Dissertations / Theses on the topic 'Determinantal'

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 125-129).
In this thesis, we apply combinatorial means for proving and generalizing classical determinantal identities. In Chapter 1, we present some historical background and discuss the algebraic framework we employ throughout the thesis. In Chapter 2, we construct a fundamental bijection between certain monomials that proves crucial for most of the results that follow. Chapter 3 studies the first, and possibly the best-known, determinantal identity, the matrix inverse formula, both in the commutative case and in some non-commutative settings (Cartier-Foata variables, right-quantum variables, and their weighted generalizations). We give linear-algebraic and (new) bijective proofs; the latter also give an extension of the Jacobi ratio theorem. Chapter 4 is dedicated to the celebrated MacMahon master theorem. We present numerous generalizations and applications. In Chapter 5, we study another important result, Sylvester's determinantal identity. We not only generalize it to non-commutative cases, we also find a surprising extension that also generalizes the master theorem. Chapter 6 has a slightly different, representation theory flavor; it involves representations of the symmetric group, and also Hecke algebras and their characters. We extend a result on immanants due to Goulden and Jackson to a quantum setting, and reprove certain combinatorial interpretations of the characters of Hecke algebras due to Ram and Remmel.
by Matjaž Konvalinka.
Ph.D.

The Determinantal Assignment Problem (DAP) is one of the central problems of Algebraic Control Theory and refers to solving a system of non-linear algebraic equations to place the critical frequencies of the system to specied locations. This problem is decomposed into a linear and a multi-linear subproblem and the solvability of the problem is reduced to an intersection of a linear variety with the Grassmann variety. The linear subproblem can be solved with standard methods of linear algebra, whereas the intersection problem is a problem within the area of algebraic geometry. One of the methods to deal with this problem is to solve the linear problem and then and which element of this linear space is closer - in terms of a metric - to the Grassmann variety. If the distance is zero then a solution for the intersection problem is found, otherwise we get an approximate solution for the problem, which is referred to as the approximate DAP. In this thesis we examine the second case by introducing a number of new tools for the calculation of the minimum distance of a given parametrized multi-vector that describes the linear variety implied by the linear subproblem, from the Grassmann variety as well as the decomposable vector that realizes this least distance, using constrained optimization techniques and other alternative methods, such as the SVD properties of the so called Grassmann matrix, polar decompositions and mother tools. Furthermore, we give a number of new conditions for the appropriate nature of the approximate polynomials which are implied by the approximate solutions based on stability radius results. The approximate DAP problem is completely solved in the 2-dimensional case by examining uniqueness and non-uniqueness (degeneracy) issues of the decompositions, expansions to constrained minimization over more general varieties than the original ones (Generalized Grassmann varieties), derivation of new inequalities that provide closed-form non-algorithmic results and new stability radii criteria that test if the polynomial implied by the approximate solution lies within the stability domain of the initial polynomial. All results are compared with the ones that already exist in the respective literature, as well as with the results obtained by Algebraic Geometry Toolboxes, e.g., Macaulay 2. For numerical implementations, we examine under which conditions certain manifold constrained algorithms, such as Newton's method for optimization on manifolds, could be adopted to DAP and we present a new algorithm which is ideal for DAP approximations. For higher dimensions, the approximate solution is obtained via a new algorithm that decomposes the parametric tensor which is derived by the system of linear equations we mentioned before.

O teorema de Hilbert-Burch fornece uma boa descrição de variedades determinantais de codi- mensão dois e de suas deformações em termos da matriz de representação. Neste trabalho, usamos esta correspondência para estudar propriedades de tais variedades usando métodos da teoria de singularidades. Na primeira parte da tese, estabelecemos a teoria de singularidades de matrizes n X p, generalizando os resultados obtidos por J. W. Bruce and F. Tari em [5], para ma- trizes quadradas, e por A. Frühbis-Krüger em [16], para matrizes n X (n+1). Na segunda parte, nos concentramos em variedades determinantais de codimensão 2, com singularidade isolada na origem. Para estas variedades, podemos mostrar a existência e a unicidade de suavizações, o que possibilita definir seu número de Milnor como o número de Betti na dimensão média de sua fibra genérica. Para superfícies em \'C POT. 4\', obtemos uma fórmula Lê-Greuel expressando o número de Milnor da superfície em termos da segunda multiplicidade polar e do número de Milnor de uma seção genérica
The theorem of Hilbert- Burch provides a good description of codimension two determinantal varieties and their deformations in terms of their presentation matrices. In this work we use this correspondence to study properties of determinantal varieties, based on methods of singularity theory of their presentation matrices. In the first part of the thesis we establish the theory of singularities for n X p matrices extending previous results of J. W. Bruce and F. Tari in [5], for classes of square matrices, and A. Frühbis-Krüger for n X (n+1) matrices in [16]. In the second part we concentrate on codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in \'C POT. 4\' , we obtain a Lê-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of the generic section

This thesis consists of two parts, Papers A and B, in which some stochastic processes, originating from random matrix theory (RMT), are studied. In the first paper we study the fluctuations of the kth largest eigenvalue, xk, of the Gaussian unitary ensemble (GUE). That is, let N be the dimension of the matrix and k depend on N in such a way that k and N-k both tend to infinity as N - ∞. The main result is that xk, when appropriately rescaled, converges in distribution to a Gaussian random variable as N → ∞. Furthermore, if k1 < ...< km are such that k1, ki+1 - ki and N - km, i =1, ... ,m - 1, tend to infinity as N → ∞ it is shown that (xk1 , ... , xkm) is multivariate Gaussian in the rescaled N → ∞ limit. In the second paper we study the Airy process, A(t), and prove that it fluctuates like a Brownian motion on a local scale. We also prove that the Discrete polynuclear growth process (PNG) fluctuates like a Brownian motion in a scaling limit smaller than the one where one gets the Airy process.
QC 20100716

In this master thesis I aim to present some of the basic theory of determinantal processes. Some preliminary theory of random measures and point-process theory is reviewed in the first chapter. In the second chapter I introduce the notion of a determinantal process, through what is called trace-class kernels. I mention a few of the most fundamental theorems from the field and go through some useful theorems for determinantal processes concerning interpolation between different processes. An algorithm for simulating determinantal processes was suggested earlier in [9]. I study this algorithm and derive more explicit formulas for implementation. The algorithm is however based on some assumptions that the underlying process is of a specific form. There is however a way to get around this assumption in order to study a wider class of processes, using another result from [9]. I will study some processes that interpolate between well-known processes, and use my implemented simulation tool to study how this interpolation manifests itself.
I denna magisteruppsats presenterar jag lite av den teori som ligger till grund för determinantprocesser. I det första kapitlet går jag igenom en del av den grundläggande teorin kring slumpmått och punktprocesser. I det andra kapitlet introduceras begreppet determinantprocess via så kallade trace-class kärnor. Jag tar upp några av de mest fundamentala satserna i ämnet och några användbara satser för interpolation mellan olika determinantprocesser. En algoritm för simulering av determinantprocesser föreslogs tidigare i [9]. Jag studerar den algoritm och härleder mer explicita formler för implementering. Algoritmen I fråga bygger dock på att den underliggande processen är av en specifik form. Det finns emellertid ett sätt att komma runt detta antagande för att studera en större klass av processer, genom att använda ytterligare ett resultat från [9]. Jag studerar vidare två interpolerande processer som båda interpolerar mellan två andra välkända processer, och använder en implementering av de former jag härlett för simulering, för att undersöka hur interpolation ter sig. På senare tid har determinantprocesser funnit tillämpningar inom det datavetenskapliga ämnet maskininlärning. Inom maskininlärning simulerar man determinantprocesser för att utnyttja deras probabilistiska egenskaper. Det skulle därför kunna vara tänkbart att simuleringsmetoderna (eventuellt även de processer som studeras) som utvecklas här skulle kunna tillämpas inom detta ämne.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 63-66).
As machine-learning techniques continue to require more data and become increasingly memory-heavy, being able to choose a subset of relevant, high-quality and diverse elements among large amounts of redundant or noisy data and parameters has become an important concern. Here, we approach this problem using Determinantal Point Processes (DPPs), probabilistic models that provide an intuitive and powerful way of balancing quality and diversity in sets of items. We introduce a novel, fixed-point algorithm for estimating the maximum likelihood parameters of a DPP, provide proof of convergence and discuss generalizations of this technique. We then apply DPPs to the difficult problem of detecting and eliminating redundancy in fully-connected layers of neural networks. By placing a DPP over a layer, we are able to sample a subset of neurons that perform non-overlapping computations and merge all other neurons of the layer into the previous diverse subset. This allows us to significantly reduce the size of the neural network while simultaneously maintaining a good performance.
by Zelda Elaine Mariet.
S.M.

Dans cette thèse, nous nous intéressons à l'étude des structures déterminantielles apparaissent dans l'optimisation semi-définie (SDP), le prolongement naturel de la programmation linéaire au cône des matrices symétrique semi-définie positives. Si l'approximation d'une solution d'un programme semi-défini peut être calculé efficacement à l'aide des algorithmes de points intérieurs, ni des algorithmes exacts efficaces pour la SDP sont disponibles, ni une compréhension complète de sa complexité théorique a été atteinte. Afin de contribuer à cette question centrale en optimisation convexe, nous concevons un algorithme exact pour décider la faisabilité d'une inégalité matricielle linéaire (LMI) $A(x)\succeq 0$. Quand le spectraèdre associé (le lieu $\spec$ des $x \in \RR^n$ ou $A(x)\succeq 0$) n'est pas vide, la sortie de cet algorithme est une représentation algébrique d'un ensemble fini qui contient au moins un point $x \in \spec$: dans ce cas, le point $x$ minimise le rang de $A(x)$ sur $\spec$. La complexité est essentiellement quadratique en le degré de la représentation en sortie, qui coïncide, expérimentalement, avec le degré algébrique de l'optimisation semi-définie. C'est un garantie d'optimalité de cette approche dans le contexte des algorithmes exacts pour les LMI et la SDP. Remarquablement, l'algorithme ne suppose pas la présence d'un point intérieur dans $\spec$, et il profite de l'existence de solutions de rang faible de l'LMI $A(x)\succeq 0$. Afin d'atteindre cet objectif principal, nous développons une approche systématique pour les variétés déterminantielles associées aux matrices linéaires. Nous prouvons que décider la faisabilité d'une LMI $A(x)\succeq 0$ se réduit à calculer des points témoins dans les variétés déterminantielles définies sur $A(x)$. Nous résolvons ce problème en concevant un algorithme exact pour calculer au moins un point dans chaque composante connexe réelle du lieu des chutes de rang de $A(x)$. Cet algorithme prend aussi avantage des structures supplémentaires, et sa complexité améliore l'état de l'art en géométrie algébrique réelle. Enfin, les algorithmes développés dans cette thèse sont implantés dans une nouvelle bibliothèque Maple appelé Spectra, et les résultats des expériences mettant en évidence la meilleure complexité sont fournis
In this thesis we focus on the study of determinantal structures arising in semidefinite programming (SDP), the natural extension of linear programming to the cone of symetric positive semidefinite matrices. While the approximation of a solution of a semidefinite program can be computed efficiently by interior-point algorithms, neither efficient exact algorithms for SDP are available, nor a complete understanding of its theoretical complexity has been achieved. In order to contribute to this central question in convex optimization, we design an exact algorithm for deciding the feasibility of a linear matrix inequality (LMI) $A(x) \succeq 0$. When the spectrahedron $\spec = \{x \in \RR^n \mymid A(x) \succeq 0\}$ is not empty, the output of this algorithm is an algebraic representation of a finite set meeting $\spec$ in at least one point $x^*$: in this case, the point $x^*$ minimizes the rank of the pencil on the spectrahedron. The complexity is essentially quadratic in the degree of the output representation, which meets, experimentally, the algebraic degree of semidefinite programs associated to $A(x)$. This is a guarantee of optimality of this approach in the context of exact algorithms for LMI and SDP. Remarkably, the algorithm does not assume the presence of an interior point in the spectrahedron, and it takes advantage of the existence of low rank solutions of the LMI. In order to reach this main goal, we develop a systematic approach to determinantal varieties associated to linear matrices. Indeed, we prove that deciding the feasibility of a LMI can be performed by computing a sample set of real solutions of determinantal polynomial systems. We solve this problem by designing an exact algorithm for computing at least one point in each real connected component of the locus of rank defects of a pencil $A(x)$. This algorithm admits as input generic linear matrices but takes also advantage of additional structures, and its complexity improves the state of the art in computational real algebraic geometry. Finally, the algorithms developed in this thesis are implemented in a new Maple library called {Spectra}, and results of experiments highlighting the complexity gain are provided

Neste trabalho estudamos variedades determinantais essencialmente isoladas (EIDS), definidas por W. Èbeling e S. M. Gusen-Zade em [23]. Este tipo de singularidades é uma generalização das singularidades isoladas. A variedade determinantal genérica Mtm, n é o subconjunto das matrizes m X n, tais que o posto seja menor que t, onde t ≤ min{n;m}. Uma variedade X ⊂ CN é determinantal se é definida como a pré-imagem de uma função holomorfa F : CN → Mm;n, sobre a variedade determinantal genérica M tIn this work, we study the essentially isolated determinantal singularities (EIDS), which have been defined by W. Èbeling and S. M. Gusen-Zade in the article [23]. This type of singularities is a natural generalization of isolated ones. A generic determinantal variety Mtm;n is a subset of the space of m X n matrices, given by matrices of rank less than t, where t ≤ min. A variety X ⊂ CN is determinantal if X is defined as the pre-image of Mtm;n by a holomorphic function F : CN → Mm;n with the condition codim X = codim Mtm;n. Determinantal varieties have isolated singularity if N ≤ (n - t + 2)(m - t + 2) and they admit smoothing if N < (n - t +2)(m - t +2). Several recent works investigate determinantal variety with isolated singularities. The Milnor number of a surface was defined in [35, 31] and the vanishing Euler characteristic was studied in [31]. In this work we study the set of limits of tangent hyperplanes to determinantal varieties X2 ⊂ C4 and X3 ⊂ C5 to give a characterization of this set by the fact that the Milnor number of its section with the surface in the first case or the 3-dimensional determinantal variety in the second case is not minimum. The first case is studied by Jawad Snoussi in [38]. We also prove that if X is a d- dimensional EIDS and H and H\' are strongly general hyperplans, if P ⊂ H and P\' are linear plans of codimension d - 2 contained in H and H\', the Milnor number of the surfaces X ∩ P and X ∩ P\' are equal. In the case that the generic section is a curve the result has been proved in [26]. We study the Nash transformation of an EIDS and give sufficient conditions for this transformation to be smooth. Another aim of our study is the Euler obstruction of essentially isolated determinantal singularities. We obtain inductive formulas associating the Euler obstruction with the vanishing Euler characteristic of the essencial smoothing of their generic sections. We study the determinantal variety with singular set of dimension 1 to illustrate the results.

