This paper is devoted to the construction of Boltzmann samplers according to various distributions, and uses stochastic bias on the parameter of a Boltzmann sampler, to produce a sampler with a different distribution for the size of the output. As a significant application, we produce Boltzmann samplers for words defined by regular specifications containing shuffle operators and linear recursio...

The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-deenable (ATR types are connned to levels 0, 1, and 2). A limitation of the original version of ATR is that the only directly expressible recursions are tail-recursio...

In this paper we consider the exact WKB analysis of a second-order non-homogeneous linear ordinary differential equation with a large parameter. We give a geometric criterion which guarantees the Borel summability of formal solutions of a non-homogeneous equation; this criterion is described in terms of exact steepest descent paths introduced in [AKT2]. An example related to the BNR equation ([...

We present pointwise gradient bounds for solutions to p-Laplacean type non-homogeneous equations employing non-linear Wolff type potentials, and then prove similar bounds, via suitable caloric potentials, for solutions to parabolic equations.

The scalar difference equation xn+1 = fn(xn, xn−1, · · · , xn−k) may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally using the semiconjugate relation on a group which yields a reduction of order through the semiconjugate factorization of the difference equation of order k + 1 into equat...

A unified technique for generating linear operations on homogeneous/non-homogeneous, Gaussian/non-Gaussian random fields defined on any subset of the multidimensional Euclidean space is provided. This is based on an approximate series representation valid for spatial random fields with arbitrary covariance function which can be readily realized. Furthermore, its applicability as a simulation to...

Sequence generators obtained by linear recursions over the two-element field F2, i.e., F2-linear generators, are widely used as pseudorandom number generators. For example, the Mersenne Twister MT19937 is one of the most successful applications. An advantage of such generators is that we can assess them quickly by using theoretical criteria, such as the dimension of equidistribution with v-bit ...