A presente dissertação investiga o argumento da distinção real entre corpo e alma presente nas Meditações Metafísicas. O objetivo central é explicar o motivo pelo qual, nesta obra, a separabilidade entre corpo e alma é posta como condição suficiente para esse tipo de distinção. Para isso, percorre, ao longo das Meditações, os conceitos de alma, de corpo e de percepção clara e distinta. Faz uma análise do argumento da distinção real entre corpo e alma exposto na Sexta Meditação e, em seguida, se utiliza das discussões de Descartes com Caterus e Arnauld presente nas Objeções e Respostas visando a esclarecer pontos do argumento que ainda permanecem obscuros. Mostra, com o estudo das Meditações associado às Objeções e Respostas, que a distinção real é aquela que se dá entre substâncias e que ser substância é ser separável. Assim, sendo o reconhecimento da separabilidade de duas coisas o reconhecimento de que essas coisas são substâncias – e, portanto, de que são realmente distintas – explica, com isso, o motivo pelo qual a separabilidade é condição suficiente para a distinção real entre corpo e alma e conclui que ela lhe é, também, uma condição necessária. / This dissertation investigates the argument of the real distinction between body and soul presented on the Meditations on First Philosophy. The main goal is to explain the reason why the separability between body and soul is considered sufficient condition for this sort of distinction. In order to reach its goal, along the Meditations, it takes the path through the concepts of soul, body and the clear and distinct perception. It analyses the argument of the real distinction between body and soul presented on the Sixth Meditation and afterwards it makes use of Descartes’ discussions with Caterus and Arnauld, presented on Objections and Replies, seeking to clarify points of the argument that yet remain obscure. Studying the Meditations associated with the Objections and Replies, this dissertation shows that the real distinction is the one that happens between substances and that being a substance is being separable. Thus, being the recognition of the separability of two things the recognition of that those things are substances – and, hence, that they are really distinct – it explains the reason why the separability is sufficient condition for the real distinction between body and soul. It concludes that the separability is also a necessary condition to that sort of distinction.

Orientadores: Reginaldo Palazzo Junior, Carlile Lavor / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-11T20:14:12Z (GMT). No. of bitstreams: 1 Gazzoni_WanessaCarla_D.pdf: 915784 bytes, checksum: d9b26e53c10c74a95fabe11a016027ce (MD5) Previous issue date: 2008 / Resumo: Este trabalho apresenta algumas contribuições para um melhor entendimento do emaranhamento quântico e suas aplicações. Com o propósito de obter a classificação de estados quânticos puros arbitrários em separáveis ou emaranhados, apresentamos um critério de separabilidade do qual tal classificação decorre. Este critério está baseado em uma interpretação homológicageométrica, que nos permitiu formalizar algumas conclusões acerca da quantificação do emaranhamento em estados puros arbitrários com três qubits. A partir desta interpretação, foi possível também associar a descriçãao do conteúdo dos kets de um estado puro arbitrário a conceitos de teoria da codificação clássica. Tendo como base esta associação, propomos uma forma bastante simplificada para determinar a descrição matemática de estados puros arbitrários que satisfazem o máximo emaranhamento global. De acordo com conceitos da teoria da codificação, analisamos os estados de máximo emaranhamento global com relaçãoo 'a proteção contra erros que esses estados possuem. Neste contexto, apresentamos uma nova classe de estados que ainda Não havia sido mencionada na literatura. / Abstract: In this thesis we present some contributions to a better understanding of quantum entanglement and its applications. With the purpose of obtaining a classification of the arbitrary pure quantum states as separable or entangled, a separability criterion is presented. This criterion is based on an homologic-geometric interpretation which allowed us to formalize some conclusions on the entanglement quantification of arbitrary pure states with three qubits. From this interpretation, it was possible to associate a description of the kets' content of an arbitrary pure state with the concepts of the classical coding theory. Based on this association, we propose a simplified form to determine a mathematical description of arbitrary quantum states satisfying the maximum global entanglement. From the concepts of coding theory we considered the states of maximum global entanglement with respect to its inherent error protection. In this context, we present a new class of states satisfying all the previous properties and which were not known in the open literature. / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

