任意分布抽样程序的设计与实现

该文描述了一个抽样的完善算法和程序实现过程,这一算法利用了高效的别名法,可使计算机从任意分布中自动抽样。目前拥有的两个函数可以完成任意离散分布和任意一元连续分布的抽样。抽样实验表明,该程序及方法是高效的。     

一维离散分布的伪随机数研究与实现

非均匀随机数在计算机模拟、算法分析与设计、统计抽样与决策、概率论与统计都有广泛应用,,但计算机一般只提供均匀概率分布的随机数。介绍了如何在计算机中产生服从一维离散分布的伪随机数的方法:直接抽样法、罐子抽样法和别名抽样法,并给出罐子抽样法的具体实现。     

Z_N上离散对数量子计算算法

文中通过多次量子Fourier变换和变量代换,给出了一个ZN上离散对数量子计算算法,刻画了元素的阶r与算法成功率的关系,当r为素数时,算法成功的概率接近于1,新算法所需基本量子门数的规模为O(L3),且不需要执行函数|f(x1,x2)〉的量子Fourier变换的反演变换,优于已有的ZN上离散对数量子计算算法,其中L=[log N]+1.     

基于锥函数逼近上的自适应拟牛顿无约束极小化方法

本文提出的算法,当f(x)的“二次性”较强时,能自动转为DFP公式,当f(x)为一锥函数时,算法具有n步终止性,对检验函数进行计算的结果表明,本算法优于DFP公式。     

一个新的直接搜索法——降维搜索法

一、引言 设f(x)为R~n上连续实函数,考虑f(x)的无约束最优问题。若f(x)不可微或难于求导,常用的方法是直接搜索法,其中最有成效的是Powell的方向加速法。设f(x)为正定二次函数     

遗传算法求f(x)=x·sin(Aπ·x)+B最大值

本实验主要用于求形如f(x)=x·sin(Aπ·x) B的函数在某指定区间中的最大值.由于此函数有多个极值点,一般方法不易找到其最优解,故在本实验中使用GA算法,通过进化寻找其最大值.     

遗传编程的实现方法

遗传编程(Genetic Programming,GP)是一种自动随机产生搜索程序的方法。理论上凡是根据多个输入值而得到一个值的函数,如:对于f(x1,x2,…,xn)这样的函数都可以使用GP来生成。它有如下一些特点:①GP求解的是一个描述问题的程序(或者说是一个算法)。②GP通常用树型结构来表示程序,描述相对复杂。③GP的每一代的个体的长度(深度)一般是不同     

单侧逼近迭代法及其在求解多项式方程根中的应用

1.引言 用通常的迭代法,例如简单选代法、牛顿迭代法等,求一般函数方程 f(x)=0 (1)的根时,首先需要选取一个比较好的初始近似x_0,使得由这个初始近似生成的迭代数列{x_n}收敛到(1)的根。如果选择不好,生成数列发散。特别是,求出了若干个根x_i后,如     

基于径向基函数网络的非线性离散时间系统的自适应控制

对于一类离散时间的非线性系统x(k+1)=f(x(k))+u(k)+d(k),当系统中的非 线性函数f(x(k))满足线性增长条件时,首先证明了{x(k)}落入一紧集中,然后根据高斯径 向基函数网络的逼近性质,给出了自适应控制器的设计方法.利用李亚普诺夫稳定性理论,证 明了控制算法是全局稳定的,跟踪误差收敛于零的某一领域中.     

一种用于连续动作空间的最小二乘行动者-评论家方法

解决具有连续动作空间的问题是当前强化学习领域的一个研究热点和难点.在处理这类问题时,传统的强化学习算法通常利用先验信息对连续动作空间进行离散化处理,然后再求解最优策略.然而,在很多实际应用中,由于缺乏用于离散化处理的先验信息,算法效果会变差甚至算法失效.针对这类问题,提出了一种最小二乘行动者-评论家方法(least square actor-critic algorithm,LSAC),使用函数逼近器近似表示值函数及策略,利用最小二乘法在线动态求解近似值函数参数及近似策略参数,以近似值函数作为评论家指导近似策略参数的求解.将LSAC算法用于解决经典的具有连续动作空间的小车平衡杆问题和mountain car问题,并与Cacla(continuous actor-critic learning automaton)算法和eNAC(episodic natural actor-critic)算法进行比较.结果表明,LSAC算法能有效地解决连续动作空间问题,并具有较优的执行性能.     

概率逻辑学基本定理的推广及其应用

利用赋值集的随机化方法,在[n]值命题逻辑系统中提出了公式的随机不可靠度概念,证明了一个有效推理结论的随机不可靠度不大于各前提的随机不可靠度与其必要度的乘积之和。通过推广的概率逻辑学基本定理,证明了随机逻辑度量空间中MP规则和HS规则成立。     

C语言中互不相同随机数的应用研究

文章对随机数的应用问题进行了详细的分析,给出了一种实现的算法,并用C语言实现。通过该问题的C实现,可使学习者清晰地观测到解决该问题的全过程。     

基于Markov过程预测的页面置换方法

页面替换是操作系统实现虚拟存换方法的缺点,提出一种基于Markov随机过程的页面调度模型.通过分析页面置换序列,发现其规律并模拟该序列,目的是接近最优替换方法以降低缺页率.实现了基于该模型的页面置换方法,通过实验证明新方法能提高页面换入命中率并控制时间耗费.     

