Ornstein-Uhlenbeck operator in convex domains of Banach spaces

Studiamo l'operatore di Ornstein-Uhlenbeck e il semigruppo di Ornstein-Uhlenbeck in un sottoinsieme aperto convesso $\Omega$ di uno spazio di Banach separabile $X$ dotato di una misura Gaussiana centrata non degnere $\gamma$. In particolare dimostriamo la disuguaglianza di Sobolev logaritmica e la disuguaglianza di Poincaré, e grazie a queste disuguaglianze deduciamo le proprietà spettrali dell'operatore di Ornstein-Uhlenbeck. Inoltre studiamo l'equazione ellittica $\lambdau+L^{\Omega}u=f$ in $\Omega$, dove $L^\Omega$ è l'operatore di Ornstein-Uhlenbeck. Dimostriamo che per $\lambda>0$ e $f\in L^2(\Omega,\gamma)$ la soluzione debole $u$ appartiene allo spazio di Sobolev $W^{2,2}(\Omega,\gamma)$. Inoltre dimostriamo che $u$ soddisfa la condizione di Neumann nel senso di tracce al bordo di $\Omega$. Questo viene fatto finita approssimazione dimensionale.

A(S) CIÊNCIA(S) DA(S) RELIGIÃO(ÕES) NO ALVORECER DE UM NOVO PARADIGMA

A reflexão proposta neste estudo está centrada na possibilidade de o Novo Paradigma Sistêmico , tal qual o concebe o físico norte-americano Fritjof Capra, fundamentar um modelo epistemológico, possível de integrar em seu âmbito os pontos de vista divergentes no debate sobre o tratamento científico do fenômeno religioso. A história das ciências da religião está marcada pelo dilema epistemológico: explicar ou compreender a religião? As ciências da natureza contrapuseram-se às ciências do espírito, que diferiam das primeiras pelo objeto, pelo método e pela relação entre o sujeito e o objeto. O debate que esteve presente no cenário dos séculos XIX e XX mostrou-nos a impossibilidade de se definir um modelo de ciência que incorporasse, em seu seio, uma integração dos pontos de vista divergentes, em razão dos princípios que norteavam o paradigma cientificista. No entanto, a emergência do paradigma dos sistemas vivos ou da complexidade , liderado pela física, veio conceber o caráter sistêmico da realidade; que o concreto material é energia sob o aspecto subatômico; que sob o aspecto subatômico, a matéria não existe em lugares definidos com certeza, mas apenas mostram tendências a existir. Estas e outras descobertas possibilitaram aos cientistas afirmar a existência de um Novo Paradigma , em que as categorias análise, regularidade e objetividade, que caracterizavam o antigo, são substituídas por: síntese, irregularidade e conduta epistêmica. O paradigma emergente possibilitou a construção de um modelo epistemológico do conhecimento científico, que apontamos como legitimador das condutas fenomenológicas, tal qual as concebem G. van der Leeuw e F. Heiler, ao mesmo tempo em que possibilita a integração de pontos de vista divergentes, no debate entre as vertentes, explicação/compreensão.(AU)

A CONSTRUÇÃO CULTURAL DA NARRATIVA NOTICIOSA: noticiabilidade, representação simbólica e regularidade cotidiana

A tese constitui uma discussão teórico-conceitual de natureza eminentemente qualitativa sobre a construção cultural dos chamados critérios de noticiabilidade no jornalismo. Sua proposta central é inserir a problemática da noticiabilidade isto é, a discussão em torno dos parâmetros que levam determinados acontecimentos a receber a valoração de notícia em detrimento de outros no interior de uma reflexão mais ampla, de ordem culturalista, que objetiva dimensionar a narrativa noticiosa como um dos elementos estético-expressivos mais consistentes na sustentação da experiência cotidiana moderna. Como objetivos específicos, busca-se: 1) a discussão teórica de algumas das mais significativas abordagens conceituais que os critérios de noticiabilidade recebem historicamente nas ciências sociais; 2) a apresentação de um conjunto alternativo de concepções teóricas que, articuladas, possam explicitar a complexidade do processo de seleção noticiosa; e 3) a proposição de uma sistematização teórico-conceitual para tais articulações de modo a sintonizar a tese com o estado da arte no campo da teoria do jornalismo. Aporta-se, ao fim, na elaboração de um modelo explicativo pendular que se institui como metáfora possível para a relação entre o jornalismo, os paradoxos cotidianos e os parâmetros simbólicos que caracterizam a regularidade cotidiana como padrão cultural da sociabilidade moderna.

General bounds on Bayes errors for regression with Gaussian processes

Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

A new entropy measure based on the Renyi entropy rate using Gaussian kernels

The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.