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Evaluating separability is fundamental to pattern recognition. A plethora of embedding methods, such as dimension reduction and network embedding algorithms, have been developed to reveal the emergence of geometrical patterns in a low-dimensional space, where high-dimensional sample and node similarities are approximated by geometrical distances. However, statistical measures to evaluate the separability attained by the embedded representations are missing. Traditional cluster validity indices (CVIs) might be applied in this context, but they present multiple limitations because they are not specifically tailored for evaluating the separability of embedded results. This work introduces a new rationale called projection separability (PS), which provides a methodology expressly designed to assess the separability of data samples in a reduced (i.e., low-dimensional) geometrical space. In a first case study, using this rationale, a new class of indices named projection separability indices (PSIs) is implemented based on four statistical measures: Mann-Whitney U-test p-value, Area Under the ROC-Curve, Area Under the Precision-Recall Curve, and Matthews Correlation Coefficient. The PSIs are compared to six representative cluster validity indices and one geometrical separability index using seven nonlinear datasets and six different dimension reduction algorithms. In a second case study, the PS rationale is extended to define and measure the geometric separability (linear and nonlinear) of mesoscale patterns in complex data visualization by solving the traveling salesman problem, offering experimental evidence on the evaluation of community separability of network embedding results using eight real network datasets and three network embedding algorithms. The results of both studies provide evidence that the implemented statistical-based measures designed on the basis of the PS rationale are more accurate than the other indices and can be adopted not only for evaluating and comparing the separability of embedded results in the low-dimensional space but also for fine-tuning embedding algorithms’ hyperparameters. Besides these advantages, the PS rationale can be used to design new statistical-based separability measures other than the ones presented in this work, providing the community with a novel and flexible framework for assessing separability.

Les générateurs stochastiques de temps sont des modèles numériques capables de générer des séquences de données climatiques de longueur souhaitée avec des propriétés statistiques similaires aux données observées. Ces modèles sont de plus en plus utilisés en sciences du climat, hydrologie, agronomie. Cependant, peu de générateurs permettent de simuler plusieurs variables, dont les précipitations, en différents sites d’une région. Dans cette thèse, nous proposons un modèle original de générateur stochastique basé sur un champ gaussien multivarié spatio-temporel. Un premier travail méthodologique a été nécessaire pour développer un modèle de covariance croisée entièrement non séparable adapté à la nature spatio-temporelle multivariée des données étudiées. Cette covariance croisée est une généralisation au cas multivarié du modèle non séparable spatio-temporel de Gneiting dans le cas de la famille de Matérn. La démonstration de la validité du modèle et l’estimation de ses paramètres par maximum de vraisemblance par paires pondérées sont présentées. Une application sur des données climatiques démontre l’intérêt de ce nouveau modèle vis-à-vis des modèles existants. Le champ gaussien multivarié permet la modélisation des résidus des variables climatiques (hors précipitation). Les résidus sont obtenus après normalisation des variables par des moyennes et écarts-types saisonniers, eux-mêmes modélisés par des fonctions sinusoïdales. L’intégration des précipitations dans le générateur stochastique nécessite la transformation d’une composante du champ gaussien par une fonction d’anamorphose. Cette fonction d’anamorphose permet de gérer à la fois l’occurrence et l’intensité des précipitations. La composante correspondante du champ gaussien correspond ainsi à un potentiel de pluie, corrélé aux autres variables par la fonction de covariance croisée développée dans cette thèse. Notre générateur stochastique de temps a été testé sur un ensemble de 18 stations réparties en zone à climat méditerranéen (ou proche) en France. La simulation conditionnelle et non conditionnelle de variables climatiques journalières (températures minimales et maximales, vitesse moyenne du vent, rayonnement solaire et précipitation) pour ces 18 stations soulignent les bons résultats de notre modèle pour un certain nombre de statistiques / Stochastic weather generators are numerical models able to simulate sequences of weather data with similar statistical properties than observed data. However, few of them are able to simulate several variables (with precipitation) at different sites from one region. In this thesis, we propose an original model of stochastic generator based on a spatio-temporal multivariate Gaussian random field. A first methodological work was needed to develop a completely non separable cross-covariance function suitable for the spatio-temporal multivariate nature of studied data. This cross-covariance function is a generalization to the multivariate case of spatio-temporal non-separable Gneiting covariance in the case of the family of Matérn. The proof of the validity of the model and the estimation of its parameters by weighted pairwise maximum likelihood are presented. An application on weather data shows the interest of this new model compared with existing models. The multivariate Gaussian random field allows the modeling of weather variables residuals (excluding precipitation). Residuals are obtained after normalization of variables by seasonal means and standard deviations, themselves modeled by sinusoidal functions. The integration of precipitation in the stochastic generator requires the transformation of a component of the Gaussian random field by an anamorphosis function. This anamorphosis function can manage both the occurrence and intensity of precipitation. The corresponding component of the Gaussian random field corresponds to a rain potential, correlated with other variables by the cross-covariance function developed in this thesis. Our stochastic weather generator was tested on a set of 18 stations distributed over the Mediterranean area (or close) in France. The conditional and non-conditional simulation of daily weather variables (maximum and minimum temperature, average wind speed, solar radiation and precipitation) for these 18 stations show good result for a number of statistics.

