有缺失数据的META-MARKOV模型的局部计算

根据meta Markov模型的特征,本文提出了有缺失数据的meta Markov模型的局部计算方法．由于最小可压缩集与局部计算关系密切,本文给出了一种搜索包含预先给定的子集的最小可压缩集的算法．     

A Decision Procedure for Nonperiodic Sequents of the First-Order Linear Temporal Logic

A deduction-based decision procedure is presented for the nonperiodic D-sequents of the first-order linear temporal logic. The D-sequents are obtained from D ₂-sequents [7], [8] by removing the periodicity condition. The deductive procedure proposed consists of decidable deductive procedures that replace infinitary and finitary induction rules for the temporal operator ``always'. The soundness and completeness of the deduction-based decision procedure proposed is proved.     

Iterative solution of the drift-diffusion equations

The drift-diffusion model can be described by a nonlinear Poisson equation for the electrostatic potential coupled with a system of convection-reaction-diffusion equations for the transport of charge. We use a Gummel-like process [10] to decouple this system. Each of the obtained equations is discretised with the finite element method. We use a local scaling method to avoid breakdown in the numerical algorithm introduced by the use of Slotboom variables. Solution of the discrete nonlinear Poisson equation is accomplished with quasi-Newton methods. The nonsymmetric discrete transport equations are solved using an incomplete LU factorization preconditioner in conjunction with some robust linear solvers, such as (CGS), (BI-CGSTAB) and (GMRES). We investigate the behaviour of these iterative methods to define the effective strategy for this class of problems. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Parallel Preconditioned Iterative Realization of the Panel Method in 3D

The parallel version of precondition iterative techniques is developed for matrices arising from the panel boundary element method for three-dimensional simple connected domains with Dirichlet boundary conditions. Results were obtained on an nCube-2 parallel computer showing that preconditioned iterative methods are very well suited also in three-dimensional cases for implementation on an MIMD computer and that they are much more efficient than usual direct solution techniques.     

The Mixturegram: A Visualization Tool for Assessing the Number of Components in Finite Mixture Models

Certain practical and theoretical challenges surround the estimation of finite mixture models. One such challenge is how to determine the number of components when this is not assumed a priori. Available methods in the literature are primarily numerical and lack any substantial visualization component. Traditional numerical methods include the calculation of information criteria and bootstrapping approaches; however, such methods have known technical issues regarding the necessary regularity conditions for testing the number of components. The ability to visualize an appropriate number of components for a finite mixture model could serve to supplement the results from traditional methods or provide visual evidence when results from such methods are inconclusive. Our research fills this gap through development of a visualization tool, which we call a mixturegram. This tool is easy to implement and provides a quick way for researchers to assess the number of components for their hypothesized mixture model. Mixtures of univariate or multivariate data can be assessed. We validate our visualization assessments by comparing with results from information criteria and an ad hoc selection criterion based on calculations used for the mixturegram. We also construct the mixturegram for two datasets.     

Sylvester矩阵方程极小范数最小二乘解的迭代解法

研究了Sylvester矩阵方程最小二乘解以及极小范数最小二乘解的迭代解法,首先利用递阶辨识原理,得到了求解矩阵方程AX+YB=C的极小范数最小二乘解的一种迭代算法,进而,将这种算法推广到一般线性矩阵方程A_iX_iB_i=C的情形,最后,数值例子验证了算法的有效性.     

A Note on Mascarenhas' Counterexample about Global Convergence of the Affine Scaling Algorithm

Mascarenhas gave an instance of linear programming problems to show that the long-step affine scaling algorithm can fail to converge to an optimal solution with the step-size λ=0.999 . In this note, we give a simple and clear geometrical explanation for this phenomenon in terms of the Newton barrier flow induced by projecting the homogeneous affine scaling vector field conically onto a hyperplane where the objective function is constant. Based on this interpretation, we show that the algorithm can fail for "any" λ greater than about 0.91 (a more precise value is 0.91071), which is considerably shorter than λ = 0.95 and 0.99 recommended for efficient implementations. Accepted 17 February 1998     

A Central Limit Theorem for a Localized Version of the SK Model

In this note, we consider a SK (Sherrington–Kirkpatrick)-type model on ℤ ^d for d≥1, weighted by a function allowing to any single spin to interact with a small proportion of the other ones. In the thermodynamical limit, we investigate the equivalence of this model with the usual SK spin system, through the study of the fluctuations of the free energy. This author’s research partially supported by CAPES.     

