O terço inferior da face exerce uma forte influência na estética dos indivíduos, e sabendo-se da importância do seu equilíbrio, e da contribuição do ortodontista quanto ao diagnóstico do perfil facial, o presente estudo teve por finalidades testar um método de correlação entre uma medida linear localizada a partir da região da glabela com medidas lineares anteroposteriores no terço inferior da face (Triviño, 2012), e verificar a previsibilidade de proporções anteroposteriores no terço inferior da face, a partir de uma linha de referência passando por um ponto na região da glabela. Desenhos anatômicos foram realizados através de telerradiografias em norma lateral de 120 indivíduos com harmonia facial, leucodermas e relação molar de classe I, com o intuito de estabelecer parâmetros cefalométricos para correlacionar referências anteroposteriores do terço inferior da face a partir das linhas Sv-PRT e PRTv, obtidas através do ponto PRT. A aplicabilidade do método foi realizada em um grupo de 24 indivíduos com perfil desagradável, em que considerou insatisfatória a aplicação das fórmulas de previsibilidade utilizando a linha Sv-PRT, como uma referência para determinar as proporções anteroposteriores do terço inferior da face em alguns pacientes. O método que considerou a linha PRTv como referência, através dos métodos estatísticos de correlação de Pearson e regressão linear múltipla, apresentou resultados estatisticamente significativos para todos os valores de referência nos indivíduos do gênero feminino e nos indivíduos do gênero masculino (PRTv-Ls, PRTv-Li e PRT-Pg\'). Foi utilizado o Teste t-Student para verificar que as medidas não foram estatisticamente significativas de acordo com o gênero. Os resultados deste estudo mostraram ser coerente considerar a região da glabela como uma referência de avaliação e diagnóstico para as proporções anteroposteriores do terço inferior da face. / The lower third of the face exerts a strong influence on the aesthetics of individuals, and knowing the importance of its balance, and the orthodontist\'s contribution to the diagnosis of the facial profile, the present study had the purpose to test a method of correlation between a linear measure located from the glabella region with linear anteroposterior measurements on the lower third of the face (Triviño, 2012), and verify the predictability of anteroposterior proportions in the lower third of the face, from a reference line through a point in the glabella region. Anatomical tracings from lateral cephalometric radiographs of 120 individuals with balanced profile, leucoderm and class I were performed in order to establish cephalometric parameters to correlate anteroposterior references of the lower third of the face from the lines Sv-PRT and PRTv, obtained through the PRT point. The applicability of the method was performed in a group of 24 individuals with an unpleasant profile, in which it considered the predictability formulas that used the Sv-PRT line as an unsatisfactory reference to determine the anteroposterior proportions of the lower third of the face in some patients. The method that considered the PRTv line as a reference, using Pearson\'s statistical methods of correlation and multiple linear regression, presented statistically significant results for all reference values in females and males (PRTv-Ls, PRTv -Li and PRT-Pg\'). The Student t-test was used to verify that the measures were not statistically significant according to gender. The results of this study showed that it is coherent to consider the glabella region as an evaluation and diagnostic reference for the anteroposterior proportions of the lower third of the face.

O terço inferior da face exerce uma forte influência na estética dos indivíduos, e sabendo-se da importância do seu equilíbrio, e da contribuição do ortodontista quanto ao diagnóstico do perfil facial, o presente estudo teve por finalidades testar um método de correlação entre uma medida linear localizada a partir da região da glabela com medidas lineares anteroposteriores no terço inferior da face (Triviño, 2012), e verificar a previsibilidade de proporções anteroposteriores no terço inferior da face, a partir de uma linha de referência passando por um ponto na região da glabela. Desenhos anatômicos foram realizados através de telerradiografias em norma lateral de 120 indivíduos com harmonia facial, leucodermas e relação molar de classe I, com o intuito de estabelecer parâmetros cefalométricos para correlacionar referências anteroposteriores do terço inferior da face a partir das linhas Sv-PRT e PRTv, obtidas através do ponto PRT. A aplicabilidade do método foi realizada em um grupo de 24 indivíduos com perfil desagradável, em que considerou insatisfatória a aplicação das fórmulas de previsibilidade utilizando a linha Sv-PRT, como uma referência para determinar as proporções anteroposteriores do terço inferior da face em alguns pacientes. O método que considerou a linha PRTv como referência, através dos métodos estatísticos de correlação de Pearson e regressão linear múltipla, apresentou resultados estatisticamente significativos para todos os valores de referência nos indivíduos do gênero feminino e nos indivíduos do gênero masculino (PRTv-Ls, PRTv-Li e PRT-Pg\'). Foi utilizado o Teste t-Student para verificar que as medidas não foram estatisticamente significativas de acordo com o gênero. Os resultados deste estudo mostraram ser coerente considerar a região da glabela como uma referência de avaliação e diagnóstico para as proporções anteroposteriores do terço inferior da face. / The lower third of the face exerts a strong influence on the aesthetics of individuals, and knowing the importance of its balance, and the orthodontist\'s contribution to the diagnosis of the facial profile, the present study had the purpose to test a method of correlation between a linear measure located from the glabella region with linear anteroposterior measurements on the lower third of the face (Triviño, 2012), and verify the predictability of anteroposterior proportions in the lower third of the face, from a reference line through a point in the glabella region. Anatomical tracings from lateral cephalometric radiographs of 120 individuals with balanced profile, leucoderm and class I were performed in order to establish cephalometric parameters to correlate anteroposterior references of the lower third of the face from the lines Sv-PRT and PRTv, obtained through the PRT point. The applicability of the method was performed in a group of 24 individuals with an unpleasant profile, in which it considered the predictability formulas that used the Sv-PRT line as an unsatisfactory reference to determine the anteroposterior proportions of the lower third of the face in some patients. The method that considered the PRTv line as a reference, using Pearson\'s statistical methods of correlation and multiple linear regression, presented statistically significant results for all reference values in females and males (PRTv-Ls, PRTv -Li and PRT-Pg\'). The Student t-test was used to verify that the measures were not statistically significant according to gender. The results of this study showed that it is coherent to consider the glabella region as an evaluation and diagnostic reference for the anteroposterior proportions of the lower third of the face.

