On the termination of some biclique operators on multipartite graphs

International audienceWe define a new graph operator, called the weak-factor graph, which comes from the context of complex network modelling. The weak-factor operator is close to the well-known clique-graph operator but it rather operates in terms of bicliques in a multipartite graph. We address the problem of the termination of the series of graphs obtained by iteratively applying the weak-factor operator starting from a given input graph. As for the clique-graph operator, it turns out that some graphs give rise to series that do not terminate. Therefore, we design a slight variation of the weak-factor operator, called clean-factor, and prove that its associated series terminates for all input graphs. In addition, we show that the multipartite graph on which the series terminates has a very nice combinatorial structure: we exhibit a bijection between its vertices and the chains of the inclusion order on the intersections of the maximal cliques of the input graph

Some applications of graph theory

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.For the abstract of this thesis, please see the attached PDF.This work was funded by a Marie Curie Early Stage Training Fellowship (NET-ACE-programme) under grant number MEST-CT-2004-6724

Evolutionary responses of fast adapting populations to opposing selection pressures

This thesis deals with the mathematical modeling of evolutionary processes that take place in heterogeneous populations. Its leitmotif is the response of complex ensembles of replicating entities to multiple (and often opposite) selection pressures. Even though the specific problems addressed in different chapters belong to different organizational levels—genome, population, and community—all of them can be conceptualized as the evolution of a heterogeneous population—let it be a population of genomic elements, viruses, or prokaryotic hosts and phages—facing a complex environment. As a result, the mathematical tools required for their study are quite similar. In contrast, the strategies that each population has discovered to perpetuate vary according to the different evolutionary challenges and environmental constraints that the population experiences. Along this thesis, there has been a special interest on connecting theoretical models with experimental results. To that end, most of the work presented here has been motivated either by laboratory findings or by the bioinformatic analysis of sequenced genomes. We strongly believe that such a multidisciplinary approach is necessary in order to improve our knowledge on how evolution works. Moreover, experiments are a must when it comes to propose antiviral strategies based on theoretical predictions, as we do in Chapter 3. This thesis is structured in two main blocks. The first one focuses on studying instances of viral evolution under the action of mutagenic drugs, paying particular attention to their possible application to the development of novel antiviral therapies. This block comprises chapters 2 and 3; the former dicussing the phenomenon of lethal defection and stochastic viral extinction; the latter dealing with the optimal way to combine mutagens and inhibitors in multidrug antiviral treatments. The second block is devoted to the study of the evolutionary forces underlying genome structure. In chapter 4, we propose a mechanism through which multipartite viruses could have originated. Interestingly, the pathway leading to genome segmentation shares some steps with lethal defection, but each outcome is reached at specific environmental conditions. Chapter 5 analyses the abundance distributions of transposable elements in prokaryotic genomes, with the aim of determining the key processes involved in their spreading. We explicitly explore the hypothesis that transposable elements follow a neutral dynamics, with a negligible fitness cost for their host genomes. A higher level of organization is studied in Chapter 6, where an agent based coevolutionary model based on Lotka-Volterra interactions is used to investigate the evolutionary dynamics of the prokaryotic antiviral immunity system CRISPR-Cas. This chapter also examines the environmental factors that are responsible for its maintenance or loss. Finally, Chapter 7 summarizes the main results obtained along the thesis and sketches possible lines of work based on them

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...