基于提升小波和自适应多项式拟合的传感器网络多模数据压缩算法

为提高无线传感器网络的感知精度,提出了一种基于提升小波变换和自适应多项式拟合的多模数据压缩算法（adaptive multiple-modalities data compression algorithm based on lifting wavelet and adaptive polynomial fitting,简称AMLP）。在给定相关度阈值的前提下,AMLP算法先对数据进行灰色关联聚类,再对类中的相关数据进行自适应的多项式拟合,然后把未拟合的特征数据抽象成一个矩阵,利用提升小波变换去除数据的时间和空间相关性。最后,通过游程编码对数据作进一步压缩。仿真结果表明,AMLP算法能够有效去除不同数据间的冗余信息以及同种数据间的时间和空间冗余信息,提高压缩比,降低网络能耗。与基于小波的自适应多模数据压缩算法（adaptive multiple-modalities data compression algorithm based on wavelet,简称AMMC）相比,AMLP算法的数据恢复精度大大优于AMMC算法,压缩比和能耗相近。因此,AMLP算法更适用于要求高精度数据的传感器网络应用,如地质灾害监测、医疗和军事领域。     

New coprimeness over multivariable polynomial matrices and its application to control delay systems

This paper presents a new notion of coprimeness over multivariable polynomial matrices, where a single variable is given priority over the remaining variables. From a characterization through a set of common zeros of the minors, it is clarified that the presented coprimeness is equivalent to weakly zero coprimeness in the particular variable. An application of the presented coprimeness to control systems with non-commensurate delays and finite spectrum assignment is also presented. Because the presented coprimeness is stronger than minor coprimeness, non-commensurate delays are difficult to deal with in algebraic control theory. The “rational ratio condition” between delays, which can reduce non-commensurate delays to commensurate delays, proves to be both powerful and practical concept in algebraic control theory for delay systems.     

基于DPT的非线性调频信号的DOA估计

提出了一种基于DPT的宽带非线性调频信号的DOA估计算法.首先将非线性调频(NLFM)信号建模为高阶多项式相位信号(PPS)模型,然后通过高阶瞬时矩进行多项式相位变换.接收信号将变换为单个正弦信号和新的噪声.再利用ROOT-MUSIC或者ESPRIT算法对变换得到的正弦信号的波达方向进行估计.理论分析和仿真结果表明,该...     

Computing monodromy via continuation methods on random Riemann surfaces

We consider a Riemann surface X defined by a polynomial f(x,y) of degree d, whose coefficients are chosen randomly. Hence, we can suppose that X is smooth, that the discriminant δ(x) of f has d(d−1) simple roots, Δ, and that δ(0)≠0, i.e. the corresponding fiber has d distinct points {y₁,…,y_d}. When we lift a loop 0∈γ⊂C−Δ by a continuation method, we get d paths in X connecting {y₁,…,y_d}, hence defining a permutation of that set. This is called monodromy.Here we present experimentations in Maple to get statistics on the distribution of transpositions corresponding to loops around each point of Δ. Multiplying families of “neighbor” transpositions, we construct permutations and the subgroups of the symmetric group they generate. This allows us to establish and study experimentally two conjectures on the distribution of these transpositions and on transitivity of the generated subgroups.Assuming that these two conjectures are true, we develop tools allowing fast probabilistic algorithms for absolute multivariate polynomial factorization, under the hypothesis that the factors behave like random polynomials whose coefficients follow uniform distributions.     

Dynamic normal forms and dynamic characteristic polynomial

We present the first fully dynamic algorithm for computing the characteristic polynomial of a matrix. In the generic symmetric case, our algorithm supports rank-one updates in O(n²logn) randomized time and queries in constant time, whereas in the general case the algorithm works in O(n²klogn) randomized time, where k is the number of invariant factors of the matrix. The algorithm is based on the first dynamic algorithm for computing normal forms of a matrix such as the Frobenius normal form or the tridiagonal symmetric form. The algorithm can be extended to solve the matrix eigenproblem with relative error 2^−b in additional O(nlog²nlogb) time. Furthermore, it can be used to dynamically maintain the singular value decomposition (SVD) of a generic matrix. Together with the algorithm, the hardness of the problem is studied. For the symmetric case, we present an Ω(n²) lower bound for rank-one updates and an Ω(n) lower bound for element updates.     

A fast algorithm for determining the linear complexity of a binary sequence with period 2 n p m

An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2 ⁿ p ^m is proposed and proved, where 2 is a primitive root modulop ². The new algorithm generalizes the algorithm for computing the linear complexity of a binary sequence with period 2 ⁿ and the algorithm for computing the linear complexity of a binary sequence with periodp ⁿ , where 2 is a primitive root modulop ².     

基于RSA的数字签名改进方案

该文在RSA数字签名的基础上,设计了两种改进方案,有效的解决了隐藏消息的问题,防止了不经意的信息泄露。这两种数字签名方案都是概率数字签名方案,因而安全性提高,具有多项式安全性。     

火星着陆任务落点误差快速分析方法

在火星着陆任务设计中,为高效地评估进入点导航误差等动力学方程中的不确定因素对着陆精度的影响,引入Galerkin投影法则,提出一种火星着陆落点不确定度快速预报与分析方法．该方法采用Wiener-Askey正交多项式逼近着陆器状态,将落点误差的预报问题转换为1个确定性微分方程的求解问题．最后以我国未来实施火星着陆探测为背景,分别用本文算法和蒙特卡洛方法进行数值仿真分析,结果表明,本文算法能够对落点偏差进行快速分析,准确预测其均值和方差,且计算效率明显提高．     

箭头矩阵在最小最大特征值条件下的完成问题

引入并讨论了对称箭头矩阵完成问题:在事先给定的对称箭头矩阵中嵌入一行一列使之成为新的对称箭头矩阵,并且具有指定最小最大特征值.利用箭头矩阵特征多项式之间的递归关系,给出并证明了这个问题存在惟一解的充要条件,以及解的一般公式与计算方法.同时还给出了存在非负解及均匀箭柄解的充要条件.利用该问题解决了逆特征值问题:求一个对称箭头矩阵,使它的各阶顺序主子阵具有给定的最小最大特征值.并给出该逆特征值问题解的计算方法.数值计算表明,该算法更有效.