New Approximation Algorithms for Minimum Cycle Bases of Graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time O(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time O(n(3+2/k) ), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega) ) bound. We also present a 2-approximation algorithm with expected running time O(M-omega root n log n), a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

Terpyridine Oxovanadium(IV) Complexes of Phenanthroline Bases for Cellular Imaging and Photocytotoxicity in HeLa Cells

Oxovanadium(IV) complexes VO(N-N-N)(N-N)](NO3)(2) (1-4) of (4'-phenyl)-2,2': 6',2 `'-terpyridine (ph-tpy in 1 and 2) or (4'-pyrenyl)-2,2':6',2 `'-terpyridine (py-tpy in 3 and 4) having N-N as 1,10-phenanthroline (phen in 1 and 3) or dipyrido3,2-a:2',3'-c]phenazine (dppz in 2 and 4) are prepared and characterized. The crystal structure of 1 has VO2+ group in VN5O coordination geometry. The terpyridine ligand coordinates in a meridional binding mode. The phen ligand displays a chelating mode of binding with an N-donor site trans to the vanadyl oxo group. The complexes show a d-d band in the range of 710-770 nm in aqueous DMF (4:1 v/v). The complexes exhibit an irreversible V-IV/V-III redox response near -1.0 V vs. SCE in aqueous DMF/0.1 M KCl. The complexes bind to CT DNA giving K-b values within 3.5 x 10(5) to 1.2 x 10(6) M-1. The complexes show poor chemical nuclease activity in dark. Complexes 2-4 show photonuclease activity in UV-A light of 365 nm forming O-1(2) and (OH)-O-center dot. Complex 4 shows DNA photocleavage activity at near-IR light of 785 nm forming (OH)-O-center dot radicals. Complexes 2 and 4 show significant photocytotoxicity in HeLa cancer cells. Uptake of the complexes in HeLa cells, studied by fluorescence imaging, show predominantly cytosolic localization inside the cells.

Photocytotoxicity and DNA photocleavage activity of La(III) and Gd(III) complexes of phenanthroline bases

Lanthanide(II) complexes La(B)(acac)(3)] (1-3) and Gd(B)(acac)(3)] (4-6), where B is a N,N-donor phenanthroline base, viz., 1,10-phenanthroline (phen in 1, 4), dipyrido3,2-d:2',3'-f]quinoxaline (dpq in 2, 5) and dipyrido3,2-a:2',3'-c]phenazine (dppz in 3, 6), have been prepared and characterized. The Gd(111) complexes 4 6 are structurally characterized by single crystal X-ray crystallography. The complexes display GdO6N2 coordination with the ligands showing bidentate chelating mode of bonding. The complexes are non-electrolytic in aqueous DMF and exhibit ligand-centered absorption bands in the UV region. The dppz complexes show a band at 380 nm in DMF. The La(111) complexes are diamagnetic. The Gd(III) complexes are paramagnetic with magnetic moment that corresponds to seven unpaired electrons. The Complexes are avid binders to calf thymus DNA giving K-b values in the range of 4.7 x 10(4) 6.1 x 10(5) M-1 with a relative binding order: 3, 6 (dppz) > 2, 5 (dpq) > 1, 4 (phen). The binding data suggest DNA surface and/or groove binding nature of the complexes. The dpq and dppz complexes efficiently cleave SC DNA to its nicked circular form in UV-A light of 365 nm via formation of both singlet oxygen (O-1(2)) and hydroxyl radical (HO center dot) species. The dppz complexes 3 and 6 exhibit significant PDT effect in He La cervical cancer cells giving respective IC50 value of 460(+/- 50) and 530(+/- 30) nM in UV-A light of 365 rim, and are essentially non-toxic in dark with an IC50 value of >100 mu M. The dppz ligand alone is cytotoxic in dark and UV-A light. A significant decrease in the dark toxicity of the dppz base is observed on binding to the Ln(III) ion while retaining its photocytotoxicity.

Schiff base oxovanadium(IV) complexes of phenanthroline bases showing DNA photocleavage activity at near-IR light and photocytotoxicity

