Implementation of Logical Functions in the Game of Life

The Game of Life cellular automaton is a classical example of a massively parallel collision-based computing device. The automaton exhibits mobile patterns, gliders, and generators of the mobile patterns, glider guns, in its evolution. We show how to construct basic logical perations, AND, OR, NOT in space-time configurations of the cellular automaton. Also decomposition of complicated Boolean functions is discussed. Advantages of our technique are demonstrated on an example of binary adder, realized via collision of glider streams

Urban Informatics

This open access book is the first to systematically introduce the principles of urban informatics and its application to every aspect of the city that involves its functioning, control, management, and future planning. It introduces new models and tools being developed to understand and implement these technologies that enable cities to function more efficiently – to become ‘smart’ and ‘sustainable’. The smart city has quickly emerged as computers have become ever smaller to the point where they can be embedded into the very fabric of the city, as well as being central to new ways in which the population can communicate and act. When cities are wired in this way, they have the potential to become sentient and responsive, generating massive streams of ‘big’ data in real time as well as providing immense opportunities for extracting new forms of urban data through crowdsourcing. This book offers a comprehensive review of the methods that form the core of urban informatics from various kinds of urban remote sensing to new approaches to machine learning and statistical modelling. It provides a detailed technical introduction to the wide array of tools information scientists need to develop the key urban analytics that are fundamental to learning about the smart city, and it outlines ways in which these tools can be used to inform design and policy so that cities can become more efficient with a greater concern for environment and equity

Mathematical modeling in cancer addressing the early stage and treatment of avascular tumors

Orientador: Hyun Mo YangTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Esta tese trata de modelos matemáticos para descrever o surgimento e tratamento de tumores avasculares. Os modelos são baseados em sistemas de equações diferenciais ordinárias. Primeiramente, propomos um modelo para descrever o surgimento do câncer como um processo multi-passo, envolvendo transições entre células normais, células pré-malignas, e células tumorais, e considerando instabilidade genética como um fator que aumenta a taxa de mutações. O modelo prevê que a agressividade das células tumorais abre espaço para a sobrevivência das células menos adaptadas. Simulações numéricas mostram que o tempo para o tumor alcançar um tamanho detectável varia de cinco a oitenta anos, em razão de alterações mínimas nos parâmetros. Em seguida, estudamos um caso particular do primeiro modelo de um ponto de vista da teoria da Resiliência Ecológica. Os resultados ilustram como o surgimento e o tratamento efetivo do câncer podem ser vistos como a alternância entre dois estados de equilíbrio estáveis antagônicos. Neste contexto, alterações genéticas em uma escala de tempo lenta podem levar à destruição ou perda de estabilidade de um destes estados, tornando impossível tanto a cura ou o surgimento da doença. Na etapa seguinte, estudamos um modelo para quimioterapia metronômica em tumores avasculares, e mostramos como este tipo de tratamento pode levar à cura do paciente. Uma condição relacionando a toxicidade do tratamento aos parâmetros do modelo surge naturalmente e sua interpretação indica que a terapia metronômica tem baixa toxicidade quando administrada em tumores de crescimento lento, tumores com alta agressividade e competitividade por recursos, ou tumores com alta capacidade de suporte. Na última etapa, consideramos tratamentos não-autônomos visando comparar diversos regimes de dosagem em busca de protocolos ótimos. Mostramos como a utilização de uma abordagem simples para parametrizar a função que descreve o tratamento implica em facilidades tanto para a aplicação de métodos de otimização, quanto para a elaboração de critérios de otimalidade que englobem diversas características, como toxicidade, risco de recidiva, tempo de recuperação, e limitações na dosagem de drogaAbstract: This thesis studies mathematical models describing the onset and treatment of avascular tumors. The models are based on systems of ordinary differential equations. Initially, we propose a model to the onset of cancer as a multi-step process, involving transitions among normal cells, pre-malignant cells and tumor cells. The model considers genetic instability as a factor that enhances the mutation rates. Results predict that aggressiveness of tumor cells opens space to survival of less adapted cells. Numerical simulations show that the time for the tumor attains a detectable size ranges from five to eighty years, depending on minimal changes in parameters. Next, we study a particular case of the first model, from the point of view of Ecological Resilience. Results illustrate how the onset and the effective treatment of cancer may be seen as the switching between two alternative stable states. In this context, genetic alterations in a slow time-scale may cause the destruction or the loss of stability of one of these states, what makes impossible either the cure or the beginning of the disease. In the next stage, we study a model for metronomic chemotherapy in an avascular tumor, and we show how this treatment may lead to cure. A condition regarding toxicity and related to parameters arises naturally. Its interpretation indicates that metronomic chemotherapy has lower toxicity when administered in slow-growing tumors, tumors with high aggressiveness or competitiveness, and tumors with a high support capacity. In last, we consider non-autonomous treatments in order to compare different dosage regimes seeking for an optimal protocol. We show how the use of a simple approach for parameterizing the function which describes the treatment implies in advantages both for applying optimization methods as well as for formulating optimality criteria encompassing diverse features such as toxicity, relapse risk, recovery time and drug dosageDoutoradoMatematica AplicadaDoutor em Matemática AplicadaCAPE