We study eigenvalues of unitary invariant random matrices and other de-terminantal point processes. Paper A investigates some generalizations ofthe Gaussian Unitary Ensemble which are motivated by the physics of freefermions. We show that these processes exhibit a transition from Poisson tosine statistics at mesoscopic scales and that, at the critical scale, fluctuationsare not Gaussian but are governed by complicated limit laws. In papers Band C, we prove limit theorems which cover the different regimes of randommatrix theory. In particular, this establishes universality of the fluctuations ofinvariant Hermitian random matrices in great generality. The techniques arebased on generalizations of the orthogonal polynomial method and the cumu-lant method developed by Soshnikov. In particular, the results rely on certaincombinatorial identities originating in the theory of random walks and on theasymptotics for Orthogonal polynomials coming from the Riemann-Hilbertsteepest descent introduced by Deift et al.

QC 20160513

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In thisthesis,westudycertaindegenerations/specializationsofthegenericsquare matrix overa eld k of characteristiczeroalongitsmainrelatedstructures,suchthe determinantofthematrix,theidealgeneratedbyitspartialderivatives,thepolarmap de ned bythesederivatives,theHessianmatrixandtheidealofsubmaximalminorsof the matrix.Thedegenerationtypesofthegenericsquarematrixconsideredhereare: (1) degenerationby\cloning"(repeating)avariable;(2)replacingasubsetofentriesby zeros, inastrategiclayout;(3)furtherdegenerationsoftheabovetypesstartingfrom certain specializationsofthegenericsquarematrix,suchasthegenericsymmetric matrix andthegenericsquareHankelmatrix.Thefocusinallthesedegenerations is intheinvariantsdescribedabove,highlightingonthehomaloidalbehaviorofthe determinantofthematrix.Forthis,weemploytoolscomingfromcommutativealgebra, with emphasisonidealtheoryandsyzygytheory.
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Les processus ponctuels déterminantaux (Determinantal Point Processes ou DPP en anglais) sont des modèles probabilistes qui modélisent les corrélations négatives ou la répulsion à l'intérieur d'un ensemble d'éléments. Ils ont tendance à générer des sous-ensembles d'éléments diversifiés ou éloignés les uns des autres. Cette notion de similarité ou de proximité entre les points de l'ensemble est définie et conservée dans le noyau associé à chaque DPP. Cette thèse étudie ces modèles dans un cadre discret, définis dans un ensemble discret et fini d'éléments. Nous nous sommes intéressés à leur application à des questions de traitement d'images, lorsque l'ensemble de points de départ correspond aux pixels ou aux patchs d'une image. Les Chapitres 1 et 2 introduisent les processus ponctuels déterminantaux dans un cadre discret général, leurs propriétés principales et les algorithmes régulièrement utilisés pour les échantillonner, c'est-à-dire pour sélectionner un sous-ensemble de points distribué selon le DPP choisi. Dans ce cadre, le noyau d'un DPP est une matrice. L'algorithme le plus utilisé est un algorithme spectral qui repose sur le calcul des valeurs propres et des vecteurs propres du noyau du DPP. Dans le Chapitre 2, nous présentons un algorithme d'échantillonnage qui repose sur une procédure de thinning (ou amincissement) et sur une décomposition de Cholesky mais qui n'a pas besoin de la décomposition spectrale du noyau. Cet algorithme est exact et, sous certaines conditions, compétitif avec l'algorithme spectral. Le Chapitre 3 présente les DPP définis sur l'ensemble des pixels d'une image, appelés processus pixelliques déterminantaux (Determinantal Pixel Processes ou DPixP en anglais). Ce nouveau cadre impose des hypothèses de périodicité et de stationnarité qui ont des conséquences sur le noyau du processus et sur les propriétés de répulsion générée par ce noyau. Nous étudions aussi ce modèle appliqué à la synthèse de textures gaussiennes, grâce à l'utilisation de modèles shot noise. Nous nous intéressons également à l'estimation du noyau de DPixP à partir d'un ou plusieurs échantillons. Le Chapitre 4 explore les processus ponctuels déterminantaux définis sur l'ensemble des patchs d'une image, c'est-à-dire la famille des sous-images carrées d'une taille donnée dans une image. L'objectif est de sélectionner une proportion de ces patchs, suffisamment diversifiée pour être représentative de l'information contenue dans l'image. Une telle sélection peut permettre d'accélérer certains algorithmes de traitements d'images basés sur les patchs, voire d'améliorer la qualité d'algorithmes existants ayant besoin d'un sous-échantillonnage des patchs. Nous présentons une application de cette question à un algorithme de synthèse de textures
Determinantal point processes (DPPs in short) are probabilistic models that capture negative correlations or repulsion within a set of elements. They tend to generate diverse or distant subsets of elements. This notion of similarity or proximity between elements is defined and stored in the kernel associated with each DPP. This thesis studies these models in a discrete framework, defined on a discrete and finite set of elements. We are interested in their application to image processing, when the initial set of points corresponds to the pixels or the patches of an image. Chapter 1 and 2 introduce determinantal point processes in a general discrete framework, their main properties and the algorithms usually used to sample them, i.e. used to select a subset of points distributed according to the chosen DPP. In this framework, the kernel of a DPP is a matrix. The main algorithm is a spectral algorithm based on the computation of the eigenvalues and the eigenvectors of the DPP kernel. In Chapter 2, we present a sampling algorithm based on a thinning procedure and a Cholesky decomposition but which does not require the spectral decomposition of the kernel. This algorithm is exact and, under certain conditions, competitive with the spectral algorithm. Chapter 3 studies DPPs defined over all the pixels of an image, called Determinantal Pixel Processes (DPixPs). This new framework imposes periodicity and stationarity assumptions that have consequences on the kernel of the process and on properties of the repulsion generated by this kernel. We study this model applied to Gaussian textures synthesis, using shot noise models. In this chapter, we are also interested in the estimation of the DPixP kernel from one or several samples. Chapter 4 explores DPPs defined on the set of patches of an image, that is the family of small square images contained in the image. The aim is to select a proportion of these patches, diverse enough to be representative of the information contained in the image. Such a selection can speed up certain patch-based image processing algorithms, or even improve the quality of existing algorithms that require patch subsampling. We present an application of this question to a texture synthesis algorithm

Avec la croissance exponentielle de la quantité de données, l’échantillonnage est une méthode pertinente pour étudier les populations. Parfois, nous avons besoin d’échantillonner un grand nombre d’objets d’une part pour exclure la possibilité d’un manque d’informations clés et d’autre part pour générer des résultats plus précis. Le problème réside dans le fait que l’échantillonnage d’un trop grand nombre d’individus peut constituer une perte de temps.Dans cette thèse, notre objectif est de chercher à établir des ponts entre la statistique et le k-processus ponctuel déterminantal(k-DPP) qui est défini via un noyau. Nous proposons trois projets complémentaires pour l’échantillonnage de grands ensembles de données en nous basant sur les k-DPPs. Le but est de sélectionner des ensembles variés qui couvrent un ensemble d’objets beaucoup plus grand en temps polynomial. Cela peut être réalisé en construisant différentes chaînes de Markov où les k-DPPs sont les lois stationnaires.Le premier projet consiste à appliquer les processus déterminantaux à la sélection d’espèces diverses dans un ensemble d’espèces décrites par un arbre phylogénétique. En définissant le noyau du k-DPP comme un noyau d’intersection, les résultats fournissent une borne polynomiale sur le temps de mélange qui dépend de la hauteur de l’arbre phylogénétique.Le second projet vise à utiliser le k-DPP dans un problème d’échantillonnage de sommets sur un graphe connecté de grande taille. La pseudo-inverse de la matrice Laplacienne normalisée est choisie d’étudier la vitesse de convergence de la chaîne de Markov créée pour l’échantillonnage de la loi stationnaire k-DPP. Le temps de mélange résultant est borné sous certaines conditions sur les valeurs propres de la matrice Laplacienne.Le troisième sujet porte sur l’utilisation des k-DPPs dans la planification d’expérience avec comme objets d’étude plus spécifiques les hypercubes latins d’ordre n et de dimension d. La clé est de trouver un noyau positif qui préserve le contrainte de ce plan c’est-à-dire qui préserve le fait que chaque point se trouve exactement une fois dans chaque hyperplan. Ensuite, en créant une nouvelle chaîne de Markov dont le n-DPP est sa loi stationnaire, nous déterminons le nombre d’étapes nécessaires pour construire un hypercube latin d’ordre n selon le n-DPP
With the exponentially growing amount of data, sampling remains the most relevant method to learn about populations. Sometimes, larger sample size is needed to generate more precise results and to exclude the possibility of missing key information. The problem lies in the fact that sampling large number may be a principal reason of wasting time.In this thesis, our aim is to build bridges between applications of statistics and k-Determinantal Point Process(k-DPP) which is defined through a matrix kernel. We have proposed different applications for sampling large data sets basing on k-DPP, which is a conditional DPP that models only sets of cardinality k. The goal is to select diverse sets that cover a much greater set of objects in polynomial time. This can be achieved by constructing different Markov chains which have the k-DPPs as their stationary distribution.The first application consists in sampling a subset of species in a phylogenetic tree by avoiding redundancy. By defining the k-DPP via an intersection kernel, the results provide a fast mixing sampler for k-DPP, for which a polynomial bound on the mixing time is presented and depends on the height of the phylogenetic tree.The second application aims to clarify how k-DPPs offer a powerful approach to find a diverse subset of nodes in large connected graph which authorizes getting an outline of different types of information related to the ground set. A polynomial bound on the mixing time of the proposed Markov chain is given where the kernel used here is the Moore-Penrose pseudo-inverse of the normalized Laplacian matrix. The resulting mixing time is attained under certain conditions on the eigenvalues of the Laplacian matrix. The third one purposes to use the fixed cardinality DPP in experimental designs as a tool to study a Latin Hypercube Sampling(LHS) of order n. The key is to propose a DPP kernel that establishes the negative correlations between the selected points and preserve the constraint of the design which is strictly confirmed by the occurrence of each point exactly once in each hyperplane. Then by creating a new Markov chain which has n-DPP as its stationary distribution, we determine the number of steps required to build a LHS with accordance to n-DPP

Ce manuscrit est dédié à l’étude des processus ponctuels déterminantaux (DPPs) ainsi qu’à leur estimation paramétrique. Ces processus sont connus pour modéliser des phénomènes répulsifs (le cas où les points ont tendance à se repousser entre eux). Dans la première partie, nous étudions la richesse de ce modèle en proposant deux définitions de la répulsion, basées sur les moments d’ordre deux du processus, plus précisément la fonction de corrélation par paires (pcf) g. Cela nous conduit à la détermination du DPP le plus répulsif. Nous présentons ensuite de nouvelles familles paramétriques de DPPs couvrant toute la plage de répulsion offerte par cette classe. Dans la seconde partie, nous démontrons que les DPPs stationnaires sont Brillinger-mélangeants. Cette propriété basée sur les moments du processus permet d’obtenir des résultats asymptotiques sur différentes statistiques. En particulier, nous démontrons un théorème limite central sur une large classe de fonctionnelles d’ordre p et nous adaptons au cadre des DPPs certains résultats déjà connus sur les estimateurs à noyaux de la pcf g d’un processus Brillinger-mélangeant. Finalement, dans la dernière partie, nous étudions l’estimation d’un DPP paramétrique par minimum de contraste, basée sur les fonctions de Ripley K et la pcf g. Nous prouvons la consistance et la normalité asymptotique de ces méthodes et en particulier, nous obtenons une forme explicite de la variance asymptotique. Ces résultats sont en fait des cas particuliers d’un théorème plus général sur les propriétés asymptotiques des estimateurs par minimum de contraste d’un processus ponctuel stationnaire que nous énonçons et prouvons dans ce chapitre
This manuscript is devoted to the study of determinantal point processes (DPPs) and their parametric estimation. These processes are known to be well adapted to inhibitive point patterns, where the points tend to repel each others. In the first chapter, we study the flexibility of this model by suggesting two definitions of the repulsiveness, both based on the second order moments of the process, namely the pair correlation function (pcf) g. This leads us to identify the most repulsive DPP. Then, we introduce new parametric families of DPPs that cover a large range of DPPs, from the stationary Poisson process to the most repulsive DPP. In the second chapter, we prove that stationary DPPs are Brillinger mixing. This property allows us to deduce asymptotic results on several statistics. Namely, we prove a central limit theorem for a wide class of functionals of order p of the process and we adapt to DPPs some results already known on kernel estimators of the function g of Brillinger mixing point processes. Finally, in the last chapter we study the minimum contrast estimation based on the Ripley’s K-function and the pcf g. We prove the consistency and the asymptotic normality of these methods for stationary DPPs. In particular, we obtain an explicit form of the asymptotic variance. These results are in fact particular cases of a more general theorem dealing with the asymptotic properties of minimum contrast estimation for stationary point processes that we state and prove in this chapter

The thesis consists of three articles concerning reproducing kernels ofweighted spaces of polyanalytic functions on the complex plane. In the first paper, we study spaces of polyanalytic polynomials equipped with a Gaussianweight. In the remaining two papers, more general weight functions are considered. More precisely, we provide two methods to compute asymptotic expansions for the kernels near the diagonal and then apply the techniques to get estimates for reproducing kernels of polyanalytic polynomial spaces equipped with rather general weight functions.

