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

Crossover of magnetoresistance in the zerogap half-metallic Heusler alloy Fe2CoSi

This work reports on the band structure and magneto-transport investigations of the inverse Heusler compound Fe2CoSi. The first-principles calculations reveal that Fe2CoSi has a very peculiar band structure with a conducting property in the majority spin channel and a nearly zero bandgap in the minority spin channel. The synthesized Fe2CoSi sample shows a high-ordered inverse Heusler structure with a magnetic moment of 4.88 {\mu}B at 5 K and a high Curie temperature of 1038 K. With increasing temperature, a crossover from positive to negative magnetoresistance (MR) is observed. Complemented with the Hall effect measurements, we suggest the intriguing crossover of MR can be ascribed to the dominant spin carriers changing from the gapless minority spin channel to the majority spin channel at Fermi level.Comment: 16 pages, 5 figures, submitted for publicatio

General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere

For a particle that is constrained on an ($N-1$)-dimensional ($N\geq2$) curved surface, the Cartesian components of its momentum in $N$-dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of a Dirac fermion on a two-dimensional sphere and we show that there is the generalized total angular momentum whose three cartesian components form the $su(2)$ algebra, obtained before by consideration of dynamics of the particle, and we demonstrate that there is no curvature-induced geometric potential for the fermion.Comment: 8 pages, no figure. Presentation improve