Essays about: "Homologi"

Showing result 1 - 5 of 16 essays containing the word Homologi.

1. 1. Unauthorised Session Detection with RNN-LSTM Models and Topological Data Analysis

   University essay from KTH/Matematik (Avd.)

   Author : Nazar Maksymchuk Netterström; [2023]
   Keywords : Recurrent Neural Network; Long-Short-Term-Memory; Topological Data Analysis; Session based data; Anomaly detection; Time-series analysis; Imbalanced data; Master thesis; Neurala nätverk; Topologisk data analys; Detektion av avvikelse; Sessionsbaserad data; Tidserieanalys; Inbalancerad data; Masteruppsats;

   Abstract : 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. READ MORE

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

   University essay from KTH/Matematik (Avd.)

   Author : Naomi Hulst; [2022]
   Keywords : 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;

   Abstract : 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. READ MORE

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

   University essay from

   Author : André Lasses Armatowski; [2022]
   Keywords : ;

   Abstract : 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. READ MORE

5. 4. Spectral sequences for composite functors

   University essay from KTH/Matematik (Avd.)

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

   Abstract : 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. READ MORE

6. 5. Properties of Discrete Laplacians With Application on Brain Networks

   University essay from KTH/Matematisk statistik

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

   Abstract : 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. READ MORE