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 20 of 33 for “"Convex Set"”.
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Convex set reconstruction from support line measurements and its application to laser radar data
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1990.
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Enhancements and computational evaluation of the hit-and-run random walk on polyhedra
The symmetry function of a convex set offers us numerous useful information about the set in relation to probabilistic theory and geometric properties. The symmetry function is a measure of how symmetric the convex set is, and for a point, intuitively it measures how symmetric the set is with …
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Topics in the Design of Political and Economic Mechanisms
… the third essay analyzes conditions for the convexifiability of an agent's utility $u(a)$ viewed a function of his type. The study shows that if the set of types A is an m-dimensional rectangle, $m\ge1,$ then u can be assumed convex in a without loss of generality. In particular, in any …
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High resolution signal and image recovery: Fast algorithms and analysis
… developing fast and efficient algorithms for convex set constrained signal recovery, analyzing resolution limits in signal recovery algorithms, and developing new regularization techniques for reducing the ill effects of noise in signal recovery algorithms.
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Convex lattice polygons
… deals with three main extremal problems on convex lattice polygons in the plane. A convex lattice polygon is the intersection of a compact convex set with the integer lattice (the set of all points with integer coordinates). Let P represent a convex lattice polygon.
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Problems in Graph Coloring and Graph Structure
Let F be a family of translates of a fixed convex set in the plane, and let G be the intersection graph of F . We studied the chromatic number of the complement of G. We also studied the transversal number of F , where the transversal number is the minimum size of a set of points that intersects …
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β-Uniform Convexity and Divisible Domains
Divisible convex sets have long been important in the study of Hilbert geometries. When a divisible convex set is an ellipsoid, the Hilbert geometry it induces is the hyperbolic space. In general, strictly convex divisible domains exhibit negative curvature properties, but only the ellipsoid is a …
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Probabilistic completion of nondeterministic models
… models of probabilistic choice over an arbitrary set X, and the finite convex set functor Cvxfin , which constructs free models of mixed choice over an arbitrary convex set (C, +lambda), as seen in [31, 33, 49]. This construction allows us to build a free mixed choice model from an arbitrary model …
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Counting Convex Sets on Products of Totally Ordered Sets
… purpose of this thesis is to find the number of convex sets on a product of two totally ordered spaces. We will give formulas to find this number for specific cases and describe a process to obtain this number for all such spaces. In the first chapter we briefly discuss the motivation behind the …
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Existence and uniqueness of best approximants, with numerical applications
… space is complete if every closed, bounded, and convex set is proximinal. It is also shown, that in a semi-reflexive, locally convex, real linear metric space, every closed, bounded and convex set is proximinal. An example is constructed which proves that not every reflexive space is sequentially …
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A strong maximum principle for reaction-diffusion systems and a weak convergence scheme for reflected stochastic differential equations by Lawrence Christopher Evans.
… regularity assumptions on the boundary of the convex set in which the system takes its values. The second result is an approximation scheme for reflected stochastic differential equations (SDE) of the Stratonovich type. This is a joint result with Professor Daniel W. Stroock. We show that the …
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Schur-class of finitely connected planar domains: the test-function approach
We study the structure of the set of extreme points of the compact convex set of matrix-valued holomorphic functions with positive real part on a finitely-connected planar domain 𝐑 normalized to have value equal to the identity matrix at some prescribed point t₀ ∈ 𝐑. This leads to an integral …
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Multichannel blind deconvolution in underwater acoustic channels
… be recast as recovering a low-rank matrix from a set of linear observations. In the second approach, we formed a cross-correlation matrix from the channel outputs and solved the problem by minimizing a quadratic function over a non-convex set. We demonstrated the efficiency and robustness of both …
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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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Boundary Properties for Almost-Minimizers of the Relative Perimeter
Let A be an Euclidean open Lipschitz set. This dissertation aims to discuss some results concerning the boundary regularity for almost-minimizers of the relative perimeter in A. An almost-minimizer of the relative perimeter in A is a measurable set E that minimizes the perimeter functional P(E;A), …
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On the explanatory value of condition numbers for convex optimization : theoretical issues and computational experience
The modern theory of condition numbers for convex optimization problems was developed for convex problems in conic format: ... The condition number C(d) for (CPd) has been shown in theory to provide upper and/or lower bounds on many behavioral and computational characteristics of (CPd), from sizes …
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Optimal estimation in high-dimensional and nonparametric models
… chapter, a new estimator for the volume of a convex set is proposed. The estimator is minimax optimal and also efficient non-asymptotically: it is nearly unbiased with minimal variance among all unbiased oracle-type estimators. Our approach is based on a Poisson point process model and as an …
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Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem
… is developed. This method is based on the convexity of the geometric interpretation of the eigenvalue problem for undamped positive definite systems. The damage detection scheme establishes various damage scenarios which are used as failure sets. These scenarios are then compared to the …
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A generalized label correcting method for optimal kinodynamic motion planning
… based on a direct forward search of the set of admissible input signals to a dynamical model. The advantage of this generalized label correcting method is that it does not require a local planning subroutine as in the case of related methods. Preliminary material focuses on new …
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Stochastic Event-Based Control and Estimation
… used to find bounds on control objectives using convex semidefinite programming. The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and …
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