<p>This thesis is based on five papers addressing variance reduction in different ways. The papers have in common that they all present new numerical methods.</p><p>Paper I investigates quantitative structure-retention relationships from an image processing perspective, using an artificial neural network to preprocess three-dimensional structural descriptions of the studied steroid molecules.</p><p>Paper II presents a new method for computing free energies. Free energy is the quantity that determines chemical equilibria and partition coefficients. The proposed method may be used for estimating, e.g., chromatographic retention without performing experiments.</p><p>Two papers (III and IV) deal with correcting deviations from bilinearity by so-called peak alignment. Bilinearity is a theoretical assumption about the distribution of instrumental data that is often violated by measured data. Deviations from bilinearity lead to increased variance, both in the data and in inferences from the data, unless invariance to the deviations is built into the model, e.g., by the use of the method proposed in paper III and extended in paper IV.</p><p>Paper V addresses a generic problem in classification; namely, how to measure the goodness of different data representations, so that the best classifier may be constructed. </p><p>Variance reduction is one of the pillars on which analytical chemistry rests. This thesis considers two aspects on variance reduction: before and after experiments are performed. Before experimenting, theoretical predictions of experimental outcomes may be used to direct which experiments to perform, and how to perform them (papers I and II). After experiments are performed, the variance of inferences from the measured data are affected by the method of data analysis (papers III-V).</p>

This thesis is based on five papers addressing variance reduction in different ways. The papers have in common that they all present new numerical methods. Paper I investigates quantitative structure-retention relationships from an image processing perspective, using an artificial neural network to preprocess three-dimensional structural descriptions of the studied steroid molecules. Paper II presents a new method for computing free energies. Free energy is the quantity that determines chemical equilibria and partition coefficients. The proposed method may be used for estimating, e.g., chromatographic retention without performing experiments. Two papers (III and IV) deal with correcting deviations from bilinearity by so-called peak alignment. Bilinearity is a theoretical assumption about the distribution of instrumental data that is often violated by measured data. Deviations from bilinearity lead to increased variance, both in the data and in inferences from the data, unless invariance to the deviations is built into the model, e.g., by the use of the method proposed in paper III and extended in paper IV. Paper V addresses a generic problem in classification; namely, how to measure the goodness of different data representations, so that the best classifier may be constructed. Variance reduction is one of the pillars on which analytical chemistry rests. This thesis considers two aspects on variance reduction: before and after experiments are performed. Before experimenting, theoretical predictions of experimental outcomes may be used to direct which experiments to perform, and how to perform them (papers I and II). After experiments are performed, the variance of inferences from the measured data are affected by the method of data analysis (papers III-V).

