Related papers: Directed animals, quadratic and rewriting systems
In this paper, we revisit the enumeration of directed animals using gas models. We show that there exists a natural construction of random directed animals on any directed graph together with a particle system that explains at the level of…
This article introduces a new, simple solvable lattice for directed animals: the directed king's lattice, or square lattice with next nearest neighbor bonds and preferred directions {W, NW, N, NE, E}. We show that the directed animals in…
These lectures provide an introduction to the directed percolation and directed animals problems, from a physicist's point of view. The probabilistic cellular automaton formulation of directed percolation is introduced. The planar duality…
We consider the local limit of finite uniformly distributed directed animals on the square lattice viewed from the root. Two constructions of the resulting uniform infinite directed animal are given: one as a heap of dominoes, constructed…
We study the phase diagram of fully directed lattice animals with nearest-neighbour interactions on the square lattice. This model comprises several interesting ensembles (directed site and bond trees, bond animals, strongly embeddable…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…
We show that the problem of directed percolation on an arbitrary lattice is equivalent to the problem of m directed random walkers with rather general attractive interactions, when suitably continued to m=0. In 1+1 dimensions, this is dual…
We introduce new combinatorial (bijective) methods that enable us to compute the average value of three parameters of directed animals of a given area, including the site perimeter. Our results cover directed animals of any one-line source…
We study directed percolation at the upper critical transverse dimension $d=4$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) behavior. Viewing directed percolation as a kinetic process, we address…
We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed…
A model of directed percolation processes with colors and flavors that is equivalent to a population model with many species near their extinction thresholds is presented. We use renormalized field theory and demonstrate that all…
Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data…
Stacked directed animals and multi-directed animals are two lattice models defined by Bousquet-M\'{e}lou and Rechnitzer in 2002. The original definitions of those models involve heaps of pieces, i.e., some geometric representation of…
A new algorithm for the derivation of low-density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems. Numerical evidence shows that the computational complexity grows…
The critical exponents for a class of one-dimensional models of interface depinning in disordered media can be calculated through a mapping onto directed percolation (DP). In higher dimensions these models give rise to directed surfaces,…
We consider a directed random walk on the backbone of the infinite cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the ``ancestral lineage'' of an individual in the stationary…
We study directed rigidity percolation (equivalent to directed bootstrap percolation) on three different lattices: square, triangular, and augmented triangular. The first two of these display a first-order transition at p=1, while the…
During our earlier research, it was recognised that in order to be successful with an indirect genetic algorithm approach using a decoder, the decoder has to strike a balance between being an optimiser in its own right and finding feasible…
We study the multi-agent formation control problem in a directed graph. The relative configurations are expressed by unit dual quaternions (UDQs). We call such a weighted directed graph a unit dual quaternion directed graph (UDQDG). We show…
We propose directed time series regression, a new approach to estimating parameters of time-series models for use in certainty equivalent model predictive control. The approach combines merits of least squares regression and empirical…