Log-space Algorithms for Paths and Matchings in k-trees

Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we improve these bounds for k-trees, where k is a constant. In particular, the main results of our paper are log-space algorithms for reachability in directed k-trees, and for computation of shortest and longest paths in directed acyclic k-trees. Besides the path problems mentioned above, we also consider the problem of deciding whether a k-tree has a perfect macthing (decision version), and if so, finding a perfect match- ing (search version), and prove that these two problems are L-complete. These problems are known to be in P and in RNC for general graphs, and in SPL for planar bipartite graphs [DKR08]. Our results settle the complexity of these problems for the class of k-trees. The results are also applicable for bounded tree-width graphs, when a tree-decomposition is given as input. The technique central to our algorithms is a careful implementation of divide-and-conquer approach in log-space, along with some ideas from [JT07] and [LMR07].Comment: Accepted in STACS 201

Interactions involving D-branes

We investigate some aspects of the spectrum of D-branes and their interactions with closed strings. As argued earlier, a collection of many D-strings behaves, at large dilaton values, as a single multiply wound string. We use this result and T-duality transformations to show that a similar phenomenon occurs for effective strings produced by wrapping p-branes on a small (p-1)-dimensional torus, for suitable coupling. To understand the decay of an excited D-string at large dilaton values, we study the decay of an elementary string at small dilaton values. A long string, multiply wound on a circle, with a small excitation energy is found to predominantly decay into another string with the same winding number and an unwound closed string (rather than two wound strings). This decay amplitude agrees, under duality, with the decay amplitude computed using the Born-Infeld action for the D-string. We compute the absorption cross section for the D-brane model studied by Callan and Maldacena. The absorption cross section for the dilaton equals that for the scalars obtained by reduction of the graviton, and both agree with the cross section expected from a classical hole with the same charges.Comment: harvmac, 23 pages; minor typos corrected and some clarifications about the Born-Infeld action adde

Absorption of angular momentum by black holes and D-branes

We consider the absorption of higher angular momentum modes of scalars into black holes, at low energies, and ask if the resulting cross sections are reproduced by a D-brane model. To get the correct dependence on the volume of the compactified dimensions, we must let the absorbing element in the brane model have a tension that is the geometric mean of the tensions of the D-string and an effective stringlike tension obtained from the D-5-brane; this choice is also motivated by T-duality. In a dual model we note that the correct dependence on the volume of the compact dimensions and the coupling arise if the absorbing string is allowed to split into many strings in the process of absorbing a higher angular momentum wave. We obtain the required energy dependence of the cross section by carrying out the integrals resulting from partitioning the energy of the incoming quantum into vibrations of the string.Comment: harvmac, 25 page

METABOLISM IN HUMAN OXIDATIVE PHENOTYPES AND THEIR RAT MODELS

Methoxyphenamine (MP), which is a ß2 agonist used clinically as a bronchodilator, is marketed in Canada in the combination non-prescription product, Orthoxicol™. It has been shown to be metabolized by three phase I metabolic pathways, namely, N-demethylation (NDMP), 0-demethylation (0DMP) and aromatic 5-hydroxylation (5HMP). Genetic polymorphism in the metabolism of MP and its relationship to debrisoquine (D) oxidation to 4-41ydroxy-debrisoquine (4HD) were investigated inhuman as well as rat models of human debrisoquine phenotypes. Such a study enabled investigation of the effects on the alternative metabolic pathways when one or more metabolic reaction of MP are genetically impaired. In order to perform the above studies, quantitative gas-liquid chranatographic (GLC) procedures for MP and three of its metabolites in biological fluids were developed. The metabolites in plasma were measured using an electron-capture detector (ECU). The lower limit of quantitation for each metabolite was less than 4 ng m1-1 of plasma, with a coefficient of variation less than 10% in each case. The poor electron-capture response of fluorinated derivatives of MP necessitated the use of nitrogen-phosphorous detection (NPD). Extractive derivatization with pentafluorcbenzoyl chloride, without the need for protein precipitation, enabled quantitation of MP down to 3.8 ng ml-1 from a 2-mi aliquot of plasma. The urinary concentration of MP and its three metabolites were determined simultaneously after derivatization with trifluoroacetic anhydride by a modified literature procedure which employed GLC-NPD

Photophysical and photochemical properties of a family of isoelectronic tris chelated ruthenium(ii) aza-/azo-aromatic complexes

We have investigated the electrochemical, spectroscopic and electroluminescent properties of a family of aza-aromatic complexes of ruthenium of type [Ru^(II)(bpy/phen)_2(L)]^(2+) (4d^6) with three isomeric L ligands, where, bpy = 2,2′-bipyridine, phen = 1,10-phenanthroline and the L ligands are 3-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L^1), 3-(2-pyridyl[1,2,3])triazolo[1,5-a]pyridine (L^2) and 2-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L^3). The complexes display two bands in the visible region near 410–420 and 440–450 nm. The complexes are diamagnetic and show well defined ^1H NMR lines. They are electroactive in acetonitrile solution and exhibit a well defined Ru^(II)/Ru^(III) couple near 1.20 to 1.30 V and −1.40 to −1.50 V due to ligand reduction versus Saturated Calomel Electrode (SCE). The solutions are also luminescent, with peaks are near 600 nm. All the complexes are electroluminescent in nature with peaks lying near 580 nm. L^1 and L^3 ligated complexes with two bpy co-ligands show weak photoluminescence (PL) but stronger electroluminescence (EL) compared to corresponding L^2 ligated analogues

Boosts, Schwarzschild Black Holes and Absorption cross-sections in M theory

$D$ dimensional neutral black strings wrapped on a circle are related to $(D-1)$ dimensional charged black holes by boosts. We show that the boost has to be performed in the covering space and the boosted coordinate has to be compactified on a circle with a Lorentz contracted radius. Using this fact we show that the transition between Schwarzschild black holes to black p-branes observed recently in M theory is the well-known black hole- black string transition viewed in a boosted frame. In a similar way the correspondence point where an excited string state goes over to a neutral black hole is mapped exactly to the correspondence point for black p-branes. In terms of the $p$ brane quantities the equation of state for an excited string state becomes identical to that of a 3+1 dimensional massless gas for all $p$. Finally, we show how boosts can be used to relate Hawking radiation rates. Using the known microscopic derivation of absorption by extremal 3-branes and near-extremal 5D holes with three large charges we provide a microscopic derivation of absorption of 0-branes by seven and five dimensional Schwarzschild black holes in a certain regime.Comment: Some references added, minor clarifications (harvmac, 16 pages