Modified multiscale permutation entropy algorithm and its application for multiscroll chaotic systems

To analyze the complexity of continuous chaotic systems better, the modified multiscale permutation entropy (MMPE) algorithm is proposed. Characteristics and parameter choices of the MMPE algorithm are investigated. The comparative study between MPE and MMPE shows that MMPE has better robustness for identifying different chaotic systems when the scale factor τ takes large values. Compared with MPE, MMPE algorithm is more suitable for analyzing the complexity of time series as it has τ time series. For its application, MMPE algorithm is used to calculate the complexity of multiscroll chaotic systems. Results show that complexity of multiscroll chaotic systems does not increase as scroll number increases. Discussions based on first‐order difference operation present a reasonable explanation on why the complexity does not increase. This complexity analysis method lays a theoretical as well as experimental basis for the applications of multiscroll chaotic systems. © 2014 Wiley Periodicals, Inc. Complexity 21: 52–58, 2016     

Steganographic algorithm based on a chaotic map

In this paper, we suggest a new steganographic spatial domain algorithm based on a single chaotic map. Unlike most existing steganographic algorithms, the proposed algorithm uses one chaotic map to determine the pixel position of the host color image, the channel (red, green or blue) and the bit position of the targeted value in which a sensitive information bit can be hidden. Furthermore, this algorithm can be regarded as a variable-sized embedding algorithm. Experimental results demonstrate that this algorithm can defeat many existing steganalytic attacks. In comparison with existing steganographic spatial domain based algorithms, the suggested algorithm is shown to have some advantages over existing ones, namely, larger key space and a higher level of security against some existing attacks.     

A novel image encryption algorithm based on a 3D chaotic map

Recently [Solak E, Çokal C, Yildiz OT Biyikogˇlu T. Cryptanalysis of Fridrich’s chaotic image encryption. Int J Bifur Chaos 2010;20:1405-1413] cryptanalyzed the chaotic image encryption algorithm of [Fridrich J. Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifur Chaos 1998;8(6):1259-1284], which was considered a benchmark for measuring security of many image encryption algorithms. This attack can also be applied to other encryption algorithms that have a structure similar to Fridrich’s algorithm, such as that of [Chen G, Mao Y, Chui, C. A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Soliton Fract 2004;21:749-761]. In this paper, we suggest a novel image encryption algorithm based on a three dimensional (3D) chaotic map that can defeat the aforementioned attack among other existing attacks. The design of the proposed algorithm is simple and efficient, and based on three phases which provide the necessary properties for a secure image encryption algorithm including the confusion and diffusion properties. In phase I, the image pixels are shuffled according to a search rule based on the 3D chaotic map. In phases II and III, 3D chaotic maps are used to scramble shuffled pixels through mixing and masking rules, respectively. Simulation results show that the suggested algorithm satisfies the required performance tests such as high level security, large key space and acceptable encryption speed. These characteristics make it a suitable candidate for use in cryptographic applications.     

基于主成分分析法的综合评价方法的改进

针对用主成分分析法做综合评价存在的问题,提出了改进的方法即当第一主成分的综合评价值和熵值法得到的综合评价值具有一致性时,将两种评价结果进行集成综合评价,若两种评价结果不具有一致性时则采用主成分聚类法进行综合评价.     

Risk evaluation of diabetes mellitus by relation of chaotic globals to HRV

This study's aim is to analyze heart rate dynamics in subjects with diabetes by measures of heart rate variability (HRV). The correlation of chaotic global parameters in the two cohorts is able to assess the probability of cardiac failure and other dynamical diseases. Adults (46) were divided into two equal groups. The autonomic evaluation consisted of measuring HRV for 30 min in supine position in absence of any physical, sensory, or pharmacological stimuli. Chaotic global parameters are able to statistically determine which series of electrocardiograph interpeak intervals in short time‐series are diabetic and which are not. The chaotic forward parameter that applies all three parameters is suggested to be the most appropriate and robust algorithm. This was decided after tests for normality; followed by one‐way analysis of variance (ANOVA1); (P < 0.09) and Kruskal–Wallis technique (P < 0.03). Principal component analysis implied two components represent 99.8% of total variance. Therefore, diabetes is a disease which reduces the chaotic response and, as such may be termed a dynamical condition such as are cardiac arrest, asthma, and epilepsy. © 2014 Wiley Periodicals, Inc. Complexity 20: 84–92, 2015     

全国国有及规模以上非国有工业企业经济发展情况综合分析

本文采用熵权法和主成份投影法对全国国有及规模以上非国有工业企业的经济发展情况进行了综合分析和评价并排序     

Examples of entropy generating sequence

We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such that the dimension of the sequence is the same as its topological entropy dimension. Hence the complexity can be measured via the dimension of an entropy generating sequence. Moreover, we construct a weakly mixing example with subexponential growth rate.     

