A crossing probability for critical percolation in two dimensions

Langlands et al. considered two crossing probabilities, pi_h and pi_{hv}, in their extensive numerical investigations of critical percolation in two dimensions. Cardy was able to find the exact form of pi_h by treating it as a correlation function of boundary operators in the Q goes to 1 limit of the Q state Potts model. We extend his results to find an analogous formula for pi_{hv} which compares very well with the numerical results.Comment: 8 pages, Latex2e, 1 figure, uuencoded compressed tar file, (1 typo changed

Illustrating phallic worship: uses of material objects and the production of sexual knowledge in eighteenth-century antiquarianism and early twentieth-century sexual science

This is the final version of the article. Available from Taylor & Francis via the DOI in this record.This article reveals previously overlooked connections between eighteenth-century antiquarianism and early twentieth-century sexual science by presenting a comparative reading of two illustrated books: An Account of the Remains of the Worship of Priapus, by British antiquarian scholar Richard Payne Knight (1750–1824), and Die Weltreise eines Sexualforschers (The World Journey of a Sexologist), by German sexual scientist Magnus Hirschfeld (1868–1935). A close analysis of these publications demonstrates the special status of material artefacts and the strategic engagement with visual evidence in antiquarian and scientific writings about sex. Through its exploration of the similarities between antiquarian and sexual scientific thought, the article demonstrates the centrality of material culture to the production of sexual knowledge in the Western world. It also opens up new perspectives on Western intellectual history and on the intellectual origins of sexual science. While previous scholarship has traced the beginnings of sexual science back to nineteenth-century medical disciplines, this article shows that sexual scientists drew upon different forms of evidence and varied methodologies to produce sexual knowledge and secure scientific authority. As such, sexual science needs to be understood as a field with diverse intellectual roots that can be traced back (at least) to the eighteenth century.All authors gratefully acknowledge financial support from the Wellcome Trust [grant numbers NC110388, 106654/Z/14/Z and 106653/Z/14/Z]

On elliptic factors in real endoscopic transfer I

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series representations. It also reinterprets the Adams-Johnson transfer of certain nontempered representations via spectral analogues of the Langlands-Shelstad factors, thereby providing structure and transfer compatible with the associated transfer of orbital integrals. The results come from two simple tools introduced here. The first concerns a family of splittings of the algebraic group G under consideration; such a splitting is based on a fundamental maximal torus of G rather than a maximally split maximal torus. The second concerns a family of Levi groups attached to the dual data of a Langlands or an Arthur parameter for the group G. The introduced splittings provide explicit realizations of these Levi groups. The tools also apply to maps on stable conjugacy classes associated with the transfer of orbital integrals. In particular, they allow for a simpler version of the definitions of Kottwitz-Shelstad for twisted endoscopic transfer in certain critical cases. The paper prepares for spectral factors in twisted endoscopic transfer that are compatible in a certain sense with the standard factors discussed here. This compatibility is needed for Arthur's global theory. The twisted factors themselves will be defined in a separate paper.Comment: 48 pages, to appear in Progress in Mathematics, Volume 312, Birkha\"user. Also renumbering to match that of submitted versio

Critical Percolation in Finite Geometries

The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only under changes of scale, but also under mappings of the region which are conformal in the interior and continuous on the boundary. This is a larger invariance than that expected for generic critical systems. Specific predictions are presented for the crossing probability between opposite sides of a rectangle, and are compared with recent numerical work. The agreement is excellent.Comment: 10 page

Universality of the Crossing Probability for the Potts Model for q=1,2,3,4

The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for percolation $q=1$. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction $\pi_{hs}$ has universal form $\pi_{hs}=A(q) Q(z)$ for $q=1,2,3,4$ as a function of the scaling variable $z= [ b(q)L^{\frac{1}{\nu(q)}}(p-p_{c}(q,L)) ]^{\zeta(q)}$. Here, $p=1-\exp(-\beta)$ is the probability of a bond to be closed, $A(q)$ is the nonuniversal crossing amplitude, $b(q)$ is the nonuniversal metric factor, $\zeta(q)$ is the nonuniversal scaling index, $\nu(q)$ is the correlation length index. The universal function $Q(x) \simeq \exp(-z)$. Nonuniversal scaling factors were found numerically.Comment: 15 pages, 3 figures, revtex4b, (minor errors in text fixed, journal-ref added

Chir99021 and Valproic acid reduce the proliferative advantage of <i>Apc</i> mutant cells