QC 20130513

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
In this work, we show relations between invariants of map germs. First, we consider an analytic function germ f : (X, 0) —(C, 0) on an isolated determinantal singularity and we present a relation between the Euler obstruction of f and the determinantal Milnor number of f. In the particular case where (X, 0) is an isolated complete intersection singularity, we obtain a simple way to calculate the Euler obstruction of f as the difference between the dimension of two algebras. After, we work with map germs f : (X, 0) —— (C2, 0), where (X, 0) is a plane curve with isolated singularity. We introduce the image Milnor number to these map germs and we present a positive answer to the Mond’s conjecture in this context. The Mond’s conjecture proposes an inequality between two other invariants, the A^-codimension and the image Milnor number, in the case of map germs f : (Cn, 0) —(Cn+1, 0) when the dimensions (n,n + 1) is in Mather’s nice dimensions. The conjecture is true for n = 1, 2, and for the cases n > 3 is an open problem.
Neste trabalho, mostramos relações entre invariantes de germes de aplicações. Primeiro, consideramos um germe de funçao analítica f : (X, 0)^(C, 0) sobre uma singularidade determinantal isolada e apresentamos uma relaçao entre a obstrução de Euler de f e o número de Milnor determinantal de f. No caso particular em que (X, 0) e uma interseçao completa com singularidade isolada, obtemos um modo simples de calcular a obstrucao de Euler de f como a diferenca entre dimensães de duas algebras. Depois, trabalhamos com germes de aplicacoes f : (X, 0)^(C2, 0), onde (X, 0) e uma curva plana com singularidade isolada. Introduzimos o número de Milnor da imagem para estes germes de aplicacães e apresentamos uma resposta positiva para a conjectura de Mond neste contexto. A conjectura de Mond propoe uma desigualdade entre outros dois invariantes, a A^-codimensao e o numero de Milnor da imagem, para o caso de germes de aplicacoes f : (Cn, 0)^(Cn+1,0) quando as dimensoes (n,n + 1) estao nas boas dimensoes de Mather. A conjectura e verdadeira para n = 1, 2, e para os casos n > 3 e um problema em aberto.

Latent variable model is a common probabilistic framework which aims to estimate the hidden states of observations. More specifically, the hidden states can be the position of a robot, the low dimensional representation of an observation. Meanwhile, various latent variable models have been explored, such as hidden Markov models (HMM), Gaussian mixture model (GMM), Bayesian Gaussian process latent variable model (BGPLVM), etc. Moreover, these latent variable models have been successfully applied to a wide range of fields, such as robotic navigation, image and video compression, natural language processing. So as to make the learning of latent variable more efficient and robust, some approaches seek to integrate latent variables with related priors. For instance, the dynamic prior can be incorporated so that the learned latent variables take into account the time sequence. Besides, some methods introduce inducing points as a small set representing the large size latent variable to enhance the optimization speed of the model. Though those priors are effective to facilitate the robustness of the latent variable models, the learned latent variables are inclined to be dense rather than diverse. This is to say that there are significant overlapping between the generated latent variables. Consequently, the latent variable model will be ambiguous after optimization. Clearly, a proper diversity prior play a pivotal role in having latent variables capture more diverse features of the observations data. In this thesis, we propose diversified latent variable models incorporated by different types of diversity priors, such as single/dual diversity encouraging prior, multi-layered DPP prior, shared diversity prior. Furthermore, we also illustrate how to formulate the diversity priors in different latent variable models and perform learning, inference on the reformulated latent variable models.

The numerical simulation of quantum many-body systems is an essential instrument in the research on condensed matter Physics. Recent years have witnessed remarkable progress in studying dynamical properties of non-relativistic Bose systems with quantum Monte Carlo (QMC) methods. On the other hand, the numerical study of Fermi systems is a still open problem of great relevance, as fermions constitute a substantial part of ordinary matter and methods for the accurate calculation of their ground-state and dynamical properties would be useful instruments for the interpretation of experimental data. In this thesis, a number of approximate schemes for studying ground-state and dynamical properties of quantum many-body systems are presented and employed to calculate ground-state and dynamical properties of Bose and Fermi systems. In particular, the Path Integral Ground State QMC method is used to investigate density fluctuations in one-dimensional systems of Helium atoms and hard rods, and the phaseless Auxiliary field QMC is used to investigate the electronic band and effective mass of the two-dimensional homogeneous electron gas.

THIS THESIS DESCRIBES THE GRADED MINIMAL FREE RESOLUTION OF A PRODUCT OF IDEALS, EACH GENERATED BY LINEAR FORMS. IT ALSO STUDIES A PHENOMENON OF LINEARIZATION OF THE RESOLUTION OF AN ARBITRARY IDEAL, UPON MULTIPLICATION BY SUFFICIENTLY MANY IDEALS OF GENERIC POINTS IN PROJECTIVE SPACE. FURTHER, IT PROVIDES A CLASS OF BASE SETS OF THE ALGEBRAIC MATROID OF THE DETERMINANTAL VARIETY AND CONJECTURES THAT THESE COMPLETELY CHARACTERIZE THE MATROID. FINALLY, IT PROVIDES DETERMINANTAL CONDITIONS FOR HOMOMORPHIC SENSING, A PROBLEM THAT STUDIES THE UNIQUENESS OF IMAGES OF POINTS IN A VECTOR SUBSPACE UNDER A FINITE SET OF LINEAR TRANSFORMATIONS.

Dans ce travail nous étudions les variétés determinantales essentiellement isolées (EIDS). Ce type de singularité est une généralization de la notion de singularité isolée. La variété determinantale générique $M_{m,n}^t$ est un sous-ensemble des matrices, mxn, tels que le rang est inférieur que t, où t≤m≤n. Une variété X est determinantal si X est définie comme la pré-image d'une fonction holomorphe, $F:\mathbb{C}^N \to M$, sur la variété determinantale générique avec la condition $codim X=codim M_{m,n}^t$.Certains travaux précédents ont étudié les variétés determinantales avec singularité isolée et ils ont défini le nombre de Milnor d'une surface determinantale et la caractéristique évanescente d'Euler.Nous étudions l'ensemble des hyperplans limites d'hyperplans tangents à une surface determinantale en $\mathbb{C}^4$ et 3-variété en $\mathbb{C}^5$ pour donner une caractérisation de ces hyperplans, par le fait que le nombre de Milnor de leur section avec la surface dans le premier cas ou la 3- variété dans le deuxième cas n'est pas minimum.Nous montrons également que, si X est une EIDS, de dimension d et H et H' sont des hyperplans fortement généraux, si $P \subset H$ et $P'\subset H'$ sont des plans de codimension d-2, les nombres de Milnor des surfaces genériques sont égaux.Nous étudions aussi la modification de Nash d'une EIDS et donnons des conditions suffisantes pour que cette transformation soit lisse.Un autre objectif de notre travail est l'étude de l'obstruction d'Euler d Nous obtenons des formules inductives qui relient l'obstruction d'Euler de X à la caractéristique d'Euler évanescente du lissage essentiel de leurs sections génériques
In this work, we study the essentially isolated determinantal singularities (EIDS). This type of singularities is a natural generalization of isolated ones. A generic determinantal variety $M_{m,n}^t$ is a subset of the space of mxn matrices, given by matrices of rank less than t, where t≤m≤n. A variety X is determinantal if X is defined as the pre-image of $M_{m,n}^t$ by a holomorphic function $F:\mathbb{C}^N \to M$ with the condition $codim X=codim M_{m,n}^t$.Several recent works investigate determinantal variety with isolated singularities and they are difened the Milnor number and the vanishing Euler characteristic.In this work we study the set of limits of tangent hyperplanes to surface in $\mathbb{C}^4$ and 3-variety in $\mathbb{C}^5$ to give a characterization of this set by the fact that the Milnor number of its section with the surface in the first case or the 3-dimensional determinantal variety in the second case is not minimum. We also prove that if X is a d- dimensional EIDS and H and H' are strongly general hyperplans, if $P \subset H$ and $P'\subset H'$ are d-2 linear plans, the Milnor number of the generic surfaces are equal.We study the Nash transformation of an EIDS and give sufficient conditions for this transformation to be smooth.Another aim of our study is the Euler obstruction of essentially isolated determinantal singularities. We obtain inductive formulas associating the Euler obstruction with the vanishing Euler characteristic of the essencial smoothing of their generic sections

This Master's Thesis deals with the demand for golf in the Czech Republic. Its aim is to identify the main determinants of the demand for golf and their influence on the golf boom in the Czech Republic. First chapters are devoted to the theory of demand and its determinants. This is followed by a general introduction to golf, namely its brief history in the Czech Republic and the basic specification of the play. The middle part is devoted to the other side of the market, the supply. There are analyzed the status and development of golf infrastructure in terms of different types of golf courses, but also their price. The status and development of the membership of the Czech Golf Federation is analyzed after the supply. A final chapter deals with determinants of demand, whose significance is assessed on the basis of data obtained from the survey.

We propose a new construction of point processes, which generalizes the class of infinitely divisible point processes. Examples are the quantum Boson and Fermion gases as well as the classical Gibbs point processes, where the interaction is given by a stable and regular pair potential.

Neste trabalho, estudamos a classificação de singularidades de curvas espaciais simples que não são intersecções completas. O Teorema de Hilbert-Burch nos permite usar a matriz de representação para estudar a variedade definida pelo ideal gerado por seus menores maximais. Da mesma forma, as deformações da variedade determinantal podem ser representadas por perturbações da matriz e qualquer perturbação da matriz fornece uma deformação da variedade. Assim, o estudo das singularidades de curvas determinantais pode ser formulado em termos da matriz de representação da curva
In this work, we study the classification of simple space curve singularities which are not complete intersections. The Theorem of Hilbert-Burch enables us to deal with the presentation matrices instead of the ideals defined by their maximal minors. In the same way, deformations of the determinantal variety can be represented by perturbations of the matrix and any perturbation of the matrix gives rise to a deformation of the variety. Therefore, the study of determinantal curves can be formulated in terms of the presentation matrices

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PROQUALI (UFJF)
O presente trabalho teve o objetivo de identificar e avaliar os determinantes do intraempreendedorismo, individual e organizacional, presentes na Pró-Reitoria de Recursos Humanos (PRORH) da Universidade Federal de Juiz de Fora (UFJF), segundo a percepção de seus gestores e servidores. O referencial teórico pautou-se em características do comportamento empreendedor e características organizacionais do intraempreendedorismo, de modo geral, destacando-se as contribuições de McClelland (1987) e Hornsby, Kuratko e Zahra (2002), cujos modelos conceituais foram adotados para fins da pesquisa realizada. A pesquisa realizada adotou o estudo de caso descritivo, com abordagem quantitativa e qualitativa. Os dados foram tratados e analisados conforme sua natureza (análise uni e bivariada e análise de conteúdo, respectivamente). A partir dos dados coletados na primeira fase da pesquisa, pode-se constatar que o perfil dos servidores pesquisados apresenta um nível mediano de desenvolvimento das características comportamentais empreendedoras. Semelhanças positivas foram identificadas entre os dados das duas fases da pesquisa no que diz respeito às principais características empreendedoras mais e menos desenvolvidas. Quanto aos determinantes organizacionais, a média geral dos fatores estruturais organizacionais do intraempreendedorismo, segundo a percepção dos gestores e servidores foi de 2,87. Uma proximidade com o nível médio de intraempreendedorismo, contudo, ainda não se pode qualificá-lo como tal. Apuraram-se semelhanças positivas entre os dados das duas fases da pesquisa no que se refere ao fator organizacional mais e menos desenvolvido na instituição. A análise comparativa entre os dados qualitativos e os quantitativos demonstra uma consonância entre a percepção dos entrevistados e a dos respondentes dos testes. Também foram identificadas tendências de correlações entre os determinantes individuais e organizacionais do intraempreendedorismo. No que diz respeito aos desafios da atuação intraempreendedora na UFJF, os entrevistados identificaram que a implantar um sistema de recompensas/reforços, gerir por competência e trabalhar o fator motivacional dos servidores deveriam ser os principais mecanismos utilizados para incentivar os funcionários a serem mais criativos, inovadores e proativos. Os entrevistados apresentaram questões políticas, burocracia e hierarquia, ausência de uma cultura intraempreendedora e rigidez estrutural e legal como as principais barreiras impostas ao desenvolvimento da iniciativa intraempreendedora na UFJF. A pesquisa avaliou o nível dos determinantes individuais e organizacionais, permitindo ações mais efetivas com o fim de estimular o intraempreendedorismo. Diante dos resultados do estudo, sugere-se a realização de outros estudos, na mesma instituição, considerando outras pró-reitorias e em outras instituições públicas, com o objetivo de se aprofundar no fenômeno intraempreendedorismo na instituição pública.
The purpose of this paper was to identify and assess organizational and individual determinants of intra-entrepreneurship in the Rectory of Human Resources (PRORH) of the Federal University of Juiz de Fora (UFJF), according to its administrators and personnel. The theoretical references were based upon the entrepreneur behavior and the organizational features of entrepreneurship, in general. There was a highlight on the contributions of McClelland (1987) and Hornsby, Kuratko & Zahra (2002), whose conceptual models were adopted for the research. It used the method of descriptive case study, with quantitative and qualitative approach. Data were dealt with and analyzed according to their nature (uni/bivaried analysis and content analysis, respectfully). From the data collected during the first phase, one could verify that the staff profile presents a medium level in the development of entrepreneurial behavior features. There were positive similarities that could be identified between data from both phases, in relation to the main entrepreneur features more and less developed. As for organizational determinants, the general average was 2.87, according to, which indicates closeness to the entrepreneurship medium level. However, it cannot be qualified as such. Also, the positive similarities between the two phases were searched in terms of the institution‟s organizational factor more and less developed. Comparative analysis of qualitative and quantitative data shows a consonance between the individuals who were interviewed and the ones who answered the tests. Furthermore, tendencies for correlations between individual and organizational determinants were detected. As for the challenges of the intra-entrepreneurial action in UFJF, interviewees showed that at implanting a system for compensations/efforts, managing through competence and dealing with the staff‟s motivational factor should be the main mechanisms towards encouraging staff to become more creative, innovative and pro-active. Interviewees indicated political issues, bureaucracy and hierarchy, lack of an intra- entrepreneurial and structural and legal rigidity, as imposed barriers for the development of intra- entrepreneurial action at UFJF. The research assessed the level of individual and organizational determinants, enabling more effective actions in order to stimulate intra-entrepreneurship. Given the results and the study limitations, a schedule was created for future research, aiming to going deeper into the issue of intra- entrepreneurship in the public institution.

