DOCSLIB.ORG

Statistical Physics Approaches to Collective Behavior in Networks of Neurons

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Statistical Physics Approaches to Collective Behavior in Networks of Neurons Statistical physics approaches to collective behavior in networks of neurons Xiaowen Chen A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of Physics Adviser: Professor William Bialek November 2020 c Copyright by Xiaowen Chen, 2020. All rights reserved. Abstract In recent years, advances in experimental techniques have allowed for the first time si- multaneous measurements of many interacting components in living systems at almost all scales, making now an exciting time to search for physical principles of collective behavior in living systems. This thesis focuses on statistical physics approaches to collective behavior in networks of interconnected neurons; both statistical inference methods driven by real data, and analytical methods probing the theory of emergent behavior, are discussed. Chapter 3 is based on work with F. Randi, A. M. Leifer, and W. Bialek [Chen et al., 2019], where we constructed a joint probability model for the neural activity of the nematode, Caenorhabditis elegans. In particular, we extended the pairwise maximum entropy model, a statistical physics approach to consistently infer distributions from data that has successfully described the activity of networks with spiking neurons, to this very different system with neurons exhibiting graded potential. We discuss signatures of collective behavior found in the inferred models. Chapter 4 is based on work with W. Bialek [Chen and Bialek, 2020], where we examine the tuning condition for the connection matrix among neurons such that the resulting dynamics exhibit long time scales. Starting from the simplest case of random symmetric connections, we combine maximum entropy and random matrix theory methods to explore the constraints required from long time scales to become generic. We argue that a single long time scale can emerge generically from realistic constraints, but a full spectrum of slow modes requires more tuning. iii Acknowledgements Since the beginning of my graduate school training and perhaps even earlier, I have been enjoying reading the acknowledgement sections of doctoral theses and books, and was in awe of how a doctoral degree cannot be completed alone. My thesis is no different. Throughout the past five years, I have met many amazingly talented and friendly mentors and colleagues, and grown thanks to my interactions with them. First and foremost, I would like to thank my advisor Professor Bill Bialek. From our first meeting during the Open House, he has introduced me to the wonderland of theoretical biophysics; provided me with continuous support, encouragement and guidance; and allowed me sufficient freedom to explore my scientific interests. In ad- dition to his fine taste of choosing research questions and rigor in conducting research, I have also been influenced by his optimism amid scientific expeditions in the field of biophysics, and his leadership both as a scientist and as a citizen. I would like to thank Professor Andrew Leifer and Dr. Francesco Randi for our collaboration on the data-analysis project in this thesis; they have taught me to be true to the facts. I also appreciate Andy's enthusiasm for science, friendliness and continuous support throughout the years, advising my experimental project, inviting me to design followup experiments, and serving on my thesis committee. I also would like to thank Professor Michael Aizenman for serving on my thesis committee; and Professor Ned Wingreen for serving as a Second Reader of this thesis, providing much feedback over the past years, and allowing me to attend his group meetings. I consider myself very lucky to study biological physics at Princeton, especially while the NSF Center for the Physics of Biological Function (CPBF) was being es- tablished. The center offers a wonderful and unique community for collaborative science and learning, financial support for participation in conferences such as the APS March Meeting and the annual iPoLS meeting, and opportunities to give back to the community through the undergraduate summer school. I would like to thank iv the leadership of Bill and Prof. Josh Shaevitz, and the administrative support from Dr. Halima Chahboune and Svitlana Rogers. I also thank Halima for her friendliness and support throughout the years. I would like to thank the theory faculty, Pro- fessors Curt Callan, David Schwab, Stephanie Palmer, and Vijay Balasubramanian, who have given me many valuable pieces of advice during theory group meetings. I also would like to thank the experimental faculty, Professors Robert Austin, Thomas Gregor, and Josh Shaevitz, for learning, teaching opportunities and career advice. I learned a tremendous amount from many discussions with the postdocs, graduate students, and