This thesis is focused on the fixed interval scheduling (FIS) problems with random delays. Firstly, we introduce the concept of FIS problems and the exogenous and endogenous uncertainty. In the next chapter we will summarize the FIS problems under decision dependent randomness and their relation to the robust coloring. We will extend previous results with proposing a new FIS problem with maintenance. This problem is a specific case of a decision-dependent probabilities as it allows to use a specific type of a job - the maintenance, which positively impacts the probability distributions of job delays. We start with defining a problem, where maintenance must be assigned only before regular jobs and then we propose the general case, when maintenances appears during the whole processing period. We show why this approach leads to an optimal solution and provide a detailed example of a small problem.We also discuss some extensions of our problem. Finally, we conduct a numerical study. We solve the FIS maintenance problem with the Cplex solver for a few different settings of inputs. It seems that the maintenance is useful only for certain settings, such as jobs with high probability of having a delay or the price of outsourcing being much higher than the cost of maintenance. It is also shown that the problem...

Yes / This paper investigates the stabilisation problem and consider transient optimisation for a class of the multi-input-multi-output (MIMO) semi-linear stochastic systems. A control algorithm is presented via an m-block backstepping controller design where the closed-loop system has been stabilized in a probabilistic sense and the transient performance is optimisable by optimised by searching the design parameters under the given criterion. In particular, the transient randomness and the probabilistic decoupling will be investigated as case studies. Note that the presented control algorithm can be potentially extended as a framework based on the various performance criteria. To evaluate the effectiveness of this proposed control framework, a numerical example is given with simulation results. In summary, the key contributions of this paper are stated as follows: 1) one block backstepping-based output feedback control design is developed to stabilize the dynamic MIMO semi-linear stochastic systems using a linear estimator; 2) the randomness and probabilistic couplings of the system outputs have been minimized based on the optimisation of the design parameters of the controller; 3) a control framework with transient performance enhancement of multi-variable semi-linear stochastic systems has been discussed. / Higher Education Innovation Fund (No. HEIF 2018-2020), De Montfort University, Leicester, UK.

<p>Fresh groundwater quality and availability in coastal areas is affected by seawater intrusion into coastal aquifers, and coastal water quality and ecosystem status may be significantly affected by groundwater pollutants that are transported into coastal waters by submarine groundwater dis-charge (SGD). This thesis uses an overall regional perspective for investigating: i) seawater intru-sion and its possible control in sustainable coastal groundwater management; ii) SGD and its relevant quantification as one interacting part among the diverse main regional pathways of freshwater and tracer/pollutant inputs from land to sea; and iii) the integrated system functioning of both i) and ii) as main components of the same coastal groundwater system.</p><p>Results show that intensive pumping rates may be maintained for a long time before major re-gional seawater intrusion problems are recognized by too high salinities in pumped groundwater. After such late recognition, pumping wells are no longer useful and a common strategy of mov-ing groundwater pumping further upstream from the coast only increases the extent of the salt-water intrusion zone into the aquifer. An alternative strategy may be to control seawater intrusion through artificial groundwater recharge, for instance by sufficiently treated wastewater, which may considerably reduce long-term trends of salinity increase in pumped groundwater, even for small artificial recharge rates compared to pumping rates. In general, account for natural spatial-temporal variability and randomness may be essential for relevant prediction of groundwater dynamics for management purposes. Spatial and temporal randomness effects, however, may not be additive, but rather largely overlapping, with either spatial or temporal randomness being the dominating part that must be accounted for in predictive groundwater dynamics calculations. Aquifer depth is identified as an important control parameter in this context, yielding much greater temporal randomness effects in shallow than in deep aquifers.</p><p>Combined simulation results suggest a simple, approximately linear regional relationship between total SGD and its hydrologically determined freshwater component. Tidal oscillation may signifi-cantly affect such linear dependence of steady-state SGD, but primarily for low SGD conditions. High SGD appears to depend mainly on a dominant freshwater component, which effectively counteracts density-driven flow of seawater into the aquifer and thus decreases also effects of sea-level oscillation on the seawater component of total SGD. Comparative analysis between different SGD estimation methods in different reported high-SGD regions of the world indicates possible anomalously large regional SGD estimation from tracer concentrations in coastal waters, by confusing different main pathways of groundwater flow and pollutant inputs to the sea.</p>

