New estimation method of degree of chaos in biosystems

10.12737/6725 ◽  
2014 ◽  
Vol 3 (3) ◽  
pp. 69-77
Author(s):  
Горленко ◽  
N. Gorlenko ◽  
Кощеев ◽  
V. Koshcheev ◽  
Бурыкин ◽  
...  
Keyword(s):  
Paired Comparison ◽  
Estimation Method ◽  
Muscular Activity ◽  
Distribution Functions ◽  
Statistical Distribution ◽  
Stochastic Methods ◽  
Transition Mechanism ◽  
Statistical Distribution Function ◽  
Case Number ◽  
Chaos Degree

. Potential application of traditional and stochastic methods in assessment of parameters of complex biosystem – complexity is presented. Their amplitude-frequency characteristics, autocorrelation functions A(t), Lyapunov exponents, statistical distribution function f(x) constantly change. In spite of such chaotic dynamics in recorded parameters of tremor, tapping, cardiograms, myograms and other parameters of homeostasis, an order in the dynamics of these processes can be observed. The order is revealed in a change of numbers of sample overlaps that are obtained as a result of some processes. Owing to all the stochastic characteristics constantly change, calculation method for statistical distribution functions with repetitions of identical experimental sets is proposed. In this case, number of sample overlaps (their belonging to the same general population) will numerically present the transition mechanism to order out of chaos or the variation of chaos degree in movement formation and electrobiological muscular activity. The current work shows some typical examples of different physiological human states presented in a form of matrices of paired comparison.

scholarly journals A group of processes related to the Poisson process

2008 ◽  
Vol 464 (2097) ◽  
pp. 2457-2466 ◽  
Author(s):  
D.J Neville
Keyword(s):  
Distribution Function ◽  
Stochastic Processes ◽  
Poisson Process ◽  
Distribution Functions ◽  
Statistical Distribution ◽  
Value Functions ◽  
Scale Invariant ◽  
Statistical Distribution Function ◽  
Special Case ◽  
Limiting Value

A group of stochastic processes akin to the Poisson process is defined in terms of rules of interactions between two types of interacting entities and in terms of a parameter corresponding to the initial relative numbers of the two types of interacting entities. One limiting value of this parameter corresponds to the Poisson process and the exponential distribution function, and the other limiting value of the parameter corresponds to a special case among the group of stochastic processes defined and a statistical distribution function used previously for incomes and fracture toughness. The related processes in between, which correspond to the intermediate values of the parameter, correspond to an intermediate statistical distribution function. The transition between the limiting cases is smooth as evinced by the change of the mean and median with change in the parameter. The scale-invariant behaviour of the fields of stress and strain at the tips of cracks is used to support the introduction of a shape parameter into the special-case function. All the distribution functions considered are found to be stable extreme-value functions, either in the sense of multiplying probabilities or in the sense of summing the variable or in a mixture of both senses.

Achieving productive reliability through applying statistical distribution functions

2019 ◽  
Vol 37 (8) ◽  
pp. 1125-1149
Author(s):  
Mahdi Karbasian ◽  
Ramin Rostamkhani
Keyword(s):  
Failure Time ◽  
Distribution Functions ◽  
Statistical Distribution ◽  
Numerical Control ◽  
Theoretical Research ◽  
Content Type ◽  
Equipment Reliability ◽  
Efficiency And Effectiveness ◽  
Statistical Distribution Function ◽  
Efficient Option

Purpose The purpose of this paper is to find the proper statistical distribution function, which can cover the failure time of a single machine or a group of machines. To this end, an innovative program is written in an Excel software, capable of assessing at least six statistical distribution functions. This research study intends to show the advantages of applying statistical distribution functions in an integrated model format to create or increase productive reliability machines. Productive reliability is a simultaneous combination of efficiency and effectiveness in reliability. Design/methodology/approach The method of theoretical research methodology comprises data collection tools, reference books and articles in addition to exploiting written reports of the Iranian Center for Defence’s Standards. The practical research method includes deploying and assessing the proposed model for a selected machine (in this case a computerized numerical control machine). Findings A comprehensive program in an Excel software having the capability of assessing at least six statistical distribution functions was developed to find the most efficient option for covering the failure times of each machine in the shortest time with the highest precision. This is regarded as the most important achievement of the present study. Furthermore, the advantages of applying the developed model are discussed and a large group of which have direct influences on the productivity of equipment reliability. Originality/value The originality of the research was ascertained by managers and experts working in maintenance issues at the different levels of the Defense Industries Organization.

A Statistical Distribution Function of Wide Applicability

1951 ◽  
Vol 18 (3) ◽  
pp. 293-297 ◽  
Author(s):  
Waloddi Weibull
Keyword(s):  
Distribution Function ◽  
Statistical Distribution ◽  
Wide Field ◽  
Wide Applicability ◽  
Statistical Distribution Function

Abstract This paper discusses the applicability of statistics to a wide field of problems. Examples of simple and complex distributions are given.

