Singular Boolean networks： Semi-tensor product approach

Singular Boolean networks are introduced in this paper. Via semi-tensor product of matrices and the matrix expression of logical functions, two kinds of the condensed algebraic expressions of singular Boolean networks are obtained. The normalization problem of singular Boolean networks is addressed; that is, under what condition singular Boolean networks can be converted into normal Boolean networks with algebraic restric- tions. Then one sufficient condition and one necessary and sufficient condition are derived for the normalization problem. Furthermore, the solvability of singular Boolean networks is discussed and the concept of admissible initial values of singular Boolean networks is presented. Finally, fixed points and cycles of singular Boolean networks are also investigated.     

Model matching of switched asynchronous sequential machines via matrix approach

This paper investigates model matching problem of switched asynchronous sequential machines (ASMs) via semi-tensor product (STP) of matrices. A switched ASM is composed of several input/state ASMs and it cut-overs between submachines in asynchronous mechanism. By using STP method, a switched ASM is depicted as a discrete-time equation form. Under this framework, stable transition matrix and admissible model-input-state transition matrix are defined. Then, two important problems, reachability and optimal control input design of switched ASMs, are discussed by these two new matrices, respectively. Finally, a necessary and sufficient condition for the existence of a controller for model matching is obtained and a practical example on asynchronous error accumulators is provided to show the feasibility of the proposed method.     

Semi-tensor product of matrices approach to reachability of finite automata with application to language recognition

This paper investigates the transition function and the reachability conditions of finite automata by using a semitensor product of matrices, which is a new powerful matrix analysis tool. The states and input symbols are first expressed in vector forms, then the transition function is described in an algebraic form. Using this algebraic representation, a sufficient and necessary condition of the reachability of any two states is proposed, based on which an algorithm is developed for discovering all the paths from one state to another. Furthermore, a mechanism is established to recognize the language acceptable by a finite automaton. Finally, illustrative examples show that the results/algorithms presented in this paper are suitable for both deterministic finite automata (DFA) and nondeterministic finite automata (NFA).     

Controllability of Boolean control networks avoiding states set

In this paper, using semi-tensor product and the vector form of Boolean logical variables, the Boolean control network （BCN） is expressed as a bilinear discrete time system about state and control variables. Based on the algebraic form, the reachability and controllability avoiding undesirable states set are discussed. The reachability and controllability discussed here are under certain constraint and tile definitions of reachability and controllability avoiding undesirable states set have practical meaning. Also, the necessary and sufficient conditions for reachability and controllability are given. At last, the control sequence that steers one state to another is constructed.     

Set reachability and set stability of Boolean networks with state-dependent asynchronous updating rule

Asynchronous behavior is significant for real biological systems. This paper explores the impact of state-dependent asynchronous updating rule (SDAUR) on the set reachability and set stability of Boolean networks (BNs). First, a set of state-dependent control variables is introduced to describe the SDAUR. Second, a new asynchronous set reachablity matrix is constructed based on an auxiliary input and semi-tensor product. Third, using the asynchronous set reachablity matrix, several necessary and sufficient conditions are obtained for the set reachablity and set stability of BNs with SDAUR. Finally, the new results proposed in this paper are verified through the immunomic network.     

Testing protocols in Internet of Things by a formal passive technique

In recent years, Extensible Messaging and Presence Protocol （XMPP） is gaining momentum in Internet of Things （IoT）. It has been widely used in chatting, message exchanging and unique addressing. As a matter of course, it raises an interesting issue： how to formally test the conformance and performance of XMPP in IoT environment. While conformance testing of communicating protocols is a functional test that verifies whether the behaviors of the protocol satisfy defined requirements, performance testing is a qualitative and quantitative test that aims at checking whether the performance requirements of the protocol are satisfied under certain conditions. In this paper, we present a logic-based passive testing approach that can test both the conformance and the performance of XMPP protocol through real execution traces and formally specified properties. To evaluate and assess our methodology, we present a developed prototype and the experiments with a set of XMPP properties. Finally, the relevant verdicts and conclusions are provided.     

Reachability matrix and relation to large-scale systems

A sequential derivation of the reachability matrix is given, related to graph theoretic considerations, and earlier results on the structural inverse of a matrix are reformulated on the basis of an observed duality. A relationship between a matrix, a full rank permutation matrix included in it and its reachability matrix are given, as well as a property of the reachability matrix of a product. A hypothesis on the reachability matrix, stating that it is ‘its own inverse’ and relating to the structural modal matrix, is confirmed and the reachability and the acyclic input-output reachable partitions of dynamic systems are discussed; forms relating them to structural controllability, structural observability and structural transfer function matrices are presented.     

