The purpose of this paper is to define and investigate some of the properties of chains. Particular attention is given to a natural topology for chains, called the interval topology, and how the chain properties and topological properties of chains affect each other.

Estudamos as propriedades aritméticas, geométricas e topológicas de uma classe dos chamados Fractais de Rauzy. Estudamos partucularmente o azulejamento periódico do plano complexo C induzido por eles, assim como a dimensão de Hausdorff de suas fronteiras. Tal trabalho exige um estudo detalhado da fronteira destes conjuntos, que está associada às propriedades aritméticas da \'alpha\' -representação dos números complexos com respeito a um certo número algébrico \'alfa\' / We study the arithmetic, geometric and topological properties of a class of the so-called Rauzy\'s fractals. In particular we study the periodic tiling of the complex plane C induced by them and the Hausdorff dimension of its boundary. Such work is connected to a detailed study of the boundary of such sets and the arithmetic properties of the \'alpha\' representation of complex numbers with respect to a certain algebraic number \'alpha\'

Estudamos as propriedades aritméticas, geométricas e topológicas de uma classe dos chamados Fractais de Rauzy. Estudamos partucularmente o azulejamento periódico do plano complexo C induzido por eles, assim como a dimensão de Hausdorff de suas fronteiras. Tal trabalho exige um estudo detalhado da fronteira destes conjuntos, que está associada às propriedades aritméticas da \'alpha\' -representação dos números complexos com respeito a um certo número algébrico \'alfa\' / We study the arithmetic, geometric and topological properties of a class of the so-called Rauzy\'s fractals. In particular we study the periodic tiling of the complex plane C induced by them and the Hausdorff dimension of its boundary. Such work is connected to a detailed study of the boundary of such sets and the arithmetic properties of the \'alpha\' representation of complex numbers with respect to a certain algebraic number \'alpha\'

Determining the set of all optimal solutions of a linear program with interval data is one of the main problems discussed in interval optimization. We review two methods based on duality in linear programming, which are used to approximate the optimal set. Additionally, another decomposition method based on complementary slackness is proposed. This method provides the exact description of the optimal set for problems with a fixed coefficient matrix. The second part of the thesis is focused on studying the topological and geometric properties of the optimal set. We examine sufficient conditions for closedness, boundedness, connectedness and convexity. We also prove that testing boundedness is co- NP-hard for inequality-constrained problems with free variables. Stronger results are derived for some special classes of interval linear programs, such as problems with a fixed coefficient matrix. Furthermore, we study the effect of transformations commonly used in linear programming on interval problems, which allows for a direct generalization of some results to different types of interval linear programs. Powered by TCPDF (www.tcpdf.org)

The topology of interconnection networks plays a key role in the performance of parallel computing systems. A new interconnection network called exchanged crossed cube (ECQ) is proposed and analyzed in this paper. We prove that ECQ has the better properties than other variations of the basic hypercube in terms of the smaller diameter, fewer links, and lower cost factor, which indicates the reduced communication overhead, lower hardware cost, and more balanced consideration among performance and cost. Furthermore, it maintains several attractive advantages including recursive structure, high partitionability, and strong connectivity. Furthermore, the optimal routing and broadcasting algorithms are proposed for this new network topology.

This paper studies the topological properties of the International Trade Network (ITN) among world countries using a network analysis. We explore the distribu- tions of the most important network statistics measuring connectivity, assortativ- ity and clustering. We show that the topological properties of the weighted rep- resentation of the ITN are very different from those obtained by a binary network approach. In particular, we find that: (i) the majority of countries are character- ized by weak trade relationships, (ii) well connected countries tend to trade with poorly connected partners and (iii) countries holding more intense trade relation- ships are more clustered. Finally, we display that all structural properties of the ITN have remained remarkably stable over time.

