Yes / The set of subsystems Sigma(m) of a finite quantum system Sigma(n) with variables in Z(n) together with logical connectives, is a Heyting algebra. The probabilities tau(m vertical bar rho(n)) Tr vertical bar B(m)rho(n)] (where B(m) is the projector to Sigma(m)) are compatible with associativity of the join in the Heyting algebra, only if the variables belong to the same chain. Consequently, contextuality in the present formalism, has the chains as contexts. Various Bell-like inequalities are discussed. They are violated, and this proves that quantum mechanics is a contextual theory.

This thesis is the synthesis of theoretical and experimental works performed in the area of quantum foundations, particularly on quantum correlations and experimental tests of multiplicative Bell inequalities. First we begin with a comprehensive theoretical work performed on the foundations of quantum mechanics, focusing on the puzzling concepts of quantum entanglement, and hidden variable theories. Specifically, we present a broad overview of different classes of hidden variable theories such as local, crypto-nonlocal, contextual and non-local theories, along with several Bell like inequalities for these theories, providing theoretical proofs based on quantum mechanics for the falsification of some of these theories. Second we present a body of experimental, and theoretical works performed on a new class of Bell inequalities, i.e., the multiplicative Bell inequalities. We experimentally report the observation of the Bell parameters close to the Tsirelson (quantum) limit, upto a large number of measurement devices $(n)$, and compare the results with a particular deterministic strategy. We also obtain classical bounds for some $n$, and report the experimental violation of these classical limits. We theoretically derive new richer bounds on the CHSH inequality (named after John Clauser, Michael Horne, Abnor Shimony and Richard Holt) and the multiplicative Bell parameter for $n=2$, based on the principle of ``relativistic independence'', and experimentally observe the distribution of Bell parameters as predicted by these bounds.

Quantum theory is a probabilistic theory, where certain variables are hidden or non-accessible. It results in lack of representation of systems under study. However, I deduce system's representation in probabilistic manner, introducing probability of existence w, and quantize it exploiting Schrödinger's quantization rule. The formalism enriches probabilistic quantum theory, and enables system's representation in probabilistic manner.

no / The finite set of subsystems of a finite quantum system with variables in Z(n), is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more general concept than superposition. Consequently, the quantum probabilities related to commuting projectors in the subsystems, are incompatible with associativity of the join in the Heyting algebra, unless if the variables belong to the same chain. This leads to contextuality, which in the present formalism has as contexts, the chains in the Heyting algebra. Logical Bell inequalities, which contain "Heyting factors," are discussed. The formalism is also applied to the infinite set of all finite quantum systems, which is appropriately enlarged in order to become a complete Heyting algebra.

Submitted by Claudinei Pracidelli (cpracide@ipen.br) on 2016-11-11T09:45:23Z No. of bitstreams: 0 / Made available in DSpace on 2016-11-11T09:45:23Z (GMT). No. of bitstreams: 0 / Um desafio recorrente em processos produtivos é o desenvolvimento de sistemas de monitoração e diagnóstico. Esses sistemas ajudam na detecção de mudanças inesperadas e interrupções, prevenindo perdas e mitigando riscos. Redes Neurais Artificiais (RNA) têm sido largamente utilizadas na criação de sistemas de monitoração. Normalmente as RNA utilizadas para resolver este tipo de problema são criadas levando-se em conta apenas parâmetros como o número de entradas, saídas e quantidade de neurônios nas camadas escondidas. Assim, as redes resultantes geralmente possuem uma configuração onde há uma total conexão entre os neurônios de uma camada e os da camada seguinte, sem que haja melhorias em sua topologia. Este trabalho utiliza o algoritmo de Otimização por Colônia de Formigas (OCF) para criar redes neurais otimizadas. O algoritmo de busca OCF utiliza a técnica de retropropagação de erros para otimizar a topologia da rede neural sugerindo as melhores conexões entre os neurônios. A RNA resultante foi aplicada para monitorar variáveis do reator de pesquisas IEA-R1 do IPEN. Os resultados obtidos mostram que o algoritmo desenvolvido é capaz de melhorar o desempenho do modelo que estima o valor de variáveis do reator. Em testes com diferentes números de neurônios na camada escondida, utilizando como comparativos o erro quadrático médio, o erro absoluto médio e o coeficiente de correlação, o desempenho da RNA otimizada foi igual ou superior ao da tradicional. / Dissertação (Mestrado em Tecnologia Nuclear) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP

L'interprétation causale de la mécanique quantique a été décrite en premier lieu par les historiens comme une conséquence de l'influence croissante du marxisme chez les physiciens des pays occidentaux. En effet, au cours des années 1950, le noyau du groupe de physiciens impliqués dans le programme causal autour de Jean-Pierre Vigier et Louis de Broglie à l'Institut Henri Poincaré est majoritairement constitué soit de membres, soit de sympathisants du PCF. Leurs travaux sont fortement influencés par les critiques soviétiques contre l'interprétation dominante de la mécanique quantique, l'interprétation dite de Copenhague. Entre autres, Vigier critique le pragmatisme qui règne dans la physique de l'après-guerre et pense que le manque de réflexion philosophique est en grande partie responsable de la crise que traverse la physique fondamentale, telle que le problème de la renormalisation. Le groupe a également porté la question de l'interprétation de la théorie au sein du PCF d'où est née une controverse au sein du parti qui a soulevé la problématique de la relation entre le marxisme et la science.La théorie fait également partie d'un programme de recherche plus global lié aux questions contemporaines en physique. Ce point est souvent oublié, ce qui mène à la conclusion erronée que la motivation du groupe IHP est seulement de nature idéologique et, par conséquent, que leur activité est hors de la science. Dès 1957, en collaboration avec des physiciens japonais, le groupe a proposé une théorie des particules élémentaires et un système de classification, à une époque où une théorie consensuelle manque encore / The Causal Interpretation of Quantum Mechanics was in the first place described by historians as a consequence of the growing influence of Marxism among physicists in Western countries. Indeed, during the 1950s, the core of the group of physicists involved in the Causal program around Jean-Pierre Vigier and Louis de Broglie at the Institut Henri Poincaré was mainly constituted either of members or sympathizers of the PCF. Their works were strongly influenced by critics from Soviet Union against the mainstream interpretation of Quantum Mechanics, the so called Copenhagen interpretation. Vigier criticized the pragmatism which prevailed in the Postwar physics and thought that the lack of philosophical considerations was in great part responsible for the crisis in fundamental physics, such as the problem of renormalization. They also put the issue of the interpretation of the theory inside the PCF and created a controversy inside the party which raised the relationship between Marxism and science. The theory was also part of a more global research program linked with contemporary questions in physics. This point is often forgotten which leads to the erroneous conclusion that the motivation of the IHP group was only ideological and, therefore, their activity was out of science. As early as 1957, in collaboration with Japanese physicists, the group proposed a theory for elementary particles and a method of their classification, in a period in where a standard theory was still missing