7 research outputs found
Modeling biological systems with delays in Bio-PEPA
Delays in biological systems may be used to model events for which the
underlying dynamics cannot be precisely observed, or to provide abstraction of
some behavior of the system resulting more compact models. In this paper we
enrich the stochastic process algebra Bio-PEPA, with the possibility of
assigning delays to actions, yielding a new non-Markovian process algebra:
Bio-PEPAd. This is a conservative extension meaning that the original syntax of
Bio-PEPA is retained and the delay specification which can now be associated
with actions may be added to existing Bio-PEPA models. The semantics of the
firing of the actions with delays is the delay-as-duration approach, earlier
presented in papers on the stochastic simulation of biological systems with
delays. These semantics of the algebra are given in the Starting-Terminating
style, meaning that the state and the completion of an action are observed as
two separate events, as required by delays. Furthermore we outline how to
perform stochastic simulation of Bio-PEPAd systems and how to automatically
translate a Bio-PEPAd system into a set of Delay Differential Equations, the
deterministic framework for modeling of biological systems with delays. We end
the paper with two example models of biological systems with delays to
illustrate the approach.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005
A Software Interface Between the Narrative Language and Bio-PEPA
AbstractWe present a software tool for the automatic translation of models from the Narrative Language, a semi-formal language for biological modelling, into the Bio-PEPA process algebra. This provides biologists with an easy way to describe systems and at the same time gives them access to the simulation and analysis techniques provided by Bio-PEPA. We present details of the translation algorithm and its integration into existing software, and discuss ways in which this idea could be further explored
Formal language for statistical inference of uncertain stochastic systems
Stochastic models, in particular Continuous Time Markov Chains, are a commonly
employed mathematical abstraction for describing natural or engineered dynamical
systems. While the theory behind them is well-studied, their specification can be
problematic in a number of ways. Firstly, the size and complexity of the model can
make its description difficult without using a high-level language. Secondly, knowledge
of the system is usually incomplete, leaving one or more parameters with unknown
values, thus impeding further analysis. Sophisticated machine learning algorithms have
been proposed for the statistically rigorous estimation and handling of this uncertainty;
however, their applicability is often limited to systems with finite state-space, and
there has not been any consideration for their use on high-level descriptions. Similarly,
high-level formal languages have been long used for describing and reasoning about
stochastic systems, but require a full specification; efforts to estimate parameters for
such formal models have been limited to simple inference algorithms.
This thesis explores how these two approaches can be brought together, drawing
ideas from the probabilistic programming paradigm. We introduce ProPPA, a process
algebra for the specification of stochastic systems with uncertain parameters. The
language is equipped with a semantics, allowing a formal interpretation of models
written in it. This is the first time that uncertainty has been incorporated into the syntax
and semantics of a formal language, and we describe a new mathematical object capable
of capturing this information. We provide a series of algorithms for inference which can
be automatically applied to ProPPA models without the need to write extra code. As
part of these, we develop a novel inference scheme for infinite-state systems, based on
random truncations of the state-space. The expressive power and inference capabilities
of the framework are demonstrated in a series of small examples as well as a larger-scale
case study. We also present a review of the state-of-the-art in both machine learning
and formal modelling with respect to stochastic systems. We close with a discussion of
potential extensions of this work, and thoughts about different ways in which the fields
of statistical machine learning and formal modelling can be further integrated
2010): Equivalences for a biological process algebra
Abstract This paper investigates Bio-PEPA, the stochastic process algebra for biological modelling developed by Ciocchetta and Hillston. It focusses on Bio-PEPA with levels where molecular counts are grouped or concentrations are discretised into a finite number of levels. Basic properties of well-defined Bio-PEPA systems are established after which equivalences used for the stochastic process algebra PEPA are considered for Bio-PEPA, and are shown to be identical for well-defined Bio-PEPA systems. Tw