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We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…
We report a refinement of Robertson-Schroedinger uncertainty relation via Wigner-Yanase skew information. Besides the well known quantum uncertainty arising from the noncommutativity of observables, there is classical uncertainty arising…
[RETRACTED]Data increasingly abounds, but distilling their underlying relationships down to something interpretable remains challenging. One approach is genetic programming, which `symbolically regresses' a data set down into an equation.…
A quantum model of neural network is introduced and its phase structure is examined. The model is an extension of the classical Z(2) gauged neural network of learning and recalling to a quantum model by replacing the Z(2) variables, $S_i =…
In recent years, the alignment between artificial neural network (ANN) embeddings and blood oxygenation level dependent (BOLD) responses in functional magnetic resonance imaging (fMRI) via neural encoding models has significantly advanced…
We formulate a new information-theoretic principle--the shifted composition rule--which bounds the divergence (e.g., Kullback-Leibler or R\'enyi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this…
The paradigm of stochastic resonance (SR)---the idea that signal detection and transmission may benefit from noise---has met with great interest in both physics and the neurosciences. We investigate here the consequences of reducing the…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
Cross-entropy loss has long been the standard choice for training deep neural networks, yet it suffers from interpretability limitations, unbounded weight growth, and inefficiencies that can contribute to costly training dynamics. The…
An SNN-junction in which the superconducting potential is a mixture between s-wave and p-wave potentials is investigated using the Usadel equation equipped with Tanaka-Nazarov boundary conditions. The article provides several ways to…
We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary…
Neuro-symbolic reinforcement learning (NS-RL) has emerged as a promising paradigm for explainable decision-making, characterized by the interpretability of symbolic policies. NS-RL entails structured state representations for tasks with…
We perform analysis of the small x non-linear evolution equation formulated in momentum space supplemented by higher order terms. The equation is defined in wide range of transverse momentum and longitudinal momentum fraction extending…
The energy structure and the thermodynamics of ferrimagnetic Heisenberg chains of alternating spins S and s are described in terms of the Schwinger bosons and modified spin waves. In the Schwinger representation, we average the local…
We introduce a new test for detection of power-law cross-correlations among a pair of time series - the rescaled covariance test. The test is based on a power-law divergence of the covariance of the partial sums of the long-range…
Understanding brain function, constructing computational models and engineering neural prosthetics require assessing two problems, namely encoding and decoding, but their relation remains controversial. For decades, the encoding problem has…
Biological systems are notoriously noisy. Noise, therefore, also plays an important role in many models of neural impulse generation. Noise is not only introduced for more realistic simulations but also to account for cooperative effects…
Responses have been numerically studied of an ensemble of $N$ (=1, 10, and 100) Hodgkin-Huxley (HH) neurons to coherent spike-train inputs applied with independent Poisson spike-train (ST) noise and Gaussian white noise. Three interrelated…
The semi-relativistic equation is cast into a second-order Schrodinger-like equation with the inclusion of relativistic corrections up to order (v/c)^2. The resulting equation is solved via the shifted-l expansion technique, which has been…
Symbolic Regression searches for a function form that approximates a dataset often using Genetic Programming. Since there is usually no restriction to what form the function can have, Genetic Programming may return a hard to understand…