visiting students that I had the fortune to overlap with at the Center, including Vasyl Alba, Ricard Alert Zenon, Marianne Bauer, Farzan Beroz, Ben Brat- ton, Katherine Copenhagen, Yuval Elhanati, Amir Erez, Kamesh Krishnamurthy, Endao Han, Caroline Holmes, Daniel Lee, Zhiyuan Li, Andreas Mayer, Lauren Mc- Gough, Leenoy Meshulam, Luisa Fernanda Ram´ırezOchoa, Pierre Ronceray, Zachary Sethna, Ben Weiner, Jim Wu, Bin Xu, and Yaojun Zhang. I have also enjoyed many informal conversations and spontaneous Icahn lunches with many of you. I thank Cassidy Yang and Diana Valverde Mendez for being amazing office mates and for befriending a theorist; I miss seeing you in the office. I also would like to thank especially the members of the Leifer Lab, including Kevin Chen, Matthew Creamer, Kelsey Hallinen, Ashley Linder, Mochi Liu, Jeffery Nguyen, Francesco Randi, Anuj Sharma, Monika Scholz, and Xinwei Yu for all the discussions related to worms and experimental techniques, and for welcoming me in the lab meetings and the lab itself. I would like to thank the training and support provided by the Department of Physics. I thank Kate Brosowsky for her support to graduate students, Laurel Lerner for organizing the departmental recitals, and all of the very friendly and supportive administrators. My attendance in many conferences and summer schools were made possible by the Compton Fund. I also thank the Women in Physics groups for the effort in creating a more inclusive environment in the Department. At the University v level, I would like to thank the Graduate School and the Counseling & Psychological Services at University Health Services for support. My last five years would be less colorful without the friends I met through graduate school, including Trithep Devakul, Christian Jepsen, Ziming Ji, Du Jin, Rocio Kiman, Ho Tat Lam, Zhaoqi Leng, Xinran Li, Sihang Liang, Jingjing Lin, Jingyu Luo, Zheng Ma, Wenjie Su, Jie Wang, Wudi Wang, Zhenbin Yang, Zhaoyue Zhang, and many others. I value my friendship with Junyi Zhang and Jiaqi Jiang, which goes back all the way to attending the same high school in Shanghai to now being in the same cohort at Princeton Physics. I treasure my friendship with Xue (Sherry) Song and Jiaqi Jiang, who have been there for me through all the ups and downs of my graduate career. I would also like to thank Hanrong Chen for company, support, proofreading this thesis and many other things. Finally, I would like to thank my parents for their unwavering support and en- couragement. It was my father, Wei Chen, who bought me a frog to observe and learn swimming from, and my mother, Yanling Guo, who started a part-time PhD degree a few years before my graduate journey, who have kindled and cultivated my curiosity and courage for this scientific quest. vi To my parents. vii Contents Abstract . iii Acknowledgements . iv List of Tables . xi List of Figures . xii 1 Introduction 1 1.1 The nervous system and its collective behavior . .4 1.2 Key problems . .7 1.3 Thesis overview . .8 2 Mathematical and statistical physics methods 11 2.1 Maximum Entropy Principle . 11 2.2 Random Matrix Theory . 16 3 Collective behavior in the small brain of C. elegans 22 3.1 Introduction . 23 3.2 Data acquisition and processing . 25 3.3 Maximum Entropy Model . 31 3.4 Does the model work? . 35 3.5 What does the model teach us? . 40 3.5.1 Energy landscape . 40 3.5.2 Criticality . 42 viii 3.5.3 Network topology . 43 3.5.4 Local perturbation leads to global response . 44 3.6 Discussion . 46 4 Searching for long time scales without fine tuning 50 4.1 Introduction . 51 4.2 Setup . 53 4.3 Time scales for ensembles with different global constraints . 57 4.3.1 Model 1: the Gaussian Orthogonal Ensemble . 57 4.3.2 Model 2: GOE with hard stability threshold . 60 4.3.3 Model 3: Constraining mean-square activity . 63 4.4 Dynamic tuning . 70 4.5 Discussion . 75 5 Conclusion and Outlook 78 A Appendices for Chapter 3 81 A.1 Perturbation methods for overfitting analysis . 81 A.2 Maximum entropy model with the pairwise correlation tensor constraint 85 A.3 Maximum entropy model fails to predict the dynamics of the neural networks as expected . 86 B Dynamical inference for C. elegans neural activity 89 B.1 Estimate correlation time from the data . 90 B.2 Coupling the neural activity and its time derivative . 93 C Appendices for Chapter 4 97 C.1 How to take averages for the time constants? . 97 C.2 Finite size effect for Model 2 . 99 C.3 Derivation for the scaling of time constants in Model 3 . 100 ix C.4 Decay of auto-correlation coefficient . 106 C.5 Model with additional constraint on self-interaction strength . 107 Bibliography 110 x List of Tables C.1 Scaling of inverse slowest time scale (gap) g0, width of the support of spectral density l, and averaged norm per neuron x2 versus the h i i Lagrange multiplier ξ (to leading order) in different regimes. 102 xi List of Figures 3.1 Schematics of data acquisition and processing of C.
