A Method for Revealing Coupling between Oscillators with Analytical Assessment of Statistical Significance

A problem of revealing a coupling between two oscillatory systems by time series of their oscillations, i.e., a discrete sequence of values of the observed char acteristics is considered in radio physics In this work, an alternative approach and the other characteristic of coupling r, i.e., the coefficient of cor relation between the phase increments are proposed. A law of the distribution of an estimate of this value for uncoupling systems with almost arbitrary properties of individual phase dynamics is analytically derived. On the basis of this law, a formula for the confidence probability of the difference of this estimate from zero is derived. The efficiency of this approach is shown using examples of reference oscillators with various coupling types and with phase nonlinearity. Condi tions for the superiority of this approach over the esti mate of phase coherence coefficient ρ in sensitivity are demonstrated. Let us consider the time series of the oscillation phases of two systems {φ 1 (t 1 ), …, φ 1 (t N )} and {φ 2 (t 1 ), …, φ 2 (t N )}, where t n = nΔt and Δt is the sampling interval. We do not consider methods for calculating the phase here and hereinafter, the up arrow means an estimate obtained by a finite length time series. Let us designate the phase increments during time The coefficient of correlation between the phase increments is used as the characteristic of a coupling between the systems, where w 1, 2 = 〈Δφ 1, 2 〉 are the mathematical expectations of the phase increments; and are their standard deviations. For independent from each other systems r = 0. If a coupling exists, r can take Abstract-A method based on calculating the coefficient of correlation between the increments of oscillation phases is proposed for revealing a coupling between two oscillatory systems according to their time series. A distribution of the estimate of this characteristic for uncoupling systems is found; it was used to obtain a criterion for judging the availability of the coupling with a specified confidence probability. The proposed method is simpler than known methods and has a wider range of application, since it also includes oscillators with fairly strong phase nonlinearity. The efficiency of this method is illustrated by examples of reference sys tems in a numerical experiment

Chaotic synchronization of coupled electron-wave systems with backward waves

The chaotic synchronization of two electron-wave media with interacting backward waves and cubic phase nonlinearity is investigated in the paper. To detect the chaotic synchronization regime we use a new approach, the so-called time scale synchronization [Chaos, 14 (3) 603-610 (2004)]. This approach is based on the consideration of the infinite set of chaotic signals' phases introduced by means of continuous wavelet transform. The complex space-time dynamics of the active media and mechanisms of the time scale synchronization appearance are considered.Comment: 11 pages, 7 figures, published in CHAOS, 15 (2005) 01370