The mathematical modeling and performance analysis of cellular networks have seen a major paradigm shift with the application of stochastic geometry. The main purpose of stochastic geometry is to endow probability distributions on the locations of the base stations (BSs) and users in a network, which, in turn, provides an analytical handle on the performance evaluation of cellular networks. To preserve the tractability of analysis, the common practice is to assume complete spatial randomness} of the network topology. In other words, the locations of users and BSs are modeled as independent homogeneous Poisson point processes (PPPs). Despite its usefulness, the PPP-based network models fail to capture any spatial coupling between the users and BSs which is dominant in a multi-tier cellular network (also known as the heterogeneous cellular networks (HetNets)) consisting of macro and small cells. For instance, the users tend to form hotspots or clusters at certain locations and the small cell BSs (SBSs) are deployed at higher densities at these locations of the hotspots in order to cater to the high data demand. Such user-centric deployments naturally couple the locations of the users and SBSs. On the other hand, these spatial couplings are at the heart of the spatial models used in industry for the system-level simulations and standardization purposes. This dissertation proposes fundamentally new spatial models based on stochastic geometry which closely emulate these spatial couplings and are conductive for a more realistic and fine-tuned performance analysis, optimization, and design of cellular networks. First, this dissertation proposes a new class of spatial models for HetNets where the locations of the BSs and users are assumed to be distributed as Poisson cluster process (PCP). From the modeling perspective, the proposed models can capture different spatial couplings in a network topology such as the user hotspots and user BS coupling occurring due to the user-centric deployment of the SBSs. The PCP-based model is a generalization of the state-of-the-art PPP-based HetNet model. This is because the model reduces to the PPP-based model once all spatial couplings in the network are ignored. From the stochastic geometry perspective, we have made contributions in deriving the fundamental distribution properties of PCP, such as the distance distributions and sum-product functionals, which are instrumental for the performance characterization of the HetNets, such as coverage and rate. The focus on more refined spatial models for small cells and users brings to the second direction of the dissertation, which is modeling and analysis of HetNets with millimeter wave (mm-wave) integrated access and backhaul (IAB), an emerging design concept of the fifth generation (5G) cellular networks. While the concepts of network densification with small cells have emerged in the fourth generation (4G) era, the small cells can be realistically deployed with IAB since it solves the problem of high capacity wired backhaul of SBSs by replacing the last-mile fibers with mm-wave links. We have proposed new stochastic geometry-based models for the performance analysis of IAB-enabled HetNets. Our analysis reveals some interesting system-design insights: (1) the IAB HetNets can support a maximum number of users beyond which the data rate drops below the rate of a single-tier macro-only network, and (2) there exists a saturation point of SBS density beyond which no rate gain is observed with the addition of more SBSs. The third and final direction of this dissertation is the combination of machine learning and stochastic geometry to construct a new class of data driven network models which can be used in the performance optimization and design of a network. As a concrete example, we investigate the classical problem of wireless link scheduling where the objective is to choose an optimal subset of simultaneously active transmitters (Tx-s) from a ground set of Tx-s which will maximize the network-wide sum-rate. Since the optimization problem is NP-hard, we replace the computationally expensive heuristic by inferring the point patterns of the active Tx-s in the optimal subset after training a determinantal point process (DPP). Our investigations demonstrate that the DPP is able to learn the spatial interactions of the Tx-s in the optimal subset and gives a reasonably accurate estimate of the optimal subset for any new ground set of Tx-s.
Doctor of Philosophy
The high speed global cellular communication network is one of the most important technologies, and it continues to evolve rapidly with every new generation. This evolution greatly depends on observing performance-trends of the emerging technologies on the network models through extensive system-level simulations. Since these simulation models are extremely time-consuming and error prone, the complementary analytical models of cellular networks have been an area of active research for a long time. These analytical models are intended to provide crisp insights on the network behavior such as the dependence of network performance metrics (such as coverage or rate) on key system-level parameters (such as transmission powers, base station (BS) density) which serve as the prior knowledge for more fine-tuned simulations. Over the last decade, the analytical modeling of the cellular networks has been driven by stochastic geometry. The main purpose of stochastic geometry is to endow the locations of the base stations (BSs) and users with probability distributions and then leverage the properties of these distributions to average out the spatial randomness. This process of spatial averaging allows us to derive the analytical expressions of the system-level performance metrics despite the presence of a large number of random variables (such as BS and user locations, channel gains) under some reasonable assumptions. The simplest stochastic geometry based model of cellular networks, which is also the most tractable, is the so-called Poisson point process (PPP) based network model. In this model, users and BSs are assumed to be distributed as independent homogeneous PPPs. This is equivalent to saying that the users and BSs independently and uniformly at random over a plane. The PPP-based model turned out to be a reasonably accurate representation of the yesteryear’s cellular networks which consisted of a single tier of macro BSs (MBSs) intended to provide a uniform coverage blanket over the region. However, as the data-hungry devices like smart-phones, tablets, and application like online gaming continue to flood the consumer market, the network configuration is rapidly deviating from this baseline setup with different spatial interactions between BSs and users (also termed spatial coupling) becoming dominant. For instance, the user locations are far from being homogeneous as they are concentrated in specific areas like residential and commercial zones (also known as hotspots). Further, the network, previously consisting of a single tier of macro BSs (MBSs), is becoming increasingly heterogeneous with the deployment of small cell BSs (SBSs) with small coverage footprints and targeted to serve the user hotspots. It is not difficult to see that the network topology with these spatial couplings is quite far from complete spatial randomness which is the basis of the PPP-based models. The key contribution of this dissertation is to enrich the stochastic geometry-based mathematical models so that they can capture the fine-grained spatial couplings between the BSs and users. More specifically, this dissertation contributes in the following three research directions. Direction-I: Modeling Spatial Clustering. We model the locations of users and SBSs forming hotspots as Poisson cluster processes (PCPs). A PCP is a collection of offspring points which are located around the parent points which belong to a PPP. The coupling between the locations of users and SBSs (due to their user-centric deployment) can be introduced by assuming that the user and SBS PCPs share the same parent PPP. The key contribution in this direction is the construction of a general HetNet model with a mixture of PPP and PCP-distributed BSs and user distributions. Note that the baseline PPP-based HetNet model appears as one of the many configurations supported by this general model. For this general model, we derive the analytical expressions of the performance metrics like coverage probability, BS load, and rate as functions of the coupling parameters (e.g. BS and user cluster size). Direction-II: Modeling Coupling in Wireless Backhaul Networks. While the deployment of SBSs clearly enhances the network performance in terms of coverage, one might wonder: how long network densification with tens of thousands of SBSs can meet the everincreasing data demand? It turns out that in the current network setting, where the backhaul links (i.e. the links between the BSs and core network) are still wired, it is not feasible to densify the network beyond some limit. This backhaul bottleneck can be overcome if the backhaul links also become wireless and the backhaul and access links (link between user and BS) are jointly managed by an integrated access and backhaul (IAB) network. In this direction, we develop the analytical models of IAB-enabled HetNets where the key challenge is to tackle new types of couplings which exist between the rates on the wireless access and backhaul links. Such couplings exist due to the spatial correlation of the signal qualities of the two links and the number of users served by different BSs. Two fundamental insights obtained from this work are as follows: (1) the IAB HetNets can support a maximum number of users beyond which the network performance drops below that of a single-tier macro-only network, and (2) there exists a saturation point of SBS density beyond which no performance gain is observed with the addition of more SBSs. Direction-III: Modeling Repulsion. In this direction, we focus on modeling another aspect of spatial coupling imposed by the intra-point repulsion. Consider a device-to-device (D2D) communication scenario, where some users are transmitting some on-demand content locally cached in their devices using a common channel. Any reasonable multiple access scheme will ensure that two nearly users are never simultaneously active as they will cause severe mutual interference and thereby reducing the network-wide sum rate. Thus the active users in the network will have some spatial repulsion. The locations of these users can be modeled as determinantal point processes (DPPs). The key property of DPP is that it forms a bridge between stochastic geometry and machine learning, two otherwise non-overlapping paradigms for wireless network modeling and design. The main focus in this direction is to explore the learning framework of DPP and bring together advantages of stochastic geometry and machine learning to construct a new class of data-driven analytical network models.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
Este trabalho trata das propriedades e aplicaÃÃes dos determinantes reconhecendo-os como uma ferramenta importante para sintetizar a representaÃÃo e o cÃlculo de algumas funÃÃes e equaÃÃes na Ãrea de geometria analÃtica e Ãlgebra linear. Nos primeiros capÃtulos apresentam-se um pouco da histÃria dos determinantes, os matemÃticos que contribuÃram na sua evoluÃÃo e a necessidade que gerou o inÃcio do seu estudo. Prossegue-se entÃo, a definiÃÃo de determinante e o cÃlculo dos determinantes a partir do teorema de Laplace via recorrÃncia, bem como o dispositivo prÃtico de Sarrus para determinante de terceira ordem. No capÃtulo seguinte, sÃo apresentadas as propriedades, num total de doze, com suas demonstraÃÃes e exemplos, pois elas serÃo utilizadas nas aplicaÃÃes dos determinantes. Logo apÃs, apresenta-se uma sÃrie de aplicaÃÃes na Ãrea de Ãlgebra linear, por exemplo: dependÃncia e independÃncia linear, matriz inversa, soluÃÃo de sistemas lineares (Regra de Cramer) e produto vetorial; alÃm de aplicaÃÃes na Ãrea de geometria analÃtica, tais como: condiÃÃo de alinhamento de trÃs pontos, Ãrea do paralelogramo e volume do paralelepÃpedo. Por fim, conclui-se que à fundamental o professor da segunda sÃrie do ensino mÃdio abordar em suas aulas um pouco da histÃria, chamando a atenÃÃo dos alunos para os matemÃticos que se destacaram neste estudo; expor as aplicaÃÃes dos determinantes, despertando a curiosidade de seus alunos e o interesse pela Ãrea de Ãlgebra linear ou geometria analÃtica.
This paper deals with the properties and applications of determinants recognizing them as an important tool to synthesize the representation and calculation of some functions and equations in the field of analytical geometry and linear algebra. In the first chapters we present some of the history of determinants, the mathematicians who contributed in its evolution and the need that generated the beginning of their study. Then we proceed, the definition of determining and calculating the determinants from the theorem of Laplace via recurrence as well as the handy device for determining Sarrus third order. In the next chapter, we present the properties, a total of twelve, with their statements and examples, as they will be used in applications of determinants. Soon after, it presents a number of applications in linear algebra, eg, linear dependence and independence, inverse matrix, solution of linear systems (Cramer's Rule) and cross product; addition to applications in analytical geometry, such as alignment condition of three points of the parallelogram area and volume of the parallelepiped. Finally, it is concluded that it is essential the teacher of the second grade of high school address in their classes a little history, calling students' attention to mathematicians who have excelled in this study; expose the applications of determinants, arousing the curiosity of their students and interest in the area of linear algebra and analytic geometry.

