A Note on the Equivalence of NARX and RNN

This paper presents several aspects with regards the application of the NARX model and Recurrent Neural Network (RNN) model in system identification and control. We show that every RNN can be transformed to a first order NARX model, and vice versa, under the condition that the neuron transfer function is similar to the NARX transfer function. If the neuron transfer function is piecewise linear, that is f(x):=x if uxu , 1 and f(x):=sign(x) otherwise, we further show that every NARX model of order larger than one can be transformed into a RNN. According to these equivalence results, there are three advantages from which we can benefit: (i) if the output dimension of a NARX model is larger than the number of its hidden unit, training an equivalent RNN will be faster, i.e. the equivalent RNN is trained instead of the NARX model. Once the training is finished, the RNN is transformed back to an equivalent NARX model. On the other hand, (ii) if the output dimension of a RNN model is less than the number of its hidden units, the training of a RNN can be speeded up by using a similar method; (iii) the RNN pruning can be accomplished in a much simpler way, i.e. the equivalent NARX model is pruned instead of the RNN. After pruning, the NARX model is transformed back to the equivalent RNN.     

关于RSA的一个注记

RSA是当前应用最广泛的公钥密码系统,它的安全性依赖于大整数分解的困难性.对RSA大整数N=pq,若存在整数t=uv,使|pv-qu|~2<4m,其中m=「N· uv~(1/2)」+1.给出了一个基于一元二次多项式的能有效分解N的算法,并用算例验证了其有效性.进而,为了保证RSA的安全性,根据连分数理论,给出了选取安全的RSA大整数的一个新的准则.     

A Note on Intensionalization

Building on Ben-Avi and Winter’s (2007) work, this paper provides a general “intensionalization” procedure that turns an extensional semantics for a language into an intensionalized one that is capable of accommodating “truly intensional” lexical items without changing the compositional semantic rules. We prove some formal properties of this procedure and clarify its relation to the procedure implicit in Montague’s (1973) PTQ.     

对HEMA模型的注记

首先通过分析HEMA模型,发现其中的若干设计缺陷,指出该模型存在的若干冗余,还分析讨论该协议中存储并加密传输密钥协商因子设计的不合理性,然后讨论一个该协议并发运行的实例,从而指出该协议可能存在的并发运行错误,进一步说明使用可信第三方存储并加密传输可以完全公开的密钥协商因子是个实质性的错误。最后,将HEMA模型与现有的若干认证与密钥交换协议进行比较,讨论HEMA的运行效率。     

A Note on Epsilon-Inflation

The epsilon-inflation proved to be useful and necessary in many verification algorithms. Different definitions of an epsilon-inflation are possible, depending on the context. Recently, certain theoretical justifications and optimality results were proved for an epsilon-inflation without absolute term. In this note we show that in currently used interval iterations the epsilon-inflation without absolute term does not serve the purpose it is defined for. A new epsilon-inflation is proposed.     

A Note on Coalgebras and Presheaves

We show that the category of coalgebras of a wide-pullback preserving endofunctor on a category of presheaves is itself a category of presheaves. This illustrates a connection between Jacobs' temporal logic of coalgebras and Ghilardi and Meloni's presheaf semantics for modal logic.     

一种基于路由器Cache的一致性协议

在大规模并分布式共享主存多处理机系统中,尽可能减少系统中远程访问时延,是提高系统整体性能的关键。该文提出了一种路由Cache结构,并详细介绍了基于路由器Cache的一致性协议,该协议在减少系统远程访问延时,提高系统有效带宽方面有较好的效果。     

A Note on Multiflows and Treewidth

We consider multicommodity flow problems in capacitated graphs where the treewidth of the underlying graph is bounded by r. The parameter r is allowed to be a function of the input size. An instance of the problem consists of a capacitated graph and a collection of terminal pairs. Each terminal pair has a non-negative demand that is to be routed between the nodes in the pair. A class of optimization problems is obtained when the goal is to route a maximum number of the pairs in the graph subject to the capacity constraints on the edges. Depending on whether routings are fractional, integral or unsplittable, three different versions are obtained; these are commonly referred to respectively as maximum MCF, EDP (the demands are further constrained to be one) and UFP. We obtain the following results in such graphs.

