Investigation of the stability of fluctuations in electrocardiography data

A new algebraic algorithm based on the concept of the rank of a sequence for the analysis of electrocardiography (ECG) signals is proposed in this paper. The task of the proposed algorithm is to develop strategy for finding the nearest algebraic progression to each segment of time series of the ECG parameters. ECG parameters of different duration were used to investigate the dynamics of different physiological processes in human heart during load. It indicates that proposed algebraic algorithm can be effectively used for the analysis of ECG parameters. Different behavior can be observed in fluctuations of ECG parameters in different fractal levels

Special solutions of Huxley differential equation

The conditions when solutions of Huxley equation can be expressed in special form and the procedure of finding exact solutions are presented in this paper. Huxley equation is an evolution equation that describes the nerve propagation in biology. It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings. It is shown that the solution produced by the Exp-function method may not hold for all initial conditions. It is proven that the analytical condition describing the existence of the produced solution in the space of initial conditions (or even in the space of the system's parameters) can not be derived by the Exp-function method because the question about the existence of that solution is omitted. The proposed operator method, on the contrary, brings the load of symbolic computations before the structure of the solution is identified. The method for the derivation of the solution is based on the concept of the rank of the Hankel matrix constructed from the sequence of coefficients representing formal solution in the series form. Moreover, the structure of the algebraic-analytic solution is generated automatically together with all conditions of the solution's existence. Computational experiments are used to illustrate the properties of derived analytical solutions

The imitation model of bursty and batch data packet flow

The imitation model of bursty and batch data packet flow is presented in this paper. The proposed imitation model was created using the convolution of Moore and Mealy automata. The imitation model of bursty and batch data packet flow Santrauka Telekomunikacinių sistemų sėkmingam funkcionavimo aprašymui ypač daug reikšmės turi įvairios duomenų srautų charakteristikos. Todėl aktualu turėti minėtų srautų analizines išraiškas. Kadangi analiziniai modeliai arba yra ganėtinai sudėtingi, arba iš viso jų neįmanoma bendresniu atveju sudaryti, tai imitacinis modeliavimas galbūt vienintelis įmanomas sudėtingesnių srautų tyrimo metodas. Vienas iš telekomunikacinių sistemų tyrimo uždavinių – turėti patogų vartotojui neordinarinio pliūpsninio srauto imitacinį modelį, kad, gautas duomenų imtis apdorojus statistiniais paketais, būtų galima naudoti toliau tirti telekomunikacines sistemas. Taigi straipsnyje pasiūlytas neordinarinio pliūpsninio paraiškų srauto imitacinis modelis, sudarytas naudojant Muro ir Milio automatų sąsūką. Reikšminiai žodžiai: neordinarinis srautas, pliūpsninis srautas, duomenų srautas, Milio ir Muro automatų sąsūka. First Published Online: 21 Oct 201

Special Multiplicative Operators for the Solution of ODE – Invariants and Representations

The generalized multiplicative operator of differentiation is introduced in this paper. It is shown that the generalized multiplicative operator can be expressed as a product of two noncommutative but multiplicative exponential operators, though the generalized multiplicative operator is not an exponential operator itself. The generalized multiplicative operator is effectively exploited for the construction of solutions to nonlinear ordinary differential equations through formal transformations of invariants and representations of initial conditions. The concept of the generalized multiplicative operator provides the insight into the algebraic structure of solutions to nonlinear ordinary differential equations which cannot be identified using conventional exponential operators

Generalized solitary waves in nonintegrable KdV equations

The generalization of the classical Korteweg-de-Vries (KdV) solitary wave solution is presented in this paper. The amplitude and the propagation speed of generalized KdV solitary waves vary in time. Generating partial differential equations and conditions of existence of the generalized KdV solitary waves are derived using the inverse balancing method. Computational experiments illustrate the variety of new solitary solutions and their generating equations

Generalized solitary waves in nonintegrable KdV equations

The generalization of the classical Korteweg-de-Vries (KdV) solitary wave solution is presented in this paper. The amplitude and the propagation speed of generalized KdV solitary waves vary in time. Generating partial differential equations and conditions of existence of the generalized KdV solitary waves are derived using the inverse balancing method. Computational experiments illustrate the variety of new solitary solutions and their generating equations

An operator-based approach for the construction of closed-form solutions to fractional differential equations

An operator-based approach for the construction of closed-form solutions to fractional differential equations is presented in this paper. The technique is based on the analysis of Caputo and Riemann-Liouville algebras of fractional power series. Explicit solutions to a class of linear fractional differential equations are obtained in terms of Mittag-Leffler and fractionally-integrated exponential functions in order to demonstrate the viability of the proposed technique

Method for Prediction of Acute Hypotensive Episodes

Hypotension is type of secondary insult and it is related to poor outcome. The ability to predict adverse hypotensive events, where a patient's arterial blood pressure drops to abnormally low levels, would be of major benefit to the fields of primary and secondary health care. The aim of the paper is to present the novel method for predicting of acute hypotensive episodes, based on ECG analysis by the complex system theory approach. 45 patients (in four neurointensive care facilities throughout Europe) data were selected for the analysis. 11 patients had EUSIG-defined hypotensive events. The method includes determining of time varying biomarkers corresponding to plurality of physiological processes in patient's organism as a non-linear dynamic complex system and generating an acute hypotension prediction classifier. The calculations of biomarkers are based on complex system approach and algebraic matrix analysis of ECG parameters. The classifier is based on the comparison of biomarkers behaviour in 3D images. It is demonstrated that the presented method allows us to predict arterial hypotension events 40-50 minutes ahead with a sensitivity of 81 %, specificity 94 %. This result was obtained from prospective real-time data collection in a live clinical intensive care environment

Human heart rhythm sensitivity to earth local magnetic field fluctuations

The sensitivity of human hearth’s rhythm to the fluctuations of Earth’s local magnetic field is analyzed in this paper. Data collected during the long-term project of heart-rate variability (HRV) data from 17 female volunteers were used to correlate to measured fluctuations of Earth magnetic signals. Magnetic signals are collected utilizing the first global network of GPS time stamped detectors designed to continuously measure magnetic signals that occur in the same range as human physiological frequencies such as the brain and cardiovascular systems