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 55 for “"polytope"”.
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Combinatorial aspects of polytope slices
We studies two examples of polytope slices, hypersimplices as slices of hypercubes and edge polytopes. For hypersimplices, the main result is a proof of a conjecture by R. Stanley which gives an interpretation of the Ehrhart h*-vector in terms of descents and excedances. Our proof is geometric …
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Generalized Characteristics Of A Generic Polytope
… We will show that, for symplectic-faced 4-polytopes ∑, we have the existence and local uniqueness of generalized characteristics of ∑. Then, we will show that symplectic-faced polytopes ∑ ⊂ R2n admit only characteristics with piecewise-linear trajectories. Finally, we will extend our …
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Polytope-based topology optimization using a mimetic-inspired method
… work of Wachspress, many interpolants for polytopes have come forth; such as, mean value coordinates, natural neighbor-based coordinates, metric coordinate method and maximum entropy shape functions. The extension of the shape functions to three-dimensions, however, has been relatively slow …
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The number of facets of a projection of a convex polytope
… $\IR\sp{d}$ onto a hyperplane and let P be a d-polytope in $\IR\sp{d}$. The following relations hold on the numbers of facets $f\sb{d-1}(P)$ of P and $f\sb{d-2}(\pi(P))$ of $\pi(P)$:$$\eqalign{f\sb2(P)&\ge{1\over2}f\sb1(\pi(P))+2\ {\rm if}\ d=3,\cr f\sb{d-1}(P)&\ge2{\sqrt{f\sb{d-2}(\pi(P))}}\ …
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From Simplest Recursion to the Recursion of Generalizations of Cross Polytope Numbers
… who recently found a new formula for the cross-polytope numbers. My topic will be focused on "Generalizations of cross-polytope numbers". It will include the proofs of the combinatorics results in Dr. Edwards and Dr. Griffiths' recently published paper. $E(n,m)$ and $O(n,m)$, the even terms and …
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Contributions to the theory of Ehrhart polynomials
… we study the Ehrhart polynomials of different polytopes. In the 1960's Eugene Ehrhart discovered that for any rational d-polytope P, the number of lattice points, i(P,m), in the mth dilated polytope mP is always a quasi-polynomial of degree d in m, whose period divides the least common multiple …
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Cutting plane algorithms for variational inference in graphical models
… give a new class of outer bounds on the marginal polytope, and propose a cutting-plane algorithm for efficiently optimizing over these constraints. When combined with a concave upper bound on the entropy, this gives a new variational inference algorithm for probabilistic inference in discrete …
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The polyhedral structure of certain combinatorial optimization problems with application to a naval defense problem
… of facets for the GUS constrained knapsack polytope. This family of facets is obtained by sequential and simultaneous lifting procedures of minimal GUS cover inequalities. Second, we develop a new family of cutting planes for the set partitioning polytope for deleting any fractional basic …
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Polyhedra Study of Mixed Integer Programs With Variable Upper Bounds
… knapsack cover and to the single binary variable polytope. We present the result of sequence independent lifting of the knapsack cover inequality and obtain lifting some coefficients for sequence dependent lifting with for specific sequences. We generate two new families of facet defining …
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Incidence homology for the hyperoctahedral group
The incidence structure of the cross-polytope gives rise to certain modular representations for the hyperoctahedral group. In this thesis we introduce and begin the study of these natural representations. In particular we show that they satisfy a branching rule. This branching rule is used to …
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Polyhedral aspects of cardinality constrained combinatorial optimization problems
… Matroid-, Wege-, und Kreis-Polytope. Wie es exemplarisch für Matroid-, Wege-, und Kreis-Polytope gezeigt wird, ist eine facettendefinierende Ungleichung für ein nicht-kardinalitätsbeschränktes Polytop gewöhnlich auch für die kardinalitätsbeschränkte Version …
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Mollified piecewise polynomial approximants of arbitrary order and smoothness
… non-overlapping partitions consisting of convex polytopes. On each polytope, an independent local polynomial approximant of arbitrary order is assumed. The basis functions are defined as the convolution of the local approximant with a mollifier. The mollifier is chosen to be smooth, have a …
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On network coding capacity : matroidal networks and network capacity regions
… we show that the region is a computable rational polytope and provide exact algorithms and approximation heuristics for computing the region. For the network linear coding capacity region, we construct a computable rational polytope, with respect to a given finite field, that inner bounds the …
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The Gomory-Chvátal closure : polyhedrality, complexity, and extensions
… the Gomory-Chvátal closure of any non-rational polytope is a polytope. Schrijver (1980) had established the polyhedrality of the Gomory-Chvdtal closure for rational polyhedra. In essence, his proof relies on the fact that the set of integer points in a rational polyhedral cone is generated by a …
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Painted Trees and Pterahedra
… hull of these points. We explore the resulting polytope and prove, using a bijection to tubings, that for <i>n</i> ≤ 4 the poset of the painted face trees with <i>n</i>+1 leaves is isomorphic to the face poset of an <i>n</i>-dimensional polytope, specifically KF<sub>1,<i>n</i></sub>, the …
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Polytopes, generating functions, and new statistics related to descents and inversions in permutations
… paths. Other parts of this thesis are devoted to polytopes relevant to the descent statistic. One such polytope is a "signed" version of the Pitman-Stanley parking function polytope, which can be viewed as a generalization of the chain polytope of the zigzag poset. We also discuss the family of …
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Root polytopes, triangulations, and subdivision algebras
… algebras in terms of subdivisions of root polytopes, several conjectures of Kirillov about the reduced forms of monomials in the algebras are proved and generalized. Other than a way of understanding Kirillov's algebras, this polytope approach also yields new results about root polytopes, …
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Pareto Task Inference Analysis of Single-Cell RNASequencing of Human Placenta Reveals Biological Insightsinto Adverse Pregnancy Outcomes
… that fits data to an n-dimensional polygon or polytope, models how cells optimize among multiple biological functions and transition between states. We applied ParTI to assess its ability to identify nuanced cellular states and intercellular relationships and to highlight biological mechanisms …
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New geometric techniques for linear programming and graph partitioning
… questions in the theory of linear programming, polytope theory, spectral graph theory, and graph partitioning. The thesis consists of two main parts. In the first part, which is joint work with Daniel Spielman, we present the first randomized polynomial-time simplex algorithm for linear …
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