In dieser Arbeit wird zuerst das Theorem von Chung, Graham und Wilson über quasi-zufällige Graphen zur sogenannten schwachen Quasi-Zufälligkeit für k-uniforme Hypergraphen verallgemeinert und somit eine Reihe äquivalenter Eigenschaften bestimmt. Basierend auf diesen Resultaten werden nichtbipartite Graphen gefunden, welche die Quasi-Zufälligkeit für Graphen ``forcieren''''. Zuvor waren nur bipartite Graphen mit dieser Eigenschaft bekannt. Desweiteren ist ein konzeptionell einfacher Algorithmus zum Verifizieren nicht erfüllbarer zufälliger k-SAT Formeln angegeben. Dann richtet sich der Fokus auf Anwendungen verschiedener Regularitätslemmata für Hypergraphen. Zuerst wird die Menge aller bezeichneten 3-uniformen Hypergraphen auf n Knoten, die keine Kopie des Hypergraphen der Fano Ebene enthalten, studiert. Es wird gezeigt, dass fast jedes Element aus dieser Menge ein bipartiter Hypergraph ist. Dies führt zu einem Algorithmus, der in polynomiell erwarteter Zeit einen zufälligen Fano-freien (und somit einen zufälligen bipartiten 3-uniformen) Hypergraphen richtig färbt. Schließlich wird die folgende extremale Funktion studiert. Es sind r Farben gegeben sowie ein k-uniformer Hypergraph F. Auf wie viele verschiedene Arten kann man die Kanten eines k-uniformen Hypergraphen H färben, so dass keine monochromatische Kopie von F entsteht? Welche Hypergraphen H maximieren die Anzahl erlaubter Kantenfärbungen? Hier wird ein strukturelles Resultat für eine natürliche Klasse von Hypergraphen bewiesen. Es wird für viele Hypergraphen F, deren extremaler Hypergraph bekannt ist, gezeigt, dass im Falle von zwei oder drei Farben die extremalen Hypergraphen die oben beschriebene Funktion maximieren, während für vier oder mehr Farben andere Hypergraphen mehr Kantenfärbungen zulassen. / This thesis presents first one possible generalization of the result of Chung, Graham and Wilson to k-uniform hypergraphs, and studies the so-called weak quasi-randomness. As applications we obtain a simple strong refutation algorithm for random sparse k-SAT formulas and we identify first non-bipartite forcing pairs for quasi-random graphs. Our focus then shifts from the study of quasi-random objects to applications of different versions of the hypergraph regularity lemmas; all these versions assert decompositions of hypergraphs into constantly many quasi-random parts, where the meaning of ``quasi-random'''' takes different contexts in different situations. We study the family of hypergraphs not containing the hypergraph of the Fano plane as a subhypergraph, and show that almost all members of this family are bipartite. As a consequence an algorithm for coloring bipartite 3-uniform hypergraphs with average polynomial running time is given. Then the following combinatorial extremal problem is considered. Suppose one is given r colors and a fixed hypergraph F. The question is: In at most how many ways can one color the hyperedges of a hypergraph H on n vertices such that no monochromatic copy of F is created? What are the extremal hypergraphs for this function? Here a structural result for a natural family of hypergraphs F is proven. For some special classes of hypergraphs we show that their extremal hypergraphs (for large n) maximize the number of edge colorings for 2 and 3 colors, while for at least 4 colors other hypergraphs are optimal.

