Orthogonal Polynomial Contrasts and Applications to Age-Period-Cohort Models

Many regression modeling problems involve ordinal predictors with equally spaced values, such as age or income groups. Orthogonal polynomial contrasts provide a useful way to incorporate the information that the groups are ordered, unlike dummy or effects coding. This technique has been useful to separate the linear and non-linear effects in age-period-cohort (APC) models. This paper addresses three practical issues when implementing orthogonal polynomial contrasts: First, if the linear effect is to be interpreted, it should be identical to the linear effect that we obtain if we treat the predictor as a metric variable. Second, if the data is unbalanced, weighted orthogonal contrasts need to be used to obtain unbiased estimates. Third, by dropping-higher order terms, orthogonal polynomials can easily be used to smooth non-linear estimates. Two examples from the APC literature are discussed, and it is found that the use of unweighted polynomials has led to small biases in the results. A R function is provided that implements weighted polynomials with an interpretable linear term.

Shape Optimization of 3D Mechanical Systems Using Metamodels

In this work resource saving technique is used for shape optimization of 3D mechanical objects. According to statistical data, appearance of cracks in the areas of barrel support pads of tank wagons often causes damages to the barrels. The shape optimization of barrel support pads of a tank wagon is implemented and, as result, the concentration of stresses is significantly reduced in the barrel support areas. The optimization technique is based on CAD/CAE, design of experiment, approximation and optimization software packages. The shape of the support pads is defined by NURBS polygon points that serve as design parameters. For reduction of computational resources, FE models of tank wagon are replaced with high-quality metamodels which are based on locally weighted polynomials. The specific recommendations for the shape of the pads are given. As the second object truly spatial tetrapod is considered. The optimal curved shape of the tetrapod for lattice structure is elaborated.

Experiment on numerical conformal mapping of unbounded multiply connected domain in fundamental solutions method

We are concerned with the experiment on numerical conformal mappings. A potentially theoretical scheme in the fundamental solutions method, different from the conventional one, has been recently proposed for numerical conformal mappings of unbounded multiply connected domains. The scheme is based on the asymptotic theorem on extremal weighted polynomials. The scheme has the characteristic called “invariant and dual.” Applying the scheme for typical examples, we will show that the numerical results of high accuracy may be obtained.