Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T2.33TC.

Hard thermal loop benchmark for the extraction of the nonperturbative QQ[over ¯] potential

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the Wilson loop. General arguments tell us that the lowest lying spectral peak encodes, through its position and shape, the real and imaginary parts of this complex potential. Here we benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. In other words, we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real and imaginary parts and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. Access to the full spectrum allows an investigation of spectral features that do not contribute to the potential but can pose a challenge to numerical attempts of an analytic continuation from imaginary time data. Differences in these contributions between the Wilson loop and gauge fixed Wilson line correlators are discussed. To better understand the difficulties in a numerical extraction we deploy the maximum entropy method with extended search space to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary parts are reproduced. Possible venues for improvement of the extraction strategy are discussed.

A new Bayesian approach to the reconstruction of spectral functions

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.

Timing of progression from Chlamydia trachomatis infection to pelvic inflammatory disease: a mathematical modelling study

Background Pelvic inflammatory disease (PID) results from the ascending spread of microorganisms from the vagina and endocervix to the upper genital tract. PID can lead to infertility, ectopic pregnancy and chronic pelvic pain. The timing of development of PID after the sexually transmitted bacterial infection Chlamydia trachomatis (chlamydia) might affect the impact of screening interventions, but is currently unknown. This study investigates three hypothetical processes for the timing of progression: at the start, at the end, or throughout the duration of chlamydia infection. Methods We develop a compartmental model that describes the trial structure of a published randomised controlled trial (RCT) and allows each of the three processes to be examined using the same model structure. The RCT estimated the effect of a single chlamydia screening test on the cumulative incidence of PID up to one year later. The fraction of chlamydia infected women who progress to PID is obtained for each hypothetical process by the maximum likelihood method using the results of the RCT. Results The predicted cumulative incidence of PID cases from all causes after one year depends on the fraction of chlamydia infected women that progresses to PID and on the type of progression. Progression at a constant rate from a chlamydia infection to PID or at the end of the infection was compatible with the findings of the RCT. The corresponding estimated fraction of chlamydia infected women that develops PID is 10% (95% confidence interval 7-13%) in both processes. Conclusions The findings of this study suggest that clinical PID can occur throughout the course of a chlamydia infection, which will leave a window of opportunity for screening to prevent PID.

Heritability of ambulatory and office blood pressure in the Swiss population

BACKGROUND Blood pressure (BP) is known to aggregate in families. Yet, heritability estimates are population-specific and no Swiss data have been published so far. We estimated the heritability of ambulatory and office BP in a Swiss population-based sample. METHODS The Swiss Kidney Project on Genes in Hypertension is a population-based family study focusing on BP genetics. Office and ambulatory BP were measured in 1009 individuals from 271 nuclear families. Heritability was estimated for SBP, DBP, and pulse pressure using a maximum likelihood method implanted in the Statistical Analysis in Genetic Epidemiology software. RESULTS The 518 women and 491 men included in this analysis had a mean (±SD) age of 48.3 (±17.4) and 47.3 (±17.7) years, and a mean BMI of 23.8 (±4.2) and 25.9 (±4.1) kg/m, respectively. Narrow-sense heritability estimates (±standard error) for ambulatory SBP, DBP, and pulse pressure were 0.37 ± 0.07, 0.26 ± 0.07, and 0.29 ± 0.07 for 24-h BP; 0.39 ± 0.07, 0.28 ± 0.07, and 0.27 ± 0.07 for day BP; and 0.25 ± 0.07, 0.20 ± 0.07, and 0.30 ± 0.07 for night BP, respectively (all P < 0.001). Heritability estimates for office SBP, DBP, and pulse pressure were 0.21 ± 0.08, 0.25 ± 0.08, and 0.18 ± 0.07 (all P < 0.01). CONCLUSIONS We found significant heritability estimates for both ambulatory and office BP in this Swiss population-based study. Our findings justify the ongoing search for the genetic determinants of BP.

Shallow Dialogue Processing Using Machine Learning Algorithms (or not)

This paper presents a shallow dialogue analysis model, aimed at human-human dialogues in the context of staff or business meetings. Four components of the model are defined, and several machine learning techniques are used to extract features from dialogue transcripts: maximum entropy classifiers for dialogue acts, latent semantic analysis for topic segmentation, or decision tree classifiers for discourse markers. A rule-based approach is proposed for solving cross-modal references to meeting documents. The methods are trained and evaluated thanks to a common data set and annotation format. The integration of the components into an automated shallow dialogue parser opens the way to multimodal meeting processing and retrieval applications.