Ce manuscrit est dédié à l'étude de l'estimation paramétrique d'une famille de processus ponctuels appelée processus déterminantaux. Ces processus sont utilisés afin de générer et modéliser des configurations de points possédant de la dépendance négative, dans le sens où les points ont tendance à se repousser entre eux. Plus précisément, nous étudions les propriétés asymptotiques de divers estimateurs classiques de processus déterminantaux paramétriques, stationnaires et non-stationnaires, dans les cas où l'on observe une unique réalisation d'un tel processus sur une fenêtre bornée. Ici, l'asymptotique se fait sur la taille de la fenêtre et donc, indirectement, sur le nombre de points observés. Dans une première partie, nous montrons un théorème limite central pour une classe générale de statistiques sur les processus déterminantaux. Dans une seconde partie, nous montrons une inégalité de béta-mélange générale pour les processus ponctuels que nous appliquons ensuite aux processus déterminantaux. Dans une troisième partie, nous appliquons le théorème limite central obtenu à la première partie à une classe générale de fonctions estimantes basées sur des méthodes de moments. Finalement, dans la dernière partie, nous étudions le comportement asymptotique du maximum de vraisemblance des processus déterminantaux. Nous donnons une approximation asymptotique de la log-vraisemblance qui est calculable numériquement et nous étudions la consistance de son maximum
This manuscript is devoted to the study of parametric estimation of a point process family called determinantal point processes. These point processes are used to generate and model point patterns with negative dependency, meaning that the points tend to repel each other. More precisely, we study the asymptotic properties of various classical parametric estimators of determinantal point processes, stationary and non stationary, when considering that we observe a unique realization of such a point process on a bounded window. In this case, the asymptotic is done on the size of the window and therefore, indirectly, on the number of observed points. In the first chapter, we prove a central limit theorem for a wide class of statistics on determinantal point processes. In the second chapter, we show a general beta-mixing inequality for point processes and apply our result to the determinantal case. In the third chapter, we apply the central limit theorem showed in the first chapter to a wide class of moment-based estimating functions. Finally, in the last chapter, we study the asymptotic behaviour of the maximum likelihood estimator of determinantal point processes. We give an asymptotic approximation of the log-likelihood that is computationally tractable and we study the consistency of its maximum

Studiamo trasformazioni di Cremona determinantale, cioè trasformazioni birazionale il cui ideale di base è l'ideale dei minori massimali di una matrice Phi, via la risoluzioni dei sistemi di polinomi definiti da Phi. Usando geometria convessa, questo approccio porta in particolare a descrivere i gradi proiettivi di alcuni trasformazioni di Cremona determinantale raccolte.
We study determinantal Cremona maps, i.e. birational maps whose base ideal is the maximal minors ideal of a given matrix Phi, via the resolution of the polynomials systems defined by Phi. Using convex geometry, this approach leads in particular to describe the projective degrees of some glued determinantal maps.

Mestrado em Finanças
Esta dissertação procura analisar os fatores que contribuem para o empreendedorismo regional. Para tal, consideramos os fatores de oferta de empreendedores, os fatores de procura de empreendedores e os fatores políticos e institucionais. Os dados utilizados são provenientes do Instituto Nacional de Estatística (INE) e PORDATA, nos quais consideramos características económicas e demográficas de cada um dos 278 municípios de Portugal continental, durante o período de 2012-2018. Desenvolvemos três regressões multilineares para proceder à nossa análise empírica. Determinámos que regiões com maior população, composta por indivíduos jovens e com educação, e com proporções maiores de população masculina em combinação com um tecido empresarial com uma taxa mais baixa de microempresas, têm taxas de entrada de empresas maiores. Verificámos também que, municípios com taxas de derrama mais reduzidas tem tendência a ter mais atividade empreendedora. Contudo não verificámos significância estatística num conjunto de variáveis no qual se incluí a densidade populacional, ganho médio mensal, taxa de desemprego ou partido político no poder, componentes dos três vetores dos nossos modelos. Concluímos ainda que as variáveis não apresentam significância estatística ao explicar as taxas de saída de empresas apesar de sugerirem relações na mesma direção e menor magnitude em termos de impacto na variável dependente. Os resultados mantêm-se ao analisar a taxa líquida de entrada de empresas.
This study aims to analyse the factors contributing to the regional entrepreneurship. We consider the entrepreneurial supply factors, entrepreneurial demand factors and, political and policy factors in our analysis. The data used is from Statistics Portugal (INE) and PORDATA and we considered economic and demographic characteristics for all 278 Portuguese mainland counties for the 2012-2018 period. We developed a multiple linear regression analysis to perform our empirical procedures. We find that regions where the population is higher, composed by a younger and high school educated people and with greater proportions of male individuals combined with an economic frame composed by smaller proportions of micro firms, have a higher firm entry rate. We have also found that regions with a lower derrama tax rate tend to have higher entrepreneurial activity. However, we found no statistical significance on a set of variables including the population density, average monthly income, unemployment rates or even the political party in control that are components of the three vectors used in our models. We also conclude that the variables do not have statistical significance when explaining the firm exit rates, even though they suggest similar direction and lower magnitude in terms of impact on the dependent variable. The results hold when analysing the net firm entry rate.
info:eu-repo/semantics/publishedVersion

La plupart des systèmes de recommandation actuels se base sur des évaluations sous forme de notes (i.e., chiffre entre 0 et 5) pour conseiller un contenu (film, restaurant...) à un utilisateur. Ce dernier a souvent la possibilité de commenter ce contenu sous forme de texte en plus de l'évaluer. Il est difficile d'extraire de l'information d'un texte brut tandis qu'une simple note contient peu d'information sur le contenu et l'utilisateur. Dans cette thèse, nous tentons de suggérer à l'utilisateur un texte lisible personnalisé pour l'aider à se faire rapidement une opinion à propos d'un contenu. Plus spécifiquement, nous construisons d'abord un modèle thématique prédisant une description de film personnalisée à partir de commentaires textuels. Notre modèle sépare les thèmes qualitatifs (i.e., véhiculant une opinion) des thèmes descriptifs en combinant des commentaires textuels et des notes sous forme de nombres dans un modèle probabiliste joint. Nous évaluons notre modèle sur une base de données IMDB et illustrons ses performances à travers la comparaison de thèmes. Nous étudions ensuite l'inférence de paramètres dans des modèles à variables latentes à grande échelle, incluant la plupart des modèles thématiques. Nous proposons un traitement unifié de l'inférence en ligne pour les modèles à variables latentes à partir de familles exponentielles non-canoniques et faisons explicitement apparaître les liens existants entre plusieurs méthodes fréquentistes et Bayesiennes proposées auparavant. Nous proposons aussi une nouvelle méthode d'inférence pour l'estimation fréquentiste des paramètres qui adapte les méthodes MCMC à l'inférence en ligne des modèles à variables latentes en utilisant proprement un échantillonnage de Gibbs local. Pour le modèle thématique d'allocation de Dirichlet latente, nous fournissons une vaste série d'expériences et de comparaisons avec des travaux existants dans laquelle notre nouvelle approche est plus performante que les méthodes proposées auparavant. Enfin, nous proposons une nouvelle classe de processus ponctuels déterminantaux (PPD) qui peut être manipulée pour l'inférence et l'apprentissage de paramètres en un temps potentiellement sous-linéaire en le nombre d'objets. Cette classe, basée sur une factorisation spécifique de faible rang du noyau marginal, est particulièrement adaptée à une sous-classe de PPD continus et de PPD définis sur un nombre exponentiel d'objets. Nous appliquons cette classe à la modélisation de documents textuels comme échantillons d'un PPD sur les phrases et proposons une formulation du maximum de vraisemblance conditionnel pour modéliser les proportions de thèmes, ce qui est rendu possible sans aucune approximation avec notre classe de PPD. Nous présentons une application à la synthèse de documents avec un PPD sur 2 à la puissance 500 objets, où les résumés sont composés de phrases lisibles
Most of current recommendation systems are based on ratings (i.e. numbers between 0 and 5) and try to suggest a content (movie, restaurant...) to a user. These systems usually allow users to provide a text review for this content in addition to ratings. It is hard to extract useful information from raw text while a rating does not contain much information on the content and the user. In this thesis, we tackle the problem of suggesting personalized readable text to users to help them make a quick decision about a content. More specifically, we first build a topic model that predicts personalized movie description from text reviews. Our model extracts distinct qualitative (i.e., which convey opinion) and descriptive topics by combining text reviews and movie ratings in a joint probabilistic model. We evaluate our model on an IMDB dataset and illustrate its performance through comparison of topics. We then study parameter inference in large-scale latent variable models, that include most topic models. We propose a unified treatment of online inference for latent variable models from a non-canonical exponential family, and draw explicit links between several previously proposed frequentist or Bayesian methods. We also propose a novel inference method for the frequentist estimation of parameters, that adapts MCMC methods to online inference of latent variable models with the proper use of local Gibbs sampling.~For the specific latent Dirichlet allocation topic model, we provide an extensive set of experiments and comparisons with existing work, where our new approach outperforms all previously proposed methods. Finally, we propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items. This class, based on a specific low-rank factorization of the marginal kernel, is particularly suited to a subclass of continuous DPPs and DPPs defined on exponentially many items. We apply this new class to modelling text documents as sampling a DPP of sentences, and propose a conditional maximum likelihood formulation to model topic proportions, which is made possible with no approximation for our class of DPPs. We present an application to document summarization with a DPP on 2 to the power 500 items, where the summaries are composed of readable sentences

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The study of determinants development through the permutations made on their lines or columns dates back to 1812, a memory presented by Cauchy to the French Academy of Sciences. The present work is, in some way, a historical rescue. Firstly, a permutation is de ned: from a superior point of view there is a bijective application and, as such, the set of permutations has a group structure; from the elementary point of view, there is an ordainment of a group's elements. The fundamental fact is, secondly, that the de nition of determinant adjusts perfectly to both conceptions, based on the parity of the permutations. Based on the de nitions, the determinants properties are presented and, therefore, it is possible to proceed with the appropriate justi cations about their validity. A rule that associates each square matrix to a real number will de ne a real function of the variable matrix, the determinant function. This is the actual way in which determinants are presented in higher levels: the determinant is the unique alternated multilinear function of the lines (columns) of a square matrix, as indicated in [10]. By this presentation there is in mind the fact that it can be served as an inspiration to posterior studies.
O estudo sobre o desenvolvimento dos determinantes por meio das permuta ções efetuadas sobre suas linhas ou colunas remonta a 1812, com uma mem ória apresentada por Cauchy a academia de ciências da Fran ça. O presente trabalho e, em certo sentido, um resgate hist órico. Em primeiro lugar de ve-se uma permuta ção: sob um ponto de vista superior tem-se uma aplica c~ao bijetiva e, como tal, o conjunto das permuta c~oes possui uma estrutura de grupo; do ponto de vista elementar, tem-se um ordenamento de elementos de um conjunto. O fato fundamental e que, em segundo lugar, a de ni c~ao de determinante se ajusta perfeitamente as duas concep ções, tomando por base a paridade das permuta ções. Baseando nas de ni ções, as propriedades dos determinantes s~ao apresentadas e, assim, pode-se proceder com as devidas justi ficativas sobre a validade das mesmas. Uma regra que associe a cada matriz quadrada um n umero real de nir a uma fun c~ao real de vari avel matricial, a fun ção determinante. E a forma atual como os determinantes s~ao apresentados em n veis superiores: o determinante e a unica fun ção multilinear alternada das linhas (colunas) de uma matriz quadrada, conforme exibido em [10]. Com tal apresenta c~ao, tem-se em mente, o fato de poder servir de inspira c~ao em estudos posteriores.

Mestrado em Economia e Políticas Públicas
A preocupação com a transparência no sector local tem crescido com a descentralização de competências para os governos locais e a independência de que estes gozam face ao governo central. As suas implicações na prestação de contas dos governos aos eleitores/contribuintes e no combate à corrupção fazem da transparência e seus determinantes um objeto de análise relevante. Em face do reduzido número de estudos na literatura, a presente dissertação visa dar um contributo nesta área ainda pouco explorada. O objetivo central consiste na identificação de impulsionadores e inibidores da transparência nos municípios portugueses, considerando que o nível de transparência é produto das características dos agentes que influenciam a sua oferta (dirigentes públicos e políticos) e procura (cidadãos). Recorrendo ao Índice de Transparência Municipal de 2013 como medida de transparência, testou-se o papel de fatores políticos, sociodemográficos, orçamentais, de situação económica, capital social e envolvimento dos cidadãos para um universo de 301 municípios portugueses. Os resultados obtidos identificam como impulsionadores da transparência o nível de instrução da população e o aumento do endividamento do município, resultado que não deixa de ser intrigante. Foi considerada significativa a dimensão do município em número de residentes, tendo-se verificado que municípios maiores tendem a ser mais transparentes revelando-se expressiva a dicotomia pequeno vs. grande município. Níveis mais elevados de despesa efetiva per capita e taxas de desemprego mais altas parecem constituir inibidores da transparência.
The concern with public transparency has increased with the decentralization of powers to local governments and their independence from central government. Transparency's role on government accountability towards its electors and taxpayers as well as on eradicating corruption makes the study of transparency and its determinants extremely relevant. Given the small number of studies addressing transparency's determinants, this dissertation aims at providing an approach to this still underexplored area. The main purpose is to identify both the drivers and inhibitors of transparency in Portuguese municipalities considering that the transparency level is a result of supply agents - (public officials and politicians) and demand agents - (citizens) features. Resorting to the Municipal Transparency Index 2013 as transparency measure, the role of political, socio-demographic, economic situation, budget, social capital and citizen engagement factors was tested across 301 municipalities. The results point to education and higher level of debt as transparency drivers, the latter being quite a puzzling outcome. It was also considered significant the number of residents as the results show that municipalities with more residents tend to be more transparent which reflects the dichotomy between small and large municipalities. The results indicate that higher levels of per capita effective expenditure as well as higher unemployment rates work as inhibitors of information disclosure by the local government.