Load more

Recommended publications
  • A Complex Adaptive Systems Perspective to Appreciative Inquiry: a Theoretical Analysis Payam Saadat George Fox University
    http://journals.sfu.ca/abr ADVANCES IN BUSINESS RESEARCH 2015, Volume 6, pages 1-13 A Complex Adaptive Systems Perspective to Appreciative Inquiry: A Theoretical Analysis Payam Saadat George Fox University Appreciate inquiry is utilized to facilitate organizational change by encouraging stakeholders to explore positives and generative capacities within their organization. In the literature, analysis of the effectiveness of AI is confined to psychological and managerial explanations such as highlighting the promotion of positive mindset and collective organizational planning. This paper will discuss a complex adaptive systems (CAS) perspective and present a new model for understanding the functionality of AI. The emphasis of this paper is placed on exploring the effects of AI on the behavior and interactions of agents/employees related to how they cope with change. An analysis of AI’s functionality through the lens of CAS reveals two critical insights: a) AI enhances adaptability to change by strengthening communication among agents, which in turn fosters the emergence of effective team arrangements and a more rapid collective response to change and b) AI possesses the potential to generate a collective memory for social systems within an organization. Furthermore, a systematic analysis of AI indicates a close connection between this method and CAS-based styles of management. This paper concludes by suggesting that AI might represent a potential method with the capacity to place organizational teams at the edge of chaos. Keywords: appreciative inquiry, organizational change, management, complex adaptive systems, edge of chaos Introduction In today’s fast-paced world where the fluctuating preferences of consumers, the growth in the global web of interdependence, and technological advancements guide the co-evolving relationship between the dominant business environment and the social systems within its domain, an organization’s capacity to cope with change in a timely manner determines its survival (Hesselbein & Goldsmith, 2006; Macready & Meyer, 1999; Senge, 2006).
    [Show full text]
  • Chapter 17: Social Change and Collective Behavior
    CHAPTER 17 SocialSocial ChangeChange andand CollectiveCollective BehaviorBehavior 566 U S Your Sections I Sociological N Imagination 1. Social Change G 2. Theoretical Perspectives on Social Change hen you see photos or films showing the Plains Indians of the 3. Collective Behavior WOld West—Sioux, Crow, and so forth—what do you think about the culture 4. Social Movements of those Native Americans? If you’re like most of us, you may assume that it had re- mained unchanged for many centuries—that these people dressed and acted in exactly Learning Objectives the same way as their ancestors. We often assume that nonindustrial soci- eties such as these stand still over time. After reading this chapter, you will be able to Actually, though, sociology teaches us that change comes to all societies. Whether by ❖ illustrate the three social processes that borrowing from other cultures, discovering contribute to social change. new ways of doing things, or creating inven- ❖ discuss how technology, population, nat- tions that ripple through society, all peoples ural environment, revolution, and war experience social change. cause cultures to change. Let’s return to the example of the Plains Indians. You may picture these tribes as ❖ describe social change as viewed by the fierce, buffalo-hunting warriors. Perhaps im- functionalist and conflict perspectives. ages of Sitting Bull and Crazy Horse astride ❖ discuss rumors, fads, and fashions. fast horses attacking Custer come to mind, ❖ compare and contrast theories of crowd leading you to think that their ancestors for centuries had also ridden horses. In fact, behavior. horses were a relatively recent introduction ❖ compare and contrast theories of social to Plains Indian culture in the 1800s.
