Spatial and temporal criticality emerge from latent-variable models Público

Abstract

Understanding activity of large populations of neurons is difficult due to the combinatorial complexity of possible cell-cell interactions. A remedy is to note that many systems may be macroscopically described with models simpler than the system's microscopic behavior. This has been probed via a coarse-graining procedure on experimental neural recordings, which shows over two decades of scaling in free energy, variance, eigenvalue spectra, and correlation time [1], hinting that a mouse hippocampus operates in a critical regime. We investigated whether this scaling behavior could be explained as a result of coupling the neural population to latent dynamic stimuli. We conducted simulations of conditionally independent binary neurons coupled to a small number of long-timescale stochastic fields with and without periodic spatial stimuli (depicting neural place cells) and replicated the coarse-graining shown in [1]. In a biologically relevant regime, we find that much of the observed scaling [1] may be recreated by this model. This suggests that aspects of the scaling may be explained by coupling to hidden dynamic processes, a ubiquitous trait of neural systems.

[1] L. Meshulam et al. arXiv:1812.11904 [physics.bio-ph], 2019

Table of Contents

Table of Contents

List of Figures ………… iii

List of Tables ………… xii

I. Introduction ………… 2

A. Motivation ………… 2

II. Experimental Background ………… 3

A. Experimental setup ………… 3

B. Place fields ………… 3

III. Theory ………… 4

A. Spin models applied to neural systems ………… 4

B. Coarse-graining schemes ………… 6

1. Coarse-graining in real space ………… 6

2. Coarse-graining in momentum space ………… 6

C. Critical Behavior and Scaling ………… 7

1. A review of critical phenomena ………… 7

2. The Ornstein-Zernike correlation form ………… 8

D. Predictions of scaling laws ………… 11

1. Scaling in activity variance ………… 11

2. Free energy scaling ………… 13

3. Scaling in eigenvalue spectra ………… 14

4. Scaling in correlation time ………… 14

5. Flow to a non-gaussian fixed point ………… 15

E. Theoretical Motivation ………… 15

1. Zipf’s Law ………… 15

2. Criticality emerges from large systems obeying Zipf’s Law ………… 16

3. Large systems coupled to latent stimuli obey Zipf’s Law ………… 18

4. Requirements for our model ………… 21

IV. Methods ………… 21

A. The model ………… 21

V. Results ………… 23

1. Scaling of activity variance ………… 25

2. Scaling in eigenvalue spectra ………… 26

3. Scaling in correlation time ………… 26

4. Flow to a non-gaussian fixed point ………… 27

5. Experimental agreement ………… 28

A. Discussion ………… 29

VI. Supplementary Information ………… 29

A. Supplementary figures ………… 29

B. Parameter sweeps ………… 30

1. Varying cell stimuli ………… 31

2. Varying the latent fields multiplier ………… 35

3. Varying the number of latent fields ………… 35

4. Varying the latent fields time constant ………… 39

5. Varying the probability of coupling to a latent fields ………… 39

6. Varying the penalty term ………… 39

7. Varying the multiplier ………… 40

References ………… 40

About this Honors Thesis

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School	Emory College
Department	Physics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Physics, Theory Biophysics, General
Palabra Clave	Coarse-graining schemes Theoretical biophysics Latent variable models
Committee Chair / Thesis Advisor	Ilya Nemenman, Emory University
Committee Members	Audrey Sederberg, Emory University Stefan Boettcher, Emory University Gordon Berman, Emory University

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