Conductivity fluctuations in polymer's networks

Polymer's network is treated as an anisotropic fractal with fractional dimensionality D = 1 + \epsilon close to one. Percolation model on such a fractal is studied. Using the real space renormalization group approach of Migdal and Kadanoff we find threshold value and all the critical exponents to be strongly nonanalytic functions of \epsilon, e.g. the critical exponent of the conductivity was obtained to be \epsilon^{-2}\exp(-1-1/\epsilon). The main part of the finite size conductivities distribution function at the threshold was found to be universal if expressed in terms of the fluctuating variable, which is proportional to the large power of the conductivity, but with dimensionally-dependent low-conductivity cut-off. Its reduced central momenta are of the order of \exp(-1/\epsilon) up to the very high order.Comment: 7 pages, one eps figure, uses epsf style, to be published in Proc. of LEES-97 (Physica B

Measuring ultracool properties from the UKIDSS Large Area Survey

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedWe discuss the properties and of ultracool and brown dwarfs that can be measured from current large area surveys and how fundamental parameters, such as the mass function and formation history can be measured, describing our own first measurement of the formation history in the sub-stellar regime using data from the UKIDSS Large Area Survey

Threshold values of Random K-SAT from the cavity method

Using the cavity equations of \cite{mezard:parisi:zecchina:02,mezard:zecchina:02}, we derive the various threshold values for the number of clauses per variable of the random $K$-satisfiability problem, generalizing the previous results to $K \ge 4$. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large $K$. The stability of the solution is also computed. For any $K$, the satisfiability threshold is found to be in the stable region of the solution, which adds further credit to the conjecture that this computation gives the exact satisfiability threshold.Comment: 38 pages; extended explanations and derivations; this version is going to appear in Random Structures & Algorithm

Seasonal changes in anthropometric and physical characteristics within English academy rugby league players.

Professional rugby league clubs implement training programmes for the development of anthropometric and physical characteristics within an academy programme. However, research that examines seasonal changes in these characteristics is limited. The purpose of the study was to evaluate the seasonal changes in anthropometric and physical characteristics of academy rugby league players by age category (i.e., under 14, 16, 18, 20). Data were collected on 75 players pre- and postseason over a 6-year period (resulting in a total of 195 assessments). Anthropometric (body mass, sum of 4 skinfolds) and physical (10- and 20-m sprint, vertical jump, Yo-Yo intermittent recovery test and 1 repetition maximum squat, bench press, and prone row) measures were collected. The under 14s and 16s showed greater seasonal improvements in body mass (e.g., under 14s = 7.4 ± 4.3% vs. under 20s = 1.2 ± 3.3%) and vertical jump performance than under 18s and under 20s. In contrast, under 18s and under 20s players showed greater seasonal improvements in Yo-Yo performance and 10-m sprint (e.g., under 14s = 1.3 ± 3.9% vs. under 20s = -1.9 ± 1.2%) in comparison to under 14s and under 16s. Seasonal strength improvements were greater for the under 18s compared with under 20s. This study provides comparative data for seasonal changes in anthropometric and physical characteristics within rugby league players aged 13-20 years. Coaches should be aware that seasonal improvements in speed may not exist within younger age categories, until changes in body mass stabilize and consider monitoring changes in other characteristics (e.g., momentum). Large interplayer variability suggests that player development should be considered on an individual and longitudinal basis

Anthropometric and physical characteristics of english academy rugby league players.

The purpose of the present study was to evaluate the anthropometric and physical characteristics of English academy rugby league players by annual-age category (under 16s-under 20s) and between backs and forwards. Data were collected on 133 academy players over a 6-year period (resulting in a total of 257 assessments). Player assessments comprised of anthropometric (height, body mass, sum of 4 skinfolds) and physical (vertical jump, 10- and 20-m sprint, estimated V[Combining Dot Above]O2max via the yo-yo intermittent recovery test level 1, absolute 1 repetition maximum [1RM], and relative squat, bench press, and prone row) measures. Univariate analysis of variance demonstrated significant (p ≤ 0.05) increases in height, body mass, vertical jump, absolute, and relative strength measures across the 5 annual-age categories (e.g., body mass: under 16s = 75.2 ± 11.1, under 20s = 88.9 ± 8.5 kg; vertical jump: under 16s = 45.7 ± 5.2, under 20s = 52.8 ± 5.4 cm; 1RM bench press: under 16s = 73.9 ± 13.2, under 20s = 114.3 ± 15.3 kg). Independent t-tests identified significant (p ≤ 0.05) differences between backs and forwards for anthropometric (e.g., under 16s body mass: backs = 68.4 ± 8.6, forwards = 80.9 ± 9.7 kg) and physical (e.g., under 19s 20-m sprint: backs = 3.04 ± 0.08, forwards = 3.14 ± 0.12s; under 18s relative squat: backs = 1.65 ± 0.18, forwards = 1.51 ± 0.17 kg·kg) characteristics that were dependent on the age category and measure assessed. Findings highlight that anthropometric and physical characteristics develop across annual-age categories and between backs and forwards in academy rugby league players. These findings provide comparative data for such populations and support the need to monitor player development in junior rugby league players

