Chapter 11 Simulation studies of efficiency,returns to scale and misspecification with nonlinear functions in DEA

Using statistically designed experiments, 12,500 observations are generated from a 4-pieced Cobb-Douglas function exhibiting increasing and decreasing returns to scale in its different pieces. Performances of DEA and frontier regressions represented by COLS (Corrected Ordinary Least Squares) are compared at sample sizes ofn=50, 100, 150 and 200. Statistical consistency is exhibited, with performances improving as sample sizes increase. Both DEA and COLS generally give good results at all sample sizes. In evaluating efficiency, DEA generally shows superior performance, with BCC models being best (except at corner points), followed by the CCR model and then by COLS, with log-linear regressions performing better than their translog counterparts at almost all sample sizes. Because of the need to consider locally varying behavior, only the CCR and translog models are used for returns to scale, with CCR being the better performer. An additional set of 7,500 observations were generated under conditions that made it possible to compare efficiency evaluations in the presence of collinearity and with model misspecification in the form of added and omitted variables. Results were similar to the larger experiment: the BCC model is the best performer. However, COLS exhibited surprisingly good performances — which suggests that COLS may have previously unidentified robustness properties — while the CCR model is the poorest performer when one of the variables used to generate the observations is omitted.     

Energetics of protein-cyclodextrin interactions

The energetics of interaction of a range of cyclodextrins with folded and unfolded proteins has been examined by sensitive microcalorimetry techniques. Weak interaction with exposed amino acid residues promotes unfolding and dissociation of proteins. The possibility that such interactions may facilitate the use of cyclodextrins as chaperone-mimics in the refolding of denatured protein has been explored with the enzyme phosphoglycerate kinase. Up to 40% regain of activity can be achieved in some cases.     

Pseudo-holomorphic maps and bubble trees

This paper proves a strong convergence theorem for sequences of pseudo-holomorphic maps from a Riemann surface to a symplectic manifoldN with tamed almost complex structure. (These are the objects used by Gromov to define his symplectic invariants.) The paper begins by developing some analytic facts about such maps, including a simple new isoperimetric inequality and a new removable singularity theorem. The main technique is a general procedure for renormalizing sequences of maps to obtain “bubbles on bubbles.” This is a significant step beyond the standard renormalization procedure of Sacks and Uhlenbeck. The renormalized maps give rise to a sequence of maps from a “bubble tree”—a map from a wedge Σ V S² V S² V ... →N. The main result is that the images of these renormalized maps converge in L^1,2 ∪C° to the image of a limiting pseudo-holomorphic map from the bubble tree. This implies several important properties of the bubble tree. In particular, the images of consecutive bubbles in the bubble tree intersect, and if a sequence of maps represents a homology class then the limiting map represents this class.