The class of bipartite permutation graphs enjoys many nice and important properties. In particular, this is critically in the study clique- rank-width graphs, because it one minimal hereditary classes unbounded rank-width. It also contains a number subclasses, which are critical with respect to other parameters, such as graph lettericity or shrub-depth, notions, well-quasi-ordering complexity a...

The following paper is the continuation of our earlier considerations on cellular automata with Toom local rule (TCA) as the alternative to kinetic Ising systems. The arguments for TCA stationary states not being the equilibrium states are found in simulations.

We discuss the critical behavior of nonequilibrium anisotropic systems, particularly the driven lattice gas and its variants. A large series of available numerical results depict a coherent picture consistent with speci c predictions drawn from novel eld theory and its renormalization group analysis. c © 2000 Elsevier Science B.V. All rights reserved. PACS: 05.10Cc; 05.10Ln; 05.70Fh; 05.70Jk; 0...

Advanced chain-growth computer simulation methodologies have been employed for a systematic statistical analysis of the critical behavior of a polymer adsorbing at a substrate. We use finite-size scaling techniques to investigate the solvent-quality dependence of critical exponents, critical temperature, and the structure of the phase diagram. Our study covers all solvent effects from the limit...

A dominating set of vertices S of a graph G is connected if the subgraph G[S] is connected. Let c(G) denote the size of any smallest connected dominating set in G. A graph G is k-connected-critical if c(G)= k, but if any edge e ∈ E(Ḡ) is added to G, then c(G+ e) k − 1. This is a variation on the earlier concept of criticality of edge addition with respect to ordinary domination where a graph G ...

– We study vortex lines in high-temperature superconductors with columnar defects produced by heavy ion irradiation. We reconsider scaling theory for the Bose glass transition with tilted magnetic fields, and propose, e.g., a new scaling form for the shape of the Bose glass phase boundary, which is relevant for experiments. We also consider Monte Carlo simulations for a vortex model with a scre...

We review some recent developments in string theory, emphasizing the importance of vacuum instabilities, their relation to the density of states, and the role of space-time fermions in non-critical string theory. We also discuss the classical dynamics of two dimensional string theory. In the last few years many people have been studying simple models of string theory , which correspond to strin...

We study the effect of mixing two rules on the dynamics of one-dimensional cellular automata by large scale numerical simulations. We calculate the decay of the magnetization for the Domany-Kinzel automaton (XOR/AND mixing) to its equilibrium value in the three phases. This requires system sizes in excess of 1 million sites. We also find severe finite size effects near the new critical points r...

We argue that the analysis of Reimers et al. (1992)] of their Monte Carlo data on the Heisenberg pyrochlore antiferromag-net, which suggests a new universality class, is not conclusive. By re-analysis of their data, we demonstrate asymptotic volume dependence in some ther-modynamic quantities, which suggests the possibility that the transition may be first order.