In the first two Chapters I outline the theory and background of separation of variables as an ansatz for solving fundamental partial differential equations (pdes) in Mathematical Physics. Two fundamental approaches will be highlighted, and more modern approaches discussed. In Chapter 3 I calculate the general trace-free conformal Killing tensor defined in Euclidean space - from the sum of symmetric tensor products of conformal Killing vectors. In Chapter 4 I determine the subcases with rotational symmetry and recover known examples pertaining to classical rotational coordinates. In Chapter 5 I obtain the induced action of the conformal group on the space of trace-free conformal Killing tensors. In Chapter 6 I use the invariants of trace-free conformal Killing tensors under the action of the conformal group to characterize, up to equivalence, the symmetric R-separable webs in E^3 that permit conformal separation of variables of the fundamental pdes in Mathematical Physics. In Chapter 7 the asymmetric R-separable metrics are obtained via a study of the separability conditions for the conformally invariant Laplace equation.

Given a bipartite density matrix ρ of a quantum state, the Quantum Separability problem (QUSEP) asks — is ρ entangled, or separable? In this thesis, we first strengthen Gurvits’ 2003 NP-hardness result for QUSEP by showing that the Weak Membership problem over the set of separable bipartite quantum states is strongly NP-hard, meaning it is NP-hard even when the error margin is as large as inverse polynomial in the dimension, i.e. is “moderately large”. Previously, this NP-hardness was known only to hold in the case of inverse exponential error. We observe the immediate implication of NP-hardness of the Weak Membership problem over the set of entanglement-breaking maps, as well as lower bounds on the maximum (Euclidean) distance possible between a bound entangled state and the separable set of quantum states (assuming P ≠ NP). We next investigate the entanglement-detecting capabilities of locally invariant unitary operations, as proposed by Fu in 2006. Denoting the subsystems of ρ as A and B, such that ρ_B = Tr_A(ρ), a locally invariant unitary operation U^B is one with the property U^B ρ_B (U^B)^† = ρ_B. We investigate the maximum shift (in Euclidean distance) inducible in ρ by applying I⊗U^B, over all locally invariant choices of U^B. We derive closed formulae for this quantity for three cases of interest: (pseudo)pure quantum states of arbitrary dimension, Werner states of arbitrary dimension, and two-qubit states. Surprisingly, similar to recent anomalies detected for non-locality measures, the first of these formulae demonstrates the existence of non-maximally entangled states attaining shifts as large as maximally entangled ones. Using the latter of these formulae, we demonstrate for certain classes of two-qubit states an equivalence between the Fu criterion and the CHSH inequality. Among other results, we investigate the ability of locally invariant unitary operations to detect bound entanglement.

In the first two Chapters I outline the theory and background of separation of variables as an ansatz for solving fundamental partial differential equations (pdes) in Mathematical Physics. Two fundamental approaches will be highlighted, and more modern approaches discussed. In Chapter 3 I calculate the general trace-free conformal Killing tensor defined in Euclidean space - from the sum of symmetric tensor products of conformal Killing vectors. In Chapter 4 I determine the subcases with rotational symmetry and recover known examples pertaining to classical rotational coordinates. In Chapter 5 I obtain the induced action of the conformal group on the space of trace-free conformal Killing tensors. In Chapter 6 I use the invariants of trace-free conformal Killing tensors under the action of the conformal group to characterize, up to equivalence, the symmetric R-separable webs in E^3 that permit conformal separation of variables of the fundamental pdes in Mathematical Physics. In Chapter 7 the asymmetric R-separable metrics are obtained via a study of the separability conditions for the conformally invariant Laplace equation.

