Sökning: "simplicial homology"

Visar resultat 1 - 5 av 9 avhandlingar innehållade orden simplicial homology.

  1. 1. Simplicial Complexes of Graphs

    Författare :Jakob Jonsson; Anders Björner; John Shareshian; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Algebra and geometry; simplicial complex; monotone graph property; discrete Morse theory; simplicial homology; homotopy type; connectivity degree; Cohen-Macaulay complex; Euler characteristic; decision tree; Algebra och geometri; Algebra and geometry; Algebra och geometri;

    Sammanfattning : Let G be a finite graph with vertex set V and edge set E. A graph complex on G is an abstract simplicial complex consisting of subsets of E. In particular, we may interpret such a complex as a family of subgraphs of G. LÄS MER

  3. 2. Topological and geometrical methods in data analysis

    Författare :Oliver Gäfvert; Sandra di Rocco; Henry Schenck; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; multiparameter persistent homology; computational algebraic geometry; algorithms; complexity; Mathematics; Matematik;

    Sammanfattning : This thesis concerns two related data analysis pipelines, using topological and geometrical methods respectively, to extract relevant information. The first pipeline, referred to as the topological data analysis (TDA) pipeline, constructs a filtered simplicial complex on a given data set in order to describe its shape. LÄS MER

  4. 3. N-complexes and Categorification

    Författare :Djalal Mirmohades; Volodymyr Mazorchuk; Steffen Oppermann; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Homological algebra; Category theory; Triangulated categories; K-theory; Hopfological algebra; Mathematics; Matematik;

    Sammanfattning : This thesis consists of three papers about N-complexes and their uses in categorification. N-complexes are generalizations of chain complexes having a differential d satisfying dN = 0 rather than d2 = 0. Categorification is the process of finding a higher category analog of a given mathematical structure. LÄS MER

  5. 4. Symplectic Embeddings and results in TDA

    Författare :Alvin Jin; Wojciech Chacholski; Gregory Arone; Henry Adams; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Matematik; Mathematics;

    Sammanfattning : This thesis is a collection of work under the theme of “applied topology."  The linking idea behind seemingly disjoint fields is the existence of a filtration that one uses to study a space. In turn, given the ubiquitous nature of filtrations, applications range from theoretical fields (e.g. LÄS MER

  7. 5. Invariants for Multidimensional Persistence

    Författare :Martina Scolamiero; Wojciech Chacholski; Vin de Silva; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; computational topology; Matematik; Mathematics;

    Sammanfattning : The amount of data that our digital society collects is unprecedented. This represents a valuable opportunity to improve our quality of life by gaining insights about complex problems related to neuroscience, medicine and biology among others. LÄS MER