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The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall…
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…
A free zero-range process (FRZP) is a simple stochastic process describing the dynamics of a gas of particles hopping between neighboring nodes of a network. We discuss three different cases of increasing complexity: (a) FZRP on a rigid…
The free distance of a convolutional code is a reliable indicator of its performance. However its computation is not an easy task. In this paper, we present some algorithms to compute the free distance with good efficiency that work for…
We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with…
Local thresholding algorithms were first presented more than a decade ago and have since been applied to a variety of data mining tasks in peer-to-peer systems, wireless sensor networks, and in grid systems. One critical assumption made by…
Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs…
We show that a tight-binding one-dimensional chain composed of interacting and non-interacting atomic sites can exhibit multiple mobility edges at different values of carrier energy in presence of external electric field. Within a mean…
We consider a dynamical system on a metric graph, that corresponds to a semiclassical solution of a time-dependent Schr\"odinger equation. We omit all details concerning mathematical physics and work with a purely discrete problem. We find…
Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is…
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…
Physical systems may couple to other systems through variables that are not gauge invariant. When we split a gauge system into two subsystems, the gauge-invariant variables of the two subsystems have less information than the gauge…
An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…
This paper introduces dynamic mechanism design in an elementary fashion. We first examine optimal dynamic mechanisms: We find necessary and sufficient conditions for perfect Bayesian incentive compatibility and formulate the optimal dynamic…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
In this report, we apply the proposed "para-model" framework in order to control the trajectory of a dynamical system-based robot. The optimization of the dynamical performances in closed-loop is performed using a derivative-free…
Web crawlers are used by internet search engines to gather information about the web graph. In this paper we investigate a simple process which models such software by walking around the vertices of a graph. Once initial random vertex…
Our previous work developed a framework for treating the motion of a small body in general relativity, based on a one-parameter-family of solutions to Einstein's equation. Here we give an analysis of the coordinate freedom allowed within…
We study the role of continuous measurement in the quantum to classical transition for a system with coupled internal (spin) and external (motional) degrees of freedom. Even when the measured motional degree of freedom can be treated…