Robust Kalman filter and smoother for errors‐in‐variables state space models with observation outliers based on the minimum‐covariance determinant estimator

In this paper, we propose a robust Kalman filter and smoother for the errors‐in‐variables (EIV) state space models subject to observation noise with outliers. We introduce the EIV problem with outliers and then present the minimum covariance determinant (MCD) estimator which is a highly robust estimator in terms of protecting the estimate from the outliers. Then, we propose the randomized algorithm to find the MCD estimate. However, the uniform sampling method has a high computational cost and may lead to biased estimates, therefore we apply the sub‐sampling method. A Monte Carlo simulation result shows the efficiency of the proposed algorithm. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

An efficient CRT-RSA algorithm secure against power and fault attacks

RSA digital signatures based on the Chinese Remainder Theorem (CRT) are subject to power and fault attacks. In particular, modular exponentiation and CRT recombination are prone to both attacks. However, earlier countermeasures are susceptible to the possibility of advanced and sophisticated attacks. In this paper, we investigate state-of-the-art countermeasures against power and fault attacks from the viewpoint of security and efficiency. Then, we show possible vulnerabilities to fault attacks. Finally, we propose new modular exponentiation and CRT recombination algorithms secure against all known power and fault attacks. Our proposal improves efficiency by replacing arithmetic operations with logical ones to check errors in the CRT recombination step. In addition, since our CRT-RSA algorithm does not require knowledge of the public exponent, it guarantees a more versatile implementation.     

An asymptotically perfect secret sharing scheme based on the Chinese Remainder Theorem

The secret sharing schemes based on the Chinese Remainder Theorem (CRT) and their applications have attracted many researchers in recent years. In this paper, we propose a weighted threshold secret sharing scheme based on the CRT and prove the scheme is asymptotically perfect. Since all CRT-based secret sharing schemes use special sequences of pairwise coprime integers as its parameters, this paper proposes the first algorithm to generate these integers. Moreover, the correctness of this algorithm is proved by using the prime number theorem. The experimental result shows the effectiveness and the efficiency of our algorithm as well as the space efficiency of our scheme using the sequences of integers generated from our algorithm. Our scheme with the parameter generation algorithm can be used in many applications such as threshold cryptosystems.     

An inversion method for parabolic equations based on quasireversibility

This paper is concerned with a new method to solve a linearized inverse problem for one-dimensional parabolic equations. The inverse problem seeks to recover the subsurface absorption coefficient function based on the measurements obtained at the boundary. The method considers a temporal interval during which time dependent measurements are provided. It linearizes the working equation around the system response for a background medium. It is then possible to relate the inverse problem of interest to an ill-posed boundary value problem for a differential-integral equation, whose solution is obtained by the method of quasireversibility. This approach leads to an iterative method. A number of numerical results are presented which indicate that a close estimate of the unknown function can be obtained based on the boundary measurements only.     

CRM strategies for a small-sized online shopping mall based on association rules and sequential patterns

As dot-com bubble burst in 2002, an uncountable number of small-sized online shopping malls have emerged every day due to many good characteristics of online marketplace, including significantly reduced search costs and menu cost for products or services and easily accessing products or services in the world. However, all the online shopping malls have not continuously flourished. Many of them even vanished because of the lack of customer relationship management (CRM) strategies that fit them. The objective of this paper is to propose CRM strategies for small-sized online shopping mall based on association rules and sequential patterns obtained by analyzing the transaction data of the shop. We first defined the VIP customers in terms of recency, frequency and monetary (RFM) value. Then, we developed a model which classifies customers into VIP or non-VIP, using various data mining techniques such as decision tree, artificial neural network, logistic regression and bagging with each of these as a base classifier. Last, we identified association rules and sequential patterns from the transactions of VIPs, and then these rules and patterns were utilized to propose CRM strategies for the online shopping mall.     

The complexity of Boolean functions in the Reed–Muller polynomials class

This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of n variables whose complexity (in terms of the number of terms) coincides with value. We investigate the properties of functions and propose their schematic realization on elements AND, XOR, and NAND.     

