Related papers: Isolated loops
Some iterative calculations can be carried out by parallel communicating processors, and yield the same results whether or not the processors are synchronized. We show that this is the case if and only if the iteration is a contraction that…
Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…
We present a new algorithm for computing upper bounds on the number of executions of each program instruction during any single program run. The upper bounds are expressed as functions of program input values. The algorithm is primarily…
We propose a new model of self-organized criticality. A particle is dropped at random on a lattice and moves along directions specified by arrows at each site. As it moves, it changes the direction of the arrows according to fixed rules. On…
The problem of detecting of information and logically independent (DILD) steps in programs is a key for equivalent program transformations. Here we are considering the problem of independence of loop iterations, the concentration of massive…
The model of self-organizing Eulerian walkers is numerically investigated on the square lattice. The critical exponents for the distribution of a number of steps ($\tau_l$) and visited sites ($\tau_s$) characterizing the process of…
The problem of real-time control and optimization of components' routing in discrete manufacturing plants, where distinct items must undergo a sequence of jobs, is considered. This problem features a large number of discrete control inputs…
We give a formula for the bivariate generating function of a stationary 1-dependent counting process in terms of its run probability generating function, with a probabilistic proof. The formula reduces to the well known bivariate generating…
A closed plane meander of order n is a closed self-avoiding loop intersecting an infinite line 2n times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on…
Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
We consider the problem of enumerating Dyck paths staying weakly above the x-axis with a limit to the number of consecutive up steps, or a limit to the number of consecutive down steps. We use Finite Operator Calculus to obtain formulas for…
Repulsive point processes arise in models where competition forces entities to be more spread apart than if placed independently. Simulation of these types of processes can be accomplished using dominated coupling from the past with a…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
Modern data collecting methods and computation tools have made it possible to monitor high-dimensional processes. In this article, Phase II monitoring of high-dimensional processes is investigated when the available number of samples…
A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of…