新IFS分形图象盒维数的EMMS位模拟计算

针对新获取的IFS分形图像进一步分析的需要，提出位模拟分维计算，极大地改进了原有盒维数计算的诸多不便，在普通PC机上一次性的计算即可满足一般性要求，或提供进一步处理的精质数据。完成了完整的实用软件，并采用该算法具体计算了墨竹叶分形集和扩散集及另外几种标准IFS集合的盒维数。     

空温式翅片管气化器结霜模型及数值模拟

以分形理论的DLA模型为基础,建立了空温式翅片管气化器深冷表面上霜晶生长的二维模型,模拟了深冷表面上的霜晶生长过程.采用计盒维数法对模拟出的霜晶生长图像进行了分形维数的计算,结果表明深冷表面上霜晶的分形维数较一般冷表面上的分形维数大,从而说明深冷表面上的霜晶具有更加复杂的结构,充满空间的能力更大.这对进一步理解空温式深...     

分形维数海豚哨声信号检测方法

针对海豚哨声信号自动检测的问题,提出一种基于分形维数的自适应阈值海豚哨声信号检测方法。对待检测声信号计算盒分形维数,根据得到的盒分形维数特征值,通过模糊C均值聚类自适应确定检测阈值,实现海豚哨声信号的自动检测。文中对水池录制的海豚声信号进行了数据分析,利用哨声信号盒分形维数对哨声信号段与非信号段进行检测,并与基于谱熵的方法进行对比,获得了较高的检测率以及较低的虚警率,可以适用于海豚哨声信号的自动检测与分割。     

核爆与雷电电磁脉冲识别

用经验模态分解和分形分析相结合的方法对核爆和雷电电磁脉冲信号进行了识别研究。计算了核爆和雷电电磁脉冲原始信号的盒维数,以及原始信号经验模态分解后前4阶固有模态分量（IMF）的盒维数。用最近邻法对核爆和雷电进行了识别,实验结果表明:原始信号经验模态分解后一阶、二阶IMF盒维数的识别率要略高于三阶、四阶IMF盒维数的识别率;原始信号盒维数的识别率高于经验模态分解后各阶IMF盒维数的识别率;二维和三维特征的识别率要高于一维特征的识别率,另外二维和三维特征的识别率更加趋于稳定,并且三维特征的识别率都在90%以上。     

变化电压下扩散限制电解沉淀过程对铜的分形维数的影响

研究了铜的二维电解沉淀物在限制条件下的分形维数.拍摄了铜沉淀物随时间变化的照片,使用盒维法分析了各种条件下的豪斯多夫分形维数,并建立了计算机评估模型,以证明电压对豪斯多夫维数的重要影响.根据照片显示沉淀物的欧几里德几何形状也有着规则的变化.     

规则表面形貌的分形和多重分形描述

以6种具有典型特征的生成元构造了6个具有相同rms粗糙度的规则表面,用变分法计算了这些表面的分形维数,结果表明,分形维数可以将具有相同rms粗糙度的表面区分开来,它定量表征了表面的总体形貌。进一步将多重分形的方法应用到对这些表面的分析中,发现多重分形谱可以全面反映表面概率的分布特征。多重分形谱的宽度可以定量表征表面的起伏程度,多重分形谱最大、最小概率子集维数的差别可以统计表面最大、最小概率处的数目比例。 关键词： 粗糙度 分形维数 多重分形谱     

IFS吸引子的计算机模拟

阐述了迭代函数系(Iterated Function System,用IFS表示)理论及确定性算法。利用计算机对某一IFS的分形吸引子进行模拟,讨论了当参数变化时吸引子的变化规律;根据IFS的分维数定理,求出某些吸引子的分维数。     

基于FRFT域分形特征的压制干扰存在性检测（英）

基于分数阶傅里叶变换（FRFT）域的分形特征研究压制干扰的存在性检测问题。首先,分析了典型的三种压制干扰的分形特征,说明了典型压制干扰信号具有分形特性,并采用盒维数和信息维数定量描述它们的分形特征。然后,发现了压制干扰和高斯白噪声在FRFT域具有不同的分形特征,进而提出了一种检测压制干扰存在性的方法。最后,仿真验证了该方法的有效性和优越性。     

高炉铁水含硅量的分形结构分析

以山东莱钢1号高炉和山西临钢6号高炉在线采集的铁水含硅量(［Si］)的时间序列为样本, 利用重标级差分析(R/S)和盒维数计算方法, 得出两座高炉［Si］时间序列的Hurst指数H分别约为0.257和0.224, 盒维数D_B分别约为1.712和1.724, 完成了对［Si］值波动复杂程度的定量估计, 证明两者的时间序列均为长程负相关的分形时间序列.随后根据分形迭代函数的理论与方法,确定相关参数,迭代生成模拟的［Si］时间序列, 拟合效果较好. 关键词： 铁水含硅量 重标级差分析 Hurst指数 分形拟合     

基于FRFT域分形特征的压制干扰存在性检测（英文）

基于分数阶傅里叶变换(FRFT)域的分形特征研究压制干扰的存在性检测问题。首先,分析了典型的三种压制干扰的分形特征,说明了典型压制干扰信号具有分形特性,并采用盒维数和信息维数定量描述它们的分形特征。然后,发现了压制干扰和高斯白噪声在FRFT域具有不同的分形特征,进而提出了一种检测压制干扰存在性的方法。最后,仿真验证了该方法的有效性和优越性。     

Iterated function system models in data analysis: detection and separation

We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete-time dynamical system in which each time step corresponds to the application of one of the finite collection of maps. The maps, which represent distinct dynamical regimes, may be selected deterministically or stochastically. Given a time series from an IFS, our algorithm detects the sequence of regime switches under the assumption that each map is continuous. This method is tested on a simple example and an experimental computer performance data set. This methodology has a wide range of potential uses: from change-point detection in time-series data to the field of digital communications.     