<p>Ispitivan&nbsp; je&nbsp; spregnut&nbsp; sistem&nbsp; jednačina&nbsp; za&nbsp; prognozu&nbsp; temperature&nbsp; na povr&scaron;ini&nbsp; i&nbsp; u&nbsp; dubljem sloju zemlji&scaron;ta.&nbsp; Računati&nbsp; su&nbsp; Ljapunovljevi eksponenti,&nbsp; bifurkacioni dijagram, atraktor i analiziran je domen re&scaron;enja. Uvedene su nove informacione mere&nbsp; bazirane na<br />Kolmogorovljevoj kompleksnosti,&nbsp; za kvantifikaciju&nbsp; stepena nasumičnosti u vremenskim serijama,.&nbsp; Nove mere su primenjene na razne serije dobijene merenjem fizičkih faktora životne sredine i pomoću klimatskih modela.</p> / <p>Coupled system of prognostic equations for&nbsp; the&nbsp; ground surface temperature and&nbsp; the deeper layer temperature was examind. Lyapunov exponents, bifurcation diagrams, attractor and the domain of solutions were analyzed.&nbsp; Novel information measures based on Kolmogorov complexity&nbsp; and used&nbsp; for the quantification of randomness in time series, were presented.Novel measures were tested on various time series obtained by measuring physical factors of the environment or as the climate model outputs.</p>

Ce travail est consacré à l’analyse et au développement de concepts et d’outils mathématiques en vue de leur application à des problématiques propres aux sites de stockage géologique profond de déchets radioactifs. La première partie porte sur l’estimation en champ lointain de la concentration de radionucléides issus du relâchement des colis de confinement, lorsque les incertitudes sur le relâchement sont prises en compte. En s’appuyant sur les travaux de A. Bourgeat et A. Piatniski sur l’homogénéisation d’une équation de convection-diffusion avec second membre aléatoire, on développe des outils numériques permettant d’approcher le comportement probabiliste du champ de concentration dans une configuration du type site de stockage. Dans une seconde partie, on s’intéresse à la migration de gaz dans et autour d’un site de stockage. Après une revue sur la modélisation physique des écoulements diphasiques de type eau/hydrogène en milieu poreux, on propose une nouvelle formulation mathématique du problème qui décrit, dans un même jeu d’équations, les écoulements à une (liquide) et deux (liquide/gaz) phases. Une étude de l’existence de solutions de cette formulation est menée à l’aide de la théorie générale des équations différentielles quasilinéaires elliptiques-paraboliques introduite par H.W. Alt et S. Luckhaus. Une méthode de résolution numérique du problème est mise en oeuvre pour la simulation de différents cas test, des plus simples au plus représentatif d’un site de stockage géologique. Enfin, l’homogénéisation périodique du modèle est effectuée et appliquée à la simulation de l’exercice Couplex-Gaz proposé par l’ANDRA / The purpose of this work is to analyze and develop mathematical concepts and tools in application to performance assessment of an underground nuclear waste disposal. The first part is concerned with estimating the far field concentration of radionuclides released by containers of waste when uncertainties on the release are taking in account. Using the work of A. Bourgeat and A. Piatniski about homogenization of a convection-diffusion equation with random source term, numerical tools are developed to approximate the random behavior of the concentration field in an underground disposal configuration. In a second part, we are interested in gas migration in and around an underground nuclear waste disposal. After a review on physical models of two-phase flow in porous media for water/hydrogen mixture, we propose a new mathematical formulation describing one- (liquid) and two- (liquid/gas) phase flow with a unique set of equation. Considering the general theory of quasilinear elliptic-parabolic differential equations introduced by H.W. Alt and S. Luckhaus, we study existence of solutions for this formulation. A numerical method to solve the problem is implemented to simulate several test cases. These test cases run from very simple situations to a representative configuration of an underground nuclear waste disposal. Finally, the periodic homogenization of the model is done and applied to simulate the Couplex-Gas exercise proposed by ANDRA.