Given a bipartite density matrix ρ of a quantum state, the Quantum Separability problem (QUSEP) asks — is ρ entangled, or separable? In this thesis, we first strengthen Gurvits’ 2003 NP-hardness result for QUSEP by showing that the Weak Membership problem over the set of separable bipartite quantum states is strongly NP-hard, meaning it is NP-hard even when the error margin is as large as inverse polynomial in the dimension, i.e. is “moderately large”. Previously, this NP-hardness was known only to hold in the case of inverse exponential error. We observe the immediate implication of NP-hardness of the Weak Membership problem over the set of entanglement-breaking maps, as well as lower bounds on the maximum (Euclidean) distance possible between a bound entangled state and the separable set of quantum states (assuming P ≠ NP). We next investigate the entanglement-detecting capabilities of locally invariant unitary operations, as proposed by Fu in 2006. Denoting the subsystems of ρ as A and B, such that ρ_B = Tr_A(ρ), a locally invariant unitary operation U^B is one with the property U^B ρ_B (U^B)^† = ρ_B. We investigate the maximum shift (in Euclidean distance) inducible in ρ by applying I⊗U^B, over all locally invariant choices of U^B. We derive closed formulae for this quantity for three cases of interest: (pseudo)pure quantum states of arbitrary dimension, Werner states of arbitrary dimension, and two-qubit states. Surprisingly, similar to recent anomalies detected for non-locality measures, the first of these formulae demonstrates the existence of non-maximally entangled states attaining shifts as large as maximally entangled ones. Using the latter of these formulae, we demonstrate for certain classes of two-qubit states an equivalence between the Fu criterion and the CHSH inequality. Among other results, we investigate the ability of locally invariant unitary operations to detect bound entanglement.

In this dissertation, we explore the properties of correlation structure for spatio-temporal point processes and a quantitative spatial process. Spatio-temporal point processes are often assumed to be separable; we propose a formal approach for testing whether a particular data set is indeed separable. Because of the resampling methodology, the approach requires minimal conditions on the underlying spatio-temporal process to perform the hypothesis test, and thus is appropriate for a wide class of models. Africanized Honey Bees (AHBs, Apis mellifera scutellata) abscond more frequently and defend more quickly than colonies of European origin. That they also utilize smaller cavities for building colonies expands their range of suitable hive locations to common objects in urban environments. The aim of the AHB study is to create a model of this quantitative spatial process to predict where AHBs were more likely to build a colony, and to explore what variables might be related to the occurrences of colonies. We constructed two generalized linear models to predict the habitation of water meter boxes, based on surrounding landscape classifications, whether there were colonies in surrounding areas, and other variables. The presence of colonies in the area was a strong predictor of whether AHBs occupied a water meter box, suggesting that AHBs tend to form aggregations, and that the removal of a colony from a water meter box may make other nearby boxes less attractive to the bees.

Missile Detection System (MDS) is one of the main components of a self-protection system developed against the threat of guided missiles for airborne platforms. The requirements such as time critical operation and high accuracy in classification performance make the &lsquo / Pattern Recognition&rsquo / problem of an MDS a hard task. Problem can be defined in two main parts such as &lsquo / Feature Set Evaluation&rsquo / (FSE) and &lsquo / Classifier&rsquo / designs. The main goal of feature set evaluation is to employ a dimensionality reduction process for the input data set, while not disturbing the classification performance in the result. In this thesis study, FSE approaches are investigated for the pattern recognition problem of a generic MDS. First, synthetic data generation is carried out in software environment by employing generic models and assumptions in order to reflect the nature of a realistic problem environment. Then, data sets are evaluated in order to draw a baseline for further feature set evaluation approaches. Further, a theoretical background including the concepts of Class Separability, Feature Selection and Feature Extraction is given. Several widely used methods are assessed in terms of convenience for the problem by giving necessary justifications depending on the data set characteristics. Upon this background, software implementations are performed regarding several feature set evaluation techniques. Simulations are carried out in order to process dimensionality reduction. For the evaluation of the resulting data sets in terms of classification performance, software implementation of a classifier is realized. Resulting classification performances of the applied approaches are compared and evaluated.

<p>One way of modeling human knowledge is by using multidimensional spaces, in which an object is represented as a point in the space, and the distances among the points reflect the similarities among the represented objects. The distances are measured with some metric, commonly some instance of the Minkowski metric. The instances differ with the magnitude of the so-called r-parameter. The instances most commonly mentioned in the literature are the ones where r equals 1, 2 and infinity.</p><p>Cognitive scientists have found out that different metrics are suited to describe different dimensional combinations. From these findings an important distinction between integral and separable dimensions has been stated (Garner, 1974). Separable dimensions, e.g. size and form, are best described by the city-block metric, where r equals 1, and integral dimensions, such as the color dimensions, are best described by the Euclidean metric, where r equals 2. Developmental psychologists have formulated a hypothesis saying that small children perceive many dimensional combinations as integral whereas adults perceive the same combinations as separable. Thus, there seems to be a shift towards increasing separability with age or maturity.</p><p>Earlier experiments show the same phenomenon in adult short-term learning with novel stimuli. In these experiments, the stimuli were first perceived as rather integral and were then turning more separable, indicated by the Minkowski-r. This indicates a shift towards increasing separability with familiarity or skill.</p><p>This dissertation aims at investigating the generality of this phenomenon. Five similarity-rating experiments are conducted, for which the best fitting metric for the first half of the session is compared to the last half of the session. If the Minkowski-r is lower for the last half compared to the first half, it is considered to indicate increasing separability.</p><p>The conclusion is that the phenomenon of increasing separability during short-term learning cannot be found in these experiments, at least not given the operational definition of increasing separability as a function of a decreasing Minkowski-r. An alternative definition of increasing separability is suggested, where an r-value ‘retreating’ 2.0 indicates increasing separability, i.e. when the r-value of the best fitting metric for the last half of a similarity-rating session is further away from 2.0 compared to the first half of the session.</p>

