this criterion assuming a molecular clock,\u0000which can be used to obtain relative edge lengths in calendar time.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yi-Duo ChenLanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou, China and Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, China, Jian-Yue GuanLanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou, China and Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, China, Zhi-Xi WuLanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou, China and Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, China
Dynamic environments shape diverse dynamics in evolutionary game systems. We introduce spatial heterogeneity of resources into the Prisoner's Dilemma Game model to explore the co-evolution of individuals' strategies and environmental resources. The adequacy of resources significantly affects the survival competitiveness of surrounding individuals. Feedback between individuals' strategies and the resources they can use leads to the dynamic of the "oscillatory tragedy of the commons". Our findings indicate that when the influence of individuals' strategies on the update rate of resources is significantly high, individuals can form sustained spatial clustered patterns. These sustained patterns can directly trigger a transition in the system from the persistent periodic oscillating state to an equilibrium state. These findings align with observed phenomena in real ecosystems, where organisms organize their spatial structures to maintain system stability. We discuss critical phenomena in detail, demonstrating that the aforementioned phase transition is robust across various system parameters including: the strength of cooperators in restoring the environment, the initial distributions of cooperators, and noise.
{"title":"Coevolutionary game dynamics with localized environmental resource feedback","authors":"Yi-Duo ChenLanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou, China and Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, China, Jian-Yue GuanLanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou, China and Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, China, Zhi-Xi WuLanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou, China and Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, China","doi":"arxiv-2407.18494","DOIUrl":"https://doi.org/arxiv-2407.18494","url":null,"abstract":"Dynamic environments shape diverse dynamics in evolutionary game systems. We\u0000introduce spatial heterogeneity of resources into the Prisoner's Dilemma Game\u0000model to explore the co-evolution of individuals' strategies and environmental\u0000resources. The adequacy of resources significantly affects the survival\u0000competitiveness of surrounding individuals. Feedback between individuals'\u0000strategies and the resources they can use leads to the dynamic of the\u0000\"oscillatory tragedy of the commons\". Our findings indicate that when the\u0000influence of individuals' strategies on the update rate of resources is\u0000significantly high, individuals can form sustained spatial clustered patterns.\u0000These sustained patterns can directly trigger a transition in the system from\u0000the persistent periodic oscillating state to an equilibrium state. These\u0000findings align with observed phenomena in real ecosystems, where organisms\u0000organize their spatial structures to maintain system stability. We discuss\u0000critical phenomena in detail, demonstrating that the aforementioned phase\u0000transition is robust across various system parameters including: the strength\u0000of cooperators in restoring the environment, the initial distributions of\u0000cooperators, and noise.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a generalization of the adaptive N-Intertwined Mean-Field Approximation (aNIMFA) model studied in emph{Achterberg and Sensi} cite{achterbergsensi2022adaptive} to a heterogeneous network of communities. In particular, the multigroup aNIMFA model describes the impact of both local and global disease awareness on the spread of a disease in a network. We obtain results on existence and stability of the equilibria of the system, in terms of the basic reproduction number~$R_0$. Under light constraints, we show that the basic reproduction number~$R_0$ is equivalent to the basic reproduction number of the NIMFA model on static networks. Based on numerical simulations, we demonstrate that with just two communities periodic behaviour can occur, which contrasts the case with only a single community, in which periodicity was ruled out analytically. We also find that breaking connections between communities is more fruitful compared to breaking connections within communities to reduce the disease outbreak on dense networks, but both strategies are viable to networks with fewer links. Finally, we emphasise that our method of modelling adaptivity is not limited to SIS models, but has huge potential to be applied in other compartmental models in epidemiology.
{"title":"A minimal model for multigroup adaptive SIS epidemics","authors":"Massimo A. Achterberg, Mattia Sensi, Sara Sottile","doi":"arxiv-2407.17639","DOIUrl":"https://doi.org/arxiv-2407.17639","url":null,"abstract":"We propose a generalization of the adaptive N-Intertwined Mean-Field\u0000Approximation (aNIMFA) model studied in emph{Achterberg and Sensi}\u0000cite{achterbergsensi2022adaptive} to a heterogeneous network of communities.\u0000In particular, the multigroup aNIMFA model describes the impact of both local\u0000and global disease awareness on the spread of a disease in a network. We obtain\u0000results on existence and stability of the equilibria of the system, in terms of\u0000the basic reproduction number~$R_0$. Under light constraints, we show that the\u0000basic reproduction number~$R_0$ is equivalent to the basic reproduction number\u0000of the NIMFA model on static networks. Based on numerical simulations, we\u0000demonstrate that with just two communities periodic behaviour can occur, which\u0000contrasts the case with only a single community, in which periodicity was ruled\u0000out analytically. We also find that breaking connections between communities is\u0000more fruitful compared to breaking connections within communities to reduce the\u0000disease outbreak on dense networks, but both strategies are viable to networks\u0000with fewer links. Finally, we emphasise that our method of modelling adaptivity\u0000is not limited to SIS models, but has huge potential to be applied in other\u0000compartmental models in epidemiology.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider evolutionary games in which the agent selected for update compares their payoff to q neighbours, rather than a single neighbour as in standard evolutionary game theory. Through studying fixed point stability and fixation times for 2x2 games with all-to-all interactions, we find that the flow changes significantly as a function of q. Further, we investigate the effects of changing the underlying topology from an all-to-all interacting system to an uncorrelated graph via the pair approximation. We also develop the framework for studying games with more than two strategies, such as the rock-paper-scissors game where we show that changing q leads to the emergence of new types of flow.
