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The understanding of human central nervous system depends on knowledge of its wiring. However, there are still gaps in our understanding of its wiring due to technical difficulties. While some information is coming out from human…
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global…
Motivation: Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into…
Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…
In this paper we derive an upper bound for the degree of the strict invariant algebraic curve of a polynomial system in the complex project plane under generic condition. The results are obtained through the algebraic multiplicities of the…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Different classes of the whorl fingerprint are discussed. A general dynamical system with a parameter theta is created using differential equations to simulate these classes by varying the value of theta. The global dynamics is studied, and…
We propose a variant of the CCS process algebra with new features aiming at allowing multiscale modelling of biological systems. In the usual semantics of process algebras for modelling biological systems actions are instantaneous. When…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
Modeling and topological analysis of networks in biological and other complex systems, must venture beyond the limited consideration of very few network metrics like degree, betweenness or assortativity. A proper identification of…
Many nonequilibrium systems, such as biochemical reactions and socioeconomic interactions, can be described by reaction-diffusion equations that demonstrate a wide variety of complex spatiotemporal patterns. The diversity of the morphology…
In this paper, we complete the global qualitative analysis of a quartic family of planar vector fields corresponding to a rational Holling-type dynamical system which models the dynamics of the populations of predators and their prey in a…
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…
We report a new system of artificial life called Lenia (from Latin lenis "smooth"), a two-dimensional cellular automaton with continuous space-time-state and generalized local rule. Computer simulations show that Lenia supports a great…
Variational system identification is a new formulation of maximum likelihood for estimation of parameters of dynamical systems subject to process and measurement noise, such as aircraft flying in turbulence. This formulation is an…
Dynamical systems containing heteroclinic cycles and networks can be invoked as models of intransitive competition between three or more species. When populations are assumed to be well-mixed, a system of ordinary differential equations…
Biological nervous systems consist of networks of diverse, sophisticated information processors in the form of neurons of different classes. In most artificial neural networks (ANNs), neural computation is abstracted to an activation…
This letter presents a technique to calculate the variance of algebraic variables of power system models represented as a set of stochastic differential-algebraic equations. The technique utilizes the solution of a Lyapunov equation and…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
This paper addresses the path-planning challenge for very large-scale robotic systems (VLSR) operating in complex and cluttered environments. VLSR systems consist of numerous cooperative agents or robots working together autonomously.…