The New Class of g-Chain Periodic Sorters

Aperiodic sorteris a sorting network that is a cascade of a number of identicalblocks, where outputiof each block is inputiof the next block. Previously, Dowd, Perl, Rudolph, and Saks introduced thebalancedmerging network, withN=2^kinputs/outputs and log Nstages of comparators. Using a very intricate proof, they showed that a cascade of log Nsuch blocks constitutes a sorting network. In this paper, we introduce a large class of merging networks with the same periodic property. This class contains 2^N/2−1networks, whereN=2^kis the number of inputs. The balanced merger is one network in this class. Other networks use fewer comparators. We provide a very simple and elegant correctness proof based on the recursive structure of the networks.     

Effect of leakage delay on the almost periodic solutions of fuzzy cellular neural networks

ABSTRACT

In this paper, fuzzy cellular neural networks with time-varying delays in leakage terms are investigated. With the help of the differential inequality theory and almost periodic function theory, a set of sufficient criteria that guarantee the existence and exponential stability of almost periodic solutions of fuzzy cellular neural networks with time-varying delays in leakage terms are established. Our results are new and complement some previously known ones. Moreover, numerical simulations are carried out to verify our theoretical results.     

Pseudo almost periodic solutions for neutral type SICNNs with D operator

In this paper, neutral type shunting inhibitory cellular neural networks with D operator are considered. Based on Lyapunov functional method and differential inequality technique, some new criteria are derived to guarantee the existence and global exponential stability of pseudo almost periodic solutions of considered systems. In addition, an example and its numerical simulations are provided to show the validity and the advantages of the obtained results.     

Existence and Exponential Stability of Multiple Periodic Solutions for a Multidirectional Associative Memory Neural Network

The paper proposes several mathematical models of the multidirectional associative memory (MAM) neural network by analyzing its structure. A model of MAM with distributed delays is studied. Under some new assumptions on activation functions, 2^n₀[m/2]{2^{n_0[m/2]}} invariant subsets of MAM are constructed. Then the existence and the exponential stability of 2^n₀[m/2]{2^{n_0[m/2]}} periodic solutions located on invariant subsets are obtained by constructing a suitable Liapunov function and a Poincaré mapping. An estimating method of the exponential convergence rate is given. The obtained results are new to MAM neural networks. An example is given to illustrate the effectiveness of the results.     

Computing Mimicking Networks

A mimicking network for a k -terminal network, N , is one whose realizable external flows are the same as those of N . Let S(k) denote the minimum size of a mimicking network for a k -terminal network. In this paper we give new constructions of mimicking networks and prove the following results (the values in brackets are the previously best known results): S(4)=5 [2 ¹⁶ ] , S(5)=6 [2 ³² ] . For bounded treewidth networks we show S(k)= O(k) [2^ 2 ^k ] , and for outerplanar networks we show S(k) 10k-6 [k ² 2 ^k+2 ] . Received April 1, 1997; revised December 10, 1997.     

Almost periodic cellular neural networks with neutral-type proportional delays

This paper presents a new result on the existence, uniqueness and generalised exponential stability of almost periodic solutions for cellular neural networks with neutral-type proportional delays and D operator. Based on some novel differential inequality techniques, a testable condition is derived to ensure that all the state trajectories of the system converge to an almost periodic solution with a positive exponential convergence rate. The effectiveness of the obtained result is illustrated by a numerical example.     

Exact Solutions to Diameter and Routing Problems in PEC Networks

Recently, the diameter problem for packed exponential connections (PEC) networks was addressed by Cho-Chin Lin and V. K. Prasanna [Proc. Symposium on Parallel and Distributed Processing, 1992, pp. 368–375], who presented asymptotically tight bounds for the diameter and showed asymptotically optimal routing algorithms. In this paper exact, solutions to the diameter and routing problems of PEC networks are derived, thereby strengthening the asymptotic bounds of Lin and Prasanna. For anN= 2ⁿnode PEC network, with[formula]an integer, it is shown that the diameter is given by the simple expression[formula]An exact expression for the diameter of PEC networks for generalNis also derived. Efficient algorithms for shortest-path routing between nodes in a PEC network are then developed. These algorithms use at mostO(log²N) time for computing the lengths of minimal routes between nodes. Finally, a simple modification to obtain symmetric PEC networks is suggested.     

