High‐Resolution Time‐Correlated Single‐Photon Counting Using Electro‐Optic Sampling

Enhancing electrooptic modulators using modulation instability

Sampling and Counting Contingency Tables Using Markov Chains

In this paper we present an overview of contingency tables, provide an introduction to the problems of almost uniform sampling and approximate counting, and show recent results achieved through the use of Markov chains. We focus specifically on contingency tables with two rows, since as of this time little progress has been made in achieving reasonable bounds on arbitrarily sized contingency ta...

From Sampling to Model Counting

We introduce a new technique for counting models of Boolean satisfiability problems. Our approach incorporates information obtained from sampling the solution space. Unlike previous approaches, our method does not require uniform or near-uniform samples. It instead converts local search sampling without any guarantees into very good bounds on the model count with guarantees. We give a formal an...

Counting and Sampling H-Colourings

For counting problems in #P which are “essentially self-reducible”, it is known that sampling and approximate counting are equivalent. However, many problems of interest do not have such a structure and there is already some evidence that this equivalence does not hold for the whole of #P. An intriguing example is the class ofH-colouring problems, which have recently been the subject of much st...

Relationship between Counting and Sampling

This course focuses on Markov chain based algorithms for randomly sampling from probability distributions defined on a large state space. Typically we are interested in generating a sample in time polynomial of the logarithm of the size of the state space. In other words, we want to sample from the distribution after exploring only an exponentially small portion of it. We’ll begin with two clas...