Polynomial-time approximation schemes for piercing and covering with applications in wireless networks

Let be a set of disks of arbitrary radii in the plane, and let be a set of points. We study the following three problems: (i) Assuming contains the set of center points of disks in , find a minimum-cardinality subset of (if exists), such that each disk in is pierced by at least h points of , where h is a given constant. We call this problem minimum h-piercing. (ii) Assuming is such that for each there exists a point in whose distance from D's center is at most αr(D), where r(D) is D's radius and 0α<1 is a given constant, find a minimum-cardinality subset of , such that each disk in is pierced by at least one point of . We call this problem minimum discrete piercing with cores. (iii) Assuming is the set of center points of disks in , and that each covers at most l points of , where l is a constant, find a minimum-cardinality subset of , such that each point of is covered by at least one disk of . We call this problem minimum center covering. For each of these problems we present a constant-factor approximation algorithm (trivial for problem (iii)), followed by a polynomial-time approximation scheme. The polynomial-time approximation schemes are based on an adapted and extended version of Chan's [T.M. Chan, Polynomial-time approximation schemes for packing and piercing fat objects, J. Algorithms 46 (2003) 178–189] separator theorem. Our PTAS for problem (ii) enables one, in practical cases, to obtain a (1+ε)-approximation for minimum discrete piercing (i.e., for arbitrary ).     

Fragmentation of carbohydrate anomeric alkoxyl radicals: new synthesis of chiral 1-fluoro-1-halo-1-iodoalditols

A new general methodology for the synthesis of 1,1,1-trihaloalditols by starting from 1,5-anhydro-2-deoxy-hex-1-enitol derivatives (glycals) is described. The halogens are introduced sequentially in each of the three different steps of the process. The fluorine is introduced in the first step by electrophilic fluorination of the starting glycal; next, hydroxyhalogenation of the resulting vinyl fluoride allows the addition of any halogen (F, Cl, Br or I) at will, and finally, an iodine atom is inserted through an alkoxyl radical fragmentation reaction. This methodology allows the preparation of diverse types of 1,1,1-trihalogenated compounds (R--CF(2)I, R--CFI(2), R--CFClI and R--CFBrI) under mild conditions compatible with sensitive substituents. In some cases, the diastereomeric mixtures generated from R--CFClI and R--CFBrI can be chromatographically separated, and their configuration determined by X-ray crystallographic analysis. The synthetic usefulness of these compounds has been preliminarily assessed by examining the reactivity of the fluorinated radical generated by rupture of the C--I bond.     

Potentiation of fibroblast growth factor activity by synthetic heparin oligosaccharide glycodendrimers

Heparin is a highly sulfated polysaccharide that regulates a variety of cellular processes by interaction with a host of proteins. We report the preparation of synthetic heparin oligosaccharide glycodendrimers and their use as heparin mimetics to regulate heparin-protein interactions. The multivalent display of sugar epitopes mimics the naturally occurring glycans found on cell surfaces and enhances their binding capacity. Binding of the heparin dendrimers to basic fibroblast growth factor (FGF-2) was analyzed using heparin microarray experiments and surface plasmon resonance measurements on gold chips. Heparin-coated dendrimers bind FGF-2 significantly more effectively than monovalent heparin oligosaccharides. Dendrimer 1, which displays multiple copies of the sulfated hexasaccharide (GlcNSO(3)[6-OSO(3)]-IdoA[2-OSO(3)])3, was employed to promote FGF-2-mediated mitogen-activated kinase activation, demonstrating the utility of glycodendrimers to modulate heparin-protein interactions.     

