Page 1 Next

Displaying 1 – 20 of 53

Showing per page

A simultaneous localization and tracking method for a worm tracking system

Mateusz Kowalski, Piotr Kaczmarek, Rafał Kabaciński, Mieszko Matuszczak, Kamil Tranbowicz, Robert Sobkowiak (2014)

International Journal of Applied Mathematics and Computer Science

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...

Analysis of Synchronization in a Neural Population by a Population Density Approach

A. Garenne, J. Henry, C. O. Tarniceriu (2010)

Mathematical Modelling of Natural Phenomena

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

Paweł Strumiłło, Michał Strzelecki (2006)

International Journal of Applied Mathematics and Computer Science

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...

Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory

R. E. Lee DeVille, C. S. Peskin, J. H. Spencer (2010)

Mathematical Modelling of Natural Phenomena

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...

Currently displaying 1 – 20 of 53

Page 1 Next