Communication complexity is an area of complexity theory that studies an abstract model of computation called a communication protocol. In a $k$-player communication protocol, an input to a known function is partitioned into $k$ pieces of $n$ bits each, and each piece is assigned to one of the players in the protocol. The goal of the players is to evaluate the function on the distributed input by using as little communication as possible. In a Number-On-Forehead (NOF) protocol, the input piece assigned to each player is metaphorically placed on that player's forehead, so that each player sees everyone else's input but its own. In a Number-In-Hand (NIH) protocol, the piece assigned to each player is seen only by that player. Overall, the study of communication protocols has been used to obtain lower bounds and impossibility results for a wide variety of other models of computation. Two of the main contributions presented in this thesis are negative results on the NOF model of communication, identifying limitations of NOF protocols. Together, these results consitute stepping stones towards a better fundamental understanding of this model. As the first contribution, we show that randomized NOF protocols are exponentially more powerful than deterministic NOF protocols, as long as $k \le n^c$ for some constant $c$. As the second contribution, we show that nondeterministic NOF protocols are exponentially more powerful than randomized NOF protocols, as long as $k \le \delta \cdot \log n$ for some constant $\delta < 1$. For the third major contribution, we turn to the NIH model and we present a positive result. Informally, we show that a NIH communication protocol for a function $f$ can simulate a Stack Machine (a Turing Machine augmented with a stack) for a related function $F$, consisting of several instances of $f$ bundled together. Using this simulation and known communication complexity lower bounds, we obtain the first known (space vs. number of passes) trade-off lower bounds for Stack Machines.

Communication complexity is an area of complexity theory that studies an abstract model of computation called a communication protocol. In a $k$-player communication protocol, an input to a known function is partitioned into $k$ pieces of $n$ bits each, and each piece is assigned to one of the players in the protocol. The goal of the players is to evaluate the function on the distributed input by using as little communication as possible. In a Number-On-Forehead (NOF) protocol, the input piece assigned to each player is metaphorically placed on that player's forehead, so that each player sees everyone else's input but its own. In a Number-In-Hand (NIH) protocol, the piece assigned to each player is seen only by that player. Overall, the study of communication protocols has been used to obtain lower bounds and impossibility results for a wide variety of other models of computation. Two of the main contributions presented in this thesis are negative results on the NOF model of communication, identifying limitations of NOF protocols. Together, these results consitute stepping stones towards a better fundamental understanding of this model. As the first contribution, we show that randomized NOF protocols are exponentially more powerful than deterministic NOF protocols, as long as $k \le n^c$ for some constant $c$. As the second contribution, we show that nondeterministic NOF protocols are exponentially more powerful than randomized NOF protocols, as long as $k \le \delta \cdot \log n$ for some constant $\delta < 1$. For the third major contribution, we turn to the NIH model and we present a positive result. Informally, we show that a NIH communication protocol for a function $f$ can simulate a Stack Machine (a Turing Machine augmented with a stack) for a related function $F$, consisting of several instances of $f$ bundled together. Using this simulation and known communication complexity lower bounds, we obtain the first known (space vs. number of passes) trade-off lower bounds for Stack Machines.

This thesis focuses on the development of an open source software capable of automatic face detection in an image captured by a thermal camera, followed by a temperature measuring. This software is supposed to aid in the COVID-19 pandemics. The developed software is independent of used thermal camera. In this thesis, I am using TIM400 thermal camera. The implementation of the face detection was achieved by an OpenCV module. The methods tested were Template Matching, Eigen Faces, and Cascade Classifier. The last-mentioned had the best results, hence was used in the final version of the software. Cascade Classifier is looking for the eyes and their surrounding area in the image, allowing the software to subsequently measure the temperature on the surface of one's forehead. One can therefore be wearing a face mask or a respirator safely. The temperature measuring works in real time and the software is able to capture several people at once. It then keeps a record of the temperature of each measured individual as well as the time of the measurement. The software as a whole is a part of an installation file compatible with the Windows operating system. The functionality of this software was tested – the video recordings are included in this thesis.