    [Show full text]
  • Collective Behaviour
    COLLECTIVE BEHAVIOUR DEFINED COLLECTIVE BEHAVIOUR • The term "collective behavior" was first used by Robert E. Park, and employed definitively by Herbert Blumer, to refer to social processes and events which do not reflect existing social structure (laws, conventions, and institutions), but which emerge in a "spontaneous" way. Collective Behaviour defined • Collective behaviour is a meaning- creating social process in which new norms of behaviour that challenges conventional social action emerges. Examples of Collective Behaviour • Some examples of this type of behaviour include panics, crazes, hostile outbursts and social movements • Fads like hula hoop; crazes like Beatlemania; hostile outbursts like anti- war demonstrations; and Social Movements. • Some argue social movements are more sophisticated forms of collective behaviour SOCIAL MOVEMENTS • Social movements are a type of group action. They are large informal groupings of individuals and/or organizations focused on specific political or social issues, in other words, on carrying out, resisting or undoing a social change. CBs and SMs 19th C. ROOTS • Modern Western social movements became possible through education and the increased mobility of labour due to the industrialisation and urbanisation of 19th century societies Tilly’s DEFINITION SM • Charles Tilly defines social movements as a series of contentious performances, displays and campaigns by which ordinary people made collective claims on others [Tilly, 2004].]: Three major elements of SMs • For Tilly, social movements are a major vehicle for ordinary people's participation in public politics [Tilly, 2004:3]. • He argues that there are three major elements to a social movement [Tilly, 2004 THREE ELEMENTS OF SMs 1. Campaigns: a sustained, organized public effort making collective claims on target authorities; 2.
    [Show full text]
  • Spring 2019 Fine Letters
    Spring 2019 • Issue 8 Department of MATHEMATICS Princeton University From the Chair Professor Allan Sly Receives MacArthur Fellowship Congratulations to Sly works on an area of probability retical computer science, where a key the Class of 2019 theory with applications from the goal often is to understand whether and all the finishing physics of magnetic materials to it is likely or unlikely that a large set graduate students. computer science and information of randomly imposed constraints on a Congratulations theory. His work investigates thresh- system can be satisfied. Sly has shown to the members of olds at which complex networks mathematically how such systems of- class of 2018 and suddenly change from having one ten reach a threshold at which solving new Ph. D.s who set of properties to another. Such a particular problem shifts from likely are reading Fine Letters for the first questions originally arose in phys- or unlikely. Sly has used a party invi- time as alumni. As we all know, the ics, where scientists observed such tation list as an analogy for the work: Math major is a great foundation for shifts in the magnetism of certain As you add interpersonal conflicts a diverse range of endeavors. This metal alloys. Sly provided a rigorous among a group of potential guests, it is exemplified by seventeen '18's who mathematical proof of the shift and can suddenly become effectively im- have gone to industry and seventeen a framework for identifying when possible to create a workable party. to grad school; ten to advanced study such shifts occur.
    [Show full text]
  • Laudatio for Michael Aizenman NAW 5/4 Nr
    Aernout van Enter, Frank den Hollander Laudatio for Michael Aizenman NAW 5/4 nr. 2 juni 2003 107 Aernout van Enter Frank den Hollander Instituut voor theoretische natuurkunde Eurandom Rijksuniversiteit Groningen Technische Universiteit Eindhoven Nijenborgh 4, 9747 AG Groningen Postbus 513, 5600 MB Eindhoven [email protected] [email protected] Laudatio Laudatio for Michael Aizenman Eens per drie jaar reikt het Wiskundig Ge- Michael is the author of seventy-five research or ‘down’) or as particles (‘occupied’ or ‘emp- nootschap in opdracht van de Koninklijke Ne- papers in journals of mathematics, physics ty’). Their finite-volume conditional distribu- derlandse Academie van Wetenschappen de and mathematical physics. He has collaborat- tions (i.e., the probabilities of events inside a Brouwermedaille uit aan een internationaal ed with many co-authors on a broad range of finite volume given the state outside) are pre- toonaangevend onderzoeker. Hij wordt uit- topics. Much of his work is inspired by proba- scribed by a nearest-neighbor interaction that genodigd om een voordracht te geven op het bility theory and statistical physics, both clas- tends to ‘align spins’ or ‘glue together parti- Nederlands Mathematisch Congres, waar na sical and quantum. In his papers he typically cles’ and that contains the temperature as a afloop de laureaat de Brouwermedaille wordt ‘rides several horses at the same time’, in the parameter. At low temperature and in two uitgereikt. In 2002 werd de medaille toege- sense that cross-fertilization between differ- or more dimensions, there exists more than kend aan Michael Aizenman voor zijn bijdra- ent areas in physics and mathematics is at one infinite-volume probability measure hav- ge aan de mathematische fysica.
