Functional magnetic resonance imaging (fMRI) has emerged as the method of choice to non-invasively investigate brain function in humans. Though brain is known to act as a nonlinear system, here has not been much effort to explore the applicability of nonlinear analysis techniques to fMRI data. Also, recent trends have suggested that functional localization as a model of brain function is incomplete and efforts are being made to develop models based on networks of regions to understand brain function. Therefore this thesis attempts to introduce the twin concepts of nonlinear dynamics and network analysis into a broad spectrum of fMRI data analysis techniques. First, we characterized the nonlinear univariate dynamics of fMRI noise using the concept of embedding to explain the origin of tissue-specific differences of baseline activity in the brain. The embedding concept was extended to the multivariate case to study nonlinear functional connectivity in the distributed motor network during resting state and continuous motor task. The results showed that the nonlinear method may be more sensitive to the desired gray matter signal. Subsequently, the scope of connectivity was extended to include directional interactions using Granger causality. An integrated approach was developed to alleviate the confounding effect of the spatial variability of the hemodynamic response and graph theory was employed to characterize the network topology. This methodology proved effective in characterizing the dynamics of cortical networks during motor fatigue. The nonlinear extension of Granger causality showed that it was more robust in the presence of confounds such as baseline drifts. Finally, we utilized the integration of the spatial correlation function to study connectivity in local brain networks. We showed that our method is robust and can reveal interesting information including the default mode network during resting state. Application of this technique to anesthesia data showed dose dependent suppression of local connectivity in the default mode network, particularly in the frontal areas. Given the body of evidence emerging from our studies, nonlinear and network characterization of fMRI data seems to provide novel insights into brain function.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 135-144).

Thesis (MSc (Mathematics))--Stellenbosch University, 2008. / LULU smoothers is a class of nonlinear smoothers and they are compositions of the maximum and minimum operators. By analogy to the discrete Fourier transform and the discrete wavelet transform, one can use LULU smoothers to create a nonlinear multiresolution analysis of a sequence with pulses. This tool is known as the Discrete Pulse Transform (DPT). Some research have been done into the distributional properties of the LULU smoothers. There exist results on the distribution transfers of the basic LULU smoothers, which are the building blocks of the discrete pulse transform. The output distributions of further smoothers used in the DPT, in terms of input distributions, has been a challenging problem. We motivate the use of these smoothers by first considering linear filters as well as the median smoother, which has been very popular in signal and image processing. We give an overview of the attractive properties of the LULU smoothers after which we tackle their output distributions. The main result is the proof of a recursive formula for the output distribution of compositions of LULU smoothers in terms of a given input distribution.

Si le concept de dignité de la personne humaine occupe une position privilégiée au frontispice de la Charte des droits fondamentaux de l’Union Européenne, il est longtemps resté absent de l’ordre juridique communautaire. Les premières Communautés, organisations d’intégration économique ne se réfèrent pas au concept malgré leur vocation humaine, portée par les objectifs de paix et de progrès social. C’est sous l’impulsion du juge et du législateur de l’Union, que le concept est reconnu puis consacré, d’abord par le droit dérivé puis par le droit primaire. L’analyse des sources du concept et de son processus d’intégration permet de déterminer avec rigueur et justesse les fonctionnalités de la dignité de la personne au sein de l’Union. Le droit est en effet dynamique et les institutions de l’Union recourent au concept de dignité selon une finalité orientée. Polyfonctionnelle, la dignité de la personne humaine joue, à l’image de ses sources, un rôle fondateur déterminant sur le continent européen. Objectivement, elle constitue le fondement du paradigme européen et détermine la substance et les frontières de son ordre juridique. Subjectivement, le concept revêt une fonction protectrice de la personne humaine et de ses droits fondamentaux. Son inscription au sein des traités marque espérons-le, un tournant humaniste de l’organisation européenne. / Human dignity is a key element in the Charter of Fundamental Rights of the European Union. Yet, EU law has long failed to incorporate the concept of human dignity. Europeans founded the European Community to promote peace and social progress. The European Community focused on economic integration first as a mean to reach this goal, however. The Union’s judge and legislator later helped turn attention to human dignity: secondary legislation then primary law integrated the concept. We analyze how