2004-2005 seminars

A fundamental problem in combinatorial optimization is the edge-disjoint paths problem (EDP). We are given a graph G=(V,E) and a set of pairs of vertices (s_1,t_1), (s_2,t_2), ..., (s_k,t_k). The objective is to decide if all the pairs can be...

The Glauber dynamics is a simple Markov chain algorithm for sampling from distributions that arise in models from statistical physics. In each step of this dynamics the value (or spin) of a random site is updated according to some rule which is...

The problem of average-case learning for decision trees is as follows: a decision tree T (over Boolean features x1,...,xn) is chosen at random from some natural distribution over decision trees. The learner is given access to uniform random examples...

The Glauber dynamics is a simple Markov chain algorithm for sampling from distributions that arise in models from statistical physics. In each step of this dynamics the value (or spin) of a random site is updated according to some rule which is...

I will present recent joint work with O. Friedland and V. Milman, where we use simple probabilistic estimates on Bernoulli random variables, together with tools from convex geometric analysis, to arrive at some new results. The first result has to...

We study properties of random Bernoulli matrices. In particular, we determine the typical value of the determinant. We also obtain a new bound on the probability that the matrix is singular. Joint work with T. Tao.

We prove a number of general theorems about CZK, the class of problems possessing computational zero-knowledge proofs. Our results are *unconditional*, in contrast to most previous works on CZK which rely on the assumption that one-way functions...

We consider the complexity of properly learning concept classes, i.e. when the learner must output a hypothesis of the same form as the unknown concept. We present the following new upper and lower bounds on well-known concept classes: 1. We show...

The goal of hardness amplification is to take a function f : {0,1}^n --> {0,1} that is mildly average-case hard (i.e., very "small" circuit fails to compute f on at least a 1/poly(n) fraction of inputs), and produce a new function f' that is very...

We consider "local-update" Markov chains for sampling from independent sets and proper 3-colourings of a graph. An example of such a chain is the well-known Glauber dynamics, which updates the state of at most one vertex of the graph at each step...