Oxovanadium(IV) complexes VO(L)(B)](ClO4) (1-3) of N-2-pyridylmethylidine-2-hydroxyphenylamine (HL) Schiff base and phenanthroline bases (B), viz. 1,10-phenanthroline (phen in 1), dipyrido3,2-d: 2',3'-f] quinoxaline (dpq in 2) or dipyrido3,2-a: 2',3'-c] phenazine (dppz in 3), were prepared, characterized and their DNA binding property, photo-induced DNA cleavage activity and photocytotoxicity in HeLa cells studied. The crystal structure of 1 shows the presence of a VO2+ moiety in VO2N4 coordination geometry. The complexes show a d-d band at similar to 830 nm in DMF. The complexes display an oxidative V(V)-V(IV) response near 0.5 V versus SCE and a reductive V(IV)/V(III) response near -0.65 V in DMF -0.1 M TBAP. The complexes that are avid binders to CT DNA giving K-b values within 7.1 x 10(4) to 3.2 x 10(5) M-1, do not show any significant chemical nuclease activity in presence of 3-mercaptopropionic acid or glutathione. The dpq and dppz complexes are photocleavers of pUC19 DNA in UV-A light of 365 nm forming both O-1(2) and (OH)-O-center dot radicals and in near-IR light of 785 nm forming (OH)-O-center dot radicals. The dppz complex exhibits photocytotoxicity in visible light in HeLa cells (IC50 = 6.8 mu M). Flow-cytometric study on this complex shows a high sub-G1 phase in light compared to dark indicating PDT effect. (C) 2011 Elsevier B. V. All rights reserved.

Mutagenic significance of proton acidities in methylated guanine and thymine bases and deoxynucleosides: A theoretical study

Proton changes have been advanced as being the key molecular basis for the mutagenecity of alkylated DNA bases and nucleosides, leading to questions as to which protons are involved and whether the protic changes are tautomeric shifts or abstractions. This semiempirical molecular orbital study seeks to clarify the issue by examining the various possibilities open for these protic changes in a number of methylated guanines and thymines and their deoxynucleosides. Proton shifts leading to tautomer formation are not predicted as being thermodynamically favourable in most cases. The most feasible proton abstractions are predicted to involve the Watson-Crick protons in all cases, which corroborates Watson-Crick proton loss as providing the key molecular basis for the induction of point mutations. The calculated proton acidities correlate well with experimental data. The gas-phase deprotonation enthalpies for a number of alkylated nucleosides are found to correlate linearly with the solvent-phase pK(a) values. The theoretically calculated enthalpies in a simulated aqueous solvent phase of the deprotonation reactions of various nucleic acid bases are also found to have good linear correlations with experimental pK(a) values. The consensus of these calculations is that O-6-alkyldeoxyguanosines, and O-2- and O-4-alkyldeoxythymidines would be mutagenic while N-7-alkyldeoxyguanosines would not be mutagenic (as experiment indicates). The untested N-3-methyldeoxyguanosine is predicted to be mutagenic. (C) 1997 Elsevier Science B.V.

Synthesis, spectral characterization and in vitro microbiological evaluation of novel glyoxal, biacetyl and benzil bis-hydrazone macrocyclic Schiff bases and their Co(II), Ni(II) and Cu(II) complexes

A series of binuclear Co(II), Ni(II) and Cu(II) complexes were synthesized by the template condensation of glyoxal, biacetyl or benzil bis-hydrazide, 2,6-diformyl-4-methylphenol and Co(11), Ni(II) or Cu(II) chloride in a 2:2:2 M ratio in ethanol. These 22-membered macrocyclic complexes were characterized by elemental analyses, magnetic, molar conductance, spectral, thermal and fluorescence studies. Elemental analyses suggest the complexes have a 2:1 stoichiometry of the type (M2LX2]center dot nH(2)O and Ni(2)LX(2)2H(2)O]center dot nH(2)O (where M = Co(II) and Cu(II); L = H2L1, H2L2 and H2L3; X = Cl; n = 2). From the spectroscopic and magnetic studies, it has been concluded that the Co(11) and Cu(11) complexes display a five coordinated square pyramidal geometry and the Ni(II) complexes have a six coordinated octahedral geometry. The Schiff bases and their metal complexes have also been screened for their antibacterial and antifungal activities by the MIC method. (C) 2011 Elsevier Ltd. All rights reserved.

Ternary copper(II) complexes of thiosemicarbazones and heterocyclic bases showing N3OS coordination as models for the type-2 centers of copper monooxygenases

