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 29 for “"hyperplanes"”.
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Geometric variational problems with cross-sectional constraints
… surface with given boundary on two parallel hyperplanes and the constraint that the intersection of the surface with each hyperplane parallel to these of the boundary encloses the same area. In Chapter 3, we study the area minimizing surface in R 3 whose intersection with each of the …
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Generalizations of no k-equal spaces
… as no $(d+c)$-intersecting translates of hyperplanes. We give results on the first two non-trivial homology groups of no $(d+c)$-intersecting translates of hyperplanes in $\R^d$.
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Incidence Problems for Slabs
… intersecting small neighborhoods of well-spaced hyperplanes in R superscript 𝑑 with the unit cube [0, 1] superscript 𝑑 . My work is an analogue of a theorem of Guth, Solomon, and Wang, who proved a version of the SzemerédiTrotter theorem for thin tubes that satisfy a certain strong spacing …
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Progress on the Interplay of Machine Learning and Optimization
… depth (up to depth 8) classification trees with hyperplanes to closely approximate neural networks. We also incorporate sparsity in the hyperplanes of the trees. In this way, we contribute in increasing the interpretability of neural networks. Computational results on real-world datasets with …
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Extending linear grouping analysis and robust estimators for very large data sets
… 2006) is an algorithm for clustering data around hyperplanes, and is most appropriate when: 1) the variables are related/correlated, which results in clusters with an approximately linear structure; and 2) it is not natural to assume that one variable is a “response”, and the remainder the …
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Homological mirror symmetry for a Calabi-Yau hypersurface in projective space
… is defined to be the complement of n + 2 generic hyperplanes in CPn. The pair of pants is conjectured to be mirror to the Landau-Ginzburg model (Cn+2 , W), where W = z1...zn+2 We construct an immersed Lagrangian sphere in the pair of pants, and show that its endomorphism A.. algebra in the Fukaya …
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The Characterization Of Graphs With Small Bicycle Spectrum
… designs are defined to be matroids in which the hyperplanes all have the same size. The dual of a matroid design is a matroid with all circuits of the same size, called a dual matroid design. The connected bicircular dual matroid designs have been characterized previously. In addition, these …
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A free boundary problem inspired by a conjecture of De Giorgi
… in one direction have levell sets that are hyperplanes, at least up to dimension 8. Recently, Del Pino, Kowalczyk and Wei gave an intricate fixed-point-argument construction of a counterexample in dimension 9, whose level sets "follow" the entire minimal non-planar graph, built by Bombieri, …
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Self-shrinkers of mean curvature flow and harmonic map heat flow with rough boundary data
… the Euclidean space, that are entire graphs, are hyperplanes. This generalizes an earlier result by Ecker and Huisken: no polynomial growth assumption at infinity is needed.
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On the Structure and Regularity of Stable Branched Minimal Hypersurfaces
… integral varifolds $V$ near higher multiplicity hyperplanes and classical cones, i.e. cones supported on half-hyperplanes which have a common boundary. A key motivation for our work is to understand the local structure of stationary integral varifolds about their branch points. In addition to the …
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Embeddings of cat(0) cube complexes in products of trees
… in the Hilbert space '2(H) where H is the set of hyperplanes. This Hilbert space may be viewed as the completion of an infinite product of trees. In this thesis, we consider the question of the existence of quasi-isometric maps from CAT(0) cube complexes to finite products of trees, restricting …
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Bicircular Matroids with Circuits of at Most Two Sizes
… 1968, was the first to study matroids with all hyperplanes having the same size. Murty called such a matroid an ``Equicardinal Matroid''. Young renamed such a matroid a ``Matroid Design''. Further work on determining properties of these matroids was done by Edmonds, Murty, and Young in their …
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Learning Probabilistic Generative Models For Fast Sampling-Based Planning
… constructed around a configuration using tangent hyperplanes of confidence ellipsoids of GMMs learned from prior collision history. For efficient sampling, we suggest a sampling method with a learned Q-function with linear function approximation based on feature representations such as Radial …
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Barrier Graphs and Extremal Questions on Line, Ray, Segment, and Hyperplane Sensor Networks
… line, line segment, and rays in the plane, and hyperplanes in higher dimensions.</p> <p>First we explore ray sensor networks in the plane, whose <em>resilience</em> is the number of sensors that must be crossed by an agent traveling between two known locations. The coverage of such a network is …
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Predictive and Prescriptive Trees for Optimization and Control Problems
… control problems, with segments separated by hyperplanes passing through the origin. We use Optimal Classification Trees with hyperplane splits (OCT-H) to learn an optimal control policy for MFQNETs. In Chapter 3, we study fluid restless multi-armed bandits (FRMABs), deriving fundamental …
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The Gomory-Chvátal closure : polyhedrality, complexity, and extensions
… planes belong to this class. Furthermore, as the hyperplanes associated with these cuts have very dense and symmetric lattices of integer points, these cutting planes are in some- sense the "simplest" cuts in the set of all Gomory-Chvátal cuts. In the second part of this thesis, we answer a …
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Topics in combinatorial and computational geometry
… j mass distributions in $\IR\sp{d}$, there are k hyperplanes so that each orthant contains a fraction 1/2$\sp{k}$ of each of the masses; it is easily shown that $j(2\sp{k}-1)/k \le \Delta(j,k)\le j2\sp{k-1}$; we believe the lower bound is tight, but can only prove it in a few cases (as a tool we …
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Holomorphic flexibility properties of complements and mapping spaces.
… a characterisation of when a complement in Pn of hyperplanes is Oka, and the result that the complement of the affine graph of a meromorphic function is Oka, subject to some restrictions. The proof of the second result involves an extension to Gromov’s technique of localisation of algebraic …
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Global and Robust Optimization for Engineering Design
… learned using optimal classification trees with hyperplanes (OCT-Hs). OCT-Hs describe union-of-polyhedra approximations of intractable constraints, which are solved efficiently using commercial solvers to find near-feasible and near-optimal solutions to the global optimization problem. The …
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