Quasi-plus sampling edge correction for spatial point patterns

A widely applicable edge correction method for estimating summary statistics of a spatial point pattern is proposed. We reconstruct point patterns in a larger region containing the sampling window by matching sampled and simulated kth nearest neighbour distance distributions of the given pattern and then apply plus sampling. Simulation studies show that this approach, called quasi-plus sampling, gives estimates with smaller root mean squared errors than estimates obtained by using other popular edge corrections. We apply the proposed approach to real data and yield an estimate of a summary statistic that is more plausible than that obtained by a popular edge correction.     

Vector quantization based approximate spectral clustering of large datasets

Spectral partitioning, recently popular for unsupervised clustering, is infeasible for large datasets due to its computational complexity and memory requirement. Therefore, approximate spectral clustering of data representatives (selected by various sampling methods) was used. Alternatively, we propose to use neural networks (self-organizing maps and neural gas), which are shown successful in quantization with small distortion, as preliminary sampling for approximate spectral clustering (ASC). We show that they usually outperform k-means sampling (which was shown superior to various sampling methods), in terms of clustering accuracy obtained by ASC. More importantly, for quantization based ASC, we introduce a local density-based similarity measure – constructed without any user-set parameter – which achieves accuracies superior to the accuracies of commonly used distance based similarity.     

A naive Bayes probability estimation model based on self-adaptive differential evolution

In the process of learning the naive Bayes, estimating probabilities from a given set of training samples is crucial. However, when the training samples are not adequate, probability estimation method will inevitably suffer from the zero-frequency problem. To avoid this problem, Laplace-estimate and M-estimate are the two main methods used to estimate probabilities. The estimation of two important parameters m (integer variable) and p (probability variable) in these methods has a direct impact on the underlying experimental results. In this paper, we study the existing probability estimation methods and carry out a parameter Cross-test by experimentally analyzing the performance of M-estimate with different settings for the two parameters m and p. This part of experimental result shows that the optimal parameter values vary corresponding to different data sets. Motivated by these analysis results, we propose an estimation model based on self-adaptive differential evolution. Then we propose an approach to calculate the optimal m and p value for each conditional probability to avoid the zero-frequency problem. We experimentally test our approach in terms of classification accuracy using the 36 benchmark machine learning repository data sets, and compare it to a naive Bayes with Laplace-estimate and M-estimate with a variety of setting of parameters from literature and those possible optimal settings via our experimental analysis. The experimental results show that the estimation model is efficient and our proposed approach significantly outperforms the traditional probability estimation approaches especially for large data sets (large number of instances and attributes).     

A consensus sampling technique for fast and robust model fitting

In this paper, a new algorithm is proposed to improve the efficiency and robustness of random sampling consensus (RANSAC) without prior information about the error scale. Three techniques are developed in an iterative hypothesis-and-evaluation framework. Firstly, we propose a consensus sampling technique to increase the probability of sampling inliers by exploiting the feedback information obtained from the evaluation procedure. Secondly, the preemptive multiple K-th order approximation (PMKA) is developed for efficient model evaluation with unknown error scale. Furthermore, we propose a coarse-to-fine strategy for the robust standard deviation estimation to determine the unknown error scale. Experimental results of the fundamental matrix computation on both simulated and real data are shown to demonstrate the superiority of the proposed algorithm over the previous methods.     

一种安全的多使用门限多秘密共享方案

在多秘密共享方案中,通常会生成大量公开值来保障多个秘密安全正确地重构,同时参与者也需要保存大量信息.为减少公开值的个数以及参与者所需保存的信息量,本文基于中国剩余定理和Shamir(t,n)-门限秘密共享方案设计了一个子秘密可多使用的门限存取结构多秘密共享方案.根据中国剩余定理将多项式产生的子秘密信息进行聚合生成公开值,减少了公开值的个数;应用转换值的方法和离散对数对参与者子秘密信息进行保护.构造了具有以下特点的多秘密共享方案:可一次共享多个秘密;不同的秘密可对应不同门限的存取结构;参与者可验证所恢复秘密值的正确性;公开值个数更少;参与者存储一个子秘密且子秘密可以多次使用.     