The random K-satisfiability problem: from an analytic solution to an efficient algorithm

We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the satisfiable region, where the proliferation of metastable states is at the origin of the slowdown of search algorithms. The fundamental order parameter introduced in the cavity method, which consists of surveys of local magnetic fields in the various possible states of the system, can be computed for one given sample. These surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems. One such algorithm is shown here for the 3-sat problem, with very good performances.Comment: 38 pages, 13 figures; corrected typo

Anomalous electrical and frictionless flow conductance in complex networks

We study transport properties such as electrical and frictionless flow conductance on scale-free and Erdos-Renyi networks. We consider the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G, with a power-law tail distribution \Phi_{SF}(G) \sim G^{g_G}, where g_G = 2\lambda - 1, where \lambda is the decay exponent for the scale-free network degree distribution. We confirm our predictions by simulations of scale-free networks solving the Kirchhoff equations for the conductance between a pair of nodes. The power-law tail in \Phi_{SF}(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erdos-Renyi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical 'transport backbone' picture we suggest that the conductances of scale-free and Erdos-Renyi networks can be approximated by ck_Ak_B/(k_A+k_B) for any pair of nodes A and B with degrees k_A and k_B. Thus, a single quantity c, which depends on the average degree of the network, characterizes transport on both scale-free and Erdos-Renyi networks. We determine that c tends to 1 for increasing , and it is larger for scale-free networks. We compare the electrical results with a model for frictionless transport, where conductance is defined as the number of link-independent paths between A and B, and find that a similar picture holds. The effects of distance on the value of conductance are considered for both models, and some differences emerge. Finally, we use a recent data set for the AS (autonomous system) level of the Internet and confirm that our results are valid in this real-world example.Comment: 8 pages, 11 figure

The discovery of a T6.5 subdwarf

We report the discovery of ULAS J131610.28+075553.0, an sdT6.5 dwarf in the UKIDSS Large Area Survey 2 epoch proper motion catalogue. This object displays significant spectral peculiarity, with the largest yet seen deviations from T6 and T7 templates in the Y and K bands for this subtype. Its large, similar to 1 arcsec yr(-1), proper motion suggests a large tangential velocity of V-tan approximate to 240-340 km s(-1), if we assume its M-J lies within the typical range for T6.5 dwarfs. This makes it a candidate for membership of the Galactic halo population. However, other metal-poor T dwarfs exhibit significant under luminosity both in specific bands and bolometrically. As a result, it is likely that its velocity is somewhat smaller, and we conclude it is a likely thick disc or halo member. This object represents the only T dwarf earlier than T8 to be classified as a subdwarf, and is a significant addition to the currently small number of known unambiguously substellar subdwarfs.Peer reviewe

Convex Hull of Points Lying on Lines in o(n log n) Time after Preprocessing

Motivated by the desire to cope with data imprecision, we study methods for taking advantage of preliminary information about point sets in order to speed up the computation of certain structures associated with them. In particular, we study the following problem: given a set L of n lines in the plane, we wish to preprocess L such that later, upon receiving a set P of n points, each of which lies on a distinct line of L, we can construct the convex hull of P efficiently. We show that in quadratic time and space it is possible to construct a data structure on L that enables us to compute the convex hull of any such point set P in O(n alpha(n) log* n) expected time. If we further assume that the points are "oblivious" with respect to the data structure, the running time improves to O(n alpha(n)). The analysis applies almost verbatim when L is a set of line-segments, and yields similar asymptotic bounds. We present several extensions, including a trade-off between space and query time and an output-sensitive algorithm. We also study the "dual problem" where we show how to efficiently compute the (<= k)-level of n lines in the plane, each of which lies on a distinct point (given in advance). We complement our results by Omega(n log n) lower bounds under the algebraic computation tree model for several related problems, including sorting a set of points (according to, say, their x-order), each of which lies on a given line known in advance. Therefore, the convex hull problem under our setting is easier than sorting, contrary to the "standard" convex hull and sorting problems, in which the two problems require Theta(n log n) steps in the worst case (under the algebraic computation tree model).Comment: 26 pages, 5 figures, 1 appendix; a preliminary version appeared at SoCG 201