Measuring Consumers' Willingness to Pay. Which Method fits best?

Gauging the maximum willingness to pay (WTP) of a product accurately is a critical success factor that determines not only market performance but also financial results. A number of approaches have therefore been developed to accurately estimate consumers’ willingness to pay. Here, four commonly used measurement approaches are compared using real purchase data as a benchmark. The relative strengths of each method are analyzed on the basis of statistical criteria and, more importantly, on their potential to predict managerially relevant criteria such as optimal price, quantity and profit. The results show a slight advantage of incentive-aligned approaches though the market settings need to be considered to choose the best-fitting procedure.

A reconstruction of atmospheric carbon dioxide and its stable carbon isotopic composition from the penultimate glacial maximum to the last glacial inception

The reconstruction of the stable carbon isotope evolution in atmospheric CO2 (δ13Catm), as archived in Antarctic ice cores, bears the potential to disentangle the contributions of the different carbon cycle fluxes causing past CO2 variations. Here we present a new record of δ13Catm before, during and after the Marine Isotope Stage 5.5 (155 000 to 105 000 yr BP). The dataset is archived on the data repository PANGEA® (www.pangea.de) under 10.1594/PANGAEA.817041. The record was derived with a well established sublimation method using ice from the EPICA Dome C (EDC) and the Talos Dome ice cores in East Antarctica. We find a 0.4‰ shift to heavier values between the mean δ13Catm level in the Penultimate (~ 140 000 yr BP) and Last Glacial Maximum (~ 22 000 yr BP), which can be explained by either (i) changes in the isotopic composition or (ii) intensity of the carbon input fluxes to the combined ocean/atmosphere carbon reservoir or (iii) by long-term peat buildup. Our isotopic data suggest that the carbon cycle evolution along Termination II and the subsequent interglacial was controlled by essentially the same processes as during the last 24 000 yr, but with different phasing and magnitudes. Furthermore, a 5000 yr lag in the CO2 decline relative to EDC temperatures is confirmed during the glacial inception at the end of MIS5.5 (120 000 yr BP). Based on our isotopic data this lag can be explained by terrestrial carbon release and carbonate compensation.

Quality Assessment and Enhancement Method for high-resolution Fourier-Domain OCT Imaging of Retina Laser Lesions

We present an image quality assessment and enhancement method for high-resolution Fourier-Domain OCT imaging like in sub-threshold retina therapy. A Maximum-Likelihood deconvolution algorithm as well as a histogram-based quality assessment method are evaluated.

Reliability of the cervical vertebrae maturation (CVM) method

OBJECTIVE To assess the reliability of the cervical vertebrae maturation method (CVM). BACKGROUND Skeletal maturity estimation can influence the manner and time of orthodontic treatment. The CVM method evaluates skeletal growth on the basis of the changes in the morphology of cervical vertebrae C2, C3, C4 during growth. These vertebrae are visible on a lateral cephalogram, so the method does not require an additional radiograph. METHODS In this website based study, 10 orthodontists with a long clinical practice (3 routinely using the method - "Routine user - RU" and 7 with less experience in the CVM method - "Non-Routine user - nonRU") rated twice cervical vertebrae maturation with the CVM method on 50 cropped scans of lateral cephalograms of children in circumpubertal age (for boys: 11.5 to 15.5 years; for girls: 10 to 14 years). Kappa statistics (with lower limits of 95% confidence intervals (CI)) and proportion of complete agreement on staging was used to evaluate intra- and inter-assessor agreement. RESULTS The mean weighted kappa for intra-assessor agreement was 0.44 (range: 0.30-0.64; range of lower limits of 95% CI: 0.12-0.48) and for inter-assessor agreement was 0.28 (range: -0.01-0.58; range of lower limits of 95% CI: -0.14-0.42). The mean proportion of identical scores assigned by the same assessor was 55.2 %(range: 44-74 %) and for different pairs of assessors was 42 % (range: 16-68 %). CONCLUSIONS The reliability of the CVM method is questionable and if orthodontic treatment should be initiated relative to the maximum growth, the use of additional biologic indicators should be considered (Tab. 4, Fig. 1, Ref. 24).