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.

UNIQUENESS OF SOLUTIONS TO SCHRODINGER EQUATIONS ON H-TYPE GROUPS

This paper deals with the Schrodinger equation i partial derivative(s)u(z, t; s) - Lu(z, t; s) = 0; where L is the sub-Laplacian on the Heisenberg group. Assume that the initial data f satisfies vertical bar f(z, t)vertical bar less than or similar to q(alpha)(z, t), where q(s) is the heat kernel associated to L. If in addition vertical bar u(z, t; s(0))vertical bar less than or similar to q(beta)(z, t), for some s(0) is an element of R \textbackslash {0}, then we prove that u(z, t; s) = 0 for all s is an element of R whenever alpha beta < s(0)(2). This result holds true in the more general context of H-type groups. We also prove an analogous result for the Grushin operator on Rn+1.

Smoothed Functional Algorithms for Stochastic Optimization Using q-Gaussian Distributions

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, especially when the objective is to improve the performance of a stochastic system However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in the literature, which include Gaussian, Cauchy, and uniform distributions, among others. This article studies a new class of kernels based on the q-Gaussian distribution, which has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with a projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also demonstrate their performance numerically through simulations on a queuing model.

An improved free surface modeling for incompressible SPH

In Incompressible Smooth Particle Hydrodynamics (ISPH), a pressure Poisson equation (PPE) is solved to obtain a divergence free velocity field. When free surfaces are simulated using this method a Dirichlet boundary condition for pressure at the free surface has to be applied. In existing ISPH methods this is achieved by identifying free surface particles using heuristically chosen threshold of a parameter such as kernel sum, density or divergence of the position, and explicitly setting their pressure values. This often leads to clumping of particles near the free surface and spraying off of surface particles during splashes. Moreover, surface pressure gradients in flows where surface tension is important are not captured well using this approach. We propose a more accurate semi-analytical approach to impose Dirichlet boundary conditions on the free surface. We show the efficacy of the proposed algorithm by using test cases of elongation of a droplet and dam break. We perform two dimensional simulations of water entry and validate the proposed algorithm with experimental results. Further, a three dimensional simulation of droplet splash is shown to compare well with the Volume-of-Fluid simulations. (C) 2014 Elsevier Ltd. All rights reserved.

UNO Gets Easier for a Single Player

This work is a follow up to 2, FUN 2010], which initiated a detailed analysis of the popular game of UNO (R). We consider the solitaire version of the game, which was shown to be NP-complete. In 2], the authors also demonstrate a (O)(n)(c(2)) algorithm, where c is the number of colors across all the cards, which implies, in particular that the problem is polynomial time when the number of colors is a constant. In this work, we propose a kernelization algorithm, a consequence of which is that the problem is fixed-parameter tractable when the number of colors is treated as a parameter. This removes the exponential dependence on c and answers the question stated in 2] in the affirmative. We also introduce a natural and possibly more challenging version of UNO that we call ``All Or None UNO''. For this variant, we prove that even the single-player version is NP-complete, and we show a single-exponential FPT algorithm, along with a cubic kernel.

On the Parameterized Complexity of the Maximum Edge 2-Coloring Problem

We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q >= 2 and a graph G, the goal is to find a coloring of the edges of G with the maximum number of colors such that every vertex of the graph sees at most q colors. This problem is NP-hard for q >= 2, and has been well-studied from the point of view of approximation. Our main focus is the case when q = 2, which is already theoretically intricate and practically relevant. We show fixed-parameter tractable algorithms for both the standard and the dual parameter, and for the latter problem, the result is based on a linear vertex kernel.

Parameterized Algorithms for MAX COLORABLE INDUCED SUBGRAPH Problem on Perfect Graphs

We address the parameterized complexity ofMaxColorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis and Gavril IPL 1987] showed that this problem is NP-complete even on split graphs if q is part of input, but gave a n(O(q)) algorithm on chordal graphs. We first observe that the problem is W2]-hard parameterized by q, even on split graphs. However, when parameterized by l, the number of vertices in the solution, we give two fixed-parameter tractable algorithms. The first algorithm runs in time 5.44(l) (n+#alpha(G))(O(1)) where #alpha(G) is the number of maximal independent sets of the input graph. The second algorithm runs in time q(l+o()l())n(O(1))T(alpha) where T-alpha is the time required to find a maximum independent set in any induced subgraph of G. The first algorithm is efficient when the input graph contains only polynomially many maximal independent sets; for example split graphs and co-chordal graphs. The running time of the second algorithm is FPT in l alone (whenever T-alpha is a polynomial in n), since q <= l for all non-trivial situations. Finally, we show that (under standard complexitytheoretic assumptions) the problem does not admit a polynomial kernel on split and perfect graphs in the following sense: (a) On split graphs, we do not expect a polynomial kernel if q is a part of the input. (b) On perfect graphs, we do not expect a polynomial kernel even for fixed values of q >= 2.

