In the design of material handling systems with complex and unpredictable dynamics, conventional search and optimization approaches that are based only on performance measures offer little guarantee of robustness. Using evidence from research into complex systems, the use of behavior-based optimization is proposed, which takes advantage of observed relationships between complexity and optimality with respect to both performance and robustness. Based on theoretical complexity measures, particularly algorithmic complexity, several simple complexity measures are created. The relationships between these measures and both performance and robustness are examined, using a model of a directly connected material handling system as a backdrop. The fundamental causes of the relationships and their applicability in the proposed behavior-based optimization approach are discussed. / Ph. D.

We used a divide-and-conquer algorithm to recursively solve the two-dimensional problem of protein folding of an HP sequence with the maximum number of H-H contacts. We derived both lower and upper bounds for the algorithmic complexity by using the newly introduced concept of multi-directional width-bounded geometric separator. We proved that for a grid graph G with n grid points P, there exists a balanced separator A subseteq P$ such that A has less than or equal to 1.02074 sqrt{n} points, and G-A has two disconnected subgraphs with less than or equal to {2over 3}n nodes on each subgraph. We also derive a 0.7555sqrt {n} lower bound for our balanced separator. Based on our multidirectional width-bounded geometric separator, we found that there is an O(n^{5.563sqrt{n}}) time algorithm for the 2D protein folding problem in the HP model. We also extended the upper bound results to rectangular and triangular lattices.

This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value.

A tecnologia de virtualização de redes é um novo paradigma de redes que permite a múltiplas redes virtuais (VNs) compartilharem de uma forma eficiente e eficaz a mesma rede de infraestrutura denominada rede de substrato (SN). A implementação e o desenvolvimento de novos protocolos, testes de novas soluções e arquiteturas para a Internet atual e do futuro podem ser tratadas por meio da virtualização de redes. Com a virtualização de redes surge um desafio denominado problema VNE. O problema de virtualização de redes embutidas (VNE) consiste em realizar o mapeamento dos nós virtuais e o mapeamento dos enlaces virtuais sobre uma rede de substrato (SN). O problema é conhecido como NP-Hard e a sua solução é realizada por meio de algoritmos heurísticos e aproximados que realizam o mapeamento de nós e enlaces virtuais em dois estágios de forma independente ou coordenada. A presente tese tem o objetivo de resolver o mapeamento dos enlaces virtuais do problema VNE com a utilização da álgebra de caminhos. A solução apresentada fornece o melhor desempenho quando comparada com as demais soluções de virtualização de redes encontradas na literatura. Os resultados obtidos nas simulações para o problema VNE foram avaliados e analisados com a utilização do algoritmo desenvolvido nesta tese denominado Path Algebra for Virtual Link Mapping (PAViLiM), que utiliza a álgebra de caminhos para realizar o mapeamento de enlaces virtuais para caminhos na rede de substrato. A álgebra de caminhos é poderosa e flexível. Tal flexibilidade permite que ocorra uma exploração detalhada do espaço de soluções e a identificação do melhor critério e política que devem ser utilizados para a virtualização de redes. / The network virtualization technology is a new paradigm of network that allows multiple virtual networks (VNs) share in an efficient and effective way the same network infrastructure called substrate network (SN). The implementation and the development of new protocols, testing of new solutions and architectures for current and future Internet can be addressed through network virtualization. With the network virtualization arises a challenge called VNE problem. The problem of virtual network embedded (VNE) is to conduct the mapping of the virtual nodes and mapping of the virtual links over a substrate network (SN).The problem is known as NP-Hard and its solution is accomplished by means of approximate and heuristic algorithms that perform the mapping of virtual nodes and links in two stages independently or coordinated. This thesis aims to solve the mapping of virtual links for VNE problem using the paths algebra. The solution presented provides the best performance when compared with other networks virtualization solutions from the literature. The results of simulation for the VNE problem were evaluated and analyzed using the algorithm developed in this thesis called Path Algebra for Virtual Link Mapping (PAViLiM), which uses the paths algebra to perform the mapping of virtual links to paths in substrate network. The paths algebra is powerful and flexible. This flexibility allows the occurrence of a detailed exploration for identifying the best solutions and political criteria to be used for network virtualization.

