The Lovasz θ function, SVMs and finding large dense subgraphs

The Lovasz θ function of a graph, is a fundamental tool in combinatorial optimization and approximation algorithms. Computing θ involves solving a SDP and is extremely expensive even for moderately sized graphs. In this paper we establish that the Lovasz θ function is equivalent to a kernel learning problem related to one class SVM. This interesting connection opens up many opportunities bridging graph theoretic algorithms and machine learning. We show that there exist graphs, which we call SVM−θ graphs, on which the Lovasz θ function can be approximated well by a one-class SVM. This leads to a novel use of SVM techniques to solve algorithmic problems in large graphs e.g. identifying a planted clique of size Θ(n√) in a random graph G(n,12). A classic approach for this problem involves computing the θ function, however it is not scalable due to SDP computation. We show that the random graph with a planted clique is an example of SVM−θ graph, and as a consequence a SVM based approach easily identifies the clique in large graphs and is competitive with the state-of-the-art. Further, we introduce the notion of a ''common orthogonal labeling'' which extends the notion of a ''orthogonal labelling of a single graph (used in defining the θ function) to multiple graphs. The problem of finding the optimal common orthogonal labelling is cast as a Multiple Kernel Learning problem and is used to identify a large common dense region in multiple graphs. The proposed algorithm achieves an order of magnitude scalability compared to the state of the art.

Lovasz theta function, SVMs and Finding Dense Subgraphs

In this paper we establish that the Lovasz theta function on a graph can be restated as a kernel learning problem. We introduce the notion of SVM-theta graphs, on which Lovasz theta function can be approximated well by a Support vector machine (SVM). We show that Erdos-Renyi random G(n, p) graphs are SVM-theta graphs for log(4)n/n <= p < 1. Even if we embed a large clique of size Theta(root np/1-p) in a G(n, p) graph the resultant graph still remains a SVM-theta graph. This immediately suggests an SVM based algorithm for recovering a large planted clique in random graphs. Associated with the theta function is the notion of orthogonal labellings. We introduce common orthogonal labellings which extends the idea of orthogonal labellings to multiple graphs. This allows us to propose a Multiple Kernel learning (MKL) based solution which is capable of identifying a large common dense subgraph in multiple graphs. Both in the planted clique case and common subgraph detection problem the proposed solutions beat the state of the art by an order of magnitude.

Broadband wavelength-selective reflectance and selective polarization by a tip-bent vertically aligned multi-walled carbon nanotube forest

The tunable optical properties of the bulk structure of carbon nanotubes (CNT) were recently revealed as a perfect black body material, optically reflective mirror and solar absorber. The present study demonstrates an enhanced optical reflectance of up to similar to 15% over a broad wavelength range in the near infrared region followed by a mechanical modification of the surface of a bulk CNT structure, which can be accounted for due to the grating-like surface abnormalities. In response to the specific arrangement of the so-formed bent tips of the CNT, a selective reflectance is achieved and results in reflecting only a dominant component of the polarized ight, which has not been realized so far. Modulation of this selective-optical reflectance can be achieved by ontrolling the degree of tip bending of the nanotubes, thus opening up avenues for the construction of novel dynamic light polarizers and absorbers.

Dense network of O-H ... O and C-H ... O interactions in the solid state structure of n-pentyl-2-chloro-2-deoxy-alpha-D-manno-sept 3-uloside

Single crystal X-ray structural analysis of a septanoside, namely, n-pentyl-2-chloro-2-deoxy sept-3-uloside (1) provides many finer details of the molecular structure, in addition to its preferred twist-chair conformation, namely, (TC3,4)-T-5,6 conformation. Structural analysis reveals a dense network of O-H...O, C-H...O and van der Waals interactions that stabilize interdigitized, planar bi-layer structure of the crystal lattice. (C) 2014 Elsevier Ltd. All rights reserved.

