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You searched for subject:( Regular Partition). Showing records 1 – 3 of 3 total matches.

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Freie Universität Berlin

1. León, Emerson. Räume der konvexen n-Aquipartitionen.

Degree: 2015, Freie Universität Berlin

Wir betrachten den Raum \C(\Rd,n) aller Aufteilungen von \Rd in n konvexe Gebiete für positive d und n. Dafür entwickeln wir grundlegende Konzepte und Definitionen, untersuchen allgemeine Eigenschaften und betrachten verwandte Räume sowie Beispiele. Zunächst entwickeln wir dafür die benötigten Konzepte der Konvexgeometrie. In Kapitel 3 definieren wir konvexe n-Aufteilungen und zeigen, dass die Teile immer Polyeder sind. Dann definieren wir sphärische Aufteilungen und Seitenhalbordnungen und leiten grundlegende Strukturergebnisse ab. Kapitel 4 beschäftigt sich mit dem Raum \C(\Rd,n) aller konvexen n-Aufteilungen des~\Rd. Wir beschreiben eine Metrik und damit eine Topologie auf diesem Raum, sowie eine natürliche Kompaktifizierung \C(\Rd, ≤ \\! n), für die auch leere Teile erlaubt sind. Wir stellen den Raum der n-Aufteilungen dann auf zwei Weisen als eine Vereinigung von semialgebraischen Teilmengen dar: Wir betrachten Hyperebenenarrangements, die Auf\\-teilungen induzieren, und beschreiben \C(\Rd,n) so in Abhängikeit von den Hyperebenen, die die Aufteilung erzeugen. Für die zweite Beschreibung führen wir Knoten und Knotensysteme ein, die Eckenmengen verallgemeinern, und definieren den kombinatorischen Typ einer Aufteilung. Diese kombinatorischen Typen ergeben semialgebraische Teile, aus denen die Räume aufgebaut sind (Theorem \ref{semialgebraic}). Am Ende des Kapitels beschreiben wir wir explizit die Räume der n-Aufteilungen von \Rd und ihre Kompaktifizierungen für n=2 und für d=1. In Kapitel 5 diskutieren wir reguläre Aufteilungen. Wir berechnen die Dimension des Raums der regulären Aufteilungen \C\reg(\Rd,n). Dann beweisen wir einen Universalitätssatz, wonach die Realiserungsräume regulärer Partitionen zu beliebigen primären basischen semialgebraischen Mengen stabil äquivalent sein können. In Kapitel 6 untersuchen wir die Dimension von Realisierungsräumen. Im Fall d=2 ist die Dimension von \C(\R2,n) für große n viel größer als \dim (\C\reg(\R2,n)). Dann konzentrieren wir uns auf den Fall d=3, wo wir vermuten, dass die Dimension von \C(\R3,n) mit der Dimension von \C\reg(\R3,n) übereinstimmt, und versuchen das mit einer Heuristik für die Zahl der Freiheitsgrade und damit der Dimensionen der Realisierungsräume zu untermauern. In Kapitel 7 führen wir die Räume von Äquipartitionen \C\equi(\Rd,n,μ) für beschränkte positive Maße μ ein. Wir untersuchen die topologische Struktur für einige kleine Fälle und beschreiben, darauf aufbauend, die Räume der n-Äquipartitionen für d=2 und n=3. Wir diskutieren auch das Problem von Nandakumar und Ramana Rao über "faire Aufteilungen von Polygonen'' und verschiedene äquivariante Abbildungen, die zeigen, dass es für dieses Problem ausreicht, reguläre Äquipartitionen zu betrachten. Advisors/Committee Members: [email protected] (contact), m (gender), Prof. Günter M. Ziegler (firstReferee), Prof. Thorsten Theobald (furtherReferee).

Subjects/Keywords: convex; polyhedral; partition; spaces; spherical; geometry; equipartitions; face structure; hyperplanes; regular partitions; 500 Naturwissenschaften und Mathematik::510 Mathematik

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

León, E. (2015). Räume der konvexen n-Aquipartitionen. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-5031

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

León, Emerson. “Räume der konvexen n-Aquipartitionen.” 2015. Thesis, Freie Universität Berlin. Accessed July 14, 2020. http://dx.doi.org/10.17169/refubium-5031.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

León, Emerson. “Räume der konvexen n-Aquipartitionen.” 2015. Web. 14 Jul 2020.

Vancouver:

León E. Räume der konvexen n-Aquipartitionen. [Internet] [Thesis]. Freie Universität Berlin; 2015. [cited 2020 Jul 14]. Available from: http://dx.doi.org/10.17169/refubium-5031.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

León E. Räume der konvexen n-Aquipartitionen. [Thesis]. Freie Universität Berlin; 2015. Available from: http://dx.doi.org/10.17169/refubium-5031

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Curado, Manuel. Structural Similarity: Applications to Object Recognition and Clustering .

