概率布尔控制网络的弱能控性

本文研究了概率布尔控制网络的弱能控性,系统的弱能控性是概率布尔网络精确能控的一个推广.首先利用矩阵的半张量积和逻辑变量的向量表示,概率布尔控制网络被表示为离散时间动态系统.接着给出概率布尔控制网络弱能控的定义,从离散时间系统的结构矩阵出发,构造了最大概率转移矩阵,矩阵中的元素表示相应状态之间可能发生转移的最大概率,在此基础上研究了概率布尔控制网络的弱能控的条件,同时给出了两个状态弱能达时控制序列的设计算法.最后通过例子进一步解释了弱能控的概念和控制序列设计算法的有效性.     

布尔控制网络的输出稳定与镇定

矩阵的半张量积是将逻辑变量转化为向量研究的主要工具.本文利用半张量积把逻辑控制系统表示为离散时间仿射线性系统,在逻辑系统的状态空间框架下研究了以布尔控制网络为代表的逻辑动态系统的输出稳定与镇定.首先给出布尔网络输出稳定的定义,研究了布尔网络输出稳定的充要条件;其次讨论了布尔控制网络的输出镇定,分别得到了布尔控制网络由常值输入变量、自由控制序列、状态反馈控制序列输出镇定的条件.本文讨论的系统输出稳定与镇定是(部分)变量稳定与镇定的推广.     

概率布尔控制网络的集可控

本文研究概率布尔控制网络的集可控性问题.首先,利用矩阵半张量积方法,得到概率布尔控制网络的代数表示.其次,借助一个新的算子构造不同的可控矩阵,进而通过可控矩阵考虑自由控制序列和网络输入控制下概率布尔控制网络的集可控性问题,得到了概率布尔控制网络集可控性的充要条件.最后,给出数值例子说明本文结果的有效性.     

采用计算机算法实现复杂体系的反应网络(英文)

基于单因素微动力学理论,开发计算机算法生成了甲醇合成汽油和柴油工艺的复杂反应网络。算法采用布尔矩阵和特征向量表示烃类分子和碳正离子,并对反应网络中涉及到的所有链烃和环烃结构采用标准编码确保每一个烃类的数字代表形式不重复。进一步通过布尔矩阵的逻辑运算实现反应网络中所有的单元反应,而所有涉及在反应网络中的烃类物种都采用特征向量的形式储存,在算法中烃类的布尔矩阵形式和特征向量形式的相互转换有效的实现了反应网络的储存和拓展。由于甲醇合成汽油和柴油工艺反应网络涉及到上百万不同的烃类物种,为了在计算机中高效的实现反应网络,智能存储算法模块是整个算法中不可缺少的部分。     

基于双分支特征融合的场景文本检测方法

研究一类布尔控制网络的集成集可控性和集成集镇定性问题.首先,利用矩阵的半张量积理论,给出布尔控制网络等价的代数表示;其次,通过自由控制序列研究布尔控制网络的集成集可控性,并给出相应的充分必要条件,对于布尔控制网络的集成集镇定性问题,使其转换为集成集可控性问题,并给出相应的判定定理;最后,给出数值例子说明所提出方法的有效性.     

人工鱼群算法在基因调控网络中的应用研究

在分析基因调控网络现状及优缺点的基础上,提出利用人工鱼群算法对阈值布尔网络模型构建下的基因调控网络进行研究。将阈值布尔网络模型应用于花发育形态模型,构建基于预定义吸引子和极限环的综合网络。比较人工鱼群算法与模拟退火算法在基因调控网络中的应用情况,分析网络节点更新机制变化时布尔网络保留吸引子的能力,发现在极限环长度为2和特定网络拓扑下网络才具有鲁棒性。实验结果表明,与模拟退火算法相比,人工鱼群算法在网络发现、鲁棒性方面具有更好的性能,因此利用人工鱼群算法学习布尔网络结构是有效可行的。     

粗糙集概念与运算的布尔矩阵表示

建立了属性集与布尔矩阵以及逻辑方程组的解之间的关系;在此基础上给出了粗糙集理论中概念与运算的布尔矩阵表示;最后证明了属性约简在布尔矩阵和代数两种不同表示下是等价的。     

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.     

延迟离散神经网络动态特征的矩阵判据S

该文利用延迟离散网络的状态转移方程与矩阵不等式的等价性研究网络的动力学性质.对于具有任意连接权阵的网络,文章给出了周期为1和2的极限环存在的一些条件.同时,对于周期为1,2和4的一些特殊极限环给出了存在的条件,还得到了网络不存在任何不动点的充分条件,即只有极限环的充分条件.计算机模拟实验表明其结果是正确的.     

延迟离散神经网络动态特征的矩阵判据

该文利用延迟离散网络的状态转移方程与矩阵不等式的等价性研究网络的动力学性质.对于具有任意连接权阵的网络,文章给出了周期为1和2的极限环存在的一些条件.同时,对于周期为1,2和4的一些特殊极限环给出了存在的条件,还得到了网络不存在任何不动点的充分条件,即只有极限环的充分条件.计算机模拟实验表明其结果是正确的.     

