Thesis (Ph.D.)--Mathematics, Georgia Institute of Technology, 2008. / Committee Chair: Dieci, Luca; Committee Member: Chow, Shui-Nee; Committee Member: Liu, Yingjie; Committee Member: Loss, Michael; Committee Member: Verriest, Erik.

Masters of Science / The communication barriers between deaf and hearing society mean that interaction between these communities is kept to a minimum. The South African Sign Language research group, Integration of Signed and Verbal Communication: South African Sign Language Recognition and Animation (SASL), at the University of the Western Cape aims to create technologies to bridge the communication gap. In this thesis we address the subject of whole hand gesture recognition. We demonstrate a method to identify South African Sign Language classifiers using an eigenvector ap- proach. The classifiers researched within this thesis are based on those outlined by the Thibologa Sign Language Institute for SASL. Gesture recognition is achieved in real- time. Utilising a pre-processing method for image registration we are able to increase the recognition rates for the eigenvector approach. / South Africa

Let G be a simple simply connected algebraic group defined over an algebraically closed field K and V an irreducible module defined over K on which G acts. Let E denote the set of vectors in V which are eigenvectors for some non-central semisimple element of G and some eigenvalue in K*. We prove, with a short list of possible exceptions, that the dimension of Ē is strictly less than the dimension of V provided dim V > dim G + 2 and that there is equality otherwise. In particular, by considering only the eigenvalue 1, it follows that the closure of the union of fixed point spaces of non-central semisimple elements has dimension strictly less than the dimension of V provided dim V > dim G + 2, with a short list of possible exceptions. In the majority of cases we consider modules for which dim V > dim G + 2 where we perform an analysis of weights. In many of these cases we prove that, for any non-central semisimple element and any eigenvalue, the codimension of the eigenspace exceeds dim G. In more difficult cases, when dim V is only slightly larger than dim G + 2, we subdivide the analysis according to the type of the centraliser of the semisimple element. Here we prove for each type a slightly weaker inequality which still suffices to establish the main result. Finally, for the relatively few modules satisfying dim V ≤ dim G + 2, an immediate observation yields the result for dim V < dim B where B is a Borel subgroup of G, while in other cases we argue directly.

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Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought. / Ph. D.

Approved for public release; distribution in unlimited. / In recent years there has been an increased interest in effective individual control and enhanced security measures, and face recognition schemes play an important role in this increasing market. In the past, most face recognition research studies have been conducted with visible imaging data. Only recently have IR imaging face recognition studies been reported for wide use applications, as uncooled IR imaging technology has improved to the point where the resolution of these much cheaper cameras closely approaches that of cooled counterparts. This study is part of an on-going research conducted at the Naval Postgraduate School which investigates the feasibility of applying a low cost uncooled IR camera for face recognition applications. This specific study investigates whether nonlinear kernel-based classifiers may improve overall classification rates over those obtained with linear classification schemes. The study is applied to a 50 subject IR database developed in house with a low resolution uncooled IR camera. Results show best overall mean classification performances around 98.55% which represents a 5% performance improvement over the best linear classifier results obtained previously on the same database. This study also considers several metrics to evaluate the impacts variations in various user-specified parameters have on the resulting classification performances. These results show that a low-cost, low-resolution IR camera combined with an efficient classifier can play an effective role in security related applications. / Captain, Hellenic Air Force

