Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 14 of 14 for “"Convex Geometry"”.
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Applications of the fourier transform to convex geometry
… to the study of various problems arising from Convex Geometry and Geometric Functional Analysis using tools of Fourier Analysis. In chapters two through four we consider the Busemann-Petty problem and its different modifications and generalizations. We solve the Busemann-Petty problem in …
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Convex Geometric Connections to Information Theory
Convex geometry is a field of mathematics that has experienced rapid growth in recent years and has proven to be an extremely useful perspective in areas of research. Problems in many different fields can be interpreted geometrically which often leads to powerful and surprising results. This thesis …
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Dispersion of mass and the complexity of geometric problems
… of dispersion and connect it to asymptotic convex geometry. We obtain a nearly quadratic lower bound on the complexity of randomized volume algorithms for convex bodies in Rn (the current best algorithm has complexity roughly n4, conjectured to be n3). Our main tools, dispersion of random …
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Generalized Matrix-fractional Functions and Their Applications
The support function of a closed convex set is a central object in convex geometry as it completely identifies the underlying set. For a particular class of sets -- the graph of matrix valued mapping $Y\mapsto -\half YY^T$ over an affine manifold $\set{Y\in\Rnm}{AY=B}$, their support functions are …
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Degenerating abelian varieties via log abelian varieties
… of algebraic spaces and higher-dimensional convex geometry to create diverse models for any given split totally degenerate semi-stable abelian variety over a complete discrete valuation field. Such models are used to construct a log abelian variety over the corresponding discrete valuation …
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The Illumination of Symmetric Spiky Balls and Cap Bodies; and a note on the Vertex Classification of Planar C-polygons
This thesis handles two problems in the field of convex geometry. The first, is the problem of illuminating the boundary of Euclidean shapes known as spiky balls and cap bodies in various dimensions. Specifically we consider illuminating the cases where a spiky ball is 2-illuminable, and the cases …
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Geometric approaches to computing Kostka numbers and Littlewood-Richardson coefficients
Using tools from combinatorics, convex geometry and symplectic geometry, we study the behavior of the Kostka numbers and Littlewood-Richardson coefficients (the type A weight multiplicities and Clebsch-Gordan coefficients). We sh w that both are given by piecewise polynomial functions in the …
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Shortest paths, Markov chains, matrix scaling and beyond : improved algorithms through the lens of continuous optimization
… build connections between classic methods from convex optimization and the modern toolkit from the fast Laplacian solver literature, in order to make progress on a number of fundamental algorithmic problems: *-- We develop a faster algorithm for the unit capacity minimum cost flow problem, which …
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Topics in shape-constrained inference
… above. To this end, we apply techniques from convex geometry and real analysis to elucidate the structural properties of such densities, and obtain some results of independent interest. In the third chapter, we consider the nonparametric estimation of an S-shaped regression function. The least …
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Manifold learning based spectral unmixing of hyperspectral remote sensing data
… spectral variability within image subsets and convex-geometry finds a solution more quickly and precisely. Experiments were conducted to evaluate the proposed methods using the AVIRIS Cuprite hyperspectral reference dataset.</p> <p>A case study of manifold learning based spectral unmixing in …
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Identifiability for latent class models
… are topic models, which model each document by a convex combination of a set of word-frequency vectors, known as topics. Although identifying such latent topics is of primary interest in many applications, it is well-known that the topic parameters are not identifiable. Prior work addressed this …
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Convex optimization methods for graphs and statistical modeling
… development of computational methods based on convex optimization, which are in turn useful in a broad array of problems in signal processing and machine learning. The specific contributions are as follows: -- We propose a convex optimization method for decomposing the sum of a sparse matrix …
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Modeling And Detection Of Uterine Contractions Using Magnetomyography
… we introduce a four-compartment volume conductor geometry, and we use a bidomain approach to model the propagation of the myometrium transmembrane potential on the human uterus. The bidomain approach is given by a set of reaction-diffusion equations. The diffusion part of the equations governs the …
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Tensorwertige additive Funktionale auf konvexen Körpern
Die Arbeit stellt eine Untersuchung von Funktionalen auf konvexen Körpern dar, die tensorwertig, stetig, additiv und bewegungskovariant sind. Es werden gemischte tensorielle Momente hergeleitet, Minkowski-Tensoren betrachtet, Integralgeometrische Formeln hergeleitet und eine Basis des Vektorraumes …