In the Bioscience we see various fluctuations that appear in the movement of primitive animals and other phenomena. We shall see possible kinds of basic fluctuations in standard cases. They depend on either time parameter or space parameter; both are not discrete, but continuous, so that mathematical approach needs profound theory in probability.

View full abstract

We introduce the convexity ratio, CR(P), which indicates how close a simple closed polygon P is to being convex. This is accomplished by considering the ratio of the area of a largest convex set (the endogon) contained in P to the area of the convex hull of P. Algorithms for determining the convex hull and for determining the endogon are exhibited. After defining when such polygons are nearly convex we then use this result to decide when legislative districts are nicely shaped. We show that this method for measuring the shape of legislative districts is better than, or as good as, other techniques in the literature. This is accomplished by pointing out flaws in the other methods and by examining examples of district shapes found in the literature.

View full abstract

In this paper we analyze the dynamics of the diffusion bridges (or tieddown diffusion processes), derived from time-non-homogeneous linear diffusion processes. For the Ornstein-Uhlenbeck and the Feller-type diffusion bridges, the distribution of first passage time through particular boundaries is determined.

View full abstract

This work presents a research agenda defining a set of perceptual experiments and behavioral analyses devoted to investigate the effects of induced emotional states and related emotional regulation strategies on word memory recognition performance and related time assessments by the involved participants. The general idea is to define a protocol for data collection that would allow to concurrently account of the four variables at the play: emotion, emotion regulation, memory performance, and time perception. In addition, the recording of the subjects facial expressions during the induction procedure will contribute to the creation of a multi-modal database of quasi-spontaneous facial emotional expressions.

View full abstract

The random flights are (continuous time) random walks with finite velocity. Often, these models describe the stochastic motions arising in biology. In this paper we study the large time asymptotic behavior of random flights. We prove the large deviation principle for conditional laws given the number of the changes of direction, and for the non-conditional laws of some standard random flights.

View full abstract

In this paper, we review the theory of time space-harmonic polynomials developed by using a symbolic device known in the literature as the classical umbral calculus. The advantage of this symbolic tool is twofold. First a moment representation is allowed for a wide class of polynomial stochastic processes involving the L´evy ones in respect to which they are martingales. This representation includes some well-known examples such as Hermite polynomials in connection with Brownian motion. As a consequence, characterizations of many other families of polynomials having the time space-harmonic property can be recovered via the symbolic moment representation. New relations with Kailath-Segall polynomials are also stated. Secondly the generalization to the multivariable framework is straightforward. Connections with cumulants and Bell polynomials are highlighted both in the univariate case and multivariate one. Open problems are addressed at the end of the paper.

View full abstract

We study a modification of a Holling–Tanner predator-prey model considering an alternative food for predator. We prove that this system does not exhibit a classical Hopf bifurcation. Nevertheless, for convenient values of the parameters a periodic orbit bifurcates from an equilibrium point and during this local bifurcation the eigenvalues of such equilibrium remain purely imaginary.

View full abstract

Central-Asia is precinctive with respect to viral hepatitis. All known 5 types of hepatitis virus circulate here. However molecular-genetic and cellular aspects of its pathogenesis are definitively not established. It can be reached by applying modern technology for the quantitative analyzing functioning regulatory mechanisms (regulatorika) of living systems at molecular-genetic level with using methods for mathematical modeling and computing experiment. In the given work the mathematical and computer modeling liver regulatorika at the norm and viral hepatitis type D on molecular-genetic level are considered.

View full abstract

This article presents a brief survey on the use of Lyapunov method for stochastic differential equations. Sufficient conditions extending Lyapunov theory for ordinary differential equations to stochastic stability in probability are given.

View full abstract