A tecnologia de virtualização de redes é um novo paradigma de redes que permite a múltiplas redes virtuais (VNs) compartilharem de uma forma eficiente e eficaz a mesma rede de infraestrutura denominada rede de substrato (SN). A implementação e o desenvolvimento de novos protocolos, testes de novas soluções e arquiteturas para a Internet atual e do futuro podem ser tratadas por meio da virtualização de redes. Com a virtualização de redes surge um desafio denominado problema VNE. O problema de virtualização de redes embutidas (VNE) consiste em realizar o mapeamento dos nós virtuais e o mapeamento dos enlaces virtuais sobre uma rede de substrato (SN). O problema é conhecido como NP-Hard e a sua solução é realizada por meio de algoritmos heurísticos e aproximados que realizam o mapeamento de nós e enlaces virtuais em dois estágios de forma independente ou coordenada. A presente tese tem o objetivo de resolver o mapeamento dos enlaces virtuais do problema VNE com a utilização da álgebra de caminhos. A solução apresentada fornece o melhor desempenho quando comparada com as demais soluções de virtualização de redes encontradas na literatura. Os resultados obtidos nas simulações para o problema VNE foram avaliados e analisados com a utilização do algoritmo desenvolvido nesta tese denominado Path Algebra for Virtual Link Mapping (PAViLiM), que utiliza a álgebra de caminhos para realizar o mapeamento de enlaces virtuais para caminhos na rede de substrato. A álgebra de caminhos é poderosa e flexível. Tal flexibilidade permite que ocorra uma exploração detalhada do espaço de soluções e a identificação do melhor critério e política que devem ser utilizados para a virtualização de redes. / The network virtualization technology is a new paradigm of network that allows multiple virtual networks (VNs) share in an efficient and effective way the same network infrastructure called substrate network (SN). The implementation and the development of new protocols, testing of new solutions and architectures for current and future Internet can be addressed through network virtualization. With the network virtualization arises a challenge called VNE problem. The problem of virtual network embedded (VNE) is to conduct the mapping of the virtual nodes and mapping of the virtual links over a substrate network (SN).The problem is known as NP-Hard and its solution is accomplished by means of approximate and heuristic algorithms that perform the mapping of virtual nodes and links in two stages independently or coordinated. This thesis aims to solve the mapping of virtual links for VNE problem using the paths algebra. The solution presented provides the best performance when compared with other networks virtualization solutions from the literature. The results of simulation for the VNE problem were evaluated and analyzed using the algorithm developed in this thesis called Path Algebra for Virtual Link Mapping (PAViLiM), which uses the paths algebra to perform the mapping of virtual links to paths in substrate network. The paths algebra is powerful and flexible. This flexibility allows the occurrence of a detailed exploration for identifying the best solutions and political criteria to be used for network virtualization.

In the present thesis, we try to compare the classical boolean complexity with the algebraic complexity, by studying problems related to polynomials. We consider the algebraic models from Valiant and from Blum, Shub and Smale (BSS). To study the algebraic complexity classes, one can start from results and open questions from the boolean case, and look at their translation in the algebraic context. The comparison of the results obtained in the two settings will then boost our understanding of both complexity theories. The first part follows this framework. By considering a polynomial canonically associated to a boolean formula, we get a link between boolean complexity issues on the formula and algebraic complexity problems on the polynomial. We studied the complexity of computing the polynomial in Valiant's model, as a function of the complexity of the boolean formula. We found algebraic counterparts to some boolean results. Along the way, we could also use some algebraic methods to improve boolean results, in particular by getting better counting reductions. Another motivation for algebraic models of computation is to offer an elegant framework to the study of numerical algorithms. The second part of this thesis follows this approach. We started from new algorithms for the search of approximate zeros of complex systems of n polynomials in n variables. Up to now, those were BSS machine algorithms. We studied the implementation of these algorithms on digital computers, and propose an algorithm using floating arithmetic for this problem.

This paper aims to apply the Kolmogorov algorithmic complexity theory using the measure proposed by Lempel and Ziv (1976) to analyze its behavior due to changes in parameters such as window size, jumps and the region of stability of high frequency financial series returns of assets traded on the BM&F BOVESPA, as well as to assess the evolution of such a measure when the intervals between the negotiations are extended and to verify the possible evidence of a relationship between the value of the complexity measure and the behavior of autocorrelation curves presented for each trading interval specified. We also discuss the criterion used to measure the relative efficiency of the market proposed by Giglio (2008). / Fundação de Amparo a Pesquisa do Estado de Alagoas / O presente trabalho tem por objetivos: 1) aplicar a teoria da complexidade de Kolmogorov utilizando a medida proposta por Lempel e Ziv (1976) para analisar o comportamento desta diante de alterações em parâmetros como tamanho de janela, salto e de região de estabilidade em séries financeiras de retornos de alta freqüência de ativos negociados na BM&F BOVESPA; 2) avaliar a evolução da medida ao se ampliarem os intervalos entre as negociações; e finalmente, 3) verificar a possibilidade de existir algum indício de relação entre o valor daquela medida e o comportamento das curvas de autocorrelação apresentadas para cada intervalo de negociação especificado. Foi também discutido o critério utilizado para a medida de eficiência relativa de mercado proposto por Giglio (2008).