Reconciling the global terrestrial water budget using satellite remote sensing

Recent retrievals of multiple satellite products for each component of the terrestrial water cycle provide an opportunity to estimate the water budget globally. In this study, we estimate the water budget from satellite remote sensing over ten global river basins for 2003-2006. We use several satellite and non-satellite precipitation (P) and evapo-transpiration (ET) products in this study. The satellite precipitation products are the GPCP, TRMM, CMORPH and PERSIANN. For ET, we use four products generated from three retrieval models (Penman-Monteith (PM), Priestley-Taylor (PT) and the Surface Energy Balance System (SEBS)) with data inputs from the Earth Observing System (EOS) or the International Satellite Cloud Climatology Project (ISCCP) products. GPCP precipitation and PM (ISCCP) ET have less bias and errors over most of the river basins. To estimate the total water budget from satellite data for each basin, we generate merged products for P and ET by combining the four P and four ET products using weighted values based on their errors with respect to non-satellite merged product. The water storage change component is taken from GRACE satellite data, which are used directly with a single pre-specified error value. In the absence of satellite retrievals of river discharge, we use in-situ gauge measurements. Closure of the water budget over the river basins from the combined satellite and in-situ discharge products is not achievable with errors of the order of 5-25% of mean annual precipitation. A constrained ensemble Kalman filter is used to close the water budget and provide a constrained best-estimate of the water budget. The non-closure error from each water budget component is estimated and it is found that the merged satellite precipitation product carries most of the non-closure error.     

一种检测单晶炉热场温度的新方法

为去除单晶炉热场温度测量信号中的低频干扰、提高温度信号的估计精度,本文提出了一种基于跨维模拟退火(trans dimensional simulated annealing,TDSA)的单晶炉热场温度检测方法.该方法首先将AIC(Akaike information criterion)信号个数判断准则纳入采样机制中以便对干扰个数采样估计,进而利用所设计的基于信号频谱和轮盘赌思想的Metropolis Hastings机制对相应个数的干扰频率进行采样,最后设计了混合均匀和高斯采样机制对单晶炉热场温度进行采样估计.仿真和单晶炉工程实验结果表明,该方法在干扰个数未知的情况下,能够有效地抑制低频干扰、准确检测单晶炉热场的温度.     

Applications of random sampling to virtual screening of combinatorial libraries

We describe statistical techniques for effective evaluation of large virtual combinatorial libraries (> 10(10) potential compounds). The methods described are used for computationally evaluating templates (prioritization of candidate libraries for synthesis and screening) and for the design of individual combinatorial libraries (e.g., for a given diversity site, reagents can be selected based on the estimated frequency with which they appear in products that pass a computational filter). These statistical methods are powerful because they provide a simple way to estimate the properties of the overall library without explicitly enumerating all of the possible products. In addition, they are fast and simple, and the amount of sampling required to achieve a desired precision is calculable. In this article, we discuss the computational methods that allow random product selection from a combinatorial library and the statistics involved in estimating errors from quantities obtained from such samples. We then describe three examples: (1) an estimate of average molecular weight for the several billion possible products in a four-component Ugi reaction, a quantity that can be calculated exactly for comparison; (2) the prioritization of four templates for combinatorial synthesis using a computational filter based on four-point pharmacophores; and (3) selection of reagents for the four-component Ugi reaction based on their frequency of occurrence in products that pass a pharmacophore filter.     

Capture-aware Bayesian RFID Tag Estimate for Large-scale Identification

Dynamic framed slotted Aloha algorithm is one of popular passive radio frequency identification (RFID) tag anticollision algorithms. In the algorithm, a frame length requires dynamical adjustment to achieve higher identification efficiency. Generally, the adjustment of the frame length is not only related to the number of tags, but also to the occurrence probability of capture effect. Existing algorithms could estimate both the number of tags and the probability of capture effect. Under large-scale RFID tag identification, however, the number of tags would be much larger than an initial frame length. In this scenario, the existing algorithm's estimation errors would substantially increase. In this paper, we propose a novel algorithm called capture-aware Bayesian estimate, which adopts Bayesian rules to accurately estimate the number and the probability simultaneously. From numerical results, the proposed algorithm adapts well to the large-scale RFID tag identification. It has lower estimation errors than the existing algorithms. Further, the identification efficiency from the proposed estimate is also higher than the existing algorithms.      

