On the sine-Gordon--Thirring equivalence in the presence of a boundary

In this paper, the relationship between the sine-Gordon model with an integrable boundary condition and the Thirring model with boundary is discussed and the reflection $R$-matrix for the massive Thirring model, which is related to the physical boundary parameters of the sine-Gordon model, is given. The relationship between the the boundary parameters and the two formal parameters appearing in the work of Ghoshal and Zamolodchikov is discussed.Comment: 14 pages, Latex, to be published in Int. J. Mod. Phys. A. Two references adde

Random attractors for stochastic evolution equations driven by fractional Brownian motion

The main goal of this article is to prove the existence of a random attractor for a stochastic evolution equation driven by a fractional Brownian motion with $H\in (1/2,1)$. We would like to emphasize that we do not use the usual cohomology method, consisting of transforming the stochastic equation into a random one, but we deal directly with the stochastic equation. In particular, in order to get adequate a priori estimates of the solution needed for the existence of an absorbing ball, we will introduce stopping times to control the size of the noise. In a first part of this article we shall obtain the existence of a pullback attractor for the non-autonomous dynamical system generated by the pathwise mild solution of an nonlinear infinite-dimensional evolution equation with non--trivial H\"older continuous driving function. In a second part, we shall consider the random setup: stochastic equations having as driving process a fractional Brownian motion with $H\in (1/2,1)$. Under a smallness condition for that noise we will show the existence and uniqueness of a random attractor for the stochastic evolution equation

Bose-Einstein condensates in RF-dressed adiabatic potentials

Bose-Einstein condensates of $^{87}$Rb atoms are transferred into radio-frequency (RF) induced adiabatic potentials and the properties of the corresponding dressed states are explored. We report on measurements of the spin composition of dressed condensates. We also show that adiabatic potentials can be used to trap atom gases in novel geometries, including suspending a cigar-shaped cloud above a curved sheet of atoms

Can the Bump be Observed in the Early Afterglow of GRBS with X-Ray Line Emission Features?

Extremely powerful emission lines are observed in the X-ray afterglow of several GRBs. The energy contained in the illuminating continuum which is responsible for the line production exceeds 10$^{51}$ erg, much higher than that of the collimated GRBs. It constrains the models which explain the production of X-ray emission lines. In this paper, We argue that this energy can come from a continuous postburst outflow. Focusing on a central engine of highly magnetized millisecond pulsar or magnetar we find that afterglow can be affected by the illuminating continuum, and therefore a distinct achromatic bump may be observed in the early afterglow lightcurves. With the luminosity of the continuous outflow which produces the line emission, we define the upper limit of the time when the bump feature appears. We argue that the reason why the achromatic bumps have not been detected so far is that the bumps should appear at the time too early to be observed.Comment: 13 pags, 2 tables, appear in v603 n1 pt1 ApJ March 1, 2004 issu

Children with 5′-end NF1 gene mutations are more likely to have glioma

Objective:To ascertain the relationship between the germline NF1 gene mutation and glioma development in patients with neurofibromatosis type 1 (NF1).Methods:The relationship between the type and location of the germline NF1 mutation and the presence of a glioma was analyzed in 37 participants with NF1 from one institution (Washington University School of Medicine [WUSM]) with a clinical diagnosis of NF1. Odds ratios (ORs) were calculated using both unadjusted and weighted analyses of this data set in combination with 4 previously published data sets.Results:While no statistical significance was observed between the location and type of the NF1 mutation and glioma in the WUSM cohort, power calculations revealed that a sample size of 307 participants would be required to determine the predictive value of the position or type of the NF1 gene mutation. Combining our data set with 4 previously published data sets (n = 310), children with glioma were found to be more likely to harbor 5′-end gene mutations (OR = 2; p = 0.006). Moreover, while not clinically predictive due to insufficient sensitivity and specificity, this association with glioma was stronger for participants with 5′-end truncating (OR = 2.32; p = 0.005) or 5′-end nonsense (OR = 3.93; p = 0.005) mutations relative to those without glioma.Conclusions:Individuals with NF1 and glioma are more likely to harbor nonsense mutations in the 5′ end of the NF1 gene, suggesting that the NF1 mutation may be one predictive factor for glioma in this at-risk population.</jats:sec

Robust H∞ feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise

The official published version can found at the link below.Noises are ubiquitous in genetic regulatory networks (GRNs). Gene regulation is inherently a stochastic process because of intrinsic and extrinsic noises that cause kinetic parameter variations and basal rate disturbance. Time delays are usually inevitable due to different biochemical reactions in such GRNs. In this paper, a delayed stochastic model with additive and multiplicative noises is utilized to describe stochastic GRNs. A feedback gene controller design scheme is proposed to guarantee that the GRN is mean-square asymptotically stable with noise attenuation, where the structure of the controllers can be specified according to engineering requirements. By applying control theory and mathematical tools, the analytical solution to the control design problem is given, which helps to provide some insight into synthetic biology and systems biology. The control scheme is employed in a three-gene network to illustrate the applicability and usefulness of the design.This work was funded by Royal Society of the U.K.; Foundation for the Author of National Excellent Doctoral Dissertation of China. Grant Number: 2007E4; Heilongjiang Outstanding Youth Science Fund of China. Grant Number: JC200809; Fok Ying Tung Education Foundation. Grant Number: 111064; International Science and Technology Cooperation Project of China. Grant Number: 2009DFA32050; University of Science and Technology of China Graduate Innovative Foundation

Photoinduced Electron Pairing in a Driven Cavity

We demonstrate how virtual scattering of laser photons inside a cavity via two-photon processes can induce controllable long-range electron interactions in two-dimensional materials. We show that laser light that is red (blue) detuned from the cavity yields attractive (repulsive) interactions whose strength is proportional to the laser intensity. Furthermore, we find that the interactions are not screened effectively except at very low frequencies. For realistic cavity parameters, laser-induced heating of the electrons by inelastic photon scattering is suppressed and coherent electron interactions dominate. When the interactions are attractive, they cause an instability in the Cooper channel at a temperature proportional to the square root of the driving intensity. Our results provide a novel route for engineering electron interactions in a wide range of two-dimensional materials including AB-stacked bilayer graphene and the conducting interface between LaAlO3 and SrTiO3

Robust H-infinity filtering for 2-D systems with intermittent measurements

This paper is concerned with the problem of robust H∞ filtering for uncertain two-dimensional (2-D) systems with intermittent measurements. The parameter uncertainty is assumed to be of polytopic type, and the measurements transmission is assumed to be imperfect, which is modeled by a stochastic variable satisfying the Bernoulli random binary distribution. Our attention is focused on the design of an H∞ filter such that the filtering error system is stochastically stable and preserves a guaranteed H∞ performance. This problem is solved in the parameter-dependent framework, which is much less conservative than the quadratic approach. By introducing some slack matrix variables, the coupling between the positive definite matrices and the system matrices is eliminated, which greatly facilitates the filter design procedure. The corresponding results are established in terms of linear matrix inequalities, which can be easily tested by using standard numerical software. An example is provided to show the effectiveness of the proposed approac