A Wilson prime is a prime p such that (p − 1)! = −1 (mod p). We report on a search for Wilson primes up to 2 × 10, and describe several new algorithms that were used in the search. In particular we give the first known algorithm that computes (p − 1)! (mod p) in average polynomial time per prime.

2+1 flavor lattice QCD simulation with O(a)-improved Wilson quarks We present simulation details and results for the light hadron spectrum in N f = 2 + 1 lattice QCD with the nonperturbatively O(a)-improved Wilson quark action and the Iwasaki gauge action. Simulations are carried out at a lattice spacing of 0.09 fm on a (2.9fm) 3 box using the PACS-CS computer. We employ the Lüscher's domain-de...

This paper presents a scheme for segmenting images on the basis of differences in localised measures of spatial texture. The scheme used was originally proposed by Wilson and Spann [1] but incorporates a new clustering algorithm which gives improved overall segmentation performance. The Wilson and Spann [1] algorithm uses a clustering algorithm which proved susceptible to initial input paramete...

For a large class of examples arising in statistical physics known as attractive spin systems (e.g., the Ising model), one seeks to sample from a probability distribution π on an enormously large state space, but elementary sampling is ruled out by the infeasibility of calculating an appropriate normalizing constant. The same difficulty arises in computer science problems where one seeks to sam...

An example of unipolar induction is a slab of material with (relative) permittivity and (relative) permeability μ that is immersed in a uniform external magnetic field H0 parallel to the plane of the slab, such that if the slab has velocity v perpendicular to H0 but also in the plane of the slab, a nonzero voltage difference V is detected between sliding contacts (fixed in the laboratory) on op...

The extreme computational costs of calculating the sign of the Wilson matrix within the overlap operator have so far prevented four dimensional dynamical overlap simulations on realistic lattice sizes, because the computational power required to invert the overlap operator, the time consuming part of the Hybrid Monte Carlo algorithm, is too high. In this series of papers we introduced the optim...

Propp & Wilson (1996) described a protocol, called coupling from the past, for exact sampling from a target distribution using a coupled Markov chain Monte Carlo algorithm. In this paper we extend coupling from the past to various MCMC samplers on a continuous state space; rather than following the monotone sampling device of Propp & Wilson, our approach uses methods related to gamma-coupling a...

In lattice gauge theory, there exist field transformations that map the theory to the trivial one, where the basic field variables are completely decoupled from one another. Such maps can be constructed systematically by integrating certain flow equations in field space. The construction is worked out in some detail and it is proposed to combine the Wilson flow (which generates approximately tr...