Boxicity of Halin graphs

A k-dimensional box is the Cartesian product R₁×R₂×?×R_k where each R_i is a closed interval on the real line. The boxicity of a graph G, denoted as is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. Halin graphs are the graphs formed by taking a tree with no degree 2 vertex and then connecting its leaves to form a cycle in such a way that the graph has a planar embedding. We prove that if G is a Halin graph that is not isomorphic to K₄, then . In fact, we prove the stronger result that if G is a planar graph formed by connecting the leaves of any tree in a simple cycle, then unless G is isomorphic to K₄ (in which case its boxicity is 1).     

The treewidth and pathwidth of hypercubes

The d-dimensional hypercube, H_d, is the graph on 2^d vertices, which correspond to the 2^dd-vectors whose components are either 0 or 1, two of the vertices being adjacent when they differ in just one coordinate. The notion of Hamming graphs (denoted by ) generalizes the notion of hypercubes: The vertices correspond to the q^dd-vectors where the components are from the set {0,1,2,…,q-1}, and two of the vertices are adjacent if and only if the corresponding vectors differ in exactly one component. In this paper we show that the and the .     

Two dimensional electrophoretic analysis of human tears: collection method in dry eye syndrome

Tear proteomics, by 2-DE, can give a fingerprint of the protein profile, which is well suited in clinical proteomics for biomarker identification and in diagnostics. The mode of tear collection can influence the representation of the proteins in the tear and therefore it is important to use the appropriate method. In this study, capillary and Schirmer mode of tear collection was done in the healthy controls and the Schirmer method was validated in dry eye syndrome conditions. 2-D PAGE of normal and dry eye tear was performed using pH 3-10 linear IPG strips followed by 13% SDS-PAGE. The spot intensity was analyzed by the PD quest software. The two methods were compared using Bland-Altman statistical tool. The 2-D map of capillary and Schirmer tear showed 147 ± 8 spots and 145 ± 7 spots respectively. Both the collection methods were in agreement with each other and were comparable. Dry eye tear protein showed differential expression of proteins as observed in 25-35 kDa region. One of the significantly reduced protein was identified as proline-rich 4 protein. Schirmer method of tear collection is reliable in patients with dry eye, which can display the differential protein expression and help in biomarker identification.     

On Eulerian orientations of even-degree hypercubes

It is well known that every Eulerian orientation of an Eulerian $2k$-edge connected (undirected) graph is strongly $k$-edge connected. A long-standing goal in the area is to obtain analogous results for other types of connectivity, such as node connectivity. We show that every Eulerian orientation of the hypercube of degree $2k$ is strongly $k$-node connected.     

Vanadia-catalyzed solar photooxidation of aniline

Vanadia photocatalyzes the oxidation of aniline to azobenzene in ethanol. The reaction was studied using natural sunlight and UV irradiation (365 nm) as a function of [aniline], catalyst loading, airflow rate, solvent composition, etc. The photocatalyst exhibits sustainable catalytic activity. The product formation is greater with illumination at 254 nm than at 365 nm. Electron donors such as triphenylphosphine, diphenylamine, and hydroquinone enhance the photocatalysis. The singlet oxygen quencher azide ion fails to inhibit the catalysis. The photocatalysis takes place in both protic and aprotic solvents. The mechanism of photocatalysis is discussed and the product formation analyzed using a kinetic model.     

Kinetics of perborate oxidation of quinol

The perborate oxidation of quinol in aqueous acetic acid is first order with respect to perborate, zero order with respect to quinol, and first order with respect to H⁺. The oxidation is faster than H₂O₂ oxidation. Breakdown of protonated perboric acid is suggested as the rate-limiting step.

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, H⁺. . , , , .

     

Hydroaromatic equilibration during biosynthesis of shikimic acid

The expense and limited availability of shikimic acid isolated from plants has impeded utilization of this hydroaromatic as a synthetic starting material. Although recombinant Escherichia coli catalysts have been constructed that synthesize shikimic acid from glucose, the yield, titer, and purity of shikimic acid are reduced by the sizable concentrations of quinic acid and 3-dehydroshikimic acid that are formed as byproducts. The 28.0 g/L of shikimic acid synthesized in 14% yield by E. coli SP1.1/pKD12.138 in 48 h as a 1.6:1.0:0.65 (mol/mol/mol) shikimate/quinate/dehydroshikimate mixture is typical of synthesized product mixtures. Quinic acid formation results from the reduction of 3-dehydroquinic acid catalyzed by aroE-encoded shikimate dehydrogenase. Is quinic acid derived from reduction of 3-dehydroquinic acid prior to synthesis of shikimic acid? Alternatively, does quinic acid result from a microbe-catalyzed equilibration involving transport of initially synthesized shikimic acid back into the cytoplasm and operation of the common pathway of aromatic amino acid biosynthesis in the reverse of its normal biosynthetic direction? E. coli SP1.1/pSC5.214A, a construct incapable of de novo synthesis of shikimic acid, catalyzed the conversion of shikimic acid added to its culture medium into a 1.1:1.0:0.70 molar ratio of shikimate/quinate/dehydroshikimate within 36 h. Further mechanistic insights were afforded by elaborating the relationship between transport of shikimic acid and formation of quinic acid. These experiments indicate that formation of quinic acid during biosynthesis of shikimic acid results from a microbe-catalyzed equilibration of initially synthesized shikimic acid. By apparently repressing shikimate transport, the aforementioned E. coli SP1.1/pKD12.138 synthesized 52 g/L of shikimic acid in 18% yield from glucose as a 14:1.0:3.0 shikimate/quinate/dehydroshikimate mixture.     

Ethylene Polymerization Studies with an MAO Synthesized by a Non‐Hydrolytic Synthetic Route

A facile nonaqueous synthetic route to methylaluminoxane (MAO) by heating a mixture of benzophenone and trimethylaluminium (TMA) is described. The MAO prepared such reveals to be an efficient activator of metallocenes and late transition metal complexes for ethylene polymerization. The [TMA]/[benzophenone] ratio used for the preparation of MAO is shown to have a dramatic effect on the catalytic activity as well as the molecular weight distribution of the resulting polyethylenes.     

The stable set problem and the thinness of a graph

We introduce a poly-time algorithm for the maximum weighted stable set problem, when a certain representation is given for a graph. The algorithm generalizes the algorithm for interval graphs and that for graphs with bounded pathwidth. By a suitable application to the frequency assignment problem, we improved several solutions to relevant benchmark instances.