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 18 of 18 for “"Simplicial complex"”.
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Using the deformable simplicial complex to reconstruct surfaces from point clouds
… in this thesis a modification to the deformable simplicial complex method that allows it to reconstruct surfaces given only a point cloud extracted from a Wavefront .obj file. By creating a velocity function that moves the vertices of an existing tetrahedral mesh towards their respective closest …
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The D-neighborhood complex of a graph
The Neighborhood complex of a graph, G, is an abstract simplicial complex formed by the subsets of the neighborhoods of all vertices in G. The construction of this simplicial complex can be generalized to use any subset of graph distances as a means to form the simplices in the associated …
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Combinatorial properties of shifted complexes
In this thesis we study the class of shifted simplicial complexes. A simplicial complex on n nodes is shifted if there exists a labelling of the nodes by 1 through n such that for any face, replacing any node of the face with a node of smaller label results in a collection which is also a face. A …
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Topological Analysis Using Morse Theory and Auditory Display
… traversal for creating an auditory display of a simplicial complex. This has application particularly when the complex is large or higher-dimensional, but audio has been shown to reinforce visual display in all cases. The auditory display is intended to convey information about the complex to the …
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Reflection arrangements and ribbon representations
Ehrenborg and Jung recently related the order complex for the lattice of d-divisible partitions with the simplicial complex of pointed ordered set partitions via a homotopy equivalence. The latter has top homology naturally identified as a Specht module. Their work unifies that of Calderbank, …
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Topological modeling with simplicial complexes
Simplicial complexes are useful for modeling shape of a discrete geometric domain and for discretizing continuous domains. A geometric triangulation of a point set S is a simplicial complex whose vertex set is contained in S and whose underlying space is the convex hull of S. In this thesis we …
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Ramsey regions and simplicial homology tables for graphs
… setting of hypergraphs. The work of persistence complex on large data sets is examined in the setting of graphs. Various simplicial complexes can be assigned to a graph. For a given simplicial complex the persistence complex can be constructed, giving a highly detailed graph invariant. …
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Vietoris–Rips metric thickenings and Wasserstein spaces
If the vertex set, X, of a simplicial complex, K, is a metric space, then K can be interpreted as a subset of the Wasserstein space of probability measures on X. Such spaces are called simplicial metric thickenings, and a prominent example is the Vietoris–Rips metric thickening. In this work we …
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Turing Decidability and Computational Complexity of MorseHomology
… introduction to computability and computational complexity. Since general point-set data equipped with a smooth structure can admit a triangulation, discrete Morse theory finds numerous applications in data analysis which can range from traffic control to geographical interpretation. Currently, …
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Computing Interesting Topological Features
… homotopy problem in a different setting. A Rips complex is a simplicial complex defined by a set of points from some metric space where every pair of points within distance 1 is connected by an edge, and every (k + 1)-clique in that graph forms a k-simplex. We prove that the projection map which …
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Simplifying and deforming through hierarchies of simplicial grids
… In the first part we study the maintenance of a simplicial grid under changing density requirements. The proposed method works in any fixed dimension and generates grids by projecting cross-sections of a monotone simplicial complex that lives in one dimension higher than the grid. The density of …
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Bounds on Urysohn width
… it can be approximated by a d-dimensional simplicial complex. Namely, the d-width of a space is at most w if it admits a continuous map to a d-complex with all fibers of diameter at most w. This notion was introduced in the context of dimension theory, used in approximation theory, appeared …
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Spacetime Meshing for Discontinuous Galerkin Methods
… a meshing algorithm to construct an unstructured simplicial spacetime mesh over an arbitrary simplicial space domain. Our algorithm is the first adaptive spacetime meshing algorithm suitable for efficient solution of nonlinear phenomena using spacetime discontinuous Galerkin finite element …
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Topological and geometric inference of data
… Following ideas from topological data analysis, simplicial complexes are used as discrete analogues of spaces suitable for computation. By utilising the prior assumption that the data lie on a manifold, topologically inspired techniques are proposed for refining the simplicial complex to better …
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Topological Approaches to Chromatic Number and Box Complex Analysis of Partition Graphs
… S4 with non-trivial homology in the box complex of the partition graph P(33), namely Bedge(︁P(33))︁, and applying the Borsuk-Ulam theorem to compute its Z2-index. This provides a robust topological lower bound for the chromatic number of P(33), termed the Lovász bound. We have verified …
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Gestión mecanizada del conocimiento matemático en topología algebraica
… The first one allows us to study the pushout of simplicial sets, an important construction in Algebraic Topology. The second one implements the simplicial complex notion (a generalization of the graph notion to higher dimensions). The last module allows us to analyse properties of 2D and 3D …
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Topics in combinatorial and computational geometry
… show the existence of a two-dimensional abstract simplicial complex, $\chi \subseteq 2\sp{B}$, which has some nice topological properties, such that the inclusion-exclusion relation $\mu(\cup B) = \Sigma \sb{\sigma\in 2\sp{B} - \{\phi\}}(-1)\sp{\rm card\ \sigma -1}\mu(\cap\sigma)$ holds when …
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Splines on polytopal complexes
… but focused primarily on the simplicial case. This thesis details a number of results that can be obtained using this algebraic perspective, particularly for splines over subdivisions by convex polytopes. The first three chapters of the thesis are devoted to introducing splines …