Measuring the spatial arrangement patterns of pathological lesions in histological sections of brain tissue

The development of abnormal protein aggregates in the form of extracellular plaques and intracellular inclusions is a characteristic feature of many neurodegenerative diseases such as Alzheimer's disease (AD), Creutzfeldt-Jakob disease (CJD) and the fronto-temporal dementias (FTD). An important aspect of a pathological protein aggregate is its spatial topography in the tissue. Lesions may not be randomly distributed within a histological section but exhibit spatial pattern, a departure from randomness either towards regularity or clustering. Information on the spatial pattern of a lesion may be useful in elucidating its pathogenesis and in studying the relationships between different lesions. This article reviews the methods that have been used to study the spatial topography of lesions. These include simple tests of whether the distribution of a lesion departs significantly from random using randomized points or sample fields, and more complex methods that employ grids or transects of contiguous fields and which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters. The usefulness of these methods in elucidating the pathogenesis of protein aggregates in neurodegenerative disease is discussed.

Methods of studying the planar distribution of objects in histological sections of brain tissue

This article reviews the statistical methods that have been used to study the planar distribution, and especially clustering, of objects in histological sections of brain tissue. The objective of these studies is usually quantitative description, comparison between patients or correlation between histological features. Objects of interest such as neurones, glial cells, blood vessels or pathological features such as protein deposits appear as sectional profiles in a two-dimensional section. These objects may not be randomly distributed within the section but exhibit a spatial pattern, a departure from randomness either towards regularity or clustering. The methods described include simple tests of whether the planar distribution of a histological feature departs significantly from randomness using randomized points, lines or sample fields and more complex methods that employ grids or transects of contiguous fields, and which can detect the intensity of aggregation and the sizes, distribution and spacing of clusters. The usefulness of these methods in understanding the pathogenesis of neurodegenerative diseases such as Alzheimer's disease and Creutzfeldt-Jakob disease is discussed. © 2006 The Royal Microscopical Society.

What does the study of the spatial patterns of pathological lesions tell us about the pathogenesis of neurodegenerative disorders?

Discrete pathological lesions, which include extracellular protein deposits, intracellular inclusions and changes in cell morphology, occur in the brain in the majority of neurodegenerative disorders. These lesions are not randomly distributed in the brain but exhibit a spatial pattern, that is, a departure from randomness towards regularity or clustering. The spatial pattern of a lesion may reflect pathological processes affecting particular neuroanatomical structures and, therefore, studies of spatial pattern may help to elucidate the pathogenesis of a lesion and of the disorders themselves. The present article reviews first, the statistical methods used to detect spatial patterns and second, the types of spatial patterns exhibited by pathological lesions in a variety of disorders which include Alzheimer's disease, Down syndrome, dementia with Lewy bodies, Creutzfeldt-Jakob disease, Pick's disease and corticobasal degeneration. These studies suggest that despite the morphological and molecular diversity of brain lesions, they often exhibit a common type of spatial pattern (i.e. aggregation into clusters that are regularly distributed in the tissue). The pathogenic implications of spatial pattern analysis are discussed with reference to the individual disorders and to studies of neurodegeneration as a whole.

The spatial patterns of beta-amyloid deposits and neurofibrillary tangles in the cerebral cortex in Alzheimer's disease

In Alzheimer's disease (AD) brain, beta-amyloid (Abeta) deposits and neurofibrillary tangles (NFT) are not randomly distributed but exhibit a spatial pattern, i.e., a departure from randomness towards regularity or clustering. Studies of the spatial pattern of a lesion may contribute to an understanding of its pathogenesis and therefore, of AD itself. This article describes the statistical methods most commonly used to detect the spatial patterns of brain lesions and the types of spatial patterns exhibited by ß-amyloid deposits and NFT in the cerebral cortex in AD. These studies suggest that within the cerebral cortex, Abeta deposits and NFT exhibit a similar spatial pattern, i.e., an aggregation of individual lesions into clusters which are regularly distributed parallel to the pia mater. The location, size and distribution of these clusters supports the hypothesis that AD is a 'disconnection syndrome' in which degeneration of specific cortical pathways results in the formation of clusters of NFT and Abeta deposits. In addition, a model to explain the development of the pathology within the cerebral cortex is proposed.

Analysis of population dispersion in histological sections

Stereology and other image analysis methods have enabled rapid and objective quantitative measurements to be made on histological sections. These mesurements may include total volumes, surfaces, lengths and numbers of cells and blood vessels or pathological lesions. Histological features, however, may not be randomly distributed across a section but exhibit 'dispersion', a departure from randomness either towards regularity or aggregation. Information of population dispersion may be valuable not only in understanding the two-or three-dimensional structure but also in elucidating the pathogenesis of lesions in pathological conditions. This article reviews some of the statistical methods available for studying dispersion. These range from simple tests of whether the distribution of a histological faeture departs significantly from random to more complex methods which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters.