    [Show full text]
  • A Life in Statistical Mechanics Part 1: from Chedar in Taceva to Yeshiva University in New York
    Eur. Phys. J. H 42, 1–21 (2017) DOI: 10.1140/epjh/e2017-80006-9 THE EUROPEAN PHYSICAL JOURNAL H Oral history interview A life in statistical mechanics Part 1: From Chedar in Taceva to Yeshiva University in New York Joel L. Lebowitz1,a and Luisa Bonolis2,b 1 Departments of Mathematics and Physics, Rutgers, The State University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA 2 Max Planck Institute for the History of Science, Boltzmannstrasse 22, 14195 Berlin, Germany Received 10 February 2017 / Accepted 10 February 2017 Published online 4 April 2017 c The Author(s) 2017. This article is published with open access at Springerlink.com Abstract. This is the first part of an oral history interview on the life- long involvement of Joel Lebowitz in the development of statistical mechanics. Here the covered topics include the formative years, which overlapped the tragic period of Nazi power and World War II in Eu- rope, the emigration to the United States in 1946 and the schooling there. It also includes the beginnings and early scientific works with Peter Bergmann, Oliver Penrose and many others. The second part will appear in a forthcoming issue of Eur. Phys. J. H. 1 From war ravaged Europe to New York L. B. Let’s start from the very beginning. Where were you born? J. L. I was born in Taceva, a small town in the Carpathian mountains, in an area which was at that time part of Czechoslovakia, on the border of Romania and about a hundred kilometers from Poland. That was in 1930, and the town then had a population of about ten thousand people, a small town, but fairly advanced.
    [Show full text]
  • Threshold Models of Collective Behavior!
    Threshold Models of Collective Behavior! Mark Granovetter State University of New York at Stony Brook Models of collective behavior are developed for situations where actors have two alternatives and the costs and/or benefits of each depend on how many other actors choose which alternative. The key concept is that of "threshold": the number or proportion of others who must make one decision before a given actor does so; this is the point where net benefits begin to exceed net costs for that particular actor. Beginning with a frequency distribution of thresholds, the models allow calculation of the ultimate or "equilibrium" number making each decision. The stability of equilibrium results against various possible changes in threshold distributions is considered. Stress is placed on the importance of exact distributions for outcomes. Groups with similar average preferences may generate very different results; hence it is hazardous to infer individual dispositions from aggregate outcomes or to assume that behavior was directed by ultimately agreed-upon norms. Suggested applications are to riot behavior, innovation and rumor diffusion, strikes, voting, and migra­ tion. Issues of measurement, falsification, and verification are dis­ cussed. BACKGROUND AND DESCRIPTION OF THE MODELS Because sociological theory tends to explain behavior by institutionalized norms and values, the study of behavior inexplicable in this way occupies a peripheral position in systematic theory. Work in the subfields which embody this concern-deviance for individuals and collective behavior for groups-often consists of attempts to show what prevented the established patterns from exerting their usual sway. In the field of collective behavior, one such effort involves the assertion that new norms or beliefs "emerge" 1 This report is heavily indebted to three co-workers.
