Although the sequence of primes is very well distributed in the reduced residue classes [Formula: see text], the distribution of pairs of consecutive primes among the permissible ϕ(q)(2) pairs of reduced residue classes [Formula: see text] is surprisingly erratic. This paper proposes a conjectural explanation for this phenomenon, based on the Hardy-Littlewood conjectures. The conjectures are th...

We describe a new method for learning text-classification rules from examples. The text consists of messages written by students in an online learning environment, and it may contain ungrammatical expressions as well as specialized expressions such as formulas. The method is based on the version-space machine learning technique. Experiments show that our method successfully generalizes over cer...

This paper takes two approaches to prediction of nancial markets using text data downloaded from web bulletin boards. The rst uses maximum entropy text classi cation to predict based on the whole body of text; the second uses a genetic algorithm to learn simple rules based solely on numerical data of trading volume, number of messages posted per day and total number of words posted per day. Whi...

We prove strong convergence of order [Formula: see text] for arbitrarily small [Formula: see text] of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying...

We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length [Formula: see text] can be generated in [Formula: see text] floating point operations. We highlight some of the connections between the different construct...

We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate (Q) and the total pressure difference ([Formula: see text]) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers a...

A simple formula for computing the generalized Hubbell radiation rectangular source integral [formula in text] is introduced. Tables are given to compare the numerical values derived from our approximation formula with those given earlier in the literature.

We compute the two-loop QCD corrections to the neutral Higgs-boson masses in the Minimal Supersymmetric Standard Model, including the effect of non-vanishing external momenta in the self-energies. We obtain corrections of [Formula: see text] and [Formula: see text], i.e., all two-loop corrections that involve the strong gauge coupling when the only non-vanishing Yukawa coupling is the top one. ...

In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-calle...

Supporting Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Factor X or Z model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Mathematical model formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Numerical methods . . . . . . ...