Sökning: "algebraisk topologi"

Visar resultat 1 - 5 av 9 uppsatser innehållade orden algebraisk topologi.

  1. 1. Topological regularization and relative latent representations

    Master-uppsats, KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Författare :Alejandro García Castellanos; [2023]
    Nyckelord :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;

    Sammanfattning : 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. 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. 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

  7. 5. An Exploration of Galois Theory with some Classical Results

    Kandidat-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematik LTH

    Författare :Olof Klingberg; [2020]
    Nyckelord :Galois theory; Algebra; Field theory; Mathematics and Statistics;

    Sammanfattning : Galois theory unites field theory and group theory to solve some field theoretical problems. The aim of this thesis is to provide a concise introduction to the topic, culminating in the proof of the insolubility of the general quintic equation by radicals. LÄS MER