On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

We consider the coupling from the past implementation of the random-cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector's problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process

Designing an intervention to help people with colorectal adenomas reduce their intake of red and processed meat and increase their levels of physical activity: a qualitative study

Background: most cases of colorectal cancer (CRC) arise from adenomatous polyps and malignant potential is greatest in high risk adenomas. There is convincing observational evidence that red and processed meat increase the risk of CRC and that higher levels of physical activity reduce the risk. However, no definitive randomised trial has demonstrated the benefit of behaviour change on reducing polyp recurrence and no consistent advice is currently offered to minimise patient risk. This qualitative study aimed to assess patients' preferences for dietary and physical activity interventions and ensure their appropriate and acceptable delivery to inform a feasibility trial.Methods: patients aged 60-74 included in the National Health Service Bowel Cancer Screening Programme (NHSBCSP) were selected from a patient tracking database. After a positive faecal occult blood test (FOBt), all had been diagnosed with an intermediate or high risk adenoma (I/HRA) at colonoscopy between April 2008 and April 2010. Interested patients and their partners were invited to attend a focus group or interview in July 2010. A topic guide, informed by the objectives of the study, was used. A thematic analysis was conducted in which transcripts were examined to ensure that all occurrences of each theme had been accounted for and compared.Results: two main themes emerged from the focus groups: a) experiences of having polyps and b) changing behaviour. Participants had not associated polyp removal with colorectal cancer and most did not remember being given any information or advice relating to this at the time. Heterogeneity of existing diet and physical activity levels was noted. There was a lack of readiness to change behaviour in many people in the target population.Conclusion: this study has demonstrated the difficulties involved in developing interventions to change dietary and physical activity behaviour in this population. The need to tailor the intervention to individuals, the lack of knowledge about the aetiology of colon cancer and the lack of motivation to change behaviour are critical factors

Search for Gravitational Waves from Primordial Black Hole Binary Coalescences in the Galactic Halo

We use data from the second science run of the LIGO gravitational-wave detectors to search for the gravitational waves from primordial black hole (PBH) binary coalescence with component masses in the range 0.2--$1.0 M_\odot$. The analysis requires a signal to be found in the data from both LIGO observatories, according to a set of coincidence criteria. No inspiral signals were found. Assuming a spherical halo with core radius 5 kpc extending to 50 kpc containing non-spinning black holes with masses in the range 0.2--$1.0 M_\odot$, we place an observational upper limit on the rate of PBH coalescence of 63 per year per Milky Way halo (MWH) with 90% confidence.Comment: 7 pages, 4 figures, to be submitted to Phys. Rev.

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

International audienceWe formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model