Related papers: Amplitude equations of associative memory patterns…
Associative memory and probabilistic modeling are two fundamental topics in artificial intelligence. The first studies recurrent neural networks designed to denoise, complete and retrieve data, whereas the second studies learning and…
Converging research suggests that the resting brain operates at the cusp of dynamic instability signified by scale-free temporal correlations. We asked if the scaling properties of these correlations differ between amplitude and phase…
We propose and analyze a new variation of the so-called {\em exponential Hopfield model}, a recently introduced family of associative neural networks with unprecedented storage capacity. Our construction is based on a cost function defined…
We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatio-temporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to…
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
Keeping a memory of evolving stimuli is ubiquitous in biology, an example of which is immune memory for evolving pathogens. However, learning and memory storage for dynamic patterns still pose challenges in machine learning. Here, we…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
We propose a novel architecture to design a neural associative memory that is capable of learning a large number of patterns and recalling them later in presence of noise. It is based on dividing the neurons into local clusters and parallel…
Little is known theoretically about the associative memory capabilities of neural networks in which information is encoded not only in the mean firing rate but also in the timing of firings. Particularly, in the case that the fraction of…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
Associative memory is a fundamental function in the brain. Here, we generalize the standard associative memory model to include long-range Hebbian interactions at the learning stage, corresponding to a large synaptic integration window. In…
We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…
Following~\cite{Arkani-Hamed:2017thz}, we derive a recursion relation by applying a one-parameter deformation of kinematic variables for tree-level scattering amplitudes in bi-adjoint $\phi^3$ theory. The recursion relies on properties of…
A Potts associative memory network has been proposed as a simplified model of macroscopic cortical dynamics, in which each Potts unit stands for a patch of cortex, which can be activated in one of S local attractor states. The internal…
Stochastic processes with long memories, known as long memory processes, are ubiquitous in various science and engineering problems. Superposing Markovian stochastic processes generates a non-Markovian long memory process serving as…
Memory is a complex phenomenon that involves several distinct mechanisms. These mechanisms operate at different spatial and temporal levels. This chapter focuses on the theoretical framework and the mathematical models that have been…
A new model of neural networks described by the memristive and diffusive Hindmarsh-Rose equations is proposed. Globally dissipative dynamics is shown with absorbing sets in the state spaces. Through sharp and uniform grouping estimates and…
The properties of the high energy behavior of the scattering amplitude of massive, neutral and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik and Zimmermann is…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
We present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment-like external system. We develop a general stability analysis that is valid for any network…