TCP Issues in Mobile Ad Hoc Networks: Challenges and Solutions

Mobile ad hoc networks （MANETs） are a kind of very complex distributed communication systems with wireless mobile nodes that can be freely and dynamically self-organized into arbitrary and temporary network topologies. MANETs inherit several limitations of wireless networks, meanwhile make new challenges arising from the specificity of MANETs, such as route failures, hidden terminals and exposed terminals. When TCP is applied in a MANET environment, a number of tough problems have to be dealt with. In this paper, a comprehensive survey on this dynamic field is given. Specifically, for the first time all factors impairing TCP performance are identified based on network protocol hierarchy, i.e., lossy wireless channel at the physical layer; excessive contention and unfair access at the MAC layer; frail routing protocol at the network layer, the MAC layer and the network layer related mobile node; unfit congestion window size at the transport layer and the transport layer related asymmetric path. How these factors degrade TCP performance is clearly explained. Then, based on how to alleviate the impact of each of these factors listed above, the existing solutions are collected as comprehensively as possible and classified into a number of categories, and their advantages and limitations are discussed. Based on the limitations of these solutions, a set of open problems for designing more robust solutions is suggested.     

Stability properties of labeling recursive auto-associative memory

Labeling recursive auto-associative memory (LRAAM) is an extension of the RAAM model by Pollack (1990) to obtain distributed reduced representations of labeled directed graphs. In this paper some mathematical properties of LRAAM are discussed. Specifically, sufficient conditions on the asymptotical stability of the decoding process along a cycle of the encoded structure are given. LRAAM can be transformed into an analog Hopfield network with hidden units and an asymmetric connections matrix by connecting the output units with the input units. In this architecture encoded data can be accessed by content and different access procedures can be defined depending on the access key. Each access procedure corresponds to a particular constrained version of the recurrent network. The authors give sufficient conditions under which the property of asymptotical stability of a fixed point in one particular constrained version of the recurrent network can be extended to related fixed points in different constrained versions of the network. An example of encoding of a labeled directed graph on which the theoretical results are applied is given and discussed.     

A multilayer incremental neural network architecture for classification

A new multilayer incremental neural network (MINN) architecture and its performance in classification of biomedical images is discussed. The MINN consists of an input layer, two hidden layers and an output layer. The first stage between the input and first hidden layer consists of perceptrons. The number of perceptrons and their weights are determined by defining a fitness function which is maximized by the genetic algorithm (GA). The second stage involves feature vectors which are the codewords obtained automaticaly after learning the first stage. The last stage consists of OR gates which combine the nodes of the second hidden layer representing the same class. The comparative performance results of the MINN and the backpropagation (BP) network indicates that the MINN results in faster learning, much simpler network and equal or better classification performance.     

A neural network approach to job-shop scheduling

A novel analog computational network is presented for solving NP-complete constraint satisfaction problems, i.e. job-shop scheduling. In contrast to most neural approaches to combinatorial optimization based on quadratic energy cost function, the authors propose to use linear cost functions. As a result, the network complexity (number of neurons and the number of resistive interconnections) grows only linearly with problem size, and large-scale implementations become possible. The proposed approach is related to the linear programming network described by D.W. Tank and J.J. Hopfield (1985), which also uses a linear cost function for a simple optimization problem. It is shown how to map a difficult constraint-satisfaction problem onto a simple neural net in which the number of neural processors equals the number of subjobs (operations) and the number of interconnections grows linearly with the total number of operations. Simulations show that the authors' approach produces better solutions than existing neural approaches to job-shop scheduling, i.e. the traveling salesman problem-type Hopfield approach and integer linear programming approach of J.P.S. Foo and Y. Takefuji (1988), in terms of the quality of the solution and the network complexity.     

Hopfield神经网络在机组组合问题中的应用

提出利用多层Hopfield神经网络求解机组组合优化问题。通过构造合适的能量函数使得单层Hopfield神经网络可以解决某一时刻的机组出力问题,与之相对应的多层神经网络可以解决任意时间段的机组出力问题。多层Hopfield神经网络的层数由所需求解问题的时间段确定。给出单层及多层神经网络的能量函数及求解算法,能量函数考虑到机组升降功率和出力上下限的约束。通过对已有文献的算例进行计算比对,所得结果和遗传算法基本一致,但Hopfield神经网络通过解微分方程组来确定最优解,计算时间相对较少。     

Implementation of the Exclusive-Or Function in a Hopfield Style Recurrent Network

It is well known that a perceptron cannot be used to implement the XOR function but that a feed forward network with some hidden neurons can. The purpose of this work is to show that a Hopfield style network can also be used to implement the XOR function. It is shown here that the XOR function can be implemented in a Hopfield style network using only two hidden neurons.     

神经网络在汽车牌照字符识别中的应用

分析了反传学习神经网络和Hopfield神经网络的基本原理,探讨了神经网络在汽车牌照字符识别中的应用.结合神经网络和汽车牌照的特点,研究了学习速率,误差精度与隐含层节点数之间的关系,最终提出了一种Hopfield神经网络和反传学习神经网络相结合用于汽车牌照字符识别的方案.Matlab仿真结果表明,所设计的汽车牌照字符识别系统可以获得较为满意的高分辨率.     

