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.

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.

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.

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.

Colonization history of the Swiss Rhine basin by the bullhead (Cottus gobio): inference under a Bayesian spatially explicit framework

The present distribution of freshwater fish in the Alpine region has been strongly affected by colonization events occurring after the last glacial maximum (LGM), some 20,000 years ago. We use here a spatially explicit simulation framework to model and better understand their colonization dynamics in the Swiss Rhine basin. This approach is applied to the European bullhead (Cottus gobio), which is an ideal model organism to study fish past demographic processes since it has not been managed by humans. The molecular diversity of eight sampled populations is simulated and compared to observed data at six microsatellite loci under an approximate Bayesian computation framework to estimate the parameters of the colonization process. Our demographic estimates fit well with current knowledge about the biology of this species, but they suggest that the Swiss Rhine basin was colonized very recently, after the Younger Dryas some 6600 years ago. We discuss the implication of this result, as well as the strengths and limits of the spatially explicit approach coupled to the approximate Bayesian computation framework.

Biodiversity effects on nitrate concentrations in soil solution: a Bayesian model

Ecosystems are faced with high rates of species loss which has consequences for their functions and services. To assess the effects of plant species diversity on the nitrogen (N) cycle, we developed a model for monthly mean nitrate (NO3-N) concentrations in soil solution in 0-30 cm mineral soil depth using plant species and functional group richness and functional composition as drivers and assessing the effects of conversion of arable land to grassland, spatially heterogeneous soil properties, and climate. We used monthly mean NO3-N concentrations from 62 plots of a grassland plant diversity experiment from 2003 to 2006. Plant species richness (1-60) and functional group composition (1-4 functional groups: legumes, grasses, non-leguminous tall herbs, non-leguminous small herbs) were manipulated in a factorial design. Plant community composition, time since conversion from arable land to grassland, soil texture, and climate data (precipitation, soil moisture, air and soil temperature) were used to develop one general Bayesian multiple regression model for the 62 plots to allow an in-depth evaluation using the experimental design. The model simulated NO3-N concentrations with an overall Bayesian coefficient of determination of 0.48. The temporal course of NO3-N concentrations was simulated differently well for the individual plots with a maximum plot-specific Nash-Sutcliffe Efficiency of 0.57. The model shows that NO3-N concentrations decrease with species richness, but this relation reverses if more than approx. 25 % of legume species are included in the mixture. Presence of legumes increases and presence of grasses decreases NO3-N concentrations compared to mixtures containing only small and tall herbs. Altogether, our model shows that there is a strong influence of plant community composition on NO3-N concentrations.