human dignity developed as a concept. We also analyze its integration into law. Doing so allows assessing carefully what role human dignity plays in the EU. Law is dynamic. EU institutions use the concept of human dignity to reach specific goals. Human dignity serves several functions. Like its sources, dignity plays a seminal role in Europe. Objectively, dignity is the basis of the European paradigm. Dignity defines the content and limits of the legal order. Subjectively, dignity protects human beings and their fundamental rights. Including human dignity into European treaties hopefully signals a humanistic shift in how Europe works. / Auch wenn das Menschenwürdekonzept eine besondere Position in der Charta der Grundrechte der Europäischen Union innehat, war dieses Konzept lange Zeit abwesend in der EU-Rechtsordnung. Die ersten EU-Mitgliedsländer hatten den Frieden und den sozialen Fortschritt als Ziel, Organisationen, die die wirtschaftliche Integration zur Aufgabe hatten, bezogen sich nicht auf das Menschenwürdekonzept trotz ihrer menschlichen Neigung. Auf Veranlassung des Richters und Gesetzgebers der Union wurde das Konzept zunächst anerkannt und setzte sich dann durch, zunächst im Sekundärrecht, dann im primären Gemeinschaftsrecht. Eine Analyse der Quellen des Würdekonzepts und des Integrationsprozesses erlauben es, mit Strenge und Schärfe die Aufgaben der Würde im EU-Recht zu bestimmen. In der Tat ist das Recht dynamisch und die Einrichtungen der EU beziehen sich auf das Würdekonzept nach einer orientierten Zielgerichtetheit. Multifunktional spielt das Menschenwürdekonzept, folgt man seinen Quellen, eine Gründungsrolle, die auf Europa festgelegt ist. Objektiv stellt sie Grundlage des europäischen Paradigma dar und legt die Substanz und die Grenzen der juristischen Ordnung fest. Subjektiv betrachtet beinhaltet das Konzept eine Schutzfunktion des Menschen und seiner Grundrechte. Die Eintragung des Menschenwürdekonzepts innerhalb des EU-Vertrags markiert, so lässt sich hoffen, einen humanistischen Wendepunkt der Europäischen Union.

Après une simplification significative des méthodes de débitage durant l'Azilien, rompant progressivement avec les normes magdaléniennes, le retour au cours du Dryas récent à des productions lamino-lamellaires élaborées marque un tournant abrupt dans la tradition lithique. Bien qu'un certain flou pèse sur la chronologie des événements, les recherches menées depuis quelques années autour des industries de la transition Pléistocène-Holocène permettent de bien cerner les transformations survenues dans les modalités et les objectifs des productions lithiques. En revanche, malgré le fait que les interrogations des chercheurs soient largement orientées vers des reconstitutions d'ordre palethnographiques, les finalités fonctionnelles des outils, leur modalité d'emploi et les chaînes opératoires dans lesquelles ils sont impliqués restent des thèmes de recherche très peu abordés. C'est afin de pallier ce manque que nous avons exploré ces questions à travers l'analyse tracéologique des industries lithiques de deux sites du nord-ouest de la France issus d'opérations récentes (Le Buhot à Calleville, Eure ; La Fosse à Villiers-Charlemagne, Mayenne). L'apport de ce travail est appréciable à différentes échelles spatio-temporelles. Sur le temps court, les résultats obtenus révèlent des contrastes saisissants entre les occupations, tant au regard des activités menées par l'intermédiaire des outils que de l'économie des produits des débitages, et enrichissent le modèle de complémentarité des sites déjà proposé. Sur le temps long, le croisement des données fonctionnelles acquises ces trente dernières années entre l'Azilien et le premier Mésolithique et les autres données du registre archéologique permet de discuter des inflexions dans les systèmes techniques et les économies préhistoriques. / After a significant simplification of the flint reduction methods during the Azilian period, which broke gradually with Magdalenian standards, the return to sophisticated laminar productions during younger Dryas marks a strong split in the lithic tradition. Beyond a state of uncertainty towards chronological boundaries, the research which have been conducted for thirty years gives a good understanding about changes in flint production methods and aims. Even though most research focuses on palethnographic reconstitutions, the functional purposes of the flint industry and the chaînes opératoires in which flint tools are implicated remain insufficiently studied. And yet, these questions are of prime importance to meet the expectation of the palethnographic reconstitutions that archaeologists covet. To overcome this deficiency, the functional analysis of two north-western France sites (le Buhot site at Calleville, Eure ; la Fosse site at Villiers-Charlemagne, Mayenne) attributed to the Pleistocene-Holocene transition were undertaken. The contribution of this doctoral research can be appreciated at different spatio-temporal scales. In the short-term, the results raise striking contrasts between sites, as much in regard to the activities performed as to the debitage products economy, and improve the current model of settlement patterns. In the long-term, the interplay of techno-functional results and other archaeological data gives food for thought about changes in the technical systems and prehistoric economies.