宽带欠采样信号处理理解模糊方法

对余数法解频率估计模糊方法作了分析,提出了虚拟采速概念,清晰地叙述了无模糊频率估计范围与虚拟采样速率之间的关系,对特殊宽带信号提出了相应的解模糊处理方法;对多信号情况,提出了利用信号参数进行配对,模糊结果显示本方法是有效的。     

一种新的基于多素数RSA认证加密方案

根据RSA加密系统和中国剩余定理,提出了一种新的基于多密钥的RSA认证加密方案。该方案与通常的RSA加密系统不同,每个用户只有一个加密密钥,但解密密钥由两个以上的短密钥组成,大大地加快了解密的速度。在解密过程中,巧妙地运用了中国剩余定理,减少了求逆元的个数,提高了效率。特别地,根据该方案可得到改进的Paixao方案和Boneh方案,计算速度更快,效果更好。分析表明,此方案可以有效地减少计算复杂度,并且不会降低其安全性,十分适合智能卡之间、智能卡和终端之间的认证和信息交换。     

区块链中基于中国剩余定理投票方案的共识机制

目前共识机制存在以下问题：1）记账权“垄断化”,即随着系统运行,记账权被一部分拥有更多资源的节点掌握,导致资源贫乏的小节点流失,影响系统安全;2）当竞选权益节点时,要遍历所有参与竞选节点的交易记录,导致共识时延快速增长。针对这些问题,提出了一种新的共识机制——CRT-PoT。首先,基于中国剩余定理（CRT）提出用于选出权益节点的投票模型CRT-Election,该模型规定竞选节点通过成功出块次数以及成功投票次数获取投票节点的投票支持,以竞争记账权。然后,基于该投票模型提出多投机制来保证小节点有更多机会竞选记账权,从而有效解决记账权“垄断化”问题;同时,保证在竞选节点数量增多时,共识时延增长速度较慢,因为该方案不需要遍历所有参与竞选节点的交易记录,共识时延只与参与竞选节点数有关,共识时延呈线性增长。最后,从理论和实验角度分析验证了与目前已有的共识机制相比,CRT-PoT不仅有效解决了记账权“垄断化”问题,同时也降低了共识时延。     

Recursive projection algorithm on FIR system identification with binary-valued observations

This paper studies the identification of finite impulse response (FIR) systems with binary-valued observations. Combining with the stochastic gradient algorithm and statistical property of the system noise, a recursive projection algorithm is proposed to estimate the unknown system parameters. Under some mild conditions on the a priori knowledge of the unknown parameters and inputs, the algorithm is proved to be convergent in the almost sure and mean square sense. Furthermore, the almost sure and mean square convergence rates of estimation errors are also obtained. A numerical example is given to demonstrate the effectiveness of the algorithm and the main results obtained.     

Estimating probabilities under the three-parameter gamma distribution using composite sampling

Composite sampling may be used in industrial or environmental settings for the purpose of quality monitoring and regulation, particularly if the cost of testing samples is high relative to the cost of collecting samples. In such settings, it is often of interest to estimate the proportion of individual sampling units in the population that are above or below a given threshold value, C. We consider estimation of a proportion of the form p=P(X>C) from composite sample data, assuming that X follows a three-parameter gamma distribution. The gamma distribution is useful for modeling skewed data, which arise in many applications, and adding a shift parameter to the usual two-parameter gamma distribution also allows the analyst to model a minimum or baseline level of the response. We propose an estimator of p that is based on maximum likelihood estimates of the parameters α, β, and γ, and an associated variance estimator based on the observed information matrix. Theoretical properties of the estimator are briefly discussed, and simulation results are given to assess the performance of the estimator. We illustrate the proposed estimator using an example of composite sample data from the meat products industry.