The uncertainty principle lies at the heart of quantum physics. It exhibits one of the key divergences between a classical and a quantum system: it is impossible to define a quantum state for which the values of two observables that do not commute are simultaneously specified with infinite precision. A paradigmatic example is given by Heisenberg’s original formulation of the uncertainty principle expressed in terms of variances of two canonically-conjugate variables, such as position x and momentum p, which was later generalized to a symplectic-invariant form by Schrödinger and Robertson. A different kind of uncertainty relations, originated by Białynicki-Birula and Mycielski, again for canonically-conjugate variables, relies on Shannon entropy instead of variances as a measure of uncertainty. In this thesis, we suggest several improvements of these entropic uncertainty relations and highlight the fact that they are better formulated in terms of entropy power, a notion borrowed from the information theory of real-valued signals. Our first novel entropic uncertainty relation takes x-p correlations into account and is consequently saturated by all pure Gaussian states in an arbitrary number of modes, improving on the original formulation by Białynicki-Birula and Mycielski. Our second main result is the derivation of an entropic uncertainty relation that holds for any n-tuples of not-necessarily canonically conjugate variables based on the matrix of their commutators. We then define a general form of the entropic uncertainty principle that combines both previous results. It expresses the incompatibility between two arbitrary variable n-uples and is saturated by all pure Gaussian states. Interestingly, we can also deduce from it the most general form of the Robertson uncertainty relation based on the covariance matrix of n variables.This line of research underlines the interest of defining an entropic uncertainty relation that is intrinsically invariant under symplectic transformations. Then, as a first attempt to reach this goal, we conjecture a symplectic-invariant uncertainty relation that is based on the joint differential entropy of the Wigner function. This conjecture is, however, only legitimate for states with a non-negative Wigner function. We also suggest a complex extension of this so-called Wigner entropy, which could provide the way towards an extension (and proof) of the above conjecture for all states. As a second attempt, we introduce the notion of multi-copy uncertainty observables, exploiting a connection with the algebra of angular momenta. Expressing the positivity of the variance of our multi-copy observable coincides with the Schrödinger-Robertson uncertainty relation, which suggests that the discrete Shannon entropy of such an uncertainty observable provides a new symplectic-invariant measure of uncertainty.Currently available separability criteria for continuous-variable systems imply a necessary and sufficient condition for a two-mode Gaussian state to be separable, but leave many entangled non-Gaussian states undetected. In this thesis, we introduce two improved separability criteria that enable a stronger entanglement detection. The first improved condition is based on the knowledge of an additional parameter, namely the degree of Gaussianity, and exploits a connection with Gaussianity-bounded uncertainty relations by Mandilara and Cerf. We exhibit families of non- Gaussian entangled states whose entanglement remains undetected by the Duan- Simon criterion. The second improved separability criterion is based on our improved entropic uncertainty relation that takes x-p correlations into account, and has the main advantage over the one proposed by Walborn et al. that it does not require any optimization procedure. / Le principe d’incertitude se situe au cœur de la physique quantique. Il représente l’une des différences majeures entre des systèmes classiques et quantiques, soit qu’il est impossible de définir un état quantique pour lequel deux observables qui ne commutent pas auraient des valeurs spécifiées simultanément et avec une précision infinie. La formulation originale du principe d’incertitude est due à Heisenberg et est exprimée en termes des variances de deux variables canoniquement conjuguées, telles que la position x et l’impulsion p. Cela fut par la suite généralisé par Schrödinger et Robertson qui ont donné au principe d’incertitude une forme invariante sous transformations symplectiques. Si l’incertitude est mesurée à l’aide de l’entropie différentielle de Shannon plutôt que des variances, il est alors possible de définir d’autres types de relations d’incertitude. Originellement introduites par Białynicki-Birula et Mycielski, elles expriment également l’incompatibilité entre deux variables canoniquement conjuguées. Dans cette thèse, nous proposons différentes améliorations de ces relations d’incertitude entropiques et mettons particulièrement l’accent sur le fait qu’elles s’expriment mieux sous forme de puissances entropiques, une notion empruntée à la théorie de l’information. En premier lieu, nous introduisons une nouvelle relation d’incertitude entropique qui tient compte des corrélations x-p et qui est par conséquent saturée par tous les états purs Gaussiens, ce qui représente une amélioration par rapport à la formulation originale de Białynicki- Birula et Mycielski. En second lieu, nous dérivons une relation d’incertitude entropique valide pour tous les n-uplets de variables non nécessairement canoniquement conjuguées et basée sur la matrice de leurs commutateurs. Nous définissons ensuite une forme plus générale du principe d’incertitude