Trabalho Complementar apresentado à Universidade Fernando Pessoa como parte dos requisitos para obtenção do grau de licenciada em Ciências da Nutrição
Introdução: A literacia em saúde inclui diversas dimensões, das quais se destacam os conhecimentos sobre alimentação e nutrição. Apesar de um elevado conhecimento alimentar/nutricional, por si só, parecer não determinar mudanças positivas nas escolhas alimentares e de outros estilos de vida, pode munir os indivíduos com ferramentas que apoiem melhores escolhas para a sua saúde. Objetivos: Este estudo teve como objetivo avaliar o nível de conhecimento sobre alimentação e nutrição de estudantes do 1ºciclo de estudos da área das Ciências da Saúde, e avaliar os seus fatores associados. Metodologia: Foi conduzido um estudo observacional transversal, que incluiu estudantes do Ensino Superior da área das Ciências da Saúde, a frequentar o 1º ano do ensino regular no ano letivo de 2019/2020 (proporção de participação de 84%, entre os elegíveis). A amostra final incluiu 150 participantes (75% do sexo feminino), com uma média de idades de 20 anos (desvio-padrão (dp)=0,30 anos). Procedeu-se à aplicação de um questionário estruturado de autopreenchimento para a recolha de dados, anónimo e confidencial. Os conhecimentos sobre alimentação/nutrição foram avaliados através de uma escala previamente testada na população portuguesa (âmbito de variação: 0-100%). As variáveis categóricas foram comparadas através do teste de Qui-quadrado e as variáveis quantitativas contínuas foram descritas através da média (dp) e foram comparadas através do teste ANOVA. Resultados: A percentagem média de respostas corretas na escala de conhecimentos sobre alimentação/nutrição foi de 77,9% (dp=12,57), com um mínimo de 36% e um máximo de 100%. Embora as diferenças sejam relativamente pequenas e maioritariamente sem significado estatístico, os indivíduos com mais conhecimentos sobre alimentação e nutrição mostraram apresentar estilos de vida mais saudáveis, isto é um maior consumo de fruta e produtos hortícolas, uma prática de atividade desportiva mais regular, melhores hábitos de sono (pelo menos 8 horas diárias) e uma maior frequência de toma de suplementos vitamínicos. Ao analisarmos os fatores associados a um conhecimento em alimentação/nutrição extremo (>90% respostas corretas), verificou-se que este foi significativamente superior nos indivíduos que reportaram um consumo médio mais elevado de fruta e produtos hortícolas (4,6 vs. 3,2 porções/dia, p=0,019), particularmente de sopa, nos estudantes com mães mais escolarizadas (12,7 vs. 11,3 anos médios de escolaridade, p=0,039) e nos estudantes da Faculdade de Ciências da Saúde comparativamente aos da Escola Superior de Saúde (55,0% vs. 45,0%, p=0,018). Conclusões: O nível de conhecimentos sobre alimentação e nutrição em estudantes do Ensino Superior da área das Ciências da Saúde foi relativamente elevado (78%). Os fatores que se mostraram significativamente associados a um maior conhecimento (>90% respostas corretas) foram o maior consumo de fruta e produtos hortícolas, uma maior escolaridade da mãe e a Faculdade/Escola que frequentavam.
Background: Health literacy includes several dimensions, including knowledge about food and nutrition. Although a high food/nutritional knowledge, by itself, does not seem to determine positive changes in food choices and other lifestyles, it can provide individuals with tools that support better choices for their health. Objectives: This study aimed to evaluate the level of knowledge in food and nutrition of students of the 1st cycle of studies in the area of Health Sciences, and to evaluate its associated factors. Methodology: An observational cross-sectional study was conducted, which included higher education students in the area of Health Sciences, attending the 1st year of regular education in the 2019/2020 school year (participation proportion of 84%, among eligible students). The final sample included 150 participants (75% female), with a mean age of 20 years (standard deviation (SD)=0.30 years). A structured self-completed questionnaire was applied for the collection of data, anonymous and confidential. Knowledge about food/nutrition was evaluated using a scale previously tested in the Portuguese population (range: 0-100%). Categorical variables were compared using the Chi-square test and the continuous quantitative variables were described by mean (standard deviation) and were compared using the ANOVA test. Results: The mean percentage of correct answers on the food/nutrition knowledge scale was 77.9% (SD=12.57), with a minimum of 36% and a maximum of 100%. Although the differences are relatively small and mostly without statistical significance, individuals with more knowledge about food and nutrition showed to have healthier lifestyles, such as a higher consumption of fruit and vegetables, a more regular practice of sports activity, better sleep habits (at least 8 hours daily) and a higher frequency of taking vitamin supplements. When analyzing the factors associated with an extreme food/nutrition knowledge (>90% correct answers), it was found that this was significantly higher in individuals who reported a higher average consumption of fruit and vegetables (4.6 vs. 3.2 portion/day, p=0.019), particularly soup, in students with more educated mothers (12.7 vs. 11.3 average years of schooling, p=0.039) and in students of the Faculty of Health Sciences compared to those of the Higher School of Health (55.0% vs. 45.0%, p=0.018). Conclusions: The level of knowledge about food and nutrition in higher education students in the area of Health Sciences was relatively high (78%). The factors that were significantly associated with a greater knowledge (>90% correct answers) were a higher consumption of fruit and vegetables, a higher maternal education and the College/School they attended.
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A não adesão à terapêutica é determinante do aumento de taxas de morbilidade e de mortalidade dos doentes e de perturbações e gastos financeiros das organizações de saúde. O presente estudo teve como objectivo identificar determinantes de não adesão à terapêutica antiagregante plaquetária em doentes que foram submetidos a angioplastia transluminal percutânea coronária. Participaram neste estudo duas amostras de doentes com características demográficas semelhantes mas que deferiam no seu comportamento de adesão. Como metodologia para a identificação das crenças dos doentes em relação à doença ao tratamento foi utilizada um entrevista semi-estruturada baseada nas dimensões do Modelo de Crenças de Saúde. Os resultados evidenciam diferenças entre os dois grupos em especial no que diz respeito a: conhecimento da situação clínica e do tratamento; benefícios/custo do tratamento; consequências; percepção de auto-eficácia e vulnerabilidade. Baseado nos resultados apontam-se pistas de intervenção para a melhoria da qualidade dos cuidados de saúde prestados a estes doentes, numa perspectiva de governança clínica. – ABSTRACT: Non-adherence to treatment prescription is determinant of morbidity and mortality and is associated to organizational problems and financial costs. This study aimed to identify determinants of non-adherence to patients with Percutaneous Transluminal Coronary Angioplasty. The sample was constituted by two groups of patients with similar demographic characteristics and with different adherence behaviour. As methodology we used a semi-structured interview based on the Health Belief Model. Results show differences between the two groups in dimensions as: knowledge about the clinical situation and the treatment; benefits/costs of the treatment; consequences of adherence behaviour; self-efficacy and vulnerability: Based on the results we present some contributions to the quality of care of these patients and doing so hope to contribute to better organization in health services.

Este estudo foi elaborado com o objetivo de elucidar os mecanismos de resistência às quinolonas presentes em enterobactérias isoladas de pacientes de duas regiões metropolitanas brasileiras. Foram avaliadas possíveis alterações nas proteínas relacionadas com o sítio de ação das quinolonas, bem como a presença de plasmídeos e integrons que carregam determinantes gênicos que codificam resistência às quinolonas. A associação destes com mecanismos plasmideais de resistência aos antibióticos -lactâmicos também foi analisada. Foram avaliadas 257 enterobactérias resistentes ao ácido nalidíxico isoladas de pacientes hospitalizados e da comunidade no período de 2000 a 2005. Por PCR e seqüenciamento, foram analisadas as mutações presentes nos genes cromossômicos gyrA e parC e as estruturas gênicas associadas com determinantes plasmideais de resistência às quinolonas, Qnr, e aos -lactâmicos de amplo espectro. Foram determinados os perfis plasmideais e a transferabilidade dos plasmídeos que carrearam estes determinantes. A extração e a análise das proteínas de membrana externa foi realizada para avaliar uma possível perda ou diminuição da expressão de porinas, também relacionada com os mecanismos de resistência avaliados. Todas as amostras foram resistentes ao ácido nalidíxico, apresentando concentração inibitória mínima (CIM) superior a 16 g/mL, e em média, 70% apresentaram diminuição de sensibilidade às fluoroquinolonas testadas. De 257 enterobactérias resistentes ao ácido nalidíxico, em seis enterobactérias (2,3%), incluindo 3 E. coli, 2 K. pneumoniae e 1 C. freundii foi encontrado o gene qnrB. Cinco linhagens apresentaram suas seqüências idênticas ao gene qnrB2, e uma linhagem, C. freundii JF79, apresentou uma seqüência idêntica ao gene qnrB8. Em uma linhagem de E. cloacae foi detectado o gene qnrA1 (0,37%). Os genes qnrA e qnrB apresentaram-se localizados em plasmídeos que apresentaram de 55 a 180 kilobases. A análise da estrutura gênica indicou que os genes qnrA1 e qnrB2 estavam associados com um integron classe 1 e localizados entre o elemento ISCR1 e a segunda cópia do segmento conservado 3. Na coleção bacteriana avaliada, as principais mutações observadas foram nos códons 83 e 87 em gyrA, e nos códons 80 e 84 em parC. Todas as enterobactérias que exibiram unicamente mutações no gene gyrA apresentaram CIM 16 µg/mL para o ácido nalidíxico. A diferença encontrada nos valores da CIM de fluoroquinolonas em enterobactérias que apresentaram as mesmas substituições em GyrA e ParC foi explicada pela ausência ou diminuição da expressão de porinas. Em relação à produção de -lactamase de espectro ampliado (ESBL), sua presença foi comprovada em 24 (9,3%) enterobactérias. O seqüenciamento de blaCTX-M identificou 18 determinantes: CTX-M-2 (n=13), incluindo dois novos variantes, CTX-M-8 (n=2) e CTX-M-9 (n=3) mediados por plasmídeos de 48 a 180 kilobases, não conjugativos, em maioria. O gene blaSHV-5 foi detectado em seis enterobactérias. Todos os determinantes do grupo 2 apresentaram-se associados com um elemento ISCR1, enquanto que aqueles do grupo 9 estiveram relacionados com ISEcp1. Concluindo, o principal mecanismo de resistência às quinolonas detectado foi a presença de substituições em GyrA e ParC, apesar de outros mecanismos, como a diminuição da expressão de porinas estarem envolvidos nas enterobactérias avaliadas. A associação da produção de ESBL foi significativa devido ao encontro de uma grande diversidade de genótipos circulando na comunidade, com uma predominância de enterobactérias produtoras de CTX-M. Quanto aos determinantes Qnr descritos neste estudo, que notoriamente foram os primeiros relatos no Brasil, somente dois deles apresentaram-se relacionados com a produção de ESBL.
The aim of this study was to investigate the main mechanisms of quinolone resistance among enterobacterial isolates recovered from hospitalized patients and outpatients in Brazil. The modification of the quinolone targets with changes of DNA gyrase and of topoisomerase IV genes and the presence of determinants codifying plasmid- mediated quinolone and oxymino- cephalosporins resistance were investigated. Two hundred fifty seven non-duplicate nalidixic-acid resistant enterobacterial isolates recovered from January 2000 to May 2005 were analysed. Mutations in the topoisomerases gyrA and parC genes and the genetic structures surrounding Qnr and CTX-M determinants were recognized by PCR and sequencing. Conjugation experiments were performed to determine whether the qnr- and blaCTX-M carrying plasmids were self transferable. Also, decrease in the level of porin expression related to quinolone resistance was assessed. All enterobacterial isolates were resistant to nalidixic-acid, showing minimal inhibitory concentrations (MIC) 16 g/mL and 70% of these isolates showed decreased susceptibility to fluoroquinolone. Six qnrB-positive (2.3%) out of 257 nalidixic-acid resistant enterobacterial isolates, were identified, including 3 Escherichia coli, 2 Klebsiella pneumoniae and 1 Citrobacter freundii. Five isolates had an identical qnrB2 sequence and one isolate, C. freundii 79, possessed the qnrB8. A single Enterobacter cloacae carrying a plasmid encoding qnrA gene was identified (0.37%). All isolates were negative for the qnrS genes. Plasmid-mediated quinolone resistance ranged from 55- to 180-kb in size. Sequence analysis of the genetic structures surrounding of the qnrA and qnrB genes identified an ISCR1 element at the left-hand boundary and a partial copy of the 3-end segment of class 1 integrons. Concerning the changes of DNA gyrase and topoisomerase IV, the most common modification in the enterobacterial isolates analyzed were present at codons 83 and 87 in GyrA and in ParC at codons 80 and 84. All isolates that exhibited mutations in gyrA gene showed nalidixic-acid MIC 16 µg/mL. The finding of different MIC values to fluoroquinolones in enterobacterial isolates with the same GyrA and ParC modification was explained by a decreasing in the level of porin expression. Regarding -lactam resistance mechanisms, twenty four (9.3%) ESBL-producing enterobacterial isolates were detected. Sequencing of the CTX-M-encoding genes identified 18 determinants belonging to CTX-M-2 (n=13), CTX-M-8 (n=2) and CTX-M-9 (n=3) groups. CTX-M-2 group determinants included blaCTX-M-2 and the two novel variants. Plasmids harboring blaCTX-M genes ranged from 48- to 180- kb in size and were not transferable, in their majority. The blaSHV-5 genes were detected in all the 6 blaCTX-M negative isolates. All alleles belonging to the group 2 were associated with ISCR1 element, while all blaCTX-M-9 genes were related to ISEcp1 element. In conclusion, alterations in the targets of quinolones, GyrA and ParC was the main mechanism of quinolone resistance identified in this study, although a decreasing of the porins expression had been identified among nalidixic-acid resistant enterobacterial isolates. In the surveyed area, the prevalence of ESBL producers was important (9.3%), provided that this finding was related to a large diversity of genotypes circulating in the community, mainly CTX-M-producing isolates. This study constituted the first epidemiological survey of QnrA and QnrB determinants among Brazilian isolates. Interestingly, the qnrB2 gene was identified in non ESBL producers isolates and qnrS genes were not found.

