Neste trabalho, inicialmente, apresentamos uma classe de núcleos positivos definidos, os núcleos de Mercer. As funções nesta classe se enquadram na representação de núcleos dada pelo conhecido Teorema de Mercer. Exploramos algumas de suas propriedades convenientes para o contexto do trabalho e construímos seu espaço nativo. Em seguida, tratamos dos núcleos em multiescalas, um caso particular dos núcleos de Mercer. Após estabelecer algumas propriedades interessantes destes núcleos, analisamos o operador integral gerado por um núcleo em multiescalas, no contexto \'L POT.2\' , considerando os seguintes aspectos: limitação, compacidade e positividade do operador, especificidades da imagem do operador e informações sobre seus autovalores e autofunções. Analisamos ainda algumas propriedades do operador integral envolvendo o espaço nativo do núcleo em multiescalas / We study Mercer like kernels, a very special class of positive definite kernels possessing the description given by many results labeled as Mercer\'s Theorem. We explore some of their properties which are needed in the development of this work and construct their native space. In the second half of the work, we consider Mercer kernels defined by a multi-scale procedure. After establishing some of its properties, we analyze integral operators generated by multi-scale kernels, in the \'L POT.2\' context, centering on the following aspects: boundedness, compactness, positiveness, eigenvalues and eigen- functions. We also consider additional properties of the operator, mainly those involving the native space of the multi-scale kernel

Spectral methods have become increasingly popular in designing fast algorithms for modern highdimensional datasets. This thesis looks at several problems in which spectral methods play a central role. In some cases, we also show that such procedures have essentially the best performance among all randomised polynomial time algorithms by exhibiting statistical and computational trade-offs in those problems. In the first chapter, we prove a useful variant of the well-known Davis{Kahan theorem, which is a spectral perturbation result that allows us to bound of the distance between population eigenspaces and their sample versions. We then propose a semi-definite programming algorithm for the sparse principal component analysis (PCA) problem, and analyse its theoretical performance using the perturbation bounds we derived earlier. It turns out that the parameter regime in which our estimator is consistent is strictly smaller than the consistency regime of a minimax optimal (yet computationally intractable) estimator. We show through reduction from a well-known hard problem in computational complexity theory that the difference in consistency regimes is unavoidable for any randomised polynomial time estimator, hence revealing subtle statistical and computational trade-offs in this problem. Such computational trade-offs also exist in the problem of restricted isometry certification. Certifiers for restricted isometry properties can be used to construct design matrices for sparse linear regression problems. Similar to the sparse PCA problem, we show that there is also an intrinsic gap between the class of matrices certifiable using unrestricted algorithms and using polynomial time algorithms. Finally, we consider the problem of high-dimensional changepoint estimation, where we estimate the time of change in the mean of a high-dimensional time series with piecewise constant mean structure. Motivated by real world applications, we assume that changes only occur in a sparse subset of all coordinates. We apply a variant of the semi-definite programming algorithm in sparse PCA to aggregate the signals across different coordinates in a near optimal way so as to estimate the changepoint location as accurately as possible. Our statistical procedure shows superior performance compared to existing methods in this problem.

Occupant une place essentielle dans la société, le sport ne pouvait échapper plus longtemps au droit, en particulier le sportif professionnel. Le statut social du sportif, acteur central du spectacle sportif, fait l'objet d'une construction de plus en plus élaborée, car nécessaire. Le régime du salariat sportif, qui se limite aux contrats conclus entre les sportifs professionnels et les clubs sportifs, sans que l'on puisse les assimiler à des artistes, obéit à la fois aux droits étatique et communautaire, mais également aux pouvoirs sportifs, que ce soit la réglementation ou la justice sportive. La spécificité du salariat sportif repose sur ce pluralisme juridique, de sources et d'organes de justice, avec l'intégration dans le régime social du sportif de la norme sportive. Le droit du travail est particulièrement propice à une telle intégration, notamment la place qu'il fait à la négociation collective et au principe de faveur. Le juge y participe également en reconnaissant cette spécificité. Cette spécificité s'exprime tant au niveau de la formation du contrat, que de son exécution ou de sa rupture. Les pratiques des transferts, des prêts, de l'homologation des contrats ou des réglementations contre le dopage attestent de celle-ci. / Occupying an essential place in the society, the sport could escape no longer the law, in particular the sportsman become professional. The social status of the sportsman, the central actor of the sports show, is the object of a more and more elaborated construction, because necessary. The regime of the sports wage-earner, who limits himself to the contract between the professional sportsmen and the sports clubs, without that we can assimilate them to artists, obeys at once the state and community rights, but also the sports powers, whether it is the regulations and the sports justice. The specificity of the sports wage-earner bases on this legal pluralism, in sources and in organs of justice, with the integration in the social diet of the sportsman of the sports standard. The labor law is particularly convenient to such an integration, in particular the place which it makes for the collective bargaining and for the principle of favour. The judge also participates in it by recognizing this specificity. This specificity expresses himself both at the level of the formation of the contract, and of its execution or of its break. The practices of transfers, loans, ratification of contracts or regulations against the doping give evidence of this one.

