A Constrained Approach to Multiscale Stochastic Simulation of\ud Chemically Reacting Systems

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper we introduce a multiscale methodology suitable to address this problem. It is based on the Conditional Stochastic Simulation Algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the Constrained Multiscale Algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems

CSM-426: Theoretical Analysis of Generalised Recombination

In this paper we propose, model theoretically and study a general notion of recombination for fixed-length strings where homologous crossover, inversion, gene duplication, gene deletion, diploidy and more are just special cases. The analysis of the model reveals similarities and differences between genetic systems based on these operations. It also reveals that the notion of schema emerges naturally from the model?s equations even for the strangest of recombination operations. The study provides a variety of fixed points for the case where recombination is used alone, which generalise Geiringer?s theorem

CSM-427: Coarse Graining in an Evolutionary Algorithm with Recombination, Duplication and Inversion

A generalised form of recombination, wherein an offspring can be formed from any of the genetic material of the parents, is analysed in the context of a two-locus recombinative GA. A complete, exact solution, is derived, showing how the dynamical behaviour is radically different to that of homologous crossover. Inversion is shown to potentially introduce oscillations in the dynamics, while gene duplication leads to an asymmetry between homogeneous and heterogeneous strings. All non-homologous operators lead to allele ?diffusion? along the chromosome. We discuss how inferences from the two-locus results extend to the case of a recombinative GA with selection and more than two loci

Perturbation Theory and the Renormalization Group in Genetic Dynamics

Although much progress has been made in recent years in the theory of GAs and GP, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article we propose and study perturbation theory as a potential tool to fill this gap. We concentrate mainly on selection-mutation systems, showing different implementations of the perturbative framework, developing, for example, perturbative expansions for the eigenvalues and eigenvectors of the transition matrix. The main focus however, is on diagrammatic methods, taken from physics, where we show how approximations can be built up using a pictorial representation generated by a simple set of rules, and how the renormalization group can be used to systematically improve the perturbation theory

A Model for Analysing the Collective Dynamic Behaviour and Characterising the Exploitation of Population-Based Algorithms

Several previous studies have focused on modelling and analysing the collective dynamic behaviour of population-based algorithms. However, an empirical approach for identifying and characterising such a behaviour is surprisingly lacking. In this paper, we present a new model to capture this collective behaviour, and to extract and quantify features associated with it. The proposed model studies the topological distribution of an algorithm's activity from both a genotypic and a phenotypic perspective, and represents population dynamics using multiple levels of abstraction. The model can have different instantiations. Here it has been implemented using a modified version of self-organising maps. These are used to represent and track the population motion in the fitness landscape as the algorithm operates on solving a problem. Based on this model, we developed a set of features that characterise the population's collective dynamic behaviour. By analysing them and revealing their dependency on fitness distributions, we were then able to define an indicator of the exploitation behaviour of an algorithm. This is an entropy-based measure that assesses the dependency on fitness distributions of different features of population dynamics. To test the proposed measures, evolutionary algorithms with different crossover operators, selection pressure levels and population handling techniques have been examined, which lead populations to exhibit a wide range of exploitation-exploration behaviours. </jats:p

High-performance computing for data analytics

One of the main challenges in data analytics is that discovering structures and patterns in complex datasets is a computer-intensive task. Recent advances in high-performance computing provide part of the solution. Multicore systems are now more affordable and more accessible. In this paper, we investigate how this can be used to develop more advanced methods for data analytics. We focus on two specific areas: model-driven analysis and data mining using optimisation techniques

Deriving mesoscopic models of collective behaviour for finite populations

Animal groups exhibit emergent properties that are a consequence of local interactions. Linking individual-level behaviour to coarse-grained descriptions of animal groups has been a question of fundamental interest. Here, we present two complementary approaches to deriving coarse-grained descriptions of collective behaviour at so-called mesoscopic scales, which account for the stochasticity arising from the finite sizes of animal groups. We construct stochastic differential equations (SDEs) for a coarse-grained variable that describes the order/consensus within a group. The first method of construction is based on van Kampen's system-size expansion of transition rates. The second method employs Gillespie's chemical Langevin equations. We apply these two methods to two microscopic models from the literature, in which organisms stochastically interact and choose between two directions/choices of foraging. These `binary-choice' models differ only in the types of interactions between individuals, with one assuming simple pair-wise interactions, and the other incorporating higher-order effects. In both cases, the derived mesoscopic SDEs have multiplicative, or state-dependent, noise. However, the different models demonstrate the contrasting effects of noise: increasing order in the pair-wise interaction model, whilst reducing order in the higher-order interaction model. Although both methods yield identical SDEs for such binary-choice, or one-dimensional, systems, the relative tractability of the chemical Langevin approach is beneficial in generalizations to higher-dimensions. In summary, this book chapter provides a pedagogical review of two complementary methods to construct mesoscopic descriptions from microscopic rules and demonstrates how resultant multiplicative noise can have counter-intuitive effects on shaping collective behaviour.Comment: Second version, 4 figures, 2 appendice

Optimisation via encodings: a renormalisation group perspective

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when local minima, that are a feature of the typically rugged landscapes encountered, arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. The processes that are typically employed involve some form of coarse-graining, and we suggest here that they can be viewed as avatars of renormalisation group transformations.Comment: 17 pages, 2 figures. arXiv admin note: text overlap with arXiv:1806.0524