寻找布尔函数的零化子

 通过解方程组来研究密码系统,是代数攻击的研究内容代.对方程组降次是降低求解复杂度的一种重要方法.为了达到这个目的,引入了布尔函数零化子的概念.然而迄今为止,尚未有求解零化子的有效算法.这篇文章提出了一种计算给定布尔函数的零化子集的算法.由前两个算法,可以得到给定布尔函数的零化子集的一组基;从第三个算法,可以得到最低次数的零化子.算法的复杂度与函数的单项式个数相关.对流密码来说,在很多情况下,相比以前的算法而言,这种算法的复杂度大为降低.最后,我们将给出一个实例,说明算法是如何工作的.     

基于Zernike多项式的人眼波前像差拟合算法

采用改进的Gram-Schmidt正交化法对矛盾方程的广义增广矩阵进行正交三角化,导出求解基于Zernike多项式的人眼波前像差拟合系数的算法。通过拟合给定模式系数和一般数学波面的两种方式对算法进行了验证。验证结果表明,该算法与直接构造法方程组解法的计算精度相当。该算法避免了因构造法方程组而引入的计算误差,易于编程,是一种比较理想的求解Zernike多项式拟合系数的算法。     

基于离散傅里叶变换和块时间递归并行格型结构的离散Gabor分析窗求解

提出了一种快速求解离散Gabor变换分析窗的方法.首先选择一个合适的基函数,同给定的综合窗函数构造一个可逆的块循环矩阵,然后根据块循环矩阵特点,利用快速离散傅里叶变换求解块循环矩阵的逆,最后采用基于块时间递归的并行格型结构来求解分析窗.本文证明了此算法获得的窗函数与给定的综合窗满足双正交关系.实验结果表明,本文算法能快...     

GF(p)上q元旋转对称弹性函数的一个等价刻画

基于旋转对称弹性函数l值支撑矩阵的性质,给出了GF(p)上q变元旋转对称弹性函数的一个等价刻画,证明了GF(p)上q变元旋转对称一阶弹性函数的构造问题等价于一个方程组的求解问题,并且利用方程组的所有解给出这类函数计数结果的一个表示。     

非线性布尔函数的智能优化设计

引言在序列密码体制的设计中,布尔函数具有十分重要的作用。过去,布尔函数的选取通常采用随机生成和直接构造的方法,然而,这两种方法都存在着诸多的欠缺。随机生成方法需要一个很大的搜索空间,要找到非线性度高、自相关性低的布尔函数是非常困难的,直接构造的布尔函数能够使得所需要的一些性质达到最优,但其它某些密码学性质又可能比较差。近年来,各种机器学习和人工智能的相关算法(诸如“爬山算法”、“遗传算法”、和“模拟退火”算法等)     

快速挖掘最大频繁项集

提出了一种基于布尔矩阵的最大频繁项集挖掘算法，通过将FP-tree映射成布尔矩阵和权值表，运用布尔逻辑运算进行矩阵投影操作得到最大频繁项集，算法在挖掘过程中不用生成最大频繁候选项集，从而大大提高了算法的时间效率和空间可伸缩性。     

解非线性方程组的神经网络方法

本文提出了一种求解非线性方程组的神经网络方法,该方法对非线性方程组的任意给定的初始点,都能稳定地收敛到它的一个实根.文中首先严格地证明了该方法的稳定性、收敛性及可行性,然后给出了一个模拟算法及其应用.最后的数值试验结果表明该方法是有效的.     

