Symbolic fractional dynamics

Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the association of Fractional calculus and symbolic dynamics. The results are visualized by means of the multidimensional technique and reveal the association between the fractal dimension and one definition of fractional derivative.

Complex evolution of a multi-particle system

This paper studies a discrete dynamical system of interacting particles that evolve by interacting among them. The computational model is an abstraction of the natural world, and real systems can range from the huge cosmological scale down to the scale of biological cell, or even molecules. Different conditions for the system evolution are tested. The emerging patterns are analysed by means of fractal dimension and entropy measures. It is observed that the population of particles evolves towards geometrical objects with a fractal nature. Moreover, the time signature of the entropy can be interpreted at the light of complex dynamical systems.

Periodic paths on nonautonomous graphs

We define nonautonomous graphs as a class of dynamic graphs in discrete time whose time-dependence consists in connecting or disconnecting edges. We study periodic paths in these graphs, and the associated zeta functions. Based on the analytic properties of these zeta functions we obtain explicit formulae for the number of n-periodic paths, as the sum of the nth powers of some specific algebraic numbers.

Reply to: Comments on “Particle Swarm Optimization with Fractional-Order Velocity”

We agree with Ling-Yun et al. [5] and Zhang and Duan comments [2] about the typing error in equation (9) of the manuscript [8]. The correct formula was initially proposed in [6, 7]. The formula adopted in our algorithms discussed in our papers [1, 3, 4, 8] is, in fact, the following: ...

Dynamic Analysis and Pattern Visualization of Forest Fires

This paper analyses forest fires in the perspective of dynamical systems. Forest fires exhibit complex correlations in size, space and time, revealing features often present in complex systems, such as the absence of a characteristic length-scale, or the emergence of long range correlations and persistent memory. This study addresses a public domain forest fires catalogue, containing information of events for Portugal, during the period from 1980 up to 2012. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses with amplitude proportional to the burnt area. First, we consider mutual information to correlate annual patterns. We use visualization trees, generated by hierarchical clustering algorithms, in order to compare and to extract relationships among the data. Second, we adopt the Multidimensional Scaling (MDS) visualization tool. MDS generates maps where each object corresponds to a point. Objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to identify forest fire patterns.

Dynamic Analysis and Pattern Visualization of Forest Fires

This paper analyses forest fires in the perspective of dynamical systems. Forest fires exhibit complex correlations in size, space and time, revealing features often present in complex systems, such as the absence of a characteristic length-scale, or the emergence of long range correlations and persistent memory. This study addresses a public domain forest fires catalogue, containing information of events for Portugal, during the period from 1980 up to 2012. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses with amplitude proportional to the burnt area. First, we consider mutual information to correlate annual patterns. We use visualization trees, generated by hierarchical clustering algorithms, in order to compare and to extract relationships among the data. Second, we adopt the Multidimensional Scaling (MDS) visualization tool. MDS generates maps where each object corresponds to a point. Objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to identify forest fire patterns.

The Persistence of Memory

This paper analyzes several natural and man-made complex phenomena in the perspective of dynamical systems. Such phenomena are often characterized by the absence of a characteristic length-scale, long range correlations and persistent memory, which are features also associated to fractional order systems. For each system, the output, interpreted as a manifestation of the system dynamics, is analyzed by means of the Fourier transform. The amplitude spectrum is approximated by a power law function and the parameters are interpreted as an underlying signature of the system dynamics. The complex systems under analysis are then compared in a global perspective in order to unveil and visualize hidden relationships among them.

Power Law Behavior and Self-similarity in Modern Industrial Accidents

Advances in technology have produced more and more intricate industrial systems, such as nuclear power plants, chemical centers and petroleum platforms. Such complex plants exhibit multiple interactions among smaller units and human operators, rising potentially disastrous failure, which can propagate across subsystem boundaries. This paper analyzes industrial accident data-series in the perspective of statistical physics and dynamical systems. Global data is collected from the Emergency Events Database (EM-DAT) during the time period from year 1903 up to 2012. The statistical distributions of the number of fatalities caused by industrial accidents reveal Power Law (PL) behavior. We analyze the evolution of the PL parameters over time and observe a remarkable increment in the PL exponent during the last years. PL behavior allows prediction by extrapolation over a wide range of scales. In a complementary line of thought, we compare the data using appropriate indices and use different visualization techniques to correlate and to extract relationships among industrial accident events. This study contributes to better understand the complexity of modern industrial accidents and their ruling principles.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Buddhism and the earth : environmental thought in early Buddhist philosophy

