Generalized Huberman-Rudnick scaling law and robustness of qq-Gaussian probability distributions

We generalize Huberman-Rudnick universal scaling law for all periodic windows of the logistic map and show the robustness of $q$-Gaussian probability distributions in the vicinity of chaos threshold. Our scaling relation is universal for the self-similar windows of the map which exhibit period-doubling subharmonic bifurcations. Using this generalized scaling argument, for all periodic windows, as chaos threshold is approached, a developing convergence to $q$-Gaussian is numerically obtained both in the central regions and tails of the probability distributions of sums of iterates.Comment: 13 pages, 3 figure

An investigation about the effect of oxazolidine on modified valonia extract tanning

This study is aimed at combining the usage of valonia and modified valonia extracts with oxazolidine to obtain an increase in hydrothermal stability, and thus to develop tanning efficiency and to produce leathers that have better properties then the ones tanned with valonia extract only. Natural and three modified valonia extracts and oxazolidine were used as tanning materials. Skin samples were divided into two groups. In group A, valonia extracts were used as tanning materials and oxazolidine as retanning agent. Group A was divided into 4 subgroups according to the used extract type. Each subgroup was also separated into four lots according to the oxazolidine percentages used. Group B; where oxazolidine was used as pretanning while valonia extracts as tanning agents, was divided into three subgroups according of oxazolidine usage. Each subgroup had four lots according to the used extracts. General means of Shrinkage Temperatures (Ts) for natural extract, group A and B were found as 65.66, 78.62 and 83.42 o C, respectively, indicating that the oxazolidine pretanning followed by valonia retanning provides better tanning efficiency. On the base of the unique experiment, 4% oxazolidine and 20% least modified vegetable tannin combination gave the best result

Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasi-periodic edge of chaos

We investigate the probability density of rescaled sum of iterates of sine-circle map within quasi-periodic route to chaos. When the dynamical system is strongly mixing (i.e., ergodic), standard Central Limit Theorem (CLT) is expected to be valid, but at the edge of chaos where iterates have strong correlations, the standard CLT is not necessarily to be valid anymore. We discuss here the main characteristics of the central limit behavior of deterministic dynamical systems which exhibit quasi-periodic route to chaos. At the golden-mean onset of chaos for the sine-circle map, we numerically verify that the probability density appears to converge to a q-Gaussian with q<1 as the golden mean value is approached.Comment: 7 pages, 7 figures, 1 tabl

Is polysomnographic examination necessary for subjects with diaphragm pathologies?

OBJECTIVES: While respiratory distress is accepted as the only indication for diaphragmatic plication surgery, sleep disorders have been underestimated. In this study, we aimed to detect the sleep disorders that accompany diaphragm pathologies. Specifically, the association of obstructive sleep apnea syndrome with diaphragm eventration and diaphragm paralysis was evaluated. METHODS: This study was performed in Süreyyapasa Chest Diseases and Thoracic Surgery Training and Research Hospital between 2014-2016. All patients had symptoms of obstructive sleep apnea (snoring and/or cessation of breath during sleep and/or daytime sleepiness) and underwent diaphragmatic plication via video-assisted mini-thoracotomy. Additionally, all patients underwent pre- and postoperative full-night polysomnography. Pre- and postoperative clinical findings, polysomnography results, Epworth sleepiness scale scores and pulmonary function test results were compared. RESULTS: Twelve patients (7 males) with a mean age of 48 (range, 27-60) years and a mean body mass index of 25 (range, 20-30) kg/m2 were included in the study. Preoperative polysomnography showed obstructive sleep apnea syndrome in 9 of the 12 patients (75%), while 3 of the patients (25%) were regarded as normal. Postoperatively, patient complaints, apnea hypopnea indices, Epworth sleepiness scale scores and pulmonary function test results all demonstrated remarkable improvement. CONCLUSION: All patients suffering from diaphragm pathologies with symptoms should undergo polysomnography, and patients diagnosed with obstructive sleep apnea syndrome should be operated on. In this way, long-term comorbidities of sleep disorders may be prevented

A comparison of Shannon, Kullback-Leibler and renormalized entropies within successive bifurcations

WOS: 000462104200006An issue in the context of self-organization is the existence of bifurcation processes that are often observed in dissipative dynamical systems. The first bifurcation occurs when a stable fixed point becomes unstable as the parameter set of the system slightly changes. Then the system eventually paves their way to new stable branches. When the most ordered spatial patterns emerge, the system implies a high level of self-organization in the phase space. Exchange of energy/matter with its surroundings is allowed for in such "open" systems. Open systems cannot be analyzed in terms of usual H-theorem of Boltzmann since it is only valid for isolated systems. Thereby, the Boltzmann-Gibbs (BG) entropy (or Shannon) is not able to explain such systems which increase their order as a signature of self-organization. However, Klimontovich showed that the BG entropy can still be used in such systems after a renormalization procedure and he also introduced the renormalized entropy as a measure of the relative degree of order by using his S-theorem. In this paper, we analyze the Henan map and the Rossler oscillator as high dimensional dissipative systems. We show that the renormalized entropy detects transition points of the systems and explains changes in relative order through successive bifurcations or chaotic band-mergings. The correlation analysis also shows that the renormalized entropy is a better measure than the Shannon or Kullback-Leibler (KL) entropies. (C) 2018 Elsevier B.V. All rights reserved

Relationships and scaling laws among correlation, fractality, Lyapunov divergence and q-Gaussian distributions

