Billiards, scattering by rough obstacles, and optimal mass transportation

This article presents a brief exposition of recent results of the author on billiard scattering by rough obstacles. We define the notion of a rough body and give a characterization of scattering by rough bodies. Then we define the resistance of a rough body; it can be interpreted as the aerodynamic resistance of the somersaulting body moving through a rarefied medium. We solve the problems of maximum and minimum resistance for rough bodies (more precisely, for bodies obtained by roughening a prescribed convex set) in arbitrary dimension. Surprisingly, these problems are reduced to special problems of optimal mass transportation on the sphere

Measurement of the electron reconstruction efficiency at LHCb

The single electron track-reconstruction efficiency is calibrated using a sample corresponding to 1.3 fb−1 of pp collision data recorded with the LHCb detector in 2017. This measurement exploits B+→ J/ψ(e+e−)K+ decays, where one of the electrons is fully reconstructed and paired with the kaon, while the other electron is reconstructed using only the information of the vertex detector. Despite this partial reconstruction, kinematic and geometric constraints allow the B meson mass to be reconstructed and the signal to be well separated from backgrounds. This in turn allows the electron reconstruction efficiency to be measured by matching the partial track segment found in the vertex detector to tracks found by LHCb's regular reconstruction algorithms. The agreement between data and simulation is evaluated, and corrections are derived for simulated electrons in bins of kinematics. These correction factors allow LHCb to measure branching fractions involving single electrons with a systematic uncertainty below 1%

Acute- and late-phase matrix metalloproteinase (MMP)-9 activity is comparable in female and male rats after peripheral nerve injury

Abstract Background In the peripheral nerve, pro-inflammatory matrix metalloproteinase (MMP)-9 performs essential functions in the acute response to injury. Whether MMP-9 activity contributes to late-phase injury or whether MMP-9 expression or activity after nerve injury is sexually dimorphic remains unknown. Methods Patterns of MMP-9 expression, activity and excretion were assessed in a model of painful peripheral neuropathy, sciatic nerve chronic constriction injury (CCI), in female and male rats. Real-time Taqman RT-PCR for MMP-9 and its endogenous inhibitor, tissue inhibitor of metalloproteinase-1 (TIMP-1) of nerve samples over a 2-month time course of CCI was followed by gelatin zymography of crude nerve extracts and purified MMP-9 from the extracts using gelatin Sepharose-beads. MMP excretion was determined using protease activity assay of urine in female and male rats with CCI. Results The initial upsurge in nerve MMP-9 expression at day 1 post-CCI was superseded more than 100-fold at day 28 post-CCI. The high level of MMP-9 expression in late-phase nerve injury was accompanied by the reduction in TIMP-1 level. The absence of MMP-9 in the normal nerve and the presence of multiple MMP-9 species (the proenzyme, mature enzyme, homodimers, and heterodimers) was observed at day 1 and day 28 post-CCI. The MMP-9 proenzyme and mature enzyme species dominated in the early- and late-phase nerve injury, consistent with the high and low level of TIMP-1 expression, respectively. The elevated nerve MMP-9 levels corresponded to the elevated urinary MMP excretion post-CCI. All of these findings were comparable in female and male rodents. Conclusion The present study offers the first evidence for the excessive, uninhibited proteolytic MMP-9 activity during late-phase painful peripheral neuropathy and suggests that the pattern of MMP-9 expression, activity, and excretion after peripheral nerve injury is universal in both sexes

Mapping, cloning and genetic characterization of the region containing the Wilson disease gene.

Wilson disease (WD) is an autosomal recessive disorder of copper transport which map to chromosome 13q14.3. In pursuit of the WD gene, we developed yeast artificial chromosome and cosmid contigs, and microsatellite markers which span the WD gene region. Linkage disequilibrium and haplotype analysis of 115 WD families confined the disease locus to a single marker interval. A candidate cDNA clone was mapped to this interval which, as shown in the accompanying paper, is very likely the WD gene. Our haplotype and mutation analyses predict that approximately half of all WD mutations will be rare in the American and Russian populations