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Redox molecular junctions are molecular conduction junctions that involve more than one oxidation state of the molecular bridge. This property is derived from the ability of the molecule to transiently localize transmitting electrons,…

We study the phenomenological model of ensemble of two FitzHugh-Nagumo neuron-like elements with symmetric excitatory couplings. The main advantage of proposed model is the new approach to model of coupling which is implemented by smooth…

Neural mass models describe the mean-field dynamics of populations of neurons. In this work we illustrate how fundamental ideas of physics, such as energy and conserved quantities, can be explored for such models. We show that…

Photonic neural networks benefit from both the high channel capacity- and the wave nature of light acting as an effective weighting mechanism through linear optics. The neuron's activation function, however, requires nonlinearity which can…

We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites,…

A growing body of research indicates that structural plasticity mechanisms are crucial for learning and memory consolidation. Starting from a simple phenomenological model, we exploit a mean-field approach to develop a theoretical framework…

This paper investigates stability conditions of continuous-time Hopfield and firing-rate neural networks by leveraging contraction theory. First, we present a number of useful general algebraic results on matrix polytopes and products of…

Neurons regulate the distribution of signaling components across an extended tree-like cellular structure using both local and global feedback control. This is hypothesized to allow homeostatic control of the electrical activity of a neuron…

In this paper we study the hydrodynamic limit for a stochastic process describing the time evolution of the membrane potentials of a system of neurons with spatial dependency. We do not impose on the neurons mean-field type interactions.…

This paper attempts to review our studies on the propagation of signals in nerves over the past decade. The need for interdisciplinary studies is stressed that helps to understand the physical mechanisms of coupling the electrical,…

Since the discovery of polar topological textures, achieving efficient control and manipulation of them has emerged as a significant challenge for their integration into nanoelectronic devices. In this study, we use second principles…

Neural circuits comprise multiple interconnected regions, each with complex dynamics. The interplay between local and global activity is thought to underlie computational flexibility, yet the structure of multiregion neural activity and its…

The Marcus theory expression for the rate of non-adiabatic electron transfer is widely used across a range of physical conditions. Although Marcus theory defines the reorganization energy classically, here we show that the reorganization…

We show that dynamical gain modulation of neurons' stimulus response is described as an information-theoretic cycle that generates entropy associated with the stimulus-related activity from entropy produced by the modulation. To articulate…

In this work, it is demonstrated that there is an additional origin of the electric potential energy of an electron orbiting a nuclei that can be, alternatively to that associated to the elementary `static' charge of the electron as…

This paper introduces a biomathematical model designed to describe the internal dynamics of dream formation and spontaneous cognitive processes. The model incorporates neurocognitive factors such as dissatisfaction, acceptance, forgetting,…

Neural networks are based on a simplified model of the brain. In this project, we wanted to relax the simplifying assumptions of a traditional neural network by making a model that more closely emulates the low level interactions of…

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…

Memristors stand out as promising components in the landscape of memory and computing. Memristors are generally defined by a conductance equation containing a state variable that imparts a memory effect. The current-voltage cycling causes…

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to…