Efficient Methods for Robust Classification Under Uncertainty in Kernel Matrices

In this paper we study the problem of designing SVM classifiers when the kernel matrix, K, is affected by uncertainty. Specifically K is modeled as a positive affine combination of given positive semi definite kernels, with the coefficients ranging in a norm-bounded uncertainty set. We treat the problem using the Robust Optimization methodology. This reduces the uncertain SVM problem into a deterministic conic quadratic problem which can be solved in principle by a polynomial time Interior Point (IP) algorithm. However, for large-scale classification problems, IP methods become intractable and one has to resort to first-order gradient type methods. The strategy we use here is to reformulate the robust counterpart of the uncertain SVM problem as a saddle point problem and employ a special gradient scheme which works directly on the convex-concave saddle function. The algorithm is a simplified version of a general scheme due to Juditski and Nemirovski (2011). It achieves an O(1/T-2) reduction of the initial error after T iterations. A comprehensive empirical study on both synthetic data and real-world protein structure data sets show that the proposed formulations achieve the desired robustness, and the saddle point based algorithm outperforms the IP method significantly.

Cubicity, degeneracy, and crossing number

A $k$-box $B=(R_1,...,R_k)$, where each $R_i$ is a closed interval on the real line, is defined to be the Cartesian product $R_1\times R_2\times ...\times R_k$. If each $R_i$ is a unit length interval, we call $B$ a $k$-cube. Boxicity of a graph $G$, denoted as $\boxi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-boxes. Similarly, the cubicity of $G$, denoted as $\cubi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-cubes. It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan: Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/ 0607092, 2006.] that, for a graph $G$ with maximum degree $\Delta$, $\cubi(G)\leq \lceil 4(\Delta +1)\log n\rceil$. In this paper, we show that, for a $k$-degenerate graph $G$, $\cubi(G) \leq (k+2) \lceil 2e \log n \rceil$. Since $k$ is at most $\Delta$ and can be much lower, this clearly is a stronger result. This bound is tight. We also give an efficient deterministic algorithm that runs in $O(n^2k)$ time to output a $8k(\lceil 2.42 \log n\rceil + 1)$ dimensional cube representation for $G$. An important consequence of the above result is that if the crossing number of a graph $G$ is $t$, then $\boxi(G)$ is $O(t^{1/4}{\lceil\log t\rceil}^{3/4})$ . This bound is tight up to a factor of $O((\log t)^{1/4})$. We also show that, if $G$ has $n$ vertices, then $\cubi(G)$ is $O(\log n + t^{1/4}\log t)$. Using our bound for the cubicity of $k$-degenerate graphs we show that cubicity of almost all graphs in $\mathcal{G}(n,m)$ model is $O(d_{av}\log n)$, where $d_{av}$ denotes the average degree of the graph under consideration. model is O(davlogn).

Photocatalytic degradation with combustion synthesized WO3 and WO3-TiO2 mixed oxides under UV and visible light

The photocatalytic activity of commercial titanium dioxide under UV and visible radiation was improved by composites of tungsten trioxide (WO3) with TiO2. WO3 was prepared by solution combustion synthesis and the mixed oxides/composites of WO3-TiO2 were prepared in different weight ratios (0, 0.10, 0.15, 0.20, 0.25, 0.50, 0.75, and 1) by physical mixing. These catalysts were characterized by XRD, DRS, BET, SEM, TEM, pH drift method, TGA and photoluminescence. The photocatalytic activity varies with the WO3 loading in the composites. The optimum loading of WO3 in the composites was found to be 15 wt% for both UV and visible radiation. This loading showed faster dye degradation rate than commercial TiO2 (TiO2-C) and WO3 (WO3-C). The effect of initial concentrations of methylene blue (MB) and orange G (OG) and the effect of the functional group on dye degradation was studied with both anionic and cationic dyes with 15 wt% WO3-TiO2. (C) 2012 Elsevier B.V. All rights reserved.

Error exponent analysis of energy-based bayesian spectrum sensing under fading channels

This paper analyzes the error exponents in Bayesian decentralized spectrum sensing, i.e., the detection of occupancy of the primary spectrum by a cognitive radio, with probability of error as the performance metric. At the individual sensors, the error exponents of a Central Limit Theorem (CLT) based detection scheme are analyzed. At the fusion center, a K-out-of-N rule is employed to arrive at the overall decision. It is shown that, in the presence of fading, for a fixed number of sensors, the error exponents with respect to the number of observations at both the individual sensors as well as at the fusion center are zero. This motivates the development of the error exponent with a certain probability as a novel metric that can be used to compare different detection schemes in the presence of fading. The metric is useful, for example, in answering the question of whether to sense for a pilot tone in a narrow band (and suffer Rayleigh fading) or to sense the entire wide-band signal (and suffer log-normal shadowing), in terms of the error exponent performance. The error exponents with a certain probability at both the individual sensors and at the fusion center are derived, with both Rayleigh as well as log-normal shadow fading. Numerical results are used to illustrate and provide a visual feel for the theoretical expressions obtained.