Modeling and analysis of colored petri net based on the semi-tensor product of matrices

This paper applies the model petri net method based on the semi-tensor product of matrices to colored petri net. Firstly, we establish the marking evolution equation for colored petri net by using the semitensor product of matrices. Then we define the concept of controllability and the control-marking adjacency matrix for colored petri net. Based on the marking evolution equation and control-marking adjacency matrix, we give the necessary and sufficient condition of reachability and controllability for colored petri net. The algorithm to verify the reachability of colored petri net is given, and we analyze the computational complexity of the algorithm. Finally, an example is given to illustrate the effectiveness of the proposed theory. The significance of the paper lies in the application of the model petri net method based on the semitensor product of matrices to colored petri net. This is a convenient way of verifying whether one marking is reachable from another one as well as finding all firing sequences between any two reachable markings. Additionally, the method lays the foundations for the analysis of other properties of colored petri net.     

Customization of Wavelet Function for Pupil Fluctuation Analysis to Evaluate Levels of Sleepiness

This paper proposes a method to customize a wavelet function for the analysis of pupil diameter fluctuation in the detection of drowsiness states under a driving simulation. The methodology relies on a genetic algorithm-based optimization and lifting schemes, which are a flexible and fast implementation of the discrete wavelet transform. To customize the wavelet function a clustering separability metric is employed as a fitness function so that the feature space created by the wavelet analysis exhibits the maximum class separability favorable for classification. Therefore, a completely new wavelet function is created, having unique characteristics customized to pupil diameter fluctuation analysis. It is demonstrated that the customized wavelet function own distinguished frequency and temporal responses suitable specifically for pupil diameter fluctuation analysis （namely, application-dependent）, and in the classification they outperform classical wavelet families including Daubechies, Coiflet and Symlet, which are assumed to be application-independent. Thus the proposed method is useful for analysis of pupil fluctuation in evaluating sleepiness levels, as has been demonstrated in other applications.     

Improving the Evaluation of Generator Matrix G by Initial Upper Bound Estimation

STTC （space-time trellis code） can achieve both the diversity and coding gains. To maximize the advantages of STTC, two design criteria for slow Rayleigh fading channels will be used： i.e., the rank and determinant criteria. This paper focuses on the determinant criteria, which involves the evaluation of the generator matrix G. Evaluation is improved by pruning the search process earlier, which is made possible by estimating the initial upper bound prior to the search. In order to reduce the search complexity, the initial upper bound will be calculated at the minimal cycle. Comparatively, it can reduce the search space by 25.8%.     

Stability analysis of constrained MPC applied to discrete-time nonlinear with CLF system

The model predictive control （MPC） strategy with a control Lyapunov function （CLF） as terminal cost is commonly used for its guaranteed stability. In most of the cases, CLF is locally designed, and the region of attraction is limited, especially when under control constraints. In this article, the stability and the region of attraction of constrained MPC that is applied to the discrete-time nonlinear system are explicitly analyzed. The region of feasibility is proposed to substitute the region of attraction, which greatly reduces the calculation burden of terminal constraints inequalities and guarantees the stability of the MPC algorithm. Also, the timevariant terminal weighted factor is proposed to improve the dynamic performance of the close-loop system. Explicit experiments verify the effectiveness and feasibility of the relative conclusions, which provide practically feasible ways to stabilize the unstable and/or fast-dynamic systems.     

Controller Design for Networked Control System with Uncertain Parameters

This paper deals with the problem of controller design for NCSs （networked control systems） with uncertain parameters and network induced time-delays. In the case of long time delay constraint and data package loss, the closed-loop model of a class of NCSs is presented for controlled objects with uncertain parameters. Based on Lyapunov stability theory combined with LMIs （linear matrix inequalities） techniques, the design method of state feedback controller for NCSs with asymptotic stability is given in the form of LMIs. Numerical example and simulation suggest that the results are effective and are an improvement over previous ones.     

A survey on distributed compressed sensing： theory and applications

The compressed sensing （CS） theory makes sample rate relate to signal structure and content. CS samples and compresses the signal with far below Nyquist sampling frequency simultaneously. However, CS only considers the intra-signal correlations, without taking the correlations of the multi-signals into account. Distributed compressed sensing （DCS） is an extension of CS that takes advantage of both the inter- and intra-signal correlations, which is wildly used as a powerful method for the multi-signals sensing and compression in many fields. In this paper, the characteristics and related works of DCS are reviewed. The framework of DCS is introduced. As DCS＇s main portions, sparse representation, measurement matrix selection, and joint reconstruction are classified and summarized. The applications of DCS are also categorized and discussed. Finally, the conclusion remarks and the further research works are provided.     

