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.

Reduced bone breakage and increased bone strength in free range laying hens fed omega-3 polyunsaturated fatty acid supplemented diets

INTRODUCTION The omega-3 and omega-6 polyunsaturated fatty acids (PUFAs) are the immediate precursors to a number of important mediators of immunity, inflammation and bone function, with products of omega-6 generally thought to promote inflammation and favour bone resorption. Western diets generally provide a 10 to 20-fold deficit in omega-3 PUFAs compared with omega-6, and this is thought to have contributed to the marked rise in incidence of disorders of modern human societies, such as heart disease, colitis and perhaps osteoporosis. Many of our food production animals, fed on grains rich in omega-6, are also exposed to a dietary deficit in omega-3, with perhaps similar health consequences. Bone fragility due to osteoporotic changes in laying hens is a major economic and welfare problem, with our recent estimates of breakage rates indicating up to 95% of free range hens suffer breaks during lay. METHODS Free range hens housed in full scale commercial systems were provided diets supplemented with omega-3 alpha linolenic acid, and the skeletal benefits were investigated by comparison to standard diets rich in omega-6. RESULTS There was a significant 40-60% reduction in keel bone breakage rate, and a corresponding reduction in breakage severity in the omega-3 supplemented hens. There was significantly greater bone density and bone mineral content, alongside increases in total bone and trabecular volumes. The mechanical properties of the omega-3 supplemented hens were improved, with strength, energy to break and stiffness demonstrating significant increases. Alkaline phosphatase (an osteoblast marker) and tartrate-resistant acid phosphatase (an osteoclast marker) both showed significant increases with the omega-3 diets, indicating enhanced bone turnover. This was corroborated by the significantly lower levels of the mature collagen crosslinks, hydroxylysyl pyridinoline, lysyl pyridinoline and histidinohydroxy-lysinonorleucine, with a corresponding significant shift in the mature:immature crosslink ratio. CONCLUSIONS The improved skeletal health in laying hens corresponds to as many as 68million fewer hens suffering keel fractures in the EU each year. The biomechanical and biochemical evidence suggests that increased bone turnover has enhanced the bone mechanical properties, and that this may suggest potential benefits for human osteoporosis.

Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.