A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions, where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998). This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Ganjali, 2009), which contains several lifetime models such as: exponential geometric (Adamidis and Loukas, 1998), exponential Poisson (Kus, 2007) and exponential logarithmic (Tahmasbi and Rezaei, 2008) distributions. The hazard function of our class can be increasing, decreasing and upside down bathtub shaped, among others, while the hazard function of an EPS distribution is only decreasing. We obtain several properties of the WPS distributions such as moments, order statistics, estimation by maximum likelihood and inference for a large sample. Furthermore, the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints. Special distributions are studied in some detail. Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions.     

时序数据的动态有界符号化方法

提出了一种时序符号化方法.根据数据集极值来确定最佳字符集及时序数据的划分基准,通过估算最大压缩比来指导降维,从而实现了与SAX同样的符号化时序转换和相同的距离计算方式.与SAX不同的是,该时序符号化方法可以有效防止极值信息的丢失,因而在一些与极值相关的时序分析中有出色的表现.     

A simple and fast algorithm for computing exponentials of power series

As was initially shown by Brent, exponentials of truncated power series can be computed using a constant number of polynomial multiplications. This note gives a relatively simple algorithm with a low constant factor.     

A Maple package for improved global mapping forecast

We present a Maple implementation of the well known global approach to time series analysis and some further developments designed to improve the computational efficiency of the forecasting capabilities of the approach. This global approach can be summarized as being a reconstruction of the phase space, based on a time ordered series of data obtained from the system. After that, using the reconstructed vectors, a portion of this space is used to produce a mapping, a polynomial fitting, through a minimization procedure, that represents the system and can be employed to forecast further entries for the series. In the present implementation, we introduce a set of commands, tools, in order to perform all these tasks. For example, the command VecTS deals mainly with the reconstruction of the vector in the phase space. The command GfiTS deals with producing the minimization and the fitting. ForecasTS uses all these and produces the prediction of the next entries. For the non-standard algorithms, we here present two commands: IforecasTS and NiforecasTS that, respectively deal with the one-step and the N$N$-step forecasting. Finally, we introduce two further tools to aid the forecasting. The commands GfiTS and AnalysTS, basically, perform an analysis of the behavior of each portion of a series regarding the settings used on the commands just mentioned above.     

Experiencing SAX: a novel symbolic representation of time series

Many high level representations of time series have been proposed for data mining, including Fourier transforms, wavelets, eigenwaves, piecewise polynomial models, etc. Many researchers have also considered symbolic representations of time series, noting that such representations would potentiality allow researchers to avail of the wealth of data structures and algorithms from the text processing and bioinformatics communities. While many symbolic representations of time series have been introduced over the past decades, they all suffer from two fatal flaws. First, the dimensionality of the symbolic representation is the same as the original data, and virtually all data mining algorithms scale poorly with dimensionality. Second, although distance measures can be defined on the symbolic approaches, these distance measures have little correlation with distance measures defined on the original time series. In this work we formulate a new symbolic representation of time series. Our representation is unique in that it allows dimensionality/numerosity reduction, and it also allows distance measures to be defined on the symbolic approach that lower bound corresponding distance measures defined on the original series. As we shall demonstrate, this latter feature is particularly exciting because it allows one to run certain data mining algorithms on the efficiently manipulated symbolic representation, while producing identical results to the algorithms that operate on the original data. In particular, we will demonstrate the utility of our representation on various data mining tasks of clustering, classification, query by content, anomaly detection, motif discovery, and visualization.     