Le problème isopérimétrique consiste, dans un espace métrique mesuré, à trouver les ensembles qui, à volume fixé, ont la plus petite mesure de surface. Il peut être formulé dans de nombreux cadres (espaces métriques mesurés généraux, variétés riemanniennes à poids, parties de l'espace euclidien...). Deux questions se dégagent de ce problème : - Quels sont les ensembles solutions, c'est-à-dire ayant la plus petite mesure de surface ? (Il faut noter que ces ensembles n'existent pas toujours). - Que vaut la plus petite mesure de surface ? La solution à la deuxième question peut être formulée sous la forme d'une fonction, appelée profil isopérimétrique, qui, à une valeur de volume (pondéré) donnée, associe la plus petite mesure de surface correspondante. La notion de mesure de surface, quant à elle, peut être définie de plusieurs manières (contenu de Minkowski, périmètre géométrique...), toutes dépendant étroitement à la fois de la distance et de la mesure ambiantes. L'objet principal de cette thèse est l'étude du problème isopérimétrique dans des espaces produits, que ce soit pour transférer des inégalités isopérimétriques d'espaces facteurs vers ces produits, ou pour comparer le profil isopérimétrique de l'espace produit à ceux des facteurs. La thèse se découpe en quatre parties : - Étude de l'opération de symétrisation (pour les ensembles) et de réarrangement (pour les fonctions), notions analogues, du point de vue de la théorie de la mesure géométrique et des fonctions à variations bornée. Ces opérations agissent de sorte à ce que n'augmente pas la mesure de surface (pour les ensembles), ou la variation (pour les fonctions). Nous introduisons notamment une nouvelle classe d'espaces modèles, pour lesquels nous obtenons des résultats qualitativement similaires à ceux obtenus pour les espaces modèles classiques : inégalités isopérimétriques transférées aux produits, comparaison d'énergies (pour des fonctionnelles convexes). - Détail d'un argument de minoration du profil isopérimétrique d'un espace métrique produit XxY par une fonction dépendant des profils de X et Y, pour une large classe de distances produits sur XxY. L'étude de ce problème est faite via la minimisation d'une fonctionnelle sur la classe des mesures de Radon. - Étude du problème isopérimétrique dans un espace métrique mesuré produit (le produit d'ordre quelconque du même espace métrique mesuré), muni de la combinaison uniforme de sa distance (élargissement uniforme). Nous donnons un critère pour que tous les profils isopérimétriques (quel que soit l'ordre d'itération du produit) soient minorés par un multiple du minorant du profil isopérimétrique de l'espace originel. Ceci est fait en utilisant notamment des méthodes ayant trait aux inégalités fonctionnelles. Nous appliquons ensuite les résultats aux influences géométriques. - Étude d'inégalités fonctionnelles dites isopérimétriques, permettant d'appréhender le comportement isopérimétrique dans l'espace produit correspondant d'ordre quelconque. Nous résumons l'état des connaissances à propos des inégalités de ce type et proposons une autre méthode qui pourrait aboutir à prouver une telle inégalité dans le cas de mesures réelles particulières, pour lesquelles le problème est ouvert. / The isoperimetric problem in a metric measured space consists in finding the sets having minimal boundary measure, with prescribed volume. It can be formulated in various settings (general metric measured spaces, Riemannian manifolds, submanifolds of the Euclidean space, ...). At this point, two questions arise : - What are the optimal sets, namely the sets having smallest boundary measure (it has to be said that they do not always exist) ? - What is the smallest boundary measure ? The solution to the second answer can be expressed by a function called the isoperimetric profile. This function maps a value of (prescribed) measure onto the corresponding smallest boundary measure. As for the precise notion of boundary measure, it can be defined in different ways (Minkowski content, geometric perimeter, ...), all of them closely