相关论文: Stability of Localized Patterns in Neural Fields
Neural fields model signals by mapping coordinate inputs to sampled values. They are becoming an increasingly important backbone architecture across many fields from vision and graphics to biology and astronomy. In this paper, we explore…
We study the existence and linear stability of stationary periodic solutions to a neural field model, an intergo-differential equation of the Hammerstein type. Under the assumption that the activation function is a discontinuous step…
We provide an empirical study of the stability of recurrent neural networks trained to recognize regular languages. When a small amount of noise is introduced into the activation function, the neurons in the recurrent layer tend to saturate…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
The elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
A fundamental problem in neuroscience is to characterize the dynamics of spiking from the neurons in a circuit that is involved in learning about a stimulus or a contingency. A key limitation of current methods to analyze neural spiking…
We generalize the scalar tensor bigravity models to the non-minimal kinetic coupling scalar tensor bigravity models with two scalar fields whose kinetic terms are non-minimally coupled to two Einstein tensors constructed by two metrics. We…
The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…
Localized patterns are spatially confined structures that arise in lattice dynamical systems and play an important role in physics, biology, and materials science. While their existence and bifurcation structure are well-understood, the…
The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts…
Learning a task induces connectivity changes in neural circuits, thereby changing their dynamics. To elucidate task related neural dynamics we study trained Recurrent Neural Networks. We develop a Mean Field Theory for Reservoir Computing…
We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function.…
We consider the initial value problem associated to the neural field equation of Amari type with plasticity \[ u_t(x,t)=-u(x,t)+\int_{\Omega}w(x,y)[1+\gamma g( u(x,t) - u(y,t) )] f(u(y,t))\; dy, \;(x,t) \in \Omega \times (0, \infty), \]…
We propose a new mechanism for stabilization of confined modes in lasers and semiconductor microcavities holding exciton-polariton condensates, with spatially uniform linear gain, cubic loss, and cubic self-focusing or defocusing…
Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…
We investigate a class of models described by two real scalar fields in two-dimensional spacetime. The study focuses mainly on the presence of exact static solutions which satisfy the first-order formalism, in models constructed to engender…
We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…
We study dilute suspensions of magnetic nanoparticles in a nematic host, on two-dimensional (2D) polygons. These systems are described by a nematic order parameter and a spontaneous magnetization, in the absence of any external fields. We…