Partial stability and stabilisation of Boolean networks

In this paper, we investigate the stability of Boolean networks and the stabilisation of Boolean control networks with respect to part of the system's states. First, an algebraic expression of the Boolean (control) network is derived by the semi-tensor product of matrices. Then, some necessary and sufficient conditions for partial stability of Boolean networks are given. Finally, the stabilisation of Boolean control networks by a free control sequence and a state-feedback control is investigated and the respective necessary and sufficient conditions are obtained. Examples are provided to illustrate the efficiency of the obtained results.     

Stability and stabilization of Boolean networks

The stability of Boolean networks and the stabilization of Boolean control networks are investigated. Using semi‐tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean (control) network can be converted to a discrete time linear (bilinear) dynamics, called the algebraic form of the Boolean (control) network. Then the stability can be revealed by analyzing the transition matrix of the corresponding discrete time system. Main results consist of two parts: (i) Using logic coordinate transformation, the known sufficient condition based on incidence matrix has been improved. It can also be used in stabilizer design. (ii) Based on algebraic form, necessary and sufficient conditions for stability and stabilization, respectively, are obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

A temporal context model for boosting video annotation

In this paper, we propose a new method to model the temporal context for boosting video annotation accuracy. The motivation of our idea mainly comes from the fact that temporally continuous shots in video are generally with relevant content, so that the performance of video annotation could be comparably boosted by mining the temporal dependency between shots in video. Based on this consideration, we propose a temporal context model to mine the redundant information between shots. By connecting our model with conditional random field and borrowing the learning and inference approaches from it, we could obtain the refined probability of a concept occurring in the shot, which is the leverage of temporal context information and initial output of video annotation. Comparing with existing methods for temporal context mining of video annotation, our model could capture different kinds of shot dependency more accurately to improve the video annotation performance. Furthermore, our model is relatively simple and efficient, which is important for the applications which have large scale data to process. Extensive experimental results on the widely used TRECVID datasets exhibit the effectiveness of our method for improving video annotation accuracy.     

切换奇异布尔网络的稳定性分析

基因调控网络的稳定性分析是系统生物学的研究热点问题之一.本文利用矩阵半张量积方法研究了切换奇异布尔网络的稳定性问题.首先给出了切换奇异布尔网络的代数表示,基于该代数表示,建立了系统解存在唯一的充要条件.然后通过将切换奇异布尔网络转化为等价的切换布尔网络,分别得到了系统在任意切换下稳定以及切换可稳的充要条件.最后给出例子验证所得结果的有效性.     

具有切换概率分布的概率布尔网络的依分布稳定和镇定

布尔网络作为研究基因调控网络的一种重要模型,近年来引起了国内外很多学者的广泛关注.本文利用代数状态空间表示方法,研究具有切换概率分布的概率布尔网络的依分布稳定和镇定问题.首先,回顾针对切换布尔网络稳定性分析的现有的研究结果.其次,给出具有切换概率分布的概率布尔网络依分布稳定的定义,并利用矩阵的半张量积建立具有切换概率分布的概率布尔网络的代数表示.再次,基于该代数表示,建立具有切换概率分布的概率布尔网络的依分布稳定的充分必要条件.最后,给出具有切换概率分布的概率布尔控制网络镇定问题可解的充要条件,并给出相应的控制设计方法.     

Morgan's problem of Boolean control networks

This paper investigates the Morgan''s problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output-decomposed form by constructing a set of consistent output-friendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan''s problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan''s problem is obtained.     

Robust network structures for conserving total activity in Boolean networks

One of the typical properties of biological systems is the law of conservation of mass, that is, the property that the mass must remain constant over time in a closed chemical reaction system. However, it is known that Boolean networks, which are a promising model of biological networks, do not always represent the conservation law. This paper thus addresses a kind of conservation law as a generic property of Boolean networks. In particular, we consider the problem of finding network structures on which, for any Boolean operation on nodes, the number of active nodes, i.e., nodes whose state is one, is constant over time. As a solution to the problem, we focus on the strongly-connected network structures and present a necessary and sufficient condition.     