Parmi les outils les plus classiques de l'Analyse Multivariée, les Composantes Principales sont aussi un des plus anciens puisqu'elles furent introduites il y a plus d'un siècle par Pearson (1901) et redécouvertes ensuite par Hotelling (1933). Aujourd'hui, cette méthode est abondamment utilisée en Sciences Sociales, en Economie, en Biologie et en Géographie pour ne citer que quelques disciplines. Elle a pour but de réduire de façon optimale (dans un certain sens) le nombre de variables contenues dans un jeu de données.<p>A ce jour, les méthodes d'inférence utilisées en Analyse en Composantes Principales par les praticiens sont généralement fondées sur l'hypothèse de normalité des observations. Hypothèse qui peut, dans bien des situations, être remise en question.<p><p>Le but de ce travail est de construire des procédures de test pour l'Analyse en Composantes Principales qui soient valides sous une famille plus importante de lois de probabilité, la famille des lois elliptiques. Pour ce faire, nous utilisons la méthodologie de Le Cam combinée au principe d'invariance. Ce dernier stipule que si une hypothèse nulle reste invariante sous l'action d'un groupe de transformations, alors, il faut se restreindre à des statistiques de test également invariantes sous l'action de ce groupe. Toutes les hypothèses nulles associées aux problèmes considérés dans ce travail sont invariantes sous l'action d'un groupe de transformations appellées monotones radiales. L'invariant maximal associé à ce groupe est le vecteur des signes multivariés et des rangs des distances de Mahalanobis entre les observations et l'origine. <p><p>Les paramètres d'intérêt en Analyse en composantes Principales sont les vecteurs propres et valeurs propres de matrices définies positives. Ce qui implique que l'espace des paramètres n'est pas linéaire. Nous développons donc une manière d'obtenir des procédures optimales pour des suite d'experiences locales courbées. <p>Les statistiques de test introduites sont optimales au sens de Le Cam et mesurables en l'invariant maximal décrit ci-dessus.<p>Les procédures de test basées sur ces statistiques possèdent de nombreuses propriétés attractives: elles sont valides sous la famille des lois elliptiques, elles sont efficaces sous une densité spécifiée et possèdent de très bonnes efficacités asymptotiques relatives par rapport à leurs concurrentes. En particulier, lorsqu'elles sont basées sur des scores Gaussiens, elles sont aussi efficaces que les procédures Gaussiennes habituelles et sont bien plus efficaces que ces dernières si l'hypothèse de normalité des observations n'est pas remplie. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is non-increasing with respect to an ordering of the vertices induced by breadth-first search. For trees the resulting structure is uniquely determined up to isomorphism. We also show that the largest spectral radius in such classes of trees is strictly monotone with respect to majorization. This paper is the revised final version of the preprint no. 35 of this research report series. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

The heavily developed Long Key is located in Pinellas County in west-central Florida. The structured Blind Pass at the north end of the barrier island interrupts the southward longshore sediment transport, resulting in severe and chronic beach erosion along the northern portion of the island. Frequent beach nourishments were conducted to mitigate the erosion. In this study, the performance of the most recent beach nourishment in 2010 is quantified through time-series beach profile surveys. Over the 34-month period, the nourished northern portion of the island, Upham Beach, lost up to 330 m3/m of sand, with a landward shoreline retreat of up to 100 m. The middle portion of the island gained up to 25 m3/m of sand, benefiting from the sand lost from Upham Beach. The southern portion of Long Key lost a modest amount of sediment, largely due to Tropical Storm Debby, which approached from the south in June 2012. The severe erosion along Upham Beach is induced by a large negative longshore transport gradient. The beach here has no sand bar and retreated landward persistently over the 34-month study period. In contrast the profiles in the central section of the island generally have a sand bar which moved landward and seaward in response to seasonal and storm-induced wave-energy changes. The sand volume across the entire profile in the central portion of the island is mostly conserved. Two typical example beach profiles, LK3A and R157, were selected to examine the ability of the commonly used principal component analysis (PCA), also commonly known as empirical orthogonal function analysis (EOF), to identify beach profile ix changes induced by longshore and cross-shore sediment transport gradients. For the longshore-transport driven changes at the non-barred profile LK3A, the principal eigenvector accounted for over 91% of the total variance, with a dominant broad peak in the cross-shore distribution. At the barred R157, the profile changes were caused mainly by cross-shore transport gradients with modest contribution from longshore transport gradient; eigenvalue one only accounted for less than 51% of the total variance, and eigenvalues two and three still contributed considerably to the overall variance. In order to verify the uniqueness of the PCA results from LK3A and R157, five numerical experiments were conducted, simulating changes at a barred and non-barred beach driven by longshore, cross-shore, and combined sediment transport gradients. Results from LK3A and R157 compare well with simulated beach erosion (or accretion) due to variable longshore sediment transport gradients and due to both cross-shore and longshore sediment transport gradients, respectively. Different PCA results were obtained from different profile change patterns.