Dynamics of Randomly Constructed Computational Systems

We studied Petri nets with five places constructed in a pseudo-random way: their underlying net is composed of join and fork. We report initial results linking the dynamical properties of these systems to the topology of their underlying net. The obtained results can be easily related to the computational power of some abstract models of computation

Predicting the outcomes of HIV treatment interruptions using computational modelling

In the past 30 years, HIV infection made a transition from fatal to chronic disease due to the emergence of potent treatment largely suppressing viral replication. However, this medication must be administered life-long on a regular basis to maintain viral suppression and is not always well tolerated. Any interruption of treatment causes residual virus to be reactivated and infection to progress, where the underlying processes occurring and consequences for the immune system are still poorly understood. Nonetheless, treatment interruptions are common due to adherence issues or limited access to antiretroviral drugs. Early clinical studies, aiming at application of treatment interruptions in a structured way, gave contradictory results concerning patient safety, discouraging further trials. In-silico models potentially add to knowledge but a review of the Literature indicates most current models used for studying treatment interruptions (equation-based), neglect recent clinical findings of collagen formation in lymphatic tissue due to HIV and its crucial role in immune system stability and efficacy. The aim of this research is the construction and application of so-called ‘Bottom-Up’ models to allow improved assessment of these processes in relation to HIV treatment interruptions. In this regard, a novel computational model based on 2D Cellular Automata for lymphatic tissue depletion and associated damage to the immune system was developed. Hence, (i) using this model, the influence of spatial distribution of collagen formation on HIV infection progression speed was evaluated while discussing aspects of computational performance. Further, (ii) direct Monte Carlo simulations were employed to explore the accumulation of tissue impairment due to repeated treatment interruptions and consequences for long-term prognosis. Finally, (iii) an inverse Monte Carlo approach was used to reconstruct yet unknown characteristics of patient groups. This is based on sparse data from past clinical studies on treatment interruptions with the aim of explaining their contradictory results

Gauge Theories of Gravitation

During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills type. The present text offers commentaries on the articles from the most prominent proponents of the theory. In the early 1960s, the gauge idea was successfully applied to the Poincar\'e group of spacetime symmetries and to the related conserved energy-momentum and angular momentum currents. The resulting theory, the Poincar\'e gauge theory, encompasses Einstein's general relativity as well as the teleparallel theory of gravity as subcases. The spacetime structure is enriched by Cartan's torsion, and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions \`a la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincar\'e gauge theory and its generalizations are explored and special topics, such as its Hamiltonian formulation and exact solutions, are studied. This guide to the literature on classical gauge theories of gravity is intended to be a stimulating introduction to the subject.Comment: 169 pages, pdf file, v3: extended to a guide to the literature on classical gauge theories of gravit

A systems biology approach to multi-scale modelling and analysis of planar cell polarity in drosophila melanogaster wing

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Systems biology aims to describe and understand biology at a global scale where biological systems function as a result of complex mechanisms that happen at several scales. Modelling and simulation are computational tools that are invaluable for description, understanding and prediction these mechanisms in a quantitative and integrative way. Thus multi-scale methods that couple the design, simulation and analysis of models spanning several spatial and temporal scales is becoming a new emerging focus of systems biology. This thesis uses an exemplar – Planar cell polarity (PCP) signalling – to illustrate a generic approach to model biological systems at different spatial scales, using the new concept of Hierarchically Coloured Petri Nets (HCPN). PCP signalling refers to the coordinated polarisation of cells within the plane of various epithelial tissues to generate sub-cellular asymmetry along an axis orthogonal to their apical-basal axes. This polarisation is required for many developmental events in both vertebrates and non-vertebrates. Defects in PCP in vertebrates are responsible for developmental abnormalities in multiple tissues including the neural tube, the kidney and the inner ear. In Drosophila wing, PCP is seen in the parallel orientation of hairs that protrude from each of the approximately 30,000 epithelial cells to robustly point toward the wing tip. This work applies HCPN to model a tissue comprising multiple cells hexagonally packed in a honeycomb formation in order to describe the phenomenon of Planar Cell Polarity (PCP) in Drosophila wing. HCPN facilitate the construction of mathematically tractable, compact and parameterised large-scale models. Different levels of abstraction that can be used in order to simplify such a complex system are first illustrated. The PCP system is first represented at an abstract level without modelling details of the cell. Each cell is then sub-divided into seven virtual compartments with adjacent cells being coupled via the formation of intercellular complexes. A more detailed model is later developed, describing the intra- and inter-cellular signalling mechanisms involved in PCP signalling. The initial model is for a wild-type organism, and then a family of related models, permitting different hypotheses to be explored regarding the mechanisms underlying PCP, are constructed. Among them, the largest model consists of 800 cells which when unfolded yields 164,000 places (each of which is described by an ordinary differential equation). This thesis illustrates the power and validity of the approach by showing how the models can be easily adapted to describe well-documented genetic mutations in the Drosophila wing using the proposed approach including clustering and model checking over time series of primary and secondary data, which can be employed to analyse and check such multi-scale models similar to the case of PCP. The HCPN models support the interpretation of biological observations reported in literature and are able to make sensible predictions. As HCPN model multi-scale systems in a compact, parameterised and scalable way, this modelling approach can be applied to other large-scale or multi-scale systems.This study was funded by Brunel University

Dynamical symmetry breaking in molecules and molecular aggregates

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 1994.Includes bibliographical references.by Günter Maximilian Schmid.Ph.D