49,473 research outputs found
SBIP 2.0: Statistical Model Checking Stochastic Real-time Systems
International audienceThis paper presents a major new release of SBIP, an extensi-ble statistical model checker for Metric (MTL) and Linear-time Temporal Logic (LTL) properties on respectively Generalized Semi-Markov Processes (GSMP), Continuous-Time (CTMC) and Discrete-Time Markov Chain (DTMC) models. The newly added support for MTL, GSMPs, CTMCs and rare events allows to capture both real-time and stochastic aspects, allowing faithful specification, modeling and analysis of real-life systems. SBIP is redesigned as an IDE providing project management, model edition, compilation, simulation, and statistical analysis
Spurious memory in non-equilibrium stochastic models of imitative behavior
The origin of the long-range memory in the non-equilibrium systems is still
an open problem as the phenomenon can be reproduced using models based on
Markov processes. In these cases a notion of spurious memory is introduced. A
good example of Markov processes with spurious memory is stochastic process
driven by a non-linear stochastic differential equation (SDE). This example is
at odds with models built using fractional Brownian motion (fBm). We analyze
differences between these two cases seeking to establish possible empirical
tests of the origin of the observed long-range memory. We investigate
probability density functions (PDFs) of burst and inter-burst duration in
numerically obtained time series and compare with the results of fBm. Our
analysis confirms that the characteristic feature of the processes described by
a one-dimensional SDE is the power-law exponent of the burst or
inter-burst duration PDF. This property of stochastic processes might be used
to detect spurious memory in various non-equilibrium systems, where observed
macroscopic behavior can be derived from the imitative interactions of agents.Comment: 11 pages, 5 figure
A variational approach to modeling slow processes in stochastic dynamical systems
The slow processes of metastable stochastic dynamical systems are difficult
to access by direct numerical simulation due the sampling problem. Here, we
suggest an approach for modeling the slow parts of Markov processes by
approximating the dominant eigenfunctions and eigenvalues of the propagator. To
this end, a variational principle is derived that is based on the maximization
of a Rayleigh coefficient. It is shown that this Rayleigh coefficient can be
estimated from statistical observables that can be obtained from short
distributed simulations starting from different parts of state space. The
approach forms a basis for the development of adaptive and efficient
computational algorithms for simulating and analyzing metastable Markov
processes while avoiding the sampling problem. Since any stochastic process
with finite memory can be transformed into a Markov process, the approach is
applicable to a wide range of processes relevant for modeling complex
real-world phenomena
Quasichemical Models of Multicomponent Nonlinear Diffusion
Diffusion preserves the positivity of concentrations, therefore,
multicomponent diffusion should be nonlinear if there exist non-diagonal terms.
The vast variety of nonlinear multicomponent diffusion equations should be
ordered and special tools are needed to provide the systematic construction of
the nonlinear diffusion equations for multicomponent mixtures with significant
interaction between components. We develop an approach to nonlinear
multicomponent diffusion based on the idea of the reaction mechanism borrowed
from chemical kinetics.
Chemical kinetics gave rise to very seminal tools for the modeling of
processes. This is the stoichiometric algebra supplemented by the simple
kinetic law. The results of this invention are now applied in many areas of
science, from particle physics to sociology. In our work we extend the area of
applications onto nonlinear multicomponent diffusion.
We demonstrate, how the mechanism based approach to multicomponent diffusion
can be included into the general thermodynamic framework, and prove the
corresponding dissipation inequalities. To satisfy thermodynamic restrictions,
the kinetic law of an elementary process cannot have an arbitrary form. For the
general kinetic law (the generalized Mass Action Law), additional conditions
are proved. The cell--jump formalism gives an intuitively clear representation
of the elementary transport processes and, at the same time, produces kinetic
finite elements, a tool for numerical simulation.Comment: 81 pages, Bibliography 118 references, a review paper (v4: the final
published version
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
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