Sökning: "Homologi"
Visar resultat 1 - 5 av 18 uppsatser innehållade ordet Homologi.
1. Unauthorised Session Detection with RNN-LSTM Models and Topological Data Analysis
Master-uppsats, KTH/Matematik (Avd.)Sammanfattning : This thesis explores the possibility of using session-based customers data from Svenska Handelsbanken AB to detect fraudulent sessions. Tools within Topological Data Analysis are employed to analyse customers behavior and examine topological properties such as homology and stable rank at the individual level. LÄS MER
2. 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
3. Comparison in Barcode and Computing Time for Persistent Homology Applied to a Subset of a Point Cloud
Kandidat-uppsats,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. 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
5. Properties of Discrete Laplacians With Application on Brain Networks
Master-uppsats, KTH/Matematisk statistikSammanfattning : 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