Shape-dependent universality in percolation

The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic boundary conditions, which for example are generally introduced when triangular lattices are used in simulations.Comment: 11 pages, 3 figures, to be published in Physica

Excess number of percolation clusters on the surface of a sphere

Monte Carlo simulations were performed in order to determine the excess number of clusters b and the average density of clusters n_c for the two-dimensional "Swiss cheese" continuum percolation model on a planar L x L system and on the surface of a sphere. The excess number of clusters for the L x L system was confirmed to be a universal quantity with a value b = 0.8841 as previously predicted and verified only for lattice percolation. The excess number of clusters on the surface of a sphere was found to have the value b = 1.215(1) for discs with the same coverage as the flat critical system. Finally, the average critical density of clusters was calculated for continuum systems n_c = 0.0408(1).Comment: 13 pages, 2 figure

Automorphic properties of low energy string amplitudes in various dimensions

This paper explores the moduli-dependent coefficients of higher derivative interactions that appear in the low-energy expansion of the four-graviton amplitude of maximally supersymmetric string theory compactified on a d-torus. These automorphic functions are determined for terms up to order D^6R^4 and various values of d by imposing a variety of consistency conditions. They satisfy Laplace eigenvalue equations with or without source terms, whose solutions are given in terms of Eisenstein series, or more general automorphic functions, for certain parabolic subgroups of the relevant U-duality groups. The ultraviolet divergences of the corresponding supergravity field theory limits are encoded in various logarithms, although the string theory expressions are finite. This analysis includes intriguing representations of SL(d) and SO(d,d) Eisenstein series in terms of toroidally compactified one and two-loop string and supergravity amplitudes.Comment: 80 pages. 1 figure. v2:Typos corrected, footnotes amended and small clarifications. v3: minor corrections. Version to appear in Phys Rev

Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation

Extensive Monte-Carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three-dimensional percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices. Systems L x L x L' with L' >> L were studied for both bond (s.c., f.c.c., b.c.c.) and site (f.c.c.) percolation. The excess number of clusters $\tilde {b}$ per unit length was confirmed to be a universal quantity with a value $\tilde {b} \approx 0.412$. Likewise, the critical crossing probability in the L' direction, with periodic boundary conditions in the L x L plane, was found to follow a universal exponential decay as a function of r = L'/L for large r. Simulations were also carried out to find new precise values of the critical thresholds for site percolation on the f.c.c. and b.c.c. lattices, yielding $p_c(f.c.c.)= 0.199 236 5 \pm 0.000 001 0$, $p_c(b.c.c.)= 0.245 961 5\pm 0.000 001 0$.Comment: 14 pages, 7 figures, LaTeX, submitted to J. Phys. A: Math. Gen, added references, corrected typo

Universality of finite-size corrections to the number of critical percolation clusters

Monte-Carlo simulations on a variety of 2d percolating systems at criticality suggest that the excess number of clusters in finite systems over the bulk value of nc is a universal quantity, dependent upon the system shape but independent of the lattice and percolation type. Values of nc are found to high accuracy, and for bond percolation confirm the theoretical predictions of Temperley and Lieb, and Baxter, Temperley, and Ashley, which we have evaluated explicitly in terms of simple algebraic numbers. Predictions for the fluctuations are also verified for the first time.Comment: 13 pages, 2 figs., Latex, submitted to Phys. Rev. Let

Systematic, comprehensive, evidence-based approach to identify neuroprotective interventions for motor neuron disease: using systematic reviews to inform expert consensus

Objectives: Motor neuron disease (MND) is an incurable progressive neurodegenerative disease with limited treatment options. There is a pressing need for innovation in identifying therapies to take to clinical trial. Here, we detail a systematic and structured evidence-based approach to inform consensus decision making to select the first two drugs for evaluation in Motor Neuron Disease-Systematic Multi-arm Adaptive Randomised Trial (MND-SMART: NCT04302870), an adaptive platform trial. We aim to identify and prioritise candidate drugs which have the best available evidence for efficacy, acceptable safety profiles and are feasible for evaluation within the trial protocol. Methods: We conducted a two-stage systematic review to identify potential neuroprotective interventions. First, we reviewed clinical studies in MND, Alzheimer’s disease, Huntington’s disease, Parkinson’s disease and multiple sclerosis, identifying drugs described in at least one MND publication or publications in two or more other diseases. We scored and ranked drugs using a metric evaluating safety, efficacy, study size and study quality. In stage two, we reviewed efficacy of drugs in MND animal models, multicellular eukaryotic models and human induced pluripotent stem cell (iPSC) studies. An expert panel reviewed candidate drugs over two shortlisting rounds and a final selection round, considering the systematic review findings, late breaking evidence, mechanistic plausibility, safety, tolerability and feasibility of evaluation in MND-SMART. Results: From the clinical review, we identified 595 interventions. 66 drugs met our drug/disease logic. Of these, 22 drugs with supportive clinical and preclinical evidence were shortlisted at round 1. Seven drugs proceeded to round 2. The panel reached a consensus to evaluate memantine and trazodone as the first two arms of MND-SMART. Discussion: For future drug selection, we will incorporate automation tools, text-mining and machine learning techniques to the systematic reviews and consider data generated from other domains, including high-throughput phenotypic screening of human iPSCs

The impact of immediate breast reconstruction on the time to delivery of adjuvant therapy: the iBRA-2 study

Background: Immediate breast reconstruction (IBR) is routinely offered to improve quality-of-life for women requiring mastectomy, but there are concerns that more complex surgery may delay adjuvant oncological treatments and compromise long-term outcomes. High-quality evidence is lacking. The iBRA-2 study aimed to investigate the impact of IBR on time to adjuvant therapy. Methods: Consecutive women undergoing mastectomy ± IBR for breast cancer July–December, 2016 were included. Patient demographics, operative, oncological and complication data were collected. Time from last definitive cancer surgery to first adjuvant treatment for patients undergoing mastectomy ± IBR were compared and risk factors associated with delays explored. Results: A total of 2540 patients were recruited from 76 centres; 1008 (39.7%) underwent IBR (implant-only [n = 675, 26.6%]; pedicled flaps [n = 105,4.1%] and free-flaps [n = 228, 8.9%]). Complications requiring re-admission or re-operation were significantly more common in patients undergoing IBR than those receiving mastectomy. Adjuvant chemotherapy or radiotherapy was required by 1235 (48.6%) patients. No clinically significant differences were seen in time to adjuvant therapy between patient groups but major complications irrespective of surgery received were significantly associated with treatment delays. Conclusions: IBR does not result in clinically significant delays to adjuvant therapy, but post-operative complications are associated with treatment delays. Strategies to minimise complications, including careful patient selection, are required to improve outcomes for patients