Controller design for disturbance decoupling of Boolean control networks

We investigate a type of disturbance decoupling problem (DDP) of Boolean control networks. Using the semi-tensor product of matrices, the dynamics of a Boolean control network is expressed in its algebraic form. Under the framework of output-friendly subspace, we give a necessary and sufficient condition for the solvability of DDP by analyzing the redundant variables, and we present a computationally feasible method to construct all the valid feedback control matrices. The logical functions of each controller can be recovered from the obtained feedback control matrix. Finally, an example is provided to show the effectiveness of the proposed method.     

Recurrent neural nets as dynamical Boolean systems with applicationto associative memory

Discrete-time/discrete-state recurrent neural networks are analyzed from a dynamical Boolean systems point of view in order to devise new analytic and design methods for the class of both single and multilayer recurrent artificial neural networks. With the proposed dynamical Boolean systems analysis, we are able to formulate necessary and sufficient conditions for network stability which are more general than the well-known but restrictive conditions for the class of single layer networks: (1) symmetric weight matrix with (2) positive diagonal and (3) asynchronous update. In terms of design, we use a dynamical Boolean systems analysis to construct a high performance associative memory. With this Boolean memory, we can guarantee that all fundamental memories are stored, and also guarantee the size of the basin of attraction for each fundamental memory.     

State feedback stabilization for probabilistic Boolean networks

A probabilistic Boolean network (PBN) is a discrete-time system composed of a family of Boolean networks (BNs) between which the PBN switches in a stochastic fashion. Studying control-related problems in PBNs may provide new insights into the intrinsic control in biological systems and enable us to develop strategies for manipulating complex biological systems using exogenous inputs. This paper investigates the problem of state feedback stabilization for PBNs. Based on the algebraic representation of logic functions, a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller, and a control design method is proposed when the presented condition holds. It is shown that the controller designed via the proposed procedure can simultaneously stabilize a collection of PBNs that are composed of the same constituent BNs.     

概率级联布尔网络的集镇定及其应用

随着系统生物学和医学的迅速发展,基因调控网络已经成为一个热点研究领域.布尔网络作为研究生物系统和基因调控网络的一种重要模型,近年来引起了包括生物学家和系统科学家在内的很多学者的广泛关注.本文利用代数状态空间方法,研究了概率级联布尔网络的集镇定问题.首先给出概率级联布尔网络集镇定的定义,并利用矩阵的半张量积给出了概率级联布尔网络的代数表示.其次基于该代数表示,定义了一组合适的概率能达集,并给出了概率级联布尔网络集镇定问题可解的充要条件.最后将所得的理论结果应用于概率级联布尔网络的同步分析及n人随机级联演化布尔博弈的策略一致演化行为分析.     

Robust stability and stabilisation of Boolean networks with disturbance inputs

This paper deals with the problems of robust stability analysis and robust stabilisation control design for Boolean networks with disturbance inputs. The main tool used in this paper is the semi-tensor product of matrices. First, a necessary and sufficient condition is presented for the robust stability of Boolean networks based on the algebraic representation of Boolean networks with disturbance inputs. Second, the concept of one-step robust reachability is defined for Boolean control networks (BCNs) with disturbance inputs, based on which a constructive procedure is proposed for the robust stabilisation control design of BCNs. The study of an illustrative example demonstrates the effectiveness of the obtained new results.     

Stability and stabilization of Boolean networks with impulsive effects

This paper investigates the stability and stabilization of Boolean networks with impulsive effects. After giving a survey on semi-tensor product of matrices, we convert a Boolean network with impulsive effects into impulsive discrete-time dynamics. Then, some necessary and sufficient conditions are given for the stability and stabilization of Boolean networks with impulsive effects. Finally, examples are provided to illustrate the efficiency of the obtained results.     

Controllability of probabilistic Boolean control networks with time-variant delays in states时变时延概率布尔控制网络的能控性

This paper investigates the controllability of probabilistic Boolean control networks (PBCNs) with time-variant delays in states. By cutting the time sequence, we split the network into at most countably infinitely many subnetworks with no delays, where any one of the longest subnetworks is called a controllability constructed path (CCP). When the CCP is of infinite length, we prove that the network is controllable iff any CCP is controllable, and give an equivalent condition for the controllability of the network. When it is of finite length, we give a necessary condition and a sufficient condition for the controllability of the network, and show that the controllability of the network is not equivalent to the controllability of a CCP.     

