Exact Ground States of Large Two-Dimensional Planar Ising Spin Glasses

Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 3000x3000 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the Bieche et al. approach.Comment: 11 pages, 5 figures; shortened introduction, extended results; to appear in Physical Review E 7

Inclusive One Jet Production With Multiple Interactions in the Regge Limit of pQCD

DIS on a two nucleon system in the regge limit is considered. In this framework a review is given of a pQCD approach for the computation of the corrections to the inclusive one jet production cross section at finite number of colors and discuss the general results.Comment: 4 pages, latex, aicproc format, Contribution to the proceedings of "Diffraction 2008", 9-14 Sep. 2008, La Londe-les-Maures, Franc

Approximating the Minimum Equivalent Digraph

The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives an approximation algorithm with performance guarantee of pi^2/6 ~ 1.64. The algorithm and its analysis are based on the simple idea of contracting long cycles. (This result is strengthened slightly in ``On strongly connected digraphs with bounded cycle length'' (1996).) The analysis applies directly to 2-Exchange, a simple ``local improvement'' algorithm, showing that its performance guarantee is 1.75.Comment: conference version in ACM-SIAM Symposium on Discrete Algorithms (1994

L\'evy-type diffusion on one-dimensional directed Cantor Graphs

L\'evy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard random walk on the sets but is also allowed to move ballistically throughout the empty regions. Using scaling relations and the mapping onto the electric network problem, we obtain the exact values of the scaling exponents for the asymptotic return probability, the resistivity and the mean square displacement as a function of the topological parameters of the sets. Interestingly, the systems undergoes a transition from superdiffusive to diffusive behavior as a function of the filling of the fractal. The deterministic topology also allows us to discuss the importance of the choice of the initial condition. In particular, we demonstrate that local and average measurements can display different asymptotic behavior. The analytic results are compared with the numerical solution of the master equation of the process.Comment: 9 pages, 9 figure

Scanning Tunneling Microscopy and Fabrication of Nanometer Scale Structures at the Liquid-Gold Interface

The Scanning Tunneling Microscope (STM) can image gold surfaces covered with a variety of liquids. This paper reviews the results obtained using the STM to image gold surfaces covered with liquid. These results include the creation of 10 nm structures, images of the electrochemical process of electroplating, and the production of atomically flat Au (111) surfaces. We conclude that in the future STM will find further application in the area of nanostructure fabrication and electrochemistry. The trend in the field is toward greater control of the electrochemical environment

On the problem of reconstructing a tournament from subtournaments

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41629/1/605_2005_Article_BF01299955.pd

Meeting the Expectations of Your Heritage Culture: Links between Attachment Style, Intragroup Marginalisation, and Psychological Adjustment

This article has been made available through the Brunel Open Access Publishing Fund.This article has been made available through the Brunel Open Access Publishing Fund.Do insecurely-attached individuals perceive greater rejection from their heritage culture? Few studies have examined the antecedents and outcomes of this perceived rejection – termed intragroup marginalisation – in spite of its implications for the adjustment of cultural migrants to the mainstream culture. The present study investigated whether anxious and avoidant attachment orientations among cultural migrants were associated with greater intragroup marginalisation and, in turn, with lower subjective well-being and flourishing, and higher acculturative stress. Anxious attachment was associated with heightened intragroup marginalisation from friends and, in turn, with increased acculturative stress; anxious attachment was also associated with increased intragroup marginalisation from family. Avoidant attachment was linked with increased intragroup marginalisation from family and, in turn, with decreased subjective well-being

Some Exact Results for Spanning Trees on Lattices

For $n$-vertex, $d$-dimensional lattices $\Lambda$ with $d \ge 2$, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant $z_{bcc(d)}$ for spanning trees on the $d$-dimensional body-centered cubic lattice. We also give an exact integral expression for $z_{fcc}$ on the face-centered cubic lattice and an exact closed-form expression for $z_{488}$ on the $4 \cdot 8 \cdot 8$ lattice.Comment: 7 pages, 1 tabl

Cutpoints in the conjunction of two graphs

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47480/1/13_2005_Article_BF01226435.pd