用Zernike多项式计算湍流介质的光学品质

流动化学激光器在光腔区内的湍流混合,激光介质折射率有序和无规则涨落引起输出光束品质的退化。有序扰动的贡献使远场峰值强度降低和发散角变大,而无规则的随机扰动还使光束抖动和焦点前后移动。用平均Strehl比来评价这种介质的光学品质,它定义为平均远场分布的极大值与相同孔径均匀平面波的远场峰值之比。

隐私保护集合交集计算技术研究综述

隐私保护集合交集(private set intersection,PSI)计算属于安全多方计算领域的特定应用问题,不仅具有重要的理论意义也具有很强的应用背景,在大数据时代,对该问题的研究更是符合人们日益强烈的在享受各种服务的同时达到隐私保护的需求.对安全多方计算基础理论进行了简要介绍,并重点介绍了目前主流的安全多方计算框架下2类PSI研究技术:传统的基于公钥加密机制,混乱电路,不经意传输的PSI协议和新型的云辅助的PSI协议,并对各类协议的过程、适用性、复杂性进行简要分析总结.同时,也对隐私保护集合交集问题的应用场景进行详细说明,进一步体现对该问题的实际研究价值.随着对该问题的不断深入研究,目前已经设计了在半诚实模型下快速完成上亿元素规模的隐私集合求交集协议.

矩阵函数的计算方法

矩阵函数的计算方法王传玉（安徽机电学院基础部，芜湖２４１０００）给定一个实方阵Ａ，如何计算如Ａ１００，，ｓｉｎＡ？对于Ａ的方幂计算即Ａｋ（ｋＮ），常见方法有ｉ）求出Ａ的约当形，即存在可逆阵Ｐ使Ｐ－１ＪＰ＝Ｊ：则Ａ＝ＰＪＰ－１，从而Ａｋ＝ＰＪ：Ｐ－１．...

一个新的基于口令的密钥协商协议

以不经意多项式计算作为核心组件,提出了一个基于口令的密钥协商协议PSKA-I,该协议能够抵抗字典攻击但只能工作于认证模型。为解决协议PSKA-I这一缺陷,根据BCK安全模型设计了消息传输认证器,将协议PSKA-I转换为非认证模型中的安全协议PSKA-Ⅱ。上述协议口令的安全性由不经意多项式计算予以保证。与GL协议相比,该协议的通信及计算复杂度明显降低。

一个高效的安全两方近似模式匹配协议

近似模式匹配是模式匹配中最适合实际应用的变体之一,其功能是确定2个字符串之间的汉明距离是否小于某给定阈值.由于其实用性,近似模式匹配在人脸识别、基因匹配等方面具有广泛的应用.然而,由于私有数据的敏感性,数据拥有者往往不愿意共享其隐私数据.幸运的是,安全近似模式匹配可以在不泄露数据前提下完成匹配功能.首次基于茫然传输(oblivious transfer,OT)、同态加密(homomorphic encryption,HE)、茫然多项式计算(oblivious polynomial evaluation,OPE)以及隐私等值比较(private equality test,PEQT)技术提出了安全的、实用的近似模式匹配协议,并通过理想现实模拟范式证明协议具有半诚实敌手安全性.就效率而言,与当前已有的安全近似模式匹配工作相比,协议在计算复杂度方面具有优势,将复杂度从O(nm)降为O(nτ),其中n为文本长度,m为模式长度,τ为给定阈值.最后,为了检验高效性,对协议进行了性能评估.实验结果表明:当模式长度为2^(6)且文本长度为2^(12)时,协议仅需要10 s运行时间.

太阳耀斑的GPS监测方法及实例分析

利用GPS伪距与载波相位联合数据处理的方法 ,分析了 2 0 0 0年 7月 1 4日太阳耀斑爆发期间 ,武汉、北京、乌鲁木齐GPS观测数据得到的电离层TEC 。

面向新型计算架构的存算融合晶体管器件研究

基于金属-氧化物-半导体场效应晶体管(metal-oxide-semiconductor field-effect transistor,MOSFET)器件和冯·诺伊曼架构的半导体芯片技术带领人类迈进了信息化时代.近年来,新型计算架构蓬勃发展.然而,专用算法和类脑智能算法映射至MOSFET电路时,通常面临硬件开销大、系统能效低等挑战.针对上述问题,本文研制了具有存算融合特点的新型晶体管器件,有效适配了专用算法和类脑计算应用:在基础数值计算方面,针对多项式计算,研制了电荷捕获型晶体管,利用器件的本征非线性动力学特征,基于单器件实现了三元素乘法运算,有效加速了多项式回归任务;在新兴智能计算方面,针对神经网络计算,研制了离子栅型神经形态晶体管,利用双栅耦合的方式实现了神经元的非线性激活和时空信息整合功能,并基于此提出了神经元相关性脉冲神经网络,实现了注意力转变现象的模拟.本文的工作将为新型计算架构芯片的构建提供新的思路.

Fingerprint singular points extraction based on orientation tensor field and Laurent series

Singular point(SP)extraction is a key component in automatic fingerprint identification system(AFIS).A new method was proposed for fingerprint singular points extraction,based on orientation tensor field and Laurent series.First,fingerprint orientation flow field was obtained,using the gradient of fingerprint image.With these gradients,fingerprint orientation tensor field was calculated.Then,candidate SPs were detected by the cross-correlation energy in multi-scale Gaussian space.The energy was calculated between fingerprint orientation tensor field and Laurent polynomial model.As a global descriptor,the Laurent polynomial coefficients were allowed for rotational invariance.Furthermore,a support vector machine(SVM)classifier was trained to remove spurious SPs,using cross-correlation coefficient as a feature vector.Finally,experiments were performed on Singular Point Detection Competition 2010(SPD2010)database.Compared to the winner algorithm of SPD2010 which has best accuracy of 31.90%,the accuracy of proposed algorithm is 45.34%.The results show that the proposed method outperforms the state-of-the-art detection algorithms by large margin,and the detection is invariant to rotational transformations.

