Quasi-Monte Carlo rules for numerical integration over the unit sphere S2\mathbb{S}^2

We study numerical integration on the unit sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by lifting a $(0,m,2)$-net given in the unit square $[0,1]^2$ to the sphere $\mathbb{S}^2$ by means of an area preserving map. A similar approach has previously been suggested by Cui and Freeden [SIAM J. Sci. Comput. 18 (1997), no. 2]. We prove three results. The first one is that the construction is (almost) optimal with respect to discrepancies based on spherical rectangles. Further we prove that the point set is asymptotically uniformly distributed on $\mathbb{S}^2$. And finally, we prove an upper bound on the spherical cap $L_2$-discrepancy of order $N^{-1/2} (\log N)^{1/2}$ (where $N$ denotes the number of points). This slightly improves upon the bound on the spherical cap $L_2$-discrepancy of the construction by Lubotzky, Phillips and Sarnak [Comm. Pure Appl. Math. 39 (1986), 149--186]. Numerical results suggest that the $(0,m,2)$-nets lifted to the sphere $\mathbb{S}^2$ have spherical cap $L_2$-discrepancy converging with the optimal order of $N^{-3/4}$

Initial presenting manifestations in 16,486 patients with inborn errors of immunity include infections and noninfectious manifestations

Background: Inborn errors of immunity (IEI) are rare diseases, which makes diagnosis a challenge. A better description of the initial presenting manifestations should improve awareness and avoid diagnostic delay. Although increased infection susceptibility is a well-known initial IEI manifestation, less is known about the frequency of other presenting manifestations. Objective: We sought to analyze age-related initial presenting manifestations of IEI including different IEI disease cohorts. Methods: We analyzed data on 16,486 patients of the European Society for Immunodeficiencies Registry. Patients with autoinflammatory diseases were excluded because of the limited number registered. Results: Overall, 68% of patients initially presented with infections only, 9% with immune dysregulation only, and 9% with a combination of both. Syndromic features were the presenting feature in 12%, 4% had laboratory abnormalities only, 1.5% were diagnosed because of family history only, and 0.8% presented with malignancy. Two-third of patients with IEI presented before the age of 6 years, but a quarter of patients developed initial symptoms only as adults. Immune dysregulation was most frequently recognized as an initial IEI manifestation between age 6 and 25 years, with male predominance until age 10 years, shifting to female predominance after age 40 years. Infections were most prevalent as a first manifestation in patients presenting after age 30 years. Conclusions: An exclusive focus on infection-centered warning signs would have missed around 25% of patients with IEI who initially present with other manifestations. (J Allergy Clin Immunol 2021;148:1332-41.

Measuring KS0K± interactions using Pb–Pb collisions at √sNN=2.76 TeV

We present the first ever measurements of femtoscopic correlations between the K0 S and K± particles. The analysis was performed on the data from Pb–Pb collisions at √sNN = 2.76 TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding via the a0(980) resonance. The extracted kaon source radius and correlation strength parameters for K0 SK− are found to be equal within the experimental uncertainties to those for K0 SK+. Comparing the results of the present study with those from published identical-kaon femtoscopic studies by ALICE, mass and coupling parameters for the a0 resonance are tested. Our results are also compatible with the interpretation of the a0 having a tetraquark structure instead of that of a diquar