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.

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.

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.

Shocks vs. Impulse-Propagation Model of Economic Dynamics

2021 ◽  
pp. 1-28
Keyword(s):  
Business Cycle ◽  
Wave Theory ◽  
Stochastic Approach ◽  
Propagation Model ◽  
Self Organization ◽  
Scientific Contribution ◽  
Economic Dynamics ◽  
New Approach ◽  
Self Development ◽  
Random Fluctuations

Ragnar Frisch, the Nobel prizer in economics, drew attention to two phenomena: propagation problems and impulse problems in dynamic economics. His deep scientific contribution relates to the interpretation of business cycle transformed under the influence of impulses (shocks). But some terminological misunderstandings arose. One of them forced the authors to focus on the phenomenon of systems' self-movement: their self-organization in statics and their self-development in dynamics. Another one relates to exogenous nature of impulses (shocks) that forced the authors to prove the endogenous embeddedness of shocks into the mechanisms of dialectical laws implementation. Eugen Slutsky demonstrated the stochastic approach as to random fluctuations as a source of cyclical processes in the economy. The confusion in the concepts of cycles and waves predetermines the need to create a wave theory of systemic self-organization (Chapter 2). Modern shocks theory develops a new approach which makes it possible to eliminate misconceptions of past theories.

scholarly journals Stochastic Modeling of Electrical Field in Potato Tuber using Polynomial Chaos Expansion

2019 ◽  
Vol 29 ◽  
pp. 01008
Author(s):  
Bartosz Sawicki ◽  
Artur Krupa
Keyword(s):  
Monte Carlo ◽  
Potato Tuber ◽  
Polynomial Chaos ◽  
Ohmic Heating ◽  
Stochastic Approach ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Computational Power ◽  
Electrical Field ◽  
Stochastic Parameters

The paper deals with numerical modeling of objects with a natural origin. The stochastic approach based on description using random variables allows processing such challenges. The Monte-Carlo methods are known a tool for simulations containing stochastic parameters however, they require significant computational power to obtain stable results. Authors compare Monte- Carlo with more advanced Polynomial Chaos Expansion (PCE) method. Both statistical tools have been applied for simulation of the electric field used in ohmic heating of potato tuber probes. Results indicate that PCE is remarkably faster, however, it simplifies some probabilistic features of the solution.

scholarly journals Limiting Behavior of the Target-Dependent Stochastic Sequential Assignment Problem

2014 ◽  
Vol 51 (4) ◽  
pp. 943-953 ◽  
Author(s):  
Golshid Baharian ◽  
Sheldon H. Jacobson
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Assignment Problem ◽  
Sequential Assignment ◽  
Threshold Probability ◽  
Limiting Behavior ◽  
Target Value ◽  
Long Run ◽  
Stochastic Parameters ◽  
Optimal Policies

The stochastic sequential assignment problem assigns distinct workers to sequentially arriving tasks with stochastic parameters. In this paper the assignments are performed so as to minimize the threshold probability, which is the probability of the long-run reward per task failing to achieve a target value (threshold). As the number of tasks approaches infinity, the problem is studied for independent and identically distributed (i.i.d.) tasks with a known distribution function and also for tasks that are derived from r distinct unobservable distributions (governed by a Markov chain). Stationary optimal policies are presented, which simultaneously minimize the threshold probability and achieve the optimal long-run expected reward per task.

Stochastic processing of chaotic dynamics outcome of biomechanical parameters in human

2015 ◽  
Vol 4 (1) ◽  
pp. 31-39
Author(s):  
Берестин ◽  
D. Berestin ◽  
Игуменов ◽  
D. Igumenov ◽  
Рассадина ◽  
...  
Keyword(s):  
Distribution Function ◽  
Stochastic Analysis ◽  
Chaotic Dynamics ◽  
Involuntary Movement ◽  
Deterministic Chaos ◽  
Special Kind ◽  
Stochastic Processing ◽  
Biomechanical Parameters ◽  
Distribution Shifts ◽  
Non Parametric

The results of the stochastic analysis of postural tremor (as alleged involuntary movement) and tapping (as supposedly voluntary movement) are considered in a comparative perspective. It is proved that the stochastic analysis of the results of chaotic dynamics in tremorogramms and tapping does not give significant differences (absence of voluntariness). Typically, all samples are significantly different and it is impossible to distinguish subjects in their tremorogramms or tapingramm. The significant differences between sites of tremorogramms in terms of a normal distribution or a non-parametric distribution are demonstrated. A continuous variation of the distribution function is observed: parametric distribution shifts to non-parametric distribution, but among themselves they (distribution function) are all different. It is well known that the unpredicta-bility and continuing changes in the state are characteristic feature of chaos. The evidence of special kind of chaos in biosystems which differs significantly from the deterministic chaos of Tom – Ar-nold is given.

