Fault-tolerant characteristics and topological properties of a hierarchical network of hypercubes

We analyse the fault-tolerant parameters and topological properties of a hierarchical network of hypercubes. We take a close look at the Extended Hypercube (EH) and the Hyperweave (HW) architectures and also compare them with other popular architectures. These two architectures have low diameter and constant degree of connectivity making it possible to expand these networks without affecting the existing configuration. A scheme for incrementally expanding this network is also presented. We also look at the performance of the ASCEND/DESCEND class of algorithms on these architectures.

Topological properties of the one dimensional exponential random geometric graph

In this article we study the one-dimensional random geometric (random interval) graph when the location of the nodes are independent and exponentially distributed. We derive exact results and limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008.

Topological analysis off charge density distribution in concomitant polymorphs of 3-acetylcoumarin, a case off packing polymorphism

Detailed investigation of the charge density distribution in concomitant polymorphs of 3-acetylcoumarin in terms of experimental and theoretical densities shows significant differences in the intermolecular features when analyzed based on the topological properties via the quantum theory of atoms in molecules. The two forms, triclinic and monoclinic (Form A and Form B), pack in the crystal lattice via weak C-H---O and C-H---pi interactions. Form A results in a head-to-head molecular stack, while Form B generates a head-to-tail stack. Form A crystallizes in PI (Z' = 2) and Form B crystallizes in P2(1)/n (Z = 1). The electron density maps of the polymorphs demonstrate the differences in the nature of the charge density distribution in general. The charges derived from experimental and theoretical analysis show significant differences with respect to the polymorphic forms. The molecular dipole moments differ significantly for the two forms. The lattice energies evaluated at the HF and DFT (B3LYP) methods with 6-31G** basis set for the two forms clearly suggest that Form A is the thermodynamically stable form as compared to Form B. Mapping of electrostatic potential over the molecular surface shows dominant variations in the electronegative region, which bring out the differences between the two forms.

Topological phases, Majorana modes and quench dynamics in a spin ladder system

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z(2) symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce and employ a new topological invariant for explicitly determining the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder and, in particular, the post-quench dynamics governed by tuning through a quantum critical point.

Intermolecular interactions, charge-density distribution and the electrostatic properties of pyrazinamide anti-TB drug molecule: an experimental and theoretical charge-density study

An experimental charge-density analysis of pyrazinamide (a first line antitubercular drug) was performed using high-resolution X-ray diffraction data (sin theta/lambda)(max) = 1.1 angstrom(-1)] measured at 100 (2) K. The structure was solved by direct methods using SHELXS97 and refined by SHELXL97. The total electron density of the pyrazinamide molecule was modeled using the Hansen-Coppens multipole formalism implemented in the XD software. The topological properties of electron density determined from the experiment were compared with the theoretical results obtained from CRYSTAL09 at the B3LYP/6-31G** level of theory. The crystal structure was stabilized by N-H center dot center dot center dot N and N-H center dot center dot center dot O hydrogen bonds, in which the N3-H3B center dot center dot center dot N1 and N3-H3A center dot center dot center dot O1 interactions form two types of dimers in the crystal. Hirshfeld surface analysis was carried out to analyze the intermolecular interactions. The fingerprint plot reveals that the N center dot center dot center dot H and O center dot center dot center dot H hydrogen-bonding interactions contribute 26.1 and 18.4%, respectively, of the total Hirshfeld surface. The lattice energy of the molecule was calculated using density functional theory (B3LYP) methods with the 6-31G** basis set. The molecular electrostatic potential of the pyrazinamide molecule exhibits extended electronegative regions around O1, N1 and N2. The existence of a negative electrostatic potential (ESP) region just above the upper and lower surfaces of the pyrazine ring confirm the pi-electron cloud.

A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background: A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data. Results: The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification. Conclusion: A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

Experimental and Theoretical Charge Density Analysis of Polymorphic Structures: The Case of Coumarin 314 Dye

Experimental charge density distributions in two known conformational polymorphs (orange and yellow) of coumarin 314 dye are analyzed based on multipole modeling of X-ray diffraction data collected at 100 K. The experimental results are compared with the charge densities derived from multipole modeling of theoretical structure factors obtained from periodic quantum calculation with density functional theory (DFT) method and B3LYP/6-31G(d,p) level of theory. The presence of disorder at the carbonyl oxygen atom of ethoxycarbonyl group in the yellow form, which was not identified earlier, is addressed here. The investigationof intermolecular interactions, based on Hirshfeld surface analysis and topological properties via quantum theory of atoms in molecule and total electrostatic interaction energies, revealed significant differences between the polymorphs. The differences of electrostatic nature in these two polymorphic forms were unveiled via construction of three-dimensional deformation electrostatic potential maps plotted over the molecular surfaces. The lattice energies evaluated from ab initio calculations on the two polymorphic forms indicate that the yellow form is likely to be the most favorable thermodynamically. The dipole moments derived from experimental and theoretical charge densities and also from Lorentz tensor approach are compared with the single-molecule dipole moments. In each case, the differences of dipole moments between the polymorphs are identified.