Ein drahtloses Multihop-Netzwerk (DMN) ist ein verteiltes Kommunikationssystem, welches vor allem die Fähigkeit zur automatischen Anpassung an sich ständig änderne Umgebungsbedingungen hat. Eine zentrale Fragestellung in DMNen ist, ob das Netzwerk partitioniert ist, ob also nicht mehr jeder Knoten mit jedem anderen Knoten kommunizieren kann. Um festzustellen, ob eine Partitionierung droht werden mit Hilfe von 2-Zusammenhangstests Brücken und Artikulationspunkte im Kommunikationsgraphen gesucht. Daraufhin können anschließend korrektive Aktionen eingeleitet werden um die Partitionierung zu verhindern und somit die Netzwerkverfügbarkeit zu erhöhen. Eine Vielzahl von 2-Zusammenhangstestverfahren wurde bereits erfolgreich bei drahtgebundenen Netzen eingesetzt. Allerdings sind diese Verfahren ungeeignet für drahtlose Netze, da die Ungenauigkeiten durch den häufigen Paketverlust in solchen Systemen bisher nicht berücksichtigt wurden. Mit Hilfe von stochastischen Modellen wird gezeigt, dass Fehler in der Entscheidungsfindung für DMNen bereits bei sehr einfachen Problemen wie der Link-Erkennung signifikant sein können. In dieser Arbeit werden daher verschiedene Verfahren präsentiert, die auch auf Grundlage unsicherer Informationen noch eine verlässliche Entscheidungsfindung ermöglichen. Die Arbeit präsentiert einen neuen verteilten Algorithmus zum Test auf 2-Zusammenhang, welcher Fehler durch Nachrichtenverlust berücksichtigt und gleichzeitig die Anzahl an Nachrichten reduziert. Basierend auf einer umfassenden Analyse der Einflüsse von Kommunikationsfehlern auf den Algorithmus, wurden Abstimmungsprozeduren entwickelt, die die Wahrscheinlichkeit von Fehlentscheidungen nochmals reduzieren. Zur weiteren Analyse werden die Algorithmen erstens in der Motelab-Umgebung und zweitens mit Hilfe von Simulationen untersucht. Die präsentierten Algorithmen zeigen überzeugende Ergebnisse unter variierenden Bedingungen, was ihre Anwendbarkeit in realen Szenarien unterstreicht. / Wireless multi-hop network (WMN) is a distributed communication system composed of autonomous processing nodes that is known for its ability to automatically adjust to rapidly changing conditions in the surrounding environment. Connectivity is one of the basic properties of a network. Removal of a bridge or an articulation point partitions a network. Biconnectivity testing identifies bridges and articulation points in a network, and once they are known corrective actions can be performed in order to improve network''s reliability. Numerous biconnectivity testing algorithms are successfully applied in graphs, wired networks and multiprocessor systems. However, they are inadequate for application in wireless networks since the frequent packet losses introduce uncertainty in the system which these algorithms cannot handle. The stochastic analysis shows that errors in decision-making in WMNs are considerable even for seemingly simple tasks such as the detection of links. The main contribution of this work is to provide means for accurate binary decision-making under uncertainty within the context of biconnectivity testing in WMNs. A distributed algorithm is developed that successfully handles the faults caused by message losses and simultaneously utilizes benefits of wireless communication to reduce message complexity from O(e) to O(n). Based on stochastic analysis of WMN topologies and a comprehensive analysis of impact of communication faults on algorithm''s behavior, the algorithm is extended by voting theory to reduce probability of erroneous decisions. The algorithm and the voting rules are evaluated in experiments in Motelab testbed and in the event-based simulator Jist/SWANS. The algorithm is accurate under various conditions which demonstrates its applicability in reality and capability of successful operation in presence of packet losses.

