CTRL: Extension of CTL with regular expressions and fairness operators to verify genetic regulatory networks

Model checking has proven to be a useful analysis technique not only for concurrent systems, but also for genetic regulatory networks (Grns). Applications of model checking in systems biology have revealed that temporal logics should be able to capture both branching-time and fairness properties (needed for specifying multistability and oscillation properties, respectively). At the same time, they should have a user-friendly syntax easy to employ by non-experts. In this paper, we define Computation Tree Regular Logic (Ctrl), an extension of Ctl with regular expressions and fairness operators that attempts to match these criteria. Ctrl subsumes both Ctl and Ltl, and has a reduced set of temporal operators indexed by regular expressions. We also develop a translation of Ctrl into Hennessy-Milner Logic with Recursion (HmlR), an equational variant of the modal μ-calculus. This has allowed us to obtain an on-the-fly model checker with diagnostic for Ctrl by directly reusing the verification technology available in the Cadp toolbox. We illustrate the application of the Ctrl model checker by analyzing the Grn controlling the carbon starvation response of Escherichia coli.     

复杂网络结构的稳定性与鲁棒性研究

在对复杂网络研究的过程中,根据网络结构中结点连接度的连接倾向而将其划分为3种类型,即异配网络、同配网络、中性网络,采用变量梯度分析法分别对其稳定性进行判定与分析。理论分析表明,异配网络在大范围内是稳定的,同配网络状态是不稳定的,中性网络的稳定性不能确定,需要根据结点总体连接度的倾向性才能确定其是否处于稳定状态。同时对复杂网络的鲁棒性研究的仿真结果表明,其稳定性与鲁棒性具有正相关性,即异配网络的鲁棒性最好,中性网络次之,同配网络的鲁棒性脆弱。     

Designing genetic regulatory networks using fuzzy Petri nets approach

In this paper, we have successfully presented a fuzzy Petri net (FPN) model to design the genetic regulatory network. Based on the FPN model, an efficient algorithm is proposed to automatically reason about imprecise and fuzzy information. By using the reasoning algorithm for the FPN, we present an alternative approach that is more promising than the fuzzy logic. The proposed FPN approach offers more flexible reasoning capability because it is able to obtain results with fuzzy intervals rather than point values. In this paper, a novel model with a new concept of hidden fuzzy transition (HFT) to design the genetic regulatory network is developed. We have built the FPN model and classified the input data in terms of time point and obtained the output data, so the system can be viewed as the two-input and one output system. This method eliminates possible false predictions from the classical fuzzy model thereby allowing a wider search space for inferring regulatory relationship. The experimental results show the proposed approach is feasible and acceptable to design the genetic regulatory network and investigate the dynamical behaviors of gene network.     

Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks

This paper is concerned with the problem of finite-time stability analysis for uncertain stochastic delayed reaction-diffusion genetic regulatory networks. The parameter uncertainties are assumed to be norm-bounded, and the time delays are assumed to be time-varying. Based on the Lyapunov functional method, sufficient conditions ensuring the networks to be finite-time robustly stochastically stable are established. When there are no norm-bounded parameter uncertainties in the networks, a finite-time stochastic stability condition is also established. All the conditions are diffusion-dependent as well as delay-dependent. Numerical examples are given to illustrate the effectiveness of the proposed results.     

Mean square exponential stability of stochastic genetic regulatory networks with time-varying delays

In this paper, we study the mean square exponential stability of stochastic genetic regulatory networks with time-varying delays. Two kinds of time-varying delays are considered: one is differentiable with bounded delay derivative the other is continuous without constraints on the delay derivative. In order to investigate the mean square exponential stability in stochastic genetic regulatory networks, some novel rate-dependent/independent mean square exponential stability criteria are derived by constructing Lyapunov-Krasovskii functional. The sufficient conditions are given in terms of linear matrix inequalities. Moreover, illustrative examples are used to substantiate the effectiveness and less conservativeness of our results.     

Robustness analysis of privacy-preserving model-based recommendation schemes

Privacy-preserving model-based recommendation methods are preferable over privacy-preserving memory-based schemes due to their online efficiency. Model-based prediction algorithms without privacy concerns have been investigated with respect to shilling attacks. Similarly, various privacy-preserving model-based recommendation techniques have been proposed to handle privacy issues. However, privacy-preserving model-based collaborative filtering schemes might be subjected to shilling or profile injection attacks. Therefore, their robustness against such attacks should be scrutinized.In this paper, we investigate robustness of four well-known privacy-preserving model-based recommendation methods against six shilling attacks. We first apply masked data-based profile injection attacks to privacy-preserving k-means-, discrete wavelet transform-, singular value decomposition-, and item-based prediction algorithms. We then perform comprehensive experiments using real data to evaluate their robustness against profile injection attacks. Next, we compare non-private model-based methods with their privacy-preserving correspondences in terms of robustness. Moreover, well-known privacy-preserving memory- and model-based prediction methods are compared with respect to robustness against shilling attacks. Our empirical analysis show that couple of model-based schemes with privacy are very robust.     

