50 resultados para Algorithmic Graph Theory


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Pragmatism has sometimes been taken as a catchphrase for epistemological stances in which anything goes. However, other authors argue that the real novelty and contribution of this tradition has to do with its view of action as the context in which all things human take place. Thus, it is action rather than, for example, discourses that should be our starting point in social theory. The introductory section of the book situates pragmatism (especially the ideas of G. H. Mead and John Dewey) within the field and tradition of social theory. This introductory also contextualizes the main core of the book which consists of four chapters. Two of these chapters have been published as articles in scientific journals and one in an edited book. All of them discuss the core problem of social theory: how is action related to social structures (and vice versa)? The argument is that habitual action is the explanation for the emergence of social structures from our action. Action produces structures and social reproduction takes place when action is habitualized; that is, when we develop social dispositions to act in a certain manner in familiar environments. This also means that even though the physical environment is the same for all of us, our habits structure it into different kinds of action possibilities. Each chapter highlights these general insights from different angles. Practice theory has gained momentum in recent years and it has many commonalities with pragmatism because both highlight the situated and corporeal character of human activity. One famous proponent of practice theory is Margaret Archer who has argued that the pragmatism of G. H. Mead leads to an oversocialized conception of selfhood. Mead does indeed present a socialized view of selfhood but this is a meta-sociological argument rather than a substantial sociological claim. Accordingly, one can argue that in this general sense intersubjectivity precedes subjectivity and not the other way around. Such a view does not indicate that our social relation would necessarily "colonize" individual action because there is a place for internal conversations (in Archer s terminology); it is especially in those phases of action where it meets obstacles due to the changes of the environment. The second issue discussed has the background assumption that social structures can fruitfully be conceptualized as institutions. A general classification of different institution theories is presented and it is argued that there is a need for a habitual theory of institutions due to the problems associated with these other theories. So-called habitual institutionalism accounts for institutions in terms of established and prevalent social dispositions that structure our social interactions. The germs of this institution theory can be found in the work of Thorstein Veblen. Since Veblen s times, these ideas have been discussed for example, by the economist Geoffrey M. Hodgson. His ideas on the evolution of institutions are presented but a critical stance is taken towards his tendency of defining institutions with the help of rules because rules are not always present in institutions. Accordingly, habitual action is the most basic but by no means the only aspect of institutional reproduction. The third chapter deals with theme of action and structures in the context of Pierre Bourdieu s thought. Bourdieu s term habitus refers to a system of dispositions which structure social fields. It is argued that habits come close to the concept of habitus in the sense that the latter consists of particular kinds of habits; those that are related to the reproduction of socioeconomic positions. Habits are thus constituents of a general theory of societal reproduction whereas habitus is a systematic combination of socioeconomic habits. The fourth theme relates to issues of social change and development. The capabilities approach has been associated with the name of Amartya Sen, for example, and it underscores problems inhering in economistic ways of evaluating social development. However, Sen s argument has some theoretical problems. For example, his theory cannot adequately confront the problem of relativism. In addition, Sen s discussion lacks also a theory of the role of the public. With the help of arguments derived from pragmatism, one gets an action-based, socially constituted view of freedom in which the role of the public is essential. In general, it is argued that a socially constituted view of agency does not necessarily to lead to pessimistic conclusions about the freedom of action.

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A distributed system is a collection of networked autonomous processing units which must work in a cooperative manner. Currently, large-scale distributed systems, such as various telecommunication and computer networks, are abundant and used in a multitude of tasks. The field of distributed computing studies what can be computed efficiently in such systems. Distributed systems are usually modelled as graphs where nodes represent the processors and edges denote communication links between processors. This thesis concentrates on the computational complexity of the distributed graph colouring problem. The objective of the graph colouring problem is to assign a colour to each node in such a way that no two nodes connected by an edge share the same colour. In particular, it is often desirable to use only a small number of colours. This task is a fundamental symmetry-breaking primitive in various distributed algorithms. A graph that has been coloured in this manner using at most k different colours is said to be k-coloured. This work examines the synchronous message-passing model of distributed computation: every node runs the same algorithm, and the system operates in discrete synchronous communication rounds. During each round, a node can communicate with its neighbours and perform local computation. In this model, the time complexity of a problem is the number of synchronous communication rounds required to solve the problem. It is known that 3-colouring any k-coloured directed cycle requires at least ½(log* k - 3) communication rounds and is possible in ½(log* k + 7) communication rounds for all k ≥ 3. This work shows that for any k ≥ 3, colouring a k-coloured directed cycle with at most three colours is possible in ½(log* k + 3) rounds. In contrast, it is also shown that for some values of k, colouring a directed cycle with at most three colours requires at least ½(log* k + 1) communication rounds. Furthermore, in the case of directed rooted trees, reducing a k-colouring into a 3-colouring requires at least log* k + 1 rounds for some k and possible in log* k + 3 rounds for all k ≥ 3. The new positive and negative results are derived using computational methods, as the existence of distributed colouring algorithms corresponds to the colourability of so-called neighbourhood graphs. The colourability of these graphs is analysed using Boolean satisfiability (SAT) solvers. Finally, this thesis shows that similar methods are applicable in capturing the existence of distributed algorithms for other graph problems, such as the maximal matching problem.

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In the thesis I study various quantum coherence phenomena and create some of the foundations for a systematic coherence theory. So far, the approach to quantum coherence in science has been purely phenomenological. In my thesis I try to answer the question what quantum coherence is and how it should be approached within the framework of physics, the metatheory of physics and the terminology related to them. It is worth noticing that quantum coherence is a conserved quantity that can be exactly defined. I propose a way to define quantum coherence mathematically from the density matrix of the system. Degenerate quantum gases, i.e., Bose condensates and ultracold Fermi systems, form a good laboratory to study coherence, since their entropy is small and coherence is large, and thus they possess strong coherence phenomena. Concerning coherence phenomena in degenerate quantum gases, I concentrate in my thesis mainly on collective association from atoms to molecules, Rabi oscillations and decoherence. It appears that collective association and oscillations do not depend on the spin-statistics of particles. Moreover, I study the logical features of decoherence in closed systems via a simple spin-model. I argue that decoherence is a valid concept also in systems with a possibility to experience recoherence, i.e., Poincaré recurrences. Metatheoretically this is a remarkable result, since it justifies quantum cosmology: to study the whole universe (i.e., physical reality) purely quantum physically is meaningful and valid science, in which decoherence explains why the quantum physical universe appears to cosmologists and other scientists very classical-like. The study of the logical structure of closed systems also reveals that complex enough closed (physical) systems obey a principle that is similar to Gödel's incompleteness theorem of logic. According to the theorem it is impossible to describe completely a closed system within the system, and the inside and outside descriptions of the system can be remarkably different. Via understanding this feature it may be possible to comprehend coarse-graining better and to define uniquely the mutual entanglement of quantum systems.

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In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.