How good are your fits? Unbinned multivariate goodness-of-fit tests in high energy physics

Multivariate analyses play an important role in high energy physics. Such analyses often involve performing an unbinned maximum likelihood fit of a probability density function (p.d.f.) to the data. This paper explores a variety of unbinned methods for determining the goodness of fit of the p.d.f. to the data. The application and performance of each method is discussed in the context of a real-life high energy physics analysis (a Dalitz-plot analysis). Several of the methods presented in this paper can also be used for the non-parametric determination of whether two samples originate from the same parent p.d.f. This can be used, e.g., to determine the quality of a detector Monte Carlo simulation without the need for a parametric expression of the efficiency.Comment: 32 pages, 12 figure

Regulator constants and the parity conjecture

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of Gal(K^\infty/Q). We also give analogous results when K/Q is non-abelian, the base field is not Q and E is replaced by an abelian variety. The heart of the paper is a study of relations between permutation representations of finite groups, their "regulator constants", and compatibility between local root numbers and local Tamagawa numbers of abelian varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat

Percolation in Models of Thin Film Depositions

We have studied the percolation behaviour of deposits for different (2+1)-dimensional models of surface layer formation. The mixed model of deposition was used, where particles were deposited selectively according to the random (RD) and ballistic (BD) deposition rules. In the mixed one-component models with deposition of only conducting particles, the mean height of the percolation layer (measured in monolayers) grows continuously from 0.89832 for the pure RD model to 2.605 for the pure RD model, but the percolation transition belong to the same universality class, as in the 2- dimensional random percolation problem. In two- component models with deposition of conducting and isolating particles, the percolation layer height approaches infinity as concentration of the isolating particles becomes higher than some critical value. The crossover from 2d to 3d percolation was observed with increase of the percolation layer height.Comment: 4 pages, 5 figure

Chronic obstructive pulmonary disease and related phenotypes: polygenic risk scores in population-based and case-control cohorts

Background Genetic factors influence chronic obstructive pulmonary disease (COPD) risk, but the individual variants that have been identified have small effects. We hypothesised that a polygenic risk score using additional variants would predict COPD and associated phenotypes. Methods We constructed a polygenic risk score using a genome-wide association study of lung function (FEV1 and FEV1/forced vital capacity [FVC]) from the UK Biobank and SpiroMeta. We tested this polygenic risk score in nine cohorts of multiple ethnicities for an association with moderate-to-severe COPD (defined as FEV1/FVC <0·7 and FEV1 <80% of predicted). Associations were tested using logistic regression models, adjusting for age, sex, height, smoking pack-years, and principal components of genetic ancestry. We assessed predictive performance of models by area under the curve. In a subset of studies, we also studied quantitative and qualitative CT imaging phenotypes that reflect parenchymal and airway pathology, and patterns of reduced lung growth. Findings The polygenic risk score was associated with COPD in European (odds ratio [OR] per SD 1·81 [95% CI 1·74–1·88] and non-European (1·42 [1·34–1·51]) populations. Compared with the first decile, the tenth decile of the polygenic risk score was associated with COPD, with an OR of 7·99 (6·56–9·72) in European ancestry and 4·83 (3·45–6·77) in non-European ancestry cohorts. The polygenic risk score was superior to previously described genetic risk scores and, when combined with clinical risk factors (ie, age, sex, and smoking pack-years), showed improved prediction for COPD compared with a model comprising clinical risk factors alone (AUC 0·80 [0·79–0·81] vs 0·76 [0·75–0·76]). The polygenic risk score was associated with CT imaging phenotypes, including wall area percent, quantitative and qualitative measures of emphysema, local histogram emphysema patterns, and destructive emphysema subtypes. The polygenic risk score was associated with a reduced lung growth pattern. Interpretation A risk score comprised of genetic variants can identify a small subset of individuals at markedly increased risk for moderate-to-severe COPD, emphysema subtyp

Overlap of Genetic Risk between Interstitial Lung Abnormalities and Idiopathic Pulmonary Fibrosis

Rationale: Interstitial lung abnormalities (ILAs) are associated with the highest genetic risk locus for idiopathic pulmonary fibrosis (IPF); however, the extent to which there are unique associations among individuals with ILAs or additional overlap with IPF is not known.Objectives: To perform a genome-wide association study (GWAS) of ILAs.Methods: ILAs and a subpleural-predominant subtype were assessed on chest computed tomography (CT) scans in the AGES (Age Gene/Environment Susceptibility), COPDGene (Genetic Epidemiology of Chronic Obstructive Pulmonary Disease [COPD]), Framingham Heart, ECLIPSE (Evaluation of COPD Longitudinally to Identify Predictive Surrogate End-points), MESA (Multi-Ethnic Study of Atherosclerosis), and SPIROMICS (Subpopulations and Intermediate Outcome Measures in COPD Study) studies. We performed a GWAS of ILAs in each cohort and combined the results using a meta-analysis. We assessed for overlapping associations in independent GWASs of IPF.Measurements and Main Results: Genome-wide genotyping data were available for 1,699 individuals with ILAs and 10,274 control subjects. The MUC5B (mucin 5B) promoter variant rs35705950 was significantly associated with both ILAs (P = 2.6 × 10-27) and subpleural ILAs (P = 1.6 × 10-29). We discovered novel genome-wide associations near IPO11 (rs6886640, P = 3.8 × 10-8) and FCF1P3 (rs73199442, P = 4.8 × 10-8) with ILAs, and near HTRE1 (rs7744971, P = 4.2 × 10-8) with subpleural-predominant ILAs. These novel associations were not associated with IPF. Among 12 previously reported IPF GWAS loci, five (DPP9, DSP, FAM13A, IVD, and MUC5B) were significantly associated (P < 0.05/12) with ILAs.Conclusions: In a GWAS of ILAs in six studies, we confirmed the association with a MUC5B promoter variant and found strong evidence for an effect of previously described IPF loci; however, novel ILA associations were not associated with IPF. These findings highlight common genetically driven biologic pathways between ILAs and IPF, and also suggest distinct ones

CHEMISTRY AND MICROSTRUCTURE AT METAL-POLYMER INTERFACES

This paper summarizes the present knowledge of the chemistry and microstructure at metal-polymer interfaces formed on PMDA-ODA polyimide. The nature of chemical bonding was deduced from electronic structures observed by photoemission spectroscopies and interpreted by molecular orbital calculations. Bonding at the initial coverages of the metals studied are well described by the formation of metal-polymer complexes as a result of delocalized charge transfer from the metal to the polymer repeat unit. The microstructure was observed directly by transmission electron microscopy and ion scattering techniques. The morphology was found to be strongly dependent on the chemical reactivity of the interface. This correlation between chemistry and microstructure is important for understanding adhesion at the metal-polymer interface