Evolving Random Geometric Graph Models for Mobile Wireless Networks

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.

Charge density distribution and electrostatic interactions of ethionamide: an inhibitor of the enoyl acyl carrier protein reductase (inhA) enzyme of Mycobacterium tuberculosis

An experimental charge density analysis of an anti-TB drug ethionamide was carried out from high resolution X-ray diffraction at 100 K to understand its charge density distribution and electrostatic properties. The experimental results were validated from periodic theoretical charge density calculations performed using CRYSTAL09 at the B3LYP/6-31G** level of theory. The electron density rho(bcp)(r) and the Laplacian of electron density del(2)(rho bcp)(r) of the molecule calculated from both the methods display the charge density distribution of the ethionamide molecule in the crystal field. The electrostatic potential map shows a large electropositive region around the pyridine ring and a large electronegative region at the vicinity of the thiol atom. The calculated experimental dipole moment is 10.6D, which is higher than the value calculated from theory (8.2D). The topological properties of C-H center dot center dot center dot S, N-H center dot center dot center dot N and N-H center dot center dot center dot S hydrogen bonds were calculated, revealing their strength. The charge density analysis of the ethionamide molecule determined from both the experiment and theory gives the topological and electrostatic properties of the molecule, which allows to precisely understand the nature of intra and intermolecular interactions.

An approximation to the QoS aware throughput region of a tree network under IEEE 802.15.4 CSMA/CA with application to wireless sensor network design

In the context of wireless sensor networks, we are motivated by the design of a tree network spanning a set of source nodes that generate packets, a set of additional relay nodes that only forward packets from the sources, and a data sink. We assume that the paths from the sources to the sink have bounded hop count, that the nodes use the IEEE 802.15.4 CSMA/CA for medium access control, and that there are no hidden terminals. In this setting, starting with a set of simple fixed point equations, we derive explicit conditions on the packet generation rates at the sources, so that the tree network approximately provides certain quality of service (QoS) such as end-to-end delivery probability and mean delay. The structures of our conditions provide insight on the dependence of the network performance on the arrival rate vector, and the topological properties of the tree network. Our numerical experiments suggest that our approximations are able to capture a significant part of the QoS aware throughput region (of a tree network), that is adequate for many sensor network applications. Furthermore, for the special case of equal arrival rates, default backoff parameters, and for a range of values of target QoS, we show that among all path-length-bounded trees (spanning a given set of sources and the data sink) that meet the conditions derived in the paper, a shortest path tree achieves the maximum throughput. (C) 2015 Elsevier B.V. All rights reserved.

Topological electron density analysis and electrostatic properties of aspirin: an experimental and theoretical study

The topological and the electrostatic properties of the aspirin drug molecule were determined from high-resolution X-ray diffraction data at 90 K, and the corresponding results are compared with the theoretical calculations. The electron density at the bond critical point of all chemical bonds induding the intermolecular interactions of aspirin has been quantitatively described using Bader's quantum theory of ``Atoms in Molecules''. The electrostatic potential of the molecule emphasizes the preferable binding sites of the drug and the interaction features of the molecule, which are crucial for drug-receptor recognition. The topological analysis of hydrogen bonds reveals the strength of intermolecular interactions.

Topological analysis of electron density and the electrostatic properties of isoniazid: an experimental and theoretical study

Isoniazid (isonicotinohydrazide) is an important first-line antitubercular drug that targets the InhA enzyme which synthesizes the critical component of the mycobacterial cell wall. An experimental charge-density analysis of isoniazid has been performed to understand its structural and electronic properties in the solid state. A high-resolution single-crystal X-ray intensity data has been collected at 90 K. An aspherical multipole refinement was carried out to explore the topological and electrostatic properties of the isoniazid molecule. The experimental results were compared with the theoretical charge-density calculations performed using CRYSTAL09 with the B3LYP/6-31G** method. A topological analysis of the electron density reveals that the Laplacian of electron density of the N-N bond is significantly less negative, which indicates that the charges at the b.c.p. (bond-critical point) of the bond are least accumulated, and so the bond is considered to be weak. As expected, a strong negative electrostatic potential region is present in the vicinity of the O1, N1 and N3 atoms, which are the reactive locations of the molecule. The C-H center dot center dot center dot N, C-H center dot center dot center dot O and N-H center dot center dot center dot N types of intermolecular hydrogen-bonding interactions stabilize the crystal structure. The topological analysis of the electron density on hydrogen bonding shows the strength of intermolecular interactions.

