Alissa Pajer's Blog

TDA Background

• Introductory Topological Data Analysis

  • date: Apr 2020
  • author: Dayten Sheffar
  • summary: high-level introduction to: metric topology, \(p\)-norm, \(\infty\)-norm, abstract simplexes, simplicial complexes, homeomorphic and homotopy equivalence, nerve theorem, mapper algorithm, betti numbers, persistent homology

• Persistent Homology

  • author: Herbert Edelsbrunner and Dmitriy Morozov
  • summary: glossary of all things persistent homology

• Persistent Homology: Theory and Practice

  • author: Herbert Edelsbrunner, Dmitriy Morozov
  • summary: persistent homology survey of methods and applications

• Statistical topological data analysis using persistence landscapes

  • date: Jul 2012
  • author: Peter Bubenik
  • summary: introduces persistence landscapes to the literature

TDA Theory: Stability

• Notes on an Elementary Proof for the Stability of Persistence Diagrams

  • date: Mar 2021
  • author: Primoz Skraba, Katharine Turner
  • summary: these notes are a self-contained short proof of the stability of persistence diagrams; the background needed for arxiv:2006.16824

• Wasserstein Stability for Persistence Diagrams

  • date: June 2020
  • author: Primoz Skraba, Katharine Turner

• An algebraic Wasserstein distance for generalized persistence modules

  • date: Sep 2018
  • author: Peter Bubenik
  • summary: persistence modules are the algebraic counterpart to persistence diagrams; defines the Wasserstein distance for persistence modules; proves that the distance of a persistence module and its persistence diagram agree

TDA Theory: Computation

• Computing Persistent Homology

  • date: Nov 2004
  • author: Afra Zomorodian and Gunnar Carlsson
  • DOI: DOI
  • summary: the persistent homology of a filtered \(d\)-dimensional simplicial complex is the standard homology of a graded module over a polynomial ring; gives an algorithm for computing individual persistent homology groups over an arbitrary PID

• Dory: Overcoming Barriers to Computing Persistent Homology

  • date: Mar 2021
  • author: Manu Aggarwal, Vipul Periwal

• GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes

  • date: Mar 2020
  • author: Simon Zhang, Mengbai Xiao, Hao Wang

TDA Applications

• Topological data analysis of C. elegans locomotion and behavior

  • date: Feb 2021
  • author: Ashleigh Thomas
  • summary: uses a sliding-window embedding to turn time series data into a point cloud that remembers the temporal information; thorough and clear intro to persistence diagrams and persistence landscapes

• Topology of Deep Neural Networks

  • date: Apr 2020
  • author: Gregory Naitzat, Andrey Zhitnikov, Lek-Heng Lim

Computer Science: Functional Programming

• Theorems for free!

  • date: June 1989
  • author: Philip Wadler

• A taste of linear logic

  • date: 1993
  • author: Philip Wadler
  • DOI: DOI
  • summary: an introduction to intuitionistic logic and linear logic; how they correspond to type systems for functional languages via the notion of 'Propositions as Type'

• Monads for functional programming

  • date: 1993
  • author: Philip Wadler
  • DOI: DOI

• There is no Fork: an Abstraction for Efficient, Concurrent, and Concise Data Access

  • date: Sep 2014
  • summary: functor concurrency

• Desugaring Haskell’s do-Notation into Applicative Operations

  • date: Sep 2016
  • summary: applicative functors

Computer Science: Parsing

• Mison: A Fast JSON Parser for Data Analytics

  • date: 2017
  • summary: push down projections and filters into the parser

• Filter Before You Parse: Faster Analytics on Raw Data with Sparser

  • date: Aug 2018
  • summary: filter pre-parsing

Logic

• What could a Boolean category be?
  • date: Jul 2006
  • author: Lutz Straßburger

Misc

• Magic: The Gathering is Turing Complete
  • date: Mar 2019
  • author: Alex Churchill, Stella Biderman, Austin Herrick