Six ternary copper(II) complexes of general formulation [CuLB] (1-6), where L is dianionic ONS-donor thiosemicarbazones derived from the condensation of salicylaldehyde with thiosemicarbazides and B is NN-donor heterocyclic bases like 2,2'-bipyridine, 1,10-phenanthroline and 2,9-dimethyl-1,10-phenanthroline, are prepared from a reaction of copper(II) acetate hydrate with the heterocyclic base (B) and the thiosemicarbazone (H2L) in MeOH, and structurally characterized by X-ray diffraction technique. Crystal structures of the complexes display a distorted square-pyramidal (4 + 1) coordination geometry having the ONS-donor thiosemicarbazone bonded at the basal plane. The chelating heterocyclic bases exhibit axial-equatorial mode of bonding. The complexes are one-electron paramagnetic and they show axial X-band EPR spectra in DMF-toluene glass at 77 K giving g(parallel to)(A(parallel to)) and g(perpendicular to) values of similar to2.2 (175 x 10(-4) cm(-1)) and similar to2.0 indicating a {d(x2-y2)}(1) ground state. The complexes show a d-d band near 570 nm and a charge transfer band near 400 nm in DMF. The complexes are redox active and exhibit a quasireversible Cu(II)-Cu(I) couple in DMF-0.1 M tetrabutylammonium perchlorate near 0.1 V vs. SCE. They are catalytically active in the oxidation of ascorbic acid in presence of dioxygen. The complexes with a CuN3OS coordination model the ascorbate oxidation property of dopamine beta-hydroxylase and peptidylglycine a-hydroxylating monooxygeanase. (C) 2003 Elsevier Science B.V. All rights reserved.

Ferrocene-Conjugated L-Tryptophan Copper(II) Complexes of Phenanthroline Bases Showing DNA Photocleavage Activity and Cytotoxicity

Ferrocene-conjugated L-tryptophan (L-Trp) reduced Schiff base (Fc-TrpH) copper(II) complexes [Cu(Fc-Trp)(L)](ClO(4)) of phenanthroline bases (L), viz. 2,2'-bipyridine (bpy in 1), 1,10-phenanthroline (phen in 2), dipyrido[3,2-d:2',3'-f]quinoxaline (dpq in 3), and dipyrido[3,2-a:2',3'-c]phenazine (dppz in 4), were prepared and characterized and their photocytotoxicity studied. Cationic reduced Schiff base (Ph-TrpH) complexes [Cu(Ph-Trp)(L)(H(2)O)] (ClO(4)) (L = phen in 5; dppz in 6) having the ferrocenyl moiety replaced by a phenyl group and the Zn(II) analogue (7) of complex 4 were prepared and used as control species. The crystal structures of 1 and 5 with respective square-planar CuN(3)O and square-pyramidal CuN(3)O(2) coordination geometry show significantly different core structures. Complexes 1-4 exhibit a Cu(II)-Cu(I) redox couple near -0.1 V and the Fc(+)-Fc couple at similar to 0.5 V vs SCE in DMF-0.1 M [Bu(4)(n)N] (ClO(4)) (Fc = ferrocenyl moiety). The complexes display a copper(II)-based d-d band near 600 nm and a Fc-centered band at similar to 450 nm in DMF-Tris-HCl buffer. The complexes are efficient binders to calf thymus DNA. They are synthetic chemical nucleases in the presence of thiol or H(2)O(2), forming hydroxyl radicals. The photoactive complexes are cleavers of pUC19 DNA in visible light, forming hydroxyl radicals. Complexes 2-6 show photocytotoxicity in HeLa cancer cells, giving IC(50) values of 4.7, 10.2, 1.3, 4.8, and 4.3 mu M, respectively, in visible light with the appearance of apoptotic bodies. The complexes also show photocytotoxicity in MCF-7 cancer cells. Nuclear chromatin cleavage has been observed with acridine orange/ethidium bromide (AO/EB) dual staining with complex 4 in visible light. The complexes induce caspase-independent apoptosis in the HeLa cells.

Bases and Ideal Generators for Projective Monomial Curves

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in P-3 and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.

Ferrocene-Conjugated Copper(II) Complexes of L-Methionine and Phenanthroline Bases: Synthesis, Structure, and Photocytotoxic Activity

Ferrocene-conjugated reduced Schiff base (Fc-metH) copper(II) complexes of L-methionine and phenanthroline bases, namely, Cu(Fc-met)(B)](NO3), where B is 1,10-phenanthroline (phen in 1), dipyrido3,2-d:2',3'-f]quinoxaline (dpq in 2), dipyrido3,2-a:2',3'-c]phenazine (dppz in 3), and 2-(naphthalen-1-yl)-1H-imidazo4,5-f]1,10]phenanthroline (nip in 4), were prepared and characterized and their photocytotoxicity studied (Fc = ferrocenyl moiety). Complexes Cu(Ph-met)(B)](NO3) of the reduced Schiff base from benzaldehyde and L-methionine (Ph-metH) and B (phen in 5, dppz in 6) were prepared and used as control species. Complexes 1 and 5 were structurally characterized by X-ray crystallography. Complex 1 as a discrete monomer has a CuN3OS core with the thiomethyl group as the axial ligand. Complex 5 has a polymeric structure with a CuN3O2 core in the solid state. Complexes 5 and 6 are formulated as Cu(Ph-met)(B)(H2O)] (NO3) in an aqueous phase based on the mass spectral data. Complexes 1-4 showed the Cu(II)-Cu(I) and Fc(+)-Fc redox couples at similar to 0.0 and similar to 0.5 V vs SCE, respectively, in DMF-0.1 M (Bu4N)-N-n](ClO4). A Cu(II)-based weak d-d band near 600 nm and a relatively strong ferrocenyl band at similar to 450 nm were observed in DMF-Tris-HCl buffer (1:4 v/v). The complexes bind to calf thymus DNA, exhibit moderate chemical nuclease activity forming (OH)-O-center dot radical species, and are efficient photocleavers of pUC19 DNA in visible light of 454, 568, and 647 rim, forming (OH)-O-center dot radical as the reactive oxygen species. They are cytotoxic in HeLa (human cervical cancer) and MCF-7 (human breast cancer) cells, showing an enhancement of cytotoxicity upon visible light irradiation. Significant change in the nuclear morphology of the HeLa cells was observed with 3 in visible light compared to the nonirradiated sample. Confocal imaging using 4 showed its nuclear localization within the HeLa cells.

An approach to chiral amino acids via reductive amination of ketones: hydride reduction of 1-(S)-phenethyl amine derived Schiff bases of C-protected alpha-keto acids

Various 1-acyl-2,4,10-trioxaadamantanes were prepared from the corresponding 1-methoxycarbonyl derivatives, via conversion to the N-acylpiperidine derivatives followed by reaction with a Grignard reagent in refluxing THF. These alpha-keto orthoformates were converted to the corresponding imines with 1-(S)-phenethyl amine (TiCl4/Et3N/toluene/reflux), with the Schiff bases being reduced further with NaBH4 (MeOH/0 degrees C) into the corresponding 1-(S)-phenethyl amines (diastereomeric excess 91:9 by NMR). Hydrogenolysis of the phenethyl group (Pd-C/MeOH) finally led to the 1-(aminoalkyl)trioxaadamantanes, which are chiral C-protected alpha-amino acids, in excellent overall yields. (C) 2012 Elsevier Ltd. All rights reserved.

Cellular uptake and remarkable photocytotoxicity of pyrenylter pyridine oxovanadium(IV) complexes of dipyridophenazine bases

Pyrenylterpyridine (pytpy) oxovanadium(IV) complexes VO(pytpy)(L)]Cl-2 (1-6) of the dipyridophenazine bases (L), viz., dipyrido-6,7,8,9-tetrahydrophenazine (dpqC in 1), dipyrido3,2-a:2',3'-c]phenazine-2-carboxylic acid (dppzc in 2), dipyrido3,2-a:2',3'-c]phenazine-11-sulfonic acid (dppzs in 3), 7-aminodipyrido3,2-a:2',3'-c]phenazine (dppza in 4), benzo-i]dipyrido3,2-a:2',3'-c]phenazine (dppn in 5) and dipyrido3,2-a:2',3'-c]phenazine (dppz in 6) were prepared, characterized and their DNA binding, photocleavage activity and photocytotoxicity studied. The complexes which showed a d-d band near 750 nm in DMF are efficient binders to calf thymus DNA (K-b: 3.2 x 10(5)-2.9 x 10(6) M-1). The complexes showed significant pUC19 DNA cleavage in near-IR light of 785 nm forming center dot OH radicals and photocytotoxicity in HeLa cells in visible light with the benzo-i] dipyrido3,2-a:2',3'-c]phenazine complex 5 showing a remarkably low IC50 value of 0.036 mu M. Flow-cytometric analysis shows a high sub-G1 phase cell cycle arrest in HeLa cells by the complexes on photo-irradiation. The photocytotoxicity correlates well with the hydrophobicity, photosensitizing ability and DNA binding propensity of the complexes. (C) 2012 Elsevier B.V. All rights reserved.

Optimal sparsifying bases for frequency-domain optical-coherence tomography

We address the reconstruction problem in frequency-domain optical-coherence tomography (FDOCT) from under-sampled measurements within the framework of compressed sensing (CS). Specifically, we propose optimal sparsifying bases for accurate reconstruction by analyzing the backscattered signal model. Although one might expect Fourier bases to be optimal for the FDOCT reconstruction problem, it turns out that the optimal sparsifying bases are windowed cosine functions where the window is the magnitude spectrum of the laser source. Further, the windowed cosine bases can be phase locked, which allows one to obtain higher accuracy in reconstruction. We present experimental validations on real data. The findings reported in this Letter are useful for optimal dictionary design within the framework of CS-FDOCT. (C) 2012 Optical Society of America