Unwinding biological systems

Unwinding conditions have been fruitfully exploited in Information Flow Security to define persistent security properties. In this paper we investigate their meaning and possible uses in the analysis of biological systems. In particular, we elaborate on the notion of robustness and propose some instances of unwinding over the process algebra Bio-PEPA and over hybrid automata. We exploit such instances to analyse two case-studies: Neurospora crassa circadian system and Influenza kinetics models

Studying the effects of adding spatiality to a process algebra model

We use NetLogo to create simulations of two models of disease transmission originally expressed in WSCCS. This allows us to introduce spatiality into the models and explore the consequences of having different contact structures among the agents. In previous work, mean field equations were derived from the WSCCS models, giving a description of the aggregate behaviour of the overall population of agents. These results turned out to differ from results obtained by another team using cellular automata models, which differ from process algebra by being inherently spatial. By using NetLogo we are able to explore whether spatiality, and resulting differences in the contact structures in the two kinds of models, are the reason for this different results. Our tentative conclusions, based at this point on informal observations of simulation results, are that space does indeed make a big difference. If space is ignored and individuals are allowed to mix randomly, then the simulations yield results that closely match the mean field equations, and consequently also match the associated global transmission terms (explained below). At the opposite extreme, if individuals can only contact their immediate neighbours, the simulation results are very different from the mean field equations (and also do not match the global transmission terms). These results are not surprising, and are consistent with other cellular automata-based approaches. We found that it was easy and convenient to implement and simulate the WSCCS models within NetLogo, and we recommend this approach to anyone wishing to explore the effects of introducing spatiality into a process algebra model

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

Phenomenological modelling: statistical abstraction methods for Markov chains

Continuous-time Markov chains have long served as exemplary low-level models for an array of systems, be they natural processes like chemical reactions and population fluctuations in ecosystems, or artificial processes like server queuing systems or communication networks. Our interest in such systems is often an emergent macro-scale behaviour, or phenomenon, which can be well characterised by the satisfaction of a set of properties. Although theoretically elegant, the fundamental low-level nature of Markov chain models makes macro-scale analysis of the phenomenon of interest difficult. Particularly, it is not easy to determine the driving mechanisms for the emergent phenomenon, or to predict how changes at the Markov chain level will influence the macro-scale behaviour. The difficulties arise primarily from two aspects of such models. Firstly, as the number of components in the modelled system grows, so does the state-space of the Markov chain, often making behaviour characterisation untenable under both simulation-based and analytical methods. Secondly, the behaviour of interest in such systems is usually dependent on the inherent stochasticity of the model, and may not be aligned to the underlying state interpretation. In a model where states represent a low-level, primitive aspect of system components, the phenomenon of interest often varies significantly with respect to this low-level aspect that states represent. This work focuses on providing methodological frameworks that circumvent these issues by developing abstraction strategies, which preserve the phenomena of interest. In the first part of this thesis, we express behavioural characteristics of the system in terms of a temporal logic with Markov chain trajectories as semantic objects. This allows us to group regions of the state-space by how well they satisfy the logical properties that characterise macro-scale behaviour, in order to produce an abstracted Markov chain. States of the abstracted chain correspond to certain satisfaction probabilities of the logical properties, and inferred dynamics match the behaviour of the original chain in terms of the properties. The resulting model has a smaller state-space which is interpretable in terms of an emergent behaviour of the original system, and is therefore valuable to a researcher despite the accuracy sacrifices. Coarsening based on logical properties is particularly useful in multi-scale modelling, where a layer of the model is a (continuous-time) Markov chain. In such models, the layer is relevant to other layers only in terms of its output: some logical property evaluated on the trajectory drawn from the Markov chain. We develop here a framework for constructing a surrogate (discrete-time) Markov chain, with states corresponding to layer output. The expensive simulation of a large Markov chain is therefore replaced by an interpretable abstracted model. We can further use this framework to test whether a posited mechanism could be the driver for a specific macro-scale behaviour exhibited by the model. We use a powerful Bayesian non-parametric regression technique based on Gaussian process theory to produce the necessary elements of the abstractions above. In particular, we observe trajectories of the original system from which we infer the satisfaction of logical properties for varying model parametrisation, and the dynamics for the abstracted system that match the original in behaviour. The final part of the thesis presents a novel continuous-state process approximation to the macro-scale behaviour of discrete-state Markov chains with large state-spaces. The method is based on spectral analysis of the transition matrix of the chain, where 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 form an ODE whose solution approximates the evolution of the CTMC mean, mapped onto the continuous space (known as the fluid limit). Our method is general and differs significantly from other continuous approximation methods; the latter rely on the Markov chain having a particular population structure, suggestive of a natural continuous state-space and associated dynamics. Overall, this thesis contributes novel methodologies that emphasize the importance of macro-scale behaviour in modelling complex systems. Part of the work focuses on abstracting large systems into more concise systems that retain behavioural characteristics and are interpretable to the modeller. The final part examines the relationship between continuous and discrete state-spaces and seeks for a transition path between the two which does not rely on exogenous semantics of the system states. Further than the computational and theoretical benefits of these methodologies, they push at the boundaries of various prevalent approaches to stochastic modelling

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first