Indiana University-Purdue University Indianapolis (IUPUI) / Survival analysis often encounters the situations of correlated multiple events including the same type of event observed from siblings or multiple events experienced by the same individual. In this dissertation, we focus on the joint modeling of bivariate time to event data with the estimation of the association parameters and also in the situation of a semi-competing risk. This dissertation contains three related topics on bivariate time to event mod els. The first topic is on estimating the cross ratio which is an association parameter between bivariate survival functions. One advantage of using cross-ratio as a depen dence measure is that it has an attractive hazard ratio interpretation by comparing two groups of interest. We compare the parametric, a two-stage semiparametric and a nonparametric approaches in simulation studies to evaluate the estimation perfor mance among the three estimation approaches. The second part is on semiparametric models of univariate time to event with a semi-competing risk. The third part is on semiparametric models of bivariate time to event with semi-competing risks. A frailty-based model framework was used to accommodate potential correlations among the multiple event times. We propose two estimation approaches. The first approach is a two stage semiparametric method where cumulative baseline hazards were estimated by nonparametric methods first and used in the likelihood function. The second approach is a penalized partial likelihood approach. Simulation studies were conducted to compare the estimation accuracy between the proposed approaches. Data from an elderly cohort were used to examine factors associated with times to multiple diseases and considering death as a semi-competing risk.

Inspiré par l'algèbre d’échange et birapport de rang n introduit par F. Labourie, nous construisons un anneau muni de la structure de Poisson--- l’algèbre d’échangée de rang n Zn(P) pour étudier les espaces de modules de birapports . Nous prouvons que Zn(P) hérite d'une structure de Poisson provenant de l’algèbre d’échangée. Pour tenir compte des “birapports” dans l’anneau de fraction, en interprétant Zn(P) par un modèle géométrique dans l'étude de la géométrie théorie des invariants, nous montrons que Zn(P) est intègre. Ensuite, nous considérons l'anneau Bn(P) engendreré par les birapports dans l'anneau de fraction de Zn(P). Pour n = 2,3, nous trouvons un homomorphisme injectif poissonienne de l'anneau engendré par coordonnées de Fock-Goncharovde sur l'espace des configurations de drapeaux dans Rn vers Bn(P). En étudiant le système intégrable discret pour l'espace des configurations de polygones N-tordus dans RP1, à une transformation de Fourier discrète, nous rapportons asymptotiquement l'algèbre d’échangée à l'algèbre de Virasoro sur une hypersurface de MN, 1. / Inspired by the swapping algebra and the rank n cross-ratio introduced by F. Labourie, we construct a ring equipped with the swapping Poisson structure---the rank n swapping algebra Zn(P) to study the moduli spaces of cross ratios. We prove that Zn(P) inherits a Poisson structure form the swapping bracket. To consider the "cross-ratios" in the fraction ring, by interpreting Zn(P) by a geometric model in the study of geometry invariant theory, we prove that Zn(P) is an integral domain. Then we consider the ring Bn(P) generated by the cross ratios in the fraction ring of Zn(P). For n = 2,3, we embed in a Poisson way the ring generated by Fock-Goncharov coordinates for configuration space of flags in Rn into Bn(P). By studying the discrete integrable system for the configuration space MN,1 of N-twisted polygons in RP1, up to a discrete Fourier transformation, we asymptotically relate the swapping algebra to the Virasoro algebra on a hypersurface of MN,1.

A crescente capacidade do poder computacional e a proliferação de dispositivos ao nosso redor vem permitindo o desenvolvimento de novas e sofisticadas interfaces para interação humano-computador que reagem à presença e ao estado de seus usuários. Como o olhar tem a capacidade de transmitir muitas informações sobre o usuário, rastreadores de olhar, dispositivos que estimam a direção para onde uma pessoa olha, tem papel importante no desenvolvimento de tais interfaces. Entre suas aplicações temos o auxílio a pessoas com dificuldades motoras, que podem utilizar um rastreador de olhar como substituto ao mouse, aplicações de diagnóstico, que estudam evidências do comportamento humano, ou ainda o desenvolvimento de interfaces que utilizem a informação sobre o olhar como um canal a mais de comunicação com o usuário para perceber suas intenções. Muitas técnicas para atingir tal objetivo foram desenvolvidas mas as tradicionais ainda oferecem certas dificuldades de uso para seus usuários como a intolerância a movimentos de cabeça e a necessidade de calibração por sessão de uso. Neste trabalho fizemos um levantamento de uma série de técnicas de rastreamento de olhar, indo das mais tradicionais até algumas mais recentes que visam melhorar a facilidade de uso destes sistemas. Uma das técnicas mais promissoras utiliza múltiplas fontes de luz fixadas nos cantos do monitor do computador. Através da análise da posição dos reflexos gerados por essas fontes de luz sobre a córnea, juntamente com a informação da posição da pupila, presentes em imagens capturadas do olho, é possível estimar o ponto observado no monitor. Devido às suas vantagens ela foi escolhida para estudo mais detalhado e implementação. Extensos testes utilizando simulações foram realizados para avaliar seu desempenho. Foi também desenvolvida uma extensão dessa técnica, utilizando um modelo mais preciso do olho, visando melhorar sua precisão. Ao final apresentamos nossa implementação, baseada nessa extensão da técnica original, que é tolerante a movimentação da face e mostramos os resultados obtidos em testes realizados com um grupo de usuários. / Recent advances in computing power and the proliferation of computing devices around us allowed the development of new computer interfaces which can react to the presence and state of its users. Since gaze can transmit a lot of information about the user, gaze trackers, devices that can estimate the direction which a person is looking at, have an important role in the development of such interfaces. Among gaze tracking applications, we have aid for people with limited motor skills, human behavior studies, and the development of interfaces that can take gaze information as an additional communication channel with the user. Lots of techniques have been developed to reach this goal, but they have some problems that make them hard to be widely used. These problems are the need of calibration for each use session and the need to keep the user\'s head still. In this work we studied some of the existing gaze tracking techniques, from the more traditional ones to more recent ones. One of the most interesting techniques makes use of multiple light sources fixed at the monitor\'s corners. By analyzing the positions of corneal reflections and the pupil present in captured images of the eye, it is possible to estimate the gaze point on the monitor screen. Due to its advantages this technique was chosen for a deeper study and implementation. Lots of experiments using simulated data have been carried out to validate the technique. Using a more accurate model of the eye, an extension for this technique was also developed to increase its precision. Finally, we present our implementation, that allows for large head movement, as well as test results obtained from real users.