Cette thèse concerne l'élaboration de stratégies de commande prédictive pour certaines classes de systèmes dynamiques continus, discrets et hybrides modélisés par des extensions de réseaux de Petri ad hoc. Pour les systèmes continus et en vue de limiter la complexité de calcul inhérente à la forme standard de la commande prédictive, plusieurs améliorations sont proposées. Celles-ci permettent de surmonter le problème de "hill climbing" caractéristique des trajectoires obtenues avec certains réseaux de Petri. Elles assurent également la possibilité d'implémenter la commande en temps réel en adaptant l'horizon de prédiction pour réduire la complexité algorithmique. Enfin, elles permettent de limiter la sollicitation des actionneurs tout en garantissant la stabilité asymptotique du système commandé. Pour les systèmes discrets temporisés et pour éviter l'exploration exhaustive du graphe d'atteignabilité, une méthode de commande est proposée, basée sur la commande prédictive appliquée à une approximation continue du système discret. Enfin pour les systèmes hybrides, une commande prédictive hybride est développée, inspirée de la commande prédictive continue. Les performances de ces différentes stratégies de commande sont évaluées et comparées avec différentes simulations numériques / This thesis concerns the development of predictive control strategies for some classes of continuous, discrete and hybrid dynamic systems modeled by specific extensions of Petri nets. For continuous systems and in order to limit the computational complexity inherent to the standard form of the predictive control, several improvements are proposed. These improvements allow overcoming the problem of hill climbing that characterizes trajectories obtained with some Petri nets. They also ensure the possibility to implement real-time control by adapting the prediction horizon in order to reduce the algorithmic complexity. Finally, they limit actuators solicitation while ensuring the asymptotic stability of the controlled system. For timed discrete systems and in order to avoid the exhaustive exploration of the reachability graph, a control method is proposed, based on the predictive control applied to a continuous approximation of the discrete system. Finally for hybrid systems, hybrid predictive control is developed, inspired by the continuous predictive control. The performance of these different control strategies are evaluated and compared to different numerical simulations.

The prediction of polypharmacy side effects is crucial to reduce the mortality and morbidity of patients suffering from complex diseases. However, its experimental prediction is unfeasible due to the many possible drug combinations, leaving in silico tools as the most promising way of addressing this problem. This thesis improves the performance and robustness of a state-of-the-art graph convolutional network designed to predict polypharmacy side effects, by feeding it with complexity properties of the drug-protein network. The modifications also involve the creation of a direct pipeline to reproduce the results and test it with different datasets. / För att minska dödligheten och sjukligheten hos patienter som lider av komplexa sjukdomar är det avgörande att kunna förutsäga biverkningar från polyfarmaci. Att experimentellt förutsäga biverkningarna är dock ogenomförbart på grund av det stora antalet möjliga läkemedelskombinationer, vilket lämnar in silico-verktyg som det mest lovande sättet att lösa detta problem. Detta arbete förbättrar prestandan och robustheten av ett av det senaste grafiska faltningsnätverken som är utformat för att förutsäga biverkningar från polyfarmaci, genom att mata det med läkemedel-protein-nätverkets komplexitetsegenskaper. Ändringarna involverar också skapandet av en direkt pipeline för att återge resultaten och testa den med olika dataset.

Dans cette thèse, nous cherchons à comparer la complexité booléenne classique et la complexité algébrique, en étudiant des problèmes sur les polynômes. Nous considérons les modèles de calcul algébriques de Valiant et de Blum, Shub et Smale (BSS). Pour étudier les classes de complexité algébriques, il est naturel de partir des résultats et des questions ouvertes dans le cas booléen, et de regarder ce qu'il en est dans le contexte algébrique. La comparaison des résultats obtenus dans ces deux domains permet ainsi d'enrichir notre compréhension des deux théories. La première partie suit cette approche. En considérant un polynôme canoniquement associé à toute formule booléenne, nous obtenons un lien entre les questions de complexité booléenne sur la formule booléenne et les questions de complexité algébrique sur le polynôme. Nous avons étudié la complexité du calcul de ce polynôme dans le modèle de Valiant en fonction de la complexité de la formule booléenne, et avons obtenu des analogues algébriques à certains résultats booléens. Nous avons aussi pu utiliser des méthodes algébriques pour améliorer certains résultats booléens, en particulier de meilleures réductions de comptage. Une autre motivation aux modèles de calcul algébriques est d'offrir un cadre pour l‘analyse d’algorithmes continus. La seconde partie suit cette approche. Nous sommes partis d’algorithmes nouveaux pour la recherche de zéros approchés d'un système de n polynômes complexes à n inconnues. Jusqu'à présent il s'agissait d'algorithmes pour le modèle BSS. Nous avons étudié l'implémentabilité de ces algorithmes sur un ordinateur booléen et proposons un algorithme booléen. / In the present thesis, we try to compare the classical boolean complexity with the algebraic complexity, by studying problems related to polynomials. We consider the algebraic models from Valiant and from Blum, Shub and Smale (BSS). To study the algebraic complexity classes, one can start from results and open questions from the boolean case, and look at their translation in the algebraic context. The comparison of the results obtained in the two settings will then boost our understanding of both complexity theories. The first part follows this framework. By considering a polynomial canonically associated to a boolean formula, we get a link between boolean complexity issues on the formula and algebraic complexity problems on the polynomial. We studied the complexity of computing the polynomial in Valiant's model, as a function of the complexity of the boolean formula. We found algebraic counterparts to some boolean results. Along the way, we could also use some algebraic methods to improve boolean results, in particular by getting better counting reductions. Another motivation for algebraic models of computation is to offer an elegant framework to the study of numerical algorithms. The second part of this thesis follows this approach. We started from new algorithms for the search of approximate zeros of complex systems of n polynomials in n variables. Up to now, those were BSS machine algorithms. We studied the implementation of these algorithms on digital computers, and propose an algorithm using floating arithmetic for this problem.