entropique qui combine les deux résultats précédents. Il exprime l’incompatibilité entre deux n-uplets arbitraires de variables et est saturé par tous les états purs Gaussiens. Notons que de ce principe d’incertitude entropique, nous pouvons déduire la forme la plus générale de la relation d’incertitude de Robertson, basée sur la matrice de covariance de n variables. Les résultats précédents soulignent un des points essentiels de notre axe de recherche: définir une relation d’incertitude entropique intrinsèquement invariante sous trans- formations symplectiques. Afin d’atteindre cet objectif, notre première tentative est de conjecturer une relation d’incertitude — invariante sous transformations symplectiques — basée sur l’entropie différentielle jointe de la fonction de Wigner. Cette conjecture n’est cependant légitime que pour des états décrits par une fonction de Wigner non-négative. Nous proposons aussi une extension complexe de cette en- tropie dite entropie de Wigner, qui pourrait ouvrir la voie vers une extension (et une preuve) de la conjecture proposée ci-dessus qui serait alors valide pour tous les états quantiques. Comme seconde tentative, en exploitant une connexion avec l’algèbre des moments angulaires, nous introduisons la notion d’observables d’incertitude agissant sur plusieurs copies d’un état. Exprimer la positivité de la variance de notre observable coïncide avec la relation d’incertitude de Schrödinger-Robertson, ce qui suggère que l’entropie discrète de Shannon d’une telle observable fournit une nouvelle mesure de l’incertitude. Cette relation d’incertitude est invariante sous transformations symplectiques.Les critères de séparabilité actuellement disponibles pour les variables continues donnent une condition nécessaire et suffisante afin qu’un état Gaussien bimodal soit séparable, mais laissent de nombreux états intriqués non-Gaussiens non détectés. Dans cette thèse, nous introduisons deux nouveaux critères de séparabilité qui permettent une meilleure détection de l’intrication. La première nouvelle condition est basée sur la connaissance d’un paramètre supplémentaire, à savoir le degré de Gaussianité de l’état, et exploite une connexion avec les relations d’incertitude de Mandilara et Cerf bornées par ce degré de Gaussianité. En particulier, nous donnons l’exemple de familles d’états intriqués non Gaussiens dont l’intrication est détectée par notre critère, mais pas par celui de Duan-Simon. Le second critère de séparabil- ité entropique que nous proposons est basé sur notre nouvelle relation d’incertitude entropique qui tient compte des corrélations x-p. Son principal avantage par rapport au critère de Walborn et al. est de ne nécessiter aucune procédure d’optimisation. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Cette thèse s'attache à décrire des algorithmes qui répondent à des questions provenant de la théorie des anneaux et des modules. Nous restreindrons essentiellement notre étude à des algorithmes déterministes, en temps polynomial, ainsi qu'aux anneaux et modules finis. Le premier des principaux résultats de cette thèse concerne le problème de l'isomorphisme entre modules : nous décrivons deux algorithmes distincts qui, étant donnée un anneau fini R et deux R-modules M et N finis, déterminent si M et N sont isomorphes. S'ils le sont, les deux algorithmes exhibent un tel isomorphisme. De plus, nous montrons comment calculer un ensemble de générateurs de taille minimale pour un module donné, et comment construire des couvertures projectives et des enveloppes injectives. Nous décrivons ensuite des tests mettant en évidence le caractère simple, projectif ou injectif d'un module, ainsi qu'un test constructif de l'existence d'un homomorphisme demodules surjectif entre deux modules finis, l'un d'entre eux étant projectif. Par contraste, nous montrons le résultat négatif suivant : le problème consistant à tester l'existence d'un homomorphisme de modules injectif entre deux modules, l'un des deux étant projectif, est NP-complet.La dernière partie de cette thèse concerne le problème de l'approximation du radical de Jacobson d'un anneau fini. Il s'agit de déterminer un idéal bilatère nilpotent tel que l'anneau quotient correspondant soit \presque" semi-simple. La notion de \semi-simplicité approchée" que nous utilisons est la séparabilité. / In this thesis we are interested in describing algorithms that answer questions arising in ring and module theory. Our focus is on deterministic polynomial-time algorithms and rings and modules that are finite. The first main result of this thesis concerns the module isomorphism problem: we describe two distinct algorithms that, given a finite ring R and two finite R-modules M and N, determine whether M and N are isomorphic. If they are, the algorithms exhibit such a isomorphism. In addition, we show how to compute a set of generators of minimal cardinality for a given module, and how to construct projective covers and injective hulls. We also describe tests for module simplicity, projectivity, and injectivity, and constructive tests for existence of surjective module homomorphisms between two finite modules, one of which is projective. As a negative result, we show that the problem of testing for existence of injective module homomorphisms between two finite modules, one of which is projective, is NP-complete. The last part of the thesis is concerned with finding a good working approximation of the Jacobson radical of a finite ring, that is, a two-sided nilpotent ideal such that the corresponding quotient ring is \almost" semisimple. The notion we use to approximate semisimplicity is that of separability.