基于PCA和改进的PSO-SVM的机器人移动方向分类

随着人们创新水平的不断提高,为了更加准确的实现机器人的导航任务,提出了一种基于改进的粒子群优化支持向量机中的参数的方法.首先利用主成分分析法对数据进行降维,然后利用改进的粒子群优化算法,对SVM中的惩罚参数c和核函数的参数g进行优化,最后代入到SVM中,以此来达到运用SVM对机器人的导航任务进行分类识别.相对于其他算法,容易发现改进的粒子群优化算法优化后的支持向量机可以达到很好的效果.这种识别分类可以帮助人们很好的对机器人进行导航,对今后机器人的研究具有很大的应用价值.     

股票综合评价的符号数据PCA方法

符号数据分析是一种新兴的数据挖掘技术,区间数是最常用的一种符号数据。研究应用区间型符号数据的PCA方法来评价股票的市场综合表现问题。首先介绍了符号数据分析的基本理论。接下来研究了区间数据样本的经验描述统计量的计算,并基于经验相关矩阵,给出了区间主成分分析的算法,该算法最终得到区间数表达形式的主成分取值。最后选取上海证券交易市场20支股票在某一周上的交易数据,进行了实证研究,基于区间主成分得分的矩形图表示,将20支股票按其市场综合表现分成了四类。     

On the complexity of the exchange algorithm for minimax optimization problems

We present an exchange algorithm for the solution of minimax optimization problems involving convex functions. For a certain class of functions, the complexity of this algorithm is shown to be either linear in the number of functions, or at least squared in that number.     

主成份投影法在证券市场上市公司统计分析中的应用

本文利用主成份投影法 ,对证券市场上 4 5家个股业绩的九个指标进行了综合评价 ,指标的权重的确定采用了熵权法 ,得到了这些公司 2 0 0 0年的财务状况的排列次序 .     

Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems

This work presents a direct approach to design stabilizing controller based on a special matrix structure to synchronize chaotic systems and extends the approach to synchronize fractional chaotic systems. With this method, chaos synchronization is implemented in Lorenz chaotic systems with known parameters and the same to Lorenz chaotic systems with unknown parameters. Especially, fractional Lorenz chaotic system with unknown parameters is synchronized by fractional Chen chaotic system too. Numerical simulations confirm the effectiveness of the method proposed.     

关于一些凸规划问题的复杂性研究结果

目前,已发表了大量研究各类不同凸规划的低复杂度的障碍函数方法的文章. 利用自和谐理论,对不同的几类凸规划问题构造相应的对数障碍函数,通过两个引理证明这些凸规划问题相应的对数障碍函数都满足自和谐,根据Nesterov 和Nemirovsky的工作证明了所给问题的内点算法具有多项式复杂性.     

Forecasting retained earnings of privately held companies with PCA and L1 regression

We use proprietary data collected by SVB Analytics, an affiliate of Silicon Valley Bank, to forecast the retained earnings of privately held companies. Combining methods of principal component analysis (PCA) and L¹/quantile regression, we build multivariate linear models that feature excellent in‐sample fit and strong out‐of‐sample predictive accuracy. The combined PCA and L¹ technique effectively deals with multicollinearity and non‐normality of the data, and also performs favorably when compared against a variety of other models. Additionally, we propose a variable ranking procedure that explains which variables from the current quarter are most predictive of the next quarter's retained earnings. We fit models to the top five variables identified by the ranking procedure and thereby, discover interpretable models with excellent out‐of‐sample performance. Copyright © 2013 John Wiley & Sons, Ltd.     

用统计分析方法探讨西部区县旅游业的发展

运用主成分分析方法,对影响西部区县旅游业发展的因素进行分析,探寻西部区县旅游业发展的规律,并建立旅游业收入的主成份回归模型。     

Approximating the complexity measure of Vavasis-Ye algorithm is NP-hard

Given an m×n integer matrix A of full row rank, we consider the problem of computing the maximum of ∥B ^-1 A∥₂ where B varies over all bases of A. This quantity appears in various places in the mathematical programming literature. More recently, logarithm of this number was the determining factor in the complexity bound of Vavasis and Ye’s primal-dual interior-point algorithm. We prove that the problem of approximating this maximum norm, even within an exponential (in the dimension of A) factor, is NP-hard. Our proof is based on a closely related result of L. Khachiyan [1]. Received November 13, 1998 / Revised version received January 20, 1999? Published online May 12, 1999     

Symbolic analysis of finite words: the complexity function

We present several properties of the complexity function of finite words, the function counting the number of different factors in a word, for each length. To establish a first set of properties, we use the de Bruijn graphs and the suffix tree representations of a word. This allows us to show some inequalities that control the variation as well as the maximal value of the complexity function. Motivated by the applications, we discuss the change of the complexity function when sliding or increasing the size of a window laid down on a sequence to be analysed.     

基于集成综合评价法和聚类分析法的综合评价方法

针对传统的主成分分析法在数据无量纲化中"中心标准化"的缺点,提出了改进的主成分分析方法,并建立了一种基于集成综合评价法和聚类分析法的新的综合评价方法,通过黑龙江省各城市综合竞争力的统计分析结果说明该方法能有效的得出合理结果.