Support-type properties of convex functions of higher order and Hadamard-type inequalities

It is well known that every convex function (where I⊂R is an interval) admits an affine support at every interior point of I (i.e. for any x₀∈IntI there exists an affine function such that a(x₀)=f(x₀) and a?f on I). Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree no greater than the order of convexity. In this paper the attaching method is developed. It is applied to obtain the general result—Theorem 2, from which the mentioned above support theorem and some related properties of convex functions of higher (both odd and even) order are derived. They are applied to obtain some known and new Hadamard-type inequalities between the quadrature operators and the integral approximated by them. It is also shown that the error bounds of quadrature rules follow by inequalities of this kind.     

Exploiting three kinds of interface propensities to identify protein binding sites

Predicting the binding sites between two interacting proteins provides important clues to the function of a protein. In this study, we present a building block of proteins called order profiles to use the evolutionary information of the protein sequence frequency profiles and apply this building block to produce a class of propensities called order profile interface propensities. For comparisons, we revisit the usage of residue interface propensities and binary profile interface propensities for protein binding site prediction. Each kind of propensities combined with sequence profiles and accessible surface areas are inputted into SVM. When tested on four types of complexes (hetero-permanent complexes, hetero-transient complexes, homo-permanent complexes and homo-transient complexes), experimental results show that the order profile interface propensities are better than residue interface propensities and binary profile interface propensities. Therefore, order profile is a suitable profile-level building block of the protein sequences and can be widely used in many tasks of computational biology, such as the sequence alignment, the prediction of domain boundary, the designation of knowledge-based potentials and the protein remote homology detection.     

Decomposition Algorithm Model for Singly Linearly-Constrained Problems Subject to Lower and Upper Bounds

Many real applications can be formulated as nonlinear minimization problems with a single linear equality constraint and box constraints. We are interested in solving problems where the number of variables is so huge that basic operations, such as the evaluation of the objective function or the updating of its gradient, are very time consuming. Thus, for the considered class of problems (including dense quadratic programs), traditional optimization methods cannot be applied directly. In this paper, we define a decomposition algorithm model which employs, at each iteration, a descent search direction selected among a suitable set of sparse feasible directions. The algorithm is characterized by an acceptance rule of the updated point which on the one hand permits to choose the variables to be modified with a certain degree of freedom and on the other hand does not require the exact solution of any subproblem. The global convergence of the algorithm model is proved by assuming that the objective function is continuously differentiable and that the points of the level set have at least one component strictly between the lower and upper bounds. Numerical results on large-scale quadratic problems arising in the training of support vector machines show the effectiveness of an implemented decomposition scheme derived from the general algorithm model.     

Using Copula distributions to support more accurate imaging-based diagnostic classifiers for neuropsychiatric disorders

Many investigators have tried to apply machine learning techniques to magnetic resonance images (MRIs) of the brain in order to diagnose neuropsychiatric disorders. Usually the number of brain imaging measures (such as measures of cortical thickness and measures of local surface morphology) derived from the MRIs (i.e., their dimensionality) has been large (e.g. > 10) relative to the number of participants who provide the MRI data (< 100). Sparse data in a high dimensional space increase the variability of the classification rules that machine learning algorithms generate, thereby limiting the validity, reproducibility, and generalizability of those classifiers. The accuracy and stability of the classifiers can improve significantly if the multivariate distributions of the imaging measures can be estimated accurately. To accurately estimate the multivariate distributions using sparse data, we propose to estimate first the univariate distributions of imaging data and then combine them using a Copula to generate more accurate estimates of their multivariate distributions. We then sample the estimated Copula distributions to generate dense sets of imaging measures and use those measures to train classifiers. We hypothesize that the dense sets of brain imaging measures will generate classifiers that are stable to variations in brain imaging measures, thereby improving the reproducibility, validity, and generalizability of diagnostic classification algorithms in imaging datasets from clinical populations. In our experiments, we used both computer-generated and real-world brain imaging datasets to assess the accuracy of multivariate Copula distributions in estimating the corresponding multivariate distributions of real-world imaging data. Our experiments showed that diagnostic classifiers generated using imaging measures sampled from the Copula were significantly more accurate and more reproducible than were the classifiers generated using either the real-world imaging measures or their multivariate Gaussian distributions. Thus, our findings demonstrate that estimated multivariate Copula distributions can generate dense sets of brain imaging measures that can in turn be used to train classifiers, and those classifiers are significantly more accurate and more reproducible than are those generated using real-world imaging measures alone.     

