Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in in the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize -using this extensive and exhaustive numerical study- the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.Comment: 7 pages, 4 figures, 2 tables, paper summary available at http://www.papercore.org/Kajantie2000. arXiv admin note: substantial text overlap with arXiv:1003.1591, arXiv:1005.5637, arXiv:1107.174

Diking, young volcanism and diffuse hydrothermal activity on the southern Mid-Atlantic Ridge: The Lilliput field at 9°33'S

Detailed exploration with remotely operated and autonomous deep submergence vehicles has revealed, at 9 degrees 33'S, the presence of the southernmost active hydrothermal field known so far on the Mid-Atlantic Ridge. The size of the hydrothermal field, which we have named "Lilliput", is about 1000 m x 250 m. It lies in a water depth of 1500 m on a ridge segment (Segment A3) with considerably thickened crust of 11 km. Four relatively small diffuse vent sites occur on a large young (estimated <100 years old) lava flow, partly covering the flow with hydrothermal Fe-oxide/hydroxide sediments. Based on homogeneous major element compositions of ca. 25 lava samples, this flow covers an area of at least 5 km x 0.6 km. The lava flow erupted from a series of parallel fissures at the western edge of the flow and a volcanic ridge consisting of up to 30 m high pillow mounds. The volcanic ridge probably represents the surface expression of an underlying dike which fed the flow. Several drained lava pond structures were observed within the flow but only one shows hydrothermal activity. The hydrothermal venting and precipitation of abundant Fe-oxyhydroxides appear to be related to the young diking and eruption event and the four different hydrothermally active sites of the Lilliput field lie along and almost equidistant from the eastern flank of the supposed dike. Although a hydrothermal plume some 500 m above the seafloor was found in two consecutive years (2005 and 2006), no high-temperature venting associated with Lilliput has been found. in agreement with findings at other ridges with thick crust such as Reykjanes. High magma supply rate and frequent diking and eruption events may lead to hot hydrothermal vents being rare in slow-spreading segments with thick crust whereas diffuse venting is abundant. Interestingly, the fauna at the Lilliput vents largely consists of small and apparently juvenile mussels (Bathymodiolus sp.) and did not show any signs of growth during the four years of continuing observations possibly reflecting pulsing hydrothermal activity

Ground states of 2d +-J Ising spin glasses via stationary Fokker-Planck sampling

We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a linear second order differential equation that depends on a diffusion-like parameter D. We apply it to the problem of finding ground states of 2d Ising spin glasses for the +-J-Model. We consider square lattices with side length up to L=24 with two different types of boundary conditions and compare the results to those obtained by exact methods. A particular value of D is found that yields an optimal performance of the algorithm. We compare this optimal value of D to a percolation transition, which occurs when studying the connected clusters of spins flipped by the algorithm. Nevertheless, even for moderate lattice sizes, the algorithm has more and more problems to find the exact ground states. This means that the approach, at least in its standard form, seems to be inferior to other approaches like parallel tempering.Comment: v1: 13 pages, 7 figures; v2: extended tex

Inference of hidden structures in complex physical systems by multi-scale clustering

We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of partitioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scales. Significant patterns are obtained by examining the correlations between different independent solvers. Similar to other combinatorial optimization problems in the NP complexity class, community detection exhibits several phases. Typically, illuminating orders are revealed by choosing parameters that lead to extremal information theory correlations.Comment: 25 pages, 16 Figures; a review of earlier work

The counselling self-estimate inventory (COSE): Does it work in Chinese counsellors?

Counselling self-efficacy is an important construct for research and evaluation in counsellors' competencies and training effectiveness. Larson et al. developed the Counselling Self-Estimate Inventory (COSE) for counsellors in America and examined its factor structure using exploratory factor analysis. They recommended a five-factor model (microskills, counselling process, difficult client behaviour, cultural competence, and awareness of values) and the use of the COSE for future research. However, little research has investigated the validity of the COSE in the context of counselling Chinese students in schools. In the present study, the factor structure of responses to the Chinese version of the Counselling Self-Estimate Inventory in a sample of 578 Hong Kong secondary school guidance teachers was examined using the EQS approach to confirmatory factor analysis. The results showed that while a five-factor model was fairly able to fit the data, the deletion of items related to the awareness of values factor yielded a better fitting model. The discussion of potential uses and limitations of the C-COSE in the context of preparing and supervising school guidance personnel in student counselling is relevant to counselling psychologists and researchers in Hong Kong and other parts of the world.postprin

Compositional variation and 226Ra-230Th model ages of axial lavas from the southern Mid-Atlantic Ridge, 8°48′S

We present geological observations and geochemical data for the youngest volcanic features on the slow-spreading Mid-Atlantic Ridge at 8°48'S that shows seismic evidence for a thickened crust and excess magma formation. Young lava flows with high sonar reflectivity cover about 14 km2 in the axial rift and were probably erupted from two axial volcanic ridges each of about 3 km in length. Three different lava units occur along an about 11 km long portion of the ridge, and lavas from the northern axial volcanic ridge differ from those of the southern axial volcanic ridge and surrounding lava flows. Basalts from the axial rift flanks and from a pillow mound within the young flows are more incompatible element depleted than those from the young volcanic field. Lavas from this volcanic area have 226Ra-230Th disequilibria model ages of 1,000 and 4,000 years whereas the older lavas from the rift flank and the pillow mound, but also some of the lava field, are older than 8,000 years. Glasses from the northern and southern ends of the southern lava unit indicate up to 100°C cooler magma temperatures than in the center and increased assimilation of hydrothermally altered material. The compositional heterogeneity on a scale of 3 km suggests small magma batches rising vertically from the mantle to the surface without significant lateral flow and mixing. The observations on the 8°48'S lava field support the model of low frequency eruptions from single ascending magma batches that has been developed for slow-spreading ridges