    [Show full text]
  • 09W5055 Statistical Mechanics on Random Structures
    09w5055 Statistical Mechanics on Random Structures Anton Bovier (Rheinische Friedrich-Wilhelms-Universitat¨ Bonn), Pierluigi Contucci (University of Bologna), Frank den Hollander (University of Leiden and EURANDOM), Cristian Giardina` (TU Eindhoven and EURANDOM). 15 November - 20 November 2009 1 Overview of the Field The theme of the workshop has been equilibrium and non-equilibrium statistical mechanics in a random spatial setting. Put differently, the question was what happens when the world of interacting particle systems is put together with the world of disordered media. This area of research is lively and thriving, with a constant flow of new ideas and exciting developments, in the best of the tradition of mathematical physics. Spin glasses were at the core of the program, but in a broad sense. Spin glass theory has found ap- plications in a wide range of areas, including information theory, coding theory, algorithmics, complexity, random networks, population genetics, epidemiology and finance. This opens up many new challenges to mathematics. 2 Recent Developments and Open Problems The workshop brought together researchers whose interest lies at the intersection of disordered statistical mechanics and random graph theory, with a clear emphasis on applications. The multidisciplinary nature of the proposed topics has attracted research groups with different backgrounds and thus provided exchange of ideas with cross-fertilisation. As an example, we mention two problems on which we focused during the workshop. The first problem has its origin in the many fundamental issues that are still open in the theory of spin glasses. Even tough today we have a rigorous proof, in the context of mean-field models, of the solution for the free energy first proposed by G.
    [Show full text]
  • A Mathematical Physicist's Perspective on Statistical Mechanics
    A mathematical physicist’s perspective on Statistical Mechanics Michael Aizenman Princeton University André Aisenstadt Lecture (I) CRM, Montreal Sept. 24, 2018 1 /14 Statistical mechanics explains and quantifies the process by which structure emerges from chaos. Its genesis is in Boltzmann’s explanation of thermodynamical behavior and in particular of the concept of entropy. The statistic mechanical perspective was instrumental for Planck’s theory of the light quantization and Einstein’s calculation of the Avogadro number. More recent developments include links between the physics of critical phenomena and the mathematics of conformally invariant random structures, stochastic integrability, and representation theory. The talk will focus on examples of observations and conjectures which turned out to point in fruitful directions. 2 /14 Statistical Mechanics: laws emerging from chaos Laws expressed in equations F = ma, E = mc2, PV = nRT . A bird of a seemingly different feather: ∆S ≥ 0 . Q: what is entropy? L. Boltzmann: Thermodynamics emerges from Statistical Mechanics! Stat-Mech starts with a quantification of chaos: S = kB log W StatMech perspective was embraced and used for further developments by: M. Planck ) quantum theory of light (surmised from the black body radiation) A. Einstein ) Avogadro number from Brownian motion (exp. Perrin) −itH R. Feynman ) path representation of quantum dynamics: Ψt = e Ψ0 J. Wheeler: “There is no law except the law that there is no law.” Paraphrased: all physics laws are emergent features. 3 /14 Statistical Mechanics: laws emerging from chaos Laws expressed in equations F = ma, E = mc2, PV = nRT . A bird of a seemingly different feather: ∆S ≥ 0 . Q: what is entropy? L.
    [Show full text]
  • On Spin Systems with Quenched Randomness: Classical and Quantum
    On Spin Systems with Quenched Randomness: Classical and Quantum Rafael L. Greenblatt(a) ∗ Michael Aizenman(b) y Joel L. Lebowitz(c)∗ (a) Department of Physics and Astronomy Rutgers University, Piscataway NJ 08854-8019, USA (b) Departments of Physics and Mathematics Princeton University, Princeton NJ 08544, USA (a) Departments of Mathematics and Physics Rutgers University, Piscataway NJ 08854-8019, USA December 5, 2009 Dedicated to Nihat Berker on the occasion of his 60th birthday Abstract The rounding of first order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a d-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when d ≤ 2. This implies absence of jumps in the associated order parameter, e.g., the magnetization in case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for d ≤ 4. Some questions concerning the behavior of related order parameters in such random systems are discussed. 1 Introduction The effect of quenched randomness on the equilibrium and transport properties of macroscopic systems is a subject of great theoretical and practical interest which is close to Nihat’s heart. He and his collaborators [1, 2, 3] made important contributions to the study of the changes brought about by such randomness in phase transitions occurring in the pure (non-random) system. These effects can be profound in low dimensions. Their understanding evolved in a somewhat interesting way.