状态翻转控制下布尔控制网络的可镇定性和Q学习算法

在给定一个子集的条件下, 本文研究了在状态翻转控制下布尔控制网络的全局镇定问题. 对于节点集的给定子 集, 状态翻转控制可以将某些节点的值从1 (或0)变成0 (或1). 将翻转控制作为控制之一, 本文研究了状态翻转控制下的 布尔控制网络. 将控制输入和状态翻转控制结合, 提出了联合控制对和状态翻转转移矩阵的概念. 接着给出了状态翻转 控制下布尔控制网络全局稳定的充要条件. 镇定核是最小基数的翻转集合, 本文提出了一种寻找镇定核的算法. 利用可 达集的概念, 给出了一种判断全局镇定和寻找联合控制对序列的方法. 此外, 如果系统是一个大型网络, 则可以利用一 种名为Q学习算法的无模型强化学习方法寻找联合控制对序列. 最后给出了一个数值例子来说明本文的理论结果.     

二进神经网络中汉明球的逻辑意义及一般判别方法

剖析二进神经元的逻辑意义对二进神经网络的规则提取是十分重要的，在布尔空间中，汉明球是一种线性可分的空间结构，如何从汉明球中提取出具有清晰逻辑意义的规则是二进神经网络研究的一个问题，通过对MofN规则表达形式的扩展，分析了汉明球的逻辑意义，提出了表达汉明球逻辑意义的LEM规则和GEM规则方法，并且讨论了汉明球和汉明补球的等价性，另一个重要的结果是证明了二进神经元和汉明球等价的充要条件，从而建立了判别汉明球的一般方法。     

布尔控制网络的能控性与能观性

利用矩阵的半张量积,布尔控制网络被转化为离散时间系统.本文从离散时间系统的结构矩阵出发,讨论了逻辑控制系统的能控能观性条件,得到了一个新的能控性条件.新的条件简化了原有能控性矩阵的计算复杂性,矩阵的最高阶数由原来的2m+n降到了2n.另外,还得到了检验布尔控制网络能观性的条件.与原有条件相比,新的条件更容易计算检验.最后,给出一个实例,检验给出的能控能观性判断条件的正确性.     

具有少量基本回路布尔网络的不动点

近来作为自然和人造非线性动态网络的一种紧凑模型,布尔网络的研究受到广泛关注.不动点和吸引子是预测布尔网络长期行为的关键.本文针对具有少量基本回路的布尔网络,提出了确定不动点的算法.我们的方法是基于构成反馈顶点集的变量所满足的一组方程.作为应用,我们还给出了检验这类布尔网络全局稳定性的充要条件.     

Approximation capability to functions of several variables,nonlinear functionals, and operators by radial basis function neuralnetworks

The purpose of this paper is to explore the representation capability of radial basis function (RBF) neural networks. The main results are: 1) the necessary and sufficient condition for a function of one variable to be qualified as an activation function in RBF network is that the function is not an even polynomial, and 2) the capability of approximation to nonlinear functionals and operators by RBF networks is revealed, using sample data either in frequency domain or in time domain, which can be used in system identification by neural networks.     

受扰布尔控制网络全局可重构分析与状态估计

受扰布尔控制网络的状态转移,因受未知干扰影响而具有不确定性,这对状态观测器设计带来了困难.本文主要研究了受扰布尔控制网络全局可重构性问题,并在此基础上设计状态观测器.首先,将受扰布尔控制模型转化为多个子系统的切换未知布尔控制网络模型,在此基础上,提出了受扰布尔控制网络的4种不同状态集.其次,基于状态集估计方法,对受扰布尔控制网络状态估计问题进行分析.再次,提出有限时间可重构与全局可重构性概念;同时,根据状态集估计与状态转移分析,分别给出有限时间可重构判定算法与全局可重构性证明的充要条件.最后,给出观测器设计方法,并通过例子证明了本文提出方法的可行性.