СЕЛЕКТИВНОЕ ОПРЕДЕЛЕНИЕ МАССОВОЙ КОНЦЕНТРАЦИИ ДИОКСИДА ХЛОРА В ПРОМЫШЛЕННЫХ ВЫБРОСАХ МЕТОДОМ КАПИЛЛЯРНОГО ЭЛЕКТРОФОРЕЗА

The task of the selective determination of chlorine dioxide in gas environments, including the emissions from the pulp and paper mills, is relevant and in demand. Current article presents a brief review of the existing methods and procedures for measuring the chlorine dioxide in liquid and gas environments, and identifies the problems in controlling the chlorine dioxide in industrial emissions from the pulp and paper production due to the influence of the related substances: molecular chlorine, hydrochloride, hydrochlorate and sulfur dioxide. As a result, to achieve the required selectivity of the chlorine dioxide determination, the procedure for its preliminary oxidation with the hydrogen peroxide to the chlorite-ion was developed, followed by the measuring of its mass concentration by the capillary electrophoresis. The conditions of sampling, all stages of sample preparation and measurements on the instrument were optimized. Based on the experimental studies, a method for measuring the chlorine dioxide in the industrial emissions in the form of chlorite ion in the range from 0.025 to 0.3 mg/m3 with an expanded uncertainty of 25% has been developed. The contributions of the components of uncertainties affecting the measurement result were summarized in the budget of the uncertainties prepared during the metrological certification of the measurement procedure. The developed method is more selective and reliable in comparison to the traditional methods (“wet chemistry”) used for the measuring of the chlorine dioxide in industrial emissions.Key words: chlorine dioxide, chlorite-ion, capillary electrophoresis, measurement techniques, industrial emissionsDOI: http://dx.doi.org/10.15826/analitika.2019.23.2.006(Russian)Irina B. Maksakova, Lydmila V. Eliseeva, Marina M. Bezruchko, Anatoliy I. Krylov D.I. Mendeleyev Institute for Metrology (VNIIM), Moskovskii pr., 19,Saint-Petersburg, 190005, Russian FederationЗадача селективного определения диоксида хлора в газовых средах, включая выбросы целлюлозно-бумажных производств (ЦБП), актуальна и востребована. В статье представлен краткий обзор существующих методов и методик измерений диоксида хлора в жидких и газовых средах, выявлены проблемы контроля диоксида хлора в промышленных выбросах ЦБП, обусловленные влиянием сопутствующих веществ: молекулярный хлор, гидрохлорид, гидрохлорат и диоксид серы. В результате для достижения необходимой селективности определения диоксида хлора отработана процедура его предварительного окисления пероксидом водорода до хлорит-иона с последующим измерением его массовой концентрации методом капиллярного электрофореза. Оптимизированы условия пробоотбора, всех стадий пробоподготовки и выполнения измерений на приборе. На основе проведенных экспериментальных исследований разработана методика измерений диоксида хлора в промышленных выбросах в виде хлорит-иона в диапазоне от 0.025 до 0.3 мг/м3 при расширенной неопределенности 25 %. Вклады составляющих неопределенностей, оказывающих влияние на результат измерений суммированы в бюджете неопределенностей, подготовленном при метрологической аттестации методики измерений. Разработанная методика является более селективной и достоверной в сравнении с используемыми традиционными методами («мокрой химии») измерений диоксида хлора в промышленных выбросах.Ключевые слова: диоксид хлора, хлорит-ион, капиллярный электрофорез, методики измерений, промышленные выбросыDOI: http://dx.doi.org/10.15826/analitika.2019.23.2.00

Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data

We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and non-vanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.Comment: 22 pages, 7 figures, the paper is to be published in Chaos, 2005, vol.15, issue 2, see http://chaos.aip.org

COMPARISON OF FOSINOPRIL AND ATENOLOL EFFECT ON HEART 0.1 HZ-RHYTHMS SYNCHRONIZATION AND BLOOD MICROCIRCULATION IN PATIENTS WITH ARTERIAL HYPERTENSION

Aim. To compare the effect of fosinopril and atenolol on synchronization of heart 0.1 Hz-rhythms and blood microcirculatory.Material and methods. 63 patients at the age of 47±8 with hypertension (HT) of grade 1-2 were enrolled in the study. 0.1 Hz-oscillations in heart rate variability (HRV) and in filling of microcirculatory bed were registered during passive tilt test under spontaneous breathing. The duration of each stage of test was 10 min. Synchronization was estimated as a phase difference between 0.1 Hz-rhythms of heart rate and filling of microcirculatory bed. Frequency values of HRV spectrum in LF- and HF-ranges were also assessed.Results. Fosinopril and atenolol showed comparable effect on blood pressure (BP) reduction. Atenolol decreased in heart rate significantly. Treatment with either fosinopril or atenolol in patients with significant vegetative dysfunction resulted in repair of functional interaction between heart 0.1 Hz-regulation and microcirculatory bed. Functional dissociation of 0.1 Hz-regulation mechanisms was observed under the treatment with fosinopril or atenolol in patients with initially sufficient interaction.Conclusions. Fosinopril and atenolol influenced similarly on heart 0.1 Hz-mechanisms and microcirculation autonomic regulation in patients with HT. Atenolol is a drug of choice in patients with sympathicotony. Both drugs should be administered in according with an individual level of 0.1-Hz rhythms synchronization assessed before start of the treatment

