Stochastic and chaotic evaluation of parameters of lectroencephalogram

2015 ◽  
Vol 4 (1) ◽  
pp. 54-59 ◽  
Author(s):  
Горбунов ◽  
D. Gorbunov ◽  
Вохмина ◽  
Yu. Vokhmina ◽  
Еськов ◽  
...  
Keyword(s):  
Phase Space ◽  
Autocorrelation Function ◽  
Compartmental Model ◽  
Mental States ◽  
Rate Of Change ◽  
Pairwise Comparisons ◽  
Estimation Of Parameters ◽  
Brain Potentials ◽  
The Matrix ◽  
Evaluation Of Parameters

Traditionally parameters of amplitude-frequency characteristics of recorded biopotentials are used in EEG. In this paper we show that they are still chaotic, which takes place for the autocorrelation function A(t). It is proposed the two new approaches for estimation of parameters of electroencephalograms. The first is based on the construction of the matrix of pairwise comparisons of recorded samples of brain potentials in subjects in different physiological (mental) states. The second method is based on calculating the parameters of quasi-attractors, which are built on the plane in the coordinates x1=U(t) – a function that changes due to registration of biopotential in cur-rent point and x2=dx1/dt - rate of change of x1. It is possible to construct a three-compartmental model quasi-attractor in the phase space of states, which is also discussed

Chaotic Dynamics of Electroencephalogram Parameters

2015 ◽  
Vol 22 (2) ◽  
pp. 38-73
Author(s):  
Горбунов ◽  
D. Gorbunov ◽  
Вохмина ◽  
Yu. Vokhmina ◽  
Еськов ◽  
...  
Keyword(s):  
Phase Space ◽  
Chaotic Dynamics ◽  
Clinical Medicine ◽  
Mental States ◽  
Rate Of Change ◽  
Estimation Of Parameters ◽  
Brain Potentials ◽  
Dimensional Phase Space ◽  
The Matrix ◽  
Entropy Parameter

A clinical medicine usually uses the amplitude-frequency characteristics of recorded biopotentials. The paper presents still chaotic dynamics, which takes place for the autocorrelation function A(t) and statistic function of distribution fix). It is proposed two new approaches for estimation of parameters of electroencephalograms. The first is based on the construction of the matrix of pairwise comparisons of recorded samples of brain potentials in subjects in different physiological (mental) states: with photostimulation and without it. The second method is based on calculating the parameters of quasi-attractors, which are built on the plane in the coordinates x1=U(t) - a function that changes due to registration of biopotential in current point and x2=dx1/dt - rate of change of x1. The quasi-attractors in this two-dimensional phase space are quantitatively different options for patients (epilepsy) and healthy subjects. It is possible to construct a three-compartmental model quasi-attractor in the phase space of states, which is also discussed. It was demonstrated the stochastic of function fix) for normal and pathological patients. It was proved the nonfictions of entropy parameter for the EEG modeling.

Thermodynamic and chaotic approaches for the estimation of parameters tremor cooling subjects

2015 ◽  
Vol 4 (1) ◽  
pp. 67-74
Author(s):  
Умаров ◽  
B. Umarov ◽  
Бурыкин ◽  
Yu. Burykin ◽  
Берестин ◽  
...  
Keyword(s):  
Cold Exposure ◽  
Research Performance ◽  
The Body ◽  
Pairwise Comparisons ◽  
Estimation Of Parameters ◽  
The North ◽  
Before And After ◽  
The Matrix ◽  
Statistical Indicators ◽  
High Adaptation

The results of the research performance of the neuromuscular system of boys and girls aged from 20 to 28 years old, living in the North for over 15 years and have a different experience of tempering procedures. Mean age was 22.8 years. Indications tremors were recorded before and after local cold exposure, based on comparing the body´s response in all groups surveyed. It is proved that the local cold exposure affects the parameters of the neuro – muscular man (tremorogrammy) in three groups of subjects (group 1 to 15 people is not quenched, 2nd group of 15 people hardenable less than a year, the third group of 15 people hardenable 2-xs). Were calculated and statistical indicators obtained amplitude – frequency characteristics of signals, calculate the area and the matrix of pairwise comparisons tremorogramm three groups of subjects before and after exposure. Quasi-attractor showed the greatest difference in comparison with the stochastics and the matrix of pairwise comparisons in trained almost do not change before and after cold exposure, which is indicative of a high adaptation to cold exposure.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

Calibrating compartmental models of neurons

1978 ◽  
Vol 235 (1) ◽  
pp. R93-R98 ◽  
Author(s):  
D. H. Perkel ◽  
B. Mulloney
Keyword(s):  
Steady State ◽  
Electrical Properties ◽  
Differential Equations ◽  
Compartmental Model ◽  
Compartmental Models ◽  
Electrical Measurements ◽  
Original Matrix ◽  
Systematic Procedure ◽  
The Matrix ◽  
Voltage Attenuation

Numerical parameters for a compartmental model of a neuron can be chosen to conform both to the neuron's structure and to its measured steady-state electrical properties. A systematic procedure for assigning parameters is described that makes use of the matrix of coefficients of the set of differential equations that embodies the compartmental model. The inverse of this matrix furnishes input resistances and voltage attenuation factors for the model, and an interactive modification of the original matrix and its inverse may be used to fit the model to anatomic and electrical measurements.