Analysis of a typical railway turnout sleeper system using grillage beam analogy

A simplified grillage beam analogy was performed to investigate the behaviour of railway turnout sleeper system with a low value of elastic modulus on different support moduli. This study aimed at determining an optimum modulus of elasticity for an emerging technology for railway turnout application - fibre composites sleeper. The finite element simulation suggests that the changes in modulus of elasticity of sleeper, E_sleeper and the sleeper support modulus, U_s have a significant influence on the behaviour of turnout sleepers. The increase in U_s from 10 to 40 MPa resulted in a 15% reduction in the bending moment while the increase in E_sleeper from 1 GPa to 10 GPa has resulted in almost 75% increase in the bending moment. The shear forces in turnout sleepers is not sensitive to both the changes of the E_sleeper and U_s while the sleeper with low E_sleeper tend to undergo greater settlement into the ballast. An E_sleeper of 4 GPa was found optimal for an alternative fibre composite turnout sleeper provided that the U_s is at least 20 MPa from the consideration of sleeper ballast pressure and maximum vertical deflection. It was established that the turnout sleeper has a maximum bending moment of 19 kN-m and a shear force of 158 kN under service conditions.     

模式识别和红外光谱法相结合鉴别中药材产地

用红外光谱法取得来自不同产地的中药材的中红外光谱,结合模式识别的方法实现中药产地的快速鉴别。采用了近邻法和多类支持向量机方法对采集自4个不同产地的269个白芷样本和6个不同产地的380个丹参样本进行了产地鉴别,得到的交叉验证准确率达99%,为中药材产地的自动鉴别探索了一条有效的途径。     

Higher order duality in multiobjective fractional programming with support functions

In this paper a new class of higher order (F,ρ,σ)-type I functions for a multiobjective programming problem is introduced, which subsumes several known studied classes. Higher order Mond-Weir and Schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are studied in both the cases assuming the involved functions to be higher order (F,ρ,σ)-type I. A number of previously studied problems appear as special cases.     

Kernel Logistic Regression and the Import Vector Machine

The support vector machine (SVM) is known for its good performance in two-class classification, but its extension to multiclass classification is still an ongoing research issue. In this article, we propose a new approach for classification, called the import vector machine (IVM), which is built on kernel logistic regression (KLR). We show that the IVM not only performs as well as the SVM in two-class classification, but also can naturally be generalized to the multiclass case. Furthermore, the IVM provides an estimate of the underlying probability. Similar to the support points of the SVM, the IVM model uses only a fraction of the training data to index kernel basis functions, typically a much smaller fraction than the SVM. This gives the IVM a potential computational advantage over the SVM.     

线性同胚于星象函数的一族解析函数

本文定义了线性同胚于星象函数的－族解析函数Ａ（，α）．我们导出Ａ（α）中函数的积分表达式：借助算子理论研究Ａ（，α）族的包含关系并确定它的闭凸包、闭凸包的极值点和它的支撑点；利用一个阶微分从属证明关于实部的二个不等式．最后，我们还证明Ａ（，α）中函数的偏差定理．     

Non-Parametric Regression Methods

The nature of the financial time series is complex, continuous interchange of stochastic and deterministic regimes. Therefore, it is difficult to forecast with parametric techniques. Instead of parametric models, we propose three techniques and compare with each other. Neural networks and support vector regression (SVR) are two universally approximators. They are data-driven non parametric models. ARCH/GARCH models are also investigated. Our assumption is that the future value of Istanbul Stock Exchange 100 index daily return depends on the financial indicators although there is no known parametric model to explain this relationship. This relationship comes from the technical analysis. Comparison shows that the multi layer perceptron networks overperform the SVR and time series model (GARCH).