“Missing moment” and perturbative methods for polynomial iterated function systems

An iterated function system (IFS) over a compact metric space X is defined by a set of contractive maps w_i: X → X, i = 1,…,N, with associated nonzero probabilities p_i > 0, p_i = 1. The “parallel” action of the maps defines a unique compact invariant attractor set A X which supports an invariant measure μ and which is balanced with respect to the p_i. For linear , the invariance of μ yields a relation between the moments g_n = ∫ χⁿ dμ which permits their recursive computation from the initial value g₀ = 1. For nonlinear w_i, however, the moment relations are incomplete and do not permit a recursive computation. This paper describes two methods of obtaining accurate estimates of the moments when the IFS maps w_i are polynomials: (i) application of the necessary Hausdorff conditions on the g_i to obtain convergent upper and lower bounds and (ii) a perturbation expansion approach. The methods are applied to some model problems.     

Toward an architecture for quantum programming

It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of classical and quantum computation. This paper investigates a possible approach to the problem of programming such machines: a template high level quantum language is presented which complements a generic general purpose classical language with a set of quantum primitives. The underlying scheme involves a run-time environment which calculates the byte-code for the quantum operations and pipes it to a quantum device controller or to a simulator. This language can compactly express existing quantum algorithms and reduce them to sequences of elementary operations; it also easily lends itself to automatic, hardware independent, circuit simplification. A publicly available preliminary implementation of the proposed ideas has been realised using the language.Received: 25 June 2002, Published online: 30 July 2003PACS: 03.67.Lx Quantum computation     

Universal quantum computation with qudits

Quantum circuit model has been widely explored for various quantum applications such as Shors algorithm and Grovers searching algorithm. Most of previous algorithms are based on the qubit systems. Herein a proposal for a universal circuit is given based on the qudit system, which is larger and can store more information. In order to prove its universality for quantum applications, an explicit set of one-qudit and two-qudit gates is provided for the universal qudit computation. The one-qudit gates are general rotation for each two-dimensional subspace while the two-qudit gates are their controlled extensions. In comparison to previous quantum qudit logical gates, each primitive qudit gate is only dependent on two free parameters and may be easily implemented. In experimental implementation, multilevel ions with the linear ion trap model are used to build the qudit systems and use the coupling of neighbored levels for qudit gates. The controlled qudit gates may be realized with the interactions of internal and external coordinates of the ion.     

Anomaly Detection of Complex Networks Based on Intuitionistic Fuzzy Set Ensemble

Ensemble learning for anomaly detection of data structured into a complex network has been barely studied due to the inconsistent performance of complex network characteristics and the lack of inherent objective function. We propose the intuitionistic fuzzy set(IFS)-based anomaly detection, a new two-phase ensemble method for anomaly detection based on IFS, and apply it to the abnormal behavior detection problem in temporal complex networks.Firstly, it constructs the IFS of a single network characteristic, which quantifies the degree of membership,non-membership and hesitation of each network characteristic to the defined linguistic variables so that makes the unuseful or noise characteristics become part of the detection. To build an objective intuitionistic fuzzy relationship, we propose a Gaussian distribution-based membership function which gives a variable hesitation degree. Then, for the fuzzification of multiple network characteristics, the intuitionistic fuzzy weighted geometric operator is adopted to fuse multiple IFSs and to avoid the inconsistence of multiple characteristics. Finally, the score function and precision function are used to sort the fused IFS. Finally, we carry out extensive experiments on several complex network datasets for anomaly detection, and the results demonstrate the superiority of our method to state-of-the-art approaches, validating the effectiveness of our method.     

系列新IFS分形图象的获取与分析

首次发现了类似墨竹叶之ＩＦＳ分形图及其系列衍生图象的生成     

Analytical nuclear gradients of the explicitly correlated Møller–Plesset second-order energy

The analytical computation of nuclear gradients has been derived and implemented for the explicitly correlated second-order Møller–Plesset method (MP2-F12). The implementation has been accomplished in the TURBOMOLE program package for ansatz MP2-F12/2*A. A Slater-type geminal expanded in six Gaussian geminals (STG-6G), a complementary auxiliary basis set (CABS), and robust density fitting approximations are used. In addition, a second-order perturbation theory correction for single excitations into the complementary auxiliary basis set (CABS singles) is included to reduce the Hartree–Fock error. Smooth convergence towards the basis set limit is observed for a selection of molecules. For computations on dimers of weakly interacting molecules in small basis sets, explicitly correlated second-order Møller–Plesset theory outperforms conventional second-order Møller–Plesset theory because basis set superposition errors are largely avoided at the MP2-F12/2*A level.     

Determining the resonator wavelength of VCSELs by Cauchy's integral formula

An algorithm is proposed for the computation of resonator wavelength of vertical cavity surface emitting lasers by Cauchy's formula and the method of lines. To calculate the laser modes an implicit eigenvalue problem has been solved. A pole-free complex function has been developed which allows the determination of all roots within the observed complex area. To test the proposed method several wavelengths of a 1.55 μm laser have been computed and compared with direct and iterative algorithms.     

New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.