Algebraic Topology for Data Scientists

This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been exposed to it, let alone data scientists, computer scientists, and analysts. I have three goals in writing this book. The first is to bring people up to speed who are missing a lot of the necessary background. I will describe the topics in point-set topology, abstract algebra, and homology theory needed for a good understanding of TDA. The second is to explain TDA and some current applications and techniques. Finally, I would like to answer some questions about more advanced topics such as cohomology, homotopy, obstruction theory, and Steenrod squares, and what they can tell us about data. It is hoped that readers will acquire the tools to start to think about these topics and where they might fit in.Comment: 322 pages, 69 figures, 5 table

Weaknesses of Margulis and Ramanujan-Margulis Low-Density Parity-Check Codes

We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with nearcodewords, which cause problems for the sum-product decoder; The RamanujanMargulis construction gives a code with low-weight codewords, which produce an error-floor

Whose shoe fits best? Dubious physics and power politics in the TMD footprint controversy

Apparent design breakthroughs in short-range missile defense systems such as Theater High-Altitude Air Defense (THAAD) have prompted questions about the legality of such systems under the 1972 Antiballistic Missile (ABM) Treaty. Prominent physicists have used computer “footprint” methodology to prove that if engineered to specifications, THAAD might exceed ABM Treaty performance limits banning highly effective missile defense systems. In response, missile defense officials commissioned Sparta, Inc. to conduct secret research casting doubt on the validity of such findings. The substantial diplomatic issues at stake and the interesting rhetorical dynamics involved in this dispute warrant close scholarly analysis. Attention to the iterative relationship between the interpenetrating spheres of public argument and scientific practice in this case yields novel insight about the processes in which technical knowledge of defense systems is forged and raises fresh issues for the “closure project” in science and technology controversy studies