No abstract

Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend critically on the chosen contour. We present methods to optimize this contour using a combination of optimized, global complex shifts and a normalizing flow. They can lead to a significant gain in precision.

Twenty-four children with idiopathic absorptive hypercalciuria (IAH) and a control group (CG) of 11 healthy children were studied. Plasma 1,25-hydroxyvitamin D₃ (calcitriol), parathyroid hormone (PTH), calcium (Ca) and phosphate (P) levels were measured during dietary manipulation. The three diets analized were: (A) calcium-restrictive diet (400 mg/l.73 m²day) for 7 days; (B) supplemented diet (1,000 mg/l.73 m²day) for 3 days; (C) supplemented diet continued for 15 days. The IAH group had higher levels of serum calcitriol than the control group for all three diets. Serum calcitriol levels in the IAH group decreased in diet B compared to diet A, and returned to levels observed with diet A during diet C. Serum Ca, P and plasma PTH levels did not vary throughout the study in either group. In IAH, two subgroups were observed. In one, serum calcitriol levels were elevated and in the other, serum calcitriol levels were not different from the controls. This second group had a lower P and maximum rate of tubular reabsorption of phosphate per 100 ml of glomerular filtrate than the IAH group with elevated serum calcitriol levels and the control group. These results suggest that IAH in children may be related both to increased serum calcitriol levels and to an altered Tmp/GFR.

No abstract

We present the new release of pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The main new features consist of an automated way to perform expansions, based on the geometric approach to the method of expansion by regions, and a new algorithm to efficiently evaluate linear combinations of integrals as needed for the calculation of scattering amplitudes. The other new features are also summarised briefly.