Abstract:
We present numerical evidence for the fact that the damage spreading transition in the Domany-Kinzel automaton found by Martins {\it et al.} is in the same universality class as directed percolation. We conjecture that also other damage spreading transitions should be in this universality class, unless they coincide with other transitions (as in the Ising model with Glauber dynamics) and provided the probability for a locally damaged state to become healed is not zero.

Abstract:
We check claims for a generalized central limit theorem holding at the Feigenbaum (infinite bifurcation) point of the logistic map, made recently by U. Tirnakli, C. Beck, and C. Tsallis (Phys. Rev. {\bf 75}, 040106(R) (2007)). We show that there is no obvious way that these claims can be made consistent with high statistics simulations. We also refute more recent claims by the same authors that extend the claims made in the above reference.

Abstract:
We simulate directed site percolation on two lattices with 4 spatial and 1 time-like dimensions (simple and body-centered hypercubic in space) with the standard single cluster spreading scheme. For efficiency, the code uses the same ingredients (hashing, histogram re-weighing, and improved estimators) as described in Phys. Rev. {\bf E 67}, 036101 (2003). Apart from providing the most precise estimates for $p_c$ on these lattices, we provide a detailed comparison with the logarithmic corrections calculated by Janssen and Stenull [Phys. Rev. {\bf E 69}, 016125 (2004)]. Fits with the leading logarithmic terms alone would give estimates of the powers of these logarithms which are too big by typically 50%. When the next-to-leading terms are included, each of the measured quantities (the average number of sites wetted at time $t$, their average distance from the seed, and the probability of cluster survival) can be fitted nearly perfectly. But these fits would not be mutually consistent. With a consistent set of fit parameters, one obtains still much improvement over the leading log - approximation. In particular we show that there is one combination of these three observables which seems completely free of logarithmic terms.

Abstract:
We present detailed simulations of a generalization of the Domany-Kinzel model to 2+1 dimensions. It has two control parameters $p$ and $q$ which describe the probabilities $P_k$ of a site to be wetted, if exactly $k$ of its "upstream" neighbours are already wetted. If $P_k$ depends only weakly on $k$, the active/adsorbed phase transition is in the directed percolation (DP) universality class. If, however, $P_k$ increases fast with $k$ so that the formation of inactive holes surrounded by active sites is suppressed, the transition is first order. These two transition lines meet at a tricritical point. This point should be in the same universality class as a tricritical transition in the contact process studied recently by L\"ubeck. Critical exponents for it have been calculated previously by means of the field theoretic epsilon-expansion ($\epsilon = 3-d$, with $d=2$ in the present case). Rather poor agreement is found with either.

Abstract:
We present improved simulations of three-dimensional self avoiding walks with one end attached to an impenetrable surface on the simple cubic lattice. This surface can either be a-thermal, having thus only an entropic effect, or attractive. In the latter case we concentrate on the adsorption transition, We find clear evidence for the cross-over exponent to be smaller than 1/2, in contrast to all previous simulations but in agreement with a re-summed field theoretic $\epsilon$-expansion. Since we use the pruned-enriched Rosenbluth method (PERM) which allows very precise estimates of the partition sum itself, we also obtain improved estimates for all entropic critical exponents.

Abstract:
We argue that Non-sequential Recursive Pair Substitution (NSRPS) as suggested by Jim\'enez-Monta\~no and Ebeling can indeed be used as a basis for an optimal data compression algorithm. In particular, we prove for Markov sequences that NSRPS together with suitable codings of the substitutions and of the substitute series does not lead to a code length increase, in the limit of infinite sequence length. When applied to written English, NSRPS gives entropy estimates which are very close to those obtained by other methods. Using ca. 135 GB of input data from the project Gutenberg, we estimate the effective entropy to be $\approx 1.82$ bit/character. Extrapolating to infinitely long input, the true value of the entropy is estimated as $\approx 0.8$ bit/character.

Abstract:
We show that recent claims for the non-stationary behaviour of the logistic map at the Feigenbaum point based on non-extensive thermodynamics are either wrong or can be easily deduced from well-known properties of the Feigenbaum attractor. In particular, there is no generalized Pesin identity for this system, the existing "proofs" being based on misconceptions about basic notions of ergodic theory. In deriving several new scaling laws of the Feigenbaum attractor, thorough use is made of its detailed structure, but there is no obvious connection to non-extensive thermodynamics.

Abstract:
We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law $p({\bf x})\sim |{\bf x}|^{-\sigma-2}$ for the probability that a site can infect another site a distance vector ${\bf x}$ apart. As in I we present detailed results for the critical case, for the supercritical case with $\sigma = 2$, and for the supercritical case with $0< \sigma < 2$. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For $\sigma=2$ we find generic power laws with $\sigma-$dependent exponents in the supercritical phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on $\sigma$ in the regime $0<\sigma <2$, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for $\sigma$ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder {\it et al.}. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same.

Abstract:
We argue that the mean crossing number of a random polymer configuration is simply a measure of opacity, without being closely related to entanglement as claimed by several authors. We present an easy way of estimating its asymptotic behaviour numerically. These estimates agree for random walks (theta polymers), self-avoiding walks, and for compact globules with analytic estimates giving $\log N, a-b/N^{2\nu-1},$ and $N^{1/3}$, respectively, for the average number of crossings per monomer in the limit $N\to \infty$. While the result for compact globules agrees with a rigorous previous estimate, the result for SAWs disagrees with previous numerical estimates.

Abstract:
We study a supposed model for branched polymers which was shown in two dimensions to be in the universality class of ordinary percolation. We confirm this by high statistics simulations and show that it is in the percolation universality class also for three dimensions, in contrast to previous claims. These previous studies seem to have been mislead by huge corrections to scaling in this model.