Dynamically changing the logical behavior of the microcomputerinterface

Industrial programmable controllers and hardware simulators currently use the software method of direct logic simulation. In this method, programs contain the logical functions of several Boolean variables that are encoded directly. Each combinational circuit expressed by a group of Boolean equations requires an independent program. An alternative solution for the software implementation of the Boolean equations, named the product terms method, is presented. This method features the use of a single program to implement any multiple-output combinational circuit. To make the distinction between different circuits, a block of data defines each circuit. The product method is extended to synchronous sequential circuits, for which two tables are used. One table determines the next state of the combinational circuit, and the second table determines the outputs. An expert system has been developed to generate the table used in the product terms by interpreting the symbolic Boolean equations supplied by the user. The implementation and testing of the method are described     

多输出弹性k-旋转对称布尔函数的存在性与构造

多输出布尔函数可由多个单输出布尔函数表示,在分组密码中有着广泛的应用.多输出k-旋转对称布尔函数(k-RSBF)是多输出旋转对称布尔函数(RSBF)的扩展.本文首先研究多输出旋转对称函数和多输出k-旋转对称函数的轨道分布情况,给出了计算两类函数中长度相同轨道个数的方法.其次研究了平衡多输出k-旋转对称布尔函数的存在性,给出了在选择合适的k的前提下,n=pr、n=2pr和n=2r时,平衡(n,m)k-RSBF的构造方法.之后研究弹性多输出k-旋转对称布尔函数的存在性,分别给出了r≥3,n=2r,2≤m≤2r-r,k=2时1阶弹性(n,m)k-RSBF的构造方法,以及p为奇素数,r≥2,n=pr,2≤m≤p-1,k=p时1阶弹性(n,m)k-RSBF的构造方法.最后我们还对两种方法得到的1阶弹性多输出k-旋转对称布尔函数进行仿真测试.     

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.     

A Semi‐Tensor Product Approach to Pseudo‐Boolean Functions with Application to Boolean Control Networks

Using the semi‐tensor product method, this paper investigates several fundamental problems of general pseudo‐Boolean functions with application to the optimal control of Boolean control networks, and establishes a new framework to deal with pseudo‐Boolean inequalities, the optimization problem and the best linear approximation of pseudo‐Boolean functions. First, the pseudo‐Boolean function is expressed in the algebraic form via constructing its unique structural matrix. Second, based on the matrix expression, solving pseudo‐Boolean inequalities is converted into finding solutions to algebraic inequalities, and a set of new formulas are presented. Third, the optimization problem and the linear approximation of the pseudo‐Boolean function are considered and several new results are established. Finally, as an application, we investigate the optimal control of Boolean control networks, and present a new optimal control design procedure. It is shown through the study of illustrative examples that the new results proposed in this paper work very well.     

Algebraic method of simplifying Boolean networks using semi‐tensor product of Matrices

The huge state space of large Boolean networks makes analysis and synthesis difficult. This paper, using a new matrix analysis tool called semi‐tensor product of matrices, to explain a simplification method of Boolean networks in a mathematical manner. The idea consists of two steps. First, remove the nodes whose logical dynamics are independent of themselves directly; second, use the logical functions (LFs) of the removed nodes to substitute for their corresponding variables in the LFs of other nodes; such nodes evolve directly with both themselves and the removed nodes. We discover that the simplified and original Boolean networks share some important topological structures such as attractor cycles, steady states and paths. An algebraic algorithm is provided to find all of the cycles and steady states of simplified Boolean networks. Finally we apply the results to the metastatic melanoma network to check the effect of the simplification method.     

The Discrete Basis Problem

Matrix decomposition methods represent a data matrix as a product of two factor matrices: one containing basis vectors that represent meaningful concepts in the data, and another describing how the observed data can be expressed as combinations of the basis vectors. Decomposition methods have been studied extensively, but many methods return real-valued matrices. Interpreting real-valued factor matrices is hard if the original data is Boolean. In this paper, we describe a matrix decomposition formulation for Boolean data, the Discrete Basis Problem. The problem seeks for a Boolean decomposition of a binary matrix, thus allowing the user to easily interpret the basis vectors. We also describe a variation of the problem, the Discrete Basis Partitioning Problem. We show that both problems are NP-hard. For the Discrete Basis Problem, we give a simple greedy algorithm for solving it; for the Discrete Basis Partitioning Problem we show how it can be solved using existing methods. We present experimental results for the greedy algorithm and compare it against other, well known methods. Our algorithm gives intuitive basis vectors, but its reconstruction error is usually larger than with the real-valued methods. We discuss about the reasons for this behavior.     

优势关系下基于浓缩布尔矩阵的属性约简方法

在优势关系粗糙集方法(DRSA)的框架下,针对不协调的目标信息系统求属性约简。基于优势矩阵的方法是最常用的一类约简方法,但矩阵中不是所有的元素都有效。浓缩优势矩阵只保留对求约简有用的最小属性集,因而可以明显降低约简过程中的计算量。进一步地,浓缩布尔矩阵通过布尔代数的形式有效地弥补了优势矩阵生成效率低的缺点。文中将等价关系上的浓缩布尔矩阵属性约简方法扩展到优势关系上,针对优势矩阵提出了浓缩布尔矩阵的概念,建立了相应的高效约简方法,使效率得到明显提高。最后采用9组UCI数据进行实验,结果验证了所提方法的有效性。     

Updating method for the computation of orbits in parallel and sequential dynamical systems

In this article, we provide a matrix method in order to compute orbits of parallel and sequential dynamical systems on Boolean functions. In this sense, we develop algorithms for systems defined over directed (and undirected) graphs when the evolution operator is a general minterm or maxterm and, likewise, when it is constituted by independent local Boolean functions, so providing a new tool for the study of orbits of these dynamical systems.     

异步时序电路反馈稳定性判据

本文提出了"含相开关代数"的概念,证明了它与布尔代数是同构的,从而使布尔代数可 用于设计时序电路.文中利用含相开关代数这一概念推导出异步时序电路反馈稳定性判据, 从而能方便地找出全部不稳定转换.