Information dissemination in socially aware networks under the linear threshold model

We provide new analytical results concerning the spread of information or influence under the linear threshold social network model introduced by Kempe et al. in, in the information dissemination context. The seeder starts by providing the message to a set of initial nodes and is interested in maximizing the number of nodes that will receive the message ultimately. A node's decision to forward the message depends on the set of nodes from which it has received the message. Under the linear threshold model, the decision to forward the information depends on the comparison of the total influence of the nodes from which a node has received the packet with its own threshold of influence. We derive analytical expressions for the expected number of nodes that receive the message ultimately, as a function of the initial set of nodes, for a generic network. We show that the problem can be recast in the framework of Markov chains. We then use the analytical expression to gain insights into information dissemination in some simple network topologies such as the star, ring, mesh and on acyclic graphs. We also derive the optimal initial set in the above networks, and also hint at general heuristics for picking a good initial set.

Fowler-Nordheim Field Emission from Carbon Nanotubes Under Intense Electric Field

In this paper, we study the Fowler-Nordheim field emission (FNFE) from carbon nanotubes on the basis of a newly formulated electron dispersion law by considering the fact that the intense electric field needed for FNFE changes the band structure in a fundamental way. It has been found that the field emitted current increases with increasing electric field in oscillatory manner due to the appearance of van Hove singularities and exhibits spikes for particular values of the electric field where the singularity occurs. The numerical values of the field emitted current in all the cases vary widely and the determined by the chiral indices and the diameter in the respective cases. The results of this paper find three applications in the fields of nanoscience and technology.

Strain localization effect on system reliability based design of bridge abutments under earthquake loading

The component and system reliability based design of bridge abutments under earthquake loading is presented in the paper. Planar failure surface has been used in conjunction with pseudo-dynamic approach to compute seismic active earth pressures on an abutment. The pseudo-dynamic method, considers the effect of phase difference in shear waves, soil amplification along with the horizontal seismic accelerations, strain localization in backfill soil and associated post-peak reduction in the shear resistance from peak to residual values along a previously formed failure plane. Four modes of stability viz. sliding, overturning, eccentricity and bearing capacity of the foundation soil are considered in the analysis. The series system reliability is computed with an assumption of independent failure modes. The lower and upper bounds of system reliability are also computed by taking into account the correlations between four failure modes, which is evaluated using the direction cosines of the tangent planes at the most probable points of failure.

k.p based closed form energy band gap and transport electron effective mass model for 100] and 110] relaxed and strained Silicon nanowire

In this paper, we address a physics based closed form model for the energy band gap (E-g) and the transport electron effective mass in relaxed and strained 100] and 110] oriented rectangular Silicon Nanowire (SiNW). Our proposed analytical model along 100] and 110] directions are based on the k.p formalism of the conduction band energy dispersion relation through an appropriate rotation of the Hamiltonian of the electrons in the bulk crystal along 001] direction followed by the inclusion of a 4 x 4 Luttinger Hamiltonian for the description of the valance band structure. Using this, we demonstrate the variation in Eg and the transport electron effective mass as function of the cross-sectional dimensions in a relaxed 100] and 110] oriented SiNW. The behaviour of these two parameters in 100] oriented SiNW has further been studied with the inclusion of a uniaxial strain along the transport direction and a biaxial strain, which is assumed to be decomposed from a hydrostatic deformation along 001] with the former one. In addition, the energy band gap and the effective mass of a strained 110] oriented SiNW has also been formulated. Using this, we compare our analytical model with that of the extracted data using the nearest neighbour empirical tight binding sp(3)d(5)s* method based simulations and has been found to agree well over a wide range of device dimensions and applied strain. (C) 2012 Elsevier Ltd. All rights reserved.

Pseudo-Static and Pseudo-Dynamic Stability Analysis of Tailings Dam Under Seismic Conditions

In this paper the seismic slope stability analyses are performed for a typical section of 44 m high water retention type tailings earthen dam located in the eastern part of India, using both the conventional pseudo-static and recent pseudo-dynamic methods. The tailings earthen dam is analyzed for different upstream conditions of reservoir like filled up with compacted and non-compacted dumped waste materials with different water levels of the pond tailings portion. Phreatic surface is generated using seepage analysis in geotechnical software SEEP/W and that same is used in the pseudo-static and pseudo-dynamic analyses to make the approach more realistic. The minimum values of factor of safety using pseudo-static and pseudo-dynamic method are obtained as 1.18 and 1.09 respectively for the chosen seismic zone in India. These values of factor of safety show clearly the demerits of conventional pseudo-static analysis compared to recent pseudo-dynamic analysis, where in addition to the seismic accelerations, duration, frequency of earthquake, body waves traveling during earthquake and amplification effects are considered.

