ECG (Electrocardiogram) signals originating from heart muscles, generate massive volume of digital data. They need to be compressed or approximated for efficient transmission and storage. ECG signal compression is traditionally performed in three ways: direct, transform and parameter extraction. Polynomial approximation which is a form of parameter extraction method, is employed here. This pape...

A model of random walk on knot diagrams is used to study the Alexander polynomial and the colored Jones polynomial of knots. In this context, the inverse of the Alexander polynomial of a knot plays the role of an Ihara-Selberg zeta function of a directed weighted graph, counting with weights cycles of random walk on a 1-string link whose closure is the knot in question. The colored Jones polyno...

A graph polynomial p(G, X̄) can code numeric information about the underlying graph G in various ways: as its degree, as one of its specific coefficients or as evaluations at specific points X̄ = x̄0. In this paper we study the question how to prove that a given graph parameter, say ω(G), the size of the maximal clique of G, cannot be a fixed coefficient or the evaluation at any point of the Tutte...

Let A = (aij) be the generic n×n circulant matrix given by aij = xi+j , with subscripts on x interpreted mod n. Define d(n) (resp. p(n)) to be the number of terms in the determinant (resp. permanent) of A. The function p(n) is well-known and has several combinatorial interpretations. The function d(n), on the other hand, has not been studied previously. We show that when n is a prime power, d(n...

The goal of this study is to develop a computer-assisted method for proving the existence periodic solutions state-dependent delayed perturbations ordinary differential equations (ODEs). We assume that unperturbed ODE has an isolated orbit, and derive set polynomial inequalities which, if satisfied, imply uniqueness solution in perturbed system. A general procedure given, which facilitates comp...

Background: Chronic administration of morphine cause physical dependence but the exact mechanism of this phenomenon remains unclear. The aim of this study is the assessment of systemic and intracerebroventricular (icv) administration of ramelteon (a melatonin receptor agonist) on morphine physical dependence. Methods: 88 adult male rats were divided into 2 major groups, namely “systematic” and ...

This paper presents the central finite-dimensional H∞ filter for nonlinear polynomial systems, that is suboptimal for a given threshold γ with respect to a modified BolzaMeyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the paper reduces the original H∞ filtering problem to the corresponding optimal H2 filter...

In this paper, free vibration analysis and forced vibration analysis of FG doubly clamped micro-beams is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations and both the classical and non-classical boundary conditions are derived using a variational approach. It is assumed that all properties of the FG micro-be...