Training Multilayer Perceptrons Via Minimization of Sum of Ridge Functions

Motivated by the problem of training multilayer perceptrons in neural networks, we consider the problem of minimizing E(x)= _i=1 ⁿ f _i ( _i x), where _i R ^s , 1in, and each f _i ( _i x) is a ridge function. We show that when n is small the problem of minimizing E can be treated as one of minimizing univariate functions, and we use the gradient algorithms for minimizing E when n is moderately large. For large n, we present the online gradient algorithms and especially show the monotonicity and weak convergence of the algorithms.     

Neural networks for of continuous optimal approximation functions in R^d

Using some regular matrices we present a method to express any multivariate algebraic polynomial of total order n in a normal form. Consequently, we prove constructively that, to approximate continuous target functions defined on some compact set of ? ^d , neural networks are at least as good as algebraic polynomials.     

The construction and approximation of some neural networks operators

In this paper,the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions.Using the modulus of continuity of function as a metric,...     

Some Geometrical Aspects of Efficient Points in Vector Optimization

We study efficient point sets in terms of extreme points, positive support points and strongly positive exposed points. In the case when the ordering cone has a bounded base, we prove that the efficient point set of a weakly compact convex set is contained in the closed convex hull of its strongly positive exposed points, thereby extending the Phelps theorem. We study also the density of positive proper efficient point sets. This research was supported by a Central Research Grant of Hong Kong Polytechnic University, Grant G-T 507. Research of the first author was also supported by the National Natural Science Foundation of P.R. China, Grant 10361008, and the Natural Science Foundation of Yunnan Province, China, Grant 2003A002M. Research of the second author was also supported by the Natural Science Foundation of Chongqing. Research of the third author was supported by a research grant from Australian Research Counsil.     

Investigation of Locally Loaded Multilayer Shells by a Mixed Finite-Element Method. 1. Geometrically Linear Statement

The Hu-Washizu functional is constructed for analyzing prestressed multilayer anisotropic Timoshenko-type shells. As unknown functions, six displacements and eleven strains of the faces of the shells are chosen. Based on mixed finite-element approximations, a numerical algorithm is developed for solving linear static problems of prestressed multilayer composite shells. The results of solving the well-known test problem on a cylindrical shell subjected to two opposite point forces and the problem on local loading of a toroidal multilayer rubber-cord shell are presented.     

Investigation of Locally Loaded Multilayer Shells by a Mixed Finite-Element Method. 2. Geometrically Nonlinear Statement

Based on mixed finite-element approximations, a numerical algorithm is developed for solving linear static problems of prestressed multilayer composite shells subjected to large displacements and arbitrarily large rotations. As the sought-for functions, six displacements and eleven strains of the shell faces are chosen, which allows us to use nonlinear deformation relationships exactly representing arbitrarily large displacements of the shell as a rigid body. The stiffness matrix of a shell element has a proper rank and is calculated based on exact analytical integration. The bilinear element developed does not allow false rigid displacements and is not subjected to the membrane, shear, or Poisson locking phenomenon. The results of solving the well-known test problem on a nonsymmetrically fixed circular arch subjected to a concentrated load and the problem on a locally loaded toroidal multilayer rubber-cord shell are presented.     

多层油资源运移聚集的数值模拟和实际应用

研究了三维问题的石油地质和渗流力学特征。提出了数学模型,构造了新的算子分裂隐式迭代格式,并成功地对胜利油田东营凹陷(厚层)和惠民凹陷(多层)带断层和通道的实际问题进行了大规的数值模拟计算。计算结果在油藏位置等方面和实际情况相吻合,完整地解决了这一石油地质和渗流力学的国际着名问题。     

Stress State of Multilayer Thin-Walled Elements with Interfacial Defects of Structure

Based on the discrete-structural theory of thin plates and shells, a calculation model for thin-walled elements consisting of a number of rigid anisotropic layers is put forward. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The solution to the problem is obtained in a geometrically nonlinear statement with account of the influence of transverse shear and compression strains. The stress-strain state of circular two-layer transversely isotropic plates, both without defects and with a local area of adhesion failure at their center, is investigated numerically and experimentally. It is found that the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of stresses and strains. With the use of three variants of calculation models, in the cases of perfect and weakened contact conditions between layers, the calculation results for circular plates are compared. It is revealed that the variant suggested in this paper adequately reflects the behavior of layered thin-walled structural elements under large deformations. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 761–772, November–December, 2005.     

供需模型在众包平台定价中的应用

以众包平台为对象,基于已有数据,考虑供求关系,通过因子分析法对原始数据加以处理,建立任务的定价模型.在实际应用中,可以对分布密集的任务进行打包,并给出针对这种情况的定价模型.结果表明:提出的模型不仅考虑了会员人数与任务数量的关系,还考虑了个人需求的差异,提高了任务的完成度,对众包平台定价的发展与完善有着重要的意义.     