The present thesis can be divided in three parts: 1) Quantum gate teleportation; 2) Numerical search of universal entanglers; 3) Connections between quantum information and number theory. Regarding the quantum gate teleportation, a separability criterion of normal matrices is used to find the analytical conditions of the preservation of separability under conjugation. That analytical condition allowed to find the general formula of an element of $mathbb{C}^{4}$ Clifford group, as well to understand the role of the basis of measurement in the quantum gate teleportation protocol. Considering the searching for universal entanglers, the same separability criterion of normal matrices was used as fitness function in a computational heuristics, in prder to find good candidates for universal entanglers in $mathbb{C}^{3} otimes mathbb{C}^{4}$ and $mathbb{C}^{4} otimes mathbb{C}^{4}$ Hilbert spaces. At last, in the connection of quantum information with the number theory, it is presented the study of the preparation and entanglement of several multi-qubit quantum states based in integer sequences, and the Riemannian quantum circuit, a quantum circuit whose eigenvalues are related to the zeros of the Riemann zeta function. The existence of such circuit proves that is always possible to construct a physical system related to a finite amount of zeros. / A presente tese està dividida em trÃs partes: 1) TeleportaÃÃo de portas quÃnticas; 2) Busca numÃrica por entrelaÃadores universais; 3) ConexÃes entre a informaÃÃo quÃntica e a teoria dos nÃmeros. No que diz a teleportaÃÃo de portas quÃnticas, um critÃrio de separabilidade para matrizes normais à usada para encontrar as condiÃÃes analÃticas da preservaÃÃo da separabilidade sob conjugaÃÃo. Tais condiÃÃes analÃticas permitiram encontrar a forma geral de um elemento do grupo de Clifford em $mathbb{C}^{4}$, assim como tambÃm entender o papel da base de mediÃÃo no protocolo de teleportaÃÃo de portas quÃnticas. Considerando a busca por entrelaÃadores universais, o mesmo critÃrio de separabilidade de matrizes normais foi utilizado como funÃÃo de aptidÃo em uma heurÃstica computacional aplicada para encontrar bons candidatos a entrelaÃadores universais nos espaÃos de Hilbert de dimensÃes $mathbb{C}^{3} otimes mathbb{C}^{4}$ e $mathbb{C}^{4} otimes mathbb{C}^{4}$. Por fim, sobre as conexÃes da informaÃÃo quÃntica com a teoria dos nÃmeros, à apresentado um estudo da preparaÃÃo e entrelaÃamento de vÃrios estados quÃnticos de mÃltiplos qubits baseados em sequÃncias de nÃmeros inteiros. Apresenta-se ainda o circuito quÃntico Riemanniano, um circuito quÃntico cujos autovalores sÃo relacionados aos zeros da funÃÃo Zeta de Riemann. A existÃncia deste circuito prova que à sempre possÃvel construir um sistema fÃsico relacionado a uma quantidade finita de zeros.