Related papers: Bump formation in a binary attractor neural networ…

Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…

This paper discusses two main themes. First, it investigates the formation of a spatiotemporal cognitive map (mental image) of a road network in travelers memory, which entails the travelers global conceptual understanding of congestion or…

This paper presents a permutation binary neural network characterized by local binary connection, global permutation connection, and the signum activation function. The dynamics is described by a difference equation of binary state…

We study stochastic processes on combinatorial state spaces with local transition constraints, as arise in local search algorithms. We show that asymmetry in local transitions induces a systematic drift in a distance process relative to a…

We performed a numerical study on random Boolean networks with power-law rank outdegree distributions to find local structural cause for the emergence of high or low degree of coherence in binary state variables. The degree of randomness…

Stripe-like and bubble-like patterns spontaneously form in numerous physical, chemical, and biological systems when competing long-range and short-range interactions banish uniformity. Stripe-like and the related nematic morphology are also…

Self-organized coherence-incoherence patterns, called chimera states, have first been reported in systems of Kuramoto oscillators. For coupled excitable units similar patterns, where coherent units are at rest, are called bump states. Here,…

We present the results of an experimental study of pattern formation in horizontally oscillating granular suspensions. Starting from a homogeneous state, the suspension turns into a striped pattern within a specific range of frequencies and…

Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…

Neural networks storing multiple discrete attractors are canonical models of biological memory. Previously, the dynamical stability of such networks could only be guaranteed under highly restrictive conditions. Here, we derive a theory of…

Learning in neural networks poses peculiar challenges when using discretized rather then continuous synaptic states. The choice of discrete synapses is motivated by biological reasoning and experiments, and possibly by hardware…

A nonlocal diffuse interface model is used to study bubble assemblies in ternary systems. As model parameters vary, a large number of morphological phases appear as stable stationary states. One open question related to the polarity…

The extreme fragility of deep neural networks, when presented with tiny perturbations in their inputs, was independently discovered by several research groups in 2013. However, despite enormous effort, these adversarial examples remained a…

A two dimensional flow model is introduced with deterministic behavior consisting of bursts which become successively larger, with longer interburst time intervals between them. The system is symmetric in one variable x and there are bursts…

The spontaneous transitions between D-dimensional spatial maps in an attractor neural network are studied. Two scenarios for the transition from on map to another are found, depending on the level of noise: (1) through a mixed state, partly…

We study both analytically and numerically the effect of presynaptic noise on the transmission of information in attractor neural networks. The noise occurs on a very short-time scale compared to that for the neuron dynamics and it produces…

We develop a learning-based framework for constructing shrinking disturbance-invariant tubes under state- and input-dependent uncertainty, intended as a building block for tube Model Predictive Control (MPC), and certify safety via a…

We study heterogeneous distribution of gains in neural fields using techniques of quantum mechanics by exploiting a relationship of our model and the time-independent Schr\"{o}dinger equation. We show that specific relationships between the…

Nonlinear waves that collide with localized defects exhibit complex behavior. Apart from reflection, transmission, and annihilation of an incident wave, a local inhomogeneity can activate internal modes of solitons, producing many…

We studied the effect of nearest pattern interaction on a globally pattern formation in a 2-dimensional space, where patterns are to grow initially from a noise in the presence of periodic supply of energy. Although our approach is general,…