Primality testing with fewer random bits

In the usual formulations of the Miller-Rabin and Solovay-Strassen primality testing algorithms for a numbern, the algorithm chooses candidatesx ₁,x ₂, ...,x _k uniformly and independently at random from _n , and tests if any is a witness to the compositeness ofn. For either algorithm, the probabilty that it errs is at most 2^–k .In this paper, we study the error probabilities of these algorithms when the candidates are instead chosen asx, x+1, ..., x+k–1, wherex is chosen uniformly at random from _n . We prove that fork=[1/2log₂ n], the error probability of the Miller-Rabin test is no more thann ^–1/2+o(1), which improves on the boundn ^–1/4+o(1) previously obtained by Bach. We prove similar bounds for the Solovay-Strassen test, but they are not quite as strong; in particular, we only obtain a bound ofn ^–1/2+o(1) if the number of distinct prime factors ofn iso(logn/loglogn).     

Converting random bits into random numbers

Converting random bits into random numbers is necessary for cryptographic protocols such as key agreements, public key encryptions, digital signatures and so on. In this paper, we propose the simple partial discard method and the complex partial discard method that convert random bits into random numbers. They are up to two times more efficient than standardized techniques.     

Function approximation with spiked random networks

Examines the function approximation properties of the "random neural-network model" or GNN, The output of the GNN can be computed from the firing probabilities of selected neurons. We consider a feedforward bipolar GNN (BGNN) model which has both "positive and negative neurons" in the output layer, and prove that the BGNN is a universal function approximator. Specifically, for any finC([0,1](s)) and any epsilon>0, we show that there exists a feedforward BGNN which approximates f uniformly with error less than epsilon. We also show that after some appropriate clamping operation on its output, the feedforward GNN is also a universal function approximator.     

Generalized Elias schemes for efficient harvesting of truly random bits

The problem of generating a sequence of true random bits (suitable for cryptographic applications) from random discrete or analog sources is considered. A generalized version, including vector quantization, of the classical approach by Elias for the generation of truly random bits is introduced, and its performance is analyzed, both in the finite case and asymptotically. The theory allows us to provide an alternative proof of the optimality of the original Elias’ scheme. We also consider the problem of deriving random bits from measurements of a Poisson process and from vectors of iid Gaussian variables. The comparison with the scheme of Elias, applied to geometric-like non-binary vectors, originally based on the iso-probability property of permutations of iid variables, confirms the potential of the generalized scheme proposed in our work.     

On protocols for increasing the uniformity of random bits generated with noisy quantum computers

The Journal of Supercomputing - Generating random numbers is important for many real-world applications, including cryptography, statistical sampling and Monte Carlo simulations. Quantum systems...     

Consensus of switched multi-agent systems with random networks

This paper studies the consensus problem of the switched multi-agent system composed of continuous-time and discrete-time subsystems. Communication among agents is modelled as a random network where the existence of any information channel is probabilistic and independent of other channels. Then, some necessary and sufficient conditions are presented for solving average consensus of the switched multi-agent system under arbitrary switching. Furthermore, we show that the average consensus in different sense (mean square, almost surely and in probability, respectively) are equivalent. Finally, simulations are provided to illustrate the effectiveness of our theoretical results.     

Stochastic comparisons for rooted butterfly networks and tree networks, with random environments

Consider a rooted tree network, where the items enter at the system and they proceed away from the root until they reach their destination and exit the system, and they are served by a FIFO policy at each arc (server) of the network. The routing is defined by a discrete probability distribution with a given probability for each destination. For such systems, stochastic modelling of the departure times and the delay times is proposed, by the incorporation of random parameters of the inter-arrival times and of the service times, describing dynamic environments. A mixture model for the departure times is introduced. This mixture has an arbitrary mixing distribution defined by the environmental parameter distributions and the routing distribution. The main results provide conditions to compare stochastically the departure times (delay times) for two rooted tree networks characterized by different routing disciplines or by environmental and correlated random vectors of parameters. Furthermore, bounds for these measures are obtained from some well-known dependence concepts, as the PQD property, and ageing properties of the random environment. Similar results for butterfly networks, tree networks with possible failure during the service and other networks are provided. Within the computer networks, our framework and our results provide explorative tools to assess the design, the performance and the security of communication systems.     