Abstract in English / The research will analyze and compare the current research on the spectral factorization of non-singular and singular matrices. We show that a nonsingular non-scalar matrix A can be written as a product A = BC where the eigenvalues of B and C are arbitrarily prescribed subject to the condition that the product of the eigenvalues of B and C must be equal to the determinant of A. Further, B and C can be simultaneously triangularised as a lower and upper triangular matrix respectively. Singular matrices will be factorized in terms of nilpotent matrices and otherwise over an arbitrary or complex field in order to present an integrated and detailed report on the current state of research in this area. Applications related to unipotent, positive-definite, commutator, involutory and Hermitian factorization are studied for non-singular matrices, while applications related to positive-semidefinite matrices are investigated for singular matrices. We will consider the theorems found in Sourour [24] and Laffey [17] to show that a non-singular non-scalar matrix can be factorized spectrally. The same two articles will be used to show applications to unipotent, positive-definite and commutator factorization. Applications related to Hermitian factorization will be considered in [26]. Laffey [18] shows that a non-singular matrix A with det A = ±1 is a product of four involutions with certain conditions on the arbitrary field. To aid with this conclusion a thorough study is made of Hoffman [13], who shows that an invertible linear transformation T of a finite dimensional vector space over a field is a product of two involutions if and only if T is similar to T−1. Sourour shows in [24] that if A is an n × n matrix over an arbitrary field containing at least n + 2 elements and if det A = ±1, then A is the product of at most four involutions. We will review the work of Wu [29] and show that a singular matrix A of order n ≥ 2 over the complex field can be expressed as a product of two nilpotent matrices, where the rank of each of the factors is the same as A, except when A is a 2 × 2 nilpotent matrix of rank one. Nilpotent factorization of singular matrices over an arbitrary field will also be investigated. Laffey [17] shows that the result of Wu, which he established over the complex field, is also valid over an arbitrary field by making use of a special matrix factorization involving similarity to an LU factorization. His proof is based on an application of Fitting's Lemma to express, up to similarity, a singular matrix as a direct sum of a non-singular and nilpotent matrix, and then to write the non-singular component as a product of a lower and upper triangular matrix using a matrix factorization theorem of Sourour [24]. The main theorem by Sourour and Tang [26] will be investigated to highlight the necessary and sufficient conditions for a singular matrix to be written as a product of two matrices with prescribed eigenvalues. This result is used to prove applications related to positive-semidefinite matrices for singular matrices. / National Research Foundation of South Africa / Mathematical Sciences / M Sc. (Mathematics)

No description available.

Microtransactions is a relatively new concept within the gaming industry witha very large monetary value for businesses. Companies utilize persuasivedesign strategies such as time-based scarcity in order to incentivize players tospend money on microtransactions which in turn creates addiction towardsmicrotransactions. The purpose of this paper is to explain the addictiveinfluence limited time scarcity possesses on purchase intention for randomizedvirtual cosmetics (RVC) or definite virtual cosmetics (DVC), and which ofRVC and DVC carries the stronger influence. To arrive to a fitting conclusion,a quantitative method was utilized in order to collect the data required. Sincethis research is explanatory in nature and built on existing research, a crosssectional approach was utilized. Two hypotheses were tested, and aquestionnaire was conducted. The findings from this study suggest that bothRVC and DVC has an impact on purchase intention, however RVC proves tocarry a stronger influence than DVC.

No description available.

No description available.

This study focuses on the clitic pronoun usage by Spanish-Quechua bilingual speakers in Cuzco, Peru when faced with a question that includes a definite article preceding the direct object. Answers are analyzed to determine whether or not the definite article has an effect on the presence or absence of the clitic pronoun. Direct objects tested were both [+human] and [-human] objects to determine if these variables affect clitic pronoun use as well. Speakers who have identified themselves as bilingual in both Spanish and Quechua were given a survey to complete in order to see what factors may contribute to the use or omission of the clitic pronouns.

Esta tese investiga o modo de organização dos domínios nominal, verbal e dos adjetivos em Português do Brasil (PB), tendo como guia a aceitabilidade de sentenças com todo. Para o inglês, a natureza do parâmetro orienta a seleção de argumentos por operadores; já para o PB, o que importa é a oposição entre tipos de escala. O PB não tem determinantes que distingam entre nome contável e massivo, como much e many. O operador aspectual progressivo não modifica estados em inglês, mas em PB sim. Em inglês, very seleciona adjetivos de parâmetro relativo. Em PB, muito + adjetivo tem parâmetro relativo, e todo + adjetivo tem parâmetro absoluto. Todo é um operador interdomínios, sensível aos tipos de escala. Todo modifica a relação de predicação. Todo impõe condições (quantitativas) sobre como a saturação de um predicado por certo argumento deve ocorrer. Todo não é nem um modificador nominal, nem um quantificador canônico como cada. Todo não cria, apenas modifica uma relação existente. A distribuição que ocorre em sentenças com todo é uma entre as muitas formas de saturação de um predicado por um argumento: uma relação incremental. Se o argumento for quantizado, o predicado necessariamente também se tornará quantizado. Analisamos uma descrição definida (DD) como um sintagma de medida (SM). O artigo definido torna um predicado nominal em denotação quantizada, mas todo não. Relacionamos ser quantizado a ser argumental, e ser cumulativo a ser predicativo. E associamos sentidos diferentes às posições de todo na sentença. / This thesis takes the distribution of todo as a probe for the structure of nominal, verbal and adjective domains in Brazilian Portuguese (BP). Todo is a Degree Modifier (DM) and is sensitive to scale structure. English DMs (e.g., very) select adjectives by their standards; the BP DMs select adjectives only by their scale structure. However, they produce phrases with standard specialization. Todo + adjective shows absolute standard interpretation. We claim that the domains show the same properties in both languages, but the nature of scale standard matters in a distinct level for each one. We claim that todo is neither a noun modifier nor a true quantifier. Todo is a relation modifier. Todo modifies the way the argument saturates the predicate. A quantized incremental argument will make the predicate quantized as well. Todo is not the true source of distributivity, since incremental relations occur even in its absence. Definite Descriptions are treated as measure phrases. The definite article relates noun predicates to situations. So it will change a bare noun into a quantized denotation, which todo cannot do. Each land site corresponds to a different meaning for floating todo.