Pattern identification in dynamical systems via symbolic time series analysis

This paper presents symbolic time series analysis (STSA) of multi-dimensional measurement data for pattern identification in dynamical systems. The proposed methodology is built upon concepts derived from Information Theory and Automata Theory. The objective is not merely to classify the time series patterns but also to identify the variations therein. To achieve this goal, a symbol alphabet is constructed from raw data through partitioning of the data space. The maximum entropy method of partitioning is extended to multi-dimensional space. The resulting symbol sequences, generated from time series data, are used to model the dynamical information as finite state automata and the patterns are represented by the stationary state probability distributions. A novel procedure for determining the structure of the finite state automata, based on entropy rate, is introduced. The diversity among the observed patterns is quantified by a suitable measure. The efficacy of the STSA technique for pattern identification is demonstrated via laboratory experimentation on nonlinear systems.     

The equality problem for Parikh simple algebraic power series

A power series r with noncommuting variables is called Parikh simple if no two words in the support of r are commutatively equivalent. We show that equality is decidable for Parikh simple algebraic power series having their coefficients in a computable field.     

符号计算对计算有理矩阵指数的一种应用

在这篇文章中,我们探讨了符号计算对计算有理矩阵指数的一种应用,并在最后的数值例中得到了可行的结果．     

Chebyshev series approximation for solving differential–algebraic equations (DAEs)

The numerical solution of differential–algebraic equations (DAEs) using the Chebyshev series approximation is considered in this article. Two different problems are solved using the Chebyshev series approximation and the solutions are compared with the exact solutions. First, we calculate the power series of a given equation system and then transform it into Chebyshev series form, which gives an arbitrary order for solving the DAE numerically.     

On transformations of formal power series

Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve recognizability, generalizing the recent results of Zhang [16] to the formal power series setting. We show, for example, that the “square-root” operation, while preserving regularity for formal languages, preserves recognizability for formal power series when the underlying semiring is commutative or locally finite, but not in general.     

Skew and infinitary formal power series

We investigate finite-state systems with weights. Departing from the classical theory, in this paper the weight of an action does not only depend on the state of the system, but also on the time when it is executed; this reflects the usual human evaluation practices in which later events are considered less urgent and carry less weight than close events. We first characterize the terminating behaviors of such systems in terms of rational formal power series. This generalizes a classical result of Schützenberger.     

基于频繁模式发现的时间序列异常检测方法

针对传统异常片段检测方法在处理增量式时间序列时效率低的问题,提出一种基于频繁模式发现的时间序列异常检测（TSAD）方法。首先,将历史输入的时间序列数据进行符号转化;其次,利用符号化特征找出历史序列数据集中的频繁模式;最后,结合最长公共子序列匹配方法度量频繁模式与当前新增加时间序列数据之间的相似度,从而发现新增加数据中的异常模式。与基于滑动窗口预测的水文时间序列异常检测方法（TSOD）和基于扩展符号聚集近似的水文时间序列异常挖掘方法（ESAA）相比,对于实验选择的三种类型的时间序列数据,TSAD的检测率都超过90%;TSOD对规则性较强的序列检测率较高,能达到99%,但对噪声干扰较大的序列检测率较低,对数据偏向性较强;ESAA对三种类型的数据检测率均不超过70%。实验结果表明,TSAD在时间序列异常检测中能够较好地发现异常片段。     

基于符号化聚合近似的时间序列相似性复合度量方法

基于关键点的符号化聚合近似(SAX)改进算法(KP_SAX)在SAX的基础上利用关键点对时间序列进行点距离度量,能更有效地计算时间序列的相似性,但对时间序列的模式信息体现不足,仍不能合理地度量时间序列的相似性。针对SAX与KP_SAX存在的缺陷,提出了一种基于SAX的时间序列相似性复合度量方法。综合了点距离和模式距离两种度量,先利用关键点将分段累积近似(PAA)法平均分段进一步细分成各个子分段;再用一个包含此两种距离信息的三元组表示每个子分段;最后利用定义的复合距离度量公式计算时间序列间的相似性,计算结果能更有效地反映时间序列间的差异。实验结果显示,改进方法的时间效率比KP_SAX算法仅降低了0.96%,而在时间序列区分度性能上优于KP_SAX算法和SAX算法。     

Applications of power series in computational geometry

A number of algorithms are presented for obtaining power series expansions of curves and surfaces at a point. Some results on the radius of convergence are given. Two applications of series are given:

1. • for curve tracing algorithms, where a truncated series is used to approximate the curve of intersection of two surfaces

2. • to define nth degree geometric continuity, for arbitrary

Floating-point number LISP

A floating-point-number-oriented LISP has been developed. Though it performs type checking on every numeric operation, it runs as fast as Fortran for simple differential-equation problems. This paper describes the implementation, provides some measurements of its efficiency, and discusses the feasibility of this type of implementation.     

