An elementary approach to dessins d'enfants and the Grothendieck-Teichm\"uller group

We give an account of the theory of dessins d'enfants which is both elementary and self-contained. We describe the equivalence of many categories (graphs embedded nicely on surfaces, finite sets with certain permutations, certain field extensions, and some classes of algebraic curves), some of which are naturally endowed with an action of the absolute Galois group of the rational field. We prove that the action is faithful. Eventually we prove that this absolute Galois group embeds into the Grothendieck-Teichm\"uller group $GT_0$ introduced by Drinfel'd. There are explicit approximations of $GT_0$ by finite groups, and we hope to encourage computations in this area. Our treatment includes a result which has not appeared in the literature yet: the Galois action on the subset of regular dessins - that is, those exhibiting maximal symmetry -- is also faithful.Comment: 58 pages, about 30 figures. Corrected a few typos. This version should match the published paper in L'enseignement Mathematiqu

Basic Neutrosophic Algebraic Structures and their Application to Fuzzy and Neutrosophic Models

The involvement of uncertainty of varying degrees when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate. For the past two or more decades, Fuzzy Theory has become the potent tool to study and analyze uncertainty involved in all problems. But, many real-world problems also abound with the concept of indeterminacy. In this book, the new, powerful tool of neutrosophy that deals with indeterminacy is utilized. Innovative neutrosophic models are described. The theory of neutrosophic graphs is introduced and applied to fuzzy and neutrosophic models. This book is organized into four chapters. In Chapter One we introduce some of the basic neutrosophic algebraic structures essential for the further development of the other chapters. Chapter Two recalls basic graph theory definitions and results which has interested us and for which we give the neutrosophic analogues. In this chapter we give the application of graphs in fuzzy models. An entire section is devoted for this purpose. Chapter Three introduces many new neutrosophic concepts in graphs and applies it to the case of neutrosophic cognitive maps and neutrosophic relational maps. The last section of this chapter clearly illustrates how the neutrosophic graphs are utilized in the neutrosophic models. The final chapter gives some problems about neutrosophic graphs which will make one understand this new subject.Comment: 149 pages, 130 figure

Bigraphs with sharing and applications in wireless networks

Bigraphs are a fully graphical process algebraic formalism, capable of representing both the position in space of agents and their inter-connections. However, they assume a topology based on sets of trees and thus cannot represent spatial locations that are shared among several entities in a simple or intuitive way. This is a problem, because shared locations are often a requirement, for example, when modelling scenarios in the physical world or in modern complex computer systems such as wireless networks and spatial-aware applications in ubiquitous computing. We propose bigraphs with sharing, a generalisation of the original definition of bigraphs, to allow for overlapping topologies. The new locality model is based on directed acyclic graphs. We demonstrate the new formalism can be defined in the general framework of bigraphical theories and wide reactive systems, as originally devised by Robin Milner. We do so by defining a categorical interpretation of bigraphs with sharing, an axiomatisation derived from the equations of a bialgebra over finite ordinals, and a normal form to express bigraphical terms. We illustrate how sharing is essential for modelling overlapping localities by presenting two example case studies in the field of wireless networking. We show that bigraphs with sharing can be used realistically in a production environment by describing the implementation of an efficient matching algorithm and a software tool for the definition, simulation, visualisation and analysis of bigraphical reactive systems

Agoric computation: trust and cyber-physical systems

In the past two decades advances in miniaturisation and economies of scale have led to the emergence of billions of connected components that have provided both a spur and a blueprint for the development of smart products acting in specialised environments which are uniquely identifiable, localisable, and capable of autonomy. Adopting the computational perspective of multi-agent systems (MAS) as a technological abstraction married with the engineering perspective of cyber-physical systems (CPS) has provided fertile ground for designing, developing and deploying software applications in smart automated context such as manufacturing, power grids, avionics, healthcare and logistics, capable of being decentralised, intelligent, reconfigurable, modular, flexible, robust, adaptive and responsive. Current agent technologies are, however, ill suited for information-based environments, making it difficult to formalise and implement multiagent systems based on inherently dynamical functional concepts such as trust and reliability, which present special challenges when scaling from small to large systems of agents. To overcome such challenges, it is useful to adopt a unified approach which we term agoric computation, integrating logical, mathematical and programming concepts towards the development of agent-based solutions based on recursive, compositional principles, where smaller systems feed via directed information flows into larger hierarchical systems that define their global environment. Considering information as an integral part of the environment naturally defines a web of operations where components of a systems are wired in some way and each set of inputs and outputs are allowed to carry some value. These operations are stateless abstractions and procedures that act on some stateful cells that cumulate partial information, and it is possible to compose such abstractions into higher-level ones, using a publish-and-subscribe interaction model that keeps track of update messages between abstractions and values in the data. In this thesis we review the logical and mathematical basis of such abstractions and take steps towards the software implementation of agoric modelling as a framework for simulation and verification of the reliability of increasingly complex systems, and report on experimental results related to a few select applications, such as stigmergic interaction in mobile robotics, integrating raw data into agent perceptions, trust and trustworthiness in orchestrated open systems, computing the epistemic cost of trust when reasoning in networks of agents seeded with contradictory information, and trust models for distributed ledgers in the Internet of Things (IoT); and provide a roadmap for future developments of our research

Paradoxes of Interactivity

Current findings from anthropology, genetics, prehistory, cognitive and neuroscience indicate that human nature is grounded in a co-evolution of tool use, symbolic communication, social interaction and cultural transmission. Digital information technology has recently entered as a new tool in this co-evolution, and will probably have the strongest impact on shaping the human mind in the near future. A common effort from the humanities, the sciences, art and technology is necessary to understand this ongoing co- evolutionary process. Interactivity is a key for understanding the new relationships formed by humans with social robots as well as interactive environments and wearables underlying this process. Of special importance for understanding interactivity are human-computer and human-robot interaction, as well as media theory and New Media Art. »Paradoxes of Interactivity« brings together reflections on »interactivity« from different theoretical perspectives, the interplay of science and art, and recent technological developments for artistic applications, especially in the realm of sound

Video object tracking : contributions to object description and performance assessment

Tese de doutoramento. Engenharia Electrotécnica e de Computadores. Universidade do Porto. Faculdade de Engenharia. 201

Paradoxes of interactivity: perspectives for media theory, human-computer interaction, and artistic investigations

Current findings from anthropology, genetics, prehistory, cognitive and neuroscience indicate that human nature is grounded in a co-evolution of tool use, symbolic communication, social interaction and cultural transmission. Digital information technology has recently entered as a new tool in this co-evolution, and will probably have the strongest impact on shaping the human mind in the near future. A common effort from the humanities, the sciences, art and technology is necessary to understand this ongoing co- evolutionary process. Interactivity is a key for understanding the new relationships formed by humans with social robots as well as interactive environments and wearables underlying this process. Of special importance for understanding interactivity are human-computer and human-robot interaction, as well as media theory and New Media Art. "Paradoxes of Interactivity" brings together reflections on "interactivity" from different theoretical perspectives, the interplay of science and art, and recent technological developments for artistic applications, especially in the realm of sound