平稳高斯过程通过无记忆非线性变换后协方差函数的恢复

在非线性变换和输出随机过程的相关函数或二维分布已知的前提条件下,我们考虑零均值平稳高斯过程通过无记忆非线性变换 f(X)后归—化协方差函数的恢复问题。得到了三种结果:(i)对于某些非线性变换,其中包括单调增函数 f,适当的区间窗函数及某些更一般的函数 f,任意的协方差函数都可以恢复;(ii)某些协方差函数对任意的非线性变换都可以恢复,其中包括正的协方差函数≥0,具有有理谐密度的协方差函数及限带协方差函数:(iii)对于某些非线性变换,其中包括对称的和不对称的 f,满足相当弱的条件且这些条件很容易通过输出相关函数来检验的某些协方差函数可以恢复.     

SIMON类非线性函数的线性性质研究

SIMON算法是由美国国家安全局(NSA)在2013年推出的一簇轻量级分组密码算法,具有实现代价低、安全性能好等优点,其轮函数采用了F(x)=(x<<相似文献   

函数变换器的计算机辅助设计

一、引言严格的函数变换器一般说是个非线性系统。该系统的输出应是输入量的某一特定函数,即 Y=f(x) (1) 我们还可以这样说:函数变换器是传输系数是输入量的函数这样一个系统。当前,函数变换器制造中存在两方面的问题:一是设计粗糙,     

基于恒模复值神经网络的正交相位编码集设计

文中研究了广泛应用于多输入多输出雷达系统中的正交相位编码集的设计问题，提出了一种基于复值神经网络的正交相位编码集设计方法。该方法将编码集设计视为非线性系统构建问题，通过最小化反映了编码集自相关和互相关性质的损失函数，在常模约束条件下对网络误差进行后向传播，从而通过网络训练获得具有良好相关性的正交相位编码集。通过与现有先进算法进行不同条件下的仿真对比，文中方法设计得到的正交相位编码集具有更好的相关特性，充分验证了本文所提方法的先进性。     

关于连续过程神经元网络的一些理论问题

针对输入/输出均为连续时间函数的非线性系统信号处理和建模问题,提出了一种连续过程神经元和过程神经元网络模型.连续过程神经元的输入/输出均为连续时间函数,其时空聚合运算能同时反映连续时变输入信号的空间聚合作用和输入过程中的时间累积效应,可实现输入/输出之间非线性实时或若干时间单元延迟的映射关系.文中给出了一种输入输出均为连续时间函数的前馈过程神经元网络模型,并证明了相应的连续性,函数逼近能力和计算能力等性质定理.     

k阶拟Bent函数在密码设计和通信中的应用

王育民、何大可提出了布尔函数关于线性函数的r阶相关度E(r)的概念来刻划布尔函数抵抗相关攻击的能力，本文以极小化所有非零相关度E(r)为主要目的，利用k阶拟Bent函数的特殊性质，给出了一类基于k阶拟Bent函数的“最佳”非线性组合设计的实现，构造了一类平衡的，具有高阶相关免疫性，而且非零相关度一致地小的非退化的布尔函数，并比较了它与基于部分Bent函数的“最佳”非线性组合设计的优劣。最后我们又利用k阶拟Bent函数构造了一类Bent互补函数族和Bent侣，Bent互补函数族和Bent侣在最佳信号设计方面意义重大，这也表明k阶拟Bent函数在密码设计和通信领域都有比较广的应用前景。     

关于完全非线性函数的非线性度的界

非线性函数在编码和密码领域中扮演着非常重要的角色,衡量函数的非线性性质很重要。非线性度和差分概率是衡量函数非线性性质的重要指标,差分概率均匀的函数称为具有完全非线性的函数。文中改进了Carlet和Ding所给出的完全非线性函数的非线性度的上界和下界,提出了更好的界的优化问题模型。     

有限域上k阶SAC/PC(l)函数的构造

本文给出了有限域F=GF(p~l)上k阶SAC/PC(l)函数的一种构造方法,这种方法不仅是文献[1]中构造方法在有限域上的推广,而且是其一般形式,另外在一定条件下这种函数还可保持平衡性和相关免疫性。最后研究了多输出k阶SAC/PC(l)函数。     

CATV网络的技术参数及计算（3）

8 非线性失真8.1 基本原理 在CATV系统中,由于非线性器件的存在,输出信号的表达式一般有无穷多项,每一项都由输入信号(假设正弦波)中的一项或多项产生,特别是由两项或多项的相互作用产生。其传输函数可以表达为:     

