Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components

Handling Markov Chains with Membrane Computing

In this paper we approach the problem of computing the n–th power of the transition matrix of an arbitrary Markov chain through membrane computing. The proposed solution is described in a semi–uniform way in the framework of P systems with external output. The amount of resources required in the construction is polynomial in the number of states of the Markov chain and in the power. The time of execution is linear in the power and is independent of the number of states involved in the Markov chain.Ministerio de Educación y Ciencia TIN2005-09345-C04-0

Percolation on the average and spontaneous magnetization for q-states Potts model on graph

We prove that the q-states Potts model on graph is spontaneously magnetized at finite temperature if and only if the graph presents percolation on the average. Percolation on the average is a combinatorial problem defined by averaging over all the sites of the graph the probability of belonging to a cluster of a given size. In the paper we obtain an inequality between this average probability and the average magnetization, which is a typical extensive function describing the thermodynamic behaviour of the model

On the effect of adding epsilon-Bernoulli percolation to everywhere percolating subgraphs of Z^d

We show that adding epsilon-Bernoulli percolation to an everywhere percolating subgraph of Z^2 results in a graph which has large scale geometry similar to that of supercritical Bernoulli percolation, in various specific senses. We conjecture similar behavior in higher dimensions.Comment: Author home pages: http://www.wisdom.weizmann.ac.il/~itai http://www.math.chalmers.se/~olleh http://www.wisdom.weizmann.ac.il/~schram

The dynamical background of polar mesosphere winter echoes from simultaneous EISCAT and ESRAD observations

On 30 October 2004 during a strong solar proton event, layers of enhanced backscatter from altitudes between 55 and 75km have been observed by both ESRAD (52MHz) and the EISCAT VHF (224MHz) radars. These echoes have earlier been termed Polar Mesosphere Winter Echoes, PMWE. After considering the morphology of the layers and their relation to observed atmospheric waves, we conclude that the radars have likely seen the same phenomenon even though the radars' scattering volumes are located about 220km apart and that the most long-lasting layer is likely associated with wind-shear in an inertio-gravity wave. An ion-chemistry model is used to determine parameters necessary to relate wind-shear induced turbulent energy dissipation rates to radar backscatter. The model is verified by comparison with electron density profiles measured by the EISCAT VHF radar. Observed radar signal strengths are found to be 2-3 orders of magnitude stronger than the maximum which can be expected from neutral turbulence alone, assuming that previously published results relating radar signal scatter to turbulence parameters, and turbulence parameters to wind shear, are correct. The possibility remains that some additional or alternative mechanism may be involved in producing PMWE, such as layers of charged dust/smoke particles or large cluster ions

Classifying States of a Finite Markov Chain with Membrane Computing

In this paper we present a method to classify the states of a finite Markov chain through membrane computing. A specific P system with external output is designed for each boolean matrix associated with a finite Markov chain. The computation of the system allows us to decide the convergence of the process because it determines in the environment the classification of the states (recurrent, absorbent, and transient) as well as the periods of states. The amount of resources required in the construction is polynomial in the number of states of the Markov chain.Ministerio de Ciencia y Educación TIN2005-09345-C04-01Junta de Andalucía TIC-58

Discrete approximations to vector spin models

We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretising continuous-spin models, and show that, except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions.Comment: 12 page

Waist circumference and a body shape index and prostate cancer risk and mortality.

We recently found a negative association between body mass index (BMI) and the risk of localised prostate cancer (PCa), no association with advanced PCa, and a positive association with PCa-specific mortality. In a 15% subpopulation of that study, we here investigated the measures of abdominal adiposity including waist circumference (WC) and A Body Shape Index (ABSI) in relation to PCa risk and mortality. We used data from 58,457 men from four Swedish cohorts to assess WC and ABSI in relation to PCa risk according to cancer risk category, including localised asymptomatic and symptomatic PCa and advanced PCa, and PCa-specific mortality. Cox regression models were used to calculate hazard ratios (HRs) and 95% confidence intervals (CIs). During, on average, 10 years of follow-up, 3290 men were diagnosed with PCa and 387 died of PCa. WC was negatively associated with the risk of total PCa (HR per 10 cm, 0.95; 95% CI 0.92-0.99), localised PCa (HR per 10 cm, 0.93, 95% CI 0.88-0.96) and localised asymptomatic PCa cases detected through a prostate-specific antigen (PSA) test (HR per 10 cm, 0.87, 95% CI 0.81-0.94). WC was not associated with the risk of advanced PCa (HR per 10 cm, 1.02, 95% CI 0.93-1.14) or with PCa-specific mortality (HR per 10 cm, 1.04, 95% CI 0.92-1.19). ABSI showed no associations with the risk of PCa or PCa-specific mortality. While the negative association between WC and the risk of localised PCa was partially driven by PSA-detected PCa cases, no association was found between abdominal adiposity and clinically manifest PCa in our population