随机谕言模型

介绍了可证明安全理论中的重要工具——随机谕言模型,包括随机谕言模型的起源、基本性质和方法、随机谕言模型中的代表方案、明文知晓性质、随机谕言的实例化、随机谕言不可实例化的性质和相关负面结论以及对弱化的随机谕言模型的研究.此外,比较了随机谕言模型和其他理想模型,简介了标准模型中的方案设计状况.     

随机约束满足问题相变研究综述

随机约束满足问题是经典的NP完全问题,在理论研究和现实生活中有着广泛应用。研究人员发现随机约束满足问题存在相变现象,近几十年来关于此问题相变的研究成果不断涌现。从随机图着色问题和随机可满足问题2个最经典的随机约束满足问题入手,从算法研究、理论物理和数学证明3个方面综述了随机图着色问题和随机可满足问题的相变研究成果。最后对随机约束满足问题相变的研究趋势进行了展望。     

Morphological analysis of discrete random shapes

In this paper I discuss a number of theoretical issues regarding the morphological analysis of discrete random shapes by means of Matheron's random set theory. I revisit this theory by limiting myself to the discrete case, since most image data are available in a discrete form. Although it may seem that the transition from the continuous to the discrete case is straightforward (since most of Matheron's theory is general enough to incorporate the discrete case as a special case), this transition is often challenging and full of exciting and, surprisingly, pleasant results. I introduce the concept of the cumulative-distribution functional of a discrete random set and review some fundamental properties of the capacity functional (a fundamental statistical quantity that uniquely defines a random set and relates random set theory to mathematical morphology). In analogy to a recent result and under a natural boundness condition, I show that there exists a one-to-one correspondence between the probability-mass function of a discrete binary random field and the corresponding cumulative-distribution functional. The relationship between the cumulative-distribution functional and the capacity functional of a discrete random set is also established. The cumulative-distribution and capacity functionals are related to the higher-order moments of a discrete binary random field, and, therefore, their computation is equivalent to computing these moments. A brief discussion of how to perform such computations for a certain class of discrete random sets is provided. The capacity functional of a morphologically transformed, continuous random set cannot be associated to the capacity functional of the random set itself, except in the case of dilation. I show that the derivation of such an association is possible in the discrete case and for the cases of dilation and erosion and more complicated morphological transformations, such as opening and closing. These relationships are then used to derive a fundamental result regarding the statistical behavior of opening and closing morphological filters. I also show that the probability-mass function of a discrete binary random field may be expressed in terms of the cumulative-distribution functional or the capacity functional of a morphologically transformed discrete random set by means of a hit-or-miss transformation. I also introduce moments for discrete random sets, which permit generalization of the concepts of autocorrelation and contact distribution. Furthermore, I demonstrate the fact that the class of opening-based size distributions, introduced axiomatically by Matheron, are higher-order moments of a discrete random set, therefore statistically demonstrating that size distributions are good statistical summaries for shape. Finally, convex random sets are viewed in the discrete domain. My final result regarding convexity, is similar to Matheron's. However, the tools used here for the derivation of such a result are different from the ones used by Matheron, whose approach to this subject is limited to the continuous case.     

A probabilistic scheme of independent random elements distributed over a finite lattice. I. Exact probability distributions of functionals of union of random elements

A probabilistic scheme of independent random elements with values in a finite lattice is introduced. For the scheme, exact expressions of probability distributions of a functional of general form and union of random corank elements are obtained. Various probabilistic combinatorial problems (on probability distributions of the number of uncovered points in a generalized scheme of grouped distribution of particles, on the number of connectivity components of a random hypergraph, on the number of solutions of a system of random linear equations over a finite ring with unity, etc.) are demonstrated to be naturally formulated in terms of the scheme constructed.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 3–15, September–October 2004.     

VFP数据库加密算法的研究与实现

对于最初给定的随机种子,随机函数会生成一个相应的数列。数据库数据随机加密,是一种利用随机函数的随机数序列与数据库数据进行异或等运算,实现数据库数据加密的方法。本文对数据库数据随机加密算法进行了研究和探讨,给出了在VFP中实现数据库数据随机加密、解密的程序代码。     

Orthogonal decompositions of 2-D nonhomogeneous discrete random fields

Imposing atotal-order on a two-dimensional (2-D) discrete random field induces an orthogonal decomposition of the random field into two components: Apurely-indeterministic field and adeterministic one. The purely-indeterministic component is shown to have a 2-D white-innovations driven moving-average representation. The 2-D deterministic random field can be perfectly predicted from the field's past with respect to the imposed total-order definition. The deterministic field is further orthogonally decomposed into anevanescent field, and aremote past field. The evanescent field is generated by the columnto-column innovations of the deterministic field with respect to the imposed nonsymmetrical-half-plane total-ordering definition. The presented decomposition can be obtained with respect to any nonsymmetrical-half-plane total-ordering definition, for which the nonsymmetrical-half-plane boundary line has rational slope.