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.

Quasi-Self-Dual Exponential Lévy Processes

The important application of semistatic hedging in financial markets naturally leads to the notion of quasi--self-dual processes. The focus of our study is to give new characterizations of quasi--self-duality. We analyze quasi--self-dual Lévy driven markets which do not admit arbitrage opportunities and derive a set of equivalent conditions for the stochastic logarithm of quasi--self-dual martingale models. Since for nonvanishing order parameter two martingale properties have to be satisfied simultaneously, there is a nontrivial relation between the order and shift parameter representing carrying costs in financial applications. This leads to an equation containing an integral term which has to be inverted in applications. We first discuss several important properties of this equation and, for some well-known Lévy-driven models, we derive a family of closed-form inversion formulae.

Using 18O/2H, 3H/3He, 85Kr and CFCs to determine mean residence times and water origin in the Grazer and Leibnitzer Feld groundwater bodies (Austria)

Two groundwater bodies, Grazer Feld and Leibnitzer Feld, with surface areas of 166 and 103 km2 respectively are characterised for the first time by measuring the combination of d18O/d2H, 3H/3He, 85Kr, CFC-11, CFC-12 and hydrochemistry in 34 monitoring wells in 2009/2010. The timescales of groundwater recharge have been characterised by 131 d18O measurements of well and surface water sampled on a seasonal basis. Most monitoring wells show a seasonal variation or indicate variable contributions of the main river Mur (0–30%, max. 70%) and/or other rivers having their recharge areas in higher altitudes. Combined d18O/d2H-measurements indicate that 65–75% of groundwater recharge in the unusual wet year of 2009 was from precipitation in the summer based on values from the Graz meteorological station. Monitoring wells downstream of gravel pit lakes show a clear evaporation trend. A boron–nitrate differentiation plot shows more frequent boron-rich water in the more urbanised Grazer Feld and more frequent nitrate-rich water in the more agricultural used Leibnitzer Feld indicating that a some of the nitrate load in the Grazer Feld comes from urban sewer water. Several lumped parameter models based on tritium input data from Graz and monthly data from the river Mur (Spielfeld) since 1977 yield a Mean Residence Time (MRT) for the Mur-water itself between 3 and 4 years in this area. Data from d18O, 3H/3He measurements at the Wagna lysimeter station supports the conclusion that 90% of the groundwaters in the Grazer Feld and 73% in the Leibnitzer Feld have MRTs of <5 years. Only in a few groundwaters were MRTs of 6–10 or 11–25 years as a result of either a long-distance water inflow in the basins or due to longer flow path in somewhat deeper wells (>20 m) with relative thicker unsaturated zones. The young MRT of groundwater from two monitoring wells in the Leibnitzer Feld was confirmed by 85Kr-measurements. Most CFC-11 and CFC-12 concentrations in the groundwater exceed the equilibration concentrations of modern concentrations in water and are therefore unsuitable for dating purposes. An enrichment factor up to 100 compared to atmospheric equilibrium concentrations and the obvious correlation of CFC-12 with SO4, Na, Cl and B in the ground waters of the Grazer Feld suggest that waste water in contact with CFC-containing material above and below ground is the source for the contamination. The dominance of very young groundwater (<5 years) indicates a recent origin of the contamination by nitrate and many other components observed in parts of the groundwater bodies. Rapid measures to reduce those sources are needed to mitigate against further deterioration of these waters.

Forcing for hat inductive definitions in arithmetic

By forcing, we give a direct interpretation of inline image into Avigad's inline image. To the best of the author's knowledge, this is one of the simplest applications of forcing to “real problems”.