Explanation and reliability of prediction models: the case of breast cancer recurrence

In this paper, we describe the first practical application of two methods, which bridge the gap between the non-expert user and machine learning models. The first is a method for explaining classifiers’ predictions, which provides the user with additional information about the decision-making process of a classifier. The second is a reliability estimation methodology for regression predictions, which helps the users to decide to what extent to trust a particular prediction. Both methods are successfully applied to a novel breast cancer recurrence prediction data set and the results are evaluated by expert oncologists.     

<Emphasis Type="Italic">hp</Emphasis>-Version <Emphasis Type="Italic">a priori</Emphasis> Error Analysis of Interior Penalty Discontinuous Galerkin Finite Element Approximations to the Biharmonic Equation

We consider the symmetric formulation of the interior penalty discontinuous Galerkin finite element method for the numerical solution of the biharmonic equation with Dirichlet boundary conditions in a bounded polyhedral domain in . For a shape-regular family of meshes consisting of parallelepipeds, we derive hp-version a priori bounds on the global error measured in the L² norm and in broken Sobolev norms. Using these, we obtain hp-version bounds on the error in linear functionals of the solution. The bounds are optimal with respect to the mesh size h and suboptimal with respect to the degree of the piecewise polynomial approximation p. The theoretical results are confirmed by numerical experiments, and some practical applications in Poisson–Kirchhoff thin plate theory are presented.     

Robust regression for high throughput drug screening

Effective analysis of high throughput screening (HTS) data requires automation of dose-response curve fitting for large numbers of datasets. Datasets with outliers are not handled well by standard non-linear least squares methods, and manual outlier removal after visual inspection is tedious and potentially biased. We propose robust non-linear regression via M-estimation as a statistical technique for automated implementation. The approach of finding M-estimates by Iteratively Reweighted Least Squares (IRLS) and the resulting optimization problem are described. Initial parameter estimates for iterative methods are important, so self-starting methods for our model are presented. We outline the software implementation, done in Matlab and deployed as an Excel application via the Matlab Excel Builder Toolkit. Results of M-estimation are compared with least squares estimates before and after manual editing.     

Robustness of representations in multilayer feedforward neural networks

Recent research has shown that multilayer feedforward networks with sigmoidal activation functions are universal approximators, and that this holds for more general activations as well. The mathematical underpinning for these results has been various: Kolmogorov's resolution of Hilbert's thirteenth problem; the Stone-Weierstrass theorem; approximation of Fourier and Radon integral representations; and convergence of probability measures. This paper

Thermal explosion in a hot gas mixture with organic gel fuel droplets

Recent experimental evidence has uncovered the peculiar behavior of certain gel droplets which, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion. In this work a preliminary foray is made into the theoretical analysis of the nature of the evolution of a hot gas mixture containing organic gel fuel droplets with oscillatory evaporation within the context of thermal-explosion theory. The problem is modeled as a system of highly nonlinear singularly perturbed ordinary differential equations. Non-dimensionalization of the equations enables identification of the parameters that play a major role in determining the dynamical regimes of the system of equations. The method of integral manifolds is exploited for the analysis and it is found, that for certain parametric regions, the system exhibits new dynamical behavior that is quite different from that found for conventional liquid droplets.     

磁控溅射法镀制氮化铝薄膜特性研究

氮化铝薄膜具有高折射率,良好的化学稳定性,耐磨摩、高电阻等特性在微电子器件和光学薄膜中有着广泛地应用.本文研究了反应式磁控溅射方法利用Ar/N2混合气体镀制氮化铝薄膜的工艺过程,实验表明在高真空和高泵浦速率条件下,放电电压直接依赖于反应气体珠浓度.薄膜的折射率,消光系数和薄膜硬度都依赖于氮气浓度的比例.通过工艺研究,找到了氮气在不同浓度下对氮化铝薄膜的折射率,消光系数以及薄膜硬度的影响,找出了镀制氮化镀制氮化铝薄膜的最佳工艺参数.在Ar/N2工作气体中氮气含量保持在40%条件下,用反应式磁控溅射方法,可以精确镀制出良好的氮化铝薄膜,其中折射率范围在2.25~2.4之间,消光系数为10-3,薄膜显微硬度大于20GPa.该薄膜可以广泛应用于微电子器件和光电器件上.     

Micromechanical Modeling of the Effective Viscoelastic Properties of Inhomogeneous Materials Using Fraction-exponential Operators

A new analytical approach for’ micromechanical modeling of the effective viscoelastic behavior of a’ composite material is presented. Fractionexponential operators are. used to describe the viscoelastic properties of the constituents. To construct the corresponding elastic solution, effective field method is used. Effective viscoelastic operators are obtained from the Volter ra’s elasticity-viscoelasticity correspondence principle. Incompatible deformation that often occurs during the manufacturiig process is taken intp account. All the formulas are obtained in explicit ready-to-use form.