Efficient algorithms for computing Reeb graphs

The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. We describe an algorithm that constructs the Reeb graph of a Morse function defined on a 3-manifold. Our algorithm maintains connected components of the two dimensional levels sets as a dynamic graph and constructs the Reeb graph in O(nlogn+nlogg(loglogg)3) time, where n is the number of triangles in the tetrahedral mesh representing the 3-manifold and g is the maximum genus over all level sets of the function. We extend this algorithm to construct Reeb graphs of d-manifolds in O(nlogn(loglogn)3) time, where n is the number of triangles in the simplicial complex that represents the d-manifold. Our result is a significant improvement over the previously known O(n2) algorithm. Finally, we present experimental results of our implementation and demonstrate that our algorithm for 3-manifolds performs efficiently in practice.

Experimental and numerical investigation of jet injection in a wall bounded supersonic flow

Numerical and experimental studies of a supersonic jet (Helium) inclined at 45 degrees to a oncoming Mach 2 flow have been carried out. The numerical study has been used to arrive at a geometry that could reduce an oncoming Mach 5.75 flow to Mach 2 flow and in determining the jet parameters. Experiments are carried out in the IISc. hypersonic shock tunnel HST2 at similar conditions obtained from numerical studies. Flow visualization studies carried out using Schlieren technique clearly show the presence of the bow shock in front of the jet exposed to supersonic cross flow. The jet Mach number is experimentally found to be approximate to 3. Visual observations show that the jet has penetrated up to 60% of the total height of the chamber.

Design of a synchronous decade down counter

Digital positioning systems often require a down counter for their operation. Due to the necessity of particular logic sequences and control of individual terminals, the design of down counters for particular use is very essential. In this paper the design procedure and logic diagram for a synchronous decade down counter with parallel carry are presented.

The Crystal and Molecular Structure of 4-Aza-5-oxo-tricyclo[4.4.0.03,8]decane (Aza-twistanone)

Die kristalline Struktur von Aza-twistanon wurde durch eine Röntgenstruktur-analyse untersucht. Die Kristalle gehören zur monoklinen Raumgruppe P21/n mit den Zelldimensionen a = 6,662(6), b = 13,36(2), c = 8,606(9) Å, = 98,97(2)°, V = 757 Å3, Z = 4. Die Struktur wurde mit Direktmethoden gelöst und bis zu R = 0,035 verfeinert (mittlere (c) = 0,003 Å3).Die cis-Amidgruppe ist relativ stark deformiert und hat einen Torsionswinkel C -C -N-C von 14,5(4)° (Deformation aus der Ebene c = 5,0(5)° und N = 13,5(4,0)°). Die gegenüberliegende äthylenbrücke weist einen Torsionswinkel von 25,1(5)° auf. Die entsprechenden Winkel in Twistan betragen je 20°. Das tricyclische Gerüst von Aza-twistanon hat approximative.

The Crystal and Molecular Structure of l-(Diphenylmethyl)azetidin-3-ol

1-(Diphenylmethyl)azetidin-3-ol is triclinic, space group P1, with a=8.479(2), b=17.294(4),c = 10.606 (3) A, a = 118.59 (2),/~ = 100.30 (2), y = 89.63 (2) °, Z = 4. The structure was solved by multisolution methods and refined to an R of 0.044 for 2755 reflexions. The four-membered rings in the two independent molecules are puckered with dihedral angles of 156 and 153 ° . The two molecules differ in conformation with respect to rotation of the phenyl rings about the C-C bonds. The structure is stabilized by a network of O-H. • • N intermolecular hydrogen bonds.

DockYard-a repository to assist modeling of protein-protein docking

In the absence of interlogs, building docking models is a time intensive task, involving generation of a large pool of docking decoys followed by refinement and screening to identify near native docking solutions. This limits the researcher interested in building docking methods with the choice of benchmarking only a limited number of protein complexes. We have created a repository called dockYard (http://pallab.serc.iisc.ernet.in/dockYard), that allows modelers interested in protein-protein interaction to access large volume of information on protein dimers and their interlogs, and also download decoys for their work if they are interested in building modeling methods. dockYard currently offers four categories of docking decoys derived from: Bound (native dimer co-crystallized), Unbound (individual subunits are crystallized, as well as the target dimer), Variants (match the previous two categories in at least one subunit with 100% sequence identity), and Interlogs (match the previous categories in at least one subunit with >= 90% or >= 50% sequence identity). The web service offers options for full or selective download based on search parameters. Our portal also serves as a repository to modelers who may want to share their decoy sets with the community.

