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 “"simplicial complexes"”.
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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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Field D* pathfinding in weighted simplicial complexes
… In this work, we extend Field D* to weighted simplicial complexes – specifically – triangulations in 2D and tetrahedral meshes in 3D.
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Non-Commutative Probability for the Spectral Analysis of Simplicial Complexes
… a new interpretation of Betti numbers for simplicial complexes in terms of distributions in an operator-valued probability space. This thesis is mostly an exposition of the areas of free probability and algebraic topology; here, we do not present cutting-edge research in either free …
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Simplicial Complexes and a Partial Classification of Almost Completely Decomposable Torsion Free Abelian Groups
The thesis treats the problem of how different two quasi-isomorphic groups can be.
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The Fréchet distance revisited and extended
Given two simplicial complexes, and start and end vertices in each complex, we show how to compute curves (in each complex) between these vertices, such that the Frechet distance between these curves is minimized. As a polygonal curve is a complex, this generalizes the regular notion of Frechet …
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Combinatorial models for surface and free group symmetries
… its action on simple closed curves. Similar complexes of spheres, free factors, and free splittings allow combinatorial representation of the automorphisms of a free group. We consider a Birman exact sequence for combinatorial models of mapping class groups and free group automorphisms. We …
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Automated cartographic generalization with a triangulated spatial model
… can be represented by a structure based on simplicial complexes which provides useful relationships for topology and proximity and facilitates many of the fundamental generalization operations. Secondly, that the epistemological structures needed for generalization can be represented by a …
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Quantitative embeddings with applications
… and in the other we prove a similar result for simplicial complexes of any dimension. We also discuss applications of these quantitative embeddings to a problem in metric geometry related to the isoperimetric inequality and a problem about constructing local quantum error-correcting codes.
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Ramsey regions and simplicial homology tables for graphs
… 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. Connections between the graph and persistence complex are investigated.
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Turing Decidability and Computational Complexity of MorseHomology
… various methods which convert point-set data to simplicial complexes or piecewise-smooth manifolds; however, this is not the focus of the thesis. Instead, this thesis will show that the Morse homology of such data is computable in the classical sense of Turing decidability, bound the complexity …
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Applications of abelian algebraic structures in quantum computation
… of both group extensions and a generalization of simplicial complexes, amongst other problems. For each of those listed, we also show that no classical algorithm can achieve similar efficiency under standard cryptographic assumptions.
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Computational topology on neural networks: from the data to the model
… a new neural network architecture based on simplicial complexes and the maps defined between them, and we have also proved certain properties such as that the new family of neural networks are universal approximators and robust to "adversarial examples".
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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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Networked interactions, graphical models and econometrics perspectives in data analysis
… Laplacian and random walks on graphs to simplicial complexes, we study a simplicial notion of PageRank centrality as defined in [Schaub et al., 2018].
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Higher-Order Interactions in Social Systems
… network models such as hypergraphs and simplicial complexes which can explicitly encode co-present contexts between three or more individuals. The first two projects describe how higher-order interactions can differ from pairwise interactions in terms of micro-level content and …
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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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A Kruskal-Katona theorem for cubical complexes
The optimal number of faces in cubical complexes which lie in cubes refers to the maximum number of faces that can be constructed from a certain number of faces of lower dimension, or the minimum number of faces necessary to construct a certain number of faces of higher dimension. If <i>m</i> is …
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Topological Deep Learning: Graphs, Complexes, Sheaves
… above. The first work proposes Message Passing Simplicial Networks (MPSNs), a family of models operating on simplicial complexes, a higher-dimensional generalisation of graphs coming from algebraic topology. We study the symmetries these models must satisfy, the topological invariants that …
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Unique Signed Minimal Wiring Diagrams and the Stanley-Reisner Correspondence
… between squarefree monomial ideals and abstract simplicial complexes. In this work, we use this correspondence to determine conditions under which a given set of inputs is guaranteed to have a unique signed minimal wiring diagram, regardless of the output assignment.</p>
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Maximal Surfaces in Complexes
Cubical complexes are defined in a manner analogous to that for simplicial complexes, the chief difference being that cubical 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. …
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