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 78 for “"metric space"”.
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Hyperconvex hulls in catergories of quasi-metric spaces
Isbell showed that every metric space has an injective hull, that is, every metric space has a “minimal” hyperconvex metric superspace. Dress then showed that the hyperconvex hull is a tight extension. In analogy to Isbell’s theory Kemajou et al. proved that each T₀-quasi-metric space X has a …
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Fourier analysis on the hypercube, the coefficient problem, and applications
… is to maximize cardinality of a subset of a metric space subject to a minimum distance constraint. Here, we use it to study anticoding problems, where the objective is to maximize cardinality of a subset of a metric space subject to a maximum distance (diameter) constraint. One motivation for …
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Coarser connected topologies and non-normality points
… question in the first topic is: When does a space have a coarser connected topology with a nice topological property? We will discuss some results when the property is Hausdorff and prove that if X is a non-compact metric space that has weight at least the cardinality of the continuum, then …
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Construction of quasi-metrics determined by orders
… a growing interest in the area of quasi-pseudometricspaces and related asymmetric structures. Problems arising from theoretical computer science, applied physics and many more areas can easily be expressed in that setting. In the asymmetric framework, many investigations on general topology …
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Lower bounds for embedding the Earth Mover Distance metric into normed spaces
… for embedding the Earth Mover Distance (EMID) metric into normed spaces. The EMID is a metric over two distributions where one is a mass of earth spread out in space and the other is a collection of holes in that same space. The EMD between these two distributions is defined as the least amount …
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Strong Orbit Equivalence and Residuality
… strongly orbit equivalent. We go on to define a metric on a strong orbit equivalence class of minimal Cantor systems and prove several properties about the metric space. If the strong orbit equivalence class contains a finite rank system, we show that the set of finite rank systems is residual in …
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DECENTRALIZED NETWORK BANDWIDTH PREDICTION AND NODE SEARCH
… can be represented approximately in a tree metric space, we focus on three specific research problems. First, we have designed a decentralized algorithm for network bandwidth prediction. The algorithm embeds the bandwidth information as distance in an edge-weighted tree, without performing …
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Frontiers of Liouville quantum gravity
… heuristic perspective. -- We analyze LQG as a metric space. We prove results necessary for the construction of LQG as a metric space, and prove fundamental estimates for these distances. We prove the most natural formulation of the Knizhnik-Polyakov-Zamolodchikov (KPZ) formula, which relates …
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Geometric Methods for Point Estimation
<p>The focus of this dissertation is on geometric aspects of point estimation problems. In the first half of this work, we examine the estimation of location parameters for non-Euclidean data that lies in a known manifold or metric space. Ideas from statistical decision theory motivate the …
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Hyperspace Topologies
In this paper we study properties of metric spaces. We consider the collection of all nonempty closed subsets, Cl(X), of a metric space (X,d) and topologies on C.(X) induced by d. In particular, we investigate the Hausdorff topology and the Wijsman topology. Necessary and sufficient conditions are …
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Hyperconvexity and endpoints in T₀-quasi-metric spaces
… made in the investigation of hyperconvexity in metric spaces. Recently Kemajou and others have published an article concerning hyperconvexity in T₀-quasi-metric spaces. In 1964 Isbell introduced and studied the concept of an endpoint of a metric space. The aim of this dissertation is to begin an …
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Metric Segments and Lines
This paper examines segments and lines of a metric space. It describes their properties and characteristics in general and those properties that arise from limiting the space to complete, compact, and/or convex spaces.
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Computational metric embeddings
… computing a low-distortion embedding between two metric spaces. More precisely given an input metric space M we are interested in computing in polynomial time an embedding into a host space M' with minimum multiplicative distortion. This problem arises naturally in many applications, including …
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Representation theory, Borel cross-sections, and minimal measures
Let E be an analytic metric space, let X be a separable metric space with a regular Borel probability measure μ and let Π: E → X be a continuous map with μ(X \ Π(E)) =0. Schwartz’s lemma states that there exists a Borel cross-section for Π defined almost everywhere (μ). The equivalence classes of …
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DATA MINING TECHNIQUES ON VOLCANO MONITORING
… 1 introduces the problem of searching in a metric space, showing the key applications (from text retrieval to computational biology and so on) and the basic concepts (e.g. metric distance function). The current solutions, together with a model for standardization, are presented in Chapter 2. …
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A quasi-pseudometrizability problem for ordered metric spaces
… results in the setting of ordered topological spaces related to the Hanai-Morita-Stone Theorem. The latter says that if f is a closed continuous map of a metric space X onto a topological space Y then the following statements are equivalent: (i) Y satisfies the first countability axiom; (ii) …
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In search of better proximity
Given a set of points in a metric space, a fundamental problem is to preprocess these points for answering nearest-neighbor queries on them. Proximity search is the problem of answering more general queries that need the first, second, or further closest neighbors of a query point, possibly in …
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Dynamics of Polish groups
… of isometries of a locally compact separable metric space has a spatial model or, in other words, has a point realization. This result extends both a classical theorem of Mackey and a recent theorem of Glasner and Weiss, and it covers interesting new examples. In order to prove our result, we …
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Stability in dynamical polysystems
… dynamical systems, all acting on a given metric space. The first chapter of the present thesis shows a generalization of control systems via dynamical polysystems and establishes the equivalence of the two notions under certain lipschitz condition on the function defining the dynamics. The …
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Some Results on G-Delta Ideals of Compact Sets
For a compact metric space E, Solecki has defined a broad natural class of Gdelta ideals of compact sets on E, called Gdelta ideals with property (*), and has shown that any ideal I in this class can be represented through the ideal of nowhere dense subsets of a closed subset F of the hyperspace of …
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