Recentemente, Barak et al. (2004) exibiram construções de extratores e dispersores determinísticos (funções computáveis em tempo polinomial) com parâmetros melhores do que era anteriormente possível. Introduziremos os conceitos envolvidos em tal trabalho e mencionaremos suas aplicações; em particular, veremos como é possível obter cotas muito melhores para o problema Ramsey bipartido (um problema bem difícil) utilizando as construções descritas no artigo. Também apresentamos resultados originais para melhorar tais construções. Tais idéias são inspiradas no trabalho de Anup Rao (2005) e utilizam o recente êxito de Jean Bourgain (2005) em obter extratores que quebram a \"barreira 1/2\". / Recently, Barak et al. (2004) constructed explicit deterministic extractors and dispersers (these are polynomial-time computable functions) with much better parameters than what was known before. We introduce the concepts involved in such a construction and mention some of its applications; in particular, we describe how it is possible to obtain much better bounds for the bipartite Ramsey problem (a very hard problem) using the machinery developed in that paper. We also present some original results that improve on these constructions. They are inspired by the work of Anup Rao (2005) and uses the recent breakthrough of Jean Bourgain (2005) in obtaining 2-source extractors that break the \"1/2-barrier\".

Neste trabalho demonstramos que padrões e aleatoriedade estão intimamente relacionados, ao contrário do que intuitivamente é considerado como campos opostos. Esta abordagem visa dois propósitos: por um lado, obter vantagens das propriedades caóticas para medir pseudo-aleatoriedade, e por outro lado, extrair padrões de diagramas espaço-tempo como método de reconhecimento de padrões. Este trabalho centrou-se em dois métodos relacionados com sistemas complexos, como sistemas dinâmicos de tempo discreto, redes complexas, autômatos celulares (AC) e suas combinações. O primeiro método foi explorar as propriedades das profundezas do caos como fonte de pseudo-aleatoriedade a partir de sistemas dinâmicos caóticos, como o mapa logístico e o mapa da tenda. Observamos que os padrões desaparecem e a pseudo-aleatoriedade é aumentada pela remoção de k dígitos à direita da vírgula dos pontos de uma órbita original de um mapa caótico. Portanto, foi encontrada uma fonte caótica interessante para obter geradores de números de pseudo-aleatórios (PRNGs) parametrizada por k. Um segundo método foi proposto com base na incorporação de autômatos celulares na topologia de rede, também chamada de rede-autômato, visando caracterizar as redes a partir da dinâmica espaço-temporal intrínseca dessas redes. Quatro problemas de grande demanda foram explorados, tais como (i) identificar redes sociais online; (ii) identificar organismos de diferentes domínios da vida através de suas redes metabólicas; (iii) classificar padrões de distribuição de estômatos variando de acordo com diferentes condições ambientais; e (iv) o problema de identificação de autoria. Finalmente, essa mesma abordagem foi utilizada para analisar as sequências de números pseudo-aleatórios gerados pelo padrão ouro do k-mapa logístico no contexto do reconhecimento de padrões. A abordagem proposta permitiu explorar padrões e pseudoaleatoriedade extraídos de uma miríade de sistemas com resultados bem-sucedidos em termos de acerto e boa pseudo-aleatoriedade. Além disso, este trabalho trouxe consigo progressos significativos em aplicações de reconhecimento de padrões do mundo real de um amplo ramo de campos como criptografia, criptoanálise, biologia e ciência dos dados. / In this work, we demonstrate that patterns and randomness are close related, contrary to what intuitively is considered as opposite fields. We aimed for a pattern recognition approach that aims for two purposes: (i) to take advantages from the chaotic properties as a source of pseudo-randomness in order to measure pseudo-randomness and (ii) to extract patterns from spatio-temporal diagrams obtained from complex systems models as a pattern recognition method. This work has focused on different complex systems such as discrete dynamical systems, complex networks, cellular automata (CA), and their combinations. The first method was to explore the chaotic properties in a deep-zoom manner as a source of pseudo-randomness from chaotic dynamical systems such as the logistic map and the tent map. We observed that the patterns vanish and therefore pseudo-randomness is increased by removing k right digits from the original orbit sequences. Therefore, we found an interesting chaotic source to obtain pseudo-randomness number generators (PRNGs). A second method was proposed based on the embedding of cellular automata (CA) over a network topology, also called network automata, aiming to characterize networks from the intrinsic spatio-temporal dynamics of these networks. Various on-demand problems were explored such as (i) identifying online social networks; (ii) identifying organisms from distinct domains of life through their metabolic networks; (iii) classifying stomata distribution patterns varying according to different environmental conditions; and (iv) the authorship identification problem. Finally, this same approach was used to analyze the sequences of pseudo-random numbers generated by the gold standard k-logistic map in the context of pattern recognition. So far, the proposed pattern recognition approach based on non-linear systems allowed us to explored patterns and pseudo-randomness extracted from a myriad of systems with successful results in terms of accuracy and good pseudorandomness. The proposed method has made significant progress in real-world pattern recognition applications from a wide branch of fields such as Cryptography, Cryptanalysis, Biology and Data Science.