Inspired by the swapping algebra and the rank n cross-ratio introduced by F. Labourie, we construct a ring equipped with the swapping Poisson structure---the rank n swapping algebra Zn(P) to study the moduli spaces of cross ratios. We prove that Zn(P) inherits a Poisson structure form the swapping bracket. To consider the "cross-ratios" in the fraction ring, by interpreting Zn(P) by a geometric model in the study of geometry invariant theory, we prove that Zn(P) is an integral domain. Then we consider the ring Bn(P) generated by the cross ratios in the fraction ring of Zn(P). For n = 2,3, we embed in a Poisson way the ring generated by Fock-Goncharov coordinates for configuration space of flags in Rn into Bn(P). By studying the discrete integrable system for the configuration space MN,1 of N-twisted polygons in RP1, up to a discrete Fourier transformation, we asymptotically relate the swapping algebra to the Virasoro algebra on a hypersurface of MN,1.

A crescente capacidade do poder computacional e a proliferação de dispositivos ao nosso redor vem permitindo o desenvolvimento de novas e sofisticadas interfaces para interação humano-computador que reagem à presença e ao estado de seus usuários. Como o olhar tem a capacidade de transmitir muitas informações sobre o usuário, rastreadores de olhar, dispositivos que estimam a direção para onde uma pessoa olha, tem papel importante no desenvolvimento de tais interfaces. Entre suas aplicações temos o auxílio a pessoas com dificuldades motoras, que podem utilizar um rastreador de olhar como substituto ao mouse, aplicações de diagnóstico, que estudam evidências do comportamento humano, ou ainda o desenvolvimento de interfaces que utilizem a informação sobre o olhar como um canal a mais de comunicação com o usuário para perceber suas intenções. Muitas técnicas para atingir tal objetivo foram desenvolvidas mas as tradicionais ainda oferecem certas dificuldades de uso para seus usuários como a intolerância a movimentos de cabeça e a necessidade de calibração por sessão de uso. Neste trabalho fizemos um levantamento de uma série de técnicas de rastreamento de olhar, indo das mais tradicionais até algumas mais recentes que visam melhorar a facilidade de uso destes sistemas. Uma das técnicas mais promissoras utiliza múltiplas fontes de luz fixadas nos cantos do monitor do computador. Através da análise da posição dos reflexos gerados por essas fontes de luz sobre a córnea, juntamente com a informação da posição da pupila, presentes em imagens capturadas do olho, é possível estimar o ponto observado no monitor. Devido às suas vantagens ela foi escolhida para estudo mais detalhado e implementação. Extensos testes utilizando simulações foram realizados para avaliar seu desempenho. Foi também desenvolvida uma extensão dessa técnica, utilizando um modelo mais preciso do olho, visando melhorar sua precisão. Ao final apresentamos nossa implementação, baseada nessa extensão da técnica original, que é tolerante a movimentação da face e mostramos os resultados obtidos em testes realizados com um grupo de usuários. / Recent advances in computing power and the proliferation of computing devices around us allowed the development of new computer interfaces which can react to the presence and state of its users. Since gaze can transmit a lot of information about the user, gaze trackers, devices that can estimate the direction which a person is looking at, have an important role in the development of such interfaces. Among gaze tracking applications, we have aid for people with limited motor skills, human behavior studies, and the development of interfaces that can take gaze information as an additional communication channel with the user. Lots of techniques have been developed to reach this goal, but they have some problems that make them hard to be widely used. These problems are the need of calibration for each use session and the need to keep the user\'s head still. In this work we studied some of the existing gaze tracking techniques, from the more traditional ones to more recent ones. One of the most interesting techniques makes use of multiple light sources fixed at the monitor\'s corners. By analyzing the positions of corneal reflections and the pupil present in captured images of the eye, it is possible to estimate the gaze point on the monitor screen. Due to its advantages this technique was chosen for a deeper study and implementation. Lots of experiments using simulated data have been carried out to validate the technique. Using a more accurate model of the eye, an extension for this technique was also developed to increase its precision. Finally, we present our implementation, that allows for large head movement, as well as test results obtained from real users.