COEXISTENCE OF LOW- AND HIGH-DIMENSIONAL SPATIOTEMPORAL CHAOS IN A CHAIN OF DISSIPATIVELY COUPLED CHUA’S CIRCUITS

1994 ◽  
Vol 04 (03) ◽  
pp. 639-674 ◽  
Author(s):  
A.L. ZHELEZNYAK ◽  
L.O. CHUA
Keyword(s):  
Phase Space ◽  
Initial Conditions ◽  
Coupling Parameter ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
Spatiotemporal Chaos ◽  
Matrix Phase ◽  
High Dimensional ◽  
The Matrix ◽  
A Chain

Spatiotemporal dynamics of a one-dimensional cellular neural network (CNN) made of Chua’s circuits which mimics a reaction-diffusion medium is considered. An approach is presented to analyse the properties of this reaction-diffusion CNN through the characteristics of the attractors of an associated infinite-dimensional dynamical system with a matrix phase space. Using this approach, the spatiotemporal correlation dimension of the CNN’s spatiotemporal patterns is computed over various ranges of the diffusion coupling parameter, length of the chain, and initial conditions. It is shown that in a finite-dimensional projection of the matrix phase space of the CNN, both low- and high-dimensional attractors corresponding to different initial conditions coexist.

scholarly journals A factorisation-aware Matrix element emulator

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
D. Maître ◽  
H. Truong
Keyword(s):  
Neural Network ◽  
Phase Space ◽  
Matrix Element ◽  
Percent Level ◽  
Matrix Elements ◽  
Leading Order ◽  
Jet Production ◽  
The Neural Network ◽  
The Matrix ◽  
The One

Abstract In this article we present a neural network based model to emulate matrix elements. This model improves on existing methods by taking advantage of the known factorisation properties of matrix elements. In doing so we can control the behaviour of simulated matrix elements when extrapolating into more singular regions than the ones used for training the neural network. We apply our model to the case of leading-order jet production in e+e− collisions with up to five jets. Our results show that this model can reproduce the matrix elements with errors below the one-percent level on the phase-space covered during fitting and testing, and a robust extrapolation to the parts of the phase-space where the matrix elements are more singular than seen at the fitting stage.

scholarly journals Multiplicative-accumulative matching of NLO calculations with parton showers

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Paolo Nason ◽  
Gavin P. Salam
Keyword(s):  
Phase Space ◽  
Matrix Element ◽  
Parton Shower ◽  
Leading Order ◽  
Positive Weight ◽  
New Approach ◽  
The Matrix ◽  
Core Features

Abstract We propose a new approach for combining next-to-leading order (NLO) and parton shower (PS) calculations so as to obtain three core features: (a) applicability to general showers, as with the MC@NLO and POWHEG methods; (b) positive-weight events, as with the KrkNLO and POWHEG methods; and (c) all showering attributed to the parton shower code, as with the MC@NLO and KrkNLO methods. This is achieved by using multiplicative matching in phase space regions where the shower overestimates the matrix element and accumulative (additive) matching in regions where the shower underestimates the matrix element, an approach that can be viewed as a combination of the MC@NLO and KrkNLO methods.

scholarly journals Cognitive Best Worst Method for Multiattribute Decision-Making

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Hongjun Zhang ◽  
Chengxiang Yin ◽  
Xiuli Qi ◽  
Rui Zhang ◽  
Xingdang Kang
Keyword(s):  
Decision Making ◽  
Rating Scale ◽  
Semantic Representation ◽  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Ratio Scale ◽  
Interval Scale ◽  
Real World Application ◽  
The Matrix ◽  
Best Worst Method

Pairwise comparison based multiattribute decision-making (MADM) methods are widely used and studied in recent years. However, the perception and cognition towards the semantic representation for the linguistic rating scale and the way in which the pairwise comparisons are executed are still open to discuss. The commonly used ratio scale is likely to produce misapplications and the matrix based comparison style needs too many comparisons and is not able to guarantee the consistency of the matrix when the number of objects involved is large. This research proposes a new MADM method CBWM (Cognitive Best Worst Method) which adopts interval scale to represent the pairwise difference and only compares each object to the best object and the worst object rather than all the other objects. CBWM is a vector based method which only needs 2n-3 pairwise comparisons and is more likely to generate consistent comparisons and reliable results. The theoretical analysis and a real world application demonstrate the effectiveness of CBWM.

Sign in / Sign up

Export Citation Format

Share Document