Stochastic stability for uncertain genetic regulatory networks with interval time-varying delays

This paper is concerned with the robust asymptotic stability analysis for uncertain genetic regulatory networks with both interval time-varying delays and stochastic noise. By using the stochastic analysis approach, employing some free-weighting matrices and introducing an appropriate type of Lyapunov functional which takes into account the ranges of delays, some new delay-range-dependent and rate-dependent stability criteria are established in terms of linear matrix inequalities (LMIs) to guarantee the delayed genetic regulatory networks to be robustly asymptotically stable in the mean square. As a result, the new criteria are applicable to both fast and slow time-varying delays. Five numerical examples are also used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.     

On delayed uncertain genetic regulatory networks: robust stability analysis

In this paper, the problem of stability analysis for uncertain genetic regulatory networks with time-varying delays is investigated. The time-varying delay function in this paper is not required to be either continuously differentiable, or its derivative less than one. By choosing an appropriate Lyapunov–Krasovskii functional and employing some free-weighting matrices, some new delay-dependent and delay-derivative-dependent stability criteria are presented in terms of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Finally, three numerical examples are used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.     

Robustness analysis of linear periodic time-varying systems subject to structured uncertainty

In this paper, we show how Floquet theory may be combined with a technique known as Lifting to cast a linear periodically time-varying system subject to structured linear time invariant uncertainty in the form of a linear fractional transformation. The stability and performance robustness of the resulting system may then be analysed using standard μ-analysis methods. A significant advantage of the proposed approach is that it allows the computation of a worst-case destabilising uncertainty combination which may be used to estimate the conservatism of the computed robustness margin. An example is given to illustrate the application of the proposed approach.     

Variance-constrained filtering for discrete-time genetic regulatory networks with state delay and random measurement delay

This paper is concerned with the variance-constrained filtering problem for a class of discrete-time genetic regulatory networks (GRNs) with state delay and random one-step measurement delay. The phenomenon of the random one-step measurement delay is characterised by a random variable, which is assumed to obey the Bernoulli distribution with known occurrence probability. The purpose of the addressed problem is to design a filter such that, in the presence of state delay and random one-step measurement delay, an upper bound of the filtering error covariance matrix can be obtained and the explicit expression of the filter gain matrix is given. Then, the proposed variance-constrained filtering method can be used to approximate the concentrations of mRNAs and proteins. Finally, a numerical example is provided to illustrate the effectiveness of the designed filtering scheme.     

Stability and bifurcation of genetic regulatory networks with small RNAs and multiple delays

In this paper, we study the stability, bifurcation and periodic oscillation of two-gene regulatory networks mediated by small RNAs (sRNAs) with multiple delays. We first show the effect of sRNAs on the stability and bifurcation of genetic regulatory networks. Then we present sufficient conditions for the local stability of two-gene genetic regulatory networks in the parameter space, and assess critical values of the Hopf bifurcation. Although such networks may have multiple delays, sRNAs, positive feedbacks and different connection strengths among two genes, their stability and bifurcation depend on the sum of all time delays among all elements (including both mRNAs and proteins). Furthermore, the period of oscillations increases with the time delay, and in the case of larger delay, the amplitude of oscillations is robust against the change in the delay. Two examples are employed to illustrate the theorems developed in this study.     

带有时变时滞的切换基因调控网络的稳定性

研究了带有时变时滞的切换基因调控网络的稳定性问题。和现有关于切换基因调控网络结果不同的是,切换基因调控网络包括稳定子系统和不稳定子系统。利用平均驻时方法和线性矩阵不等式技术,得到了带有时变时滞的切换基因调控网络指数稳定的判据。最后的仿真实例验证了结果的有效性。     

具动态不确定性系统的观测器-控制器设计的鲁棒性

研究存在动态不确定性的线性化系统的龙伯格观测器-控制器设计的鲁棒稳定性问题,并给出了易于通过系统参数摄动界来验证鲁棒稳定的充分条件.