FPGA-based system for frequency detection of the main periodic component in time series information

This paper presents a novel algorithm, called the DFSWT, and its FPGA-based hardware processing unit for frequency estimation of a time series main periodic component. Since the DFSWT uses just additions and subtractions, it is simpler to compute than the FFT, and since its spectrum is a frequency function, it is more intuitive than the Walsh transform. The results show that the proposed algorithm is very efficient in detecting the frequency of the main periodic component, even in low SNR. The proposed hardware processing unit is 3 orders of magnitude faster than its respective software implementation and presents advantages regarding to power consumption, footprint, and computation speed against highly optimized commercially available FFT cores.     

On a new procedure for finding nonclassical symmetries

A new technique for deriving the determining equations of nonclassical symmetries associated with a partial differential equation system is introduced. The problem is reduced to computing the determining equations of the classical symmetries associated with a related equation with coefficients which depend on the nonclassical symmetry operator. As a consequence, all the symbolic manipulation programs designed for the latter task can also be used to find the determining equations of the nonclassical symmetries, without any adaptation of the program. The algorithm was implemented as the MAPLE routine GENDEFNC and uses the MAPLE package DESOLV (authors Carminati and Vu). As an example, we consider the Huxley partial differential equation.     

任意直角梯形截面梁扭转刚度的无穷级数解法

分析研究截面为底角10°～80°直角梯形的弹性梁扭转刚度的解法,并用有限元模拟进行了检验。为解决这一弹性梁自由扭转问题(圣维南问题)的特殊情形,在本文中首次采用了基于布赛乃斯克流体力学假设的无穷级数解法。分析解法与软件模拟的结果对比显示,在所研究的范围内其误差精度不超过3%。对于底角为54.74°的特殊直角梯形截面梁,该解法的精度误差小于1.5%。     

Robustness and efficiency of geometric programs: The Predicate Construction Kit (PCK)

In this article, I focus on the robustness of geometric programs (e.g., Delaunay triangulation, intersection between surfacic or volumetric meshes, Voronoi-based meshing …) w.r.t. numerical degeneracies. Some of these geometric programs require “exotic” predicates, not available in standard libraries (e.g., J.-R. Shewchuk’s implementation and CGAL). I propose a complete methodology and a sample Open Source implementation of a toolset (PCK: Predicate Construction Kit) that makes it reasonably easy to design geometric programs free of numerical errors. The C++ code of the predicates is automatically generated from its formula, written in a simple specification language. Robustness is obtained through a combination of arithmetic filters, expansion arithmetics and symbolic perturbation.As an example of my approach, I give the formulas and PCK source-code for the 4 predicates used to compute the intersection between a 3d Voronoi diagram and a tetrahedral mesh, as well as symbolic perturbations that provably escapes the corner cases. This allows to robustly compute the intersection between a Voronoi diagram and a triangle mesh, or the intersection between a Voronoi diagram and a tetrahedral mesh. Such an algorithm may have several applications, including surface and volume meshing based on Lloyd relaxation.     

Irreducible constituents of monomial representations

We describe an algorithm for obtaining the central primitive idempotents of the algebra associated with a monomial representation. As a consequence, we obtain its irreducible constituents. This is implemented in Magma, using an algorithm based on Dixon’s modular approach. In the case of permutation representations, we get a simplified version of the algorithms of Michler and Weller.