Logarithmic corrections to extremal black hole entropy in N=2, 4 and 8 supergravity

We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter-BPS black holes in N = 4 supergravity and one-eighth BPS black holes in N = 8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half-BPS black holes in N = 2 supergravity depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the results we had previously obtained for heat kernel coefficients on Z(N) orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to an expression involving the Harish-Chandra character of sl (2, R), a result which is of possible mathematical interest.

A meshless adaptive multiscale method for fracture

The paper presents a multiscale method for crack propagation. The coarse region is modelled by the differential reproducing kernel particle method. Fracture in the coarse scale region is modelled with the Phantom node method. A molecular statics approach is employed in the fine scale where crack propagation is modelled naturally by breaking of bonds. The triangular lattice corresponds to the lattice structure of the (111) plane of an FCC crystal in the fine scale region. The Lennard-Jones potential is used to model the atom-atom interactions. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively refined and coarsened as the crack propagates. The centro symmetry parameter is used to detect the crack tip location. The method is implemented in two dimensions. The results are compared to pure atomistic simulations and show excellent agreement. (C) 2014 Elsevier B. V. All rights reserved.

AN OPTIMUM SHRINKAGE ESTIMATOR BASED ON MINIMUM-PROBABILITY-OF-ERROR CRITERION AND APPLICATION TO SIGNAL DENOISING

We address the problem of designing an optimal pointwise shrinkage estimator in the transform domain, based on the minimum probability of error (MPE) criterion. We assume an additive model for the noise corrupting the clean signal. The proposed formulation is general in the sense that it can handle various noise distributions. We consider various noise distributions (Gaussian, Student's-t, and Laplacian) and compare the denoising performance of the estimator obtained with the mean-squared error (MSE)-based estimators. The MSE optimization is carried out using an unbiased estimator of the MSE, namely Stein's Unbiased Risk Estimate (SURE). Experimental results show that the MPE estimator outperforms the SURE estimator in terms of SNR of the denoised output, for low (0 -10 dB) and medium values (10 - 20 dB) of the input SNR.

On Hermite pseudo-multipliers

In this article we deal with a variation of a theorem of Mauceri concerning the L-P boundedness of operators M which are known to be bounded on L-2. We obtain sufficient conditions on the kernel of the operator M so that it satisfies weighted L-P estimates. As an application we prove L-P boundedness of Hermite pseudo-multipliers. (C) 2014 Elsevier Inc. All rights reserved.

Transverse single spin asymmetry in e plus p up arrow -> e plus J/psi plus X and Q(2) evolution of Sivers function-II

We present estimates of single spin asymmetry in the electroproduction of J/psi taking into account the transverse momentum-dependent (TMD) evolution of the gluon Sivers function. We estimate single spin asymmetry for JLab, HERMES, COMPASS and eRHIC energies using the color evaporation model of J/psi. We have calculated the asymmetry using recent parameters extracted by Echevarria et al. using the Collins-Soper-Sterman approach to TMD evolution. These recent TMD evolution fits are based on the evolution kernel in which the perturbative part is resummed up to next-to-leading logarithmic accuracy. We have also estimated the asymmetry by using parameters which had been obtained by a fit by Anselmino et al., using both an exact numerical and an approximate analytical solution of the TMD evolution equations. We find that the variation among the different estimates obtained using TMD evolution is much smaller than between these on one hand and the estimates obtained using DGLAP evolution on the other. Even though the use of TMD evolution causes an overall reduction in asymmetries compared to the ones obtained without it, they remain sizable. Overall, upon use of TMD evolution, predictions for asymmetries stabilize.

An interior penalty method for distributed optimal control problems governed by the biharmonic operator

In this paper, a C-0 interior penalty method has been proposed and analyzed for distributed optimal control problems governed by the biharmonic operator. The state and adjoint variables are discretized using continuous piecewise quadratic finite elements while the control variable is discretized using piecewise constant approximations. A priori and a posteriori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions. Numerical results justify the theoretical results obtained. The a posteriori error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement. (C) 2014 Elsevier Ltd. All rights reserved.

Heat kernels on the AdS(2) cone and logarithmic corrections to extremal black hole entropy

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N = 4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter-BPS black holes in N = 4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over ZN orbifolds of higher-dimensional spheres and hyperboloids.

On flame-turbulence interaction in constant-pressure expanding flames

In this paper we present one of the first high-speed particle image velocimetry measurements to quantify flame-turbulence interaction in centrally-ignited constant-pressure premixed flames expanding in nearisotropic turbulence. Measurements of mean flow velocity and rms of fluctuating flow velocity are provided over a range of conditions both in the presence and absence of the flame. The distributions of stretch rate contributions from different terms such as tangential straining, normal straining and curvature are also provided. It is found that the normal straining displays non-Gaussian pdf tails whereas the tangential straining shows near Gaussian behavior. We have further tracked the motion of the edge points that reside and co-move with the edge of the flame kernel during its evolution in time, and found that within the measurement conditions, on average the persistence time scales of stretch due to pure curvature exceed that due to tangential straining by at least a factor of two. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.