Reaction–Diffusion models: From particle systems to SDE’s

Solving large systems arising from fractional models by preconditioned methods

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

From Interacting Particle Systems to Random Matrices

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuat...

Interacting Particle Systems – featuring Ising Models

From cognitive models to neurofuzzy systems

Phenomenological theory of mind based on simple concepts related to human cognition is introduced. Basic concepts of this theory are directly related to neurophysiological events in the brain and may also be extended to explain higher cognitive functions realized by the mind. This theory on the one hand solves fundamental problems in cognitive sciences, explaining puzzling behavior of human con...

From UML Models to Graph Transformation Systems

In this paper we present an approach that allows to validate properties of UML models. The approach is based on an integrated semantics for central parts of the UML. We formally cover UML use case, class, object, statechart, collaboration, and sequence diagrams. Additionally full OCL is supported in the common UML fashion. Our semantics is based on the translation of a UML model into a graph tr...