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Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…

Phase separation, the spontaneous segregation of density, is a ubiquitous phenomenon observed across diverse physical and biological systems. Within a crowd of motile elements, active phase separation emerges from the interplay of activity…

We study the behaviour of interacting self-propelled particles, whose self-propulsion speed decreases with their local density. By combining direct simulations of the microscopic model with an analysis of the hydrodynamic equations obtained…

A block of rubber eventually buckles under severe flexure, and several axial wrinkles appear on the inner curved face of the bent block. Experimental measurements reveal that the buckling occurs earlier ---at lower compressive strains---…

The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…

We examine the large-network, low-loading behaviour of an attractor neural network, the so-called bistable gradient network (BGN). We use analytical and numerical methods to characterize the attractor states of the network and their basins…

We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…

Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…

Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…

We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…

Inspired by recent experiments of cells accumulating on anisotropic substrates, we study a two-dimensional, compressible, isotropic, active fluid in the presence of anisotropic friction. We find that regions of anisotropic friction that are…

Understanding and controlling the informational complexity of neural networks is a central challenge in machine learning, with implications for generalization, optimization, and model capacity. While most approaches rely on entropy-based…

We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint…

Many organisms can remember locations they have previously visited during a search. Visual search experiments have shown exploration is guided away from these locations, reducing the overlap of the search path before finding a hidden…

A binary system of particles that move in opposite directions under an applied field can exhibit disordered states as well as laned states where the particles organize into oppositely moving high-mobility lanes to reduce collisions.…

An active system consisting of many self-spinning dimers is simulated, and a distinct local rotational jamming transition is observed as the density increases. In the low density regime, the system stays in an absorbing state, in which each…

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to…

We present a model for a class of random binary lattices by introducing a one-dimensional system where impurities are placed in one sublattice while host atoms lie on the other sublattice. The source of disorder is the stochastic…

We examine the ordering, pinning, and dynamics of two-dimensional pattern forming systems interacting with a periodic one-dimensional substrate. In the absence of the substrate, particles with competing long-range repulsion and short-range…

This paper studies a permutation binary neural network characterized by local binary connections, global permutation connections, and the signum activation function. Depending on the permutation connections, the network can generate various…