Sökning: "matematik topologi"
Visar resultat 1 - 5 av 19 uppsatser innehållade orden matematik topologi.
1. Exploring persistent homology as a method for capturing functional connectivity differences in Parkinson’s Disease.
Master-uppsats, KTH/Matematik (Avd.)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
2. Spectral sequences for composite functors
Master-uppsats, KTH/Matematik (Avd.)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
3. From Relations to Simplicial Complexes: A Toolkit for the Topological Analysis of Networks
Master-uppsats, KTH/Matematik (Avd.)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
4. An investigation of average stable ranks : On plane geometric objects and financial transaction data
Master-uppsats, KTH/Matematik (Avd.)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
5. Algebraic Simplifications of Metric Information
Master-uppsats, KTH/Matematik (Avd.)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