Sökning: "persistent homologi"

Visar resultat 1 - 5 av 10 uppsatser innehållade orden persistent homologi.

  1. 1. Exploring persistent homology as a method for capturing functional connectivity differences in Parkinson’s Disease.

    Master-uppsats, KTH/Matematik (Avd.)

    Författare :Naomi Hulst; [2022]
    Nyckelord :persistent homology; topological data analysis; computational topology; parkinson s disease; parkinson; functional connectivity; stable rank; ihållande homologi; topologisk data analys; beräknings topologi; Parkinsons sjukdom; parkinson; funktionell konnektivitet; stable ranks;

    Sammanfattning : Parkinson’s Disease (PD) is the fastest growing neurodegenerative disease, currently affecting two to three percent of the population over 65. Studying functional connectivity (FC) in PD patients may provide new insights into how the disease alters brain organization in different subjects. LÄS MER

  3. 2. Comparison in Barcode and Computing Time for Persistent Homology Applied to a Subset of a Point Cloud

    Kandidat-uppsats,

    Författare :André Lasses Armatowski; [2022]
    Nyckelord :;

    Sammanfattning : At the intersection of topology and computer science lies the field of topological data analysis(TDA). TDA uses the concept of persistence to identify low dimensional topological features of data embedded in high dimensions. LÄS MER

  4. 3. Properties of Discrete Laplacians With Application on Brain Networks

    Master-uppsats, KTH/Matematisk statistik

    Författare :David Thinsz; [2022]
    Nyckelord :Graph Laplacian; Combinatorial Laplacian; Persistent Laplacian; Topological data analysis; Spectral theory; Homology; Clustering.; Graf-Laplacian; Kombinatorisk Laplacian; Beständig Laplacian; Topologisk dataanalys; Spektralteori; Homologi; Klustring.;

    Sammanfattning : This thesis investigates three discrete Laplace operators: the graph Laplacian, combinatorial Laplacian, and the more recently introduced persistent Laplacian. We discuss how these operators relate to each other and study their spectral properties. The graph Laplacian is a well-studied operator that plays a central role in spectral graph theory. LÄS MER

  5. 4. Traffic Prediction From Temporal Graphs Using Representation Learning

    Master-uppsats, KTH/Matematisk statistik

    Författare :Andreas Movin; [2021]
    Nyckelord :Dynamic time warping DTW ; embedding; graph convolutional networks GCN ; graph neural networks GNN ; persistent homology; spectral graph theory; temporal graphs; topological data analysis TDA ; Dynamisk time warping DTW ; inbäddning; convolutional grafnätverk GCN ; neurala grafnätverk GNN ; persistent homologi; spektral graf teori; dynamisk graf; topologisk dataanalys TDA ;

    Sammanfattning : With the arrival of 5G networks, telecommunication systems are becoming more intelligent, integrated, and broadly used. This thesis focuses on predicting the upcoming traffic to efficiently promote resource allocation, guarantee stability and reliability of the network. LÄS MER

  7. 5. From Relations to Simplicial Complexes: A Toolkit for the Topological Analysis of Networks

    Master-uppsats, KTH/Matematik (Avd.)

    Författare :Johan Lord; [2021]
    Nyckelord :applied algebraic topology; complex networks; topological data analysis; brain network analysis;

    Sammanfattning : We present a rigorous yet accessible introduction to structures on finite sets foundational for a formal study of complex networks. This includes a thorough treatment of binary relations, distance spaces, their properties and similarities. LÄS MER