Structural studies on supramolecular adducts of cyclodextrins with the complex [Ru([9]aneS3)(bpy)Cl]Cl

The complex [Ru([9]aneS₃)(bpy)Cl]Cl (bpy = 2,2′-bipyridine) was immobilised in plain β-cyclodextrin (β-CD) and permethylated β-CD (TRIMEB) to yield two adducts with a 1:1 host:guest stoichiometry. The adducts were studied by powder X-ray diffraction (XRD), thermogravimetric analysis (TGA), ¹³C{¹H} CP/MAS NMR and vibrational spectroscopy (FT-IR and Raman). Results support the formation of stable supramolecular adducts with a proposed geometry in which the coordinated bypiridine fragment of the guest is partially included in the host cavities, and the bulky [9]aneS₃ fragment protrudes out to the interstitial spaces. A packing mode is proposed for [Ru([9]aneS₃)(bpy)Cl]Cl · TRIMEB, obtained by Monte Carlo optimisation of the XRD data. TRIMEB molecules are stacked in tilted channels, with the voluminous part of the guest molecules in the inter-channel space. The behaviour of [Ru([9]aneS₃])(bpy)Cl]Cl upon CD encapsulation and the chloride ligand hydrolysis process in solution for all compounds were studied in detail by Raman spectroscopy.     

Synthesis of [60]fullerene-glycopyranosylaminopyrimidin-4-one conjugates

The synthesis of several C₆₀ derivatives containing a 6-(β-d-glycopyranosylamino)pyrimidin-4-one unit and a C₆₀-uridine conjugate is described. The fullerene derivatives bearing a 4-(β-d-glycopyranosylamino)pyrimidin-4-one moiety were synthesised by 1,3-dipolar cycloaddition reactions of C₆₀ with azomethine ylides generated in situ from the corresponding 5-formylpyrimidin-4-one derivatives and N-methylglycine. The synthesis of the C₆₀-uridine conjugate involved the selective protection of the 2′- and 3′-hydroxyl groups of uridine, esterification, cyclopropanation of C₆₀ and, finally, the deprotection of the hydroxyl groups. One of the fullerene-glycopyranosylaminopyrimidin-4-one conjugates was characterised by single-crystal X-ray crystallography. Differentiation between pairs of diastereoisomers, for several fullerene derivatives, was achieved through the study of their gas-phase fragmentations.     

Targeted therapy of the insulin-like growth factor-1 receptor in cancer

Recently, significant progress has been made towards understanding the pathogenesis of cancer from the molecular standpoint. To this end, a growing number of approaches are being exploited for the identification and validation of new therapeutic targets suitable for potent and specific intervention. The type 1 insulin-like growth factor receptor (IGF-1R) system has recently become the focus of major attention in the arena of cancer research. The involvement of the receptor and its downstream signaling cascades in the carcinogenesis process makes this system an excellent target for potential cancer therapy. Indeed, advances in the understanding of the molecular mechanisms behind IGF-1R activation have led to the discovery of agents designed selectively for targeting IGF-1R. The potential application of these inhibitors is currently under intense clinical investigation. This review describes the biology of IGF-1R particularly from a cancer perspective. The attempts to develop effective IGF-1R antagonists are discussed comprehensively with special emphasis on antibodies and small tyrosine kinase inhibitors.     

Synthesis, crystal structure, and modelling of a new tetramer complex of europium

A new compound with the formula [Eu4(ETA)9(OH)3(H2O)3)], where ETA is ethyl 4,4,4-trifluoroacetoacetate, has been synthesized and investigated by photoluminescence spectroscopy. The compound was characterized by means of chemical analysis, vibrational (IR), UV-vis absorption, and luminescence spectroscopies, and X-ray crystallography. The crystal structure of the [Eu4(ETA)9(OH)3(H2O)3)] complex in the solid state, determined by X-ray diffraction analysis, revealed that it crystallizes in the triclinic crystal system, space group P, with four crystallographically independent europium centers. From these structural data, the ground-state geometry of the tetramer has been calculated by using the Sparkle/AM1 model. The emission spectrum shows the characteristic transitions of the Eu3+ ion. The features displayed by the5D0-->7F0 transition in the emission spectrum are consistent with the Eu3+ ion occupying four different sites in chemical environments of low symmetries, in agreement with the X-ray data and the optimized geometry obtained from the Sparkle/AM1 model. These structural results have allowed the theoretical calculation of 4f-4f intensity parameters, including the forced electric dipole and dynamic coupling mechanisms as well as ligand singlet and triplet states, in good agreement with experiment.     

Molecular structure, vinyl rotation barrier, and vibrational dynamics of 2,6-dichlorostyrene. A theoretical and experimental research

The molecular structure of 2,6-dichlorostyrene has been analyzed at MP2 and DFT levels using different basis sets concluding in a nonplanar geometry. The influence of either the level of theory or the nature of the substituent has been assessed. The vinyl-phenyl torsion barrier has also been investigated as a function of level of theory. The ultimate factors responsible for the torsion barrier have been studied using two different partitioning schemes, i.e., the total electronic potential energy and the natural bond orbital, NBO. A topological analysis of the electron density within the atom-in-molecule, AIM, theory predicts soft intramolecular chlorine (ring)-hydrogen (vinyl) contacts when the system becomes planar. A first complete vibrational study has been performed using theoretical data and experimental vibrational frequencies from IR, Raman and, for the first time, inelastic neutron scattering, INS, spectra. The new assignment proposed is based on a scaled quantum mechanical, SQM, force field and the wavenumber linear scaling, WLS, approach.     

Cyclopentadienyl molybdenum dicarbonyl η-allyl complexes as catalyst precursors for olefin epoxidation. Crystal structures of Cp′Mo(CO)2(η-C3H5) (Cp′ = η-C5H4Me, η-C5Me5)

The complexes Cp′Mo(CO)₂(η³-C₃H₅) [Cp′ = η⁵-C₅H₅ (1), η⁵-C₅H₄Me (2), η⁵-C₅Me₅ (3)] have been prepared, structurally characterised by X-ray diffraction (2, 3), and tested as catalyst precursors for the epoxidation of olefins at 55 °C. Complex 1 gave a turnover frequency (TOF) of 310 mol mol_Mo⁻¹ h⁻¹ in the epoxidation of cis-cyclooctene with tert-butylhydroperoxide (TBHP, in decane) as oxidant, and 1,2-epoxycyclooctane was obtained quantitatively within 6 h. A similar result was obtained for complex 2, while the TOF for 3 was about one order of magnitude lower, suggesting a possible activity dependence on the ring substituents. For 1 the use of 1,2-dichloroethane as solvent increased the initial reaction rate to 361 mol mol_Mo⁻¹ h⁻¹, with no decrease in epoxide selectivity. Under these conditions the reaction rates for other olefins increased in the order 1-octene < trans-2-octene < cyclododecene < (R)-(+)-limonene < cis-cyclooctene, and, with the exception of limonene, the corresponding epoxide was the only product. For 1 the selective epoxidation of cis-cyclooctene could also be achieved in aqueous solution, using TBHP or H₂O₂ as oxidants, which gave epoxide yields of 99% and 27% at 24 h, respectively. The possibility of facilitating catalyst recycling by using ionic liquids as solvents was investigated.     

Alterations in Skin Immune Response Throughout Chronic UVB Irradiation—Skin Cancer Development and Prevention by Naproxen

Skin exposure to UVB radiation has been reported to produce both a significant inflammatory response and marked immunosuppression. This work was aimed to evaluate whether the response of murine skin to an acute UVB dose was modified by pre-exposure to chronic UVB irradiation and by topical treatment with naproxen, a nonsteroidal anti-inflammatory drug. Moreover, the effect of naproxen on the incidence of UV-induced skin tumors was studied. Prostaglandin E₂ (PGE₂) and tumor necrosis factor alpha (TNF-α) levels were increased 96 h post-UVB in acutely irradiated animals and both mediators were modified by topical naproxen application—PGE₂ was decreased while TNF-α was increased. Such inflammatory response was suppressed when mice were chronically irradiated. Naproxen application on chronically irradiated mice reduced the incidence of tumor lesions. Taken together, our data suggest that chronic UVB irradiation generates an immunosuppressive state that prevents skin cells from responding normally to an acute irradiation challenge, thus impairing the protective effect of TNF-α against skin tumor development. Furthermore, reduction in the incidence of tumor lesions by naproxen may be due to its ability to increase TNF-α levels as well as to decrease PGE₂.