A Note on the Ohya-Masuda Quantum Algorithm

We analyze the Ohya-Masuda quantum algorithm that solves the so-called satisfiability problem, which is an NP-complete problem of the complexity theory. We distinguish three steps in the algorithm, and analyze the second step, in which a coherent superposition of states (a pure state) transforms into an incoherent mixture presented by a density matrix. We show that, if nonideal (in analogy with nonideal quantum measurement), this transformation can make the algorithm to fail in some cases. On this basis we give some general notions on the physical implementation of the Ohya-Masuda algorithm.     

A Dual-Microphone Speech Enhancement Algorithm Based on the Coherence Function

A novel dual-microphone speech enhancement technique is proposed in the present paper. The technique utilizes the coherence between the target and noise signals as a criterion for noise reduction and can be generally applied to arrays with closely-spaced microphones, where noise captured by the sensors is highly correlated. The proposed algorithm is simple to implement and requires no estimation of noise statistics. In addition, it offers the capability of coping with multiple interfering sources that might be located at different azimuths. The proposed algorithm was evaluated with normal hearing listeners using intelligibility listening tests and compared against a well-established beamforming algorithm. Results indicated large gains in speech intelligibility relative to the baseline (front microphone) algorithm in both single and multiple-noise source scenarios. The proposed algorithm was found to yield substantially higher intelligibility than that obtained by the beamforming algorithm, particularly when multiple noise sources or competing talker(s) were present. Objective quality evaluation of the proposed algorithm also indicated significant quality improvement over that obtained by the beamforming algorithm. The intelligibility and quality benefits observed with the proposed coherence-based algorithm make it a viable candidate for hearing aid and cochlear implant devices.     

A Note on the Monotonicity of Reducible Quantifiers

We provide necessary and sufficient conditions determining how monotonicity of some classes of reducible quantifiers depends on the monotonicity of simpler quantifiers of iterations to which they are equivalent.     

A Note on Trust-Enhanced Security

With our ever-increasing reliance on a digital economy, most business and government activities now depend on networked information systems for their basic operation. Clearly, we're seeing a renewed urgency to get a better handle on capturing and reasoning about trust in computing systems and information services. Even Microsoft has adopted the term trustworthy computing as a company initiative in both its internal software development and its commercial offerings. In this installment of On the Horizon, the author takes a short journey through the concept and evolution of trust in the secure computing technology world, and examines some of the challenges involved in trusted computing today.     

一种基于光线相关性的快速光线跟踪算法

在分析和比较现有光线跟踪快速求交算法的基础上,基于光线相关性研究和探索了逐步细分光线跟踪算法,以减少光线求交次数。本方法为实时生成真实感图形提供了一条很有潜力的实现途径。     

A Note on Rotation Matrices

Properly establishing the relation between linear algebra and geometry makes it easier to obtain the three-by-three orthogonal matrix that describes a specified rotation.     

A Note on Sugihara's Claim

This correspondence debates a theorem formulated by K. Sugihara in a recent publication. The theorem deals with the mathematical structures of line drawings, and serves as a basis for a substantial part of the paper. This note claims that the theorem as formulated is not valid. The claim is substantiated by a counterexample.     

基于相关性和小波变换的纹理合成算法

提出一种快速的纹理合成方法,采用小波变换对原样图分解,只在分解后的低频部分进行最佳匹配块的搜索,使合成速度得到了很大提高;同时,在合成过程中利用邻域块的相关性,把搜索范围限制在当前块的邻域,避免了对样图的穷尽搜索。结果表明,该算法在很大程度上减少了合成时间。     

一种基于约束特征的网格编辑技术

为了改进自由变形技术在用户交互和编辑灵活性的不足,提出了一种直观的交互式网格模型编辑技术,该技术可以根据不同的约束变形特征、封闭的变形边界以及编辑参考曲线来完成网格模型的编辑,并且为了模型的平滑和自然,采用了自适应细分策略。实验证明,该方法简便直观,有良好的交互性,并能得到很好的编辑结果。此技术可以方便地应用于CAD/CAM和计算机动画系统中。