O entendimento dos princípios básicos do enovelamento proteico pode conduzir a muitas aplicações importantes. Embora não se conheçam todos os aspectos significativos envolvidos neste problema, experimentos e aproximações teóricas têm produzido avanços relevantes na sua compreensão, como, por exemplo, o papel dominante das forças hidrofóbicas. Com o propósito de contribuir para a identificação de alguns parâmetros determinantes no processo de folding, o objetivo deste trabalho consiste em estudar o potencial estéreo-hidrofóbico (isto é, o potencial hidrofóbico e um conjunto de especificidades estéricas adequadas) relacionado ao processo de enovelamento de proteínas globulares, evidenciando o papel das restrições estéricas e as características topológicas do estado nativo. Para tanto, empregou-se um modelo simplificado em rede cúbica, estudando-se, através de simulações Monte Carlo, o comportamento de mais de 40 cadeias tipo-proteínas, que apresentam estados nativos caracterizados pelos seguintes parâmetros topológicos: ordem de contato, χ, ordem de longo alcance e número φ de estruturas tipo grande manivela. Claramente, os resultados das simulações para as cadeias com configurações nativas, caracterizadas por baixo valor de χ e elevado valor de φ, são bastante diferenciados daqueles obtidos para as cadeias que apresentam configurações nativas com χ elevado e φ pequeno, evidenciando que o potencial estéreo-hidrofóbico, adotado neste trabalho, permite relacionar os comportamentos termodinâmico e cinético da cadeia tipo-proteína com os atributos topológicos da configuração nativa correspondente. Adicionalmente, mostrou-se que as restrições estéricas consideradas introduzem fortes mudanças na atividade configuracional, aumentando a estabilidade do estado nativo, bem como alterando, drasticamente, a curva da capacidade térmica, em função da temperatura, em comparação com os resultados das simulações obtidos com o potencial hidrofóbico (sem restrições estéricas). / The understanding of the basic principles of the protein folding process may lead to very important applications. Although all significant aspects of this problem are not yet known, experimental and theoretical results have given important contribution on the subject, as, for instance, about the dominant role of the hydrophobic forces. In order to contribute to the identification of significant ingredients for the folding process, the main goal of this work consists in studying the stereo-hydrophobic potential (that is, the hydrophobic potential and a set of steric specificities) related to the folding process of globular proteins, revealing the importance of the steric constraints and the role of the native structure. A minimalist lattice model was employed for this purpose, and more than forty distinct protein-like chains were studied. These chains were designed based on native structures characterized by topological parameters as contact order, χ, long range order and number φ of crankshaft-like structures. The Monte Carlo simulation results show clearly that the folding process depends strongly on the topological attributes of the native structure: thermodynamical and kinetic behavior for chains designed from native structures, presenting smaller χ and higher φ, are very distinguishable from those with higher χ and lower φ. Additionally it was shown that the steric constraints significantly modify the configurational activity, increasing the general conditions for the globule stability, as well changing drastically the shape of the thermal capacity behavior, as a function of the temperature, in comparison with the corresponding results obtained using the hydrophobic potential only, i.e., without the steric specificities.

O entendimento dos princípios básicos do enovelamento proteico pode conduzir a muitas aplicações importantes. Embora não se conheçam todos os aspectos significativos envolvidos neste problema, experimentos e aproximações teóricas têm produzido avanços relevantes na sua compreensão, como, por exemplo, o papel dominante das forças hidrofóbicas. Com o propósito de contribuir para a identificação de alguns parâmetros determinantes no processo de folding, o objetivo deste trabalho consiste em estudar o potencial estéreo-hidrofóbico (isto é, o potencial hidrofóbico e um conjunto de especificidades estéricas adequadas) relacionado ao processo de enovelamento de proteínas globulares, evidenciando o papel das restrições estéricas e as características topológicas do estado nativo. Para tanto, empregou-se um modelo simplificado em rede cúbica, estudando-se, através de simulações Monte Carlo, o comportamento de mais de 40 cadeias tipo-proteínas, que apresentam estados nativos caracterizados pelos seguintes parâmetros topológicos: ordem de contato, χ, ordem de longo alcance e número φ de estruturas tipo grande manivela. Claramente, os resultados das simulações para as cadeias com configurações nativas, caracterizadas por baixo valor de χ e elevado valor de φ, são bastante diferenciados daqueles obtidos para as cadeias que apresentam configurações nativas com χ elevado e φ pequeno, evidenciando que o potencial estéreo-hidrofóbico, adotado neste trabalho, permite relacionar os comportamentos termodinâmico e cinético da cadeia tipo-proteína com os atributos topológicos da configuração nativa correspondente. Adicionalmente, mostrou-se que as restrições estéricas consideradas introduzem fortes mudanças na atividade configuracional, aumentando a estabilidade do estado nativo, bem como alterando, drasticamente, a curva da capacidade térmica, em função da temperatura, em comparação com os resultados das simulações obtidos com o potencial hidrofóbico (sem restrições estéricas). / The understanding of the basic principles of the protein folding process may lead to very important applications. Although all significant aspects of this problem are not yet known, experimental and theoretical results have given important contribution on the subject, as, for instance, about the dominant role of the hydrophobic forces. In order to contribute to the identification of significant ingredients for the folding process, the main goal of this work consists in studying the stereo-hydrophobic potential (that is, the hydrophobic potential and a set of steric specificities) related to the folding process of globular proteins, revealing the importance of the steric constraints and the role of the native structure. A minimalist lattice model was employed for this purpose, and more than forty distinct protein-like chains were studied. These chains were designed based on native structures characterized by topological parameters as contact order, χ, long range order and number φ of crankshaft-like structures. The Monte Carlo simulation results show clearly that the folding process depends strongly on the topological attributes of the native structure: thermodynamical and kinetic behavior for chains designed from native structures, presenting smaller χ and higher φ, are very distinguishable from those with higher χ and lower φ. Additionally it was shown that the steric constraints significantly modify the configurational activity, increasing the general conditions for the globule stability, as well changing drastically the shape of the thermal capacity behavior, as a function of the temperature, in comparison with the corresponding results obtained using the hydrophobic potential only, i.e., without the steric specificities.

