Cycle symmetry, limit theorems, and fluctuation theorems for diffusion processes on the circle

Cyclic structure and dynamics are of great interest in both the fields of stochastic processes and nonequilibrium statistical physics. In this paper, we find a new symmetry of the Brownian motion named as the quasi-time-reversal invariance. It turns out that such an invariance of the Brownian motion is the key to prove the cycle symmetry for diffusion processes on the circle, which says that the distributions of the forming times of the forward and backward cycles, given that the corresponding cycle is formed earlier than the other, are exactly the same. With the aid of the cycle symmetry, we prove the strong law of large numbers, functional central limit theorem, and large deviation principle for the sample circulations and net circulations of diffusion processes on the circle. The cycle symmetry is further applied to obtain various types of fluctuation theorems for the sample circulations, net circulation, and entropy production rate.Comment: 28 page

A Light Higgs at the LHC and the B-Anomalies

After the Higgs discovery, the LHC has been looking for new resonances, decaying into pairs of Standard Model (SM) particles. Recently, the CMS experiment observed an excess in the di-photon channel, with a di-photon invariant mass of about 96~GeV. This mass range is similar to the one of an excess observed in the search for the associated production of Higgs bosons with the $Z$ neutral gauge boson at LEP, with the Higgs bosons decaying to bottom quark pairs. On the other hand, the LHCb experiment observed a discrepancy with respect to the SM expectations of the ratio of the decay of $B$-mesons to $K$-mesons and a pair of leptons, $R_{K^{(*)}} = BR(B \to K^{(*)} \mu^+\mu^-)/BR(B\to K^{(*)} e^+e^-)$. This observation provides a hint of the violation of lepton-flavor universality in the charged lepton sector and may be explained by the existence of a vector boson originating form a $U(1)_{L_\mu - L_\tau}$ symmetry and heavy quarks that mix with the left-handed down quarks. Since the coupling to heavy quarks could lead to sizable Higgs di-photon rates in the gluon fusion channel, in this article we propose a common origin of these anomalies identifying a Higgs associated with the breakdown of the $U(1)_{L_\mu - L_\tau}$ symmetry and at the same time responsible to the quark mixing, with the one observed at the LHC. We also discuss the constraints on the identification of the same Higgs with the one associated with the bottom quark pair excess observed at LEP.Comment: 34 pages, 5 figures, 3 tables. v2: 1 figure added, motivation clarified, version matched to JHE

Kinetic behavior of the general modifier mechanism of Botts and Morales with non-equilibrium binding

In this paper, we perform a complete analysis of the kinetic behavior of the general modifier mechanism of Botts and Morales in both equilibrium steady states and non-equilibrium steady states (NESS). Enlightened by the non-equilibrium theory of Markov chains, we introduce the net flux into discussion and acquire an expression of product rate in NESS, which has clear biophysical significance. Up till now, it is a general belief that being an activator or an inhibitor is an intrinsic property of the modifier. However, we reveal that this traditional point of view is based on the equilibrium assumption. A modifier may no longer be an overall activator or inhibitor when the reaction system is not in equilibrium. Based on the regulation of enzyme activity by the modifier concentration, we classify the kinetic behavior of the modifier into three categories, which are named hyperbolic behavior, bell-shaped behavior, and switching behavior, respectively. We show that the switching phenomenon, in which a modifier may convert between an activator and an inhibitor when the modifier concentration varies, occurs only in NESS. Effects of drugs on the Pgp ATPase activity, where drugs may convert from activators to inhibitors with the increase of the drug concentration, are taken as a typical example to demonstrate the occurrence of the switching phenomenon.Comment: 19 pages, 10 figure

Postoperative steroids after Kasai portoenterostomy for biliary atresia: A meta-analysis

AbstractAim: The aim of this systematic review and meta-analysis was to determine if adjunct steroids affect jaundice-free, cholangitis, and survival rates after Kasai portoenterostomy. Methods: The literature was searched using the following terms: biliary atresia, portoenterostomy, steroids, glucocorticoids, dexamethasone, prednisolone, and hydrocortisone. The primary outcome was the jaundice-free rate. Secondary outcomes were cholangitis and survival rates. Results: Ten studies were included in the systematic review and 8 in the meta-analyses. Steroid treatment regimens were inconsistent between studies. The pooled odds ratio (OR) for the jaundice-free rate did not significantly favor steroid over non-steroid treatment (1.95; 95% confidence interval [CI]: 0.91–4.11; P = 0.087), nor did the pooled OR for the cholangitis rate (0.75; 95% CI: 0.48–1.17; P = 0.202). Overall survival ranged from 58 to 95% in the steroid group and from 36 to 96% in the control group. Native liver survival ranged from 30 to 56% in the steroid group and from 31 to 48% in the control group. The survival data were not suitable for meta-analysis. Conclusions: Although these results imply that adjunct steroids after Kasai portoenterostomy for BA may not improve jaundice-free or cholangitis rates, the quality of available evidence is limited and therefore not definitive. Additional high quality studies are needed