Restrictions of Minimum Spanner Problems

At-spanner of a graphGis a spanning subgraphHsuch that the distance between any two vertices inHis at mostttimes their distance inG. Spanners arise in the context of approximating the original graph with a sparse subgraph (Peleg, D., and Schäffer, A. A. (1989),J. Graph. Theory13(1), 99–116). The MINIMUMt-SPANNER problem seeks to find at-spanner with the minimum number of edges for the given graph. In this paper, we completely settle the complexity status of this problem for various values oft, on chordal graphs, split graphs, bipartite graphs and convex bipartite graphs. Our results settle an open question raised by L. Cai (1994,Discrete Appl. Math.48, 187–194) and also greatly simplify some of the proofs presented by Cai and by L. Cai and M. Keil (1994,Networks24, 233–249). We also give a factor 2 approximation algorithm for the MINIMUM 2-SPANNER problem on interval graphs. Finally, we provide approximation algorithms for the bandwidth minimization problem on convex bipartite graphs and split graphs using the notion of tree spanners.     

The Importance of Distributed Loading and Cantilever Angle in Piezo-Force Microscopy

Piezo-force microscopy (PFM) is a variation of atomic force microscopy that is widely applied to investigate piezoelectric thin films at the nanometer scale. Curiously, PFM experiments are found to be remarkably sensitive to the position along the cantilever at which deflection is detected, complicating attempts to use this technique to quantify surface actuation and thereby measure the converse piezoelectric coefficient. A straightforward analytical theory is proposed that accounts for this observation by combining standard PFM analyses with subtleties of the typical AFM detection mechanism as well as the concept of distributed loading. Corresponding simulations of PFM measurements indicate that these experimental artifacts can even lead to an apparent inversion of the detected domain orientation. To better understand the importance of these effects, simulations are used to qualitatively map the theoretical PFM response for a wide range of typical experimental parameters, as well as the relative difference between these measurements and true piezoactuation.This work was made possible by NSF-International and NRC-postdoctoral fellowships.     

An Efficient Nelson-Oppen Decision Procedure for Difference Constraints over Rationals

Nelson and Oppen provided a methodology for modularly combining decision procedures for individual theories to construct a decision procedure for a combination of theories. In addition to providing a check for satisfiability, the individual decision procedures need to provide additional functionalities, including equality generation.In this paper, we propose a decision procedure for a conjunction of difference constraints over rationals (where the atomic formulas are of the form xy+c or x<y+c). The procedure extends any negative cycle detection algorithm (like the Bellman-Ford algorithm) to generate (1) equalities between all pair of variables, (2) produce proofs and (3) generates models that can be extended by other theories in a Nelson-Oppen framework. All the operations mentioned above can be performed with only a linear overhead to the cycle detection algorithm, in the average case.     

Fluid filled scleral contact lens in pediatric patients: challenges and outcome

PurposeTo study the indications and the challenges while fitting scleral contact lens (ScCL) filled with fluid prior to lens insertion in pediatric patients.MethodsWe retrospectively reviewed charts of patients of 16 years or less who received ScCL (PROSE – Prosthetic Replacement of the Ocular Surface Ecosystem, Boston Foundation for Sight, Needham Heights, MA, USA) that were filled with fluid (Normal saline) before lens insertion during July 2006 to April 2010. The main goal of ScCL fitting was to improve vision in patients having keratoconus (KC) and improve the ocular microenvironment in ocular surface disease (OSD). Visual acuity before and after lens wear was noted.ResultsFluid-filled ScCL were dispensed to 15 patients (20 eyes). The indications for ScCL fitting were KC (n = 3 eyes), Stevens Johnson syndrome (SJS, n = 13 eyes), radiation keratopathy (n = 1 eye), combined KC and SJS (n = 1 eye) and KC and vernal keratoconjunctivitis (VKC, n = 2 eyes). Mean age of the patients was 12.85 years. The average daily lens wear was 9 h. The vision improved by 2 lines or more in 85% and dropped by 2 lines or more in 45% eyes after 4 h of lens wear due to tear debris collection. None of the patients had any complications. Patients were self sufficient inserting and removing ScCL. Two patients had broken lenses during the follow-up.ConclusionsScCL are useful for pediatric patients who have OSD, irregular astigmatism or the two coexisting; KC combined with VKC or SJS, helping to maintain the health of the ocular surface and improves vision in these patients.