Minor parties and independents in times of change: Scottish local elections 1974 to 2007

This article explores the electoral performance of minor party and Independent candidates in Scottish local elections from 1974 to 2007. This is a period which began with a major restructuring of local government and ended with a change in the electoral system from first-past-the-post to the single transferable vote. It encompasses a second restructuring in the 1990s, the consolidation of the Scottish National Party as an electoral force, and the creation of the Scottish Parliament. Throughout the period, while there have been ebbs and flows, Independents and minor parties have remained significant players in local electoral politics in Scotland

Structurally specific thermal fluctuations identify functional sites for DNA transcription

We report results showing that thermally-induced openings of double stranded DNA coincide with the location of functionally relevant sites for transcription. Investigating both viral and bacterial DNA gene promoter segments, we found that the most probable opening occurs at the transcription start site. Minor openings appear to be related to other regulatory sites. Our results suggest that coherent thermal fluctuations play an important role in the initiation of transcription. Essential elements of the dynamics, in addition to sequence specificity, are nonlinearity and entropy, provided by local base-pair constraints

SLE local martingales in logarithmic representations

A space of local martingales of SLE type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases not much is known about this representation. The purpose of this article is to exhibit examples of representations where L_0 is not diagonalizable - a phenomenon characteristic of logarithmic conformal field theory. Furthermore, we observe that the local martingales bear a close relation with the fusion product of the boundary changing fields. Our examples reproduce first of all many familiar logarithmic representations at certain rational values of the central charge. In particular we discuss the case of SLE(kappa=6) describing the exploration path in critical percolation, and its relation with the question of operator content of the appropriate conformal field theory of zero central charge. In this case one encounters logarithms in a probabilistically transparent way, through conditioning on a crossing event. But we also observe that some quite natural SLE variants exhibit logarithmic behavior at all values of kappa, thus at all central charges and not only at specific rational values.Comment: 40 pages, 7 figures. v3: completely rewritten, new title, new result

W-Extended Fusion Algebra of Critical Percolation

Two-dimensional critical percolation is the member LM(2,3) of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p'). We consider the continuum scaling limit of this lattice model as a `rational' logarithmic conformal field theory with extended W=W_{2,3} symmetry and use a lattice approach on a strip to study the fundamental fusion rules in this extended picture. We find that the representation content of the ensuing closed fusion algebra contains 26 W-indecomposable representations with 8 rank-1 representations, 14 rank-2 representations and 4 rank-3 representations. We identify these representations with suitable limits of Yang-Baxter integrable boundary conditions on the lattice and obtain their associated W-extended characters. The latter decompose as finite non-negative sums of W-irreducible characters of which 13 are required. Implementation of fusion on the lattice allows us to read off the fusion rules governing the fusion algebra of the 26 representations and to construct an explicit Cayley table. The closure of these representations among themselves under fusion is remarkable confirmation of the proposed extended symmetry.Comment: 30 page

Pain sensitivity and shoulder function among breast cancer survivors compared to matched controls: a case-control study

Objective Persistent pain and loss of shoulder function are common adverse effects to breast cancer treatment, but the extent of these issues in comparison with healthy controls is unclear for survivors beyond 1.5 years after treatment. The purpose of this study was to benchmark differences in pressure pain thresholds (PPT), maximal isokinetic muscle strength (MIMS), and active range of motion (ROM) of females with persistent pain ≥1.5 years after breast cancer treatment (BCS) compared with pain-free matched controls (CON), and examine the presence of movement-evoked pain (MEP) during assessment of MIMS. Methods The PPTs of 18 locations were assessed using a pressure algometer and a numeric rating scale was used to assess intensity of MEP. Active ROM and MIMS were measured using a universal goniometer and an isokinetic dynamometer, respectively. Results A two-way analysis of variance revealed that PPTs across all locations,MIMS for horizontal shoulder extension/flexion and shoulder adduction, active ROM for shoulder flexion, horizontal shoulder extension, shoulder abduction, and external shoulder rotation were significantly lower for BCS compared with CON (P < 0.05). MEP was significantly higher for BCS and MEP intensity had a significant, negative correlation with PPTs (P < 0.01). Discussion/conclusion BCS with persistent pain ≥1.5 years after treatment demonstrates widespread reductions in PPTs and movement-specific reductions inMIMS and active ROMof the affected shoulder, along with MEP during physical performance assessment. Implications for cancer survivors BCS with persistent pain ≥1.5 years after treatment shows signs of central sensitization andmay benefit from individualized rehabilitation.Danish Cancer Association R204-A1246

