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Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network…
An abstract network approach is proposed for the description of the dynamics in reactive processes. The phase space of the variables (concentrations in reactive systems) is partitioned into a finite number of segments, which constitute the…
Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles,…
We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical…
Cells moving on a two dimensional substrate generate motion by polymerizing actin filament networks inside a flat membrane protrusion. New filaments are generated by branching off existing ones, giving rise to branched network structures.…
We have applied the generating functional analysis (GFA) to the continuous Hopfield model. We have also confirmed that the GFA predictions in some typical cases exhibit good consistency with computer simulation results. When a retarded…
In recent years, the study of coupled excitable oscillators has largely benefited from a new analytical technique developed by Ott and Antonsen. This technique allows to express the dynamics of certain macroscopic observable in the ensemble…
Inspired by experiments on dynamic extensile gels of biofilaments and motors, we propose a model of a network of linear springs with a kinetics consisting of growth at a prescribed rate, death after a lifetime drawn from a distribution, and…
The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
Many efforts have been devoted to training generative latent variable models with autoregressive decoders, such as recurrent neural networks (RNN). Stochastic recurrent models have been successful in capturing the variability observed in…
The Dense Associative Memory generalizes the Hopfield network by allowing for sharper interaction functions. This increases the capacity of the network as an autoassociative memory as nearby learned attractors will not interfere with one…
Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With…
We study a mechanism of activity sustaining on networks inspired by a well-known model of neuronal dynamics. Our primary focus is the emergence of self-sustaining collective activity patterns, where no single node can stay active by itself,…
We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities $p$ of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief…
Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…
The neural dynamics of the nematode C. elegans are experimentally low-dimensional and correspond to discrete behavioral states, where previous modeling work has found neural proxies for some of these states. Experimental results further…
This paper addresses the problem of estimating link flows in a road network by combining limited traffic volume and vehicle trajectory data. While traffic volume data from loop detectors have been the common data source for link flow…
We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…
Recent work in modeling the coupling between disease dynamics and dynamic social network geometry has led to the examination of how human interactions force a rewiring of connections in a population. Rewiring of the network may be…