WOS: 000333513500003We numerically introduce the relationships among correlation, fractality, Lyapunov divergence and q-Gaussian distributions. The scaling arguments between the range of the q-Gaussian and correlation, fractality, Lyapunov divergence are obtained for periodic windows (i.e., periods 2,3 and 5) of the logistic map as chaos threshold is approached. Firstly, we show that the range of the q-Gaussian (g) tends to infinity as the measure of the deviation from the correlation dimension (D-corr = 0.5) at the chaos threshold, (this deviation will be denoted by l), approaches to zero. Moreover, we verify that a scaling law of type 1/g proportional to l(tau) is evident with the critical exponent tau = 0.23 +/- 0.01. Similarly, as chaos threshold is approached, the quantity l scales as l proportional to (a - a(c))(gamma), where the exponent is gamma = 0.84 +/- 0.01. Secondly, we also show that the range of the q-Gaussian exhibits a scaling law with the correlation length (1/g proportional to xi(-mu)), Lyapunov divergence (1/g proportional to lambda(mu)) and the distance to the critical box counting fractal dimension (1/g proportional to (D - D-c)(mu)) with the same exponent mu congruent to 0.43. Finally, we numerically verify that these three quantities (xi, lambda, D - D-c) scale with the distance to the critical control parameter of the map (i.e., a - a(c)) in accordance with the universal Huberman-Rudnick scaling law with the same exponent v = 0.448 +/- 0.003. All these findings can be considered as a new evidence supporting that the central limit behaviour at the chaos threshold is given by a q-Gaussian. (C) 2014 Elsevier B.V. All rights reserved.TUBITAK (Turkish Agency)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [112T083]We are indebted to Ayse Erzan for very fruitful discussions. This work has been supported by TUBITAK (Turkish Agency) under the Research Project number 112T083. U.T. is a member of the Science. Academy, Istanbul, Turkey

Limit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustness

WOS: 000350192200028In this paper we numerically investigate the distribution of the sums of the iterates of the logistic map and the relationships among the important properties of the nonlinear dynamics in the vicinity of the chaos threshold by adding two kinds of contributions with different densities. The first one is the well-known white noise, whereas the second is a newly defined one, named as quartic term, which makes contributions from the own structure of the map. As the chaos threshold is approached, the iterates of the standard logistic map (i.e. noise-free) have strong correlations and the standard Central Limit Theorem is not valid anymore. In a recent work (Tirnakli, 2009), it has been shown that the limit distribution seems to converge to q-Gaussian distribution, which maximizes the nonadditive entropy S-q equivalent to (1 -Sigma(i)p(i)(q)) / (q - 1) under appropriate conditions. In this work, we investigate the effect of these contributions (i.e. white noise and quartic term) on the limit distribution and on the range of the obtained q-Gaussian distribution. As a result of these findings, under the existence of white noise and also the quartic term, we analyse the validity of the scaling relations among correlation, fractality, the Lyapunov divergence and q-Gaussian distributions, which have recently been observed in (Afsar, 2014). The results obtained here strengthen the argument that the central limit behaviour is given by a q-Gaussian as the chaos threshold is approached and indicate that the scaling relations, obtained for the standard logistic map, among the range of the q-Gaussian, the correlation dimension, the correlation length, the Lyapunov exponent, fractality and the distance from the chaos threshold are robust under the existence of white noise and the quartic term. (C) 2014 Elsevier B.V. All rights reserved.TUBITAK (Turkish Agency)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [112T083]; Ege UniversityEge University [2012FEN076]This work has been supported by TUBITAK (Turkish Agency) under the Research Project number 112T083 and by Ege University under the Research Project number 2012FEN076. U.T. is a member of the Science Academy, Istanbul, Turkey

Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rossler System

WOS: 000435181600005In this paper, using the Poincare section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the Rossler system, which is one of the most popular three-dimensional continuous systems. As Poincare section points of the flow show similar behavior to that of the logistic map, for the Rossler system we also investigate the relationships with respect to important properties of nonlinear dynamics, such as correlation length, fractal dimension, and the Lyapunov exponent in the vicinity of the chaos threshold.John Templeton Foundation; TUBITAK (Turkish Agency)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [115F492]U.T. is a member of the Science Academy, Istanbul, Turkey and acknowledges partial support from the John Templeton Foundation. This work has been supported by TUBITAK (Turkish Agency) under Research Project number 115F492

Entropy-based complexity measures for gait data of patients with Parkinson's disease

WOS: 000371600200015PubMed ID: 26931596Shannon, Kullback-Leibler, and Klimontovich's renormalized entropies are applied as three different complexity measures on gait data of patients with Parkinson's disease (PD) and healthy control group. We show that the renormalized entropy of variability of total reaction force of gait is a very efficient tool to compare patients with respect to disease severity. Moreover, it is a good risk predictor such that the sensitivity, i.e., the percentage of patients with PD who are correctly identified as having PD, increases from 25% to 67% while the Hoehn-Yahr stage increases from 2.5 to 3.0 (this stage goes from 0 to 5 as the disease severity increases). The renormalized entropy method for stride time variability of gait is found to correctly identify patients with a sensitivity of 80%, while the Shannon entropy and the Kullback-Leibler relative entropy can do this with a sensitivity of only 26.7% and 13.3%, respectively. (C) 2016 AIP Publishing LLC.TUBITAK (Turkish Agency)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [112T083]; TUBITAK-BIDEBTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [2219]This work has been supported by TUBITAK (Turkish Agency) under the Research Project No. 112T083. O.A. was financially supported by TUBITAK-BIDEB under 2219 Post-Doctoral Research Program. U.T. is a member of the Science Academy, Istanbul, Turkey