<p>In the thesis are introduced and investigated spaces of Burling and of Roumieu type tempered ultradistributions, which are natural generalization of the space of Schwartz&rsquo;s tempered distributions in Denjoy-Carleman-Komatsu&rsquo;s theory of ultradistributions.&nbsp; It has been proved that the introduced spaces preserve all of the good properties Schwartz space has, among others, a remarkable one, that the Fourier transform maps continuposly the spaces into themselves.<br />In the first chapter the necessary notation and notions are given.<br />In the second chapter, the spaces of ultrarapidly decreasing ultradifferentiable functions and their duals, the spaces of Beurling and of Roumieu tempered ultradistributions, are introduced; their topological properties and relations with the known distribution and ultradistribution spaces and structural properties are investigated;&nbsp; characterization of&nbsp; the Hermite expansions&nbsp; and boundary value representation of the elements of the spaces are given.<br />The spaces of multipliers of the spaces of Beurling and of Roumieu type tempered ultradistributions are determined explicitly in the third chapter.<br />The fourth chapter is devoted to the investigation of&nbsp; Fourier, Wigner, Bargmann and Hilbert transforms on the spaces of Beurling and of Roumieu type tempered ultradistributions and their test spaces.<br />In the fifth chapter the equivalence of classical definitions of the convolution of Beurling type ultradistributions is proved, and the equivalence of, newly introduced definitions, of ultratempered convolutions of Beurling type ultradistributions is proved.<br />In the last chapter is given a necessary and sufficient condition for a convolutor of a space of tempered ultradistributions to be hypoelliptic in a space of integrable ultradistribution, is given, and hypoelliptic convolution equations are studied in the spaces.<br />Bibliograpy has 70 items.</p> / <p>U ovoj tezi su proučavani prostori temperiranih ultradistribucija Beurlingovog&nbsp; i Roumieovog tipa, koji su prirodna uop&scaron;tenja prostora Schwarzovih temperiranih distribucija u Denjoy-Carleman-Komatsuovoj teoriji ultradistribucija. Dokazano je ovi prostori imaju sva dobra svojstva, koja ima i Schwarzov prostor, izmedju ostalog, značajno svojstvo da Furijeova transformacija preslikava te prostore neprekidno na same sebe.<br />U prvom poglavlju su uvedene neophodne oznake i pojmovi.<br />U drugom poglavlju su uvedeni prostori ultrabrzo opadajucih ultradiferencijabilnih funkcija i njihovi duali, prostori Beurlingovih i Rumieuovih temperiranih ultradistribucija; proučavana su njihova topolo&scaron;ka svojstva i veze sa poznatim prostorima distribucija i ultradistribucija, kao i strukturne osobine; date su i karakterizacije Ermitskih ekspanzija i graničnih reprezentacija elemenata tih prostora.<br />Prostori multiplikatora Beurlingovih i Roumieuovih temperiranih ultradistribucija su okarakterisani u trećem poglavlju.<br />Četvrto poglavlje je posvećeno proučavanju Fourierove, Wignerove, Bargmanove i Hilbertove transformacije na prostorima Beurlingovih i Rouimieovih temperiranih ultradistribucija i njihovim test prostorima.<br />U petoj glavi je dokazana ekvivalentnost klasičnih definicija konvolucije na Beurlingovim prostorima ultradistribucija, kao i ekvivalentnost novouvedenih definicija ultratemperirane konvolucije ultradistribucija Beurlingovog tipa.<br />U poslednjoj glavi je dat potreban i dovoljan uslov da konvolutor prostora temperiranih ultradistribucija bude hipoeliptičan u prostoru integrabilnih ultradistribucija i razmatrane su neke konvolucione jednačine u tom prostoru.<br />Bibliografija ima 70 bibliografskih jedinica.</p>