Metric Embeddings—Beyond One-Dimensional Distortion

The extensive study of metric spaces and their embeddings has so far focused on embeddings that preserve pairwise distances. A very intriguing concept introduced by Feige allows us to quantify the extent to which larger structures are preserved by a given embedding. We investigate this concept, focusing on several major graph families such as paths, trees, cubes, and expanders. We find some similarities to the regular (pairwise) distortion, as well as some striking differences.     

Mode beating in spot-size converter lasers

An anomalous modulation in the wavelength spectrum has been observed in lasers with spot-size converters. This intensity modulation is shown to be caused by beating between the fundamental lasing mode and radiation modes in the taper. This results in a periodic modulation in the net gain spectrum, which causes wavelength jumps between adjacent net gain maxima, and a drive current dependent spectral width that is expected to affect system performance. The amplitude of this spectral modulation is reduced significantly by either using an angled rear-facet which reflects the beating radiation modes away from the laser axis, or by using a nonlinear, adiabatic taper.     

An iterative procedure for differential analysis of gene expression

Microarrays are a popular technology to study genes that are differentially expressed between two conditions. In this Note, we propose an iterative procedure to determine the biggest subset of non-differentially expressed genes. We prove a pseudo Markov relationship that allows practical computations. We obtain explicit expressions for FDR and the level of the proposed test at each step. To cite this article: A. Bar-Hen, S. Robin, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Bang-bang optimal control for the dam problem

The dam problem with general geometry is considered. Fluid is drawn from the bottomS ₁ at a ratek where 0 k N, _{S 1} k M; the objective is to minimize the total pressure of the fluid in the dam. A bang-bang principle is established for any optimal controlk ₀, that is,k ₀ = 0 on a setA andk ₀ =N on the complement setS ₁ A. In the case of a rectangular dam the structure ofA is determined and the uniqueness of the minimizerk ₀ is established.This work is partially supported by National Science Foundation Grants DMS-8501397 and DMS-8420896.     

Biocatalytic reversible control of the stiffness of DNA-modified responsive hydrogels: applications in shape-memory,self-healing and autonomous controlled release of insulin

The enzymes glucose oxidase (GOx), acetylcholine esterase (AchE) and urease that drive biocatalytic transformations to alter pH, are integrated into pH-responsive DNA-based hydrogels. A two-enzyme-loaded hydrogel composed of GOx/urease or AchE/urease and a three-enzyme-loaded hydrogel composed of GOx/AchE/urease are presented. The biocatalytic transformations within the hydrogels lead to the dictated reconfiguration of nucleic acid bridges and the switchable control over the stiffness of the respective hydrogels. The switchable stiffness features are used to develop biocatalytically guided shape-memory and self-healing matrices. In addition, loading of GOx/insulin in a pH-responsive DNA-based hydrogel yields a glucose-triggered matrix for the controlled release of insulin, acting as an artificial pancreas. The release of insulin is controlled by the concentrations of glucose, hence, the biocatalytic insulin-loaded hydrogel provides an interesting sense-and-treat carrier for controlling diabetes.

Biocatalytic control over the stiffness of pH-responsive hydrogels is applied to develop shape-memory, self-healing and controlled release matrices.