linked to the ambient distance and measure. The main object of this thesis is the study of the isoperimetric problem in product spaces, in order to transfer isoperimetric inequalities from factor spaces to the product spaces, or to compare their isoperimetric profiles. The thesis is divided into four parts : - Study of the symmetrization operation (for sets) and the rearrangement operation (for functions), analogous notions, from the point of view of Geometric Measure Theory and Bounded Variation functions. These operations cause the boundary measure to decrease (for sets), or the variation (for functions). We introduce a new class of model spaces, for which we obtain similar results to those concerning classic model spaces : transfer of isoperimetric inequalities to the product spaces, energy comparison (for convex functionals). - Detailed proof of an argument of minorization of the isoperimetric profile of a metric measured product space XxY by a function depending on the profiles of X and Y, for a wide class of product distances over XxY. The study of this problem uses the minimization of a functional defined on Radon measures class. - Study of the isoperimetric problem in a metric measured space (n times the same space) equipped with the uniform combination of its distance (uniform enlargement). We give a condition under which every isoperimetric profile (whatever the order of iteration might be) is bounded from below by a quantity which is proportional to the isoperimetric profile of the underlying space. We then apply the result to geometric influences. - Study of isoperimetric functional inequalities, which give information about the isoperimetric behavior of the product spaces. We give an overview of the results about this kind of inequalities, and suggest a method to prove such an inequality in a particular case of real measures for which the problem reamins open.

Made available in DSpace on 2015-12-10T14:23:45Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-02-24. Added 1 bitstream(s) on 2015-12-10T14:29:45Z : No. of bitstreams: 1 000851910.pdf: 2512713 bytes, checksum: 213411a21fdec9803efc190d0200efae (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Introdução. A demanda espontânea é considerada um problema na gestão dos serviços de atenção primária à saúde e na garantia do acesso oportuno. Adicionalmente, o Brasil passa por processo de transição demográfica e epidemiológica que modifica o uso dos serviços. Assim, a carga de morbimortalidade é deslocada dos grupos mais jovens para os mais idosos e a predominância da mortalidade dá lugar à morbidade. Desta maneira, esse estudo propõe: 1. Classificar e quantificar o padrão de comportamento da ocorrência das morbidades diagnosticadas nos atendimentos não agendados de idosos em uma Unidade de Saúde da Família; 2. Mostrar a adequação da análise não linear em fenômeno social humano. Método. Estudo de abordagem quantitativa, observacional, ecológico de tendência temporal. Utilizouse a Dinâmica Simbólica e a Quantificação da Recorrência para análise não linear das séries históricas (categórica e temporais) construídas. As morbidades identificadas no atendimento não agendado de idosos em uma unidade de saúde da família do interior paulista, no período de maio/2012 a maio/2014, foram convertidas em séries históricas. Resultados. A morbidade musculoesquelética apresenta uma tendência de comportamento aleatório, porém é a mais prevalente. A morbidade respiratória apresenta tendência de comportamento periódico, enquanto a morbidade circulatória e as crônicas prevalentes (hipertensão arterial sistêmica e diabetes mellitus) apresentam tendência caótica. A análise não linear demonstrou-se mais adequada que a estatística clássica na avaliação da dinâmica do fenômeno investigado / Introduction. The unscheduled encounters represent a significant problem for primary care clinics management and to provide timely access. Additionally, Brazil has undergone a demographic and epidemiological transition process that modifies the use of health services. Thus, the burden