Nodal Superconvergence of SDFEM for Singularly Perturbed Problems

In this paper, we analyze the streamline diffusion finite element method for one dimensional singularly perturbed convection-diffusion-reaction problems. Local error estimates on a subdomain where the solution is smooth are established. We prove that for a special group of exact solutions, the nodal error converges at a superconvergence rate of order (ln ε ⁻¹/N)^2k (or (ln N/N)^2k ) on a Shishkin mesh. Here ε is the singular perturbation parameter and 2N denotes the number of mesh elements. Numerical results illustrating the sharpness of our theoretical findings are displayed.     

A three-stage construction for multiconnection networks

Summary A multiconnection network of size N is a switching network with N inputs and N outputs which realizes multiconnections, i.e., connections between the N inputs and N outputs in such a way that every output is connected to exactly one input, but an input can be connected to an arbitrary number of outputs. That network is complete if it can realize all N ^N multiconnections. This structure generalizes the permutation network. We consider here the design of multiconnection networks by a three-stage Clos network using complete substitution networks as its building cells and we show that the resulting multiconnection network is complete if and only if the cells in the middle stage have size 2. Moreover, we describe the control algorithm for such a network. This leads to the design of cellular multiconnection networks of arbitrary size with a relatively simple control algorithm.     

Almost Periodic Solutions for SICNNs with Neutral Type Proportional Delays and <Emphasis Type="Italic">D</Emphasis> Operators

This article is concerned with shunting inhibitory cellular neural networks involving neutral type proportional delays and D operators. Applying Lyapunov functional method and differential inequality techniques, we employ a novel argument to establish some new criteria on the existence and generalized exponential stability of almost periodic solutions of the addressed systems. In addition, numerical simulations are carried out to verify our theoretical findings.     

Time Series Generation by Recurrent Neural Networks

The properties of time series, generated by continuous valued feed-forward networks in which the next input vector is determined from past output values, are studied. Asymptotic solutions developed suggest that the typical stable behavior is (quasi) periodic with attractor dimension that is limited by the number of hidden units, independent of the details of the weights. The results are robust under additive noise, except for expected noise-induced effects – attractor broadening and loss of phase coherence at large times. These effects, however, are moderated by the size of the network N.     

Pseudo almost periodic solutions of discrete-time neutral-type neural networks with delays

This paper is concerned with discrete-time neutral-type neural networks with delays. The existence and uniqueness results of pseudo almost periodic solutions are established by applying the contraction mapping principal. By using some mathematical analysis techniques, we further obtain the boundness, exponential attractivity and global exponential stability of pseudo almost periodic solutions for the considered networks. Finally, a typical example and the corresponding numerical simulations have been carried out to support our analytic findings.     

Global Asymptotic Stability of Periodic Solutions for Discrete Time Delayed BAM Neural Networks by Combining Coincidence Degree Theory with LMI Method

In this paper, we are concerned with the existence and global asymptotic stability of periodic solutions for a class of delayed discrete-time BAM neural networks. Instead of using the method of the priori estimate of periodic solutions in existing papers to study periodic solutions of neural networks, by combining Mawhin’s continuation theorem of coincidence degree theory with linear matrix inequality (LMI) method as well as inequality techniques, some novel LMI-based sufficient conditions to guarantee the existence and global asymptotic stability of periodic solutions for the neural networks are established. Our results which are both dependent on time delay and external inputs of the neural networks are new and complementary to the existing papers.     

