Statistical Physics and Representations in Real and Artificial Neural Networks

This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we consider the neural representations of space (maps) in the hippocampus. We introduce an extension of the Hopfield model, able to store multiple spatial maps as continuous, finite-dimensional attractors. The phase diagram and dynamical properties of the model are analyzed. We then show how spatial representations can be dynamically decoded using an effective Ising model capturing the correlation structure in the neural data, and compare applications to data obtained from hippocampal multi-electrode recordings and by (sub)sampling our attractor model. In a second part, we focus on the problem of learning data representations in machine learning, in particular with artificial neural networks. We start by introducing data representations through some illustrations. We then analyze two important algorithms, Principal Component Analysis and Restricted Boltzmann Machines, with tools from statistical physics

Can grid cell ensembles represent multiple spaces?

The way grid cells represent space in the rodent brain has been a striking discovery, with theoretical implications still unclear. Di\u21b5erently from hippocampal place cells, which are known to encode multiple, environment-dependent spatial maps, grid cells have been widely believed to encode space through a single low dimensional manifold, in which coactivity relations between di\u21b5erent neurons are preserved when the environment is changed. Does it have to be so? Here, we compute \u2013 using two alternative mathematical models \u2013 the storage capacity of a population of grid-like units, embedded in a continuous attractor neural network, for multiple spatial maps. We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the potential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map. This suggests that a population of grid cells can encode multiple non-congruent metric relationships, a feature that could in principle allow a grid-like code to represent environments with a variety of di\u21b5erent geometries and possibly conceptual and cognitive spaces, which may be expected to entail such context-dependent metric relationships

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

Activité de cellules de lieu de l'hippocampe : modélisation et analyse par des méthodes de physique statistique

Place cells in the hippocampus are neurons with interesting properties such as the corre-lation between their activity and the animal’s position in space. It is believed that theseproperties can be for the most part understood by collective behaviours of models of inter-acting simplified neurons. Statistical mechanics provides tools permitting to study thesecollective behaviours, both analytically and numerically.Here, we address how these tools can be used to understand place-cell activity withinthe attractor neural network paradigm, a theory for memory. We first propose a modelfor place cells in which the formation of a localized bump of activity is accounted for byattractor dynamics. Several aspects of the collective properties of this model are studied.Thanks to the simplicity of the model, they can be understood in great detail. The phasediagram of the model is computed and discussed in relation with previous works on at-tractor neural networks. The dynamical evolution of the system displays particularly richpatterns. The second part of this thesis deals with decoding place-cell activity, and theimplications of the attractor hypothesis on this problem. We compare several decodingmethods and their results on the processing of experimental recordings of place cells in afreely behaving rat.Les cellules de lieu de l’hippocampe sont des neurones aux propriétés intrigantes, commele fait que leur activité soit corrélée à la position spatiale de l’animal. Il est généralementconsidéré que ces propriétés peuvent être expliquées en grande partie par les comporte-ments collectifs de modèles schématiques de neurones en interaction. La physique statis-tique fournit des outils permettant l’étude analytique et numérique de ces comportementscollectifs.Nous abordons ici le problème de l’utilisation de ces outils dans le cadre du paradigmedu “réseau attracteur”, une hypothèse théorique sur la nature de la mémoire. La questionest de savoir comment ces méthodes et ce cadre théorique peuvent aider à comprendrel’activité des cellules de lieu. Dans un premier temps, nous proposons un modèle de cellulesde lieu dans lequel la localisation spatiale de l’activité neuronale est le résultat d’unedynamique d’attracteur. Plusieurs aspects des propriétés collectives de ce modèle sontétudiés. La simplicité du modèle permet de les comprendre en profondeur. Le diagrammede phase du modèle est calculé et discuté en comparaison avec des travaux précedents.Du point de vue dynamique, l’évolution du système présente des motifs particulièrementriches. La seconde partie de cette thèse est à propos du décodage de l’activité des cellulesde lieu. Nous nous demandons quelle est l’implication de l’hypothèse des attracteurs surce problème. Nous comparons plusieurs méthodes de décodage et leurs résultats sur letraitement de données expérimentales

Neuropeptides and bacterial interactions: The example of the impact of the C-type natriuretic peptide (CNP) on Pseudomonas aeruginosa biofilm formation

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Host Peptidic Hormones Affecting Bacterial Biofilm Formation and Virulence

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