Search results for "Quantitative Biology::Neurons and Cognition"
showing 10 items of 111 documents
Standard polynomials are characterized by their degree and exponent
2011
Abstract By the Giambruno–Zaicev theorem (Giambruno and Zaicev, 1999) [5] , the exponent exp ( A ) of a p.i. algebra A exists, and is always an integer. In Berele and Regev (2001) [2] it was shown that the exponent exp ( St n ) of the standard polynomial St n of degree n is not smaller than the exponent of any polynomial of degree n. Here it is proved that exp ( St n ) is strictly larger than the exponent of any other polynomial of degree n which is not a multiple of St n .
A simple algorithm for generating neuronal dendritic trees
1990
Abstract A simple, efficient algorithm is presented for generating the codewords of all neuronal dendritic trees with a given number of terminal nodes. Furthermore, a procedure is developed for deciding if different codewords correspond to topologically equivalent trees.
Periodic and Chaotic Orbits of a Neuron Model
2015
In this paper we study a class of difference equations which describes a discrete version of a single neuron model. We consider a generalization of the original McCulloch-Pitts model that has two thresholds. Periodic orbits are investigated accordingly to the different range of parameters. For some parameters sufficient conditions for periodic orbits of arbitrary periods have been obtained. We conclude that there exist values of parameters such that the function in the model has chaotic orbits. Models with chaotic orbits are not predictable in long-term.
Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness
2012
Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.
Comparison of Causality Network Estimation in the Sensor and Source Space: Simulation and Application on EEG
2021
The usage of methods for the estimation of the true underlying connectivity among the observed variables of a system is increasing, especially in the domain of neuroscience. Granger causality and similar concepts are employed for the estimation of the brain network from electroencephalogram (EEG) data. Also source localization techniques, such as the standardized low resolution electromagnetic tomography (sLORETA), are widely used for obtaining more reliable data in the source space. In this work, connectivity structures are estimated in the sensor and in the source space making use of the sLORETA transformation for simulated and for EEG data with episodes of spontaneous epileptiform discha…
Characteristics of neuronal systems in the visual cortex
1987
The coupling complexity of cortical areas makes it very difficult to analyse them experimentally. Studies of model systems provide the possibility of adapting the analysis to the available data base and elaborating the fundamental properties that depend on the structure of the system. We propose a model system of variable complexity that is spatially two-dimensional and time-dependent, uses feedback for iteration and smoothing, includes the mapping of the cortical networks and can be nonlinear as the case requires. Combining such elementary systems on the basis of neuroanatomical findings enables us to simulate cortical mappings and to interpret neurophysiological data. The decisive factor …
The resemblance of an autocorrelation function to a power spectrum density for a spike train of an auditory model
2013
In this work we develop an analytical approach for calculation of the all-order interspike interval density (AOISID), show its connection with the autocorrelation function, and try to explain the discovered resemblance of AOISID to the power spectrum of the same spike train.
The Method of Fundamental Solutions in Solving Coupled Boundary Value Problems for M/EEG
2015
The estimation of neuronal activity in the human brain from electroencephalography (EEG) and magnetoencephalography (MEG) signals is a typical inverse problem whose solution pro- cess requires an accurate and fast forward solver. In this paper the method of fundamental solutions is, for the first time, proposed as a meshfree, boundary-type, and easy-to-implement alternative to the boundary element method (BEM) for solving the M/EEG forward problem. The solution of the forward problem is obtained by numerically solving a set of coupled boundary value problems for the three-dimensional Laplace equation. Numerical accuracy, convergence, and computational load are investigated. The proposed met…
On the long-term response of elastic-perfectly plastic solids to dynamic cyclic loads
1992
It is shown that the long-term response of an elastic-perfectly plastic solid subjected to dynamic actions cyclically varying in time is characterized by stresses, plastic strain rates and velocities that are all periodic with the same period of the external actions, and are in perfect analogy with the quasi-static case; on the other hand, plastic strains and displacements are in general nonperiodic (except in case of alternating plasticity) and may increase indefinitely (except when elastic or plastic shakedown occurs). Besides, the work performed by the external actions in the steady cycle equals the work performed by the elastic stresses (i.e. pertaining to the elastic response of the bo…
Regularity of Spike Trains and Harmony Perception in a Model of the Auditory System
2011
Spike train regularity of the noisy neural auditory system model under the influence of two sinusoidal signals with different frequencies is investigated. For the increasing ratio m/n of the input signal frequencies (m, n are natural numbers) the linear growth of the regularity is found at the fixed difference (m - n). It is shown that the spike train regularity in the model is high for harmonious chords of input tones and low for dissonant ones.