Alexander K. Hartmann

Number of guards needed by a museum: a phase transition in vertex covering of random graphs.

In this Letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This transition is characterized by means of exact numerical simulations as well as by analytical replica calculations. The replica symmetric phase diagram is in excellent agreement with numerical findings up to average connectivity e, where replica symmetry becomes locally unstable.

Random number generators for massively parallel simulations on GPU

High-performance streams of (pseudo) random numbers are crucial for the efficient implementation of countless stochastic algorithms, most importantly, Monte Carlo simulations and molecular dynamics simulations with stochastic thermostats. A number of implementations of random number generators has been discussed for GPU platforms before and some generators are even included in the CUDA supporting libraries. Nevertheless, not all of these generators are well suited for highly parallel applications where each thread requires its own generator instance. For this specific situation encountered, for instance, in simulations of lattice models, most of the high-quality generators with large states such as Mersenne twister cannot be used efficiently without substantial changes. We provide a broad review of existing CUDA variants of random-number generators and present the CUDA implementation of a new massively parallel high-quality, high-performance generator with a small memory load overhead.

Sampling rare events: Statistics of local sequence alignments

A method to calculate probability distributions in regions where the events are very unlikely (e.g., p approximately 10(-40)) is presented. The basic idea is to map the underlying model on a physical system. The system is simulated at a low temperature, such that preferably configurations with originally low probabilities are generated. Since the distribution of such a physical system is known, the original unbiased distribution can be obtained. As an application, local alignment of protein sequences is studied. The deviation of the distribution p(S) of optimum scores from the extreme-value distribution is quantified. This deviation decreases with growing sequence length.

Propagation of ripples in Monte Carlo models of sputter-induced surface morphology

Periodic ripples generated from the off-normal-incidence ion-beam bombardment of solid surfaces have been observed to propagate with a dispersion in the velocity. We investigate this ripple behavior by means of a Monte Carlo model of the erosion process, in conjuction with one of two different surface-diffusion mechanisms, representative of two different classes of materials; one is a Arrhenius-type Monte Carlo method including a term (possibly zero) that accounts for the Schwoebel effect, while the other is a thermodynamic mechanism without the Schwoebel effect. We find that the behavior of the ripple velocity and wavelength depends on the sputtering time scale, which is qualitatively consistent with experiments. Futhermore, we observe a strong temperature dependance of the ripple velocity, calling for experiments at different temperatures. Also, we observe that the ripple velocity vanishes ahead of the periodic ripple pattern.

SCALING OF STIFFNESS ENERGY FOR THREE-DIMENSIONAL J ISING SPIN GLASSES

Large numbers of ground states of 3d EA Ising spin glasses are calculated for sizes up to 10^3 using a combination of a genetic algorithm and Cluster-Exact Approximation. A detailed analysis shows that true ground states are obtained. The ground state stiffness (or domain wall) energy D is calculated. A D ~ L^t behavior with t=0.19(2) is found which strongly indicates that the 3d model has an equilibrium spin-glass-paramagnet transition for non-zero T_c.

Conformal invariance and stochastic Loewner evolution processes in two-dimensional Ising spin glasses.

We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with

Hiding solutions in random satisfiability problems: a statistical mechanics approach.

\kappa \approx 2.1

Searching for Ground States of Ising Spin Glasses with Hierarchical BOA and Cluster Exact Approximation

. An argument is given that their fractal dimension

Long-time effects in a simulation model of sputter erosion

d_f

Influence of collision cascade statistics on pattern formation of ion-sputtered surfaces

is related to their interface energy exponent