Degree: 2018, University of Alicante

In this thesis, we propose many developments in the context of Structural Similarity. We address both node (local) similarity and graph (global) similarity. Concerning node similarity, we focus on improving the diffusive process leading to compute this similarity (e.g. Commute Times) by means of modifying or rewiring the structure of the graph (Graph Densification), although some advances in Laplacian-based ranking are also included in this document. Graph Densification is a particular case of what we call graph rewiring, i.e. a novel field (similar to image processing) where input graphs are rewired to be better conditioned for the subsequent pattern recognition tasks (e.g. clustering). In the thesis, we contribute with an scalable an effective method driven by Dirichlet processes. We propose both a completely unsupervised and a semi-supervised approach for Dirichlet densification. We also contribute with new random walkers (Return Random Walks) that are useful structural filters as well as asymmetry detectors in directed brain networks used to make early predictions of Alzheimer's disease (AD). Graph similarity is addressed by means of designing structural information channels as a means of measuring the Mutual Information between graphs. To this end, we first embed the graphs by means of Commute Times. Commute times embeddings have good properties for Delaunay triangulations (the typical representation for Graph Matching in computer vision). This means that these embeddings can act as encoders in the channel as well as decoders (since they are invertible). Consequently, structural noise can be modelled by the deformation introduced in one of the manifolds to fit the other one. This methodology leads to a very high discriminative similarity measure, since the Mutual Information is measured on the manifolds (vectorial domain) through copulas and bypass entropy estimators. This is consistent with the methodology of decoupling the measurement of graph similarity in two steps: a) linearizing the Quadratic Assignment Problem (QAP) by means of the embedding trick, and b) measuring similarity in vector spaces. The QAP problem is also investigated in this thesis. More precisely, we analyze the behaviour of m-best Graph Matching methods. These methods usually start by a couple of best solutions and then expand locally the search space by excluding previous clamped variables. The next variable to clamp is usually selected randomly, but we show that this reduces the performance when structural noise arises (outliers). Alternatively, we propose several heuristics for spanning the search space and evaluate all of them, showing that they are usually better than random selection. These heuristics are particularly interesting because they exploit the structure of the affinity matrix. Efficiency is improved as well. Concerning the application domains explored in this thesis we focus on object recognition (graph similarity), clustering (rewiring), compression/decompression of graphs (links with Extremal Graph Theory), 3D shape… Advisors/Committee Members: Escolano, Francisco (advisor), Sáez Martínez, Juan Manuel (advisor).

Subjects/Keywords: Graph densification; Cut similarity; Spectral clustering; Dirichlet problems; Random walkers; Commute Times; Graph algorithms; Regular Partition; Szemeredi; Alzheimer's disease; Graphs; Return Random Walk; Net4lap; Directed graphs; Spectral graph theory; Graph entropy; Mutual information; Manifold alignment; m-Best Graph Matching; Binary-Tree Partitions; QAP; Graph sparsification; Shape simplification; Alpha shapes

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Curado, M. (2018). Structural Similarity: Applications to Object Recognition and Clustering . (Thesis). University of Alicante. Retrieved from http://hdl.handle.net/10045/98110

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Curado, Manuel. “Structural Similarity: Applications to Object Recognition and Clustering .” 2018. Thesis, University of Alicante. Accessed July 14, 2020. http://hdl.handle.net/10045/98110.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Curado, Manuel. “Structural Similarity: Applications to Object Recognition and Clustering .” 2018. Web. 14 Jul 2020.

Vancouver:

Curado M. Structural Similarity: Applications to Object Recognition and Clustering . [Internet] [Thesis]. University of Alicante; 2018. [cited 2020 Jul 14]. Available from: http://hdl.handle.net/10045/98110.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Curado M. Structural Similarity: Applications to Object Recognition and Clustering . [Thesis]. University of Alicante; 2018. Available from: http://hdl.handle.net/10045/98110

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Bellissimo, Michael Robert. A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK.

Degree: MS, Mathematics, 2018, University of Akron

Our goal is to be able to determine the distance between two partitions in the same Rouquier block. This paper explores a lower bound on the number of steps required to get from the quotient of a partition lambda; to (empty set, empty set, ..., (w)). We will use the Young diagrams in the quotient of lambda and a process of right and left steps to obtain a new partition that is connected to lambda in the Brauer graph of these representations. Paired with this process we will incorporate a notation called the badness of each box in the Young diagram representation of the quotient of lambda;. This will allow us to show that the lower bound on the number of steps is less than or equal to the initial badness, b, of the starting partition divided by the maximum reduction of badness by each right and left step, 2w2. Advisors/Committee Members: Cossey, James P. (Advisor), Kreider, Kevin L. (Committee Chair).

Subjects/Keywords: Mathematics; partitions; badness; Rouquier Block; representation theory; combinatorics; Brauer Graph; diameter of a Brauer Graph; partition theory; Young Diagram; decomposition matrix; p-core; abacus; p-regular partitions; Littlewood-Richardson Rule

…2.1 Example of a p-regular partition . . . . . . . . . . . . . . . . . . . . . . 5 2.2… …Example of a non p-regular partition . . . . . . . . . . . . . . . . . . . 5 2.3… …theorems. 2.1 p-Regular Partitions We say a partition λ of a non-negative integer n is p… …Example of a non p-regular partition Figure 2.1: Example of a p-regular partition 5 Note… …here that the partition in Figure 2.1 is p-regular, where as the partition in Figure 2.2 is… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Bellissimo, M. R. (2018). A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK. (Masters Thesis). University of Akron. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=akron1523039734121649

Chicago Manual of Style (16th Edition):

Bellissimo, Michael Robert. “A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK.” 2018. Masters Thesis, University of Akron. Accessed July 14, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=akron1523039734121649.

MLA Handbook (7th Edition):

Bellissimo, Michael Robert. “A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK.” 2018. Web. 14 Jul 2020.

Vancouver:

Bellissimo MR. A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK. [Internet] [Masters thesis]. University of Akron; 2018. [cited 2020 Jul 14]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1523039734121649.

Council of Science Editors:

Bellissimo MR. A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK. [Masters Thesis]. University of Akron; 2018. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1523039734121649

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