239 research outputs found
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Applying Mean-field Approximation to Continuous Time Markov Chains
The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent
deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications
of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique,
moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and
uid model checking analysis techniques
Transient Reward Approximation for Continuous-Time Markov Chains
We are interested in the analysis of very large continuous-time Markov chains
(CTMCs) with many distinct rates. Such models arise naturally in the context of
reliability analysis, e.g., of computer network performability analysis, of
power grids, of computer virus vulnerability, and in the study of crowd
dynamics. We use abstraction techniques together with novel algorithms for the
computation of bounds on the expected final and accumulated rewards in
continuous-time Markov decision processes (CTMDPs). These ingredients are
combined in a partly symbolic and partly explicit (symblicit) analysis
approach. In particular, we circumvent the use of multi-terminal decision
diagrams, because the latter do not work well if facing a large number of
different rates. We demonstrate the practical applicability and efficiency of
the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit
Spatial Fluid Limits for Stochastic Mobile Networks
We consider Markov models of large-scale networks where nodes are
characterized by their local behavior and by a mobility model over a
two-dimensional lattice. By assuming random walk, we prove convergence to a
system of partial differential equations (PDEs) whose size depends neither on
the lattice size nor on the population of nodes. This provides a macroscopic
view of the model which approximates discrete stochastic movements with
continuous deterministic diffusions. We illustrate the practical applicability
of this result by modeling a network of mobile nodes with on/off behavior
performing file transfers with connectivity to 802.11 access points. By means
of an empirical validation against discrete-event simulation we show high
quality of the PDE approximation even for low populations and coarse lattices.
In addition, we confirm the computational advantage in using the PDE limit over
a traditional ordinary differential equation limit where the lattice is modeled
discretely, yielding speed-ups of up to two orders of magnitude
Fluid Model Checking
In this paper we investigate a potential use of fluid approximation
techniques in the context of stochastic model checking of CSL formulae. We
focus on properties describing the behaviour of a single agent in a (large)
population of agents, exploiting a limit result known also as fast simulation.
In particular, we will approximate the behaviour of a single agent with a
time-inhomogeneous CTMC which depends on the environment and on the other
agents only through the solution of the fluid differential equation. We will
prove the asymptotic correctness of our approach in terms of satisfiability of
CSL formulae and of reachability probabilities. We will also present a
procedure to model check time-inhomogeneous CTMC against CSL formulae
Geometric fluid approximation for general continuous-time Markov chains
Fluid approximations have seen great success in approximating the macro-scale
behaviour of Markov systems with a large number of discrete states. However,
these methods rely on the continuous-time Markov chain (CTMC) having a
particular population structure which suggests a natural continuous state-space
endowed with a dynamics for the approximating process. We construct here a
general method based on spectral analysis of the transition matrix of the CTMC,
without the need for a population structure. Specifically, we use the popular
manifold learning method of diffusion maps to analyse the transition matrix as
the operator of a hidden continuous process. An embedding of states in a
continuous space is recovered, and the space is endowed with a drift vector
field inferred via Gaussian process regression. In this manner, we construct an
ODE whose solution approximates the evolution of the CTMC mean, mapped onto the
continuous space (known as the fluid limit)
Domain-specific languages for modeling and simulation
Simulation models and simulation experiments are increasingly complex. One way to handle this complexity is developing software languages tailored to specific application domains, so-called domain-specific languages (DSLs). This thesis explores the potential of employing DSLs in modeling and simulation. We study different DSL design and implementation techniques and illustrate their benefits for expressing simulation models as well as simulation experiments with several examples.Simulationsmodelle und -experimente werden immer komplexer. Eine Möglichkeit, dieser Komplexität zu begegnen, ist, auf bestimmte Anwendungsgebiete spezialisierte Softwaresprachen, sogenannte domänenspezifische Sprachen (\emph{DSLs, domain-specific languages}), zu entwickeln. Die vorliegende Arbeit untersucht, wie DSLs in der Modellierung und Simulation eingesetzt werden können. Wir betrachten verschiedene Techniken für Entwicklung und Implementierung von DSLs und illustrieren ihren Nutzen für das Ausdrücken von Simulationsmodellen und -experimenten anhand einiger Beispiele
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