Dense shallow granular flows

Simplified equations are derived for a granular flow in the `dense' limit where the volume fraction is close to that for dynamical arrest, and the `shallow' limit where the stream-wise length for flow development (L) is large compared with the cross-stream height (h). The mass and diameter of the particles are set equal to 1 in the analysis without loss of generality. In the dense limit, the equations are simplified by taking advantage of the power-law divergence of the pair distribution function chi proportional to (phi(ad) - phi)(-alpha), and a faster divergence of the derivativ rho(d chi/d rho) similar to (d chi/d phi), where rho and phi are the density and volume fraction, and phi(ad) is the volume fraction for arrested dynamics. When the height h is much larger than the conduction length, the energy equation reduces to an algebraic balance between the rates of production and dissipation of energy, and the stress is proportional to the square of the strain rate (Bagnold law). In the shallow limit, the stress reduces to a simplified Bagnold stress, where all components of the stress are proportional to (partial derivative u(x)/partial derivative y)(2), which is the cross-stream (y) derivative of the stream-wise (x) velocity. In the simplified equations for dense shallow flows, the inertial terms are neglected in the y momentum equation in the shallow limit because the are O(h/L) smaller than the divergence of the stress. The resulting model contains two equations, a mass conservation equations which reduces to a solenoidal condition on the velocity in the incompressible limit, and a stream-wise momentum equation which contains just one parameter B which is a combination of the Bagnold coefficients and their derivatives with respect to volume fraction. The leading-order dense shallow flow equations, as well as the first correction due to density variations, are analysed for two representative flows. The first is the development from a plug flow to a fully developed Bagnold profile for the flow down an inclined plane. The analysis shows that the flow development length is ((rho) over barh(3)/B) , where (rho) over bar is the mean density, and this length is numerically estimated from previous simulation results. The second example is the development of the boundary layer at the base of the flow when a plug flow (with a slip condition at the base) encounters a rough base, in the limit where the momentum boundary layer thickness is small compared with the flow height. Analytical solutions can be found only when the stream-wise velocity far from the surface varies as x(F), where x is the stream-wise distance from the start of the rough base and F is an exponent. The boundary layer thickness increases as (l(2)x)(1/3) for all values of F, where the length scale l = root 2B/(rho) over bar. The analysis reveals important differences between granular flows and the flows of Newtonian fluids. The Reynolds number (ratio of inertial and viscous terms) turns out to depend only on the layer height and Bagnold coefficients, and is independent of the flow velocity, because both the inertial terms in the conservation equations and the divergence of the stress depend on the square of the velocity/velocity gradients. The compressibility number (ratio of the variation in volume fraction and mean volume fraction) is independent of the flow velocity and layer height, and depends only on the volume fraction and Bagnold coefficients.

Deep searches for decametre-wavelength pulsed emission from radio-quiet gamma-ray pulsars

We report the results of extensive follow-up observations of the gamma-ray pulsar J1732-3131, which has recently been detected at decametre wavelengths, and the results of deep searches for the counterparts of nine other radio-quiet gamma-ray pulsars at 34 MHz, using the Gauribidanur radio telescope. No periodic signal from J1732-3131 could be detected above a detection threshold of 8 sigma, even with an effective integration time of more than 40 h. However, the average profile obtained by combining data from several epochs, at a dispersion measure of 15.44 pc cm(-3), is found to be consistent with that from the earlier detection of this pulsar at a confidence level of 99.2 per cent. We present this consistency between the two profiles as evidence that J1732-3131 is a faint radio pulsar with an average flux density of 200-400 mJy at 34 MHz. Despite the extremely bright sky background at such low frequencies, the detection sensitivity of our deep searches is generally comparable to that of higher frequency searches for these pulsars, when scaled using reasonable assumptions about the underlying pulsar spectrum. We provide details of our deep searches, and put stringent upper limits on the decametre-wavelength flux densities of several radio-quiet gamma-ray pulsars.