Introduction Fundamental to the philosophy of Buddhism, is the insight that there is "unsatisfactohness" (dukkha) in the world and that it can be eliminated through the practice of the Noble Eight Fold Path. Buddhism also maintains that the world as we experience and entities that exist are bereft of any substantiality. Instead existence is manifest through dependent origination. All things are conditional; nothing is permanent. However, inherent in this dependent existence is the interconnectedness of all beings and their subjection to the cosmic law of karma. Part of cultivating the Eight Fold path includes a deep compassion for all other living things, 'trapped' within this cycle of dependent origination. This compassion or empathy (karuna) is crucial to the Buddhist path to enlightenment. It is this emphasis on karuna that shows itself in Mahayana Buddhism with respect to the theory of the boddhisatva (or Buddha-to-be) since the boddhisatva willingly postpones his/her own enlightenment to help others on the same path. One of the ramifications of the theory of dependent origination is that there is no anthropocentric bias placed on humans over the natural world. Paradoxically the doctrine of non-self becomes an ontology within Buddhism, culminating in the Mayahana realization that a common boundary exists between samsara and nirvana. Essential to this ontology is the life of dharma or a moral life. Ethics is not separated from ontology. As my thesis will show, this basic outlook of Buddhism has implications toward our understanding of the Buddhist world-view with respect to the current human predicament concerning the environment. While humans are the only ones who can 4 attain "Buddhahood", it is because of our ability to understand what it means to follow the Eight fold path and act accordingly. Because of the interconnectedness of all entities {dharmas), there is an ontological necessity to eliminate suffering and 'save the earth' because if we allow the earth to suffer, we ALL suffer. This can be understood as an ethical outlook which can be applied to our interaction with and treatment of the natural environment or environment in the broadest sense, not just trees plants rocks etc. It is an approach to samsara and all within it. It has been argued that there is no ontology in Buddhism due to its doctrine of "non-self". However, it is a goal of this thesis to argue that there does exist an original ontology in Buddhism; that according to it, the nature of Being is essentially neither "Being nor non-being nor not non-being" as illustrated by Nagarjuna. Within this ontology is engrained an ethic or 'right path' (samma marga) that is fundamental to our being and this includes a compassionate relationship to our environment. In this dissertation I endeavour to trace the implications that the Buddhist worldview has for the environmental issues that assail us in our age of technology. I will explore questions such as: can the Buddhist way of thinking help us comprehend and possibly resolve the environmental problems of our day and age? Are there any current environmental theories which are comparable to or share common ground with the classical Buddhist doctrines? I will elucidate some fundamental doctrines of early Buddhism from an environmental perspective as well as identify some comparable modern environmental theories such as deep ecology and general systems theory, that seem to share in the wisdom of classical Buddhism and have much to gain from a deeper appreciation of Buddhism.

Active living in municipal parks and recreation : a case study

If quality of life is an important recreation outcome, then municipal parks and recreation management's efforts have to change because:· Over one-third of all the little kids in schools will be diabetic in their lifetime if the trends we are looking at continue. The average loss of life is about 15 years, and there is an average reduction in quality oflife by about 20 years (Jackson, 2007). This thesis is about municipal parks and recreation, an agency that controls and limits physical activity opportunity. It is also about active living; from an ecological perspective, a multi-disciplinary approach to incorporate physical activity into more 111 people's daily lives. In particular, this thesis examines one case --'. the Donutville Case - . with the intent of providing an explanation of how municipal parks and recreation can advance its management efforts to improve health outcomes of people suffering from daily physical activity deficits. More specifically, how can the tension between external and internal environments to municipal parks and recreation be better balanced to affect the change needed? Given that changing the current social reality is through making decisions, decision-making functions connected with systems theory helps identify how recreation authorities can more effectively influence environmental physical activity determinants. , Sallis et al.' (2006) ·social ecological model provides the a priori focus on active living decision-making. An integrated analogous emerging logic model is developed and presented as an efficacious strategy for how municipal parks and recreation decisionmakers can affect change. Keywords: physical activity, benefits outcomes, healthy livable community, quality of life, systems thinking, social ecological model, deci~ion-making, logic modeling, municipal parks and recreation, active living.

Children's rights in rural Punjab : the story of a border-dweller

There is currently a disconnect between the universal and general children's rights as presented in the United Nation's Convention on the Rights of the Child and the lived experiences of children in various countries. This thesis uses the authors' struggle to exist between two cultures as a lens through which the disconnect is explored. The author returns to her village in Punjab and looks at spaces created for children through institutions such as the education system and spaces that children create on their own. Luhmann's social systems theory is used to critique anti-humanist institutions and systems. As an alternative to Luhmann, H~dt and Negri's concept of the multitude is explored to provide insight into the political spaces that children create for themselves.

