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

Binomial coefficients, Catalan numbers and Lucas quotients

Let $p$ be an odd prime and let $a,m$ be integers with $a>0$ and $m \not\equiv0\pmod p$. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ mod $p^2$ for $d=0,1$; for example, $$\sum_{k=0}^{p^a-1}\frac{\binom{2k}k}{m^k}\equiv\left(\frac{m^2-4m}{p^a}\right)+\left(\frac{m^2-4m}{p^{a-1}}\right)u_{p-(\frac{m^2-4m}{p})}\pmod{p^2},$$ where $(-)$ is the Jacobi symbol, and $\{u_n\}_{n\geqslant0}$ is the Lucas sequence given by $u_0=0$, $u_1=1$ and $u_{n+1}=(m-2)u_n-u_{n-1}$ for $n=1,2,3,\ldots$. As an application, we determine $\sum_{0<k<p^a,\, k\equiv r\pmod{p-1}}C_k$ modulo $p^2$ for any integer $r$, where $C_k$ denotes the Catalan number $\binom{2k}k/(k+1)$. We also pose some related conjectures.Comment: 24 pages. Correct few typo

Delivering sustainable buildings in retail construction

Session: Sustainability: Theory and DesignThe demand for high performance ‘green’ or ‘sustainable’ buildings is becoming increasingly important in the retail industry. Large construction companies in this sector have started to show leadership by working with their customers and supply chains towards sustainability in both products and operations. However, it remains unclear how clients’ benefits from achieving sustainability can be maximized and the associated risks be minimized, in order to add value and differentiate the output of retail construction. This paper reviews the practice of sustainable buildings within the context of retail construction, and also explores how the UK mainstream retail sector is currently addressing the challenges of sustainable retail buildings. The arguments are informed by a combination of literature review, a desk study of sustainability strategies of large client organizations and construction companies, and a case study with a leading construction company in the UK. The results demonstrate that businesses can benefit from embracing a sustainable approach while they need to adapt their business models to the rapidly changing environment. A demand-driven sustainability agenda is called for in the UK retail sector. The results also provide the basis for an in-depth, longitudinal case study to develop a framework to optimize process, energy and carbon efficiency in retail construction using sustainable technology. Such a framework should provide a sustainable technology model for retail customers to realize the full benefits of sustainable buildings and also assist construction companies and their professional advisors deliver green buildings more efficiently in the future.link_to_OA_fulltex

A decision making system for selecting sustainable technologies for retail buildings

Papers from the Designated Session TG66 - Energy and the Built EnvironmentCIB Publication 382: Selected papers presented at the CIB World Building Congres Construction and Society, Brisbane 5-9 May 2013The implementation of sustainable technologies can improve the energy and carbon efficiency of existing retail buildings. However, the selection of an appropriate sustainable technology is a complex task due to the large number of technological alternatives and decision criteria that need to be considered. Also, there exist series of uncertainties that are associated with the use of sustainable technologies, but have to be evaluated to achieve realistic and transparent results. The selection of sustainable technology is therefore most challenging. An earlier study was conducted with UK experienced practitioners including clients/developers, engineers, contractors and suppliers to identify the drivers and barriers for the use of sustainable technologies in UK retail construction. One major barrier identified from the study was the lack of a decision making tool, highlighted by both construction professionals and stakeholders in the retail industry. The large number of alternatives and potential solutions require a decision support method to be implemented. Information data on the economic variables, energy performance and impact on the environment of these systems is presently affected by vagueness and lack of knowledge. To deal with this high level of complexity and uncertainty an evaluation support approach is needed. This paper aims to develop a decision making framework to assist both retailers and construction professionals to define and evaluate the selection of sustainable technological options for delivering retail buildings. The research was carried out through a combination of a critical literature review and a survey-based study using expert opinions of retailers and contractors. The developed framework of decision criteria should provide a sustainable technology model to assist both construction professionals and stakeholders in the retail industry to systematically and effectively select the most appropriate technology. This approach should make the decision progression more transparent and facilitate sustainable development of retail buildings in achieving the carbon targets set by the UK and other governments.published_or_final_versio