Approximating the monomer-dimer constants through matrix permanent

The monomer-dimer model is fundamental in statistical mechanics. However, it is #P-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is proposed in this paper, by transforming the number of all matchings of a bipartite graph into the number of perfect matchings of an extended bipartite graph, which can be given by a matrix permanent. Sequential importance sampling algorithm is applied to compute the permanents. For two-dimensional lattice with periodic condition, we obtain $0.6627\pm0.0002$, where the exact value is $h_2=0.662798972834$. For three-dimensional lattice with periodic condition, our numerical result is $0.7847\pm0.0014$, {which agrees with the best known bound $0.7653 \leq h_3 \leq 0.7862$.}Comment: 6 pages, 2 figure

Shear-induced reaction-limited aggregation kinetics of Brownian particles at arbitrary concentrations

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the range considered. By generalizing Kramers' rate theory to the presence of collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration

Universal scaling behavior at the upper critical dimension of non-equilibrium continuous phase transitions

In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of the upper critical dimension. We apply our method to a non-equilibrium continuous phase transition. But focusing on the equation of state of the phase transition it is easy to extend our analysis to all equilibrium and non-equilibrium phase transitions observed numerically or experimentally.Comment: 4 pages, 3 figure

An investigation of standard thermodynamic quantities as determined via models of nuclear multifragmentation

Both simple and sophisticated models are frequently used in an attempt to understand how real nuclei breakup when subjected to large excitation energies, a process known as nuclear multifragmentation. Many of these models assume equilibriumthermodynamics and produce results often interpreted as evidence of a phase transition. This work examines one class of models and employs standard thermodynamical procedure to explore the possible existence and nature of a phase transition. The role of various terms, e.g. Coulomb and surface energy, is discussed.Comment: 19 two-column format pages with 24 figure

The liquid to vapor phase transition in excited nuclei

For many years it has been speculated that excited nuclei would undergo a liquid to vapor phase transition. For even longer, it has been known that clusterization in a vapor carries direct information on the liquid- vapor equilibrium according to Fisher's droplet model. Now the thermal component of the 8 GeV/c pion + 197Au multifragmentation data of the ISiS Collaboration is shown to follow the scaling predicted by Fisher's model, thus providing the strongest evidence yet of the liquid to vapor phase transition.Comment: four pages, four figures, first two in color (corrected typo in Ref. [26], corrected error in Fig. 4

Education and myopia: assessing the direction of causality by mendelian randomisation

Objectives To determine whether more years spent in education is a causal risk factor for myopia, or whether myopia is a causal risk factor for more years in education. Design Bidirectional, two sample mendelian randomisation study. Setting Publically available genetic data from two consortiums applied to a large, independent population cohort. Genetic variants used as proxies for myopia and years of education were derived from two large genome wide association studies: 23andMe and Social Science Genetic Association Consortium (SSGAC), respectively. Participants 67 798 men and women from England, Scotland, and Wales in the UK Biobank cohort with available information for years of completed education and refractive error. Main outcome measures Mendelian randomisation analyses were performed in two directions: the first exposure was the genetic predisposition to myopia, measured with 44 genetic variants strongly associated with myopia in 23andMe, and the outcome was years in education; and the second exposure was the genetic predisposition to higher levels of education, measured with 69 genetic variants from SSGAC, and the outcome was refractive error. Results Conventional regression analyses of the observational data suggested that every additional year of education was associated with a more myopic refractive error of −0.18 dioptres/y (95% confidence interval −0.19 to −0.17; P<2e-16). Mendelian randomisation analyses suggested the true causal effect was even stronger: −0.27 dioptres/y (−0.37 to −0.17; P=4e-8). By contrast, there was little evidence to suggest myopia affected education (years in education per dioptre of refractive error −0.008 y/dioptre, 95% confidence interval −0.041 to 0.025, P=0.6). Thus, the cumulative effect of more years in education on refractive error means that a university graduate from the United Kingdom with 17 years of education would, on average, be at least −1 dioptre more myopic than someone who left school at age 16 (with 12 years of education). Myopia of this magnitude would be sufficient to necessitate the use of glasses for driving. Sensitivity analyses showed minimal evidence for genetic confounding that could have biased the causal effect estimates. Conclusions This study shows that exposure to more years in education contributes to the rising prevalence of myopia. Increasing the length of time spent in education may inadvertently increase the prevalence of myopia and potential future visual disability

Spin-transfer in an open ferromagnetic layer: from negative damping to effective temperature

Spin-transfer is a typical spintronics effect that allows a ferromagnetic layer to be switched by spin-injection. Most of the experimental results about spin transfer are described on the basis of the Landau-Lifshitz-Gilbert equation of the magnetization, in which additional current-dependent damping factors are added, and can be positive or negative. The origin of the damping can be investigated further by performing stochastic experiments, like one shot relaxation experiments under spin-injection in the activation regime of the magnetization. In this regime, the N\'eel-Brown activation law is observed which leads to the introduction of a current-dependent effective temperature. In order to justify the introduction of these counterintuitive parameters (effective temperature and negative damping), a detailed thermokinetic analysis of the different sub-systems involved is performed. We propose a thermokinetic description of the different forms of energy exchanged between the electric and the ferromagnetic sub-systems at a Normal/Ferromagnetic junction. The corresponding Fokker Planck equations, including relaxations, are derived. The damping coefficients are studied in terms of Onsager-Casimir transport coefficients, with the help of the reciprocity relations. The effective temperature is deduced in the activation regime.Comment: 65 pages, 10 figure

The postulates of gravitational thermodynamics

The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.Comment: 28 pages, Revtex, no figures. An important sentence and several minor corrections included. To appear in Physical Review

A Datasheet for the INSIGHT Birmingham, Solihull, and Black Country Diabetic Retinopathy Screening Dataset

Purpose: Diabetic retinopathy (DR) is the most common microvascular complication associated with diabetes mellitus (DM), affecting approximately 40% of this patient population. Early detection of DR is vital to ensure monitoring of disease progression and prompt sight saving treatments as required. This article describes the data contained within the INSIGHT Birmingham, Solihull, and Black Country Diabetic Retinopathy Dataset. / Design: Dataset descriptor for routinely collected eye screening data. / Participants: All diabetic patients aged 12 years and older, attending annual digital retinal photography-based screening within the Birmingham, Solihull, and Black Country Eye Screening Programme. / Methods: The INSIGHT Health Data Research Hub for Eye Health is a National Health Service (NHS)–led ophthalmic bioresource that provides researchers with safe access to anonymized, routinely collected data from contributing NHS hospitals to advance research for patient benefit. This report describes the INSIGHT Birmingham, Solihull, and Black Country DR Screening Dataset, a dataset of anonymized images and linked screening data derived from the United Kingdom's largest regional DR screening program. / Main Outcome Measures: This dataset consists of routinely collected data from the eye screening program. The data primarily include retinal photographs with the associated DR grading data. Additional data such as corresponding demographic details, information regarding patients’ diabetic status, and visual acuity data are also available. Further details regarding available data points are available in the supplementary information, in addition to the INSIGHT webpage included below. / Results: At the time point of this analysis (December 31, 2019), the dataset comprised 6 202 161 images from 246 180 patients, with a dataset inception date of January 1, 2007. The dataset includes 1 360 547 grading episodes between R0M0 and R3M1. / Conclusions: This dataset descriptor article summarizes the content of the dataset, how it has been curated, and what its potential uses are. Data are available through a structured application process for research studies that support discovery, clinical evidence analyses, and innovation in artificial intelligence technologies for patient benefit. Further information regarding the data repository and contact details can be found at https://www.insight.hdrhub.org/