This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a ...

In order to evaluate and compare different recursive filters, simulation is a common tool and numerous simulation models are widely used as 'benchmark'. In the simulation, the continuous time dynamic system is converted into a discrete-time recursive system. As a result of this, the state indeed evolves by Markov transitions in the simulation rather than in continuous time. One significant issu...

A new form of SAT-based symbolic model checking is described. Instead of unrolling the transition relation, it incrementally generates clauses that are inductive relative to (and augment) stepwise approximate reachability information. In this way, the algorithm gradually refines the property, eventually producing either an inductive strengthening of the property or a counterexample trace. Our e...

We study the problem of fault diagnosis in the context of timed discrete event systems (TDES). If an incorrect behaviour of the system is detected, the second phase denotes to the fault location. The aim of the fault location is to find the cause of a system dysfunction. Proposed method for fault location works with the timed model (timed automata) and is based on a model-checking technique. Th...

Automatic shot boundary detection is a field, where many techniques and methods have been proposed and have claimed to perform reliably, especially for abrupt scene cut detection. However, all the proposed methods share a common drawback: the necessity of a threshold value, which is used as a reference for detecting scene changes. The determination of the appropriate value or the dynamic reesti...

We consider the Hartree equation for infinitely many electrons with a constant external magnetic field. For system, we show local well-posedness result when initial data is pertubation of Fermi sea, which non-trace class stationary solution to system. In this case, one particle Hamiltonian Pauli operator, possesses distinct properties from Laplace example, it has discrete spectrum and infinite-...

This paper develops a classification of transition behaviors for hybrid dynamic systems. Physical system behaviors often comprise of multiple temporal and spatial scales. A hybrid system model abstracts the operational domain of a continuous system into patches of similar behaviors. Behaviors in each patch are described by simpler models. When state variables cross threshold values, the system ...