The Fracture Characteristics of a Near Eutectic Al-Si Based Alloy Under Compression

The fracture of eutectic Si particles dictates the fracture characteristics of Al-Si based cast alloys. The morphology of these particles is found to play an important role in fracture initiation. In the current study, the effects of strain rate, temperature, strain, and heat treatment on Si particle fracture under compression were investigated. Strain rates ranging from 3 x 10(-4)/s to 10(2)/s and three temperatures RT, 373 K, and 473 K (100 A degrees C and 200 A degrees C) are considered in this study. It is found that the Si particle fracture shows a small increase with increase in strain rate and decreases with increase in temperature at 10 pct strain. The flow stress at 10 pct strain exhibits the trend similar to particle fracture with strain rate and temperature. Particle fracture also increases with increase in strain. Large and elongated particles show a greater tendency for cracking. Most fracture occurs on particles oriented nearly perpendicular to the loading axis, and the cracks are found to occur almost parallel to the loading axis. At any strain rate, temperature, and strain, the Si particle fracture is greater for the heat-treated condition than for the non-heat-treated condition because of higher flow stress in the heat-treated condition. In addition to Si particle fracture, elongated Fe-rich intermetallic particles are also seen to fracture. These particles have specific crystallographic orientations and fracture along their major axis with the cleavage planes for their fracture being (100). Fracture of these particles might also play a role in the overall fracture behavior of this alloy since these particles cleave along their major axis leading to cracks longer than 200 mu m.

Surface Instabilities and Generation of Multielectron Bubbles Under Pulsed Electric Fields

We studied the development of surface instabilities leading to the generation of multielectron bubbles (MEBs) in superfluid helium upon the application of a pulsed electric field. We found the statistical distribution of the charge of individual instabilities to be strongly dependent on the duration of the electric field pulse. The rate and probability of generation of these instabilities in relation to the temporal characteristics of the applied field was also investigated.

Physics-Based Solution for Electrical Resistance of Graphene Under Self-Heating Effect

In this brief, we present a physics-based solution for the temperature-dependent electrical resistance of a suspended metallic single-layer graphene (SLG) sheet under Joule self-heating. The effect of in-plane and flexural phonons on the electron scattering rates for a doped SLG layer has been considered, which particularly demonstrates the variation of the electrical resistance with increasing temperature at different current levels using the solution of the self-heating equation. The present solution agrees well with the available experimental data done with back-gate electrostatic method over a wide range of temperatures.

Durability of Pt/C and Pt/MC-PEDOT catalysts under simulated start-stop cycles in polymer electrolyte fuel cells

A composite of mesoporous carbon (MC) with poly(3,4-ethylenedioxythiophene) (PEDOT) is studied as catalyst support for platinum nanoparticles. The durability of commercial Pt/carbon and Pt/MC-PEDOT as cathode catalyst is investigated by invoking air-fuel boundary at the anode side so as to foster carbon corrosion at the cathode side of a polymer electrolyte fuel cell (PEFC). Pt/MC-PEDOT shows higher resistance to carbon corrosion in relation to Pt/C. Electrochemical techniques such as cyclic voltammetry (CV) and impedance measurements are used to evaluate the extent of degradation in the catalyst layer. It is surmised that the resistance of MC-PEDOT as catalyst support toward electrochemical oxidation makes Pt/MC-PEDOT a suitable and stable cathode catalyst for PEFCs.

Noise tolerance under risk minimization

In this paper, we explore noise-tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an unobservable training set that is noise free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper, we analyze the noise-tolerance properties of risk minimization (under different loss functions). We show that risk minimization under 0-1 loss function has impressive noise-tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude this paper with some discussion on the implications of these theoretical results.

Analytical theory and stability analysis of an elongated nanoscale object under external torque

We consider the rotational motion of an elongated nanoscale object in a fluid under an external torque. The experimentally observed dynamics could be understood from analytical solutions of the Stokes equation, with explicit formulae derived for the dynamical states as a function of the object dimensions and the parameters defining the external torque. Under certain conditions, multiple analytical solutions to the Stokes equations exist, which have been investigated through numerical analysis of their stability against small perturbations and their sensitivity towards initial conditions. These experimental results and analytical formulae are general enough to be applicable to the rotational motion of any isolated elongated object at low Reynolds numbers, and could be useful in the design of non-spherical nanostructures for diverse applications pertaining to microfluidics and nanoscale propulsion technologies.