逐步回归方法的拓广研究

本文在运用泛函分析的观点详细剖析逐步回归方法的基础上,提出了一种改进的计算过程,可使逐步回归方法得以广泛地用于静态、动态和分布参数等系统的模型辨识。     

Customizing methods for global optimization-a geometric viewpoint

A new class of global optimization algorithms, extending the multidimensional bisection method of Wood, is described geometrically. New results show how the geometry of the global minimum relates to performance. Remarkably, the epigraph of the objective function, turned upside down, plays a key role. Algorithms customized to take advantage of special information about the objective function belong to the class. A number of algorithms in the literature, including those of Piyavskii-Shubert, Mladineo, Wood and Breiman & Cutler, also belong, and simple modifications of them produce customized algorithms. Comparison of various algorithms in the class is provided.Paper presented at the II. IIASA-workshop on Global Optimization, December 9–12, 1990, Sopron (Hungary).     

General financial equilibrium with policy interventions: a variational inequality approach

In this paper a model of general financial equilibrium with policy interventions is introduced, which yields the optimal composition of assets and liabilities in each sector's portfolio, as well as the market prices for each instrument. The policy interventions considered are taxes and price ceilings. The variational inequality formulation of the equilibrium conditions is derived and then utilized to establish existence and uniqueness properties of the solution pattern. An algorithm is proposed for the computation of the problem. Finally, the algorithm is applied to some special utility functions as numerical examples.     

Statistical analysis of steady-state simulations: survey of recent progress

For non-terminating simulations with steady-state responses the following alternative analysis techniques are evaluated: (i) replicated runs (ii) approximately independent subruns or batches (iii) renewal or regenerative analysis. Two general techniques for reducing nonnormality and bias are presented: grouping (or batching) and jackknifing. Applications of the various techniques are discussed. Besides the estimation of the mean, the estimation of variances and quantiles is presented.     

Algebras of creation and destruction operators

A general analysis of bilinear algebras of creation and destruction operators is performed. Generalizing the earlier work on the single-parameterq-deformation of the Heisenberg algebra, we study two-parameter and four-parameter algebras. Two new forms of quantum statistics called orthofermi and orthobose statistics and aq-deformation interpolating between them have been found. In the Fock representation, quadratic relations among destruction operators, wherever they are allowed, are shown to follow from the bilinear algebra of creation and destruction operators. Postitivity of the Hilbert space for the four-parameter algebra has been studied in the two-particle sector, but for the two-parameter algebra, results are presented up to the four-particle sector.     

常相关样本统计量公布的应用

本文利用来自正态总体的常相关样本的一个统计量的分布，对广东省和辽宁省的一些企业１９８８年一１９８９年的利润额增值进行了分析．     

Statistical and linguistic features of noncoding DNA: A heterogeneous «Complex system»

Summary We present evidence supporting the idea that the DNA sequence in genes containingnoncoding regions is correlated, and that the correlation is remarkably long range-indeed, base pairsthousands of base pairs distant are correlated. We do not find such a long-range correlation in the coding regions of the gene; we utilize this fact to build aCoding Sequence Finder algorithm, which uses statistical ideas to locate the coding regions of an unknown DNA sequence. We resolve the problem of the ?non-stationarity? feature of the sequence of base pairs (that the relative concentration of purines and pyrimidines changes in different regions of the mosaic-like chain) by describing a new algorithm calledDetrended Fluctuation Analysis (DFA). We address the claim of Voss that there is no difference in the statistical properties of coding and noncoding regions of DNA by systematically applying the DFA algorithm, as well as standard FFT analysis, to every DNA sequence (33 301 coding and 29 453 non-coding) in the entire GenBank database. We describe a simple model to account for the presence of long-range power law correlations (and the systematic variation of the scaling exponent α with evolution) which is based upon a generalization of the classic Lévy walk. Finally, we describe briefly some recent work showing that thenoncoding sequences have certain statistical features in common with natural languages. Specifically, we adapt to DNA the Zipf approach to analyzing linguistic texts, and the Shannon approach to quantifying the ?redundancy? of a linguistic text in terms of a measurable entropy function. We suggest that noncoding regions in eukaryotes may display a smaller entropy and larger redundancy than coding regions for plants and invertebrates, further supporting the possibility that noncoding regions of DNA may carry biological information. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Multiple nonlinear regressions derived with choice of free parameters

The common procedure of nonlinear approximation using linear multiple regressions developed in logarithmic space suffers from a number of inherent defects. Nonlinear approximation with choice of free parameters allows us to derive multiple regressions of varied structure, consisting of several members and an intercept. The calculations required for the proposed approximation are simple and can be implemented using standard statistical subprograms. More than 50 equations of the proposed type have been fitted for various purposes. The coefficient of determination is generally higher than 0.90. The application of the proposed method is demonstrated with two numerical examples and a number of equations derived for practical application in hydrology, geomorphology and water pollution studies. The proposed method can be used in any area of study where nonlinear multiple approximations are applicable.     

Airport noise modelling and aircraft scheduling so as to minimize community annoyance

A mathematical model of the annoyance created at an airport by aircraft operations is developed. The model incorporates population distribution considerations around an airport and the annoyance caused by aircraft noise. The objective function of this model corresponds to seeking to minimize total population annoyance created by all aircraft operations in a 24-hour period. Several factors are included in this model as constraint relationships. Aircraft operations by type and time period are upper bounded. Demand for flight services is incorporated by including lower bounds on the number of operations by type of aircraft, runway used and time period. Also upper bounds on the number of operations for each runway are included. The mathematical model as formulated is recognized as corresponding to a nonlinear integer mathematical programming problem.The solution technique selected makes use of a successive linear approximation optimization algorithm. An especially attractive feature of this solution algorithm is that it is capable of obtaining solutions to large problems. For example, it would be feasible to attempt the solution of problems involving several thousand variables and over 500 linear constraints. This suggested solution algorithm was implemented on a computer and computational results obtained for example problems.     

DNA denaturation for a tangled chain

Summary We have considered a model of a lattice gas defined on a periodic tangled chain to study the DNA denaturation by a modified transfer matrix method. By using an iterative algorithm we have obtained numerically different kinds of melting curves for different configurations of the tangled chain and different types of interactions. In some special cases of configurations and interactions we have found the same melting curves, which we have obtained before studying some simple lattice gas models, using different techniques. This more generalized model and the new results could be useful for the experimental investigations.