A characterization of solvability for a class of networks

In this paper,we find that Property P can be generalized to characterize the solvability of a kind of networks with any number of sources,thus partially answering the open problem as to whether there are properties similar to Property P to characterize the solvability of some networks.As an application,for a given integer n,we construct such a solvable network that has no solvable solution if its alphabet size is less than n.     

A real-time messaging system for token ring networks

The Computer Networks Laboratory at the University of Virginia has developed a real-time messaging service that runs on IBM PCs and PC/ATs when interconnected with a Proteon ProNET-10 token ring local area network. The system is a prototype for a real-time communications network to be used aboard ships. The system conforms to the IEEE 802.2 logical link control standard for type I (connectionless, or datagram) service, with an option for acknowledged datagrams. The application environment required substantial network throughput and bounded message delay. Thus, the development philosophy was to emphasize performance initially and to offer only primitive user services. After providing and measuring the performance of a basic datagram service, the intent is to add additional user services one at a time and to retain only those which the user can ‘afford’ in terms of their impact on throughput, delay, and CPU utilization. The current system is programmed in C. The user interface is a set of C procedure calls that initialize tables, reserve buffer space, send and receive messages, and report network status. The system is now operational, and initial performance measurements are complete. Using this system, an individual PC can transmit or receive approximately 200 short (about 100 bytes) messages per second, and the PC/AT operates at nearly 500 short messages per second.     

A class of nonlinear proximal point algorithms for variational inequality problems

This work is motivated by a recent work on an extended linear proximal point algorithm (PPA) [B.S. He, X.L. Fu, and Z.K. Jiang, Proximal-point algorithm using a linear proximal term, J. Optim. Theory Appl. 141 (2009), pp. 299–319], which aims at relaxing the requirement of the linear proximal term of classical PPA. In this paper, we make further contributions along the line. First, we generalize the linear PPA-based contraction method by using a nonlinear proximal term instead of the linear one. A notable superiority over traditional PPA-like methods is that the nonlinear proximal term of the proposed method may not necessarily be a gradient of any functions. In addition, the nonlinearity of the proximal term makes the new method more flexible. To avoid solving a variational inequality subproblem exactly, we then propose an inexact version of the developed method, which may be more computationally attractive in terms of requiring lower computational cost. Finally, we gainfully employ our new methods to solve linearly constrained convex minimization and variational inequality problems.     

Penalty approximation method for a class of elliptic variational inequality problems

In this paper, two existence results of solutions for a class of elliptic variational inequalities are obtained by considering the approximations of the solutions to a class of penalized differential equations.     

A heuristic approach to solving a class of bilinear matrix inequality problems

Many canonical and modern control problems can be recast into the problem of a group of matrix inequalities. Some of them are in the form of linear matrix inequalities (LMIs), which can be solved very efficiently by the powerful LMI toolbox in Matlab, but some others are in the form of bilinear matrix inequalities. The characteristic of this latter class of problems is that when the so called “communicating variables” are fixed, the overall problem will be reduced to the problem in LMIs. Thus, how to find the communicating variables is the key to solve the whole problem. In this paper, an optimal estimate for the communicating variables is presented. We will illustrate our method by completely solving the problems of overshoot bound control and reachable set analysis for uncertain systems. Numerical examples are provided to show the effectiveness of the proposed method.     

A class of neural networks for independent component analysis

Independent component analysis (ICA) is a recently developed, useful extension of standard principal component analysis (PCA). The ICA model is utilized mainly in blind separation of unknown source signals from their linear mixtures. In this application only the source signals which correspond to the coefficients of the ICA expansion are of interest. In this paper, we propose neural structures related to multilayer feedforward networks for performing complete ICA. The basic ICA network consists of whitening, separation, and basis vector estimation layers. It can be used for both blind source separation and estimation of the basis vectors of ICA. We consider learning algorithms for each layer, and modify our previous nonlinear PCA type algorithms so that their separation capabilities are greatly improved. The proposed class of networks yields good results in test examples with both artificial and real-world data.     

Stability analysis for a special class of dynamical networks

In this article, stability analysis and decentralised control problems are studied for a special class of linear dynamical networks. Necessary and sufficient conditions for stability and stabilisability under a decentralised control strategy are given for this type of linear networks. Especially, two types of linear regular networks, star-shaped networks and globally coupled networks, are studied in detail, respectively. A dynamical network can be viewed as a large-scale system composed of some subsystems with some coupling structures, based on this, the relationship between the stability of a network and the stability of its corresponding subsystems is studied. Different from the discussions that the subsystems in networks vary with different coupling structures (Duan, Z.S., Wang, J.Z., Chen, G.R., and Huang, L. (2008), ‘Stability Analysis and Decentralised Control of a Class of Complex Dynamical Networks’, Automatica, 44, 1028–1035), the subsystems in network discussed in this article remain unchanged with different interconnections which is the same as in general large-scale system. It is also pointed out that some subsystems must be made unstable for the whole network to be stable in some special cases. Moreover, the controller design method based on parameter-dependent Lyapunov function is provided.     

A new class of projection and contraction methods for solving variational inequality problems

This paper presents a new class of projection and contraction methods for solving monotone variational inequality problems. The methods can be viewed as combinations of some existing projection and contraction methods and the method of shortest residuals, a special case of conjugate gradient methods for solving unconstrained nonlinear programming problems. Under mild assumptions, we show the global convergence of the methods. Some preliminary computational results are reported to show the efficiency of the methods.     

