Equitable Efficiency in Multiple Criteria Optimization

Equitable efficiency in multiple criteria optimization was introduced mathematically in the middle of nineteen-nineties. The concept tends to strengthen the notion of Pareto efficiency by imposing additional conditions on the preference structure defining the Pareto preference. It is especially designed to solve multiple criteria problems having commensurate criteria where different criteria values can be compared directly. In this dissertation we study some theoretical and practical aspects of equitably efficient solutions. The literature on equitable efficiency is not very extensive and provides very limited number of ways of generating such solutions. After introducing some relevant notations, we develop some scalarization based methods of generating equitably efficient solutions. The scalarizations developed do not assume any special structure of the problem. We prove an existence result for linear multiple criteria problems. Next, we show how equitably efficient solutions arise in the context of a particular type of linear complementarity problem and matrix games. The set of equitably efficient solutions, in general, is a subset of efficient solutions. The multiple criteria alternative of the linear complementarity problem dealt in our dissertation has identical efficient and equitably efficient solution sets. Finally, we demonstrate the relevance of equitable efficiency by applying it to the problem of regression analysis and asset allocation

Ethanol Production in US

Vijay Singh - Associate Professor, Department of Agricultural & Biological Engineering, University of Illinois at Urbana-Champaign. The following topics were covered during this presentation: Ethanol Production Process (Video), Ethanol Industry including Ethanol Production Capacity and Growth in Industry, Issues Facing Ethanol Industry, Emerging Dry Grind Ethanol Processes, and Future of Ethanol Industry including Cellulosic Ethanol.Ope

Director Field Model of the Primary Visual Cortex for Contour Detection

We aim to build the simplest possible model capable of detecting long, noisy contours in a cluttered visual scene. For this, we model the neural dynamics in the primate primary visual cortex in terms of a continuous director field that describes the average rate and the average orientational preference of active neurons at a particular point in the cortex. We then use a linear-nonlinear dynamical model with long range connectivity patterns to enforce long-range statistical context present in the analyzed images. The resulting model has substantially fewer degrees of freedom than traditional models, and yet it can distinguish large contiguous objects from the background clutter by suppressing the clutter and by filling-in occluded elements of object contours. This results in high-precision, high-recall detection of large objects in cluttered scenes. Parenthetically, our model has a direct correspondence with the Landau - de Gennes theory of nematic liquid crystal in two dimensions.Comment: 9 pages, 7 figure