一个计算独立回路矩阵元素的新公式

本文从场论说给出了非线性网络中独立回路方程组形式，并将其改写成网孔方程组，求此方程组的解答，得到一个从非线性网络到线性网络的可按网孔行列式来计算独立回路矩阵元素的理论公式。文中最后以实例验证了该公式的正确性。     

性能驱动系统划分的均场退火方法

本文通过把时延约束条件转化为一个布尔矩阵，利用这个布尔矩阵构造能量函数的时延约束项，从而解决了用神经网络处理时延约束这类不等式约束的难题，并据此提出了一个性能驱动的ＶＬＳＩ系统划分的均场退火算法．算法不仅考虑了模块间的连接关系，还考虑了版图的物理结构，是一种逻辑与版图相结合的划分方法．实验表明，该算法具有较强的寻优能力     

C-RAN网络中基于稀疏性的预测矩阵求解算法

在C-RAN（Centralized,Cooperative,Cloud Radio Access Network）无线网络基于转移矩阵的负载预测方法中,虽然该预测矩阵具有稀疏特性,但是现有的技术缺乏对稀疏特性加以利用,从而造成计算复杂。针对此问题,提出了一种基于稀疏性的预测矩阵求解算法。该算法对网络状态转移矩阵进行分块迭代,每次等分4块,并分别定义4块矩阵的偏移量。当属于同一行的块矩阵的偏移量有一个是零矩阵时,直接得出所求矩阵对应块的元素全部为零,然后进行下一次迭代;当属于同一行的块矩阵偏移量都不为零矩阵时,通过对矩阵方程组变形处理,转换成迭代格式,然后分块处理。最后,结合仿真定量分析稀疏矩阵稀疏度的临界值问题,给出了稀疏度与计算量之间的关系,并证明了其合理性。仿真结果表明,所提算法能够在不影响预测准确度前提下,降低复杂度。     

一种大数据集上的非线性PSVM训练方法

PSVM作为一种新型SVM方法，避免了求解二次规划问题，具有更快的计算速度，但对于大规模数据集，采用传统方法求解非线性PSVM面临大矩阵求逆的困难。文章基于共轭梯度法结合低秩估计提出了一个大数据集上的非线性PSVM训练方法NPSVM-LD，通过多次迭代的矩阵乘积运算避免了对大矩阵的求逆。在UCI数据集上的实验表明。该方法能够在应用非线性核函数条件下，使PSVM有效处理规模在10000以内的训练集的情况。     

From Boolean to probabilistic Boolean networks as models of genetic regulatory networks

Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrative and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on first-passage times in Markov chains. Examples from biology are presented throughout the paper.     

Generalized Differential Transfer Matrix for Fast and Efficient Analysis of Arbitrary-Shaped Nonlinear Distributed Feedback Structures

A new, fast, and efficient approach based on the differential transfer matrix idea, is proposed for analysis of nonuniform nonlinear distributed feedback structures. The a priori knowledge of the most-likely electromagnetic field distribution within the distributed feedback region is exploited to speculate and factor out the rapidly varying portion of the electromagnetic fields. In this fashion, the transverse electromagnetic fields are transformed into a new set of envelope functions, whereupon the numerical difficulty of solving the nonlinear coupled differential equations is partly imparted to the analytical factorization of the fields. This process renders a new set of well-behaved nonlinear differential equations that can be readily solved. Strictly periodic, linearly tapered, and linearly chirped structures are analyzed to justify the accuracy and the efficiency of the proposed method.     

Microwave remote sensing of a two-layer random medium

A two-variable expansion technique is used to solve for the mean Green's function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.     

Perturbation-Based Fourier Series Analysis of Transistor Amplifier

A perturbation-based Fourier series model is proposed to approximate the nonlinear distortion in weakly nonlinear circuits. This general model is applicable to any set of multi-variable state equations that completely describe a nonlinear circuit. This model is applied to a common emitter amplifier circuit wherein the transistor is represented by Ebers–Moll nonlinear current equations. Appropriate state variables are defined, then the linear and nonlinear parts of the Ebers–Moll current equations are separated, and a small perturbation parameter is incorporated into the nonlinear part. Now these current equations are incorporated into the set of KCL, KVL equations defined for the circuit and the state variables are perturbatively expanded. Hence, multi-variable state equations are obtained from these equations. The state variables are approximated up to first order through Fourier series expansion, as described in the proposed model. The main advantage of the proposed model is that it is simple and straightforward approach to analyze weakly nonlinear circuits, as it involves matrix computations and the calculations of exponential Fourier coefficients.     

