Manifolds 1.3 : More Examples (Animation Included)
In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5
From playlist Manifolds
Manifolds 1.2 : Examples of Manifolds
In this video, I describe basic examples of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/IZO0G25
From playlist Manifolds
Manifolds #5: Tangent Space (part 1)
Today, we introduce the notion of tangent vectors and the tangent vector space at a point on a manifold.
From playlist Manifolds
What is a Manifold? Lesson 3: Separation
He we present some alternative topologies of a line interval and then discuss the notion of separability. Note the error at 4:05. Sorry! If you are viewing this on a mobile device, my annotations are not visible. This is due to a quirck of YouTube.
From playlist What is a Manifold?
What is a Manifold? Lesson 2: Elementary Definitions
This lesson covers the basic definitions used in topology to describe subsets of topological spaces.
From playlist What is a Manifold?
What is a Manifold? Lesson 8: Diffeomorphisms
What is a Manifold? Lesson 8: Diffeomorphisms
From playlist What is a Manifold?
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
Manifolds - Part 6 - Second-Countable Space
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From playlist Manifolds
Manifolds - Part 2 - Interior, Exterior, Boundary, Closure
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From playlist Manifolds
Jose Perea (6/15/22): Vector bundles for data alignment and dimensionality reduction
A vector bundle can be thought of as a family of vector spaces parametrized by a fixed topological space. Vector bundles have rich structure, and arise naturally when trying to solve synchronization problems in data science. I will show in this talk how the classical machinery (e.g., class
From playlist AATRN 2022
Joshua Mike (6/15/20): TALLEM: Topological Assembly of Locally Linear Euclidean Models
Title: TALLEM: Topological Assembly of Locally Linear Euclidean Models Abstract: We present a new topological data analysis tool for nonlinear dimensionality reduction. This method, dubbed TALLEM, assembles a collection of local Euclidean coordinates, and leverages ideas from the theory o
From playlist ATMCS/AATRN 2020
The Dimpled Manifold Model of Adversarial Examples in Machine Learning (Research Paper Explained)
#adversarialexamples #dimpledmanifold #security Adversarial Examples have long been a fascinating topic for many Machine Learning researchers. How can a tiny perturbation cause the neural network to change its output by so much? While many explanations have been proposed over the years, t
From playlist Papers Explained
AMMI Course "Geometric Deep Learning" - Lecture 10 (Gauges) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 10: Gauges • Gauge transformat
From playlist AMMI Geometric Deep Learning Course - First Edition (2021)
Koopman Observable Subspaces & Nonlinearization
This video illustrates the use of the Koopman operator to simulate a nonlinear dynamical system using a linear dynamical system on an observable subspace. For more details, see our papers: https://scholar.google.com/citations?user=TjzWdigAAAAJ&hl=en http://arxiv.org/abs/1510.03007 http
From playlist Research Abstracts from Brunton Lab
Lecture 5: Equivariant CNNs II (Riemannian manifolds) - Maurice Weiler
Video recording of the First Italian School on Geometric Deep Learning held in Pescara in July 2022. Slides: https://www.sci.unich.it/geodeep2022/slides/CoordinateIndependentCNNs.pdf
From playlist First Italian School on Geometric Deep Learning - Pescara 2022
Sayan Mukherjee (8/29/21): Modeling shapes and fields: a sheaf theoretic perspective
We will consider modeling shapes and fields via topological and lifted-topological transforms. Specifically, we show how the Euler Characteristic Transform and the Lifted Euler Characteristic Transform can be used in practice for statistical analysis of shape and field data. The Lifted Eul
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Luis Scoccola (5/3/21): Approximate and discrete vector bundles
Synchronization problems, such as the problem of reconstructing a 3D shape from a set of 2D projections, can often be modeled by principal bundles. Similarly, the application of local PCA to a point cloud concentrated around a manifold approximates the tangent bundle of the manifold. In th
From playlist TDA: Tutte Institute & Western University - 2021
Ian Dryden : Bayesian ambient space inference for object data
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the September 01, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Today, we take a look at atlases, provide an example for the circle, and discuss different types of atlases we may wish to have on our manifold.
From playlist Manifolds
Roy Lederman - Approaches for Exploring the Geometry of Molecular Conformations in Cryo-EM
Recorded 14 November 2022. Roy Lederman of Yale University Applied Mathematics presents "Approaches for Exploring the Geometry of Molecular Conformations in Cryo-EM" at IPAM's Cryo-Electron Microscopy and Beyond Workshop. Abstract: While other methods for structure determination, such as x
From playlist 2022 Cryo-Electron Microscopy and Beyond