B样条快速求值算法及其在数控插补中的应用

通过对B样条的de Boor-Cox定义式分析,给出了一种基于向量扩展的B样条基函数快速求值算法。该算法能够将k次B样条非零值计算效率提高2k+1倍。该算法用于数控实时插补中的B样条曲线求值求导运算时,可获得比de Boor算法更高的计算效率。     

A fast Legendre transform algorithm and applications to the adhesion model

A new algorithm for the computation of discrete Legendre transforms is discussed. Classical solutions have a running time proportional toN ^2d , whereN is the size of the spatial grid andd is the space dimension. The new algorithm has a running timeO((N log₂ N) ^d ). A general application of this algorithm is to the weak solutions of hyperbolic systems of conservation laws as considered by Lax (1973,Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, S.I.A.M.). The potential of the method is illustrated on the adhesion model, a multi-dimensional version of the Burgers equation, used to study the formation of large-scale structures in cosmology.     

A new program to compute and evaluate continuously monitored stopping boundaries for clinical trials

We present code for the calculation and evaluation of continuously monitored stopping boundaries for use in one-arm and two-arm clinical trials. These designs were first developed for one-arm trials by Thall, Simon and Estey (TSE) (P.F. Thall, R. Simon, E.H. Estey, Bayesian sequential monitoring designs for single-arm clinical trials with multiple outcomes, Stat. Med. 14 (1995) 357-379). Our code corrects some problems in the original TSE algorithms and extends these algorithms for use in a two-arm trial setting. It is written in S-Plus to improve interactivity for the statistically adept user, and employs external routines, dynamically loaded into S-Plus, to improve calculation efficiency. Efficient versions of our code require both a C compiler and the S-Plus program. Our code has been tested in UNIX and Microsoft Windows environments, and compiled code is available from our website. A numerical integration routine for the convolution of beta distributions is included.     

Piecewise fractional Legendre functions for nonlinear fractional optimal control problems with ABC fractional derivative and non-smooth solutions

In this study, to solve fractional problems with non-smooth solutions (which include some terms in the form of piecewise or fractional powers), a new category of basis functions called the orthonormal piecewise fractional Legendre functions is introduced. The upper bound of the error of the series expansion of these functions is obtained. Two explicit formulas for computing the Riemann–Liouville and Atangana–Baleanu fractional integrals of these functions are derived. A direct method based on these functions and their fractional integral is proposed to solve a family of optimal control problems involving the ABC fractional differentiation whose solutions are non-smooth in the above expressed forms. By the proposed technique, solving the original fractional problem turns into solving an equivalent system of algebraic equations. The established method accuracy is studied by solving some examples.     

A new approach to the epsilon expansion of generalized hypergeometric functions

Assuming that the parameters of a generalized hypergeometric function depend linearly on a small variable ε$\epsilon$, the successive derivatives of the function with respect to that small variable are evaluated at ε=0$\epsilon =0$ to obtain the coefficients of the ε$\epsilon$-expansion of the function. The procedure, which is quite naive, benefits from simple explicit expressions of the derivatives, to any order, of the Pochhammer and reciprocal Pochhammer symbols with respect to their argument. The algorithm may be used algebraically, irrespective of the values of the parameters. It reproduces the exact results obtained by other authors in cases of especially simple parameters. Implemented numerically, the procedure improves considerably, for higher orders in ε$\epsilon$, the numerical expansions given by other methods.     

Granular type-2 membership functions: A new approach to formation of footprint of uncertainty in type-2 fuzzy sets

In this study, a new approach for the formation of type-2 membership functions is introduced. The footprint of uncertainty is formed by using rectangular type-2 fuzzy granules and the resulting membership function is named as granular type-2 membership function. This new approach provides more degrees of freedom and design flexibility in type-2 fuzzy logic systems. Uncertainties on the grades of membership functions can be represented independently for any region in the universe of discourse and free of any functional form. So, the designer could produce nonlinear, discontinuous or hybrid membership functions in granular formation and therefore could model any desired discontinuity and nonlinearity. The effectiveness of the proposed granular type-2 membership functions is firstly demonstrated by simulations done on noise corrupted Mackey–Glass time series prediction. Secondly, flexible design feature of granular type-2 membership functions is illustrated by modeling a nonlinear system having dead zone with uncertain system parameters. The simulation results show that type-2 fuzzy logic systems formed by granular type-2 membership functions have more modeling capabilities than the systems using conventional type-2 membership functions and they are more robust to system parameter changes and noisy inputs.     