AHP中判断矩阵一致性改进的迭代算法

本文研究了扰动矩阵与判断矩阵的不一致性的关系 ,提出了一种新的改进判断矩阵一致性的迭代算法 .     

A characterization of Kruskal sharing rules for minimum cost spanning tree problems

In Tijs et al. (Eur J Oper Res 175:121–134, 2006) a new family of cost allocation rules is introduced in the context of cost spanning tree problems. In this paper we provide the first characterization of this family by means of population monotonicity and a property of additivity.     

A Geometric Approach to Maximum Likelihood Estimation of the Functional Principal Components From Sparse Longitudinal Data

In this article, we consider the problem of estimating the eigenvalues and eigenfunctions of the covariance kernel (i.e., the functional principal components) from sparse and irregularly observed longitudinal data. We exploit the smoothness of the eigenfunctions to reduce dimensionality by restricting them to a lower dimensional space of smooth functions. We then approach this problem through a restricted maximum likelihood method. The estimation scheme is based on a Newton–Raphson procedure on the Stiefel manifold using the fact that the basis coefficient matrix for representing the eigenfunctions has orthonormal columns. We also address the selection of the number of basis functions, as well as that of the dimension of the covariance kernel by a second-order approximation to the leave-one-curve-out cross-validation score that is computationally very efficient. The effectiveness of our procedure is demonstrated by simulation studies and an application to a CD4+ counts dataset. In the simulation studies, our method performs well on both estimation and model selection. It also outperforms two existing approaches: one based on a local polynomial smoothing, and another using an EM algorithm. Supplementary materials including technical details, the R package fpca, and data analyzed by this article are available online.     

A Multiresolution Gaussian Process Model for the Analysis of Large Spatial Datasets

We develop a multiresolution model to predict two-dimensional spatial fields based on irregularly spaced observations. The radial basis functions at each level of resolution are constructed using a Wendland compactly supported correlation function with the nodes arranged on a rectangular grid. The grid at each finer level increases by a factor of two and the basis functions are scaled to have a constant overlap. The coefficients associated with the basis functions at each level of resolution are distributed according to a Gaussian Markov random field (GMRF) and take advantage of the fact that the basis is organized as a lattice. Several numerical examples and analytical results establish that this scheme gives a good approximation to standard covariance functions such as the Matérn and also has flexibility to fit more complicated shapes. The other important feature of this model is that it can be applied to statistical inference for large spatial datasets because key matrices in the computations are sparse. The computational efficiency applies to both the evaluation of the likelihood and spatial predictions.     

Two algorithms for generating and ranking the family of solutions of a finite irreflexive relation

The family of solutions, also known as 1-bases or kernels, of a finite irreflexive relation has a variety of many interesting applications. Furthermore, the decision as towhether the associated digraph posesses a solution belongs to the class of computationally intractable problems known as NP-complete. In this paper we present (a) a tree search algorithm to generate the family of solutions of a digraph and (b) a dynamic programming algorithm to generate the family of solutions ranked in increasing order of their cardinality. Extensive computational experience with the tree search algorithm on more than 1000 randomly generated digraphs ranging from 50 to 150 vertices and from 15% to 60% densities has shown that the proposed algorithm is effective.     

A Gaussian upper bound for the fundamental solutions of a class of ultraparabolic equations

We prove Gaussian estimates from above of the fundamental solutions to a class of ultraparabolic equations. These estimates are independent of the modulus of continuity of the coefficients and generalize the classical upper bounds by Aronson for uniformly parabolic equations.     

