Related papers: Coupling continuous neural networks to the electro…
The common description of the electrical behavior of a nematic liquid crystal as an anisotropic dielectric medium with (weak) ohmic conductivity is extended to an electrodiffusion model with two active ionic species. Under appropriate, but…
Most models of neurons incorporate a capacitor to account for the marked capacitive behavior exhibited by the cell membrane. However, such capacitance is widely considered constant, thereby neglecting the possible effects of time-dependent…
In this work, we present a mathematical model for cyclic and sequential patterns of brain activity, combining heteroclinic dynamics with discrete neural-field models. We first show that spatial-discrete neural-field equations with…
We show that the electric dipole-dipole interaction between a pair of polar molecules undergoes an all-out transformation when superimposed by a far-off resonant optical field. The combined interaction potential becomes tunable by variation…
This paper is an introduction to the membrane potential equation for neurons. Its properties are described, as well as sample applications. Networks of these equations can be used for modeling neuronal systems, which also process images and…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
We study a model of interacting neurons. The structure of this neural system is composed of two layers of neurons such that the neurons of the first layer send their spikes to the neurons of the second one: if $N$ is the number of neurons…
The formation of nanoscale domains (NDs) in correlated liquids and the emerging collective magnetic properties have been suggested as key mechanisms governing ion transport under external magnetic fields (eMFs). However, the molecular-level…
Functions of brain areas in complex animals are believed to rely on the dynamics of networks of neurons rather than on single neurons. On the other hand, the network dynamics reflect and arise from the integration and coordination of the…
Neuronal cable theory is usually derived from an electric analogue of the membrane, which contrasts with the slow movement of ions in aqueous media. We show here that it is possible to derive neuronal cable equations from a different…
We advance our approach of analyzing the dynamics of interacting complex systems with the nonlinear dynamics of interacting nonlinear elements. We replace the widely used lattice-like connection topology of cellular neural networks (CNN) by…
We present a derivation of a multidomain model for the electric potential in bundles of randomly distributed axons with different radii. The FitzHugh-Nagumo dynamics is assumed on the axons' membrane, and the conductivity depends…
Neurons integrate synaptic inputs and convert them to action potential output at electrically distant locations. The computational power of a neuron is hence enhanced by subcellular compartmentalization and nonlinear synaptic integration,…
We investigate dielectric saturation and increment in polar liquids under external fields. We couple a previously introduced dipolar solvent model to a uniform electric field and derive the electrostatic kernel of interacting dipoles. This…
This paper investigates the online estimation of neural activity within the primary visual cortex (V1) in the framework of observability theory. We focus on a low-dimensional neural fields modeling hypercolumnar activity to describe…
The study of cortical dynamics during different states such as decision making, sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate the neural rhythms present in cortical recordings to the underlying…
Resonant energy transfer, energy transfer upconversion, and energy pooling are considered within optical cavities to elucidate the relationship between exciton dynamics and donor/acceptor separation distance. This is accomplished using…
Synaptic plasticity and neuron cross-talk are some of the important key mechanisms underlying formation of dynamic clusters of active neurons. The essence of this study is to model and decipher the mechanism of emergence of a task-specific…
In the Nernst-Planck equations in two or more dimensions, a non-Faradaic electric current can arise as a consequence of connecting patches with different liquid junction potentials. Whereas this current vanishes for binary electrolytes or…
Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in…