A basis-set based Fortran program to solve the Gross-Pitaevskii equation for dilute Bose gases in harmonic and anharmonic traps

Inhomogeneous boson systems, such as the dilute gases of integral spin atoms in low-temperature magnetic traps, are believed to be well described by the Gross-Pitaevskii equation (GPE). GPE is a nonlinear Schrödinger equation which describes the order parameter of such systems at the mean field level. In the present work, we describe a Fortran 90 computer program developed by us, which solves the GPE using a basis set expansion technique. In this technique, the condensate wave function (order parameter) is expanded in terms of the solutions of the simple-harmonic oscillator (SHO) characterizing the atomic trap. Additionally, the same approach is also used to solve the problems in which the trap is weakly anharmonic, and the anharmonic potential can be expressed as a polynomial in the position operators x, y, and z. The resulting eigenvalue problem is solved iteratively using either the self-consistent-field (SCF) approach, or the imaginary time steepest-descent (SD) approach. Iterations can be initiated using either the simple-harmonic-oscillator ground state solution, or the Thomas-Fermi (TF) solution. It is found that for condensates containing up to a few hundred atoms, both approaches lead to rapid convergence. However, in the strong interaction limit of condensates containing thousands of atoms, it is the SD approach coupled with the TF starting orbitals, which leads to quick convergence. Our results for harmonic traps are also compared with those published by other authors using different numerical approaches, and excellent agreement is obtained. GPE is also solved for a few anharmonic potentials, and the influence of anharmonicity on the condensate is discussed. Additionally, the notion of Shannon entropy for the condensate wave function is defined and studied as a function of the number of particles in the trap. It is demonstrated numerically that the entropy increases with the particle number in a monotonic way.

Program summary

Title of program:bose.xCatalogue identifier:ADWZ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWZ_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandDistribution format:tar.gzComputers:PC's/Linux, Sun Ultra 10/Solaris, HP Alpha/Tru64, IBM/AIXProgramming language used:mostly Fortran 90Number of bytes in distributed program, including test data, etc.:27 313Number of lines in distributed program, including test data, etc.:28 015Card punching code:ASCIINature of physical problem:It is widely believed that the static properties of dilute Bose condensates, as obtained in atomic traps, can be described to a fairly good accuracy by the time-independent Gross-Pitaevskii equation. This program presents an efficient approach of solving this equation.Method of solution:The solutions of the Gross-Pitaevskii equation corresponding to the condensates in atomic traps are expanded as linear combinations of simple-harmonic oscillator eigenfunctions. Thus, the Gross-Pitaevskii equation which is a second-order nonlinear differential equation, is transformed into a matrix eigenvalue problem. Thereby, its solutions are obtained in a self-consistent manner, using methods of computational linear algebra.Unusual features of the program:None     

A structure theorem for the elementary functions and its application to the identity problem

This paper uses elementary algebraic methods to obtain new proofs for theorems on algebraic relationships between the logarithmic and exponential functions. The main result is a multivariate version of a special case of the structure theorem due to Risch that gives, in a very explicit fashion, the possible algebraic relationships between the exponential and logarithm functions. The structure theorem has important applications to symbolic mathematical computation in that it in essence provides a canonical form for the elementary transcendental functions, and hence solves the identity problem for this class of functions. Such applications are discussed in the last section.This research was supported in part by National Science Foundation Grants GJ-30125X and MCS76-23762.     

A new linear time algorithm to compute the genomic distance via the double cut and join distance

The genomic distance problem in the Hannenhalli–Pevzner (HP) theory is the following: Given two genomes whose chromosomes are linear, calculate the minimum number of translocations, fusions, fissions and inversions that transform one genome into the other. This paper presents a new distance formula based on a simple tree structure that captures all the delicate features of this problem in a unifying way, and a linear time algorithm for computing this distance.     

A modified hybrid neural network for pattern recognition and its application to SSW complex in EEG

In this study, a modified hybrid neural network with asymmetric basis functions is presented for feature extraction of spike and slow wave complexes in electroencephalography (EEG). Feature extraction process has a great importance in all pattern recognition and classification problems. A gradient descent algorithm, indeed a back propagation type, is adapted to the proposed artificial neural network. The performance of the proposed network is measured using a support vector machine classifier fed by features extracted using the proposed neural network. The results show that the proposed neural network model can effectively be used in pattern recognition tasks. In experiments, real EEG data are used.     