This work is dealing with detecting and recongnizing matrix codes. It is experimenting use of PCLines algorithm. PCLines is using Hough transform and parallel coordinates for fast detection of lines. Suggested algorithm with double use PCLines detects sets of parallels and problem with image distorted by with parallel projection is solved by cross-ratio equation. We did some optimizations for realtime running and created experimental implementation. Test results shows, that use PCLines one way to detect matrix codes.

<p>I denna uppsats presenteras grundläggande delar av hyperbolisk geometri. Uppsatsen är indelad i två kapitel. I första kapitlet studeras Möbiusavbildningar på Riemannsfären. Andra kapitlet presenterar modellen av hyperbolisk geometri i övre halvplanet H, skapad av Poincaré på 1880-talet.</p><p>Huvudresultatet i uppsatsen är Gauss – Bonnét´s sats för hyperboliska trianglar.</p> / <p>In this thesis we present fundamental concepts in hyperbolic geometry. The thesis is divided into two chapters. In the first chapter we study Möbiustransformations on the Riemann sphere. The second part of the thesis deal with hyperbolic geometry in the upper half-plane. This model of hyperbolic geometry was created by Poincaré in 1880.</p><p>The main result of the thesis is Gauss – Bonnét´s theorem for hyperbolic triangles.</p>

I denna uppsats presenteras grundläggande delar av hyperbolisk geometri. Uppsatsen är indelad i två kapitel. I första kapitlet studeras Möbiusavbildningar på Riemannsfären. Andra kapitlet presenterar modellen av hyperbolisk geometri i övre halvplanet H, skapad av Poincaré på 1880-talet. Huvudresultatet i uppsatsen är Gauss – Bonnét´s sats för hyperboliska trianglar. / In this thesis we present fundamental concepts in hyperbolic geometry. The thesis is divided into two chapters. In the first chapter we study Möbiustransformations on the Riemann sphere. The second part of the thesis deal with hyperbolic geometry in the upper half-plane. This model of hyperbolic geometry was created by Poincaré in 1880. The main result of the thesis is Gauss – Bonnét´s theorem for hyperbolic triangles.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-16T14:45:10Z No. of bitstreams: 1 arquivototal.pdf: 923276 bytes, checksum: 684d210a074aefcedef691723f8d04e0 (MD5) / Made available in DSpace on 2017-08-16T14:45:10Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 923276 bytes, checksum: 684d210a074aefcedef691723f8d04e0 (MD5) Previous issue date: 2016-03-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / It is well-known that planes and quadric surfaces in the projective space contain in - nitely many lines. For smooth cubic surface Cayley and Salmon, 1847, (and Clebsch later) proved that it has exactly 27 lines. For degree 4, in 1943 Segre proved that the maximum number of lines contained in a smooth quartic surface is 64. For surfaces of degree greater than 4 this number is unknown. In this work, we are going to explore what is the maximum number of lines that a smooth complex surface of degree d of the family Fd ; may contain. Thus, we obtain a lower bound to the maximum number of lines that non singular surfaces of degree d in P3 may contain. We emphasize that the determination of this numbers is based on the Klein's classi cation theorem of nitte subgroups of Aut(P1) and the study of 􀀀C; the subgroup of Aut(P1) whose elements leaves invariant the nite subset C of P1: / Sabe-se que planos e superf cies qu adricas no espa co projetivo cont em in nitas retas. No caso de uma superf cie c ubica n~ao singular Cayley e Salmon, em 1847, (e Clebsch, mais tarde) provaram que ela cont em exatamente 27 retas. No caso de grau 4, em 1943 Segre provou que o n umero m aximo de retas contidas numa superf cie qu artica n~ao singular e 64. Para superf cies de grau maior que 4 esse n umero e desconhecido. Neste trabalho vamos explorar qual e a quantidade m axima de retas que uma superf cie complexa n~ao singular de grau d na fam lia Fd ; pode conter. Assim obtemos uma cota inferior para o n umero m aximo de retas que as superf cies n~ao singulares de grau d em P3 podem conter. Salientamos que a determina c~ao destes n umeros tem como base o Teorema de Classi ca cao de Klein dos sugbrupos nitos de Aut(P1) e o estudo dos subgrupos 􀀀C de Aut(P1) que deixam invariante um subconjunto nito C de P1:

This thesis deals with problematics of PTZ-camera re-calibration during movement. The objective of this work is to keep the camera in calibration mode from default status when the known positions of Vanishing Points are in the image. With their use during movement, which is changing with motion of the camera, their positions are kept with help of two implemented methods. The first method is based on the principle of homography, the second on the principle of cross ratio. The results show that both of these methods work especially for keeping the positions of First Vanishing Points. In the case of the Second Vanishing Points there appear various problems and the results are often quite inaccurate.