There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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Differential Evolution: A Survey of the State-of-the-Art

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

System Identification I

This paper compares the use of different thermal non-destructive testing techniques to rapidly inspect carbon fibre composite aircraft components. Samples were prepared to simulate inclusions and barely visible impact damage in carbon fibre reinforced plastic laminate which represent faults in the manufacturing process and in-service environment respectively. The limits of material fault detection were then compared for transient and lock-in thermography and the results were verified with underwater ultrasonic c-scans. The paper concludes that lock-in thermography is a more powerful technique to detect impact damage and that transient thermography is more suitable for detecting inclusions. Thermal non-destructive testing is up to 30 times quicker than underwater ultrasonic c-scanning and may ultimately provide the solution to the problem of rapid quantitative in-service and manufacturing process inspection of commercial aircraft components.

Rapid thermal non-destructive testing of aircraft components

Introduction of synthetic circuits into microbes creates competition between circuit and host genes for shared cellular resources, such as ribosomes. This can lead to the emergence of unwanted coupling between the expression of different circuit genes, complicating the design process and potentially leading to circuit failure. By expressing a synthetic 16S rRNA with altered specificity, we can partition the ribosome pool into host-specific and circuit-specific activities. We show mathematically and experimentally that the effects of resource competition can be alleviated by targeting genes to different ribosomal pools. This division of labour can be used to increase flux through a metabolic pathway. We develop a model of cell physiology which is able to capture these observations and use it to design a dynamic resource allocation controller. When implemented, this controller acts to decouple genes by increasing orthogonal ribosome production as the demand for translational resources by a synthetic circuit increases.

/pdf/dynamic-allocation-of-orthogonal-ribosomes-facilitates-4f8suuf6ta.pdf

Dynamic Allocation of Orthogonal Ribosomes Facilitates Uncoupling of Co-Expressed Genes

Biological systems that have been experimentally verified to be robust to significant changes in their environments require mathematical models that are themselves robust. In this context, a necessary condition for model robustness is that the model dynamics should not be sensitive to small variations in the model's parameters. Robustness analysis problems of this type have been extensively studied in the field of robust control theory and have been found to be very difficult to solve in general. The authors describe how some tools from robust control theory and nonlinear optimisation can be used to analyse the robustness of a recently proposed model of the molecular network underlying adenosine 3',5'-cyclic monophosphate (cAMP) oscillations observed in fields of chemotactic Dictyostelium cells. The network model, which consists of a system of seven coupled nonlinear differential equations, accurately reproduces the spontaneous oscillations in cAMP observed during the early development of D. discoideum. The analysis by the authors reveals, however, that very small variations in the model parameters can effectively destroy the required oscillatory dynamics. A biological interpretation of the analysis results is that correct functioning of a particular positive feedback loop in the proposed model is crucial to maintaining the required oscillatory dynamics.

Robustness analysis of biochemical network models

Introduction What is feedback control? Feedback control in biological systems Application of control theory to biological systems: a historical perspective References Linear systems Introduction State-space models Linear time-invariant systems and the frequency response Fourier analysis Transfer functions and the Laplace transform Stability Change of state variables and canonical representations Characterising system dynamics in the time domain Characterising system dynamics in the frequency domain Block diagram representations of interconnected systems Case Study I: Characterising the frequency dependence of osmo-adaptation in Saccharomyces cerevisiae Case Study II: Characterising the dynamics of the Dictyostelium external signal receptor network References Nonlinear systems Introduction Equilibrium points Linearisation around equilibrium points Stability and regions of attractions Optimisation methods for nonlinear systems Case study III: Stability analysis of tumor dormancy equilibrium Case study IV: Global optimisation of a model of the tryptophan control system against multiple experiment data References Negative feedback systems Introduction Stability of negative feedback systems Performance of negative feedback systems Fundamental tradeoffs with negative feedback Case Study V: Analysis of stability and oscillations in the p53-Mdm2 feedback system Case Study VI: Perfect adaptation via integral feedback control in bacterial chemotaxis References Positive feedback systems Introduction Bifurcations, bistability and limit cycles Monotone systems Chemical reaction network theory Case Study VII: Positive feedback leads to multistability, bifurcations and hysteresis in a MAPK cascade Case Study VIII: Coupled positive and negative feedback loops in the yeast galactose pathway References Model validation using robustness analysis Introduction Robustness analysis tools for model validation New robustness analysis tools for biological systems Case Study IX: Validating models of cAMP oscillations in aggregating Dictyostelium cells Case Study X: Validating models of the p53-Mdm2 System References Reverse engineering biomolecular networks Introduction Inferring network interactions using linear models Least squares Exploiting prior knowledge Dealing with measurement noise Exploiting time-varying models Case Study XI: Inferring regulatory interactions in the innate immune system from noisy measurements Case Study XII: Reverse engineering a cell cycle regulatory subnetwork of Saccharomyces cerevisiae from experimental microarray data References Stochastic effects in biological control systems Introduction Stochastic modelling and simulation A framework for analysing the effect of stochastic noise on stability Case Study XIII: Stochastic effects on the stability of cAMP oscillations in aggregating Dictyostelium cells Case Study XIV: Stochastic effects on the robustness of cAMP oscillations in aggregating Dictyostelium cells References Index

Feedback Control in Systems Biology

A general anti-windup (AW) compensation scheme is provided for a class of input constrained feedback-linearizable nonlinear systems. The controller considered is an inner-loop nonlinear dynamic inversion controller, augmented with an outer-loop linear controller, of arbitrary structure. For open-loop globally exponentially stable plants, it is shown that (i) there always exists a globally stabilizing AW compensator corresponding to a nonlinear generalization of the Internal-Model-Control (IMC) AW solution; (ii) important operator theoretic parallels exist between the AW design scheme for linear control and the suggested AW design scheme for nonlinear affine plants and (iii) a more attractive AW compensator may be obtained by using a nonlinear state-feedback term, which plays a role similar to the linear state-feedback term in linear coprime factor-based AW compensation. The results are demonstrated on a dual-tank simulation example. Copyright © 2009 John Wiley & Sons, Ltd.

Declan G. Bates

Papers

Rapid thermal non-destructive testing of aircraft components

Dynamic Allocation of Orthogonal Ribosomes Facilitates Uncoupling of Co-Expressed Genes

Robustness analysis of biochemical network models

Feedback Control in Systems Biology

Anti-windup synthesis for nonlinear dynamic inversion control schemes