An Iterative Method for Deciding SVM and Single Layer Neural Network Structures

We present two new classifiers for two-class classification problems using a new Beta-SVM kernel transformation and an iterative algorithm to concurrently select the support vectors for a support vector machine (SVM) and the hidden units for a single hidden layer neural network to achieve a better generalization performance. To construct the classifiers, the contributing data points are chosen on the basis of a thresholding scheme of the outputs of a single perceptron trained using all training data samples. The chosen support vectors are used to construct a new SVM classifier that we call Beta-SVN. The number of chosen support vectors is used to determine the structure of the hidden layer in a single hidden layer neural network that we call Beta-NN. The Beta-SVN and Beta-NN structures produced by our method outperformed other commonly used classifiers when tested on a 2-dimensional non-linearly separable data set.     

A constructive design method for two-layer perceptrons and its applicatio to the design of modular neural networks

Abstract: A multilayer perceptron is known to be capable of approximating any smooth function to any desired accuracy if it has a sufficient number of hidden neurons. But its training, based on the gradient method, is usually a time consuming procedure that may converge toward a local minimum, and furthermore its performance is greatly influenced by the number of hidden neurons and their initial weights. Usually these crucial parameters are determined based on the trial and error procedure, requiring much experience on the designer's part.
In this paper, a constructive design method (CDM) has been proposed for a two-layer perceptron that can approximate a class of smooth functions whose feature vector classes are linearly separable. Based on the analysis of a given data set sampled from the target function, feature vectors that can characterize the function'well'are extracted and used to determine the number of hidden neurons and the initial weights of the network. But when the classes of the feature vectors are not linearly separable, the network may not be trained easily, mainly due to the interference among the hyperplanes generated by hidden neurons. Next, to compensate for this interference, a refined version of the modular neural network (MNN) has been proposed where each network module is created by CDM. After the input space has been partitioned into many local regions, a two-layer perceptron constructed by CDM is assigned to each local region. By doing this, the feature vector classes are more likely to become linearly separable in each local region and as a result, the function may be approximated with greatly improved accuracy by MNN. An example simulation illustrates the improvements in learning speed using a smaller number of neurons.     

关于BP 网络变结构问题的研究

BP神经网络的收敛性涉及诸如网络初始权重赋值、隐结点个数以及隐层具数等问题。通过对BP神经网络隐结点个数的讨论,以及对BP神经网络训练样本空研究,得出一个重要结论,即网络结构可以随训练样本空间进行变换,从面使BP神经网络能够进行结构化简。     

Computing association probabilities using parallel Boltzmannmachines

A new computational method is presented for solving the data association problem using parallel Boltzmann machines. It is shown that the association probabilities can be computed with arbitrarily small errors if a sufficient number of parallel Boltzmann machines are available. The probability beta(i)(j) that the i th measurement emanated from the jth target can be obtained simply by observing the relative frequency with which neuron v(i,j) in a two-dimensional network is on throughout the layers. Some simple tracking examples comparing the performance of the Boltzmann algorithm to the exact data association solution and with the performance of an alternative parallel method using the Hopfield neural network are also presented.     

一种基于聚类技术的Hopfield网络求解TSP方法

Hopfiled神经网络方法已被广泛用于求解旅行商问题（TSP）,但对于解中规模和大规模的TSP,存在效果不理想甚至难以求解的问题。为了较好地解决这个问题,该文提出一种K-Means聚类算法与Hopfield网络方法相结合求解TSP的新方法,先应用聚类算法对所给城市进行聚类以获得几组规模较小的城市,然后对每一组城市应用Hopfield网络方法进行求解,最后把求解后的每组城市连接起来。计算机仿真结果表明,该方法可以获得最优有效解,并且解的质量明显提高,对求解中大规模的TSP比较有效。     

Estimating the Number of Hidden Neurons in a Feedforward Network Using the Singular Value Decomposition

In this letter, we attempt to quantify the significance of increasing the number of neurons in the hidden layer of a feedforward neural network architecture using the singular value decomposition (SVD). Through this, we extend some well-known properties of the SVD in evaluating the generalizability of single hidden layer feedforward networks (SLFNs) with respect to the number of hidden layer neurons. The generalization capability of the SLFN is measured by the degree of linear independency of the patterns in hidden layer space, which can be indirectly quantified from the singular values obtained from the SVD, in a postlearning step. A pruning/growing technique based on these singular values is then used to estimate the necessary number of neurons in the hidden layer. More importantly, we describe in detail properties of the SVD in determining the structure of a neural network particularly with respect to the robustness of the selected model     

基于并行PSO算法的RBF建模

针对RBF网络的建模问题,提出了基于并行PSO算法的RBF网络建模方法。其中,隐层单元数由一系列随机产生的整数训练得到;中心向量从输入样本空间内随机选择。随后,通过误差适应度来评价全局最优粒子,进而实现网络性能。从对非线性系统的仿真效果看,该方法隐层单元数比较少,与相同隐层的RBF网络相比,显示出了一定的优越性。     

