Approximation of fractional Brownian motion by martingales

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given

Evidence for Top Quark Production in Nucleus-Nucleus Collisions

Peer reviewe

Observation of the B-s(0) -> X(3872)phi Decay

Using a data sample of proton-proton collisions at root s = 13 TeV, corresponding to an integrated luminosity of 140 fb(-1) collected by the CMS experiment in 2016-2018, the B-s(0) -> X(3872)phi decay is observed. Decays into J/psi pi(+)pi(-) and K+K- are used to reconstruct, respectively, the X(3872) and phi. The ratio of the product of branching fractions B[B-s(0) -> X(3872)phi]B[X(3872) -> J/psi pi(+)pi(-)] to the product B[B-s(0) ->psi(2S)phi]B[psi(2S) -> J/psi pi(+)pi(-)] is measured to be [2.21 +/- 0.29(stat) +/- 0.17(syst)]%. The ratio B[B-s(0) -> X(3872)phi]/B[B-0 -> X(3872)K-0] is found to be consistent with one, while the ratio B[B-s(0) -> X(3872)phi]/B[B+-> X(3872)K+] is two times smaller. This suggests a difference in the production dynamics of the X(3872) in B-0 and B(0)s meson decays compared to B+. The reported observation may shed new light on the nature of the X(3872) particle.Peer reviewe

Persistent histone modifications at the BDNF and Cdk-5 promoters following extinction of nicotine-seeking in rats

Drugs of addiction lead to a wide range of epigenetic changes at the promoter regions of genes directly implicated in learning and memory processes. We have previously shown that the histone deactylase inhibitor, sodium butyrate (NaB), accelerates the extinction of nicotine-seeking and provides resistance to relapse. Here, we explore the potential molecular mechanisms underlying this effect. Rats received intravenous nicotine or saline self-administration, followed by 6 days of extinction training, with each extinction session followed immediately by treatment with NaB or vehicle. On the last day of extinction, rats were killed and the medial ventral prefrontal cortex retained for chromatin immunoprecipitation and quantitative polymerase chain reaction (qPCR). A history of nicotine exposure significantly decreased H3K14 acetylation at the brain-derived neurotrophic factor (BDNF) exon IV promoter, and this effect was abolished with NaB treatment. In contrast, nicotine self-administration alone, resulted in a significant decrease in histone methylation at the H3K27me3 and H3K9me2 marks in the promoter regions of BDNF exon IV and cyclin-dependent kinase 5 (Cdk-5). Quantitative PCR-identified changes in several genes associated with NaB treatment that were independent of nicotine exposure; however, an interaction of nicotine history and NaB treatment was detected only in the expression of BDNF IV and BDNF IX. Together these results suggest that nicotine self-administration leads to a number of epigenetic changes at both the BDNF and Cdk-5 promoters, and that these changes may contribute to the enhanced extinction of nicotine-seeking by NaB