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

Microscopic origin of local moments in a zinc-doped high-TcT_{c} superconductor

The formation of a local moment around a zinc impurity in the high-$T_{c}$ cuprate superconductors is studied within the framework of the bosonic resonating-valence-bond (RVB) description of the $t-J$ model. A topological origin of the local moment has been shown based on the phase string effect in the bosonic RVB theory. It is found that such an $S=1/2$ moment distributes near the zinc in a form of staggered magnetic moments at the copper sites. The corresponding magnetic properties, including NMR spin relaxation rate, uniform spin susceptibility, and dynamic spin susceptibility, etc., calculated based on the theory, are consistent with the experimental measurements. Our work suggests that the zinc substitution in the cuprates provide an important experimental evidence for the RVB nature of local physics in the original (zinc free) state.Comment: The topological reason of local moment formation is given. One figure is adde

Nodeless superconductivity in Ir1−x_{1-x}Ptx_xTe2_2 with strong spin-orbital coupling

The thermal conductivity $\kappa$ of superconductor Ir$_{1-x}$Pt$_{x}$Te$_2$ ($x$ = 0.05) single crystal with strong spin-orbital coupling was measured down to 50 mK. The residual linear term $\kappa_0/T$ is negligible in zero magnetic field. In low magnetic field, $\kappa_0/T$ shows a slow field dependence. These results demonstrate that the superconducting gap of Ir$_{1-x}$Pt$_{x}$Te$_2$ is nodeless, and the pairing symmetry is likely conventional s-wave, despite the existence of strong spin-orbital coupling and a quantum critical point.Comment: 5 pages, 4 figure

Improved algorithms for computing determinants and resultants

AbstractOur first contribution is a substantial acceleration of randomized computation of scalar, univariate, and multivariate matrix determinants, in terms of the output-sensitive bit operation complexity bounds, including computation modulo a product of random primes from a fixed range. This acceleration is dramatic in a critical application, namely solving polynomial systems and related studies, via computing the resultant. This is achieved by combining our techniques with the primitive-element method, which leads to an effective implicit representation of the roots. We systematically examine quotient formulae of Sylvester-type resultant matrices, including matrix polynomials and the u-resultant. We reduce the known bit operation complexity bounds by almost an order of magnitude, in terms of the resultant matrix dimension. Our theoretical and practical improvements cover the highly important cases of sparse and degenerate systems

Photoemission Spectroscopy of Magnetic and Non-magnetic Impurities on the Surface of the Bi2_2Se3_3 Topological Insulator

Dirac-like surface states on surfaces of topological insulators have a chiral spin structure that suppresses back-scattering and protects the coherence of these states in the presence of non-magnetic scatterers. In contrast, magnetic scatterers should open the back- scattering channel via the spin-flip processes and degrade the state's coherence. We present angle-resolved photoemission spectroscopy studies of the electronic structure and the scattering rates upon adsorption of various magnetic and non-magnetic impurities on the surface of Bi$_2$Se$_3$, a model topological insulator. We reveal a remarkable insensitivity of the topological surface state to both non-magnetic and magnetic impurities in the low impurity concentration regime. Scattering channels open up with the emergence of hexagonal warping in the high-doping regime, irrespective of the impurity's magnetic moment.Comment: 5 pages, 4 figure