Fresh groundwater quality and availability in coastal areas is affected by seawater intrusion into coastal aquifers, and coastal water quality and ecosystem status may be significantly affected by groundwater pollutants that are transported into coastal waters by submarine groundwater dis-charge (SGD). This thesis uses an overall regional perspective for investigating: i) seawater intru-sion and its possible control in sustainable coastal groundwater management; ii) SGD and its relevant quantification as one interacting part among the diverse main regional pathways of freshwater and tracer/pollutant inputs from land to sea; and iii) the integrated system functioning of both i) and ii) as main components of the same coastal groundwater system. Results show that intensive pumping rates may be maintained for a long time before major re-gional seawater intrusion problems are recognized by too high salinities in pumped groundwater. After such late recognition, pumping wells are no longer useful and a common strategy of mov-ing groundwater pumping further upstream from the coast only increases the extent of the salt-water intrusion zone into the aquifer. An alternative strategy may be to control seawater intrusion through artificial groundwater recharge, for instance by sufficiently treated wastewater, which may considerably reduce long-term trends of salinity increase in pumped groundwater, even for small artificial recharge rates compared to pumping rates. In general, account for natural spatial-temporal variability and randomness may be essential for relevant prediction of groundwater dynamics for management purposes. Spatial and temporal randomness effects, however, may not be additive, but rather largely overlapping, with either spatial or temporal randomness being the dominating part that must be accounted for in predictive groundwater dynamics calculations. Aquifer depth is identified as an important control parameter in this context, yielding much greater temporal randomness effects in shallow than in deep aquifers. Combined simulation results suggest a simple, approximately linear regional relationship between total SGD and its hydrologically determined freshwater component. Tidal oscillation may signifi-cantly affect such linear dependence of steady-state SGD, but primarily for low SGD conditions. High SGD appears to depend mainly on a dominant freshwater component, which effectively counteracts density-driven flow of seawater into the aquifer and thus decreases also effects of sea-level oscillation on the seawater component of total SGD. Comparative analysis between different SGD estimation methods in different reported high-SGD regions of the world indicates possible anomalously large regional SGD estimation from tracer concentrations in coastal waters, by confusing different main pathways of groundwater flow and pollutant inputs to the sea. / QC 20101012

Im Beitrag werden Forschungsergebnisse zum numerischen Entwurf textilbewehrter Verstärkungsschichten zusammengefasst. Die Ergebnisse resultieren im Wesentlichen aus den Arbeiten der Teilprojekte D2-Numerische Simulation, E3-Sicherheitsbeurteilung und E4-Numerische Langzeitprognose des Sonderforschungsbereichs 528. Zusätzlich wird auf Transferleistungen verwiesen. / The paper provides a summary of research results concerning numerical design approaches for textile reinforced structures. The outcome mainly results from the work done in the subprojects of the Collaborative Research Centre 528: D2-Numerical Simulation, E3-Reliability Assessment und E4-Numerical Long-term Prognosis. Further, the paper also points out the transfer potential.