Oxide nanotubes prepared using carbon nanotubes as templates

Hollow nanotubes of SiO2, Al2O3, V2O5, and MoO3 have been prepared using carbon nanotubes as templates. The procedure involves coating the carbon nanotubes with tetraethylorthosilicate, aluminum isopropoxide, or vanadium pentoxide gel, followed by calcination and heating at higher temperatures in air to oxidize the carbon. SiO2 nanotubes containing transition metal ions have been prepared by this procedure since such materials may be of use in catalysis.

N-3-benzoyl-2 ',3 '-di-O-benzoyluridine

The structure of N-3-benzoyl-2',3'-di-O-benzoyluridine, C30H24N2O9, has two molecules in the asymmetric unit. The uracil bases of both the molecules are in the anti conformation with respect to the ribose moiety and the furanosyl rings adopt a C3'-endo conformation. The orientation about the C4'-C5' bond is gauche-gauche. The two crystallographically independent molecules are linked through several C-H ... O hydrogen bonds. The nucleoside molecules pack as columns along the a axis and these columns repeat along the c axis.

Scaling analysis of momentum, heat, and mass transfer in binary alloy solidification problems

A systematic approach is developed for scaling analysis of momentum, heat and species conservation equations pertaining to the case of solidification of a binary mixture. The problem formulation and description of boundary conditions are kept fairly general, so that a large class of problems can be addressed. Analysis of the momentum equations coupled with phase change considerations leads to the establishment of an advection velocity scale. Analysis of the energy equation leads to an estimation of the solid layer thickness. Different regimes corresponding to different dominant modes of transport are simultaneously identified. A comparative study involving several cases of possible thermal boundary conditions is also performed. Finally, a scaling analysis of the species conservation equation is carried out, revealing the effect of a non-equilibrium solidification model on solute segregation and species distribution. It is shown that non-equilibrium effects result in an enhanced macrosegregation compared with the case of an equilibrium model. For the sake of assessment of the scaling analysis, the predictions are validated against corresponding computational results.

On concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle pa, a ? (1, 2], at infinity. In this paper, we show that every such function is close-to-convex of order (a - 1) and is included in the set of univalent functions of bounded boundary rotation. Many interesting consequences of this result are obtained. We also determine the extreme points of the set of concave functions with respect to the linear structure of the Hornich space.

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.

Network properties of protein-decoy structures

Convergence of the vast sequence space of proteins into a highly restricted fold/conformational space suggests a simple yet unique underlying mechanism of protein folding that has been the subject of much debate in the last several decades. One of the major challenges related to the understanding of protein folding or in silico protein structure prediction is the discrimination of non-native structures/decoys from the native structure. Applications of knowledge-based potentials to attain this goal have been extensively reported in the literature. Also, scoring functions based on accessible surface area and amino acid neighbourhood considerations were used in discriminating the decoys from native structures. In this article, we have explored the potential of protein structure network (PSN) parameters to validate the native proteins against a large number of decoy structures generated by diverse methods. We are guided by two principles: (a) the PSNs capture the local properties from a global perspective and (b) inclusion of non-covalent interactions, at all-atom level, including the side-chain atoms, in the network construction accommodates the sequence dependent features. Several network parameters such as the size of the largest cluster, community size, clustering coefficient are evaluated and scored on the basis of the rank of the native structures and the Z-scores. The network analysis of decoy structures highlights the importance of the global properties contributing to the uniqueness of native structures. The analysis also exhibits that the network parameters can be used as metrics to identify the native structures and filter out non-native structures/decoys in a large number of data-sets; thus also has a potential to be used in the protein `structure prediction' problem.