Abstract WP291: Stochastic Methods Can Resolve the Dilemma of Emergency Stroke Transport

Stroke ◽  
2020 ◽  
Vol 51 (Suppl_1) ◽  
Author(s):  
Daniel A Paydarfar ◽  
David Paydarfar ◽  
Peter J Mucha ◽  
Joshua Chang
Keyword(s):  
Census Data ◽  
Infarct Volume ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Practical Significance ◽  
Stochastic Methods ◽  
Model Parameters ◽  
Collateral Flow ◽  
Acute Stroke Care

Introduction: Drip and Ship (DNS) and Mothership (MS) are well-known emergency transport strategies in acute stroke care, but the criteria for choosing between the two is widely debated. Existing models define time-dependent outcomes but cannot resolve this debate with statistical significance because the independent variables are deterministic. We propose a novel stochastic framework that quantifies statistical significance between DNS and MS in a network of primary and comprehensive stroke centers. Methods: We represented the physiology of ischemic core growth as a stochastic first-order differential equation, enabling infarct volume at time of reperfusion to be calculated and mapped to 90-day mRS. Using Texas as a case study, we configured the state’s stroke network within 15,811 geographic blocks as defined by census data. For each block, we ran Monte Carlo simulations to generate Beta distributions of large- and small-vessel infarct volumes, which were then translated into cumulative distribution functions of mRS. A two-sample Kolmogorov-Smirnov test for significance, and Cohen’s d effect size statistic for practical significance were computed between each DNS and MS pair. Stable effect sizes were assured by sampling > 5,000 total infarct volumes for each block. All model parameters were established from large cohort studies or trials. Results: Of the 13,113 blocks where the primary stroke center is the closest hospital from origin, DNS produces significantly better stroke outcomes than MS in 79.0% (0.3% SEM; P < 0.05; 0.2 < d < 0.5). For the subset of patients with large-vessel strokes, MS produces significantly better outcomes in 44.6% of blocks (1.3% SEM; P < 0.05; 0.4 < d < 0.85). Conclusion: Stochastic methods enable the use of clinically relevant metrics for comparative significance of DNS and MS in a geographic region. This formalism, which has not been incorporated in previous models, can be further generalized beyond stochastic infarct volumes if sufficiently large datasets become available. For example, the kinetic growth model can integrate the statistical distributions of times (pre-hospital and hospital) leading up to intervention, and patient attributes that affect outcomes, such as the degree of collateral flow and comorbidities.

scholarly journals DOA Tracking of Two-Dimensional Coherent Distribution Source Based on Fast Approximated Power Iteration

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Tao Wu ◽  
Pengtao Zhang ◽  
Yiwen Li ◽  
Yangjun Gao ◽  
Chaoqi Fu ◽  
...  
Keyword(s):  
Estimation Method ◽  
Doa Estimation ◽  
Distribution Functions ◽  
Tracking Algorithm ◽  
Signal Subspace ◽  
Two Dimensional ◽  
Model Errors ◽  
Rectangular Array ◽  
Linear Arrays ◽  
Power Iteration

Aiming at two-dimensional (2D) coherent distributed (CD) sources, this paper has proposed a direction of arrival (DOA) tracking algorithm based on signal subspace updating under the uniform rectangular array (URA). First, based on the hypothesis of small angular spreads of distributed sources, the rotating invariant relations of the signal subspace of the receive vector of URA are derived. An ESPRIT-like method is constructed for DOA estimation using two adjacent parallel linear arrays of URA. Through the synthesis of estimation by multiple groups of parallel linear arrays within URA arrays, the DOA estimation method for 2D CD sources based on URA is obtained. Then, fast approximated power iteration (FAPI) subspace tracking algorithm is used to update the signal subspace. In this way, DOA tracking of 2D CD sources can be realized by DOA estimation through signal subspace updating. This algorithm has a low computational complexity and good real-time tracking performance. In addition, the algorithm can track multiple CD sources without knowing the angular signal distribution functions, which is robust to model errors.

The Development of Estimators for the Peaks-Over-Threshold Method

2002 ◽  
Author(s):  
A. Naess ◽  
P. H. Clausen
Keyword(s):  
Wind Speed ◽  
Synthetic Data ◽  
Distribution Functions ◽  
Statistical Distribution ◽  
Peaks Over Threshold ◽  
Threshold Method

The paper discusses the accuracy and efficiency of some of the standard estimators used in conjunction with the Peaks-Over-Threshold (POT) method. A comparison is made between some commonly adopted estimators and two types of estimators proposed by the authors. The comparison is based on an extensive set of synthetic data simulated from a range of different statistical distribution functions that have been assumed to describe wind speed processes.

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