A new equation of state and Fortran 77 program to calculate vapor–liquid phase equilibria of CH4–H2O system at low temperatures

A new equation of state (EOS) and the corresponding computer program package VLEWM are developed to calculate vapor–liquid phase equilibria and volumetric properties of CH₄–H₂O system at low temperatures. The EOS can predict vapor–liquid equilibria and volumetric properties of CH₄–H₂O system accurately at temperatures 273–383 K, and at pressures 0–1000 bar. The program package VLEWM is written in FORTRAN 77. It provides two main functions: (1) to calculate the composition in vapor phase and liquid phase of CH₄–H₂O system at equilibrium and (2) to judge the phase and to calculate molar volume of CH₄–H₂O mixture.     

A new cluster validity measure and its application to image compression

Many validity measures have been proposed for evaluating clustering results. Most of these popular validity measures do not work well for clusters with different densities and/or sizes. They usually have a tendency of ignoring clusters with low densities. In this paper, we propose a new validity measure that can deal with this situation. In addition, we also propose a modified K-means algorithm that can assign more cluster centres to areas with low densities of data than the conventional K-means algorithm does. First, several artificial data sets are used to test the performance of the proposed measure. Then the proposed measure and the modified K-means algorithm are applied to reduce the edge degradation in vector quantisation of image compression.     

A relation between certain transfer functions and their application to the identifiability of linear models

In this paper it is shown that when a linear system has several inputs and outputs, certain transfer functions may be interdependent. An easily applied sufficient condition is stated : hi particular, it shows which transfer functions are thus interdependent. A consequence important in the study of the identifiability of linear models is derived.     

A new parallel-by-cell approach to undistorted data compression based on cellular automaton and genetic algorithm

In this paper,a new parallel-by-cell approach to the undistorted data compression based on cellular automaton and genetic algorithm is presented.The local compression rules in a cellular automaton are obtained by using a gnetic evolutionary algorithm.The correctness of the hyper-parallel compression,the time complexity,and the relevant symbolic dynamic behaviour are discussed.In comparison with other traditional sequential or small-scale parallel methods for undistorted data compression,the proposed approcah shows much higher real-time performance,better suitability and feasibility for the systolic hardware implementation.     

A collocation and Cartesian grid methods using new radial basis function to solve class of partial differential equations

In the present paper, a class of partial differential equation represented by Poisson's type problems are solved using a proposed Cartesian grid method and a collocation technique using a new radial basis function. The advantage of using this new radial basis function represented by overcoming singularity from the diagonal elements when thin plate radial basis function is used. The new function is a combination of both multiquadric and thin plate radial basis functions. The new radial basis function contains a control parameter ?, that takes one when evaluating the singular elements and equals zero elsewhere. Collocation of the approximate solution of the potential over the governing and boundary condition equations leads to a double linear system of equations. A proposed algebraic procedure is then developed to solve the double system. Examples of Poisson and Helmholtz equations are solved and the present results are compared with the their analytical solutions. A good agreement with analytical results is achieved.     

A new feature extractor invariant to intensity, rotation, and scaling of color images

This paper proposes a new method for extracting the invariant features of an image based on the concept of principal component analysis and a competitive learning algorithm. The proposed algorithm can be applied to binary, gray-level, or colored-texture images with a size greater than 256 × 256 pixels. In addition to translation, scaling, and rotation invariant extraction, the extraction of a feature invariant to color intensity can be implemented by using this method. In our experiment, the proposed method shows the capability to differentiate images having the same shape but different colored textures. The experimental results report the effectiveness of this technique and its performance as measured by recognition accuracy rate and computational time. These results are also compared with those obtained by classical techniques.     

A new approach to the decomposition of Boolean functions by the method of <Emphasis Type="Italic">q</Emphasis>-partitions. III. Joint decomposition of a function system

The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean functions of variables specified in different representation forms. The approach is based on the method of q-partitions of conjuncterms and concept of decomposition clones. Theorems on joint decomposition of a system of full and partial functions are formulated. The approach is illustrated by examples. Parts I and II of this article are published in No. 5 (2001) and No. 1 (2002). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 39–58, March–April 2007.     

A new approach to solve the k-server problem based on network flows and flow cost reduction

This paper is concerned with two algorithms for solving the k-server problem: the optimal off-line algorithm (OPT) and the on-line work function algorithm (WFA). Both algorithms are usually implemented by network flow techniques including the flow augmentation method. In the paper a new implementation approach is proposed, which is again based on network flows, but uses simpler networks and the cost reduction method. The paper describes in detail the corresponding new implementations of OPT and WFA, respectively. All necessary correctness proofs are given. Also, experiments are presented, which confirm that the new approach assures faster execution of both algorithms.