Scale Invariance Properties in the Simulated Annealing Algorithm

The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed.     

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.     

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.     

Synthesis of angular triquinanes from 1-Alkynylbicyclo[3.2. 0]hept-2-en-7-ones. A tandem alkoxy-cope ring Expansion/Transannular ring closure reaction

Addition of ethenyllithium reagents to the carbonyl group of dialkyl squarate-derived 1-alkynylbicyclo[3.2.0]hept-2-ene-7-ones (15), followed by a TBAF workup, results in a low-temperature anion-accelerated alkoxy-Cope rearrangement which proceeds by way of a strained cyclic allene intermediates (e.g.,17). This leads to the formation of angularly fused triquinanes (e.g., 20) in which each of the rings is functionally differentiated. Bicyclo[6.3. 0]undecadienones (e.g., 36) are the major products when the reactions are quenched with aqueous bicarbonate rather than TBAF. Under analogous conditions 2-alkylidene-1-alkynylbicyclo[3.2. 0]heptan-7-ones also give bicyclo[6.3.0]undecadienones by a mechanism that was established to involve a 1,5-hydrgen shift in a strained allene intermediate. The synthetic scope and mechanism of these and related transformations are discussed.     

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.     

Doppler-broadening measurements of microvoids at the Au/GaAs interface

Recent positron lifetime studies made on the Au/GaAs interface with an applied electric field returning a significant fraction of bulk implanted positrons to the interface have revealed the presence of microvoids( 1 nm diameter) at the interface. In this work an attempt has been made to study these microvoids by observing the Doppler broadening on the annihilation radiation coming from them. This is done both by observing theS-parameter as a function of applied bias and by applying the generalized least-squares method to the deconvolution of the annihilation radiation lineshape. The general conclusion is that the Doppler-broadened data are consistent with the majority of positrons trapping into microvoids, probably associated with grain boundaries. The data suggest that these open volume defects are more associated with the Au film rather than the Au-Ga alloyed interfacial region.Paper presented at the 132nd WE-Heraeus-Seminar on Positron Studies of Semiconductor Defects, Halle, Germany, 29 August to 2 September 1994