非线性分类的分割超平面快速集成方法

直接营销策略的分割超平面(Separating HyperPlane,SHP)方法所构建的线性超平面(Linear HyperPlane,LHP)函数集的Vapnik-Chervonenkis(VC)维不超过9,并且能够快速分类和保护数据隐私,但其训练速度慢,对样本分布敏感以及不能解决非线性等问题。为此,该文提出一种适合大样本问题的非线性分类方法,称为分割超平面的快速集成方法(Fast Ensemble of Separating HyperPlane,FE-SHP)。此方法先将训练样本划分为多个集合并分别构造它们的次优线性超平面,然后利用径向基函数(Radical Basis Function,RBF)改善次优线性超平面的非线性能力,同时引进优化权提升次优线性超平面的非线性集成效果,并将集成输出转化为概率输出,进而通过梯度下降法最大化训练样本的交叉熵对数似然函数求解相关参数。UCI数据集的实验结果表明,FE-SHP在处理大样本方面具有较好的优势。     

Eigenvalues of (↓2)H and convergence of the cascade algorithm

This paper is about the eigenvalues and eigenvectors of (↓2)H. The ordinary FIR filter H is a convolution with a vector h=(h(O),...,h(N)), which is the impulse response. The operator (↓2) downsamples the output y=h*x, keeping the even-numbered components y(2n). Where H is represented by a constant-diagonal matrix, this is a Toeplitz matrix with h(k) on its kth diagonal, the odd-numbered rows are removed in (↓2)H. The result is a double shift between rows, yielding a block Toeplitz matrix with 1×2 blocks. Iteration of the filter is governed by the eigenvalues. If the transfer function H(z)=Σh(k)z^-k has a zero of order p at z=-1, corresponding to ω=π, then (↓2)H has p special eigenvalues ½,¼...,(½)^p. We show how each additional “zero at π” divides all eigenvalues by 2 and creates a new eigenvector for λ=½. This eigenvector solves the dilation equation φ(t)=2Σh(k)φ(2t-k) at the integers t=n. The left eigenvectors show how 1,t,...,t^p-1 can be produced as combinations of φ(t-k). The dilation equation is solved by the cascade algorithm, which is an infinite iteration of M=(↓2)2H. Convergence in L² is governed by the eigenvalues of T=(↓2)2HH^T corresponding to the response 2H(z)H(z^-1 ). We find a simple proof of the necessary and sufficient condition for convergence     

Approximation of nonlinear systems having outputs

Suppose we have a nonlinear system with output $$\begin{gathered} \dot x = f(x) + g(x)u, \hfill \\ y = h(x), \hfill \\ \end{gathered}$$ an open setO of state spaceR ⁿ , and a positive integerk. We find conditions onf,g, andh so that for eachx ₀ ε O there is ann-dimensional affine linear system, which depends onx ₀ but not onu, having the property that the output time responses (starting at the statex ₀ of the original nonlinear system and this approximating linear system agree through orderk for any admissable controlu. Several possible applications of our results are examined.     

On the optimal filtering problem for the cubic sensor

We consider the problem of optimal filtering of a scalar diffusion process measured by a monotone nonlinear sensor in a low-noise channel. The specific sensors considered are of the formh _n(x)=¦x¦ⁿ sgn(x). This case represents a wide class of sensors with a critical inflection point, since it is the leading term in Taylor's expansion of the measurement function in the critical region.We give for the first time a formal asymptotic approximation of the conditional and of the mean square estimation errors of the optimal filter as interpolation formulas. We also construct an asymptotic approximation to the optimal filter and compare its performance with that of a constant gain filter.This work was partially supported by a research grant from the Foundation for Research in Electronics, Computers, and Communications, administered by the Israel Academy of Sciences and Humanities.     

求流图的1-因子和1-因子连通

正 文献[1]曾用有向图表示一组线性方程,然后利用这个图(称为流图或Coates图)写出方程的解。此法在各方面,尤其是在电路理论方面得到广泛的应用,不过在计算中需要列举流图中全部1-因子(1-factor)和1-因子连通(1-factorial connection),对于较复杂     

Measurement of second-order nonlinear optical susceptibility of cBN crystal synthesized at high pressure and high temperature

We demonstrate a transverse electro-optical modulator based on a tiny and irregular octahedral wafer of cubic boron nitride (cBN) crystal that is prepared by hexagonal boron nitride at high pressure and high temperature using nitride as the catalyst. A continuous wave semiconductor laser at the wavelength of 650 nm is used as a light source. A novel electrode fabrication is designed, a developed method different from the conventional transverse electro-optical modulator is introduced and the expression of the intensity of output beam is thought over. We obtain the half-wave voltage based on experiments of transverse electro-optical modulation. The second-order nonlinear optical susceptibility χ_ijk⁽²⁾(ω,0)=1.919×10⁻¹² m/V of cBN crystal is calculated by means of the half-wave voltage.     