Dans cette thèse, on s’intéresse à un problème inverse classique en ingénierie pétrolière, àsavoir le calage d’historique. Plus précisément, une nouvelle méthode de paramétrisation géostatistiqueainsi qu’un nouvel algorithme d’optimisation sans dérivées adaptés aux particularitésdu problème sont présentés ici. La nouvelle méthode de paramétrisation repose sur les principes des méthodes de déformation graduelle et de déformation de domaines. Comme la déformation graduelle locale, elle consiste àcombiner à l’intérieur de zones préalablement définies deux réalisations ou plus de modèle avec lapossibilité supplémentaire de modifier dynamiquement la forme des zones choisies. La flexibilitéapportée par cette méthode dans le choix des zones a ainsi permis de garantir l’obtention d’unbon point initial pour l’optimisation. Concernant l’optimisation, l’hypothèse que les paramètres locaux dans le modèle de réservoir n’influent que faiblement sur les données de puits distants conduit à considérer que la fonction àoptimiser est à variables partiellement séparables. La nouvelle méthode d’optimisation développée,nommée DFO-PSOF, de type région de confiance avec modèle quadratique d’interpolation,exploite alors au maximum cette propriété de séparabilité partielle. Les résultats numériquesobtenus sur plusieurs cas de réservoir valident à la fois l’hypothèse effectuée ainsi que la qualitéde l’algorithme pour le problème de calage d’historique. En complément de cette validation numérique,un résultat théorique de convergence vers un point critique est prouvé pour la méthoded’optimisation construite / We worked in this thesis on a classical inverse problem in the petroleum industry, historymatching. We proposed a new geostatistical parameterization technique as well as a new derivativefree optimization algorithm adapted to the problem specificities. The parameterization method is based on two approaches found in the literature, the local gradual deformation method and the domain deformation method. Similarly to the local gradual deformation method, our method combines two or more model realizations inside previouslydefined zones. Moreover, our method adds the possibility to dynamically update the shape ofthe zones during the optimization process. This property substantially improves its robustnesswith regard to the initial choice of the zones. Thus, the greater flexibility brought by our methodallowed us to develop an initialization methodology which garantees a good initial point for theoptimization. To reduce the number of evaluations needed to minimize the objective function, we madethe assumption that a local parameter does not influence the production data of a distantwell. With this hypothesis, the objective function is then considered partially separable. Theoptimization algorithm we developped, called DFO-PSOF, is a trust region algorithm basedon quadratic interpolation models which exploits this partial separability property. Numericalresults obtained on some reservoir test cases validate both the hypothesis and the quality of ouralgorithm for the history matching problem. Moreover, a theoretical convergence result towardsa first order critical point, is proved for this new optimization method

