Optimizing constrained subtrees of trees

Given a treeG = (V, E) and a weight function defined on subsets of its nodes, we consider two associated problems. The first, called the rooted subtree problem, is to find a maximum weight subtree, with a specified root, from a given set of subtrees.The second problem, called the subtree packing problem, is to find a maximum weight packing of node disjoint subtrees chosen from a given set of subtrees, where the value of each subtree may depend on its root.We show that the complexity status of both problems is related, and that the subtree packing problem is polynomial if and only if each rooted subtree problem is polynomial. In addition we show that the convex hulls of the feasible solutions to both problems are related: the convex hull of solutions to the packing problem is given by pasting together the convex hulls of the rooted subtree problems.We examine in detail the case where the set of feasible subtrees rooted at nodei consists of all subtrees with at mostk nodes. For this case we derive valid inequalities, and specify the convex hull whenk 4.Research supported in part by Nato Collaborative Research Grant CRG 900281, Science Program SC1-CT91-620 of the EEC, and contract No 26 of the programme Pôle d'attraction interuniversitaire of the Belgian government.     

Electrospray/mass spectrometric identification and analysis of 4-hydroxy-2-alkylquinolines (HAQs) produced by <Emphasis Type="Italic">Pseudomonas aeruginosa</Emphasis>

The opportunistic pathogen Pseudomonas aeruginosa produces a large array of 4-hydroxy-2-alkylquinolines (HAQs). These compounds were analyzed by LC/MS, using positive electrospray ionization, in the culture supernatant of strain PA14. Fifty-six HAQs and related compounds were detected and their [M + H](+) ions were further analyzed by collision induced dissociation (CID). These HAQs were grouped into five different series based on the presence of an hydrogen or hydroxyl group at the 3 position, an N-oxide group in place of the quinoline nitrogen, and an unsaturation on their alkyl side chain. Two new analogs of 3,4-dihydroxy-2 heptylquinoline, the Pseudomonas quinolone signal (PQS), were found with an alkyl chain longer by one and two methylene groups. Moreover, two additional series of compounds were identified in which a saturated or unsaturated alkyl side chain is located at the 3 position along with an hydroxyl group at the 3 position and a ketone at the 2 position. No HAQ N-oxides, nor any compounds from the latter two series, were detected in a pqsL mutant derivative of PA14, indicating that this gene is involved in the biosynthesis of these compounds. This work demonstrates the large repertoire of HAQ and HAQ-related compounds produced by P. aeruginosa, and provides insight into N-oxides biosynthesis and confirm the hypothesis that N-oxides are the precursors of compounds from Series 6 and 7.     

Influence of the Lanthanide Ion and Solution Conditions on Formation of Lanthanide Wells–Dawson Polyoxotungstates

Lanthanide complexes of polyoxometalates, including the α₂-P₂W₁₇O₆₁ ¹⁰⁻ ligand, have been pioneered by Michael T. Pope, to whom this paper is dedicated. Examination of the solid-state and solution behavior of lanthanide complexes of the α₂-P₂W₁₇O₆₁ ¹⁰⁻ ligand are reported here to identify trends that will facilitate rational synthesis of hybrid organic lanthanide polyoxometalate complexes. Therefore, combining our data with that obtained by Pope and others a number of trends come into view. It is clear that there are two structural types for the 1:1 or 2:2 [Ln(H₂O)_X(α₂-P₂W₁₇O₆₁)]₂ ¹⁴⁻ species. The early lanthanides show a “cap to cap” structure that allows the Ln ion to be 9 coordinate and accommodates the longer bond lengths. The mid-late lanthanides show a “cap to belt” structure that allows the lanthanides to be 8 coordinate; this structural type is appropriate for the shorter bond lengths of the later lanthanides. The 1:1⇌1:2 equilibrium, that was observed by Pope for the Ce(III) analog is prevalent for the early- mid lanthanides. This equilibrium is slightly dependent on pH; however, cations have a major influence on this equilibrium. Larger, poorly hydrated cations appear to favor the 1:2 species for the early to mid lanthanides. Cations do not appear to influence the equilibrium for the later lanthanides; for all counterions, the 1:1 species was stable with no trace of the 1:2 species. Stability constants, K1 and K2, for the early to mid lanthanides were measured in this study by a competitive method and compared well with other published stability constant determinations. We suggest that the stability constants are not only dependent on the strength of interaction of the Ln with the α₂-P₂W₁₇O₆₁ ¹⁰⁻ ligand, but are also significantly influenced by the medium. The medium may bias the equilibria of the early-mid lanthanides and later lanthanides. The log K₁/log K₂ ratios are very close, suggesting that it is difficult to separate the 1:1 and 1:2 Ln: α₂-P₂W₁₇O₆₁ ¹⁰⁻ species.Electronic Supplementary Material Supplementary material for this article is available at and is accessible for authorized users.This paper is dedicated to Professor Michael T. Pope in honor of his substantial and sustained contributions to polyoxometalate chemistry and his inspiration to scientists working in the field.     

SHAPE MEMORY EFFECT OF PU IONOMERS WITH IONIC GROUPS ON HARD-SEGMENTS

SMPU （shape memory polyurethane） non-ionomers and ionomers, synthesized with poly（c-caprolactone） （PCL）, 4, 4＇-diphenylmethane diisocyanate （MDI）, 1,4-butanediol （BDO）, dimethylolpropionic acid （DMPA） were measured with cyclic tensile test and strain recovery test. The relations between the structure and shape memory effect of these two series were studied with respect to the ionic group content and the effect of neutralization. The resulting data indicate that, with the introduction of asymmetrical extender, the stress at 100% elongation is decreased for PU non-ionomer and ionomer series, especially lowered sharply for non-ionomer series; the fixation ratio of ionomer series is not affected obviously by the ionic group content; the total recovery ratio of ionomer series is decreased greatly. After sufficient relaxation time for samples stretched beforehand, the switching temperature is raised slightly, whereas the recovery ratio measured with strain recovery test method is lowered with increased DMPA content. The characterization with FT-IR, DSC, DMA elucidated that, the ordered hard domain of the two series is disrupted with the introduction of DMPA which causes more hard segments to dissolve in soft phase; ionic groups on hard segment enhance the cohesion between hard segments especially at high ionic group content and significantly facilitate the phase separation compared with the corresponding non-ionomer at moderate ionic group content.     

Recyclability of a layered silicate-thermoplastic olefin elastomer nanocomposite

A multiple-pass study was undertaken with a layered silicate-thermoplastic olefin elastomer (TPO) nanocomposite to study the impact of processing history on the properties of the material. A set of 10 passes were completed through a co-rotating intermeshing twin-screw extruder with samples collected to monitor changes in the composite. The microstructure of the nanocomposite was characterized using TEM, XRD, FT-IR, steady and complex shear rheology, and mechanical testing. With progressive passes through the extruder, the TPO nanocomposite experienced both delamination of the organoclay as well as thermo-oxidative degradation. The onset and extent of degradation were found to be unaffected by the presence of the organoclay species in the polymer, though, inclusion of a maleated compatibilizer led to increased chain scission. The generated carbonyl groups along the polymer chain as a result of oxidation were speculated to have a significant effect on the developing percolating network of clay within the material and on the final rheological properties of the composite. Despite the occurrence of degradation in the nanocomposite during recycling, its rheological and mechanical properties remained significantly higher than those of the unfilled resin.     

Determination of carnitine and acylcarnitines in urine by high-performance liquid chromatography-electrospray ionization ion trap tandem mass spectrometry

A high-performance liquid chromatography-mass spectrometry method has been developed for the simultaneous determination of native carnitine and eight acylcarnitines in urine. The procedure uses a solid-phase extraction on a cation-exchange column and the separation is performed without derivatization within 17 min on a reversed-phase C8 column in the presence of a volatile ion-pairing reagent. The detector was an ion trap mass spectrometer and quantification was carried out in the MS-MS mode. Validation was done for aqueous standards at ranges between 0.75 and 200 micromol/l, depending on the compound. Carnitine was quantified in urine and comparison with a radioenzymatic assay gave a satisfactory correlation (R2 = 0.981). The assay could be successfully applied to the diagnostic of pathological acylcarnitines profile of metabolic disorders in urines of patients suffering from different organic acidurias.     

Combinatorial enantiomeric separation of diverse compounds using capillary array electrophoresis

Combinatorial chiral separations were performed on a 96-capillary array electrophoresis system. A comprehensive enantioseparation protocol employing neutral and sulfated cyclodextrins as chiral selectors for common basic, neutral and acidic compounds was developed. By using only four judiciously chosen separation buffers, successful enantioseparations were achieved for 49 out of 54 test compounds spanning a large variety of pK and structures. Therefore, unknown compounds can be screened in this manner to identify the optimal enantioselective conditions in just one run.     

Chemical Synthesis of Oligonucleotides Containing N6-Methyladenine Residues in the GATC Site

To investigate by NMR the effects of adenine methylation, a set of oligodeoxynucleotides has been synthesized by phosphotriester or phosphoramidite procedures on silica-gel support. The preparation of fully protected 2′-deoxy-N⁶-methyladenosine 3′-phosphate 4 and (2′-deoxy-N⁶-methyladenosin-3′-O-yl)(methoxy)morpholinophosphine 5 is described. The large-scale chemical synthesis, purification by HPLC, and characterization by MS of these molecules containing N⁶-methyladenine is reported.     

Ecdysteroid glycosides: identification, chromatographic properties, and biological significance

Ecdysteroid glycosides are found in both animals and plants. The chromatographic behavior of these molecules is characteristic, as they appear much more polar than their corresponding free aglycones when analyzed by normal-phase high-performance liquid chromatography (HPLC), whereas the presence of glycosidic moieties has a very limited (if any) impact on polarity when using reversed-phase HPLC. Biological activity is greatly reduced because the presence of this bulky substituent probably impairs the interaction with ecdysteroid receptor(s). 2-Deoxy-20-hydroxyecdysone 22-O-beta-D-glucopyranoside, which has been isolated from the dried aerial parts of Silene nutans (Caryophyllaceae), is used as a model compound to describe the rationale of ecdysteroid glycoside purification and identification.     

Improved straightforward chemical synthesis of dihydroxyacetone phosphate through enzymatic desymmetrization of 2,2-dimethoxypropane-1,3-diol

Dihydroxyacetone phosphate (DHAP) was synthesized in high purity and yield in four steps starting from dihydroxyacetone dimer (DHA) (47% overall yield). DHA was converted into 2,2-dimethoxypropane-1,3-diol, which was desymmetrized by acetylation with lipase AK. The alcohol function was phosphorylated to give dibenzyl phosphate ester 4. From 4, two routes were investigated for large-scale synthesis of DHAP. First, acetate hydrolysis was performed prior to hydrogenolysis of the phosphate protective groups. The acetal hydrolysis was finally catalyzed by the phosphate group itself. Second, acetate and acetal hydrolysis were performed in one single step after hydrogenolysis.