Possibilities of stochastic processing of system parameters with chaotic dynamics

10.12737/5519 ◽  
2014 ◽  
Vol 3 (2) ◽  
pp. 59-67
Author(s):  
Берестин ◽  
D. Berestin ◽  
Попов ◽  
Yuriy Popov ◽  
Вохмина ◽  
...  
Keyword(s):  
Phase Space ◽  
General Population ◽  
Chaotic Dynamics ◽  
Estimation Method ◽  
Pairwise Comparison ◽  
Wilcoxon Test ◽  
Self Organization ◽  
Postural Tremor ◽  
System Parameters ◽  
Stochastic Processing

The paper presents the first attempt to combine methods of stochastics (mathematical statistics) and methods of theory of chaos and self-organization for studying such complex (chaotic) processes as postural tremor. It was established that when re-registering tremor in each subject by n=15 or n=30 obtained tremorograms do not exhibit normal distribution, and non-parametric distributions show distinctions at pairwise comparison on Wilcoxon test (only 2 or 3 pairs from 210 may belong to the same general population). Static physical load sharply changes this picture and the number of such ("similar") pairs increases. The estimation method for effect of a load on tremor is proposed. Simultaneously, within calculating quasi-attractors there is a clear picture of division of chaotic dynamics of tremor parameters with load and without load. Prospects of a new method application in physiological measurements are discussed. Limited method of stochas- tics in description of complexity is underlined, and necessity of calculation quasi-attractor´s parameters in phase space of state is proved.

Stochastic and Chaotic Assessment of Human Involuntary Movements

10.12737/4988 ◽  
2014 ◽  
Vol 21 (2) ◽  
pp. 10-15
Author(s):  
Бурыкин ◽  
Yu. Burykin ◽  
Вохмина ◽  
Yu. Vokhmina ◽  
Филатова ◽  
...  
Keyword(s):  
Distribution Function ◽  
Chaotic Dynamics ◽  
Static Load ◽  
Pairwise Comparison ◽  
Stochastic Approach ◽  
Self Organization ◽  
Postural Tremor ◽  
Stochastic Parameters ◽  
General Number ◽  
Lyapunov Constants

According to theory of chaos and self-organization calculation of chaotic dynamics of postural tremor parameters is presented. We have shown that stochastic approach, calculation of distribution function for reiterations of measurements, tremorograms in one subject exhibits chaotic dynamics of these functions f(x). Otherwise 15 measurements by 5 seconds tremerograms show impossibility of coincidence f(x) at pairwise comparison (105 pairs) of tremerograms. Functions f(x) can coincide (for pairs of tremorograms) less than 2-5% from the general number without effect on a person. However, physical load increases the coincidence to 10-15%. Simultaneously, all the amplitude-frequency characteristics do not coincide, Lyapunov constants cannot be calculated, but autocorrelation functions do not reach zero. All the stochastic parameters exhibit constant changes. Calculation of quasi-attractors can provide real distinction between biomechanical system before static load and after. Sizes of quasi-attractor (square and volume) can show distinctions in physiological body states for continuous motions x(t), i.e. for dx/dt≠ 0.

Methods of chaos and self-organization in psychophysiology

10.12737/3394 ◽  
2014 ◽  
Vol 3 (1) ◽  
pp. 13-28
Author(s):  
Поскина ◽  
T. Poskina ◽  
Филатова ◽  
D. Filatova ◽  
Филатов ◽  
...  
Keyword(s):  
Phase Space ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Self Organization ◽  
Deterministic Approach ◽  
System Behavior ◽  
System Parameters ◽  
A Value ◽  
Identification Theory

. All the H. Haken’s postulates (1970-2013) emphasize deterministic approach and level a value of trajectory of behavior of biological dynamic system in phase space of states. The significance of the latter theory is hard to overestimate, because according to phase space of states the new identification theory is being created and behavioral descriptions of biological dynamic systems are given. This new theory is based on measures of biological dynamic system parameters in phase space of states and does not need any concrete equations, it can be based on detection of quasi-attractors’ parameters of biological dynamic system behavior in phase space of states and characters are quasi-attractor parameters.

Physiotherapy for hypertensive disease from the perspectives of chaotic dynamics of cardiovascular system parameters in patients

10.12737/7242 ◽  
2014 ◽  
Vol 8 (1) ◽  
pp. 0-0 ◽  
Author(s):  
Горбунов ◽  
D. Gorbunov ◽  
Эльман ◽  
Kseniya Elman ◽  
Гараева ◽  
...  
Keyword(s):  
Phase Space ◽  
Cardiovascular System ◽  
Chaotic Dynamics ◽  
Hypertensive Disease ◽  
Initial State ◽  
Hypertensive Patients ◽  
System Parameters ◽  
Calculation Of Parameters ◽  
Effi Ciency ◽  
Two Stages

The problem of one-type uncertainty is solved when cardiovascular system parameters in hypertensive patients undergoing physiotherapy aren’t differentiated by stochastics, but these differences are clearly revealed by the methods of neurocomputing and calculation of parameters of quasi-attractors. Simultaneously, the solution of system synthesis problem is possible, i.e. identification of more important diagnostic characters xi from the whole set of state vector of cardiovascular system x(t) in hypertensive patients. Efficiency of physiotherapy is estimated at two stages of course of treatment: in the initial state (initial physiotherapy) and after the termination of course of treatment. The dynamics of motion of quasi-attractors in phase space of states in hypertensive patients is shown. Thus, the problem of elimination of one-type uncertainty in studying the effi-ciency of curative measures is solved.

