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# DEMAT - Departamento de Matemática

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### Navegando DEMAT - Departamento de Matemática por Autor "Almeida, Alexandre Celestino Leite de"

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Item Data-driven inference for the spatial scan statistic.(2011) Almeida, Alexandre Celestino Leite de; Duarte, Anderson Ribeiro; Duczmal, Luiz Henrique; Oliveira, Fernando Luiz Pereira de; Takahashi, Ricardo Hiroshi CaldeiraMostrar mais Background: Kulldorff’s spatial scan statistic for aggregated area map s searches for cluster s of case s without specifying their size (numb er of areas) or geo graphic location in advance . Their statistical significance is tested while adjusting for the multiple testing inherent in such a procedure. However, as is shown in this work, this adjustment is not don e in an even manner for all possible cluster sizes .Results: A modification is proposed to the usual inference test of the spatial scan statistic, incorporating additional information about the size of the most likely cluster found. A new interpretation of the results of the spatial scan statistic is done, posing a modified inference question: what is the probability that the null hypo thesis is rejected for the original observed cases map with a most likely cluster of size k, taking into account only those most likely clusters of size k found un der null hypothesis for comparison? This question is especially important when the p-value computed by the usual inference process is near the alpha significance level, regarding the correctness of the decision based in this inference. Conclusions : A practical procedure is provide d to make more accurate inferences about the most likely cluster found by the spatial scan statistic.Mostrar mais Item Roughness as classicality indicator of a quantum state.(2018) Lemos, Humberto César Fernandes; Almeida, Alexandre Celestino Leite de; Amaral, Barbara Lopes; Oliveira, Adélcio Carlos deMostrar mais We define a new quantifier of classicality for a quantum state, the Roughness, which is given by the L2(R2)distance between Wigner and Husimi functions. We show that the Roughness is bounded and therefore it is a useful tool for comparison between different quantum states for single bosonic systems. The state classification via the Roughness is not binary, but rather it is continuous in the interval [0, 1], being the state more classic as the Roughness approaches to zero, and more quantum when it is closer to the unity. The Roughness is maximum for Fock states when its number of photons is arbitrarily large, and also for squeezed states at the maximum compression limit. On the other hand, the Roughness approaches its minimum value for thermal states at infinite temperature and, more generally, for infinite entropy states. The Roughness of a coherent state is slightly below one half, so we may say that it is more a classical state than a quantum one. Another important result is that the Roughness performs well for discriminating both pure and mixed states. Since the Roughness measures the inherent quantumness of a state, we propose another function, the Dynamic Distance Measure (DDM), which is suitable for measure how much quantum is a dynamics. Using DDM, we studied the quartic oscillator, and we observed that there is a certain complementarity between dynamics and state, i.e. when dynamics becomes more quantum, the Roughness of the state decreases, while the Roughness grows as the dynamics becomes less quantum.Mostrar mais