A geometrical description of visual sensation
A geometrical description of visual sensation II
A simultaneous localization and tracking method for a worm tracking system
The idea of worm tracking refers to the path analysis of Caenorhabditis elegans nematodes and is an important tool in neurobiology which helps to describe their behavior. Knowledge about nematode behavior can be applied as a model to study the physiological addiction process or other nervous system processes in animals and humans. Tracking is performed by using a special manipulator positioning a microscope with a camera over a dish with an observed individual. In the paper, the accuracy of a nematode's...
Abstract action potential models for toxin recognition.
Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions.
Amplified molecular binding of prion protein homologues in self-progressive injury of neuronal membranes and trafficking systems.
Analysis of Synchronization in a Neural Population by a Population Density Approach
In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich’s two - dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase density population, and use Malkin theorem to calculate...
Application of coupled neural oscillators for image texture segmentation and modeling of biological rhythms
The role of relaxation oscillator models in application fields such as modeling dynamic systems and image analysis is discussed. A short review of the Van der Pol, Wilson-Cowan and Terman-Wang relaxation oscillators is given. The key property of such nonlinear oscillators, i.e., the oscillator phase shift (called the Phase Response Curve) as a result of external pulse stimuli is indicated as a fundamental mechanism to achieve and sustain synchrony in networks of coupled oscillators. It is noted...
Automatic recognition of muscle-invasive T-lymphocytes expressing dipeptidyl-peptidase IV (CD26) and analysis of the associated cell surface phenotypes.
Bifurcations of FitzHugh-Nagumo excitable systems with chemical delayed coupling
Biomolecular nonlinear dynamic mechanisms as a foundation for human traits of information processing machine.
Brain-like functor control machine for general humanoid biodynamics.
Calculating the number of people with Alzheimer's disease in any country using saturated mutation models of brain cell loss that also predict widespread natural immunity to the disease.
Canonical models in mathematical neuroscience.
Computation of the topological entropy in chaotic biophysical bursting models for excitable cells.
Dynamical morphology of the brain's ventricular cavities in hydrocephalus.
Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory
We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...
Einschliessungsaussagen bei Systemen semilinearer parabolischer Differentialgleichungen
Für die Lösungen seminlinearer parabolischer Differentialgleichungen werden Einschliessungsaussagen hergeleitet. Hierbei werden Aussagen zur Stabilität von Lösungen ermittelt. Die Resultate werden am Beispiel der Fitzhugh-Nagumo Gleichungen diskutiert.
Elektronický model neuronu podle N. I. Vvedenského
Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations.