Approximating Node Connectivity Problems via Set Covers

Given a graph (directed or undirected) with costs on the edges, and an integer $k$, we consider the problem of finding a $k$-node connected spanning subgraph of minimum cost. For the general instance of the problem (directed or undirected), there is a simple $2k$-approximation algorithm. Better algorithms are known for various ranges of $n,k$. For undirected graphs with metric costs Khuller and Raghavachari gave a $( 2+{2(k-1)}/{n})$-approximation algorithm. We obtain the following results: (i) For arbitrary costs, a $k$-approximation algorithm for undirected graphs and a $(k+1)$-approximation algorithm for directed graphs. (ii) For metric costs, a $(2+({k-1})/{n})$-approximation algorithm for undirected graphs and a $(2+{k}/{n})$-approximation algorithm for directed graphs. For undirected graphs and $k=6,7$, we further improve the approximation ratio from $k$ to $\lceil (k+1)/2 \rceil=4$; previously, $\lceil (k+1)/2 \rceil$-approximation algorithms were known only for $k \leq 5$. We also give a fast $3$-approximation algorithm for $k=4$. The multiroot problem generalizes the min-cost $k$-connected subgraph problem. In the multiroot problem, requirements $k_u$ for every node $u$ are given, and the aim is to find a minimum-cost subgraph that contains $\max\{k_u,k_v\}$ internally disjoint paths between every pair of nodes $u,v$. For the general instance of the problem, the best known algorithm has approximation ratio $2k$, where $k=\max k_u$. For metric costs there is a 3-approximation algorithm. We consider the case of metric costs, and, using our techniques, improve for $k \leq 7$ the approximation guarantee from $3$ to $2+{\lfloor (k-1)/2 \rfloor}/{k} < 2.5$.     

Evaluation of bent-crystal x-ray backlighting and microscopy techniques for the Sandia Z machine

X-ray backlighting and microscopy systems for the 1-10-keV range based on spherically or toroidally bent crystals are discussed. These systems are ideal for use on the Sandia Z machine, a megajoule-class x-ray facility. Near-normal-incidence crystal microscopy systems have been shown to be more efficient than pinhole cameras with the same spatial resolution and magnification [Appl. Opt. 37, 1784 (1998)]. We show that high-resolution (< or = 10 microm) x-ray backlighting systems using bent crystals can be more efficient than analogous point-projection imaging systems. Examples of bent-crystal-backlighting results that demonstrate 10-microm resolution over a 20-mm field of view are presented.     

Three-dimensional point spread functions of an optical heterodyne scanning image processor

We study the three-dimensional (3-D) imaging properties of an optical heterodyne scanning image processor. The image processor is a two-pupil optical system capable of 3-D imaging coherently or incoherently, depending on the detection scheme used. We derive the imaging properties in terms of the two pupils and then show an important 3-D imaging application in scanning holography by deriving its 3-D point spread functions and compare them with conventional 3-D imaging systems.     

On the designing of densely dispersion-managed optical fiber systems for ultrafast optical communication

We present some theoretical and experimental results which suggest the possibility of constructing a non-empirical methodology of designing optical transmission systems with ultra high bit-rate per channel. Theoretically, we present an average dispersion decreasing densely dispersion-managed (A4dm) fiber system, which exhibits many advantages over the densely dispersion-managed fiber system, such as the possibility of transmitting chirp-free Gaussian pulses at 160 Gbit/s per channel over transoceanic distances, with a reduced energy and minimal intra-channel interaction. Experimentally we present generation of a 160-GHz picosecond pulse train at 1550 nm using multiple four-wave mixing temporal compression of an initial dual frequency beat signal in the anomalous-dispersion regime of a non-zero dispersion shifted fiber. A complete intensity and phase characterization of the pulse train by means of a frequency-resolved optical gating technique is achieved, showing generation of transform-limited pedestal-free Gaussian pulses.     

Fiber optic applications of multiple quantum well electroabsorption modulators

Electroabsorption modulators (eam) have proved to be very attractive both as optical sources (monolithically integrated NRZ transmitters andrz pulse generators) as well as for very fast signal processing (demultiplexing, regeneration, wavelength conversion,...). Their design criteria, technology and implementation in future networks are reviewed, and the main issues are discussed.     

FTMS structure elucidation of natural products: application to muraymycin antibiotics using ESI multi-CHEF SORI-CID FTMS(n), the top-down/bottom-up approach,and HPLC ESI capillary-skimmer CID FTMS

The molecular formulas for the structures and substructures of muraymycin antibiotics A1 (C52H90N14O19, MW 1214) and B1 (C49H83N11O18, MW 1113) were determined using electrospray ionization (ESI) Fourier transform mass spectrometry (FTMS). The muraymycin A1 and B1 structures were elucidated by utilizing capillary-skimmer fragmentation with up to five stages of mass spectrometry (MS5). Multi-CHEF, a multiple ion isolation method, was used at each stage of MS(n) to isolate a parent ion and up to four reference ions, for exact-mass calibration. The parent ions were fragmented by SORI-CID and the product ions internally calibrated with average absolute mass errors less than 1 ppm at each stage in the fragmentation processes. Using the top-down/bottom-up approach, the molecular formulas for the antibiotics were determined by summing the elemental formulas of the neutral losses, obtained by measuring the mass differences (<500 Da) between the genetically related sequential parent ion masses in the MS(n) spectra, with the unique elemental formula of the lowest parent ion mass (<500 Da). The structures of 12 additional compounds in the muraymycin complex were elucidated using HPLC ESI capillary-skimmer CID FTMS by correlating their fragmentation patterns with those of muraymycins A1 and B1. Sequential neutral losses of an aminosugar, a valine, a uridine, and an ester fatty acid from the muraymycin parent ions provided diagnostic fragments for characterization.     