Solving large scale combinatorial optimisation problems based on a divide and conquer strategy

A Hopfield neural network for a large scale problem optimisation poses difficulties due to the issues of stability and the determination of network parameters. In this paper, we introduce the concept of a divide and conquer algorithm to solve large scale optimisation problems using the Hopfield neural network. This paper also introduces the Grossberg Regularity Detector (GRD) neural network as a partition tool. This neural network based partition tool has the advantages of reducing the complexity of partition selection as well as removing the recursive division process during the divide and conquer operation. A large scale combinatorial optimisation problem (i.e. sequence-dependent set-up time minimisation problem with a large number of parts (N> 100)) is linearly partitioned into smaller sets of sub-problems based on their similarity relations. With a large number of parts (N>100), the problem could not effectively be verified with other methods, such as the heuristic or branch and bound methods. Hence, the effectiveness of the divide and conquer strategy implemented by the GRD neural network in conjunction with a Hopfield neural network was benchmarked against the first-come first-serve method, and the Hopfield neural network based on arbitrary separations. The results showed that the divide and conquer strategy of the GRD neural network was far superior to the other methods.     

On the computational complexity of binary and analog symmetric hopfield nets

We investigate the computational properties of finite binary- and analog-state discrete-time symmetric Hopfield nets. For binary networks, we obtain a simulation of convergent asymmetric networks by symmetric networks with only a linear increase in network size and computation time. Then we analyze the convergence time of Hopfield nets in terms of the length of their bit representations. Here we construct an analog symmetric network whose convergence time exceeds the convergence time of any binary Hopfield net with the same representation length. Further, we prove that the MIN ENERGY problem for analog Hopfield nets is NP-hard and provide a polynomial time approximation algorithm for this problem in the case of binary nets. Finally, we show that symmetric analog nets with an external clock are computationally Turing universal.     

基于灵敏度分析法的ELM剪枝算法

针对极端学习机(ELM)网络结构设计问题,提出基于灵敏度分析法的ELM剪枝算法.利用隐含层节点输出和相对应的输出层权值向量,定义学习残差对于隐含层节点的灵敏度和网络规模适应度,根据灵敏度大小判断隐含层节点的重要性,利用网络规模适应度确定隐含层节点个数,删除重要性较低的节点.仿真结果表明,所提出的算法能够较为准确地确定与学习样本相匹配的网络规模,解决了ELM网络结构设计问题.     

The convergence properties of a clipped Hopfield network and itsapplication in the design of keystream generator

We first present a modified Hopfield network, the clipped Hopfield network, with synaptic weights assigned to three values {-1,0,+1}. We give the necessary conditions under which a set of 2n binary vectors can be stored as stable points of the network. We show that in the parallel updating mode, for most of the state vectors, the network will always converge to these 2n stable points. We further demonstrate that these 2n stable points can be divided into two groups, the alpha group and the beta group, each with n stable points. It is shown that the basins of attraction of the stable points in the alpha group are evenly distributed, and the basins of attraction of the stable points in the beta group are also evenly distributed. By ways of application, we show that this class of Hopfield network can be used to build a cryptographically secure keystream generator.     

A Hopfield Neural Network for Image Change Detection

This paper outlines an optimization relaxation approach based on the analog Hopfield neural network (HNN) for solving the image change detection problem between two images. A difference image is obtained by subtracting pixel by pixel both images. The network topology is built so that each pixel in the difference image is a node in the network. Each node is characterized by its state, which determines if a pixel has changed. An energy function is derived, so that the network converges to stable states. The analog Hopfield's model allows each node to take on analog state values. Unlike most widely used approaches, where binary labels (changed/unchanged) are assigned to each pixel, the analog property provides the strength of the change. The main contribution of this paper is reflected in the customization of the analog Hopfield neural network to derive an automatic image change detection approach. When a pixel is being processed, some existing image change detection procedures consider only interpixel relations on its neighborhood. The main drawback of such approaches is the labeling of this pixel as changed or unchanged according to the information supplied by its neighbors, where its own information is ignored. The Hopfield model overcomes this drawback and for each pixel allows a tradeoff between the influence of its neighborhood and its own criterion. This is mapped under the energy function to be minimized. The performance of the proposed method is illustrated by comparative analysis against some existing image change detection methods.     

Theoretical limitations of a Hopfield network for crossbarswitching

It has been reported through simulations that Hopfield networks for crossbar switching almost always achieve the maximum throughput. It has therefore appeared that Hopfield networks of high-speed computation by parallel processing could possibly be used for crossbar switching. However, it has not been determined whether they can always achieve the maximum throughput. In the paper, the capabilities and limitations of a Hopfield network for crossbar switching are considered. The Hopfield network considered in the paper is generated from the most familiar and seemingly the most powerful neural representation of crossbar switching. Based on a theoretical analysis of the network dynamics, we show what switching control the Hopfield network can or cannot produce. Consequently, we are able to show that a Hopfield network cannot always achieve the maximum throughput.