Concentrating solutions of some singularly perturbed elliptic equations

We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.      

An algorithmic framework for convex mixed integer nonlinear programs

This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent years. Wishing to exploit expertise in these areas as well as on previous work in mixed integer nonlinear programming, this work represents the first step in an ongoing and ambitious project within an open-source environment. COIN-OR is our chosen environment for the development of the optimization software. A class of hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme cases, are proposed and implemented. Computational results that demonstrate the effectiveness of this framework are reported. Both the library of mixed integer nonlinear problems that exhibit convex continuous relaxations, on which the experiments are carried out, and a version of the software used are publicly available.     

Comparing different metaheuristic approaches for the median path problem with bounded length

In this paper we consider the Bounded Length Median Path Problem which can be defined as the problem of locating a path-shaped facility that departures from a given origin and arrives at a given destination in a network. The length of the path is assumed to be bounded by a given maximum length. At each vertex of the network (customer-point) the demand for the service is given and the cost to reach the closest service-point is computed. The objective is to minimize the sum of these costs over all the customer-points in the network.     

Development and validation of a gas chromatography/mass spectrometry method for the assessment of genomic DNA methylation

A method for the determination of DNA global methylation, taken as the ratio (%) of 5‐methylcytosine (5mCyt) versus the sum of cytosine (Cyt) and 5mCyt, via gas chromatography/mass spectrometry (GC/MS), was developed and validated. DNA (2.5 µg) was hydrolyzed with aqueous formic acid 88%, spiked with cytosine‐2,4‐¹³C₂,¹⁵N₃ and 5‐methyl‐²H₃‐cytosine‐6‐²H₁ as internal standards, and derivatized with N‐methyl‐N‐(tert‐butyldimethylsilyl)trifluoroacetamide and 1% tert‐butyldimethylchlorosilane, in the presence of acetonitrile and pyridine. GC/MS, operating in single ion monitoring mode, separated and specifically detected all nucleobases as tert‐butyldimethylsilyl derivatives, without interferences, with the exception of guanosine. The method was linear throughout the range of clinical interest and had good sensitivity, with a limit of quantification of 3.2 pmol for Cyt and 0.056 pmol for 5mCyt, the latter corresponding to a methylation level of 0.41%. Intra‐ and inter‐day precision and accuracy were below 4.0% for both analytes and methylation. The matrix absolute effect, process efficiency and coefficient of variation ranged from 96.5 to 101.2%. The matrix relative effect was below 1%. The method was applied to the analysis of different human DNAs, including: nonmethylated DNA from PCR (methylation 0.00%), hypermethylated DNA prepared using M.SssI CpG methyltransferase (methylation 18.05%), DNA from peripheral blood leukocytes of healthy subjects (N = 6, median methylation 5.45%), DNA from bone marrow of leukemia patients (N = 5, 3.58%) and DNA from myeloma cell lines (N = 4, 2.74%). Copyright © 2009 John Wiley & Sons, Ltd.     

Targeted analysis of protein citrullination using chemical modification and tandem mass spectrometry

Protein citrullination originates from enzymatic deimination of polypeptide‐bound arginine and is involved in various biological processes during health and disease. However, tools required for a detailed and targeted proteomic analysis of citrullinated proteins in situ, including their citrullination sites, are limited. A widely used technique for detection of citrullinated proteins relies on antibody staining after specific derivatization of citrulline residues by 2,3‐butanedione and antipyrine. We have recently reported on the details of this reaction. Here, we show that this chemical modification can be utilized to specifically detect and identify citrullinated peptides and their citrullination sites by liquid chromatography/tandem mass spectrometry (LC/MS/MS) analysis. Using model compounds, we demonstrate that in collision‐induced dissociation (CID) a specific, modification‐derived fragment ion appears as the dominating signal at m/z 201.1 in the MS/MS spectra. When applying electron transfer dissociation (ETD), however, the chemical modification of citrulline remained intact and extensive sequence coverage allowed identification of peptides and their citrullination sites. Therefore, LC/MS/MS analysis with alternating CID and ETD has been performed, using CID for specific, signature ion‐based detection of derivatized citrullinated peptides and ETD for sequence determination. The usefulness of this targeted analysis was demonstrated by identifying citrullination sites in myelin basic protein deiminated in vitro. Combining antibody‐based enrichment of chemically modified citrulline‐containing peptides with specific mass spectrometric detection will increase the potential of such a targeted analysis of protein citrullination in the future. Copyright © 2009 John Wiley & Sons, Ltd.     

Simple ingredients leading to very efficient heuristics for the maximum clique problem

Starting from an algorithm recently proposed by Pullan and Hoos, we formulate and analyze iterated local search algorithms for the maximum clique problem. The basic components of such algorithms are a fast neighbourhood search (not based on node evaluation but on completely random selection) and simple, yet very effective, diversification techniques and restart rules. A detailed computational study is performed in order to identify strengths and weaknesses of the proposed algorithms and the role of the different components on several classes of instances. The tested algorithms are very fast and reliable: most of the DIMACS benchmark instances are solved within very short CPU times. For one of the hardest tests, a new putative optimum was discovered by one of our algorithms. Very good performances were also shown on recently proposed and more difficult instances. It is important to remark that the heuristics tested in this paper are basically parameter free (the appropriate value for the unique parameter is easily identified and was, in fact, the same value for all problem instances used in this paper).     

Steplike currents in confined two dimensional systems

In a confined two dimensional system of non-interacting electrons in a normal constant magnetic field, the current is calculated along the sample as a response to an electric field in the same direction which is switched on and then off. The resulting stationary current is shown to be a step-like function of the electron density.