Spatial arrangement patterns of senile plaques in post-mortem senile dementia of the Alzheimer type brains

We have studied the spatial distribution of plaques in coronal and tangential sections of the parahippocampal gyrus (PHG), the hippocampus, the frontal lobe and the temporal lobe of five SDAT patients. Sections were stained with cresyl violet and examined at two magnifications (x100 and x400). in all cases (and at both magnifications) statistical analysis using the Poisson distribution showed that the plaques were arranged in clumps (x100: V/M = 1.48 - 4.49; x400 V/M = 1.17 - 1.95). this indicates that both large scale and small scale clumping occurs. Application of the statistical techniques of pattern analysis to coronal sections of frontal and temporal cortex and PHG showed. furthermore, that both large (3200-6400 micron) and small scale (100 - 400 micron) clumps were arranged with a high degree of regularity in the tissue. This suggests that the clumps of plaques reflect underlying neural structure.

A novel entropy measure for analysis of the electrocardiogram

There has been much recent research into extracting useful diagnostic features from the electrocardiogram with numerous studies claiming impressive results. However, the robustness and consistency of the methods employed in these studies is rarely, if ever, mentioned. Hence, we propose two new methods; a biologically motivated time series derived from consecutive P-wave durations, and a mathematically motivated regularity measure. We investigate the robustness of these two methods when compared with current corresponding methods. We find that the new time series performs admirably as a compliment to the current method and the new regularity measure consistently outperforms the current measure in numerous tests on real and synthetic data.

A deficit in encoding the order of visual sequences in developmental dyslexia: a non -phonological deficit

The present thesis tested the hypothesis of Stanovich, Siegel, & Gottardo (1997) that surface dyslexia is the result of a milder phonological deficit than that seen in phonological dyslexia coupled with reduced reading experience. We found that a group of adults with surface dyslexia showed a phonological deficit that was commensurate with that shown by a group of adults with phonological dyslexia (matched for chronological age and verbal and non-verbal IQ) and normal reading experience. We also showed that surface dyslexia cannot be accounted for by a semantic impairment or a deficit in the verbal learning and recall of lexical-semantic information (such as meaningful words), as both dyslexic subgroups performed the same. This study has replicated the results of our published study that surface dyslexia is not the consequence of a mild retardation or reduced learning opportunities but a separate impairment linked to a deficit in written lexical learning, an ability needed to create novel lexical representations from a series of unrelated visual units, which is independent from the phonological deficit (Romani, Di Betta, Tsouknida & Olson, 2008). This thesis also provided evidence that a selective nonword reading deficit in developmental dyslexia persists beyond poor phonology. This was shown by finding a nonword reading deficit even in the presence of normal regularity effects in the dyslexics (when compared to both reading and spelling-age matched controls). A nonword reading deficit was also found in the surface dyslexics. Crucially, this deficit was as strong as in the phonological dyslexics despite better functioning of the sublexical route for the former. These results suggest that a nonword reading deficit cannot be solely explained by a phonological impairment. We, thus, suggested that nonword reading should also involve another ability relating to the processing of novel visual orthographic strings, which we called 'orthographic coding'. We then investigated the ability to process series of independent units within multi-element visual arrays and its relationship with reading and spelling problems. We identified a deficit in encoding the order of visual sequences (involving both linguistic and nonlinguistic information) which was significantly associated with word and nonword processing. More importantly, we revealed significant contributions to orthographic skills in both dyslexic and control individuals, even after age, performance IQ and phonological skills were controlled. These results suggest that spelling and reading do not only tap phonological skills but also order encoding skills.

Spelling acquisition in English and Italian:a cross-linguistic study

We examined the spelling acquisition in children up to late primary school of a consistent orthography (Italian) and an inconsistent orthography (English). The effects of frequency, lexicality, length, and regularity in modulating spelling performance of the two groups were examined. English and Italian children were matched for both chronological age and number of years of schooling. Two-hundred and seven Italian children and 79 English children took part in the study. We found greater accuracy in spelling in Italian than English children: Italian children were very accurate after only 2 years of schooling, while in English children the spelling performance was still poor after 5 years of schooling. Cross-linguistic differences in spelling accuracy proved to be more persistent than the corresponding ones in reading accuracy. Orthographic consistency produced not only quantitative, but also qualitative differences, with larger frequency and regularity effects in English than in Italian children.

Determining the temperature from incomplete boundary data

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2-space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)