This article studies the inhomogeneous geometric polynuclear growth model; distribution of which is related to Schur functions. We explain a method derive its functions in both space-like and time-like directions, focusing on two-time distribution. Asymptotics KPZ-scaling limit then considered, extending two times several single-time distributions KPZ universality class.

We introduce inhomogeneous parsimonious Markov models for modeling statistical patterns in discrete sequences. These models are based on parsimonious context trees, which are a generalization of context trees, and thus generalize variable order Markov models. We follow a Bayesian approach, consisting of structure and parameter learning. Structure learning is a challenging problem due to an over...

We study statistical properties of inhomogeneous Burgers lattices which are solved by the discrete Cole–Hopf transformation. Using exact solutions we investigate effect of various kinds of noise on the dynamics of solutions.

In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Gröbner bases via Buchberger’s Algorithm. In a nutshell, the idea is to extend the advantages of computing with homogeneous polynomials or vectors to the general case. When the input data are not homogeneous, we use a technique described in Section 2: the main tool ...