Tese apresentada à Universidade de Aveiro para cumprimento dos requisitos necessários à obtenção do grau de Doutor em Turismo.
O presente trabalho de investigação estuda o fenómeno da sazonalidade no mercado turístico. A perspetiva adotada é a da procura, com enquadramento nas áreas de pesquisa do comportamento do consumidor e do lazer, ambas com foco nas perceções dos turistas que visitam a região do Minho situada no Noroeste de Portugal. A revisão da literatura permite uma compreensão sobre os determinantes da procura turística, os conceitos e estruturas do comportamento de consumo turístico, e os conceitos do lazer, com particular enfase para os determinantes (inibidores/ facilitadores) que intervêm nos processos de consumo. A revisão bibliográfica sobre a sazonalidade no turismo inclui definições, conceitos, formas de medição, a avaliação das consequências e, sobretudo, a natureza das suas causas. Com base neste processo de revisão são formuladas hipóteses de pesquisa, que se testam na parte empírica da investigação. A análise incide nos dados obtidos num inquérito aos turistas, realizado ao longo das três épocas turísticas (alta, média e baixa) na região do Minho. O estudo proporcionou 942 respostas válidas, com informação sobre o comportamento de férias dos turistas, as suas motivações e perceções sobre o destino, e uma avaliação da importância dos determinantes do comportamento de consumo turístico a nível sazonal. O destino turístico de realização do estudo é descrito sob diversos pontos de vista, com particular enfase na estrutura da procura, e no padrão de sazonalidade que o carateriza. O debate sobre as causas da sazonalidade no destino faz-se ao nível dos aspetos comportamentais, com base teórica no modelo não-hierárquico dos inibidores ao lazer, aplicado ao estudo da sazonalidade. O comportamento sazonal do turista é estruturado com base nas suas preferências e decisões sazonais de consumo, por sua vez influenciadas por um conjunto de componentes que encontram correspondência nas classes de causas naturais, institucionais, e psicossociais da sazonalidade. As componentes são agrupadas em duas classes - antecedentes e estruturais, e identificadas através da análise fatorial em componentes principais. As suas relações com as preferências e decisões são testadas através da aplicação do modelo de regressão ordinal. Complementarmente, estudam-se as diferenças entre as três épocas turísticas ao nível do perfil sociodemográfico dos turistas, das motivações de visita ao destino, e da importância atribuída aos determinantes do comportamento sazonal. Os segmentos sazonais de procura identificados nesta parte da investigação são identificados como potenciais alvos das estratégias e medidas de gestão da sazonalidade no destino. A partir da integração dos resultados da pesquisa sugerem-se determinadas implicações para a gestão da sazonalidade, que se complementam com um conjunto de pistas para futuros trabalhos nesta área.
The current research focuses on seasonal variation in tourism market through a demand and seasonal behavior consumption perspective. The theoretical approach relies on consumption behavior and leisure areas of study, both of which analyze the perception tourists have while visiting Minho region situated on the northwest of Portugal. Literature reviewing enables the understanding of base determinants of touristic demand, the concepts and key structures of consumption behavior, as well as theories of leisure with particular emphasis on the determinants (inhibitors and facilitators) that influence the processes of consumption. This approach to seasonality in tourism implies pinpointing definitions and concepts, measuring strategies, evaluating consequences and, above all, analyzing the nature of its causes. Based on this debate, search hypotheses will be formulated and subsequently tested throughout the empirical part of this study. The analysis will use data obtained from enquiries to tourists held during different periods in Minho region. The investigation led to 942 valid answers that contain sociodemographic information, data about tourist behavior on holidays, their motivation and perception of the destination and the evaluation of aspects that may condition seasonal consumption behaviors. The implementation of this study is analyzed through several perspectives, with particular emphasis on the structure of tourist demand and the seasonal pattern that is inherent to it. Identifying the causes of a certain seasonal pattern implies bearing in mind behavioral aspects theoretically grounded on the non-hierarchical model of leisure inhibitors applied to seasonality studies. The seasonal consumption behavior is the result of seasonal consumption preferences and decisions, influenced by certain factors that are closely related to the natural, institutional, psychosocial causes of seasonality. According to support theory, these factors can be divided into two different categories – prior to and structural – and are identified through a factor analysis of the main components. Their connection to seasonal consumption preferences and decisions are presented bearing in mind the results of the application of the ordinal regression model. Additionally, differences in terms of touristic seasons, particularly, tourist sociodemographic characteristics, as well as their motivation and perception of the destination, are analyzed. The demand segments identified in this part are considered potential targets of strategies and management models of seasonality in Minho region. From the overall research results some suggestions will be made concerning seasonal pattern management, accompanied by other suggestions related to future research in this area.
Orientação: Professora Doutora Elisabeth Kastenholz.

Mestrado em Economia Internacional e Estudos Europeus
Uma investigação empírica é apresentada sobre os determinantes das Obrigações do Tesouro de 11 estados-membro da UEM, vis-à-vis a Alemanha. Os determinantes dizem respeito às condições de crédito, liquidez, bem como a condições internacionais, e o objectivo é compreender se a determinação do preço é sensível ao país em questão, bem como ao tempo. É uma investigação que cobre o tempo de vida do Euro, até ao fim de 2014. As análises de painel e SUR, juntamente com variáveis qualitativas, confirmam que a avaliação da dívida Europeia não foi estática ao longo do tempo e foi sensível ao país em questão. Os participantes no mercado de Obrigações estão crescentemente conscientes dos fundamentais macro-económicos e orçamentais.
An empirical investigation is presented on the determinants of 10-year Sovereign bond yield spreads of 11 EMU member states, vis-à-vis Germany. The determinants cover credit, liquidity and international conditions and the goal is to understand if the pricing is country and time ?sensitive. It spans over the lifetime of the euro, up until the end of 2014. Panel and SUR analyses coupled with qualitative variables have confirmed the pricing of European debt has not been static across time and EMU countries. Market participants are increasingly aware of macro-economic and fiscal fundamentals.

Mestrado em Finanças
Esta tese estuda os fatores que influenciam a detenção de casa através de um modelo logit que prevê se um indivíduo é proprietário de uma casa ou não com base nas suas caraterísticas. Este estudo é feito com base na Wave 6 do inquérito Survey of Health Ageing and Retirement in Europe (SHARE). Assim, através da amostra de 46 003 inquiridos de toda a Europa, foram testados os vários determinantes sugeridos pela revisão bibliográfica e comparados com a mesma. Os resultados mostram que a localização geográfica, idade, género, número de filhos, estado civil, situação laboral, renda familiar, educação superior, anos de educação, orientação política e deter obrigações, ações, fundos de investimentos, contas bancárias, contas de poupança, conta reforma individual, e seguro de vida são fatores que influenciam a detenção de casa. Destes fatores, destacam-se a localização geográfica e, inesperadamente, a orientação política do indivíduo é um determinante da detenção de casa. Posteriormente, o modelo foi aplicado a quatro amostras diferentes constituídas pelos indivíduos da Europa do norte, sul, leste e ocidental. Os resultados mostram que os determinantes não são iguais em todas as regiões, nem mesmo considerando apenas países europeus.
This thesis studies the determinants of homeownership using a logit model that predicts if an individual is homeowner or not based on their characteristics. To examine this the Wave 6 (2015) from the Survey of Health Ageing and Retirement in Europe (SHARE) is used. Using a sample of 46 003 respondents across all of Europe, the various determinants suggested by the literature review were tested and the results are compared with the literature. The results show that the following factors influence homeownership: geographic location, age, gender, number of children, marital status, job situation, household income, high education, years of education, political orientation and holding bonds, stocks, mutual funds, bank accounts, saving accounts, IRA and life insurance. The main determinant to homeownership is the respondent's geographical location and unexpectedly, political orientation is a determinant of homeownership. The model was also performed in four different samples constituted each with respondents from eastern, southern, northern and western Europe. The results obtained between them and the full sample test prove that the determinants of homeownership are not the same for every region, even considering only European countries.
info:eu-repo/semantics/publishedVersion

Este estudo tem como objectivo analisar quais os factores que determinam a estrutura de capitais do sector bancário Português. Com o intuito de atingir o objectivo e assumindo a existência de uma estrutura óptima de capitais, recorrer-se-á ao modelo de regressão linear múltipla para verificar a aderência do processo de decisão às teorias acerca da estrutura de capitais, bem como quais dos factores analisados a afectarão significativamente. Os resultados obtidos sugerem que a rendibilidade, a dimensão, o risco e a tangibilidade são os principais determinantes da estrutura de capitais do sector bancário português. ABSTRACT: The main aim for this study is to verify which determinants influence the Portuguese bank's capital structure. ln order to achieve the above mentioned aim and assuming an optimal capital structure, we will apply a multiple linear regression model with the purpose of proving the capital structure theories existence and to observe which determinants influence it. The obtained results mention that profitability, size, risk and tangibility are the principal determinants of Portuguese bank's capital structure.

The study about bi-Lipschitz equisingularity has been a very important subject in Singularity Theory in last decades. Many different approach have cooperated for a better understanding about. One can see that the bi-Lipschitz geometry is able to detect large local changes in curvature more accurately than other kinds of equisingularity. The aim of this thesis is to investigate the bi-Lipschitz geometry in an algebraic viewpoint. We define some algebraic tools developing classical properties. From these tools, we obtain algebraic criterions for the bi-Lipschitz equisingularity of some families of analytic varieties. We present a categorical and homological viewpoints of these algebraic structure developed before. Finally, we approach algebraically the bi-Lipschitz equisingularity of a family of Essentially Isolated Determinantal Singularities.
O estudo da equisingularidade bi-Lipschitz tem sido amplamente investigado nas últimas décadas. Diversas abordagens têm contribuído para uma melhor compreensão a respeito. Observa-se que a geometria bi-Lipschitz é capaz de detectar grandes alterações locais de curvatura com maior precisão quando comparada a outros padrões de equisingularidade. O objetivo desta tese é investigar a geometria bi-Lipschitz do ponto de vista algébrico. Definimos algumas estruturas algébricas desenvolvendo algumas propriedades clássicas. A partir de tais estruturas obtemos critérios algébricos para a equisingularidade bi-Lipschitz de algumas classes de famílias de variedades analíticas. Apresentamos uma visão categórica e homológica dos elementos desenvol- vidos. Finalmente abordamos algebricamente a equisingularidade de famílias de Singularidades Determinantais Essencialmente Isoladas.

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A inovaÃÃo à um processo dinÃmico que possibilita a implementaÃÃo de algo novo ou substancialmente aperfeiÃoado, podendo suscitar mudanÃas tanto na empresa quanto no contexto socioeconÃmico o qual està inserido. Os resultados inovativos sÃo diversos, uma vez que sua prÃpria criaÃÃo pode encadear novos processos ou melhorias nos procedimentos e tÃcnicas empregados na produÃÃo ou no fornecimento de serviÃos. A proposta deste trabalho à analisar quais os fatores determinantes da implementaÃÃo de inovaÃÃes de produto e/ou processo pelas empresas brasileiras. Para este fim, se utilizou dados provenientes da Pesquisa de InovaÃÃo (PINTEC 2011), realizada pelo Instituto Brasileiro de Geografia e EstatÃstica (IBGE), com apoio do MCTI e FINEP. Os dados tÃm como referÃncia o total Brasil de empresas do setor industrial e de serviÃo, no perÃodo de 2009 a 2011. Com base na literatura, construiu-se um modelo economÃtrico relacionando fatores que podem influenciar o percentual de empresas que implementam inovaÃÃes. Algumas hipÃteses foram levantadas e testadas empiricamente. O modelo tem como variÃveis independentes o apoio do governo, relaÃÃes de cooperaÃÃo com outras organizaÃÃes, dispÃndio em atividades inovativas sobre a receita lÃquida de vendas, pessoas ocupadas em atividades internas de P&D com nÃvel superior e financiamento por recursos de terceiros, mensuradas proporcionalmente ao nÃmero de empresas investigadas. Os resultados obtidos confirmam a hipÃtese formulada de que o apoio do governo està positivamente relacionado ao percentual de empresas brasileiras que implementam inovaÃÃes de produto e/ou processo. E, no caso de inovaÃÃo de processo, dispÃndios em atividades inovativas e qualificaÃÃo profissional tambÃm se mostraram como fatores significativos. A significÃncia global do modelo confirmou a atuaÃÃo conjunta dos fatores como determinantes da implementaÃÃo de inovaÃÃes de produtos e/ou processos novos ou substancialmente aprimorados.
Innovation is a dynamic process that enables the implementation of something new or substantially improved, changes may raise both the company and the socioeconomic context which is inserted. Innovative results are various, since his own creation can chain new processes or improvements to procedures and techniques employed in the production or supply of services. The purpose of this project is to analyze the determinants of implementation of innovations in product or process by braziliancompanies. For this purpose, used data from the Research of Innovation ( PINTEC 2011), conducted by the Instituto Brasileiro de Geografia e EstatÃstica (IBGE), with support from FINEP and MCTI. The data has reference to the total Brazil, the companies in the industrial and service sector in the period 2009-2011. Based on the literature, constructed an econometric model relating factors that can influence the percentage of companies that implement innovations. Some hypotheses were developed and tested empirically. The model has as independent variables the government's support, cooperative relationships with other organizations, expenditure on innovation activities of the sales revenue, persons employed in internal R&D with degree and funding from third resources, measured in proportion to the number companies investigated. The results confirm the hypothesis formulated that government support is positively related to the percentage of brazilian companies that implement product innovations and/or process. And in the case of process innovation, expenditure on innovation activities and professional qualification also proved to be significant factors. The global significance of the model confirmed the joint action of the factors as determinants of the implementation of product innovations and/or new or significantly improved processes.

Este trabalho tem como objetivo apresentar os conteúdos de matrizes, determinantes e sistemas lineares aos professores de matemática que lecionam no ensino médio, ressaltando as situações-problema bem como suas aplicações, contextualizando através de problemas.
The goal of this work is to present an introduction to matrices, determinants, and linear systems to high school mathematics teachers highlighting some applications.