Solvable Critical Dense Polymers

A lattice model of critical dense polymers is solved exactly for finite strips. The model is the first member of the principal series of the recently introduced logarithmic minimal models. The key to the solution is a functional equation in the form of an inversion identity satisfied by the commuting double-row transfer matrices. This is established directly in the planar Temperley-Lieb algebra and holds independently of the space of link states on which the transfer matrices act. Different sectors are obtained by acting on link states with s-1 defects where s=1,2,3,... is an extended Kac label. The bulk and boundary free energies and finite-size corrections are obtained from the Euler-Maclaurin formula. The eigenvalues of the transfer matrix are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. This yields a selection rule for the physically relevant solutions to the inversion identity and explicit finitized characters for the associated quasi-rational representations. In particular, in the scaling limit, we confirm the central charge c=-2 and conformal weights Delta_s=((2-s)^2-1)/8 for s=1,2,3,.... We also discuss a diagrammatic implementation of fusion and show with examples how indecomposable representations arise. We examine the structure of these representations and present a conjecture for the general fusion rules within our framework.Comment: 35 pages, v2: comments and references adde

A spatial model of autocatalytic reactions

Biological cells with all of their surface structure and complex interior stripped away are essentially vesicles - membranes composed of lipid bilayers which form closed sacs. Vesicles are thought to be relevant as models of primitive protocells, and they could have provided the ideal environment for pre-biotic reactions to occur. In this paper, we investigate the stochastic dynamics of a set of autocatalytic reactions, within a spatially bounded domain, so as to mimic a primordial cell. The discreteness of the constituents of the autocatalytic reactions gives rise to large sustained oscillations, even when the number of constituents is quite large. These oscillations are spatio-temporal in nature, unlike those found in previous studies, which consisted only of temporal oscillations. We speculate that these oscillations may have a role in seeding membrane instabilities which lead to vesicle division. In this way synchronization could be achieved between protocell growth and the reproduction rate of the constituents (the protogenetic material) in simple protocells.Comment: Submitted to Phys. Rev.

Wind on the boundary for the Abelian sandpile model

We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge c=-2, by introducing two new boundary conditions. These have two unusual features: they carry an intrinsic orientation, and, more strangely, they cannot be imposed uniformly on a whole boundary (like the edge of a cylinder). They lead to seven new boundary condition changing fields, some of them being in highest weight representations (weights -1/8, 0 and 3/8), some others belonging to indecomposable representations with rank 2 Jordan cells (lowest weights 0 and 1). Their fusion algebra appears to be in full agreement with the fusion rules conjectured by Gaberdiel and Kausch.Comment: 26 pages, 4 figure

Phase diagram for diblock copolymer melts under cylindrical confinement

We extensively study the phase diagram of a diblock copolymer melt confined in a cylindrical nanopore using real-space self-consistent mean-field theory. We discover a rich variety of new two-dimensional equilibrium structures that have no analog in the unconfined system. These include non-hexagonally coordinated cylinder phases and structures intermediate between lamellae and cylinders. We map the stability regions and phase boundaries for all the structures we find. As the pore radius is decreased, the pore accommodates fewer cylindrical domains and structural transitions occur as cylinders are eliminated. Our results are consistent with experiments, but we also predict phases yet to be observed.Comment: 12 pages, 3 figures. submitted to Physical Review Letter