本論文主要是介紹並評估一個R的軟體套件叫做"rBeta2009"。此套件是由Cheng et al. (2012) [8] 所設計，其目的是用來產生貝他分配(Beta Distribution)及狄氏分配(Dirichlet Distribution)的亂數。本論文特別針對此套件之(i)有效性(effiniency)、(ii)精確性(accuracy)及(iii)隨機性(randomness)進行評估，並與現有的R套件作比較。此外，本論文也介紹如何應用此套件來產生(i)反貝他分配(Inverted Beta Distribution)、(ii)反狄氏分配(Inverted Dirichlet Distribution)、(iii)Liouville分配及(iv)凸面區域上的均勻分配之亂數。 / A package in R called "rBeta2009", originally designed by Cheng et al. (2012) [6], was introduced and evaluated in this thesis. The purpose of the package is generating beta random numbers and Dirichlet random vectors. In this paper, we not only evaluated (i) the efficiency, (ii) the accuracy and (iii) the randomness, but also compare it with other R packages currently in use. In addition, it was also scrutinized in this thesis how to generate (i) inverted beta random numbers, (ii) inverted Dirichlet random vectors, (iii) Liouville random vectors, and (iv) uniform random vectors over convex polyhedron by using the same package.

Sannolikhet och statistik är ett ämne lärare har svårt att undervisa i. Dels för att ämnet är relativt nytt, dels för att lärare saknar fördjupade kunskaper inom området. Syftet med den här litteraturstudien är att bidra med kunskap om undervisningsaktiviteter i sannolikhet och statistik i grundskolan, år f-6, för lärare. Databaserna ERIC, WoS och DiVA användes för att samla in vetenskapligt underlag till denna systematiska litteraturstudie. Resultatet visar att aktiviteter med konkret material är användbart i alla delar i sannolikhet och statistik samt att det ger bättre resultat för elevers kunskapsinhämtande om aktiviteterna följs upp av diskussioner. I resultatet framkommer även konkreta förslag på hur aktiviteter med konkret material kan användas i en undervisningssituation. Konsekvenser för undervisning samt förslag till vidare forskning avslutar den här studien. / Probability and statistics is a subject that teachers find difficult to teach. Partly because this area is relatively new in the mathematics course, partly because of the lack of deepened knowledge amongst teachers in this subject area. The purpose of this study is to contribute with knowledge about teaching activities in the probability and statistics course in the early years of elementary school, years K–6, for teachers. The databases used to collect scientific foundation to this systematic literature study is ERIC, WoS and DiVA. The result showed that activities with manipulatives are useful in all subareas in probability and statistics and that students’ knowledge acquirement improves if the activities are followed up by discussions. However, the result also brought out tangible suggestions of how activities with concrete materials can be used in a teaching situation. To round up this study is a discussion of consequences for teaching as well as suggestions for further research.

Les résultats de mesures quantiques sont généralement considérés comme aléatoires, mais leur nature aléatoire, malgré son importance dans la théorie de l’information quantique, est mal comprise. Dans cette thèse, nous étudions plusieurs problèmes liés à l’origine et la certification de l’aléatoire et l’imprévisibilité quantique. L’un des résultats clés dans la formation de notre compréhension de la mécanique quantique comme théorie intrinsèquement indéterministe est le théorème de Kochen et Specker, qui démontre l’impossibilité d’attribuer simultanément, de façon cohérente, des valeurs définies et non-contextuelles à chaque observable avant la mesure. Cependant, si nous présumons qu’une observable à valeur définie doit être non-contextuelle, alors lethéorème ne montre que le fait qu’il existe au moins une observable à valeur indéfinie. Nous renforçons ce résultat en démontrant une variante du théorème de Kochen et Specker qui montre que si un système est préparé dans un état quelconque j i, alors chaque observable A est à valeur indéfinie sauf si j i est un état propre de A. La nature indéterministe de la mesure quantique n’explique pas bien la différence de qualité entre l’aléatoire quantique et classique. Soumise à certaines hypothèses physiques, nous montrons qu’une suite de bits produite par la mesure des observables à valeurs indéfinies est garantie, dans la limite infinie, d’être fortement incalculable. De plus, nous discutons comment utiliser ces résultats afin de construire un générateur quantique de nombres aléatoires qui est certifié par des observables à valeurs indéfinies. Dans la dernière partie de cette thèse, nous étudions la notion d’imprévisibilité, qui est au coeur du concept d’aléatoire (quantique). Ce faisant, nous proposons un modèle formel de (im)prévisibilité qui peut servir à évaluer la prévisibilité d’expériences physiques arbitraires. Ce modèle est appliqué aux mesures quantiques afin de comprendre comment la valeur indéfinie et la complémentarité quantique peuvent être utilisées pour certifier différents degrés d’imprévisibilité, et nous démontrons ainsi que le résultat d’une seule mesure d’une observable à valeur indéfinie est formellement imprévisible. Enfin, nous étudions la relation entre cette notion d’imprévisibilité et la certification de l’incalculabilité des suites aléatoires quantiques. / The outcomes of quantum measurements are generally considered to be random, but despite the fact that this randomness is an important element in quantum information theory, its nature is not well understood. In this thesis, we study several issues relating to the origin and certification of quantum randomness and unpredictability. One of the key results in forming our understanding of quantum mechanics as an intrinsically indeterministic theory is the Kochen-Specker theorem, which shows the impossibility to consistently assign simultaneous noncontextual definite values to all quantum mechanical observables prior to measurement. However, the theorem, under the assumption that any definite values must be noncontextual, only strictly shows that some observables must be value indefinite. We strengthen this result, proving a stronger variant of the Kochen-Specker theorem showing that, under the same assumption, if a system is prepared in an arbitrary state j i, then every observable A is value indefinite unless j i is an eigenstate of A. The indeterministic nature of quantum measurements does little to explain how the quality of quantum randomness differs from classical randomness. We show that, subject to certain physical assumptions, a sequence of bits generated by the measurement of value indefinite observables is guaranteed, in the infinite limit, to be strongly incomputable. We further discuss how this can be used to build a quantum random number generator certified by value indefiniteness. Next, we study the notion of unpredictability, which is central to the concept of (quantum) randomness. In doing so, we propose a formal model of prediction that can be used to asses the predictability of arbitrary physical experiments. We investigate how the quantum features of value indefiniteness and complementarity can be used to certify different levels of unpredictability, and show that the outcome of a single measurement of a value indefinite quantum observable is formally unpredictable. Finally, we study the relation between this notion of unpredictability and the computability-theoretic certification of quantum randomness.

