On the Structure of Contractible Edges in k-connected Partial k-trees

Contraction of an edge e merges its end points into a new single vertex, and each neighbor of one of the end points of e is a neighbor of the new vertex. An edge in a k-connected graph is contractible if its contraction does not result in a graph with lesser connectivity; otherwise the edge is called non-contractible. In this paper, we present results on the structure of contractible edges in k-trees and k-connected partial k-trees. Firstly, we show that an edge e in a k-tree is contractible if and only if e belongs to exactly one (k + 1) clique. We use this characterization to show that the graph formed by contractible edges is a 2-connected graph. We also show that there are at least |V(G)| + k - 2 contractible edges in a k-tree. Secondly, we show that if an edge e in a partial k-tree is contractible then e is contractible in any k-tree which contains the partial k-tree as an edge subgraph. We also construct a class of contraction critical 2k-connected partial 2k-trees.

Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control chemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Low-temperature polymer precursor-based synthesis of nanocrystalline particles of lanthanum calcium manganese oxide (La0.67Ca0.33MnO3) with enhanced ferromagnetic transition temperature

We report a simple modified polymeric precursor route for the synthesis of highly crystalline and homogenous nanoparticles of lanthanum calcium manganese oxide (LCMO). The LCMO phase formation was studied by thermal analysis, x-ray powder diffraction, and infrared spectroscopy at different stages of heating. These nanocrystallites (average particle size of 30 nm) possess ferromagnetic-paramagnetic transition temperature (T-c) of 300 K, nearly 50 K higher than that of a single crystal. The Rietveld analysis of the powder x-ray diffraction data of the nanopowders reveals significant lattice contraction and reduction in unit cell anisotropy-these structural changes are correlated to the enhancement in T-c.

Complete Pick positivity and unitary invariance

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S) (z, w) = (1 - z (w) over tilde)(-1) for |z|, |w| < 1, by means of (1/k(S))(T,T*) >= 0, we consider an arbitrary open connected domain Omega in C-n, a complete Pick kernel k on Omega and a tuple T = (T-1, ..., T-n) of commuting bounded operators on a complex separable Hilbert space H such that (1/k)(T,T*) >= 0. For a complete Pick kernel the 1/k functional calculus makes sense in a beautiful way. It turns out that the model theory works very well and a characteristic function can be associated with T. Moreover, the characteristic function is then a complete unitary invariant for a suitable class of tuples T.

Non-contractible non-edges in 2-connected graphs

Any pair of non-adjacent vertices forms a non-edge in a graph. Contraction of a non-edge merges two non-adjacent vertices into a single vertex such that the edges incident on the non-adjacent vertices are now incident on the merged vertex. In this paper, we consider simple connected graphs, hence parallel edges are removed after contraction. The minimum number of nodes whose removal disconnects the graph is the connectivity of the graph. We say a graph is k-connected, if its connectivity is k. A non-edge in a k-connected graph is contractible if its contraction does not result in a graph of lower connectivity. Otherwise the non-edge is non-contractible. We focus our study on non-contractible non-edges in 2-connected graphs. We show that cycles are the only 2-connected graphs in which every non-edge is non-contractible. (C) 2010 Elsevier B.V. All rights reserved.

Synthesis, Reactivity, Structural Aspects, and Solution Dynamics of Cyclopalladated Compounds of N,N `,N `'-Tris(2-anisyl)guanidine

N,N',N `'-Tris(2-anisyl)guanidine, (ArNH)(2)C=NAr (Ar = 2-(MeO)C6H4), was cyclopallaclated with Pd(OC(O)R)(2) (R = Me, CF3) in toluene at 70 degrees C to afford palladacycles Pd{kappa(2)(C,N)-C6H3-(OMe)-3(NHC(NHAr)(=NAr))-2}(mu-OC(O)R)](2)(R = Me (1a) and CF3 (1b)) in 87% and 95% yield, respectively. Palladacycle 1a was subjected to a metathetical reaction with LiBr in aqueous ethanol at 78 degrees C to afford palladacycle Pd{kappa(2)(C,N)-C6H3(OMe)-3(NHC(NHAr)(=NAr))-2}(mu-Br)](2) (2) in 90% yield. Palladacycle 2 was subjected to a bridge-splitting reaction with Lewis bases in CH2Cl2 to afford the monomeric palladacycles Pd{kappa(2)(C,N)-C6H3(OMe)-3(NHC(NHAr)(=NAr))-2}Br(L)] (L = 2,6-Me2C5H3N (3a), 2,4-Me2C5H3N (3b), 3,5-Me2C5H3N (3c), XyNC (Xy = 2,6-Me2C6H3; 4a), (BuNC)-Bu-t (4b), and PPh3 (5)) in 87-95% yield. Palladacycle 2 upon reaction with 2 equiv of XyNC in CH2Cl2 afforded an unanticipated palladacycle, Pd{kappa(2)(C,N)-C(=NXy)(C6H3(OMe)-4)-2(N=C-(NH Ar)(2))-3} Br(CNXy)] (6) in 93% yield, and the driving force for the formation of 6 was ascribed to a ring contraction followed by amine-imine tautomerization. Palladacycles 1 a,b revealed a dimeric transoid in-in conformation with ``open book'' framework in the solid state. In solution, 1 a exhibited a fluxional behavior ascribed to the six-membered ``(C,N)Pd'' ring inversion and partly dissociates to the pincer type and kappa(2)-O,O'-OAc monomeric palladacycles by an anchimerically assisted acetate cleavage process as studied by variable-temperature H-1 NMR data. Palladacycles 3a,b revealed a unique trans configuration around the palladium with lutidine being placed trans to the Pd-C bond, whereas cis stereochemistry was observed between the Pd-C bond and the Lewis base in 4a (as determined by X-ray diffraction data) and 5 (as determined by P-31 and C-13 NMR data). The aforementioned stereochemical difference was explained by invoking relative hardness/softness of the donor atoms around the palladium center. In solution, palladacycles 3a-c exist as a mixture of two interconverting boat conformers via a planar intermediate without any bond breaking due to the six-membered ``(C,N)Pd'' ring inversion, whereas palladacycles 4a,b and 5 exist as a single isomer, as deduced from detailed H-1 NMR studies.

Symmetry Properties of the Large-Deviation Function of the Velocity of a Self-Propelled Polar Particle

A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.

Link Conditions for Simplifying Meshes with Embedded Structures

Interactive visualization applications benefit from simplification techniques that generate good-quality coarse meshes from high-resolution meshes that represent the domain. These meshes often contain interesting substructures, called embedded structures, and it is desirable to preserve the topology of the embedded structures during simplification, in addition to preserving the topology of the domain. This paper describes a proof that link conditions, proposed earlier, are sufficient to ensure that edge contractions preserve the topology of the embedded structures and the domain. Excluding two specific configurations, the link conditions are also shown to be necessary for topology preservation. Repeated application of edge contraction on an extended complex produces a coarser representation of the domain and the embedded structures. An extension of the quadric error metric is used to schedule edge contractions, resulting in a good-quality coarse mesh that closely approximates the input domain and the embedded structures.

Polymerization and Pressure-Induced Amorphization of C60 and C70

Scanning tunneling microscopy of solid films of C-60 and C-70 clearly demonstrate the occurrence of photochemical polymerization of these fullerenes in the solid state. X-ray diffraction studies show that such a polymerization is accompanied by contraction of the unit-cell volume in the case of C-60 and expansion in the case of C-70. This is also evidenced from the STM images. These observations help to understand the differences in the amorphization behavior of C-60 and C-70 under pressure. Amorphization of C-60 under pressure is irreversible because it is accompanied by polymerization associated with a contraction of the unit cell volume. Monte Carlo simulations show how pressure-induced polymerization is favored in C-60 because of proper orientation as well as the required proximity of the molecules. Amorphization of C-70, on the other hand, is reversible because C-70 is less compressible and polymerization is not favored under pressure.

A new strategy for the alpha-vinylation of ketones: Application to an enantioselective synthesis of sesquiterpene (+)-alpha-elemene

A new, simple and preparatively useful protocol for the construction of a-vinyl ketones, particularly those bearing a quaternary carbon centre, from the corresponding alkenes has been devised. Our four-step strategy consists of dichloroketene addition, base catalysed ring contraction to 'push-pull' cyclopropane esters, reduction and eliminative cyclopropane fragmentation to unravel the a-vinyl ketone moiety. The generality of this approach has been demonstrated with a few representative olefins and good regio- and stereocontrol has been observed. As an application of this methodology, an enantioselective synthesis of sesquiterpene hydrocarbon (+)-alpha-elemene (42) from R-(+)-limonene (43) has been accomplished.

Vasomodulatory effect of novel peroxovanadate compounds on rat aorta: Role of rho kinase and nitric oxide/cGMP pathway

The present study was undertaken to assess the role of reactive oxygen species (ROS) in rat aortic ring vasoreactivity and integrity by using various peroxovanadate (pV) compounds. All the pV compounds (1 nM-300 mu M) used in the present study exerted concentration-dependent contractions on endothelium intact rat aortic rings. All compounds with an exception of DPV-asparagine (DPV-asn) significantly altered vascular integrity as shown by diminished KCl responses. Phenylephrine (PE)-mediated contractions (3 nM-300 mu M) were unaltered in the presence of these compounds. Acetylcholine (Ach)-mediated relaxation in PE (1 mu M) pre-contracted rings was significantly reduced in presence of diperoxovanadate (DPV), poly (sodium styrene sulfonate-co-maleate)-pV (PSS-CoM-pV) and poly (sodium styrene 4-sulfonate)-pV (PSS-pV). However, no significant change in Ach-mediated responses was observed in the presence of poly (acrylate)-pV (PM-pV) and DPV-asn. DPV-asn was thus chosen to further elucidate mechanism involved in peroxide mediated modulation of vasoreactivity. DPV-asn (30 nM-300 mu M) exerted significantly more stable contractions, that was found to be catalase (100 U/ml) resistant in comparison with H(2)O(2) (30 nM-300 mu M) in endothelium intact aortic rings. These contractile responses were found to be dependent on extracellular Ca(2+) and were significantly inhibited in presence of ROS scavenger N-acetylcysteine (100 mu M). Intracellular calcium chelation by BAPTA-AM (10 mu M) had no significant effect on DPV-asn (30 nM-300 mu M) mediated contraction. Pretreatment of aortic rings by rho-kinase inhibitor Y-27632 (10 mu M) significantly inhibited DPV-asn-mediated vasoconstriction indicating role of voltage-dependent Ca(2+) influx and downstream activation of rho-kinase. The small initial relaxant effect obtained on addition of DPV-asn (30 nM-1 mu M) in PE (1 mu M) pre-contracted endothelium intact rings, was prevented in the presence of guanylate cyclase inhibitor, methylene blue (10 mu M) and/or nitric oxide synthase (NOS) inhibitor, L-NAME (100 mu M) suggesting involvement of nitric oxide and cGMP. DPV-asn, like H(2)O(2), exerted a response of vasoconstriction in normal arteries and vasodilation at low concentrations (30 nM-1 mu M) in PE-pre contracted rings with overlapping mechanisms. These findings suggest usefulness of DPV-asn having low toxicity, in exploring the peroxide-mediated effects on various vascular beds. The present study also convincingly demonstrates role of H(2)O(2) in the modulation of vasoreactivity by using stable peroxide DPV-asn and warrants future studies on peroxide mediated signaling from a newer perspective. (C) 2011 Published by Elsevier Ltd.

Low temperature crystallographic data on Kevlar 49 fibres

Using X-ray diffraction data, the behaviour of Kevlar 49 fibres at low temperatures, up to -100degreesC, has been analysed. During cooling, the basal plane of the monoclinic unit cell shrinks whereas the c- (unique, chain axis) length is not significantly affected. In contrast, in the return heating cycle to ambient temperature, the basal plane expands and contraction occurs along the chain direction. The unit cell registers a reduction in volume in both the cooling and heating cycles. Conspicuously, after a cycle of cooling and heating, the unit cell does not return to its initial volume. (C) 2003 Kluwer Academic Publishers.

Abstract Characteristic Function

The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel k(S)(z, w) = ( 1 - z(w)over bar)- 1 for |z|, |w| < 1, by means of (1/k(S))( T, T *) = 0, we consider an arbitrary open connected domain Omega in C(n), a kernel k on Omega so that 1/k is a polynomial and a tuple T = (T(1), T(2), ... , T(n)) of commuting bounded operators on a complex separable Hilbert spaceHsuch that (1/k)( T, T *) >= 0. Under some standard assumptions on k, it turns out that whether a characteristic function can be associated with T or not depends not only on T, but also on the kernel k. We give a necessary and sufficient condition. When this condition is satisfied, a functional model can be constructed. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples T.

Dilations of Gamma-contractions by solving operator equations

For a contraction P and a bounded commutant S of P. we seek a solution X of the operator equation S - S*P = (1 - P* P)(1/2) X (1 - P* P)(1/2) where X is a bounded operator on (Ran) over bar (1 - P* P)(1/2) with numerical radius of X being not greater than 1. A pair of bounded operators (S, P) which has the domain Gamma = {(z(1) + z(2), z(2)): vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar <= 1} subset of C-2 as a spectral set, is called a P-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a Gamma-contraction (S, P). This allows us to construct an explicit Gamma-isometric dilation of a Gamma-contraction (S, P). We prove the other way too, i.e., for a commuting pair (S, P) with parallel to P parallel to <= 1 and the spectral radius of S being not greater than 2, the existence of a solution to the above equation implies that (S, P) is a Gamma-contraction. We show that for a pure F-contraction (S, P), there is a bounded operator C with numerical radius not greater than 1, such that S = C + C* P. Any Gamma-isometry can be written in this form where P now is an isometry commuting with C and C. Any Gamma-unitary is of this form as well with P and C being commuting unitaries. Examples of Gamma-contractions on reproducing kernel Hilbert spaces and their Gamma-isometric dilations are discussed. (C) 2012 Elsevier Inc. All rights reserved.

Cobalt-doped ZnO nanowires on quartz: Synthesis by simple chemical method and characterization

The synthesis of cobalt-doped ZnO nanowires is achieved using a simple, metal salt decomposition growth technique. A sequence of drop casting on a quartz substrate held at 100 degrees C and annealing results in the growth of nanowires of average (modal) length similar to 200 nm and diameter of 15 +/- 4 nm and consequently an aspect ratio of similar to 13. A variation in the synthesis process, where the solution of mixed salts is deposited on the substrate at 25 degrees C, yields a grainy film structure which constitutes a useful comparator case. X-ray diffraction shows a preferred 0001] growth direction for the nanowires while a small unit cell volume contraction for Co-doped samples and data from Raman spectroscopy indicate incorporation of the Co dopant into the lattice; neither technique shows explicit evidence of cobalt oxides. Also the nanowire samples display excellent optical transmission across the entire visible range, as well as strong photoluminescence (exciton emission) in the near UV, centered at 3.25 eV. (C) 2012 Elsevier B.V. All rights reserved.