C^1 C^2INTERPOLATION OF SCATTERED DATA POINTS

In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.

Smooth interpolation on homogeneous matrix groups for computer animation

Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been proposed to address this problem, including computing matrix curves from curves in Euclidean space by registration, representing one-parameter curves on manifold by rational representations, changing subdivisional methods generating curves in Euclidean space to corresponding methods working for matrix curve generation, and variational methods. In this paper, we propose a scheme to generate rational one-parameter matrix curves based on exponential map for interpolation, and demonstrate how to obtain higher smoothness from existing curves. We also give an iterative technique for rapid computing of these curves. We take the computation as solving an ordinary differential equation on manifold numerically by a generalized Euler method. Furthermore, we give this algorithm’s bound of the error and prove that the bound is proportional to the shift length when the shift length is sufficiently small. Compared to direct computation of the matrix functions, our Euler solution is faster.

A Ternary 4-Point Approximating Subdivision Scheme

In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.

Calculations of Invariants for Some 3-manifolds

In this paper,we give some ways of computing invariants of some 3 manifolds,obtained by surgery on circular Hopf link,by using Kauffman polynomial.

On the value distribution of f^nf^(k)

This paper presents an inequality, by use of which some results about the value distribution of f nf (k) are proved, where n and k are two positive integers.

A class of quasi Bézier curves based on hyperbolic polynomials

This paper presents a basis for the space of hyperbolic polynomials Гm=span { 1, sht, cht, sh2t, ch2t shmt, chmt} on the interval [0,a] from an extended Tchebyshev system, which is analogous to the Bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we construct quasi Bézier curves and discuss some of their properties. At last, we give an example and extend the range of the parameter variable t to arbitrary close interval [r, s] （r〈s）.

一种准最优多用户检测方法

由于 Verdu 提出的最优多用户检测方法采用Viterbi算法 ,它的计算复杂度与用户数成指数关系 ,无法在实际中应用 ,因此提出了一种采用半正定规划 (positive se-mi- definite programming,SDP)的新的准最优多用户检测方法。这种方法将最优多用户检测方法转化成一个二次规划(quadratic programm ing,QP)的求解问题 ,并通过半正定规划松弛来解决这个二次规划问题。由于这种方法采用的半正定规划问题求解方法具有多项式程度的复杂性 ,所以这种新的 SDP多用户检测方法也具有多项式程度的复杂性。仿真表明 :这种新的

The RCH Method for Computing Minimal Polynomials of Polynomial Matrices

In this paper,a randomized Cayley-Hamilton theorem based method(abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented.It determines the coefficient polynomials term by term from lower to higher degree.By using a random vector and randomly shifting,it requires no condition on the input matrix and works with probability one.In the case that coefficients of entries of the given polynomial matrix are all integers and that the algorithm is performed in exact computation,by using the modular technique,a parallelized version of the RCH method is also given.Comparisons with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.

An efficient algorithm for factoring polynomials over algebraic extension field

An efficient algorithm is proposed for factoring polynomials over an algebraic extension field defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its CrSbner basis, no extra Grbbner basis computation is needed for factoring a polynomial over this extension field. Nothing more than linear algebraic technique is used to get a characteristic polynomial of a generic linear map. Then this polynomial is factorized over the ground field. From its factors, the factorization of the polynomial over the extension field is obtained. The algorithm has been implemented in Magma and computer experiments indicate that it is very efficient, particularly for complicated examples.

A new proof for the correctness of the F5 algorithm

In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness of the syzygy criterion, but the proof for the correctness of the rewritten criterion was left. Since then, F5 has been studied extensively. Some proofs for the correctness of F5 were proposed, but these proofs are valid only under some extra assumptions. In this paper, we give a proof for the correctness of F5B, an equivalent version of F5 in Buchberger＇s style. The proof is valid for both homogeneous and non-homogeneous polynomial systems. Since this proof does not depend on the computing order of the S-pairs, any strategy of selecting S-pairs could be used in F5B or F5. Furthermore, we propose a natural and non-incremental variant of F5 where two revised criteria can be used to remove almost all redundant S-pairs.

Algorithms for computing the global infimum and minimum of a polynomial function

By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial function.For a multivariate real polynomial f ,the algorithm in this paper is able to decide whether or not the global infimum of f is finite.In the case of f having a finite infimum,the global infimum of f can be accurately coded in the Interval Representation.Another usage of our algorithm to decide whether or not the infimum of f is attained when the global infimum of f is finite.In the design of our algorithm,Wu’s well-known method plays an important role.

On the Unique Minimal Monomial Basis of Birkhoff Interpolation Problem

This paper studies the minimal monomial basis of the n-variable Birkhoff interpolation problem. First, the authors give a fast B-Lex algorithm which has an explicit geometric interpretation to compute the minimal monomial interpolation basis under lexieographie order and the algorithm is in fact a generalization of lex game algorithm. In practice, people usually desire the lowest degree interpolation polynomial, so the interpolation problems need to be solved under, for example, graded monomial order instead of lexicographie order. However, there barely exist fast algorithms for the non- lexicographic order problem. Hence, the authors in addition provide a criterion to determine whether an n-variable Birkhoff interpolation problem has unique minimal monomial basis, which means it owns the same minimal monomial basis w.r.t, arbitrary monomial order. Thus, for problems in this case, the authors can easily get the minimal monomial basis with little computation cost w.r.t, arbitrary monomial order by using our fast B-Lex algorithm.