Stability Analysis of Periodic Solution for a Complex‐valued Neural Networks With Bounded and Unbounded Delays

This paper is devoted to investigating a class of complex‐valued neural networks with bounded and unbounded delays. By means of Mawhin's continuation theorem, some criteria on existence and uniqueness of periodic solution are established for the complex‐valued neural networks. By constructing an appropriate Lyapunov‐Krasovskii functional and M?matrix theory, some sufficient conditions are derived for the global exponential stability of periodic solutions to the complex‐valued neural networks. Finally, two numerical examples are given to show the effectiveness and merits of the present results.     

The changes on synchronizing ability of coupled networks from ring networks to chain networks

In this paper, two different ring networks with unidirectional couplings and with bidirectional couplings were discussed by theoretical analysis. It was found that the effects on synchronizing ability of the two different structures by cutting a link are completely opposite. The synchronizing ability will decrease if the change is from bidirectional ring to bidirectional chain. Moreover, the change on synchro- nizing ability will be four times if the number of N is large enough. However, it will increase obviously from unidirectional ring to unidirectional chain. It will be N 2/(2π2) times if the number of N is large enough. The numerical simulations confirm the conclusion in quality. This paper also discusses the effects on synchronization by adding one link with different length d to these two different structures. It can be seen that the effects are different. Theoretical results are accordant to numerical simulations. Synchronization is an essential physics problem. These results pro- posed in this paper have some important reference meanings on the real world networks, such as the bioecological system networks, the designing of the circuit, etc.     

On necessary conditions for scale-freedom in complex networks,with applications to computer communication systems

Many complex networks exhibit a scale-free, power-law distribution of vertex degrees. This common feature is a consequence of two generic mechanisms relating to the formation of real networks: (i) networks tend to expand over time through the addition of new vertices and (ii) new vertices attach preferentially to those that are already well connected. We show that for many natural or man-made complex networks possessing a scale-free power-law distribution with the exponent γ ≥ 2, the number of degree-1 vertices, when nonzero, is of the same order as the network size N and that the average degree is of order at most log N. Our results expose another necessary characteristic of such networks. Furthermore, our method has the benefit of relying only on conditions that are static and easily verified for arbitrary networks. We use the preceding results to derive a closed-form formula approximating the distance distribution in scale-free networks. Such distributions are applied extensively in the fields of computer communication and software architecture, among other domains.     

Exponential Stability of Pseudo Almost Periodic Solutions for Cellular Neural Networks with Multi-Proportional Delays

This paper concerns with the pseudo almost periodic solutions for a class of cellular neural networks model with multi-proportional delays. By applying contraction mapping fixed point theorem and differential inequality techniques, we establish some sufficient conditions for the existence and exponential stability of pseudo almost periodic solutions for the model, which improve and supplement existing ones. Moreover, an example and its numerical simulation are given to support the theoretical results.     

Work-efficient BSR-based parallel algorithms for some fundamental problems in graph theory

This paper presents BSR-parallel algorithms for some problems in fundamental graph theory : transitive closure, connected components, spanning tree, bridges and articulation points of a graph and bipartite graph recognition. There already exist constant time algorithms to solve these problems on a mesh with reconfigurable bus system using O(N ⁴) processors. Here we show that these problems can be solved in constant time using only O(N ²) processors on the BSR model (N is the number of vertices of the graph G). Therefore, our algorithms are more work-efficient. These new results suggest that many other problems in graph theory can be solved in constant time using the BSR model.     

Advanced splitting-integrating methods with high convergence rates for restoring images and patterns

The restoration of digital images and patterns by the splitting-integrating method (SIM) proposed by Li (1993) and Liet al. (1992) is much simpler than other algorithms because no solutions of nonlinear algebraic equations are required. Let a pixel in 2D images be split intoN ² subpixels; the convergence rates areO(1/N) andO/(1/N ²) for pixel greyness under image normalization by SIM. In this paper, the advanced SIM using spline functions can raise the convergence rates to (O(1/N ³) andO(1/N ⁴). Error bounds of pixel greyness obtained are derived from numerical analysis, and numerical experiments are carried out to confirm the high convergence rates ofO(1/N ³) andO(1/N ⁴).