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 24 for “"simplices"”.
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Multidimensional Adaptive Quadrature Over Simplices
… adaptive quadrature routines defined over simplices (MAQS). MAQS pro- vides an approximation to the integral of a function defined over the unit hypercube and provides an error estimate that is used to drive a global subdivision strategy. The quadrature estimate is based on Lagrangian …
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Minimal Volume K-Point Lattice D-Simplices
… show that there can only be one such class of simplices with this property. Interestingly, this statement is not true for d = 2, and counterexamples are provided within.
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Lattice Subdivisions and Tropical Oriented Matroids, Featuring Products of Simplices
Subdivisions of products of simplices, and their applications, appear across mathematics. In this thesis, they are the tie between two branches of my research: polytopal lattice subdivisions and tropical oriented matroid theory. The first chapter describes desirable combinatorial properties of …
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Nonconvex optimization algorithm with a new Bi-criteria selection of potential simplices using an estimate of Lipschitz constant /
… is proposed, which is based on Disimpl (DIviding SIMPLices) algorithms. The novelty of the proposed algorithm is that a single estimate of the Lipschitz constant is used instead of a set to select potential simplices for division. Experimental analysis is conducted and the competitiveness of the …
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Neiškiliojo optimizavimo algoritmas su nauju bikriteriniu potencialiųjų simpleksų išrinkimu naudojant Lipšico konstantos įvertį /
… is proposed, which is based on Disimpl (DIviding SIMPLices) algorithms. The novelty of the proposed algorithm is that a single estimate of the Lipschitz constant is used instead of a set to select potential simplices for division. Experimental analysis is conducted and the competitiveness of the …
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Computer-assisted proofs in geometry and physics
… existence of many hitherto unknown tight regular simplices in quaternionic projective spaces and in the octonionic projective plane. We also consider regular simplices in real Grassmannians. The second application is to gravitational choreographies, i.e., periodic trajectories of point particles …
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Homological Illusions of Persistence and Stability
… the persistence pairing from an ordering of the simplices in a triangulation and takes worst-case time cubic in the number of simplices. We describe how to maintain the pairing in linear time per transposition of consecutive simplices. A side effect of the update algorithm is an elementary proof …
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The topology of Baues complexes and flip graphs
… of triangulations of a product of two simplices and the sphericity of extension spaces of realizable oriented matroids. This thesis covers the main construction which is common to these proofs, but defers the details specific to each problem to other papers.
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Arrangement of minors in the positive Grassmannian
… Maximal arrangements of this form correspond to simplices of the alcoved triangulation of the hypersimplex; and the number of such arrangements equals the Eulerian number. On the other hand, we prove in many cases that arrangements of equal minors of smallest value are weakly separated sets. …
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Topological Approaches to Chromatic Number and Box Complex Analysis of Partition Graphs
… classification informs the construction of all simplices of Bedge(︁P(33)). Following a detailed and technical exploration, we uncover both the maximal size of the pairwise intersections of its maximal simplices and their underlying structure. Our study proposes an algorithm for building the box …
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Constructing quantum spacetime
… discretisation / triangulation, ranging from few simplices up to the continuum limit. In the regime of very few simplices we confirm and deepen the connection of spin foam models to discrete gravity. Moreover, we discuss dynamical, e.g. diffeomorphism invariance in the discrete, to fix the …
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The D-neighborhood complex of a graph
… subset of graph distances as a means to form the simplices in the associated simplicial complex. Consider a simple graph G with diameter d. Let D be a subset of {0,1,..., d}. For each vertex, u, the D-neighborhood is the simplex consisting of all vertices whose graph distance from u lies in D. The …
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Prescribing Dilatations in Space
… mapping on the domain that is a union of two simplices sharing a common face.
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On quasi-categories as a foundation for higher algebraic stacks
… simply as the large simplicial set whose n-simplices consist of all left fibrations over S x [delta]n.
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Maximal Surfaces in Complexes
… complexes are unions of cubes rather than of simplices. A very natural cubical complex to consider is the complex C(k_1,...,k_n) where k_1,...,k_n are nonnegative integers. This complex has as its underlying space [0,k_1]x...x[0,k_n] subset of R^n with vertices at all points having integer …
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Spacetime meshing of stratified spaces for spacetime discontinuous Galerkin methods in arbitrary spatial dimensions
… We first discuss preliminary concepts behind simplices, simplicial complexes, and the generalization to oriented simplicies. Using these ideas, we define stratified spaces and how they can be used to model a mesh comprised of multiple oriented manifolds. We construct a graphical representation …
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Automated cartographic generalization with a triangulated spatial model
… object is described by a set of two-dimensional simplices (triangles) that are maintained in the form of a constrained Delaunay triangulation. This structure gives a fully connected two-dimensional plenum that stores important spatial relationships such as "enclosed", "adjacent" and "between" …
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Symmetric products of cubes
… σ<sub>2</sub>, ...,σ<sub>k</sub> are simplices in E<sup>n</sup>, then the vertex set of <sup>k</sup>∩<sub>1</sub> σ<sub>i</sub> may be obtained by examining all maximal nonsingular submatrices of a matrix obtained from the coordinates of the vertices of each of σ<sub>1</sub>, …
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An Efficient Storage And Retrieval Mechanism For Large Unstructured Grids
… Data values found at the vertices of the simplices may be dispersed throughout a datafile, producing especially poor disk locality. Partitioning multidimensional arrays across several machines or disks has become increasingly necessary. However, relatively little work has been done for …
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Problems in extremal graph theory
… structures such as the so-called strong simplices and clusters. The {\em $n$-dimensional hypercube}, $Q_n$, is the graph whose vertex set is $\{0,1\}^n$ and whose edge set consists of the vertex pairs differing in exactly one coordinate. The generalized Tur\'an problem asks for the …
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