Modeling uncertain processes with interval random vector functional-link networks

This paper presents a new approach to building an interval model for an industrial process with uncertainty that employs an interval neural network (INN), which can solve problems such as model structure demands and complexity limitations in the conventional unknown but bounded (UBB) errors method. A new architecture for an interval random vector functional-link network (IRVFLN) and its learning algorithm with penalty factors are proposed, to solve the problems such as the local minima, slow convergence, and very poor sensitivity to learning rate settings in the interval feed-forward neural networks with error back-propagation (IBPNNs). As an application case study, the IRVFLN is used to model the glutamic acid fermentation process under the condition of bounded-error data, and the test results indicate that the accuracy of the IRVFLN model meets the manufacturing requirements. The comparison is performed with IBPNN, and the results demonstrate that the proposed network outperforms IBPNN both on effectiveness and efficiency. Also, a comparison is given with a crisp (point-valued) approach using RVFLN, and the results show that the crisp approach is less reliable when existing uncertainties in measuring or process.     

Service networks with multichannel nodes in a random environment

Service networks with multichannel nodes of semi-Markovian type are considered. The parameters of a source of demands depend on the state of the Markovian random environment. For the process of servicing demands, the conditions of existence of a stationary mode are found, and the properties of stationary distribution in terms of spectral characteristics of the routing matrix are investigated. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 167–172, January–February, 2000.     

具有随机耦合强度两个复杂网络的自适应同步

探究当耦合强度不是常数而是随机变化时,两个不同复杂网络是否能够达到同步。假设耦合强度满足正态分布,在随机耦合强度的数学期望和网络拓扑结构分别已知和未知的情况下,设计合适的非线性自适应控制器使得两个网络获得同步。与假定耦合强度是一个确定值的研究成果相比,该结论更具有一般性。数值仿真表明了该方法的可行性和有效性。     

Filtering random graphs to synthesize interconnection networks with multiple objectives

Synthesizing networks that satisfy multiple requirements, such as high reliability, low diameter, good embeddability, etc., is a difficult problem to which there has been no completely satisfactory solution. We present a simple, yet very effective, approach to this problem. The crux of our approach is a filtration process that takes as input a large set of randomly generated graphs and filters out those that do not meet the specified requirements. Our experimental results show that this approach is both practical and powerful. The use of random regular networks as the raw material for the filtration process was motivated by their surprisingly good performance with regard to almost all properties that characterize a good interconnection network. We provide results related to the generation of networks that have low diameter, high fault tolerance, and good embeddability. Through this, we show that the generated networks are serious competitors to several traditional well-known networks. We also explore how random networks can be used in a packaging hierarchy and comment on the scope of application of these networks.     

Finite-time stability of neutral-type neural networks with random time-varying delays

This paper is devoted to the finite-time stability analysis of neutral-type neural networks with random time-varying delays. The randomly time-varying delays are characterised by Bernoulli stochastic variable. This result can be extended to analysis and design for neutral-type neural networks with random time-varying delays. On the basis of this paper, we constructed suitable Lyapunov–Krasovskii functional together and established a set of sufficient linear matrix inequalities approach to guarantee the finite-time stability of the system concerned. By employing the Jensen's inequality, free-weighting matrix method and Wirtinger's double integral inequality, the proposed conditions are derived and two numerical examples are addressed for the effectiveness of the developed techniques.     

Diagnosis of fatigue crack growth with recursive random weight networks

Recursive random weight networks (RRWNs) have been developed to diagnose fatigue crack growth in ductile alloys under variable amplitude loading. The fatigue crack growth process is considered as a recursive network system. RRWNs are constructed by taking the current loading, crack opening stress, and the previous computed crack length as inputs of the network system. The input weights of conventional single-layer feed-forward neural networks are uniformly and randomly selected. The output weights of RRWNs are globally optimized with the batch learning type of least squares. The trained RRWNs are capable of determining the dynamics of crack development. The proposed model is validated with fatigue test data for different types of variable amplitude loading in alloys. Compared with other experimental diagnosis models, RRWNs show excellent performance in predicting crack length growth.     