A demanda atual pela utilização de materiais reciclados na construção deve-se ao aumento crescente do consumo de agregados, à exaustão de jazidas próximas aos grandes centros e à proibição de deposição de resíduos inertes em aterros sanitários. Paralelamente, com o crescimento evidente do setor da construção em muitos países, o gerenciamento dos resíduos de construção e demolição (RCD) tornou-se uma questão econômica e ambiental prioritária. Para a sustentabilidade do meio ambiente construído é imprescindível o desenvolvimento de novas aplicações para o agregado reciclado visando a ampliação das taxas de reciclagem. No entanto, a situação da fração areia de RCD é crítica, pois apesar de representar de 40 a 60% em massa do resíduo, é descartada como resíduo da própria reciclagem ou utilizada em aplicações de baixo valor agregado. Dentro deste contexto, o objetivo deste trabalho consiste em estudar alternativas para a produção de areia reciclada a partir do processamento integral de resíduos de construções e demolições da região metropolitana de São Paulo, em uma abordagem inédita mundialmente. O estudo realizado pode ser subdividido em quatro etapas principais: a) amostragem; b) produção de areia a partir dos resíduos amostrados; c) estudos de separabilidade da areia reciclada; d) caracterização tecnológica dos produtos gerados como ferramenta de controle de qualidade de eficiência dos processos. Os resultados demonstraram que o processamento integral de RCD por britagem terciária em impactador de eixo vertical é determinante na cominuição seletiva das fases porosas e na liberação entre a pasta de cimento e as fases minerais. O produto gerado apresentou menor conteúdo de pasta de cimento, partículas mais esféricas e reduzida porosidade. Adicionalmente demonstrou-se a separabilidade densitária e magnética entre as fases minerais dos agregados e a pasta de cimento. Dentre os procedimentos de caracterização destaca-se o desenvolvimento de uma metodologia para definição das associações das fases presentes, particularmente da individualização da pasta de cimento e carbonatos. / The current demand for recycling on construction is due to the increasing consumption of aggregates, the exhaustion of deposits close to large cities as well as the ban on inert materials dumping in landfills and the rising cost of its disposal. Moreover, with the remarkable increasing on construction activities in many countries, the management of Construction and Demolition Waste (CDW) became an economical and environmental priority issue. To the sustainability of the built environment, the development of new applications for recycled aggregates and the increase of recycling rates are vital. However, the situation of the sand fraction of CDW is critical; although it accounts for 40 to 60% by weight of the waste, it is disregarded as waste recycling material or used in applications with low added-value. In this context, the present research explores the potential of mineral processing technologies to produce recycled sand by total comminution of the CDW on sand fractions in an unprecedented approach worldwide. The improvement on recycled sand quality is crucial for the enlargement of recycling rates. The study may be described in four main steps: a) sampling of construction and demolition waste from Sao Paulo metropolitan area, Brazil; b) production of recycled sand from the sampled waste; c) separability studies of the recycled sand; d) technological characterization of the attained products to evaluate the processing efficiency. The results demonstrated that the processing of the whole waste by tertiary crushing is fundamental to the selective comminution of porous phases and to the separation of cement paste from mineral phases. The attained product exhibited reduced content of cement paste, particles with higher sphericity and lower porosity. Additionally, it was demonstrated that the separability of aggregates from cement paste is feasible by density and magnetic separation. Regarding the characterization procedures, the development of an innovative method for a precise evaluation of the content of cement paste and phases associations, must be highlighted, especially on the measurement of cement paste and carbonates separately.

One way of modeling human knowledge is by using multidimensional spaces, in which an object is represented as a point in the space, and the distances among the points reflect the similarities among the represented objects. The distances are measured with some metric, commonly some instance of the Minkowski metric. The instances differ with the magnitude of the so-called r-parameter. The instances most commonly mentioned in the literature are the ones where r equals 1, 2 and infinity. Cognitive scientists have found out that different metrics are suited to describe different dimensional combinations. From these findings an important distinction between integral and separable dimensions has been stated (Garner, 1974). Separable dimensions, e.g. size and form, are best described by the city-block metric, where r equals 1, and integral dimensions, such as the color dimensions, are best described by the Euclidean metric, where r equals 2. Developmental psychologists have formulated a hypothesis saying that small children perceive many dimensional combinations as integral whereas adults perceive the same combinations as separable. Thus, there seems to be a shift towards increasing separability with age or maturity. Earlier experiments show the same phenomenon in adult short-term learning with novel stimuli. In these experiments, the stimuli were first perceived as rather integral and were then turning more separable, indicated by the Minkowski-r. This indicates a shift towards increasing separability with familiarity or skill. This dissertation aims at investigating the generality of this phenomenon. Five similarity-rating experiments are conducted, for which the best fitting metric for the first half of the session is compared to the last half of the session. If the Minkowski-r is lower for the last half compared to the first half, it is considered to indicate increasing separability. The conclusion is that the phenomenon of increasing separability during short-term learning cannot be found in these experiments, at least not given the operational definition of increasing separability as a function of a decreasing Minkowski-r. An alternative definition of increasing separability is suggested, where an r-value ‘retreating’ 2.0 indicates increasing separability, i.e. when the r-value of the best fitting metric for the last half of a similarity-rating session is further away from 2.0 compared to the first half of the session.