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Segundo a Organização Mundial da Saúde, as infecções respiratórias agudas das vias inferiores (IRAVIs)constituem as principais causas de morbidade e mortalidade em crianças menores de cinco anos de idade no mundo. Dos atendimentos ambulatoriais em pediatria, entre 40 a 60% são devidos a IRAVIs. Nos países de renda baixa são a primeira causa de morte. Das IRAVIs a pneumonia (PN) é a mais frequente. É responsável por 18% do total de morte nesta faixa etária. Aproximadamente 99% dos casos ocorrem nos países de baixa renda. Uma parcela importante da PN pode ser prevenida pelo uso da vacina contra o Hib. OBJETIVO. Estudar a ocorrência da PN em crianças menores de cinco anos. METODO. Trata-se de um estudo de caso-controle pareado por idade e vizinhança. Os casos (n=527) foram crianças de 6 até 47 meses de idade hospitalizadas por IRAVIs, de junho 2006 até maio 2008, nos principais hospitais da rede do SUS em Salvador. Os controles (n=1.045) foram crianças da comunidade da mesma idade do que o caso (mais/menos 6 meses do que o caso). Os dados foram submetidos à análise bivariada e multivariada por meio de regressão logística condicional. A análise foi feita usando STATA V.10. RESULTADOS. Os determinantes sociais em saúde modelam o caminho causal das IRAVIs em crianças menores de cinco anos e incluem fatores socioeconômicos, médio ambiente e fatores individuais. Na população estudada, a média e mediana de idade foi de 19 e16 meses respectivamente. Foram encontrados como fatores de risco: ter mãe empregada (OR 1,34 IC95% 1,06 1,69), morar em casa construída de material inapropriado (OR 2,38 IC95% 1,23 4,62), freqüentar a creche (OR 2,12 IC95% 1,49 3,01), o fumo da mãe durante a gravidez (OR 2,02 IC95% 1,42 2,89) e a prematuridade (OR 2,15 IC95% 1,28 3,63). O fato de ter mãe empregada contribui com 9% da ocorrência de IRAVIs (PAF 9%), seguido de freqüentar creche (PAF 8%), fumo da mãe durante a gravidez (PAF 7%), entanto que a construção de casa de material inapropriado e a prematuridade 3% cada (PAF 3%). A efetividade da vacina contra o Hib na redução de internações devida a PN foi de 3% (OR 0.97 IC 95% 0,71 1,37). CONCLUSÃO. Os fatores de risco para IRAVIs na população estudada estão ligada as condições de vida da família. A vacina conjugada contra o Hib, sob condições de aplicação do calendário regular de vacinação do SUS, mostra evidencias inconclusas relativo ao efeito protetor na prevenção de internações devida a PN em crianças de 6 até 47 meses de idade em Salvador, provavelmente devido ao efeito da vacina na eliminação de portadores do Hib.
Salvador

A point process is a mechanism, which realizes randomly locally finite point measures. One of the main results of this thesis is an existence theorem for a new class of point processes with a so called signed Levy pseudo measure L, which is an extension of the class of infinitely divisible point processes. The construction approach is a combination of the classical point process theory, as developed by Kerstan, Matthes and Mecke, with the method of cluster expansions from statistical mechanics. Here the starting point is a family of signed Radon measures, which defines on the one hand the Levy pseudo measure L, and on the other hand locally the point process. The relation between L and the process is the following: this point process solves the integral cluster equation determined by L. We show that the results from the classical theory of infinitely divisible point processes carry over in a natural way to the larger class of point processes with a signed Levy pseudo measure. In this way we obtain e.g. a criterium for simplicity and a characterization through the cluster equation, interpreted as an integration by parts formula, for such point processes. Our main result in chapter 3 is a representation theorem for the factorial moment measures of the above point processes. With its help we will identify the permanental respective determinantal point processes, which belong to the classes of Boson respective Fermion processes. As a by-product we obtain a representation of the (reduced) Palm kernels of infinitely divisible point processes. In chapter 4 we see how the existence theorem enables us to construct (infinitely extended) Gibbs, quantum-Bose and polymer processes. The so called polymer processes seem to be constructed here for the first time. In the last part of this thesis we prove that the family of cluster equations has certain stability properties with respect to the transformation of its solutions. At first this will be used to show how large the class of solutions of such equations is, and secondly to establish the cluster theorem of Kerstan, Matthes and Mecke in our setting. With its help we are able to enlarge the class of Polya processes to the so called branching Polya processes. The last sections of this work are about thinning and splitting of point processes. One main result is that the classes of Boson and Fermion processes remain closed under thinning. We use the results on thinning to identify a subclass of point processes with a signed Levy pseudo measure as doubly stochastic Poisson processes. We also pose the following question: Assume you observe a realization of a thinned point process. What is the distribution of deleted points? Surprisingly, the Papangelou kernel of the thinning, besides a constant factor, is given by the intensity measure of this conditional probability, called splitting kernel.
Ein Punktprozess ist ein Mechanismus, der zufällig ein lokalendliches Punktmaß realisiert. Ein Hauptresultat dieser Arbeit ist ein Existenzsatz für eine sehr große Klasse von Punktprozessen mit einem signierten Levy Pseudomaß L. Diese Klasse ist eine Erweiterung der Klasse der unendlich teilbaren Punktprozesse. Die verwendete Methode der Konstruktion ist eine Verbindung der klassischen Punktprozesstheorie, wie sie von Kerstan, Matthes und Mecke ursprünglich entwickelt wurde, mit der sogenannten Methode der Cluster-Entwicklungen aus der statistischen Mechanik. Ausgangspunkt ist eine Familie von signierten Radonmaßen. Diese definiert einerseits das Levysche Pseudomaß L; andererseits wird mit deren Hilfe der Prozess lokal definiert. Der Zusammenhang zwischen L und dem Prozess ist so, dass der Prozess die durch L bestimmte Integralgleichung (genannt Clustergleichung) löst. Wir zeigen, dass sich die Resultate aus der klassischen Theorie der unendlich teilbaren Punktprozesse auf natürliche Weise auf die neue Klasse der Punktprozesse mit signiertem Levy Pseudomaß erweitern lassen. So erhalten wir z.B. ein Kriterium für die Einfachheit und eine Charackterisierung durch die Clustergleichung für jene Punktprozesse. Unser erstes Hauptresultat in Kapitel 3 zur Analyse der konstruierten Prozesse ist ein Darstellungssatz der faktoriellen Momentenmaße. Mit dessen Hilfe werden wir die permanentischen respektive determinantischen Punktprozesse, die in die Klasse der Bosonen respektive Fermionen Prozesse fallen, identifizieren. Als ein Nebenresultat erhalten wir eine Darstellung der (reduzierten) Palm Kerne von unendlich teilbaren Punktprozessen. Im Kapitel 4 konstruieren wir mit Hilfe unseres Existenzsatzes unendlich ausgedehnte Gibbsche Prozesse sowie Quanten-Bose und Polymer Prozesse. Unseres Wissens sind letztere bisher nicht konstruiert worden. Im letzten Teil der Arbeit zeigen wir, dass die Familie der Clustergleichungen gewisse Stabilitätseigenschaften gegenüber gewissen Transformationen ihrer Lösungen aufweist. Dies wird erstens verwendet, um zu verdeutlichen, wie groß die Klasse der Punktprozesslösungen einer solchen Gleichung ist. Zweitens wird damit der Ausschauerungssatz von Kerstan, Matthes und Mecke in unserer allgemeineren Situation gezeigt. Mit seiner Hilfe können wir die Klasse der Polyaschen Prozesse auf die der von uns genannten Polya Verzweigungsprozesse vergrößern. Der letzte Abschnitt der Arbeit beschäftigt sich mit dem Ausdünnen und dem Splitten von Punktprozessen. Wir beweisen, dass die Klassen der Bosonen und Fermionen Prozesse abgeschlossen unter Ausdünnung ist. Die Ergebnisse über das Ausdünnen verwenden wir, um eine Teilklasse der Punktprozesse mit signiertem Levy Pseudomaß als doppelt stochastische Poissonsche Prozesse zu identifizieren. Wir stellen uns auch die Frage: Angenommen wir beobachten eine Realisierung einer Ausdünnung eines Punktprozesses. Wie sieht die Verteilung der gelöschten Punktkonfiguration aus? Diese bedingte Verteilung nennen wir splitting Kern, und ein überraschendes Resultat ist, dass der Papangelou-Kern der Ausdünnung, abgesehen von einem konstanten Faktor, gegeben ist durch das Intensitätsmaß des splitting Kernes.

Com o aumento no número de pessoas idosas devido ao aumento da expectativa de vida e diminuição das taxas de natalidade, esse trabalho partiu da hipótese de que o idoso, além de apresentar uma forte demanda por cuidados médicos, também têm uma demanda crescente por outros tipos de bens e serviços, como, por exemplo, cosméticos e viagens. Ademais, a importância desse grupo, com sua renda mais estável oriunda dos benefícios da seguridade social e uso de ativos ou bens acumulados, altera de forma significativa a estrutura de consumo da família na qual pertence, criando uma forte relação de interdependência com os filhos e netos. O objetivo principal do presente trabalho foi analisar, através de alguns determinantes sócio-econômicos, o comportamento de consumo das famílias com idosos chefes e famílias que não apresentavam nenhum indivíduo com mais de 60 anos, nas principais áreas metropolitanas brasileiras, Distrito Federal e Goiânia. A base de dados utilizada corresponde a Pesquisa de Orçamentos Familiares 1995/96 do Instituto Brasileiro de Geografia e Estatística. Inicialmente, na revisão de literatura, foram mencionados os principais aspectos demográficos que estão causando o envelhecimento populacional, assim como a importância do idoso na família e algumas considerações sobre as políticas previdenciárias que melhoram a vida dessas pessoas e de seus dependentes. Através da análise de estatística descritiva dos dados, observou-se que a aposentadoria representa a maior parte dos rendimentos dos idosos. No entanto, também existem parcelas significativas da renda que são provenientes do trabalho na condição de empregado e de conta-própria. Constatou-se que os dispêndios com medicamentos, serviços de saúde, despesas pessoais, roupas, alimentação fora de casa, comunicação e transporte, ocupam parcelas substanciais no consumo individual dos idosos e de suas famílias. Observou-se também que a renda mensal per capita de famílias que possuem idosos chefe é de aproximadamente 200 reais a mais do que de famílias que não possuem idoso. Posteriormente, utilizando o modelo lógite, foi possível mostrar que as variáveis: renda per capita familiar, idade, chefe que trabalha, escolaridade do chefe e localização geográfica da família, explicaram satisfatoriamente a probabilidade de consumir das famílias com idosos e famílias sem idosos, para os seguintes agregados de consumo: produtos farmacêuticos, serviços de assistência à saúde, despesas pessoais, fumo e seus derivados, roupas, viagens, lazer, comunicação e transporte. Entre os resultados mais importantes pode-se constatar que: a medida que os indivíduos envelhecem aumenta a demanda por com cuidados médicos; não existem diferenças significativas de consumo entre os chefes idosos e não-idosos que trabalham; quanto maior a escolaridade dos chefes idosos e não-idosos maior é a probabi lidade de consumo da maioria dos bens e serviços analisados; as famílias idosas e não-idosas residentes na área metropolitana de São Paulo apresentam menor probabilidade de dispender com bens e serviços de saúde e maior probabilidade de dispender com comunicação e transporte, com relação as outras áreas de pesquisa da POF.
As the number of elderly people increase, mainly due to life expectancy increases and birthrate decreases, this study supports the hypothesis that the elderly, besides showing a high demand for medical care, also presents an increasing demand for other types of goods and services, such as, cosmetics and travel. Besides, the importance of this group, with a more stable income deriving from pensions of social security and the use of assets or accumulated goods, alters significantly the family consumption structure to which they belong, generating a strong relation of interdependence with their sons and grandchildren. The main goal of this study was to analyze, through some social-economic determinants, the family consumption behavior of families having elderly as the head of the family and families which showed no individual over 60 years old, in the most important metropolitan Brazilian cities, Federal District and Goiânia. The used database corresponds to the Household Budget Survey 1995/96 from IBGE (The Brazilian Geographical and Statistical Institute). Initially, in the literature review, it was mentioned the main demographic aspects which are causing the population to age, as well as the importance of the elderly in the family and some considerations about the social security policies which have improved the life conditions of these people and their dependents. Through the analysis of descriptive statistics, it was observed that retirement represents a major part of income for the elderly. However, there are also significant income parts coming from formal jobs and self-employment. It was noticed that the expenses on medicines, health assistance, personal expenses, clothing, eating out, communication and transportation, take up important parts of the consumption of the elderly and their families. It was noticed that monthly income per capita from families whose head is the elderly is approximately R$200,00 more than those which do not have an elderly. Later, using the Logit model, it was possible to show the variables: family per capita income, age, head working out of his house, school background of the head of the family, and geographical location of the family, explained satisfactorily the consumption probability of families having elderly and not having elderly, for the following consumption aggregates: pharmaceutical products, health service assistance, personal expenses, cigarette smoking and its derivatives, clothing, traveling, leisure, communication and transportation. Among the most important results it is possible to conclude that: the demand for medical assistance increases, not having significant differences in consumption between elderly heads of families and non-elderly heads of family which work outside of the house, more years in school increases consumption probability for most of the goods and services analyzed. The elderly families and non-elderly residing in the metropolitan area of São Paulo showed smaller probability of spending on goods and health services, higher probability of spending on communication and transportation, compared to the other areas of study of household budget survey 1995/96.

The BRIC nations are Brazil, Russia, India and China, for the purpose of this thesis I concentrate on Brazil and India. Potential is the word that springs to mind when Brazil and India are mentioned. Brazil and India are developing countries with low GDP per capita (PPP). I demonstrate that Brazil and India have the potential to become world economy leaders in the very near future. This thesis therefore focuses on aspects that have a significant if not a crucial impact on fulfilling the potential of Brazil and India as world economical leaders.