Learning new physics from biology and data Público

Abstract

In an attempt to understand various phenomena in living systems and properties of data, we found new physical phenomena that were previously unstudied. In an effort to better understand interface propagation in {\em Dictyostelium discoideum}, we deduced a new interface growth rule that may describe a broad class of biological interfaces. Simulations and analysis of the new growth rule gave rise to a new universality class of interface growth with three dynamic exponents instead of the usual two. By studying thermal learning in {\em C. elegans}, we constructed a new model of associative learning that incorporates classical and operant conditioning, and generalization. Our new model gives rise to a mechanism that explains learning phenomena such as extinction and spontaneous recovery, which previous learning models could not explain. Finally, we attempt to understand the underlying process of Bayesian entropy estimation. We show that Bayesian entropy estimators depend on a few emergent data statistics that rely on states that are sampled once or more.

Table of Contents

Table of Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Interfaces in nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Ballistic deposition . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.2 Roughening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.3 Dynamic scaling. . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.4 Interface growth with memory . . . . . . . . . . . . . . . . . . . 5

1.2 Animal learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 The Rescorla-Wagner model . . . . . . . . . . . . . . . . . . . . 7

1.2.2 Rescorla-Wagner and the blocking effect . . . . . . . . . . . . . . 8

1.2.3 Rescorla-Wagner and associative strength loss despite pairings with

the US . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.4 Rescorla-Wagner and conditioned inhibition . . . . . . . . . . . . 9

1.2.5 Problems with the Rescorla-Wagner model. . . . . . . . . . . . . 10

1.2.6 A new learning model . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3 Entropy Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3.1 The birthday problem . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3.2 Inferring the number of states from coincidences. . . . . . . . . . 13

1.3.3 Problems with inference . . . . . . . . . . . . . . . . . . . . . . 14

1.3.4 What is new here? . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Ballistic deposition with memory: a new universality class of

surface growth with a new scaling law . . . . . . . . . . . . . . . . 16

2.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Model formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 A random walker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.5 Determining the unit of time . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6 Dynamical exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.7 Dynamical scaling relation and the scaling law. . . . . . . . . . . . . . . 23

2.8 Varying the memory time scale . . . . . . . . . . . . . . . . . . . . . . . 24

2.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.10 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.10.1 Solving the propensity recursion relation . . . . . . . . . . . . . . 27

2.10.2 Computing deposition probabilities. . . . . . . . . . . . . . . . . 28

2.10.3 Expanding the random walk regime . . . . . . . . . . . . . . . . 28

2.10.4 Extracting exponents from data . . . . . . . . . . . . . . . . . . . 29

3 C. elegans thermotaxis reveals general mechanisms of extinc-

tion and recovery in animal learning . . . . . . . . . . . . . . . . . 31

3.1 Author contributions: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4.1 Measuring thermal preference . . . . . . . . . . . . . . . . . . . 35

3.4.2 Dynamics of thermal preference . . . . . . . . . . . . . . . . . . 35

3.4.3 Constructing a model of thermal preference dynamics . . . . . . . 38

3.4.4 Fitting the model to data . . . . . . . . . . . . . . . . . . . . . . 41

3.4.5 Thermotactic dynamics in mutants . . . . . . . . . . . . . . . . . 42

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.6 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.6.1 Nonlinear dynamics of animal learning. . . . . . . . . . . . . . . 47

3.6.2 Strains and preparation . . . . . . . . . . . . . . . . . . . . . . . 50

3.6.3 μ droplet assay . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.6.4 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.6.5 Bounding the dimensionality of the thermal memory dynamics . . 53

3.6.6 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.6.7 Constraints on the model parameters . . . . . . . . . . . . . . . . 58

3.6.8 Constraints on parameters for mutants . . . . . . . . . . . . . . . 60

3.6.9 Constructing the loss function . . . . . . . . . . . . . . . . . . . 60

3.6.10 Optimization and parameter values . . . . . . . . . . . . . . . . . 63

3.6.11 Model reduction and fitted values. . . . . . . . . . . . . . . . . . 64

3.6.12 Mutant fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.6.13 Parameter and model trajectory error bars . . . . . . . . . . . . . 68

3.6.14 Data and material availability: . . . . . . . . . . . . . . . . . . . 71

4 Entropy Estimation for under-sampled discrete distribution . 72

4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.3 Overview of Bayesian entropy estimation . . . . . . . . . . . . . . . . . 74

4.3.1 The Nemenman-Shafee-Bialek (NSB) Estimator. . . . . . . . . . 76

4.3.2 The Dirichlet and the Pitman-Yor Processes . . . . . . . . . . . . 77

4.3.3 Expectations over DP and PYP Posteriors . . . . . . . . . . . . . 78

4.4 Determining data statistics that define entropy estimates . . . . . . . . . . 80

4.5 Tail-hypothesis and entropy estimation phase diagrams . . . . . . . . . . 84

4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.7.1 Marginal likelihood approximation for a Pitman-Yor process . . . 89

4.7.2 Maximum likelihood Entropy in terms of coincidences . . . . . . 91

4.7.3 Mean posterior entropy approximation for the Pitman-Yor Process 92

5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.1 Surface Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.2 Animal Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.3 Data statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

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School	Laney Graduate School
Department	Physics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Biophysics, General Physics, Theory Biology, Neuroscience
Palavra-chave	reinforcement learning dynamic exponents family-viscek scaling spontaneous recovery interface growth Coincidences extinction operant conditioning Entropy Pavlovian Learning KPZ universality class classical conditioning Rescorla Wagner scaling law C. elegans thermal learning Entropy Estimation generalization Pitman-Yor
Committee Chair / Thesis Advisor	Ilya Nemenman, Emory University
Committee Members	Gordon Berman, Emory University Samuel Sober, Emory University Justin Burton, Emory University Eric Weeks, Emory University

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