Statistical and evaluation chaotic parameters under cardio exertion

2015 ◽  
Vol 4 (2) ◽  
pp. 5-10
Author(s):  
Филатова ◽  
D. Filatova ◽  
Карпин ◽  
Vladimir Karpin ◽  
Еськов ◽  
...  
Keyword(s):  
Phase Space ◽  
Cardiovascular System ◽  
Chaos Theory ◽  
Chaotic Dynamics ◽  
Stochastic Approach ◽  
Dynamic Exercise ◽  
Self Organization ◽  
Dimensional Phase Space ◽  
Classical Statistics ◽  
Fitness Indicators

Methods of classical statistics and the theory of chaos and self-organization studied the behavior of the vector of the cardiovascular system in groups of students trained and untrained in response to dosed physical stress .It was found that students without physical fitness indicators of cardio area quasi-attractors increased after exercise . The study had shown significant changes in the dynamics of the behavior of the parameters of functional systems of the human body compared to the stochastic approach based on the histogram and Shannon entropy . It is shown the feasibility of application of chaos theory, self-organization in the evaluation of the reaction of the cardiovascular system of the person on the dynamic exercise. As a measure of the cardiovascular system of the person (to load and after the load) used quasi-attractor motion of the state vector of the system in the two-dimensional phase space of states. Within the framework of the theory of chaos and self-organization may determine the parameters of the spacecraft for individual subjects and their groups to compare their chaotic dynamics in time or in the phase space of states.

Complex System Stationary Mode According to the Theory of Chaos-Self-Organization

10.12737/3329 ◽  
2014 ◽  
Vol 21 (1) ◽  
pp. 141-144
Author(s):  
Бикмухаметова ◽  
L. Bikmukhametova ◽  
Полухин ◽  
L. Polukhin ◽  
Вохмина ◽  
...  
Keyword(s):  
Phase Space ◽  
State Vector ◽  
Chaotic Dynamics ◽  
Main Idea ◽  
Self Organization ◽  
Stationary Mode ◽  
Cluster Approach ◽  
Classical Statistics ◽  
Complex Biosystems ◽  
Real Complex

Traditional biological science (biophysics, systems analyses of biosystems) stationary mode of biosystems describes according to equation dx/dt=0 for the systems state vector x=x(t)=(x1, x2,…xm)T. But real biosystems demonstrated uninterrupted chaotic dynamics when dx/dt≠0 is always uninterrupted. The authors present two types of approaches to stationary mode investigation for biosystems. The first approach is based on the compartmental-cluster theory and the second approach is based on the theory of chaos-self-organization. The last is more convenient for real biosystems description because there are pragmatic results of its use. The compartmental-cluster approach may be used for real complex biosystems and the authors present some typical examples of such theory. The stationary mode of hierarchical neural networks were illustrated according to specific audi - analyzator. It was demonstrated that short intervals of tremogram demonstrate the real difference of distribution function parameters. As a result of such experiments – the classical statistics methods don’t usefulness for investigation of postural tremor. The tremogram, cardiogram, encephalogram are the systems of third type. The main idea consists of uninterrupted chaotic movements (glimmering property) of system’s vector in phase space of state and evolution of such system’s state vector in phase space of state. The glimmering property and evolution don’t have properties which can be modeled by traditional deterministic and stochastic approaches.

An Estimation of Generalized Bradley-Terry Models Based on the em Algorithm

2011 ◽  
Vol 23 (6) ◽  
pp. 1623-1659 ◽  
Author(s):  
Yu Fujimoto ◽  
Hideitsu Hino ◽  
Noboru Murata
Keyword(s):  
Em Algorithm ◽  
Estimation Method ◽  
Pairwise Comparison ◽  
Information Geometry ◽  
Point Of View ◽  
Ranking Data ◽  
Statistical Representation ◽  
Comparison Results ◽  
The Em Algorithm ◽  
Probability Simplex

The Bradley-Terry model is a statistical representation for one's preference or ranking data by using pairwise comparison results of items. For estimation of the model, several methods based on the sum of weighted Kullback-Leibler divergences have been proposed from various contexts. The purpose of this letter is to interpret an estimation mechanism of the Bradley-Terry model from the viewpoint of flatness, a fundamental notion used in information geometry. Based on this point of view, a new estimation method is proposed on a framework of the em algorithm. The proposed method is different in its objective function from that of conventional methods, especially in treating unobserved comparisons, and it is consistently interpreted in a probability simplex. An estimation method with weight adaptation is also proposed from a viewpoint of the sensitivity. Experimental results show that the proposed method works appropriately, and weight adaptation improves accuracy of the estimate.

Sign in / Sign up

Export Citation Format

Share Document