of morbidity and mortality is shifted from younger to older groups and the prevalence of morbidity replaces mortality. We propose: 1. To classify the behavior pattern of morbidities diagnosed in the unplanned appointments resulting from the elderly in a service provider; 2. To show the adequacy of nonlinear analysis in human social phenomenon. Method. It is a quantitative research, observational, ecological design to temporal trend. We used the Symbolic Dynamic and Recurrence quantification analysis to analyze the time-series. The morbidities diagnosed in the unplanned appointments from elderly were transformed into time series. The data was collect in a Primary Care Unit locate in the country of São Paulo State, between May/2012 to May/2014. Results. Musculoskeletal discords has a tendency to random behavior, however, it is the most prevalent. The circulatory morbidity and prevalent chronic (Hypertension and Diabetes Mellitus) present chaotic trend and the linear respiratory diseases were linear. The nonlinear analysis was more appropriate than the classic statistic in assessing the dynamic of investigated phenomenon

Quelques aspects de la géométrie des espaces LipschitzEn premier lieu, nous donnons les propriétés fondamentales des espaces Lipschitz libres. Puis, nous démontrons que l'image canonique d'un espace métrique M est faiblement fermée dans l'espace libre associé F(M). Nous prouvons un résultat similaire pour l'ensemble des molécules.Dans le second chapitre, nous étudions les conditions sous lesquelles F(M) est isométriquement un dual. En particulier, nous généralisons un résultat de Kalton sur ce sujet. Par la suite, nous nous focalisons sur les espaces métriques uniformément discrets et sur les espaces métriques provenant des p-Banach.Au chapitre suivant, nous explorons le comportement de type l1 des espaces libres. Entre autres, nous démontrons que F(M) a la propriété de Schur dès que l'espace des fonctions petit-Lipschitz est 1-normant pour F(M). Sous des hypothèses supplémentaires, nous parvenons à plonger F(M) dans une somme l_1 d'espaces de dimension finie.Dans le quatrième chapitre, nous nous intéressons à la structure extrémale de $F(M)$. Notamment, nous montrons que tout point extrémal préservé de la boule unité d'un espace libre est un point de dentabilité. Si F(M) admet un prédual, nous obtenons une description précise de sa structure extrémale.Le cinquième chapitre s'intéresse aux fonctions Lipschitziennes à valeurs vectorielles. Nous généralisons certains résultats obtenus dans les trois premiers chapitres. Nous obtenons également un résultat sur la densité des fonctions Lipschitziennes qui atteignent leur norme. / Some aspects of the geometry of Lipschitz free spaces.First and foremost, we give the fundamental properties of Lipschitz free spaces. Then, we prove that the canonical image of a metric space M is weakly closed in the associated free space F(M). We prove a similar result for the set of molecules.In the second chapter, we study the circumstances in which F(M) is isometric to a dual space. In particular, we generalize a result due to Kalton on this topic. Subsequently, we focus on uniformly discrete metric spaces and on metric spaces originating from p-Banach spaces.In the next chapter, we focus on l1-like properties. Among other things, we prove that F(M) has the Schur property provided the space of little Lipschitz functions is 1-norming for F(M). Under additional assumptions, we manage to embed F(M) into an l1-sum of finite dimensional spaces.In the fourth chapter, we study the extremal structure of F(M). In particular, we show that any preserved extreme point in the unit ball of a free space is a denting point. Moreover, if F(M) admits a predual, we obtain a precise description of its extremal structure.The fifth chapter deals with vector-valued Lipschitz functions.We generalize some results obtained in the first three chapters.We finish with some considerations of norm attainment. For instance, we obtain a density result for vector-valued Lipschitz maps which attain their norm.