Non-stationary stationarity in systems of third type and philosophy of instability

2015 ◽  
Vol 4 (2) ◽  
pp. 65-74
Author(s):  
Гавриленко ◽  
T. Gavrilenko ◽  
Еськов ◽  
Valeriy Eskov ◽  
Еськов ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Complex Systems ◽  
Biological Systems ◽  
Deterministic Chaos ◽  
Stochastic Approach ◽  
Distribution Functions ◽  
Self Organization ◽  
Deterministic Approach ◽  
The Third ◽  
Specific Assessment

There are several criteria in science for stationarity (stability) of different dynamical systems. The stationarity in physics, engineering and chemistry is being interpreted as matching the requirements of dx/dt=0, where x=x(t) - is the vector of system’s state, or the equality of distribution functions f(x) for different samples which characterize the system. However, in case of social or biological systems the matching of the requirements is impossible and there is a problem of specific assessment of stationary regimes of complex systems of the third type. The possibility of studying of such systems within the frame of deterministic chaos, stochastic approach and theory of chaos and self-organization is being discussed. This article explains why I.R. Prigogine refused from materialistic (in fact deterministic) approach in the description of such special systems of third type and tried to get away from the traditional science in the description of biological systems.

Compartment-cluster modeling of uncertainties according to determinism

10.12737/5520 ◽  
2014 ◽  
Vol 3 (2) ◽  
pp. 68-80
Author(s):  
Бурыкин ◽  
Yu. Burykin ◽  
Даянова ◽  
D. Dayanova ◽  
Козупица ◽  
...  
Keyword(s):  
Experimental Data ◽  
Chaotic Dynamics ◽  
Self Organization ◽  
Test Model ◽  
Dynamics Modeling ◽  
Cluster Modeling ◽  
Global Challenges ◽  
Human Movements ◽  
The Neural Networks ◽  
The Brain

Transition from determinism to stochastic sand further to chaos (self-organization) in the study of biomechanical systems leads to the problem of chaotic dynamics modeling of a post- ural tremor. In general, there is a problem of identifying the voluntary human movements. In other words biophysics of complex systems has approached the global challenges of voluntary and involuntary performance of any motor functions. The possibility of modeling these processes qualitatively and quantitativelyisdiscussed. Specific models demonstrate the effectiveness of the compartment-cluster modeling of biosystems and possibilities of controlof such models from the neural networks of the brain. Comparative analysis of the simulated and real recorded signals has shown a high consistent dynamics of simulated and real signals of complex biological systems. In particular, changes in tremor parameters can be described by the change in quasi-attractors which essentially depend on the mental state of a person. In experiments it is shown in the form of sight effects, which are considered in the report as a test model on experimental data.

scholarly journals Modeling the Daily Number of Reported Cases of Infection from the COVID-19 Pandemic in Nigeria: A Stochastic Approach

2020 ◽  
pp. 217-235
Author(s):  
Patrick Osatohanmwen ◽  
Francis O. Oyegue ◽  
Sunday M. Ogbonmwan
Keyword(s):  
Distribution Function ◽  
Stochastic Model ◽  
Stochastic Approach ◽  
Return Periods ◽  
Daily Number ◽  
Corona Virus ◽  
Time Period ◽  
Random Behavior

The focus of this paper is to present a stochastic model to capture the random behavior of the number of reported daily infections due to the Corona Virus (COVID-19) in Nigeria. The model expressed in form of a distribution function has five parameters. The model was fitted to the logarithm of the reported daily number of infection cases for the time period March 18th - June 11th, 2020. While the results obtained established the adequacy of the model in fitting and explaining the random behavior of the number of reported daily infections, it was also possible to use the model to study the situation of the number of infections exceeding certain thresholds. The procedure for the determination of these thresholds was established and a number of them were estimated for some given return periods.

NEUROCOMPUTER use in an assessment of chaotic dynamics of parameters of neuromuscular system of the person at various acoustic influences

10.12737/5515 ◽  
2014 ◽  
Vol 3 (2) ◽  
pp. 13-28
Author(s):  
Нехайчик ◽  
S. Nekhaychik ◽  
Козлова ◽  
V. Kozlova ◽  
Берестин ◽  
...  
Keyword(s):  
Chaotic Dynamics ◽  
Classical Music ◽  
Stochastic Approach ◽  
Neuromuscular System ◽  
Behavioral Dynamics ◽  
Hands On ◽  
Different Types ◽  
Left And Right ◽  
The Common ◽  
Acoustic Impact

The behavior of the human body state vector (for example, the reaction of tremoro-gram parameters) in response to different acoustic impacts (white noise, rhythmic music, classical music, hard rock) was studied by using the methods of neurocomputing. We showed the distinctions in the estimation of the behavioral dynamics of the parameters of the neuromuscular system, such as various motor reaction (tremor) of the left and right hands on the acoustic impact. The common regularities in the dynamics of behavior parameters of tremor at various acoustic impact on Surgut students hands were revealed. The analysis of quasi-attractors of differentiated reactions of left and right hands using neural emulators showed significant distinction on different types of acoustic impacts. Asymmetry of motor responses from the standpoint of the theory of chaos and self-organization was more marked than according to the stochastic approach. Neural emulator demonstrated the significance of all impacts on tremor parameters (system synthesis problem is being solved).

Sign in / Sign up

Export Citation Format

Share Document