Synchronization of low-frequency oscillations in the human cardiovascular system

We investigate synchronization between the low-frequency oscillations of heart rate and blood pressure having in humans a basic frequency close to 0.1 Hz. A method is proposed for quantitative estimation of synchronization between these oscillating processes based on calculation of relative time of phase synchronization of oscillations. It is shown that healthy subjects exhibit on average substantially longer epochs of internal synchronization between the low-frequency oscillations in heart rate and blood pressure than patients after acute myocardial infarction. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3187794͔ The human cardiovascular system (CVS) is one of the most important physiological systems whose operation is governed by several rhythmic processes interacting with each other. The most significant among them are the main heart rhythm, respiration, and low-frequency (LF) oscillations in heart rate and blood pressure with a basic frequency close to 0.1 Hz having a great importance for maintaining cardiovascular homeostasis. The origin of these LF oscillations is still a subject of controversy. According to one hypothesis, the 0.1 Hz oscillations in heart rate and blood pressure are largely an index of baroreflex gain. On another hypothesis, these oscillations have a central origin and represent an intrinsic property of autonomous neural network. We have investigated interaction between the 0.1 Hz cardiovascular oscillations in healthy subjects and patients after acute myocardial infarction (AMI). Peculiarities of interaction of the elements of CVS reflect its state and may contain useful information for medical diagnostics. The interaction between the rhythms is studied using a phase synchronization measure based on the Hilbert transform. A method is proposed for quantitative estimation of synchronization by using an algorithm of automated detection of phase synchronization epochs. The method is based on a linear approximation of instantaneous phase difference of analyzed signals in a moving window. Recommendations on a choice of the method parameters ensuring its high efficiency are given. A statistical significance of the calculated synchronization measure is analyzed using surrogate data. It is shown that healthy subjects exhibit on average substantially longer epochs of synchronization between the LF oscillations in heart rate and blood pressure than patients after AMI. Arguments are adduced in favor of the concept that oscillations of heart rate and blood pressure with a frequency of about 0.1 Hz have a central origin. Moreover, these oscillations may be considered as different processes that exhibit a comparatively high internal synchronization between themselves in healthy subjects ensuring a high adaptability of the CVS

Structure of herd immunity to SARS-COV-2 in the Krasnoyarsk region population in the COVID-19 epidemic

Purpose. Determination of the SARS-CoV-2 population humoral immunity among the population of the Krasnoyarsk Territory during the COVID-19 epidemic.Materials and methods. The study was carried out as a part of project for assessing population immunity to SARS-CoV-2 among the population of Russian Federation using unified methodology developed by Rospotrebnadzor, with the participation of the Research Institute for Epidemiology and Microbiology named by Pasteur, and taking into account the recommendations of the WHO. The work involved 2907 volunteers, selected by the online survey and randomization by age and territory. All volunteers were divided into 7 age groups: 1–17, 18–29, 30–39, 40–49, 50–59, 60–69, 70 and older (70+), including a total 246–449 people. Population immunity testing was carried out during the formation of groups (1st stage), and then twice more, with the interval of 6–8 weeks. Serum was obtained from venous blood samples obtained from volunteers, in which antibodies to the SARS-CoV-2 nucleocapsid were determined by the enzyme immunoassay. The results were analyzed by methods of nonparametric statistics: median, interquartile range, rank correlation coefficient were calculated in the Excel statistical package. The confidence interval to seroprevalence indicators (95% CI) was calculated using the WinPepi statistical package (version 11.65). The statistical significance of the differences was assessed with a probability level of p ≤ 0.05.Results. The seroprevalence of the population of the Krasnoyarsk Territory during the 5-month period of seromonitoring had increased 3.3 times from 12.8% (95% CI 11.3–14.4) to 41.7% (95% CI 39.4–4.0) , while the grouping by age had not revealed any peculiarities throughout the study. The trend towards a decrease in the incidence was formed on the 6th week of 2021. The seroprevalence of convalescents after COVID-19 during the initial testing was 61.5% (95% CI 40,6–79.8), among those who were in contact with patients with COVID-19 or convalescents –23.8% (95% CI 13.9–36.2) . Among the volunteers, 347 seropositive persons were identified, 324 of which were observed asymptomatic course.Conclusion. The structure of the population humoral immunity to SARS-CoV-2 of he population of the Krasnoyarsk Territory has been investigated. It was found that an increase in seroprevalence to 41.7% (95% CI 39.4–4.0) was accompanied by a decrease in morbidity

Spurious causalities due to low temporal resolution: Towards detection of bidirectional coupling from time series

The detection of causal influences is a topical problem in time series analysis. A traditional approach is based on Granger causality and increasingly often used in very diverse fields. However, a principal possibility of spurious detection of a bidirectional coupling due to low sampling rate, noted by statisticians and econometricians, remains overlooked in physical research. With models widely used in physics, including linear oscillators and nonlinear chaotic maps, we show that spurious coupling characteristics can be rather large and one may even incorrectly identify directionality of a unidirectional coupling if a sampling interval is not small enough. To avoid erroneous conclusions, we suggest a practical test to distinguish between uni- and bi-directional couplings and illustrate it with mathematical systems and climatic data