Multi-user image encryption algorithm based on synchronized random bits generator in semiconductor lasers network

A chaos-based public channel image encryption algorithm among three users is proposed, where the random bits (RBs) generated in a star-type chaotic laser network can be well synchronized and are used as the keys. The proposed algorithm is simple and efficient. Firstly, random bits with verified randomness are generated from the synchronized chaotic semiconductor lasers in a star-type network at a rate of 10Gb/s. Next, lower-triangular error-bits detection is employed to delete the different bits among all the parties over the public channel. Based on the synchronized RBs, the XOR operation is used to diffuse the plain image. Then the hash algorithm is used to get the control parameters matrix from the plain image, and 3D cat map is used to confuse the pixel position through the parameters matrix. Finally, the encrypted image is transmitted in the public channel. The performance tests results, such as key sensitivity, histogram, correlation, differential attack, robustness and entropy analysis, show that the suggested algorithm prevents a powerful computational eavesdropper. Besides, the running speed of this algorithm is linear with the size of plain image. These results open possibilities for multi-user secure communication application.

     

Spike-timing-dependent plasticity in balanced random networks

The balanced random network model attracts considerable interest because it explains the irregular spiking activity at low rates and large membrane potential fluctuations exhibited by cortical neurons in vivo. In this article, we investigate to what extent this model is also compatible with the experimentally observed phenomenon of spike-timing-dependent plasticity (STDP). Confronted with the plethora of theoretical models for STDP available, we reexamine the experimental data. On this basis, we propose a novel STDP update rule, with a multiplicative dependence on the synaptic weight for depression, and a power law dependence for potentiation. We show that this rule, when implemented in large, balanced networks of realistic connectivity and sparseness, is compatible with the asynchronous irregular activity regime. The resultant equilibrium weight distribution is unimodal with fluctuating individual weight trajectories and does not exhibit development of structure. We investigate the robustness of our results with respect to the relative strength of depression. We introduce synchronous stimulation to a group of neurons and demonstrate that the decoupling of this group from the rest of the network is so severe that it cannot effectively control the spiking of other neurons, even those with the highest convergence from this group.     

随机阿波罗网络的动力学同步研究

应用随机交叉边法在不改变网络度分布的情况下研究了随机阿波罗网络（Random Apollonian network）的拓扑结构与其上所加的动力学系统同步行为间的关系,发现在一定范围内,随着网络聚集系数的减小,网络的同步能力增加,但当继续减小聚集系数时,同步能力又会迅速减弱。     

Utility-optimal random access control in wireless multi-hop networks with queuing constraints

In this paper, a model of network utility maximization （NUM） is presented for random access control in multi-hop wireless networks. Different from the classical NUM framework, our model considers the queueing stability. We propose a distributed iterative prices and link probabilities adaption algorithm by using dual decomposition techniques, which only requires limited message passing, but converges to the global optimum of the total network utility. Numerical results and simulation comparison validate our conclusion.     

End-to-end delay estimation for multi-hop wireless networks with random access policy

End-to-end delay analysis is an important element of network performance analysis in multi-hop wireless networks.In this paper,we propose an analytical model for estimating the end-to-end delay performance of wireless networks employing a random access policy for managing node’transmissions on shared channels with time-varying capacity.To obtain the closed form expression,a new concept of residual effective capacity is presented using the definitions of effective bandwidth theory and effective capacity theory.This allows us to calculate the cumulative distribution function of the queuing delay.Based on this concept,we derive a formula to calculate the average end-to-end delay for multi-hop wireless networks,with the result including the effect of a random access protocol,which has not previously been considered.Finally,we validate our analysis through simulations and provide an example application for our results.     

Universal approximation using incremental constructive feedforward networks with random hidden nodes

According to conventional neural network theories, single-hidden-layer feedforward networks (SLFNs) with additive or radial basis function (RBF) hidden nodes are universal approximators when all the parameters of the networks are allowed adjustable. However, as observed in most neural network implementations, tuning all the parameters of the networks may cause learning complicated and inefficient, and it may be difficult to train networks with nondifferential activation functions such as threshold networks. Unlike conventional neural network theories, this paper proves in an incremental constructive method that in order to let SLFNs work as universal approximators, one may simply randomly choose hidden nodes and then only need to adjust the output weights linking the hidden layer and the output layer. In such SLFNs implementations, the activation functions for additive nodes can be any bounded nonconstant piecewise continuous functions g:R/spl rarr/R and the activation functions for RBF nodes can be any integrable piecewise continuous functions g:R/spl rarr/R and /spl int//sub R/g(x)dx/spl ne/0. The proposed incremental method is efficient not only for SFLNs with continuous (including nondifferentiable) activation functions but also for SLFNs with piecewise continuous (such as threshold) activation functions. Compared to other popular methods such a new network is fully automatic and users need not intervene the learning process by manually tuning control parameters.