Abstract More than 90% of colorectal cancers carry mutations in Apc that drive tumourigenesis. A 'just-right' signalling model proposes that Apc mutations stimulate optimal, but not excessive Wnt signalling, resulting in a growth advantage of Apc mutant over wild-type cells. Reversal of this growth advantage constitutes a potential therapeutic approach. We utilised intestinal organoids to compare the growth of Apc mutant and wild-type cells. Organoids derived from Apc Min/+ mice recapitulate stages of intestinal polyposis in culture. They eventually form spherical cysts that reflect the competitive growth advantage of cells that have undergone loss of heterozygosity (LOH). We discovered that this emergence of cysts was inhibited by Chiron99021 and Valproic acid, which potentiates Wnt signalling. Chiron99021 and Valproic acid restrict the growth advantage of Apc mutant cells while stimulating that of wild-type cells, suggesting that excessive Wnt signalling reduces the relative fitness of Apc mutant cells. As a proof of concept, we demonstrated that Chiron99021-treated Apc mutant organoids were rendered susceptible to TSA-induced apoptosis, while wild-type cells were protected

Evaluation of a disease specific rheumatoid arthritis self-management education program, a single group repeated measures study

Background: Rheumatoid Arthritis is a progressive and disabling disease, predicted to increase in prevalence over the next 50 years. Self-management is acknowledged as an integral part in the management of chronic disease. The rheumatoid arthritis specific self-management program delivered by health professionals was developed by Arthritis Western Australia in 2006. The purpose of this study was to determine whether this program would achieve early benefits in health related outcomes, and whether these improvements would be maintained for 12 months. Methods: Individuals with rheumatoid arthritis were referred from rheumatologists. Participants with co-existing inflammatory musculoskeletal conditions were excluded. All participants completed a 6-week program. Assessments occurred at baseline (8 weeks prior to intervention), pre-intervention, post-intervention, and 6 and 12 month follow ups. Outcomes measured included pain and fatigue (numerical rating scale, 0-10), depression and anxiety (hospital anxiety and depression questionnaire), health distress, and quality of life (SF-36 version 2). Results: There were significant improvements in mean [SD] fatigue (5.7 [2.4] to 5.1 [2.6]), depression (6.3 [4.3] to 5.6 [3.9]) and SF-36 mental health (44.5 [11.1] to 46.5 [9.5]) immediately following intervention, with long term benefits for depression (6.3 [4.3] to 4.9 [3.9]), and SF-36 subscales mental health (44.5 [11.1] to 47.8 [10.9]), role emotional (41.5 [13.2] to 46.5 [11.8]), role physical (35.0 [11.0] to 40.2 [12.1]) and physical function (34.8 [11.5] to 38.6 [10.7]). Conclusion: Participants in the program recorded significant improvements in depression and mental health post-intervention, which were maintained to 12 months follow up

Statistical properties of the low-temperature conductance peak-heights for Corbino discs in the quantum Hall regime

A recent theory has provided a possible explanation for the ``non-universal scaling'' of the low-temperature conductance (and conductivity) peak-heights of two-dimensional electron systems in the integer and fractional quantum Hall regimes. This explanation is based on the hypothesis that samples which show this behavior contain density inhomogeneities. Theory then relates the non-universal conductance peak-heights to the ``number of alternating percolation clusters'' of a continuum percolation model defined on the spatially-varying local carrier density. We discuss the statistical properties of the number of alternating percolation clusters for Corbino disc samples characterized by random density fluctuations which have a correlation length small compared to the sample size. This allows a determination of the statistical properties of the low-temperature conductance peak-heights of such samples. We focus on a range of filling fraction at the center of the plateau transition for which the percolation model may be considered to be critical. We appeal to conformal invariance of critical percolation and argue that the properties of interest are directly related to the corresponding quantities calculated numerically for bond-percolation on a cylinder. Our results allow a lower bound to be placed on the non-universal conductance peak-heights, and we compare these results with recent experimental measurements.Comment: 7 pages, 4 postscript figures included. Revtex with epsf.tex and multicol.sty. The revised version contains some additional discussion of the theory and slightly improved numerical result

The Tails of the Crossing Probability

The scaling of the tails of the probability of a system to percolate only in the horizontal direction $\pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails of the crossing probability far from the critical point have shape $\pi_{hs}(p) \simeq D \exp(c L[p-p_{c}]^{\nu})$ where $\nu$ is the correlation length index, $p=1-\exp(-\beta)$ is the probability of a bond to be closed. At criticality we observe crossover to another scaling $\pi_{hs}(p) \simeq A \exp (-b {L [p-p_{c}]^{\nu}}^{z})$. Here $z$ is a scaling index describing the central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical change