Ada Lovelace blazed a trail in science – we need more women to follow in her footsteps

First paragraph: Ada Lovelace day falls on the second Tuesday of October every year – it is a time to celebrate the achievements of women in STEM subjects: science, technology, engineering and mathematics. But who was Ada Lovelace and why choose a Victorian titled lady as a champion for today’s potential heroes?  Access this article at The Conversation website: https://theconversation.com/ada-lovelace-blazed-a-trail-in-science-we-need-more-women-to-follow-in-her-footsteps-6666

A Survey of formal methods applied to leader election in IEEE 1394

We present a survey of formal specification techniques appiled to the leader election protocol of the IEEE 1394 High Performance Serial Bus. Specifications written in a variety of formalisms are compared with regard to a number of criteria including expressiveness, readability, standardisation, and level of analysis

But what if I don't want to wait forever?

We present an abstract model of the leader election protocol used in the IEEE 1394 High Performance Serial Bus standard. The model is expressed in the probabilistic Guarded Command Language. By formal reasoning based on this description, we establish the probability of the root contention part of the protocol successfully terminating in terms of the number of attempts to do so. Some simple calculations then allow us to establish an upper bound on the time taken for those attempts

Deriving Mean Field Equations from Large Process Algebra Models

In many domain areas the behaviour of a system can be described at two levels: the behaviour of individual components, and the behaviour of the system as a whole. Often deriving one from the other is impossible, or at least intractable, especially when realistically large systems are considered. Here we present a rigorous algorithm which, given an individual based model in the process algebra WSCCS describing the components of a system and the way they interact, can produce a system of mean field equations which describe the mean behaviour of the system as a whole. This transformation circumvents the state explosion problem, allowing us to handle systems of any size by providing an approximation of the system behaviour. From the mean field equations we can investigate the transient dynamics of the system. This approach was motivated by problems in biological systems, but is applicable to distributed systems in general

Process Algebra Models of Population Dynamics

It is well understood that populations cannot grow without bound and that it is competition between individuals for resources which restricts growth. Despite centuries of interest, the question of how best to model density dependent population growth still has no definitive answer. We address this question here through a number of individual based models of populations expressed using the process algebra WSCCS. The advantage of these models is that they can be explicitly based on observations of individual interactions. From our probabilistic models we derive equations expressing overall population dynamics, using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. Further, the approach is applied to epidemiology, combining population growth with disease spread

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

From Individuals to Populations: a mean field semantics for process algebra

A new semantics in terms of Mean Field Equations is presented for WSCCS (Weighted Synchronous Calculus of Communicating Systems). The semantics captures the average behaviour of the system over time, but without computing the entire state space, therefore avoiding the state space explosion problem. This allows easy investigation of models with large numbers of components. The new semantics is shown to be equivalent to the standard Discrete Time Markov Chain semantics of WSCCS as the number of processes tends to infinity. The method of deriving the semantics is illustrated with examples drawn from biology and from computing

From Individuals to Populations: A Symbolic Process Algebra Approach to Epidemiology

Is it possible to symbolically express and analyse an individual-based model of disease spread, including realistic population dynamics? This problem is addressed through the use of process algebra and a novel method for transforming process algebra into Mean Field Equations. A number of stochastic models of population growth are presented, exploring different representations based on alternative views of individual behaviour. The overall population dynamics in terms of mean field equations are derived using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. The utility of our approach for epidemiology is confirmed by constructing a model combining population growth with disease spread and fitting it to data on HIV in the UK population

IEEE 1394 Tree Identify Protocol: Introduction to the case study

We introduce a comparative case study on the application of formal methods and techniques to the Tree Identify Protocol of the IEEE standard 1394 serial multimedia bus. The Tree Identify Protocol makes an ideal subject for this purpose because it is small yet complex, and may be modelled in a variety of ways. We provide an informal explanation of the protocol, describe how the case study was conducted, and give an overview of the results

Decision Support Based on Bio-PEPA Modeling and Decision Tree Induction: A New Approach, Applied to a Tuberculosis Case Study

The problem of selecting determinant features generating appropriate model structure is a challenge in epidemiological modelling. Disease spread is highly complex, and experts develop their understanding of its dynamic over years. There is an increasing variety and volume of epidemiological data which adds to the potential confusion. We propose here to make use of that data to better understand disease systems. Decision tree techniques have been extensively used to extract pertinent information and improve decision making. In this paper, we propose an innovative structured approach combining decision tree induction with Bio-PEPA computational modelling, and illustrate the approach through application to tuberculosis. By using decision tree induction, the enhanced Bio-PEPA model shows considerable improvement over the initial model with regard to the simulated results matching observed data. The key finding is that the developer expresses a realistic predictive model using relevant features, thus considering this approach as decision support, empowers the epidemiologist in his policy decision making