Tailoring of Electronic Structure and Thermoelectric Properties of a Topological Crystalline Insulator by Chemical Doping

Topological crystalline insulators (TCIs) are a new quantum state of matter in which linearly dispersed metallic surface states are protected by crystal mirror symmetry. Owing to its vanishingly small bulk band gap, a TCI like Pb0.6Sn0.4Te has poor thermoelectric properties. Breaking of crystal symmetry can widen the band gap of TCI. While breaking of mirror symmetry in a TCI has been mostly explored by various physical perturbation techniques, chemical doping, which may also alter the electronic structure of TCI by perturbing the local mirror symmetry, has not yet been explored. Herein, we demonstrate that Na doping in Pb0.6Sn0.4Te locally breaks the crystal symmetry and opens up a bulk electronic band gap, which is confirmed by direct electronic absorption spectroscopy and electronic structure calculations. Na doping in Pb0.6Sn0.4Te increases p-type carrier concentration and suppresses the bipolar conduction (by widening the band gap), which collectively gives rise to a promising zT of 1 at 856 K for Pb0.58Sn0.40Na0.02Te. Breaking of crystal symmetry by chemical doping widens the bulk band gap in TCI, which uncovers a route to improve TCI for thermoelectric applications.

Tuning the Conductance of Dirac Fermions on the Surface of a Topological Insulator

We study the transport properties of the Dirac fermions with a Fermi velocity v(F) on the surface of a topological insulator across a ferromagnetic strip providing an exchange field J over a region of width d. We show that the conductance of such a junction, in the clean limit and at low temperature, changes from oscillatory to a monotonically decreasing function of d beyond a critical J. This leads to the possible realization of a magnetic switch using these junctions. We also study the conductance of these Dirac fermions across a potential barrier of width d and potential V-0 in the presence of such a ferromagnetic strip and show that beyond a critical J, the criteria of conductance maxima changes from chi = eV(0)d/(h) over barv(F) = n pi to chi = (n + 1/2)pi for integer n. We point out that these novel phenomena have no analogs in graphene and suggest experiments which can probe them.

Synthesis, structure, transformation studies and catalytic properties of open-framework cadmium thiosulfate compounds

Five new thiosulfate based inorganic-organic hybrid open-framework compounds have been synthesized employing mild reaction conditions. Of the five compounds, [Na-2(H2O)(8)][Cd(C10H8N2)( S2O3)(2)]center dot 2H(2)O, I and [Cd-2(C10H8N2)(2)(HS2O3)(2)(S2O3)(2)][(C10H9N2)(2)(C10H8N2)(2)]center dot 8H(2)O, II have one-dimensional (1D) structures and [Cd(C10H8N2)(H2O)(2)(S2O3)]center dot 2H(2)O, III, [Cd-2(C10H8N2)(3)(S2O3)(2)], IV and [Cd-2(C10H8N2)(2.5)(S2O3)(2)], V have three- dimensional (3D) structures. The 1D structures are somewhat related, formed by the bonding between tetrahedral Cd centers (CdN2S2) and 4,4'-bipyridine (bpy) units. The inter-chain spaces are occupied by the hanging thiosulfate units in both the cases along with Na(H2O)(6) chains in I and free bpy units in II. The three 3D structures have one-dimensional cadmium thiosulfate chains linked by bpy units. Interpenetration has been observed in all the 3D structures. The 3D structures appear to be related and can be derived from fgs net. Transformation studies on the 1D compound, [Na-2(H2O)(8)][Cd(C10H8N2)(S2O3)(2)]center dot 2H(2)O, I, indicated a facile formation of [Cd(C10H8N2)(H2O)(2)(S2O3)]center dot 2H(2)O, III. Prolonged heating of I gave rise to a 3D cadmium sulfate phase, [Cd-2(C10H8N2)(2)(H2O)(3)(SO4)(2)]center dot 2H(2)O, VI. Compound VI has one-dimensional cadmium sulfate chains formed by six-membered rings connected by bpy units to form a 3D structure, which appears to resemble the topological arrangement of III. Transformation studies of III indicates the formation of IV and V, and at a higher temperature a new 3D cadmium sulfate, [Cd(C10H8N2)(SO4)], VII. Compound VII has a 4 x 4 grid cadmium sulfate layers pillared by bpy units. All the compounds were characterized by PXRD, TGA, IR and UV-visible studies. Preliminary studies on the possible use of the 3D compounds (III-VII) in heterogeneous cyanosilylation of imines appear to be promising.