Browsing by Author "Almeida, Alexandre Celestino Leite de"

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    Coberturas de tabuleiros : o problema do diamante de Aztec.
    (2019) Praxedes, Washington Mariano; Couto, Rodrigo Geraldo do; Couto, Rodrigo Geraldo do; Almeida, Alexandre Celestino Leite de; Alves, Rogério Gomes
    O objetivo deste trabalho é tratar de problemas gerais de coberturas de tabuleiros por poliminós, tendo como foco a análise da cobertura de uma região plana específica, denominada diamante de Aztec. Tal análise irá propor o estabelecimento da quantidade de coberturas distintas por dominós possíveis de serem realizadas nesta região. Além das ideias relacionadas aos problemas de cobertura de tabuleiros, o resultado é obtido a partir da utilização de estratégias bastante elegantes e engenhosas, tendo os conceitos da Teoria dos Grafos como ferramentas essenciais para modelar e encontrar uma relação de recorrência para resolver o problema. Nesse contexto, as teorias apresentadas tendem reforçar a justificativa de que o tema de Coberturas de Tabuleiros e demais regiões planas é um campo altamente rico e fértil para o desenvolvimento de projetos de oficinas de estudos de conteúdos da Matemática.
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    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 Caldeira
    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.
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    Roughness as classicality indicator of a quantum state.
    (2018) Lemos, Humberto César Fernandes; Almeida, Alexandre Celestino Leite de; Amaral, Barbara Lopes; Oliveira, Adélcio Carlos de
    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.
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    Space-time border analysis to evaluate and detect clusters.
    (2021) Duarte, Anderson Ribeiro; Silva, Spencer Barbosa da; Oliveira, Fernando Luiz Pereira de; Almeida, Alexandre Celestino Leite de; Duczmal, Luiz Henrique
    This article presents a statistic to identify the proportional intensity of an area to belong to a space-time cluster, which is very important in spatial statistics. A significant extension of the so-called F-function has been described in detail, which, associated with new technology, allows the evaluation of the intensity of change moments in the time process and outline possible occurrences of clusters. The justification of the study is performed through an extensive review of the current literature of the area. The developed algorithms are detailed via computational experiments with simulated data. Real situations are presented and discussed in detail. Finally, topics for future research are indicated.
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    Vertical social distancing policy is ineffective to contain the COVID-19 pandemic.
    (2020) Duczmal, Luiz Henrique; Almeida, Alexandre Celestino Leite de; Duczmal, Denise Bulgarelli; Alves, Claudia Regina Lindgren; Magalhães, Flávia Costa Oliveira; Lima, Max Sousa de; Silva, Ivair Ramos; Takahashi, Ricardo Hiroshi Caldeira
    Considering numerical simulations, this study shows that the so-called vertical social distancing health policy is ineffective to contain the COVID-19 pandemic. We present the SEIR-Net model, for a network of social group interactions, as a development of the classic mathematical model of SEIR epidemics (Susceptible-Exposed-Infected (symptomatic and asymptomatic)- Removed). In the SEIR-Net model, we can simulate social contacts between groups divided by age groups and analyze different strategies of social distancing. In the vertical distancing policy, only older people are distanced, whereas in the horizontal distancing policy all age groups adhere to social distancing. These two scenarios are compared to a control scenario in which no intervention is made to distance people. The vertical distancing scenario is almost as bad as the control, both in terms of people infected and in the acceleration of cases. On the other hand, horizontal distancing, if applied with the same intensity in all age groups, significantly reduces the total infected people “flattening the disease growth curve”. Our analysis considers the city of Belo Horizonte, Minas Gerais State, Brazil, but similar conclusions apply to other cities as well. Code implementation of the model in R-language is provided in the supplementary material.