Échantillonnage dynamique de champs markoviens

L'un des modèles d'apprentissage non-supervisé générant le plus de recherche active est la machine de Boltzmann --- en particulier la machine de Boltzmann restreinte, ou RBM. Un aspect important de l'entraînement ainsi que l'exploitation d'un tel modèle est la prise d'échantillons. Deux développements récents, la divergence contrastive persistante rapide (FPCD) et le herding, visent à améliorer cet aspect, se concentrant principalement sur le processus d'apprentissage en tant que tel. Notamment, le herding renonce à obtenir un estimé précis des paramètres de la RBM, définissant plutôt une distribution par un système dynamique guidé par les exemples d'entraînement. Nous généralisons ces idées afin d'obtenir des algorithmes permettant d'exploiter la distribution de probabilités définie par une RBM pré-entraînée, par tirage d'échantillons qui en sont représentatifs, et ce sans que l'ensemble d'entraînement ne soit nécessaire. Nous présentons trois méthodes: la pénalisation d'échantillon (basée sur une intuition théorique) ainsi que la FPCD et le herding utilisant des statistiques constantes pour la phase positive. Ces méthodes définissent des systèmes dynamiques produisant des échantillons ayant les statistiques voulues et nous les évaluons à l'aide d'une méthode d'estimation de densité non-paramétrique. Nous montrons que ces méthodes mixent substantiellement mieux que la méthode conventionnelle, l'échantillonnage de Gibbs.

Aspects géométriques et intégrables des modèles de matrices aléatoires

Travail réalisé en cotutelle avec l'université Paris-Diderot et le Commissariat à l'Energie Atomique sous la direction de John Harnad et Bertrand Eynard.

Réorganiser les services de réadaptation destinés aux enfants : utilisation d'une recherche-action participative pour documenter un nouveau modèle de services

Cette thèse a pour but de documenter la réorganisation des services effectuée au programme Enfants et adolescents (PEA) du Centre de réadaptation Estrie, Sherbrooke. Une démarche de recherche-action participative (RAP) est utilisée afin de collaborer au développement, à l’implantation et à l’évaluation d’un nouveau modèle de services visant à accroître l’accessibilité et la qualité des services de réadaptation offerts aux enfants ayant une déficience physique. Spécifiquement, les objectifs sont : 1) de documenter les retombées de la réorganisation des services; 2) de réaliser une analyse critique du processus de changement. Des méthodes quantitatives et qualitatives sont utilisées afin d’atteindre ces objectifs. Tout d’abord, la Mesure des processus de soins (MPOC) documente la perception de la qualité avant (2007), pendant (2008) et après (2009) l’implantation du nouveau modèle de services. Au total, cet outil est employé auprès de 222 familles et 129 intervenants. À quatre reprises, les intervenants et les gestionnaires répondent également à un questionnaire sur leurs perceptions des forces, des faiblesses, des opportunités et des menaces au PEA. En 2008 et en 2009, des focus groups et des entrevues téléphoniques sont réalisées auprès des familles (n=5), des intervenants (n=19) et des gestionnaires (n=13) afin de documenter leurs perceptions sur le processus de changement et sur les retombées de la réorganisation des services. Quant à l’observation participante, elle permet de recueillir de l’information sur le processus de réorganisation des services tout au long de ces trois années. Enfin, les informations recueillies sont analysées à l’aide de différentes approches, dont des tests statistiques et des analyses de contenu utilisant une grille de codification inspirée de la théorie des systèmes d’actions organisées. Les résultats indiquent que davantage d’enfants reçoivent des services en 2009 en comparaison à 2007. De plus, la qualité des services s’est maintenue selon les perceptions évaluées par la MPOC (article 1). L’utilisation d’interventions de groupe contribue fort probablement à augmenter le nombre d’enfants qui reçoivent des services, mais plusieurs défis doivent être adressés afin que cette modalité d’intervention soit réellement efficiente (article 2). Les résultats font ressortir que le processus de réorganisation des services est complexe. L’évaluation des forces, des faiblesses, des opportunités et des menaces d’un programme, de même que l’implication des acteurs dans le processus de développement d’un nouveau modèle de services, favorisent l’amélioration continue de la qualité (article 3). Or, les facilitateurs et les obstacles à l’implantation du nouveau modèle de services évoluent durant la réorganisation des services. Considérant cela, il est important de poser les actions nécessaires afin de soutenir le changement tout au long du processus (article 4). En résumé, cette thèse contribue à l’avancement des connaissances en réadaptation en comblant une lacune dans les écrits scientifiques. En effet, peu de projets visant le développement et l’implantation de nouveaux modèles de services sont évalués et documentés. Pourtant, des modèles tels que celui développé par le PEA semblent prometteurs afin d’améliorer l’accessibilité, et éventuellement, la qualité des services de réadaptation chez l’enfant.