Josephson-junction mixer analysis using frequency-conversion and noise-correlation matrices

A complete characterization and optimization have been carried out for an externally pumped Josephson-junction mixer. A noise-driven nonlinear pump equation is first solved in the time domain on a computer in order to obtain a conversion matrix and noise-correlation matrix for the small-signal current and voltage. A set of linear circuit equations formed by the matrices is then solved in the frequency domain for the mixer noise temperature and conversion efficiency. Finally, optimization is made with respect to circuit, bias, and junction parameters to find the ultimate theoretical performance.     

Realization of Boolean Functions via CNN: Mathematical Theory, LSBF and Template Design

As a paradigm for nonlinear spatial-temporal processing, cellular nonlinear networks (CNN) are biologically inspired systems where computation emerges from a collection of simple locally coupled nonlinear cells. Our investigation is an exploration of an important and difficult aspect of implementing arbitrary Boolean functions by using CNN. A typical class of basic key Boolean functions is the class of linearly separable ones. In this paper, we focus on establishing a complete set of mathematical theories for the linearly separable Boolean functions (LSBF) that are identical to a class of uncoupled CNN. First, we obtain an essential relationship between the template and the offset levels as well as the basis of the binary input vector set in the uncoupled CNN. More precisely, we construct a neat binary input–output truth table and some interesting properties of the offset levels of the uncoupled CNN, and develop a practical design formula for the class of CNN template. Especially, we found a criterion for LSBF, which depends only on symbolic relations between a Boolean function's outputs. Furthermore, we develop a method for representing any linearly nonseparable Boolean function into a logic operation of a sequence of linearly separable ones for a small number of inputs.     

A difference-set cyclic code (1057,813,34)

This paper presents an overview of the implementation of a difference-set cyclic code (1057,813,34). It is easy to achieve coding and decoding circuits. The decoding lays on the analysis of the composite remainder R_c (x) and the use of a decoding matrix of 33 Boolean equations. The error-correcting algorithm has been improved, so the difference-set cyclic code (1057,813,34) can correct up to 26 random errors instead of the 16 previous random errors found by the theory. Moreover, 3 decoding algorithms have been simulated and allow the comparison of their respective efficiency. The hardware achievement is quite easy because the necessary logical elements such as shift delay registers, positive-and gates, positive-or gates, positive-exclusive-or gates exist as a set of libraries.     

Some new algorithms for recursive estimation in constant linear systems

Recursive least-squares estimates for processes that can be generated from finite-dimensional linear systems are usually obtained via ann times nmatrix Riccati differential equation, wherenis the dimension of the state space. In general, this requires the solution ofn(n + 1)/2simultaneous nonlinear differential equations. For constant parameter systems, we present some new algorithms that in several cases require only the solution of less than2nporn(m + p)simultaneous nonlinear differential equations, wheremandpare the dimensions of the input and observation processes, respectively. These differential equations are said to be of Chandrasekhar type, because they are similar to certain equations introduced in 1948 by the astrophysicist S. Chandrasekhar, to solve finite-interval Wiener-Hopf equations arising in radiative transfer. Our algorithms yield the gain matrix for the Kalman filter directly without having to solve separately for the error-covariance matrix and potentially have other computational benefits. The simple method used to derive them also suggests various extensions, for example, to the solution of nonsymmetric Riccati equations.     

Global identifiability of nonlinear models of biological systems

A prerequisite for well-posedness of parameter estimation of biological and physiological systems is a priori global identifiability, a property which concerns uniqueness of the solution for the unknown model parameters. Assessing a priori global identifiability is particularly difficult for nonlinear dynamic models. Various approaches have been proposed in the literature but no solution exists in the general case. In this paper, we present a new algorithm for testing global identifiability of nonlinear dynamic models, based on differential algebra. The characteristic set associated to the dynamic equations is calculated in an efficient way and computer algebra techniques are used to solve the resulting set of nonlinear algebraic equations. The algorithm is capable of handling many features arising in biological system models, including zero initial conditions and time-varying parameters. Examples of usage of the algorithm for analyzing a priori global identifiability of nonlinear models of biological and physiological systems are presented.