Essays about: "algebraic topology"

Showing result 1 - 5 of 14 essays containing the words algebraic topology.

  1. 1. Topological regularization and relative latent representations

    University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Author : Alejandro García Castellanos; [2023]
    Keywords : Algebraic Topology; Large Language Models; Relative Representation; Representation Learning; Model Stitching; Topological DataAnalysis; Zero-shot; Algebraisk topologi; Stora språkmodeller; Relativ representation; Representationsinlärning; Modell sömmar; Topologisk dataanalys; Zero-shot;

    Abstract : This Master's Thesis delves into the application of topological regularization techniques and relative latent representations within the realm of zero-shot model stitching. Building upon the prior work of Moschella et al. READ MORE

  3. 2. Braids and configuration spaces

    University essay from Uppsala universitet/Geometri och fysik

    Author : Andersson Rasmus; [2023]
    Keywords : braids; braid groups; configuration space; algebraic topology; group theory; fundamental group; covering spaces;

    Abstract : A configuration space is a space whose points represent the possible states of a given physical system. As such they appear naturally both in theoretical physics and technical applications. READ MORE

  4. 3. Profinite groups

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Juan Moreno Poncela; [2023]
    Keywords : Profinite Groups; Infinite Galois Theory; Mathematics and Statistics;

    Abstract : This thesis provides a comprehensive study of profinite groups, which are fascinating mathematical objects that have attracted significant interest in modern algebraic research. Profinite groups are infinite generalizations of finite groups and share many similarities with them. READ MORE

  5. 4. Persistent Homology : A Modern Application of Algebraic Topology in Data Analysis

    University essay from

    Author : Staffan Leijnse; [2023]
    Keywords : Data; Algebraic Topology; Persistent; Homology; Graded; Representation;

    Abstract : Topological data analysis emerged as a field in the 2000s and has proven very useful for examining the shape of data sets. Using persistent homology as their main methodology researchers has succesfully applied the theory presented in this paper to study as varied subjects as robot motion, brain connectivity, network theory, finger print analysis and computer vision. READ MORE

  6. 5. 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