Finite series solutions for the transition matrix and the covariance of a time-invariant system

The transition matrixvarphicorresponding to then-dimensional matrixAcan be represented byvarphi(t) = g_{1}(t)I + g_{2}(t)A + ... + g_{n}(t)A^{n-1}, where the vectorg^{T} = (g_{1}, ... , g_{n})is generated fromdot{g}^{T} = g^{T}A_{c}, g^{T}(0) = (1, 0, ... , 0)and Acis the companion matrix toA. The result is applied to the covariance differential equationdot{C} = AC + CA^{T} + Qand its solution is written as a finite series. The equations are presented in a form amenable for implementation on a digital computer.     

Random Matrix Theory Based Cognitive Radio Spectrum Sensing

A cognitive radio system allows higher data transmission rates due to the efficient spectrum utilization. Spectrum sensing plays a substantial role in such a cognition scenario. In this paper, a novel multiple antenna sensing algorithm is proposed for detecting the presence or the absence of the primary user signal. The scheme is called CRABWISE （Cognitive RAdio sensing Based on the joint distribution of pseudo WIShart matrix Eigenvalues）. It turns out that without prior information about the PU （primary user） signal, CRABWISE performs near to the optimal sensing performance, which is observed for an energy detection sensing being equipped with perfect prior information of the PU signal. The performance of CRABWISE is investigated using the receiver operating characteristic for signals transmitted over a delay-dispersive channel. Moreover, we study how to find the optimum threshold for the proposed test numerically. The achievable performance is considered for increasing length of the received signal frame in terms of both probability of detection and probability of a wrong decision.     

The Mysterious Behavior of Term by Term Expectation

Generalizing detection performance expressions by incorporating new fading models such as Weibul and generalized Gamma （α-μ） can be accomplished at the expense of mathematical complexity. Non-integer powers combined with exponential or special functions represent a real challenge in evaluating the necessary integrals. In this paper the authors highlight the divergence problems associated with solving complicated integrals by series expansions focusing on detection problems and illustrating the common mistakes encountered when carrying term by term integration. Additionally, the authors collected different mathematical theories to consolidate the sufficient conditions to achieve convergent results.     

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.     

Construction of a key-dependent message secure symmetric encryption scheme in the ideal cipher model

Key-dependent message （KDM） security is an important security issue that has attracted much research in recent years. In this paper, we present a new construction of the symmetric encryption scheme in the the ideal cipher model （ICM）; we prove that our scheme is KDM secure against active attacks with respect to arbitrary polynomialtime challenge functions. Our main idea is to introduce a universal hash function （UHF） h as a random value for each encrypfion, and then use s = h（sk） as the key of the ideal cipher F, where sk is the private key of our symmetric encryption scheme. Although many other schemes that are secure against KDM attacks have already been proposed, in both the ideal standard models, the much more significance of our paper is the simplicity in which we implement KDM security against active attacks.     

Design of semi-tensor product-based kernel function for SVM nonlinear classification

The kernel function method in support vector machine (SVM) is an excellent tool for nonlinear classification. How to design a kernel function is difficult for an SVM nonlinear classification problem, even for the polynomial kernel function. In this paper, we propose a new kind of polynomial kernel functions, called semi-tensor product kernel (STP-kernel), for an SVM nonlinear classification problem by semi-tensor product of matrix (STP) theory. We have shown the existence of the STP-kernel function and verified that it is just a polynomial kernel. In addition, we have shown the existence of the reproducing kernel Hilbert space (RKHS) associated with the STP-kernel function. Compared to the existing methods, it is much easier to construct the nonlinear feature mapping for an SVM nonlinear classification problem via an STP operator.     

An approach to cyclic protocol validation

In this paper, the notion of fair reachability is generalized to cyclic protocols with more than two processes, where all the processes in a protocol are connected via a unidirectional ring and each process might contain internal transitions and can be non-deterministic. We identify ‘indefiniteness’ as a new type of logical error due to reachable internal transition cycles. By properly incorporating internal transitions into the formulation, we show that, with a few modifications, all the previous results established for cyclic protocols without non-deterministic and internal transitions still hold in the augmented model. Furthermore, by combining fair progress and maximal progress during state exploration, we prove that the following three problems are all decidable for Q, the class of cyclic protocols with finite fair reachable state spaces: (1) global state reachability; (2) abstract state reachability; and (3) execution cycle reachability. In the course of the investigation, we also show that detection of k-indefiniteness and k-livelock are decidable for Q.