Motivated by the huge success of the applications of the abstract fractional equations in many areas of science and engineering, and by the unsolved question in this theory, in this work we study several matters related to abstract fractional Cauchy problems of order \'alpha\' \'it belongs\' (0, 1). We search to answer some questions that were open: for instance, we analyze the existence of local mild solutions for the problem, and its possible continuation to a maximal interval of existence. The case of critical nonlinearities and corresponding regular mild solutions is also studied. Finally, by establishing some general comparison results, we apply them to conclude the global well-posedness of a fractional partial differential equation coming from heat conduction theory / Motivados pelo êxito das aplicações nas equações abstratas em muitas áreas da ciência e da engenharia, e pelas perguntas ainda abertas, neste trabalho estudamos questões relativas aos problemas fracionários abstratos de Cauchy de ordem \'alpha\' \'pertence a\' (0, 1). Buscamos responder algumas perguntas: por exemplo, analisamos a existência de soluções locais fracas do problema e sua possível continuação em um intervalo maximal de existência. O caso da não-linearidade crítica e sua correspondente solução regular fraca também é abordado. Por último, mediante o estabelecimento de alguns resultados gerais de comparação, chegamos a conclusão de que as soluções de uma equação diferencial parcial fracionária, proveniente da teoria de condução de calor, existe globalmente

Made available in DSpace on 2016-06-02T19:46:06Z (GMT). No. of bitstreams: 1 DissFDTS.pdf: 3954092 bytes, checksum: a7d3c33070e69f75ad31211d9583e87d (MD5) Previous issue date: 2004-08-30 / The objective of this study was to implement and evaluate the effects of a workshop for English language teachers in how to plan teaching strategies based on a functional analysis of the student s performance. An underlying supposition was that teaching centered on student needs could result in academic and social inclusion for students as a by product of learning achievement. The workshop was taught in two modules, the first to supply a conceptual base on learning differences and special educational needs and the second to supply a conceptual base and teach functional analysis skills. The researcher made a functional analysis of the data from observation of classes taught by participants before the workshop. The analysis focused on the repeated errors made by students, the conditions which may have produced their occurrence and possible alternatives to change these conditions. In some cases, changes were implemented and their effect was successful in students overcoming errors. Participants were seven teachers in a private English language school. Two instruments to evaluate sense of efficacy as a teacher (TES) and sense of responsibility for student achievement (RSA), were applied before and after the second workshop module. Interviews with the teachers were conducted one year after the conclusion of the workshop. The results of the standard instruments showed that teachers presented intermediate or elevated levels of sense of teacher efficacy and responsibility for student achievement at the beginning of the study, most probably due to the established standards and constant supervision of their teaching. Significant change was not observed in the final scores at the end of the workshop. In accordance with the interviews, two participants related improvement in performance for students who presented learning difficulties, as a result of using new teaching strategies based on a functional analysis of student performance. The limitations of the workshop are discussed, particularly in terms of its brief duration and the necessity for a longer period for teaching practice, to maximize the effects on teacher practice. The necessity for evaluation instruments which focus more directly on the skills targeted by the training were also discussed. / O estudo teve como objetivo implementar e avaliar os efeitos de uma oficina, conduzida com professores de língua inglesa, visando habilitá-los a fazer planejamento de ensino com base em uma análise funcional do desempenho do aluno. A suposição subjacente era a de que o ensino centrado nas necessidades do aluno pode resultar em inclusão social e acadêmica, como decorrência do sucesso na aprendizagem. A oficina foi ministrada em dois módulos, um para fornecer bases conceituais sobre diferenças e necessidades especiais de ensino e outro para fornecer bases conceituais e instalar habilidades em análise funcional. A análise funcional foi conduzida a partir de dados de observação de aulas dos participantes, realizada pela pesquisadora, antes do início da oficina. A análise focalizou erros cometidos repetidamente pelos alunos, as condições que poderiam estar promovendo sua ocorrência e o levantamento de alternativas para alterar essas condições. Em alguns casos, foram implementadas mudanças e verificados os seus efeitos na superação dos erros. Participaram da oficina sete professores de uma escola privada de ensino de inglês. Antes e depois do segundo módulo de ensino, foram aplicados dois instrumentos para avaliar o Senso de Eficácia como Professor (TES) e o senso de Responsabilidade pelo desempenho do aluno (RSA). Além disso, os professores foram entrevistados um ano após a conclusão da oficina. Os resultados dos dois instrumentos padronizados mostraram que no início do estudo os professores apresentavam níveis intermediários ou elevados de senso de eficácia e senso de responsabilidade pelo desempenho do aluno, provavelmente em função das exigências e do monitoramento da eficácia do ensino que ministravam. Não foram observadas mudanças significativas nos escores ao final da oficina. De acordo com as entrevistas, dois dos participantes relataram melhoras no desempenho de alunos que apresentavam dificuldades de aprendizagem, como resultado da análise funcional e do emprego de novas estratégias de ensino. Foram discutidos os limites da oficina, especialmente a curta duração e a necessidade de expandir o trabalho prático, para maximizar os efeitos sobre a prática do professor. Discutiu-se, também, a necessidade de instrumentos de avaliação que focalizem mais diretamente as habilidades que foram alvo do treinamento.