DEA models for ratio data:convexity consideration

Data envelopment analysis (DEA) is defined based on observed units and by finding the distance of each unit to the border of estimated production possibility set (PPS). The convexity is one of the underlying assumptions of the PPS. This paper shows some difficulties of using standard DEA models in the presence of input-ratios and/or output-ratios. The paper defines a new convexity assumption when data includes a ratio variable. Then it proposes a series of modified DEA models which are capable to rectify this problem.

General bounds on Bayes errors for regression with Gaussian processes

Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

A generalized Drucker–Prager viscoplastic yield surface model for asphalt concrete

A generalized Drucker–Prager (GD–P) viscoplastic yield surface model was developed and validated for asphalt concrete. The GD–P model was formulated based on fabric tensor modified stresses to consider the material inherent anisotropy. A smooth and convex octahedral yield surface function was developed in the GD–P model to characterize the full range of the internal friction angles from 0° to 90°. In contrast, the existing Extended Drucker–Prager (ED–P) was demonstrated to be applicable only for a material that has an internal friction angle less than 22°. Laboratory tests were performed to evaluate the anisotropic effect and to validate the GD–P model. Results indicated that (1) the yield stresses of an isotropic yield surface model are greater in compression and less in extension than that of an anisotropic model, which can result in an under-prediction of the viscoplastic deformation; and (2) the yield stresses predicted by the GD–P model matched well with the experimental results of the octahedral shear strength tests at different normal and confining stresses. By contrast, the ED–P model over-predicted the octahedral yield stresses, which can lead to an under-prediction of the permanent deformation. In summary, the rutting depth of an asphalt pavement would be underestimated without considering anisotropy and convexity of the yield surface for asphalt concrete. The proposed GD–P model was demonstrated to be capable of overcoming these limitations of the existing yield surface models for the asphalt concrete.