A note on the functional law of iterated logarithm for maxima of Gaussian sequences

Let {X_n, n ≥ 1} be a real-valued stationary Gaussian sequence with mean zero and variance one. Let M_n = max{X_t, i ≤ n} and H_n(t) = (M_[nt] ? b_n)a_n^?1 be the maximum resp. the properly normalised maximum process, where $\text{c}{}_{\mathrm{n}}\text{= (2}\text{log}\text{n)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{a}{}_{\mathrm{n}}\text{=}\text{(}\text{log log}\text{n)}\text{c}{}_{\mathrm{n}}$ and $\text{b}{}_{\mathrm{n}}\text{= c}{}_{\mathrm{n}}\text{?}\text{1}\text{2}\text{(}\text{log}\text{(4π}\text{log}\text{n))}\text{c}{}_{\mathrm{n}}$. We characterize the almost sure limit functions of (H_n)_n≥3 in the set of non-negative, non-decreasing, right-continuous, real-valued functions on (0, ∞), if r(n) (log n)^3?Δ = O(1) for all Δ > 0 or if r(n) (log n)^2?Δ = O(1) for all Δ > 0 and r(n) convex and fulfills another regularity condition, where r(n) is the correlation function of the Gaussian sequence.     

A variable-metric variant of the Karmarkar algorithm for linear programming

The most time-consuming part of the Karmarkar algorithm for linear programming is the projection of a vector onto the nullspace of a matrix that changes at each iteration. We present a variant of the Karmarkar algorithm that uses standard variable-metric techniques in an innovative way to approximate this projection. In limited tests, this modification greatly reduces the number of matrix factorizations needed for the solution of linear programming problems. Research sponsored by DOE DE-AS05-82ER13016, ARO DAAG-29-83-K-0035, AFOSR 85-0243. Research sponsored by ARO DAAG-29-83-K-0035, AFOSR 85-0243, Shell Development Company.     

A Method for the Computer Calculation of Edgeworth Expansions for Smooth Function Models

Abstract

In this article I describe, in detail, a method for the computer calculation of Edgeworth expansions for a smooth function model accurate in the O(n ^–1) term. For such models, these expansions are an important tool for the analysis of normalizing transformations, the correction of an approximately normally distributed quantity for skewness, and the comparison of bootstrap inference procedures. The method is straightforward and is efficient in a sense described in the article. The implementation of the method in general is clear from its implementation in the Mathematica program (available through StatLib) for the particular case of the studentized mean.     

A capacity-rounding algorithm for the minimum-cost circulation problem: A dual framework of the Tardos algorithm

Recently, É. Tardos gave a strongly polynomial algorithm for the minimum-cost circulation problem and solved the open problem posed in 1972 by J. Edmonds and R.M. Karp. Her algorithm runs in O(m ² T(m, n) logm) time, wherem is the number of arcs,n is the number of vertices, andT(m, n) is the time required for solving a maximum flow problem in a network withm arcs andn vertices. In the present paper, taking an approach that is a dual of Tardos's, we also give a strongly polynomial algorithm for the minimum-cost circulation problem. Our algorithm runs in O(m ² S(m, n) logm) time and reduces the computational complexity, whereS(m, n) is the time required for solving a shortest path problem with a fixed origin in a network withm arcs,n vertices, and a nonnegative arc length function. The complexity is the same as that of Orlin's algorithm, recently developed by efficiently implementing the Edmonds-Karp scaling algorithm.     

A hybrid genetic model for the prediction of corporate failure

This study examines the potential of a neural network (NN) model, whose inputs and structure are automatically selected by means of a genetic algorithm (GA), for the prediction of corporate failure using information drawn from financial statements. The results of this model are compared with those of a linear discriminant analysis (LDA) model. Data from a matched sample of 178 publicly quoted, failed and non-failed, US firms, drawn from the period 1991 to 2000 is used to train and test the models. The best evolved neural network correctly classified 86.7 (76.6)% of the firms in the training set, one (three) year(s) prior to failure, and 80.7 (66.0)% in the out-of-sample validation set. The LDA model correctly categorised 81.7 (75.0)% and 76.0 (64.7)% respectively. The results provide support for a hypothesis that corporate failure can be anticipated, and that a hybrid GA/NN model can outperform an LDA model in this domain.MSC codes: 62M45, 68W10, 90B50, 91C20     

一类可逆矩阵逆矩阵的图论解法

设 M( G)是简单无向图 G的关联矩阵 ,A是 M( G)的可逆子矩阵 ,γ( A)是逆矩阵 A- 1中非零元素的个数 .获得了求逆矩阵 A- 1的一种图论方法 ,并且得到了γ( A)的精确上下界以及达到上下界时子矩阵 A的图论刻划