Current state of the art of biphasic calcium phosphate bioceramics

We have developed 15 years ago, with the collaboration of Lynch, Nery, and LeGeros in the USA, a bioactive concept based on biphasic calcium phosphate (BCP) ceramics. The concept is determined by an optimum balance of the more stable phase of HA and more soluble TCP. The material is soluble and gradually dissolves in the body, seeding new bone formation as it releases calcium and phosphate ions into the biological medium. The bioactive concept based on the dissolution/transformation processes of HA and TCP has been applied to both Bulk, Coating and Injectable Biomaterials. The events at the calcium phosphate (CaP) biomaterial/bone interface represent a dynamic process, including physico-chemical processes, crystal/proteins interactions, cells and tissue colonization, bone remodeling, finally contributing to the unique strength of such interfaces. An important literature and numerous techniques have been used for the evaluation of the fundamental physico chemical and biological performance of BCP concept. This type of artificial bone used from a long time in preclinical and in clinical trial, revealed the efficiency for bone filling, performance for bone reconstruction and efficacy for bone ingrowth at the expense of the micro macroporous BCP bioceramics.     

Tamoxifen derivatives for delivery of the antitumoral (DACH)Pt group: selective synthesis by McMurry coupling,and biochemical behaviour

The goal of our study was to potentiate the effects of the ((R,R)-trans-1,2-diaminocyclohexane)-platinum(II) fragment [(DACH)Pt], known for its cytotoxic properties, either with tamoxifen (Tam), the most widely used antiestrogen in the treatment of hormone-dependent breast cancers, or with its active metabolite hydroxytamoxifen (hydroxy-Tam). We coupled Tam or hydroxy-Tam derivatives bearing a malonato group at the para position of the beta aromatic ring with the (DACH)Pt fragment. The malonato-Tam and malonato-hydroxy-Tam compounds were prepared through McMurry coupling of the appropriate ketones. The presence of the malonate group resulted in a pronounced stereospecificity in the reaction, since malonato-Tam was obtained only as the Z isomer, while malonato-hydroxy-Tam was obtained as an 80/20 E/Z mixture. Attribution of the isomeric structures was achieved by 2D NMR spectroscopy. The platinum complexes (DACH)Pt-malonato-Tam and (DACH)Pt-malonato-hydroxy-Tam were then prepared by coupling the barium salts derived from the malonato-Tam and malonato-hydroxy-Tam with the nitrate derived from (DACH)PtCl(2). Study of the biochemical properties of these two platinum complexes showed that, while the hydroxy-Tam complex is satisfactorily recognized by the estrogen receptor (relative binding affinity, RBA=6.4 %), the Tam complex is less well recognized (RBA=0.5 %). The effects of these complexes on two hormone-dependent breast cancer cell lines (MCF7 and MVLN) were studied in vitro. Both complexes showed an antiproliferative effect on MCF7 cells, and an antiestrogenic effect on MVLN cells. The observed effects appear to be essentially antihormonal, since incorporation of the (DACH)Pt fragment into the tamoxifen skeleton did not cause an increase in the cytotoxicity of the complexes.     

Oxidative catabolism of α-tocopherol in rat liver microsomes

The goal of this study was to clarify the mechanism responsible for the catabolism of α-tocopherol. The vitamin, bound to albumin, was incubated with rat liver microsomes and appeared to be broken down. Optimal production of the metabolite was obtained when 1 mg of microsomal protein was incubated with 36 μM of α-tocopherol in the presence of 1.5 mM of NADPH. Chromatographic and mass spectrometric analyses of the metabolite led to the conclusion that it consists of an ω-acid with an opened chroman ring, although we could not perform nuclear magnetic resonance analysis to confirm this. Our data show that α-tocopherol is ω-oxidized to a carboxylic acid and that this process can occur in rat liver microsomes in the presence of NADPH and O₂. The oxidation to the quinone structure appears to be a subsequent event that may be artifactual and/or catalyzed by a microsomal enzyme(s).     

Further characterization of rat dihydroceramide desaturase: Tissue distribution, subcellular localization, and substrate specificity

The introduction of the double bond in the sphingoid backbone of sphingolipids occurs at the level of dihydroceramide via an NADPH-dependent desaturase, as discovered in permeabilized rat hepatocytes. In the rat, the enzyme activity, which has now been further characterized, appeared to be mostly enriched in liver and Harderian gland. By means of subcellular fractionation of rat liver homogenates and density gradient separation of microsomal fractions, the desaturase was localized to the endoplasmic reticulum. Various detergents were inhibitory to the enzyme, and maximal activities were obtained in the presence of NADPH and when the substrate was complexed to albumin. In the presence of albumin, the chain length of the fatty acid of the truncated dihydroceramides hardly affected the activity. Finally, in view of a likely evolutionary relationship between desaturases and hydroxylases, the formation of hydroxylated intermediates was analyzed. No evidence for their presence was found under our assay conditions. In part presented at the Conférence Jacques Monod “Cell lipids: Topology, transport and signalling functions”, Aussois, May 1997 (France); Van Veldhoven, P.P. “Ceramide biosynthesis: Characterisation of the conversion of dihydroceramide to ceramide”. Contributed equally to this study.