Urban Informatics

This open access book is the first to systematically introduce the principles of urban informatics and its application to every aspect of the city that involves its functioning, control, management, and future planning. It introduces new models and tools being developed to understand and implement these technologies that enable cities to function more efficiently – to become ‘smart’ and ‘sustainable’. The smart city has quickly emerged as computers have become ever smaller to the point where they can be embedded into the very fabric of the city, as well as being central to new ways in which the population can communicate and act. When cities are wired in this way, they have the potential to become sentient and responsive, generating massive streams of ‘big’ data in real time as well as providing immense opportunities for extracting new forms of urban data through crowdsourcing. This book offers a comprehensive review of the methods that form the core of urban informatics from various kinds of urban remote sensing to new approaches to machine learning and statistical modelling. It provides a detailed technical introduction to the wide array of tools information scientists need to develop the key urban analytics that are fundamental to learning about the smart city, and it outlines ways in which these tools can be used to inform design and policy so that cities can become more efficient with a greater concern for environment and equity

Models of self-organization in biological development

Bibliography: p. 297-320.In this thesis we thus wish to consider the concept of self-organization as an overall paradigm within which various theoretical approaches to the study of development may be described and evaluated. In the process, an attempt is made to give a fair and reasonably comprehensive overview of leading modelling approaches in developmental biology, with particular reference to self-organization. The work proceeds from a physical or mathematical perspective, but not unduly so - the major mathematical derivations and results are relegated to appendices - and attempts to fill a perceived gap in the extant review literature, in its breadth and attempted impartiality of scope. A characteristic of the present account is its markedly interdisciplinary approach: it seeks to place self-organization models that have been proposed for biological pattern formation and morphogenesis both within the necessary experimentally-derived biological framework, and in the wider physical context of self-organization and the mathematical techniques that may be employed in its study. Hence the thesis begins with appropriate introductory chapters to provide the necessary background, before proceeding to a discussion of the models themselves. It should be noted that the work is structured so as to be read sequentially, from beginning to end; and that the chapters in the main text were designed to be understood essentially independently of the appendices, although frequent references to the latter are given. In view of the vastness of the available information and literature on developmental biology, a working knowledge of embryological principles must be assumed. Consequently, rather than attempting a comprehensive introduction to experimental embryology, chapter 2 presents just a few biological preliminaries, to 'set the scene', outlining some of the major issues that we are dealing with, and sketching an indication of the current status of knowledge and research on development. The chapter is aimed at furnishing the necessary biological, experimental background, in the light of which the rest of the thesis should be read, and which should indeed underpin and motivate any theoretical discussions. We encounter the different hierarchical levels of description in this chapter, as well as some of the model systems whose experimental study has proved most fruitful, some of the concepts of experimental embryology, and a brief reference to some questions that will not be addressed in this work. With chapter 3, we temporarily move away from developmental biology, and consider the wider physical and mathematical concepts related to the study of self-organization. Here we encounter physical and chemical examples of spontaneous structure formation, thermodynamic considerations, and different approaches to the description of complexity. Mathematical approaches to the dynamical study of self-organization are also introduced, with specific reference to reaction-diffusion equations, and we consider some possible chemical and biochemical realizations of self-organizing kinetics. The chapter may be read in conjunction with appendix A, which gives a somewhat more in-depth study of reaction-diffusion equations, their analysis and properties, as an example of the approach to the analysis of self-organizing dynamical systems and mathematically-formulated models. Appendix B contains a more detailed discussion of the Belousov-Zhabotinskii reaction, which provides a vivid chemical paradigm for the concepts of symmetry-breaking and self-organization. Chapter 3 concludes with a brief discussion of a model biological system, the cellular slime mould, which displays rudimentary development and has thus proved amenable to detailed study and modelling. The following two chapters form the core of the thesis, as they contain discussions of the detailed application of theoretical concepts and models, largely based on self-organization, to various developmental situations. We encounter a diversity of models which has arisen largely in the last quarter century, each of which attempts to account for some aspect of biological pattern formation and morphogenesis; an aim of the discussion is to assess the extent of the underlying unity of these models in terms of the self-organization paradigm. In chapter 4 chemical pre-patterns and positional information are considered, without the overt involvement of cells in the patterning. In chapter 5, on the other hand, cellular interactions and activities are explicitly taken into account; this chapter should be read together with appendix C, which contains a brief introduction to the mathematical formulation and analysis of some of the models discussed. The penultimate chapter, 6, considers two other approaches to the study of development; one of these has faded away, while the other is still apparently in the ascendant. The assumptions underlying catastrophe theory, the value of its applications to developmental biology and the reasons for its decline in popularity, are considered. Lastly, discrete approaches, including the recently fashionable cellular automata, are dealt with, and the possible roles of rule-based interactions, such as of the so-called L-systems, and of fractals and chaos are evaluated. Chapter 7 then concludes the thesis with a brief assessment of the value of the self-organization concept to the study of biological development