We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space R ×E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rate...

In order to support, for example, a quantitative analysis of various algorithms, protocols etc. probabilistic features have been introduced into a number of programming languages and calculi. It is by now quite standard to define the formal semantics of (various) probabilistic languages, for example, in terms of Discrete Time Markov Chains (DTMCs). In most cases however the probabilities involv...

We show the existence of independent random matching of a large population in a continuous-time dynamical system, where the matching intensities could be general nonnegative jointly continuous functions on the space of type distributions and the time line. In particular, we construct a continuum of independent continuous-time Markov processes that is derived from random mutation, random matchin...

The paper proves by means of the state space theory the theorem in which the characteristic polynomial of the determinate feedback connection of two controllable and observable dynamical systems is stated. The characteristic polynomial is expressed by the use of the transfer function matrices of each dynamical system.

Many sequences of p-adic integers project modulo p to p-automatic sequences for every α ≥ 0. Examples include algebraic sequences of integers, which satisfy this property for every prime p, and some cocycle sequences, which we show satisfy this property for a fixed p. For such a sequence, we construct a profinite automaton that projects modulo p to the automaton generating the projected sequenc...

We consider a generic mean-field scenario, in which a sequence of population models, described by discretetime Markov chains (DTMCs), converges to a deterministic limit in discrete time. Under the assumption that the limit has a globally attracting equilibrium, the steady states of the sequence of DTMC models converge to the point-mass distribution concentrated on this equilibrium. In this pape...

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Since crystals are made of periodic structures in space, determining their three independent period vectors in theory (starting from any values) is a basic physics problem. For the general situation where crystals are under constant external stress, we derived dynamical equations of the period vectors in the framework of Newtonian dynamics, for pair potentials recently (doi:/10.1139/cjp-2014-05...

A parametric model of the complex time-dependent geometry of the ventricles of the human heart is constructed. The geometry model is created by means of a boundary value approach, solving an elliptic partial differential equation to generate a representation of the inner surface of the ventricles. The technique provides a closed-form description of the geometry with the advantage that the geome...

In this paper, global uniform exponential stability of perturbed dynamical systems is studied by using Lyapunov techniques. The system presents a perturbation term which is bounded by an integrable function with the assumption that the nominal system is globally uniformly exponentially stable. Some examples in dimensional two are given to illustrate the applicability of the main results.