The Indian Buffet Process: An Introduction and Review; Thomas L. Griffiths, Zoubin Ghahramani; 12(Apr):1185–1224, 2011. – JMLR
6, There is a short course on Algorithmic Group Testing and Applications (09/05/2011 — 27/05/2011) by Ngô Quang Hưng at SUNY Buffalo
This is a short course on algorithmic combinatorial group testing and applications. The basic setting of the group testing problem is to identify a subset of “positive” items from a huge item population using as few “tests” as possible. The meaning of “positive”, “tests” and “items” are dependent on the application. For example, dated back to World War II when the area of group testing started, “items” are blood samples, “positive” means syphilis-positive, and a “test” contains a pool of blood samples which results in a positive outcome if there is at least one sample in the pool positive for syphylis. This basic problem paradigm has found numerous applications in biology, cryptography, networking, signal processing, coding theory, statistical learning theory, data streaming, etc. This short course aims to introduce group testing from a computational view point, where not only the constructions of group testing strategies are of interest, but also the computational efficiency of both the construction and the decoding procedures are studied. We will also briefly introduce the probabilistic method, algorithmic coding theory, and several direct applications of group testing.
“…Another main result is related to the design of query-optimal and minimal-adaptive strategies. We have shown that a 2-stage randomized strategy with prescribed success probability can asymptotically achieve the information-theoretic lower bound for d much less than n and growing much slower than n. Similarly, we can approach the entropy lower bound in 4 stages when d = o(n)…”
This paper is base on talks which I gave in May, 2010 at Workshop in Trieste (ICTP). In the first part we present an introduction to knots and knot theory from an historical perspective, starting from Summerian knots and ending on Fox 3-coloring. We show also a relation between 3-colorings and the Jones polynomial. In the second part we develop the general theory of Fox colorings and show how to associate a symplectic structure to a tangle boundary so that tangles becomes Lagrangians (a proof of this result has not been published before).
Chapter VI of the book “KNOTS: From combinatorics of knot diagrams to combinatorial topology based on knots will be based on this paper.