List: Topology | Curated by Simon Kwan

Jan 23, 2025
42 stories
2 saves
Topology
Agrover112
PageRank and Banach’s Fixed Point TheoremI wrote this blog as a question that popped into my head during a lecture on PageRank where I couldn’t quite understand how convergence of…
Jul 22, 2024
Jul 22, 2024
In
Intuition
by
Selena Routley
Mathematics is Highly Refined LiteracyThe surprising overarching structure of norms affords quadratic forms and Pythagoras’s theorem a surprising, powerful universality in…
Aug 23, 2024
5
Aug 23, 2024
5
Simon Kwan
Hahn-Banach theoremThis is article on the Hahn-Banach theorem. I write this article down to serve both as a note for me as well as a tutorial for the…
May 14, 2024
May 14, 2024
Simon Kwan
The magic of Artificial Neural Network — Part 3This is my third article on the magic of the Artificial Neural Network. I have sketched the proof of the Universal Approximation Theorem…
May 22, 2024
May 22, 2024
Simon Kwan
The magic of Artificial Neural Network — Part 2This is my second article on unlocking the magic of Artificial Neural Network. In part 1, the space of real-valued continuous function…
Apr 10, 2024
Apr 10, 2024
In
AIRI.Institute
by
AIRI Team
Persistent homology helped robust detection of AI-generated textsEvery year, new neural language models appear, and the texts generated by them become increasingly difficult to distinguish from those…
Dec 18, 2023
Dec 18, 2023
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Simon Kwan
General Topology — Part 8 (Cheat Sheet)Definition
Nov 27, 2023
Nov 27, 2023
Simon Kwan
General Topology — Part 7 (Locally Compact Hausdroff Space)In the Locally Compact Hausdroff Space, when a compact set is contained by an open set, a “bump” function over this open set will exist…
Nov 27, 2023
Nov 27, 2023
Simon Kwan
General Topology — Part 6 (Hausdorff Space)Hausdorff Space and Compact Set
Nov 9, 2023
Nov 9, 2023
Simon Kwan
General Topology — Part 5 (Compact Set)Extreme Value Theorem
Oct 29, 2023
Oct 29, 2023
In
Nautilus Magazine
by
Nautilus
Can Topology Prevent Another Financial Crash?New regulations are applying network science to restructure global finance
Apr 11, 2019
2
Apr 11, 2019
2
In
TDS Archive
by
Albers Uzila
Homotopy Method: How to Use Topology as an Optimizer For Your Machine Learning ModelYes, it’s the “mugs-are-doughnuts” kind of topology!
Jan 10, 2022
Jan 10, 2022
In
Cantor’s Paradise
by
Kasper Müller
Powerful Theorems of Topology That Everyone Should KnowApplications of the theory of shapes to the real world and beyond
Jul 17, 2023
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Jul 17, 2023
6
Cristian Velasquez
Predicting Market Crashes With Topology in PythonBeyond Traditional Indicators for Insights Into Market Behavior
Sep 25, 2023
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Sep 25, 2023
11
Simon Kwan
General Topology — Part 4What is Urysohn’s Lemma ?
Jan 21, 2022
Jan 21, 2022
In
TDS Archive
by
Francesco Palma
From cutting-edge research to industrial applications with GiottoA guide to creating your own transformers for topological machine learning.
Jan 23, 2020
Jan 23, 2020
In
TDS Archive
by
Francesco Palma
The shape of population dynamicsStudy population dynamics using topological data analysis
Dec 5, 2019
Dec 5, 2019
In
TDS Archive
by
Michael Bronstein
Graph Neural Networks through the lens of Differential Geometry and Algebraic TopologyNew perspectives on old problems in Graph ML
Nov 18, 2021
Nov 18, 2021
In
TDS Archive
by
Mathieu Carrière
Mixing Topology and Deep Learning with PersLayIn a former post, I presented Topological Data Analysis and its main descriptor, the so-called persistence diagram. In this post, I would…
Jun 22, 2019
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Jun 22, 2019
1