星载柔性转发器中一种近似精确重构原型滤波器的设计

宽带柔性转发器作为下一代卫星通信有效载荷,采用星上数字信道化处理,可以很好地解决传统有效载荷存在的问题,实现卫星信号任意频段、任意带宽之间的灵活交换。该文分析了柔性转发器中调制滤波器组的性能特性,将滤波器组的设计转换为原型滤波器的设计,提出了一种近似精确重构的原型滤波器设计方法。该方法通过间接设计的思想,首先采用Parks-McClellan算法设计得到低阶的双通道滤波器h(2)(n)和实对称FIR滤波器g(n),然后利用g(n)实现对h(2)(n)的非零值M倍内插与2倍抽取,得到近似精确重构的原型滤波器h(M)(n),从而避免了IFIR法设计过程中镜像分量产生的性能损失。仿真结果表明,采用该文方法设计得到的调制滤波器组较传统设计方法表现出良好的性能。     

复合矩形域上二维电磁场边值问题的直线法分析

本文基于直线法的基本思想提出了一种分析复合矩形域上二维电磁场边值问题的新方法,即将偏微分方程沿一维离散化,从而转化为对于另一维变量的常微分方程组。在离散化过程中,本文引入了截断误差O(h4)的高精度格式,提出了在各种齐次边界条件下确定离散化常微分方程组通解的反推法,最后用最小二乘逼近提高解的精度。对矩形同轴线和脊波导的主模和高次模截止波长以及矩形域内静电位分布的数值计算结果与有关文献中的结果吻合得很好,体现了该方法简便、精度高和计算量小的优点。     

Investigation of the Mθ/G/1/m system with service regime switchings and threshold blocking of the input flow

The M^θ/G/1/m queueing system with the group arrival of customers, switchings of service regimes, and threshold blocking of the flow of customers is studied. The input flow is blocked if, at the instant of the successive customer service start, the number of customers in the system exceeds specified threshold level h. If, at instant t of the customer service start, number of customers in the system ξ(t) satisfies the condition h_i < x(t) \leqslant h_{i + 1} (i = [`(1,r)] )h_i < \xi (t) \leqslant h_{i + 1} (i = \overline {1,r} ), then the service time for this customer corresponds to distribution function F _i (t). At 1 ≤ ξ(t) ≤ h = h ₁, the service time for a customer is distributed according to law F(t) (basic service time). The Laplace transforms for the distribution of the number of customers in the system on the busy period and for the distribution function of the busy period are found, the mean length of the busy period (including the case m = ∞) is determined and formulas for the ergodic distribution of the number of customers in the system (including the case m = ∞) are obtained. An effective algorithm for calculation of the ergodic distribution is proposed. The recurrence relations of the algorithm are not explicitly dependent on m.     

Robust pole placement in discrete-time systems

The problem of robust pole placement via a state-space feedback is discussed for discrete-time systems. It is assumed that a discrete-time system is described in terms of the state-space equation x(k+1)=Ax(k)+bu(k),y(k)=c^Tx(k)+eu(k) with uncertain entries of matrices (c, A, b,e). A feedback matrix f is calculated such that the real stability radius of the characteristic polynomial of the closed-loop system is possibly maximal.     

Stationary characteristics of the Mθ/G/1/m system with the threshold functioning strategy

The M^θ/G/1 queueing system with the group arrival of customers, switchings of service regimes, and threshold blocking of the flow of customers is considered. The input flow is blocked if, at the instant of the beginning of the service of a successive customer, the number of customers in the system exceeds given threshold level h. If, at instant t of the beginning of the service of the customer, the number of customers in the system satisfies the condition h _i < ɛ(t) ≤ h _{i + 1} h_i < e(t) \leqslant h_{i + 1} (i = [`(1,r)] )h_i < \varepsilon (t) \leqslant h_{i + 1} (i = \overline {1,r} ), then, the service time of this customer is associated with distribution function F _i (t). When 1 ≤ ɛ(t) ≤ h = h ₁, the service time of the customer is distributed according to law F(t) (the basic service regime). For the case of a single switching (r = 1), the mean duration of the busy period intervals with the absence and presence of the input flow blocking, the probability of customer service, and the stationary characteristics of the queue are determined. The character of the dependences of the mean busy period duration and the probability of service on parameters m and h is investigated. For the case m = ∞, some problems of optimal synthesis of systems with given characteristics and the problem of minimization of the service cost are solved.