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Testing halfspaces
 IN PROC. 20TH ANNUAL SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 2009
"... This paper addresses the problem of testing whether a Booleanvalued function f is a halfspace, i.e. a function of the form f(x) = sgn(w ·x−θ). We consider halfspaces over the continuous domain R n (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean ..."
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Cited by 33 (15 self)
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. We prove analogous results for the Boolean cube {−1, 1} n (with Fourier coefficients in place of Hermite coefficients) for balanced halfspaces in which all degree1 Fourier coefficients are small. Dealing with general halfspaces over {−1, 1} n poses significant additional complications and requires
Optimal expecteddistance separating halfspace
, 2004
"... One recently proposed criterion to separate two datasets in discriminant analysis, is to use a hyperplane which minimises the sum of distances to it from all the misclassified data points. Here all distances are supposed to be measured by way of some fixed norm, while misclassification means lying ..."
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Cited by 2 (0 self)
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separating halfspace always balances the misclassified points. Moreover, under polyhedrality assumptions on the support of X, there always exists an optimal separating halfspace passing through d affinely independent points. It follows that the problem is polynomially solvable in fixed dimension
Finding optimal separating halfspaces by Variable Neighbourhood Search ∗
, 2006
"... We consider the linear classification method consisting of separating two sets of points in dspace by a hyperplane. We investigate the situation where the two sets are nonseparable, and we wish to find the hyperplane which minimises the sum of distances from all misclassified points to the hyperpla ..."
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We consider the linear classification method consisting of separating two sets of points in dspace by a hyperplane. We investigate the situation where the two sets are nonseparable, and we wish to find the hyperplane which minimises the sum of distances from all misclassified points to the hyperplane. To this end two local descent methods are developed, one gridbased and one optimisationtheory based, and are embedded in several ways into a VNS metaheuristic scheme. Computational results show these approaches to be complementary, leading to a single hybrid VNS strategy which combines both approaches to exploit the strong points of each. Extensive computational tests show that the resulting method performs well.
Surface Wave Characteristics at the Interface of Welded Elastic Halfspaces
, 2011
"... The present article concentrates on the propagation of generalized surface acoustic waves in a composite structure consisting of piezoelectric and nonpiezoelectric semiconductor media. The mathematical model of the problem is depicted by a set of partial differential equations of motion, Gauss equ ..."
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The present article concentrates on the propagation of generalized surface acoustic waves in a composite structure consisting of piezoelectric and nonpiezoelectric semiconductor media. The mathematical model of the problem is depicted by a set of partial differential equations of motion, Gauss equation in piezoelectric and electron diffusion equation in semiconductor along with boundary conditions to be satisfied at the interface. The secular equation that governs the propagation of surface waves has been derived in compact form after obtaining the formal solution. The analytic expressions for displacements, stresses, piezoelectric potential and electron concentration during the surface wave propagation at the interface have also been obtained. The numerical solution of the secular equation is carried out for the cadmium selenide and silicon composite by employing fixed point functional iteration numerical method along with irreducible Cardano method. The computer simulated results with the help of MATLAB software in respect of dispersion curves, attenuation coefficient, displacements, stresses, carrier concentration and piezoelectric potential are presented graphically. This work may be useful in surface acoustic wave (SAW) devices and electronic industry.
TRAVELING WAVE SOLUTIONS IN A HALFSPACE FOR BOUNDARY REACTIONS
"... Abstract. We prove the existence and uniqueness of a traveling front and of its speed for the homogeneous heat equation in the halfplane with a Neumann boundary reaction term of nonbalanced bistable type or of combustion type. We also establish the monotonicity of the front and, in the bistable ca ..."
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Abstract. We prove the existence and uniqueness of a traveling front and of its speed for the homogeneous heat equation in the halfplane with a Neumann boundary reaction term of nonbalanced bistable type or of combustion type. We also establish the monotonicity of the front and, in the bistable
Research Article Exact Solutions of RayleighStokes Problem for Heated Generalized Maxwell Fluid in a Porous HalfSpace
, 2008
"... The RayleighStokes problem for a generalized Maxwell fluid in a porous halfspace with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fr ..."
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The RayleighStokes problem for a generalized Maxwell fluid in a porous halfspace with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform
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