Soft-spring wall based non-periodic boundary conditions for non-equilibrium molecular dynamics of dense fluids

Non-equilibrium molecular dynamics (MD) simulations require imposition of non-periodic boundary conditions (NPBCs) that seamlessly account for the effect of the truncated bulk region on the simulated MD region. Standard implementation of specular boundary conditions in such simulations results in spurious density and force fluctuations near the domain boundary and is therefore inappropriate for coupled atomistic-continuum calculations. In this work, we present a novel NPBC model that relies on boundary atoms attached to a simple cubic lattice with soft springs to account for interactions from particles which would have been present in an untruncated full domain treatment. We show that the proposed model suppresses the unphysical fluctuations in the density to less than 1% of the mean while simultaneously eliminating spurious oscillations in both mean and boundary forces. The model allows for an effective coupling of atomistic and continuum solvers as demonstrated through multiscale simulation of boundary driven singular flow in a cavity. The geometric flexibility of the model enables straightforward extension to nonplanar complex domains without any adverse effects on dynamic properties such as the diffusion coefficient. (c) 2015 AIP Publishing LLC.

Highly Dense ZnO Nanowires Grown on Graphene Foam for Ultraviolet Photodetection

Growth of highly dense ZnO nanowires (ZnO NWs) is demonstrated on three-dimensional graphene foam (GF) using resistive thermal evaporation technique. Photoresponse of the as-grown hybrid structure of ZnO NWs on GF (ZnO NWs/GF) is evaluated for ultraviolet (UV) detection. Excellent photoresponse with fast response and recovery times of 9.5 and 38 s with external quantum efficiency of 2490.8% is demonstrated at low illumination power density of 1.3 mW/cm(2). In addition, due to excellent charge carrier transport, mobility of graphene reduces the recombination rate of photogenerated charge carriers, hence the lifetime of photogenerated free charge carriers enhances in the photodetectors.

Study on effect of optical wavelength on photo induced strain sensitivity in carbon nanotubes using fiber Bragg grating

In this work, the role of optical wavelength on the photo induced strain in carbon nanotubes (CNT) is probed using a Fiber Bragg Grating (FBG), upon exposure to infrared (IR) (21 mu epsilon mW(-1)) and visible (9 mu epsilon mW(-1)) radiations. The strain sensitivity in CNT is monitored over a smaller range (10(-3) to 10(-9) epsilon) by exposing to a low optical power varying in the range 10(-3) to 10(-6) W. In addition, the wavelength dependent response and recovery periods of CNT under IR (tau(rise) = 150 ms, tau(fall) = 280 ms) and visible (tau(rise) = 1.07 s, tau(fall) = 1.18 s) radiations are evaluated in detail. This study can be further extended to measure the sensitivity of nano-scale photo induced strains in nano materials and opens avenues to control mechanical actuation using various optical wavelengths.

Kinematic flow patterns in slow deformation of a dense granular material

The kinematic flow pattern in slow deformation of a model dense granular medium is studied at high resolution using in situ imaging, coupled with particle tracking. The deformation configuration is indentation by a flat punch under macroscopic plane-strain conditions. Using a general analysis method, velocity gradients and deformation fields are obtained from the disordered grain arrangement, enabling flow characteristics to be quantified. The key observations are the formation of a stagnation zone, as in dilute granular flow past obstacles; occurrence of vortices in the flow immediately underneath the punch; and formation of distinct shear bands adjoining the stagnation zone. The transient and steady state stagnation zone geometry, as well as the strength of the vortices and strain rates in the shear bands, are obtained from the experimental data. All of these results are well-reproduced in exact-scale non-smooth contact dynamics simulations. Full 3D numerical particle positions from the simulations allow extraction of flow features that are extremely difficult to obtain from experiments. Three examples of these, namely material free surface evolution, deformation of a grain column below the punch and resolution of velocities inside the primary shear band, are highlighted. The variety of flow features observed in this model problem also illustrates the difficulty involved in formulating a complete micromechanical analytical description of the deformation.

Complex patterns arise through spontaneous symmetry breaking in dense homogeneous networks of neural oscillators

There has been much interest in understanding collective dynamics in networks of brain regions due to their role in behavior and cognitive function. Here we show that a simple, homogeneous system of densely connected oscillators, representing the aggregate activity of local brain regions, can exhibit a rich variety of dynamical patterns emerging via spontaneous breaking of permutation or translational symmetries. Upon removing just a few connections, we observe a striking departure from the mean-field limit in terms of the collective dynamics, which implies that the sparsity of these networks may have very important consequences. Our results suggest that the origins of some of the complicated activity patterns seen in the brain may be understood even with simple connection topologies.