{"title":"q-deformed evolutionary dynamics in simple matrix games","authors":"Christopher R. Kitching, Tobias Galla","doi":"arxiv-2407.16380","DOIUrl":"https://doi.org/arxiv-2407.16380","url":null,"abstract":"We consider evolutionary games in which the agent selected for update\u0000compares their payoff to q neighbours, rather than a single neighbour as in\u0000standard evolutionary game theory. Through studying fixed point stability and\u0000fixation times for 2x2 games with all-to-all interactions, we find that the\u0000flow changes significantly as a function of q. Further, we investigate the\u0000effects of changing the underlying topology from an all-to-all interacting\u0000system to an uncorrelated graph via the pair approximation. We also develop the\u0000framework for studying games with more than two strategies, such as the\u0000rock-paper-scissors game where we show that changing q leads to the emergence\u0000of new types of flow.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled systems, we enforce non-negativity of the solutions, aligning with realistic scenarios in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction in measurement/observation data due to averaging effects, the nonlinear coupling between multiple equations, and the nonlocality arising from fractional-type derivatives. These factors present significant challenges to our inverse problem, and such inverse problems have never been explored in previous literature. To address these challenges, we develop new and effective schemes. Our approach involves properly controlling the injection of different source terms to obtain multiple sets of mean flux data. This allows us to achieve unique identifiability results and accurately determine the unknown parameters. Finally, we establish a connection between our study and practical applications in biology, further highlighting the relevance of our work in real-world contexts.
{"title":"Inverse problems for coupled nonlocal nonlinear systems arising in mathematical biology","authors":"Ming-Hui Ding, Hongyu Liu, Catharine W. K. Lo","doi":"arxiv-2407.15713","DOIUrl":"https://doi.org/arxiv-2407.15713","url":null,"abstract":"In this paper, we propose and study several inverse problems of determining\u0000unknown parameters in nonlocal nonlinear coupled PDE systems, including the\u0000potentials, nonlinear interaction functions and time-fractional orders. In\u0000these coupled systems, we enforce non-negativity of the solutions, aligning\u0000with realistic scenarios in biology and ecology. There are several salient\u0000features of our inverse problem study: the drastic reduction in\u0000measurement/observation data due to averaging effects, the nonlinear coupling\u0000between multiple equations, and the nonlocality arising from fractional-type\u0000derivatives. These factors present significant challenges to our inverse\u0000problem, and such inverse problems have never been explored in previous\u0000literature. To address these challenges, we develop new and effective schemes.\u0000Our approach involves properly controlling the injection of different source\u0000terms to obtain multiple sets of mean flux data. This allows us to achieve\u0000unique identifiability results and accurately determine the unknown parameters.\u0000Finally, we establish a connection between our study and practical applications\u0000in biology, further highlighting the relevance of our work in real-world\u0000contexts.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Sackin index is an important measure for the balance of phylogenetic trees. We investigate two extensions of the Sackin index to the class of galled trees and two of its subclasses (simplex galled trees and normal galled trees) where we consider both labeled and unlabeled galled trees. In all cases, we show that the mean of the Sackin index for a network which is uniformly sampled from its class is asymptotic to $mu n^{3/2}$ for an explicit constant $mu$. In addition, we show that the scaled Sackin index convergences weakly and with all its moments to the Airy distribution.
{"title":"Sackin Indices for Labeled and Unlabeled Classes of Galled Trees","authors":"Michael Fuchs, Bernhard Gittenberger","doi":"arxiv-2407.13892","DOIUrl":"https://doi.org/arxiv-2407.13892","url":null,"abstract":"The Sackin index is an important measure for the balance of phylogenetic\u0000trees. We investigate two extensions of the Sackin index to the class of galled\u0000trees and two of its subclasses (simplex galled trees and normal galled trees)\u0000where we consider both labeled and unlabeled galled trees. In all cases, we\u0000show that the mean of the Sackin index for a network which is uniformly sampled\u0000from its class is asymptotic to $mu n^{3/2}$ for an explicit constant $mu$.\u0000In addition, we show that the scaled Sackin index convergences weakly and with\u0000all its moments to the Airy distribution.","PeriodicalId":501044,"journal":{"name":"arXiv - QuanBio - Populations and Evolution","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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