    [Show full text]
  • Information Socialtaxis and Efficient Collective Behavior Emerging In
    Information socialtaxis and efficient collective behavior emerging in groups of information-seeking agents Ehud D. Karpasa, Adi Shklarsha, and Elad Schneidmana,1 aDepartment of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel Edited by Curtis G. Callan Jr., Princeton University, Princeton, NJ, and approved April 17, 2017 (received for review October 31, 2016) Individual behavior, in biology, economics, and computer science, is highly efficient in finding a sparsely signaling source in a tur- is often described in terms of balancing exploration and exploita- bulent environment. These infotaxis search trajectories resemble tion. Foraging has been a canonical setting for studying reward the paths of foraging insects, suggesting a biological implication seeking and information gathering, from bacteria to humans, of this model. mostly focusing on individual behavior. Inspired by the gradient- In nature, many species, including bacteria (15), amoebae (16), climbing nature of chemotaxis, the infotaxis algorithm showed insects (17, 18), fish (19), birds (3), and mammals (20, 21), dis- that locally maximizing the expected information gain leads to play complex group behavior, including foraging. The mecha- efficient and ethological individual foraging. In nature, as well as nisms that underlie group behavior have been of great experi- in theoretical settings, conspecifics can be a valuable source of mental and theoretical interest, focusing on the computation that information about the environment. Whereas the nature and role each individual performs (22–24) and emergent collective behav- of interactions between animals have been studied extensively, ior (24, 25). In terms of social behavior, such models have been the design principles of information processing in such groups used to describe exploration and exploitation of the environment, are mostly unknown.
    [Show full text]
  • Curriculum Vitae
    Jack Hanson City College of NY [email protected] Dept. of Mathematics 1 (212) 650 - 5174 NAC 6/292 Appointments • Assistant Professor, City College of NY Dept. of Mathematics, 01/2016{present • Visiting Assistant Professor, GA Tech Dept. of Mathematics, 8/2015{01/2016 • Zorn Postdoctoral Fellow, Indiana University Dept. of Mathematics. 8/2013{7/2015 Education • Ph.D., Physics, Princeton University, June 2013. Advisor: Michael Aizenman • M.A., Physics, Princeton University, 2010. • B.S. Summa cum Laude, Physics, Rutgers University, 2008. Double major, Physics and Mathematics. Funding • NSF Grant DMS-1612921, \Correlations and Scaling in Disordered and Critical Stochastic Models", 2016 { 2019. $100,000. • (Funded but declined in favor of NSF) NSA Young Investigator Grant, 2016 { 2018. $40,000. • AMS-Simons travel grant, 2015 { 2016. • NSF Graduate Research Fellow, 2008 - 2013. Talks • Upcoming, untitled { Conference on Random Walks, Random Graphs and Random Media at LMU, Munich, 9 / 2019 • \Universality of the time constant for critical first-passage percolation on the triangular lat- tice" { MIT Probability Seminar, 3/2019 1 { CUNY Probability Seminar, 3/2019 { Ohio State U. Probability Seminar, 4/2019 • \Geodesics in First-Passage Percolation" { Montr´ealsummer workshop on challenges in probability and mathematical physics, 7/2018. • \Half-space critical exponents in high-dimensional percolation." { Conference on Recent Trends in Continuous and Discrete Probability, GA Tech, 6/2018. { U. of Rochester Probability Seminar, 9/2018 { Columbia U. Probability Seminar, 2/2019 { NYU Probability Seminar, 2/2019 • \The boundary in first-passage percolation" { Cornell Probability Seminar, 11/2017 • \Strict inequality for the chemical distance exponent in 2d percolation." { Stockholm University Probability/Statistics seminar, 8/2017 { CUNY Probability seminar, 9/2017 • \Geodesics and Busemann functions in first-passage percolation" { AMS short course, Atlanta, 1/2017.
    [Show full text]