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.

Nous étudions le problème de maintenir une distribution donnée de graphes aléatoires après une séquence arbitraire d’insertions et de suppressions de sommets. Dans l’objectif de modéliser l’évolution de réseaux logiques dynamiques,nous travaillons dans un modèle local où l’accès à la liste des sommets est restreint. À la place, nous faisons l’hypothèse d’un accès à une primitive globale qui retourne un sommet aléatoire, choisi uniformément dans l’ensemble total des sommets. Le problème de maintenance a été exploré sur plusieurs modèles simples de graphes aléatoires (graphes d’Erdos–Rényi, graphes basés sur le modèle par paires, graphes k-sortants uniformes). Pour chacun des modèles, un ou plusieurs algorithmes pour la tâche de maintenance ont été décris et analysés ; les plus élaborés de ces algorithmes sont asymptotiquement optimaux. Le problème de maintenance soulève plusieurs problèmes de simulation liés à notre contexte distribué. Nous nous sommes intéressé en particulier à la maintenabilité de distributions de graphes et à la simulabilité de familles de distributions de probabilité sur les entiers, dans le modèle d’aléa présenté.Une attention particulière a été portée sur la simulation efficace de lois spécifiques nous intéressant (certaines lois binomiales). Cette dernière a pu être obtenue en exploitant les propriétés d’un nouvel arbre de génération pour les permutations, que nous avons introduit. / We study the problem of maintaining a given distribution of randomgraphs under an arbitrary sequence of vertex insertions and deletions. Keeping inmind our objective to model the evolution of dynamic logical networks, we work ina local model where we do not have direct access to the list of all vertices. Instead,we assume access to a global primitive that returns a random vertex, chosen uniformlyfrom the whole vertex set. The maintenance problem has been explored onseveral simple random graph models (Erdos–Rényi random graphs, pairing modelbased random graphs, uniform k-out graphs). For each model, one or several updatealgorithms for the maintenance task have been described and analyzed ; the mostelaborate of them are asymptically optimal. The maintenance task rise several simulationissues linked to our distributed context. In particular, we have focused onmaintenability of random graph distributions and simulability of families of probabilitydistributions over integers in our local random model. Special attention hasbeen paid to efficient simulation of particular distributions we were interested in(certain binomial distributions). The latter has been obtained through the use ofproperties of a new generation tree for permutations, which has been introducedalong the way

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\".

The paper maps the use of the principle of randomness in artistic activity with a focus on visual art and the placement of Czech art into the world context. It examines the hypothesis whether randomness in the hands of the artist becomes an instrument to objectify his or her work and to approach the general principles of the natural world, which, according to the assumption, add novelty and consequently increases its artistic value. The text begins with an etymological interpretation of the concept of randomness, further observes the randomness as phenomenon in various social spheres, and eventually presents the artistic movements and artworks that systematically use randomness. An overview of avant-garde art and abstraction of the first half of the 20th century will allow the author to interpret the principles of randomness used in computer art. The work concludes with a detailed analysis of Zdeněk Sýkora's work, in which, according to the author, the development line of precomputational art is mirrored, along with a breakthrough to digital tools. The conclusion of the work reveals the diversity of the application of the principle of randomness in the art world and finds a common divisor in the objectivizing function, respectively the rising aesthetic value. Through this interpretation, Zdeněk...

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.

This paper presents the overall sinkhole distributions and conducts hypothesis tests of sinkhole distributions and sinkhole formation using data stored in the Karst Feature Database (KFD) of Minnesota. Nearest neighbor analysis (NNA) was extended to include different orders of NNA, different scales of concentrated zones of sinkholes, and directions to the nearest sinkholes. The statistical results, along with the sinkhole density distribution, indicate that sinkholes tend to form in highly concentrated zones instead of scattered individuals. The pattern changes from clustered to random to regular as the scale of the analysis decreases from 10-100 km2 to 5-30 km 2 to 2-10 km2. Hypotheses that may explain this phenomenon are: (1) areas in the highly concentrated zones of sinkholes have similar geologic and topographical settings that favor sinkhole formation; (2) existing sinkholes change the hydraulic gradient in the surrounding area and increase the solution and erosional processes that eventually form more new sinkholes.

No description available.