A parallel algorithm for solving special tridiagonal systems on ring networks

The solution of special linear, circulant-tridiagonal systems is considered. In this paper, a fast parallel algorithm for solving the special tridiagonal systems, which includes the skew-symmetric and tridiagonal-Toeplitz systems, is presented. Employing the diagonally dominant property, our parallel solver does need only local communications between adjacent processors on a ring network. An error analysis is also given. On the nCUBE/2E multiprocessors, some experimental results demonstrate the good performance of our stable parallel solver.     

A new class of wavelet networks for nonlinear system identification

A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions.     

A class of multistage conference switching networks for group communication

There is a growing demand for network support for group applications, in which messages from one or more sender(s) are delivered to a large number of receivers. Here, we propose a network architecture for supporting a fundamental type of group communication, conferencing. A conference refers to a group of members in a network who communicate with each other within the group. We consider adopting a class of multistage networks, such as a baseline, an omega, or an indirect binary cube network, composed of switch modules with fan-in and fan-out capability for a conference network which supports multiple disjoint conferences. The key issue in designing a conference network is to determine the multiplicity of routing conflicts, which is the maximum number of conflict parties competing a single interstage link when multiple disjoint conferences simultaneously present in the network. Our results show that, for a network of size n /spl times/ n, the multiplicities of routing conflicts are small constants (between 2 and 4) for an omega network or an indirect binary cube network; while it can be as large as /spl radic/n/q + 1 for a baseline network, where q is the minimum allowable conference size. Thus, our design for conference networks is based on an omega network or an indirect binary cube network. We also develop fast self-routing algorithms for setting up routing paths in the newly designed conference networks. As can be seen, such an n /spl times/ n conference network has O(logn) routing time and communication delay and O(nlogn) hardware cost. The conference networks are superior to existing designs in terms of routing complexity, communication delay and hardware cost. The conference network proposed is rearrangeably nonblocking in general, and is strictly nonblocking under some conference service policy. It can be used in applications that require efficient or real-time group communication.     

An algorithm of optimization for a special class of networks

In this paper the author presents an algorithm of optimization for a special class of networks not having the Markov property. A definition of the class of networks under consideration and a formulation of the optimization problem are given. A conception of the algorithm is discussed and next the general and detailed flow diagrams of the algorithm are offered. The realization of the algorithm is illustrated with a simple example showing the process of execution of the tasks included in the algorithm. Some possibilities of applying the algorithm in allocation problems and nonlinear integer programming are presented. The computer program in FORTRAN IV for the execution of the algorithm is enclosed.     

A robust adaptive tracking controller using neural networks for a class of nonlinear systems

A neural networkbased robust adaptive tracking control scheme is proposed for a class of nonlinear systems. It is shown that, unlike most neural control schemes using the back-propagation training technique, one hidden layer neural controller is designed in the Lyapunov sense, and the parameters of the neural controller are then adaptively adjusted for the compensation of unknown dynamics and nonlinearities. Using this scheme, not only strong robustness with respect to unknown dynamics and nonlinearities can be obtained, but also asymptotic error convergence between the plant output and the reference model output can be guaranteed. A simulation example based on a one-link non-linear robotic manipulator is given in support of the proposed neural control scheme.     

A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks

In real life, information about the world is uncertain and imprecise. The cause of this uncertainty is due to: deficiencies on given information, the fuzzy nature of our perception of events and objects, and on the limitations of the models we use to explain the world. The development of new methods for dealing with information with uncertainty is crucial for solving real life problems. In this paper three interval type-2 fuzzy neural network (IT2FNN) architectures are proposed, with hybrid learning algorithm techniques (gradient descent backpropagation and gradient descent with adaptive learning rate backpropagation). At the antecedents layer, a interval type-2 fuzzy neuron (IT2FN) model is used, and in case of the consequents layer an interval type-1 fuzzy neuron model (IT1FN), in order to fuzzify the rule’s antecedents and consequents of an interval type-2 Takagi-Sugeno-Kang fuzzy inference system (IT2-TSK-FIS). IT2-TSK-FIS is integrated in an adaptive neural network, in order to take advantage the best of both models. This provides a high order intuitive mechanism for representing imperfect information by means of use of fuzzy If-Then rules, in addition to handling uncertainty and imprecision. On the other hand, neural networks are highly adaptable, with learning and generalization capabilities. Experimental results are divided in two kinds: in the first one a non-linear identification problem for control systems is simulated, here a comparative analysis of learning architectures IT2FNN and ANFIS is done. For the second kind, a non-linear Mackey-Glass chaotic time series prediction problem with uncertainty sources is studied. Finally, IT2FNN proved to be more efficient mechanism for modeling real-world problems.     

A new robust training algorithm for a class of single-hidden layer feedforward neural networks

A robust training algorithm for a class of single-hidden layer feedforward neural networks (SLFNs) with linear nodes and an input tapped-delay-line memory is developed in this paper. It is seen that, in order to remove the effects of the input disturbances and reduce both the structural and empirical risks of the SLFN, the input weights of the SLFN are assigned such that the hidden layer of the SLFN performs as a pre-processor, and the output weights are then trained to minimize the weighted sum of the output error squares as well as the weighted sum of the output weight squares. The performance of an SLFN-based signal classifier trained with the proposed robust algorithm is studied in the simulation section to show the effectiveness and efficiency of the new scheme.