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Visar resultat 1 - 5 av 19 uppsatser som matchar ovanstående sökkriterier.

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. Spectral sequences for composite functors

   Master-uppsats, KTH/Matematik (Avd.)

   Författare :Adam Erlandsson; [2022]
   Nyckelord :Algebraic topology; homological algebra; spectral sequences; fibrations; derived functors; derived categories; Algebraisk topologi; homologisk algebra; spektralsekvenser; fibreringar; deriverade funktorer; deriverade kategorier;

   Sammanfattning : Spectral sequences were developed during the mid-twentieth century as a way of computing (co)homology, and have wide uses in both algebraic topology and algebraic geometry.  Grothendieck introduced in his Tôhoku paper the Grothendieck spectral sequence, which given left exact functors $F$ and $G$ between abelian categories, uses the right-derived functors of $F$ and $G$ as initial data and converges to the right-derived functors of the composition $G\circ F. LÄS MER

4. 3. 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

5. 4. An investigation of average stable ranks : On plane geometric objects and financial transaction data

   Master-uppsats, KTH/Matematik (Avd.)

   Författare :Linn Odelius; [2020]
   Nyckelord :Topological data analysis; TDA; Mathematics; Stable rank; Topology; Data analysis; Financial transactions; Topologisk dataanalys; Topologi; TDA; Matematik; Teoretisk Matematik; Dataanalys; Finans; Stabil rang;

   Sammanfattning : This thesis concerns the topological features of plane geometric shapes and financial transaction data. Topological properties of the data such as homology groups and their stable ranks are analysed. LÄS MER

7. 5. Algebraic Simplifications of Metric Information

   Master-uppsats, KTH/Matematik (Avd.)

   Författare :Klas Erninger; [2020]
   Nyckelord :Topological data analysis; algebraic topology; Topologisk data analys; algebraisk topologi;

   Sammanfattning : This thesis is about how to interpret metric data with topological tools, such as homology. We show how to go from a metric space to a topological space via Vietoris-Rips complexes. We use the usual approach to Topological Data Analysis (TDA), and transform our metric space into tame parametrised vector spaces. LÄS MER