Fractional Exclusion Statistics and Anyons

Do anyons, dynamically realized by the field theoretic Chern-Simons construction, obey fractional exclusion statistics? We find that they do if the statistical interaction between anyons and anti-anyons is taken into account. For this anyon model, we show perturbatively that the exchange statistical parameter of anyons is equal to the exclusion statistical parameter. We obtain the same result by applying the relation between the exclusion statistical parameter and the second virial coefficient in the non-relativistic limit.Comment: 9 pages, latex, IFT-498-UN

Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

An Evaluation of the Fe-N Phase Diagram Considering Long-Range Order of N Atoms in γ'-Fe4N1-x and ε-Fe2N1-z

The chemical potential of nitrogen was described as a function of nitrogen content for the Fe-N phases α-Fe[N], γ'-Fe4N1-x, and ε-Fe2N1-z. For α-Fe[N], an ideal, random distribution of the nitrogen atoms over the octahedral interstices of the bcc iron lattice was assumed; for γ'-Fe4N1-x and ε-Fe2N1-z, the occurrence of a long-range ordered distribution of the nitrogen atoms over the octahedral interstices of the close packed iron sublattices (fcc and hcp, respectively) was taken into account. The theoretical expressions were fitted to nitrogen-absorption isotherm data for the three Fe-N phases. The α/α + γ', α + γ'/γ', γ'/γ' + ε, and γ' + ε/ε phase boundaries in the Fe-N phase diagram were calculated from combining the quantitative descriptions for the absorption isotherms with the known composition of NH3/H2 gas mixtures in equilibrium with coexisting α and γ' phases and in equilibrium with coexisting γ' and ε phases. Comparison of the present phase boundaries with experimental data and previously calculated phase boundaries showed a major improvement as compared to the previously calculated Fe-N phase diagrams, where long-range order for the nitrogen atoms in the γ' and ε phases was not accounted for

Nutrition for the ageing brain: towards evidence for an optimal diet

As people age they become increasingly susceptible to chronic and extremely debilitating brain diseases. The precise cause of the neuronal degeneration underlying these disorders, and indeed normal brain ageing remains however elusive. Considering the limits of existing preventive methods, there is a desire to develop effective and safe strategies. Growing preclinical and clinical research in healthy individuals or at the early stage of cognitive decline has demonstrated the beneficial impact of nutrition on cognitive functions. The present review is the most recent in a series produced by the Nutrition and Mental Performance Task Force under the auspice of the International Life Sciences Institute Europe (ILSI Europe). The latest scientific advances specific to how dietary nutrients and non-nutrient may affect cognitive ageing are presented. Furthermore, several key points related to mechanisms contributing to brain ageing, pathological conditions affecting brain function, and brain biomarkers are also discussed. Overall, findings are inconsistent and fragmented and more research is warranted to determine the underlying mechanisms and to establish dose-response relationships for optimal brain maintenance in different population subgroups. Such approaches are likely to provide the necessary evidence to develop research portfolios that will inform about new dietary recommendations on how to prevent cognitive decline

Gene × dietary pattern interactions in obesity: Analysis of up to 68 317 adults of European ancestry

Obesity is highly heritable. Genetic variants showing robust associations with obesity traits have been identified through genome-wide association studies. We investigated whether a composite score representing healthy diet modifies associations of these variants with obesity traits. Totally, 32 body mass index (BMI)- and 14 waist-hip ratio (WHR)-associated single nucleotide polymorphisms were genotyped, and genetic risk scores (GRS) were calculated in 18 cohorts of European ancestry (n = 68 317). Diet score was calculated based on self-reported intakes of whole grains, fish, fruits, vegetables, nuts/seeds (favorable) and red/processed meats, sweets, sugar-sweetened beverages and fried potatoes (unfavorable). Multivariable adjusted, linear regression within each cohort followed by inverse variance-weighted, fixed-effects meta-analysis was used to characterize: (a) associations of each GR

A case-only study to identify genetic modifiers of breast cancer risk for BRCA1/BRCA2 mutation carriers

Breast cancer (BC) risk for BRCA1 and BRCA2 mutation carriers varies by genetic and familial factors. About 50 common variants have been shown to modify BC risk for mutation carriers. All but three, were identified in general population studies. Other mutation carrier-specific susceptibility variants may exist but studies of mutation carriers have so far been underpowered. We conduct a novel case-only genome-wide association study comparing genotype frequencies between 60,212 general population BC cases and 13,007 cases with BRCA1 or BRCA2 mutations. We identify robust novel associations for 2 variants with BC for BRCA1 and 3 for BRCA2 mutation carriers, P < 10−8, at 5 loci, which are not associated with risk in the general population. They include rs60882887 at 11p11.2 where MADD, SP11 and EIF1, genes previously implicated in BC biology, are predicted as potential targets. These findings will contribute towards customising BC polygenic risk scores for BRCA1 and BRCA2 mutation carriers

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Generating Random Polygons with Given Vertices

The problem of generating &quot;random&quot; geometric objects is motivated by the need to generate test instances for geometric algorithms. We examine the specific problem of generating a random x-monotone polygon on a given set of n vertices. Here, &quot;random&quot; is taken to mean that we select uniformly at random a polygon, from among all those x-monotone polygons having the given n vertices. We give an algorithm that generates a random monotone polygon in O(n) time and space after O(K) preprocessing time, where n ! K ! n 2 is the number of edges of the visibility graph of the x-monotone chain of the given vertex set. We also give an O(n 3 ) time algorithm for generating a random convex polygon whose vertices are a subset of a given set of n points. Finally, we discuss some further extensions, as well as the challenging open problem of generating random simple polygons. &quot;Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.&quot; --- John v..

Approximating Polygons and Subdivisions with Minimum-Link Paths

We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate objects with the minimum number of line segments, or with near the minimum, by using efficient greedy algorithms. We give some variants that have linear or O(n log n) algorithms approximating polygonal chains of n segments. We also show that approximating subdivisions and approximating with chains with no self-intersections are NP-hard