Research in the Limiting Efficiency of Plastic Deformation of Multilayer Tension (Compression) Bars

A method is proposed for calculating the limiting loads of multilayer bars in plastic deformation. The regularities of changes in the efficiency factor (EF) of plastic deformation in relation to the elastic moduli of the materials of which the bars are composed, the stress which causes the material plasticity, and variations in the cross-sectional areas of layers are examined. Mathematical expressions are derived which allow one to easily calculate the EF for arbitrary values of variable parameters and to find the limiting values of EF when one of the parameters is changed. The equivalent tension diagram for a multilayer bar is obtained in relation to the strength and stiffness of materials and their number and cross-sectional areas.     

信息产品在非线性效用函数下的二度价格歧视研究

本中假定消费的效用函数为非线性的效用函数，垄断厂商提供同一种信息产品的两种质量版本，消费根据两类约束做出自己的消费选择。厂商通过消费的两个无差异点来对消费进行二度价格歧视，通过分析我们得出厂商的歧视条件。     

轻质热防护系统多层材料组合结构的热应力分析

提出了轻质热防护系统外面板使用多层结构的概念,设计了2种热防护材料组合构成的3种铺层方案．通过模拟飞行器再入大气层时受到的机械和热载荷条件,数值计算得到了层间剪切力、底部温度和y方向位移．计算结果发现,层间剪切力发生在边缘部位且呈反对称分布;选用高热导率和高热容材料能够减少材料内的温度梯度,进而有效地降低结构的热应力和热变形;在均匀温度场情况下,两种材料的热膨胀系数之差越小,则层间剪切力越小．该研究表明不同的材料组合和铺层次序的多层结构,可以满足不同设计要求,具有优化设计潜力．     

Algebraic foundations of split hypercomplex nonlinear adaptive filtering

A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of hypercomplex algebra and hypercomplex calculus, some of which have been neglected in existing learning approaches (e.g., for quaternions). Already in the case of quaternions, we can predict improvements in performance of hypercomplex processes. The convergence of the proposed algorithms is rigorously analyzed. Copyright © 2012 John Wiley & Sons, Ltd.     

Role and Results of statistical methods in protein fold class prediction

Statistical methods of discrimination and classification are used for the prediction of protein structure from amino acid sequence data. This provides information for the establishment of new paradigms of carcinogenesis modeling on the basis of gene expression. Feed forward neural networks and standard statistical classification procedures are used to classify proteins into fold classes. Logistic regression, additive models, and projection pursuit regression from the family of methods based on a posterior probabilities; linear, quadratic, and a flexible discriminant analysis from the class of methods based on class conditional probabilities, and the nearest-neighbors classification rule are applied to a data set of 268 sequences. From analyzing the prediction error obtained with a test sample (n = 125) and with a cross validation procedure, we conclude that the standard linear discriminant analysis and nearest-neighbor methods are at the same time statistically feasible and potent competitors to the more flexible tools of feed forward neural networks. Further research is needed to explore the gain obtainable from statistical methods by the application to larger sets of protein sequence data and to compare the results with those from biophysical approaches.     

Convergence of BP Algorithm for Training MLP with Linear Output

The capability of multilayer perceptrons(MLPs)for approximating continuous functions with arbitrary accuracy has been demonstrated in the past decades.Back propagation(BP)algorithm is the most popular learning algorithm for training of MLPs.In this paper,a simple iteration formula is used to select the leaming rate for each cycle of training procedure,and a convergence result is presented for the BP algo- rithm for training MLP with a hidden layer and a linear output unit.The monotonicity of the error function is also guaranteed during the training iteration.     

A Geometrical Proof of Shiota's Theorem on a Conjecture of S. P. Novikov

We give a new proof of Shiota's theorem on Novikov's consecture, which states that the K.P. equation characters Jacobians among all indecomposable principally polarized abelian varieties.     

正线性方程组正解的判别

本文给出了正线性方程组正解的概念，给出了正线性方程组正解的若干判别方法     

INTERPOLATION BY LOOP＇S SUBDIVISION FUNCTIONS

For the problem of constructing smooth functions over arbitrary surfaces from discretedata, we propose to use Loop‘s subdivision functions as the interpolants. Results on theexistence, uniqueness and error bound of the interpolants are established. An efficientprogressive computation algorithm for the interpolants is also presented.     

Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

Aspects of Number Theory in Terms of Potential Theory

We develop the Potential Theory on the set N^* of all natural numbers 2 associated with the kernel V (resp. V ^*) given by