«Constrained-optimal strategy-proof assignment: beyond the groves mechanisms»

A single object must be allocated to at most one of n agents. Money transfers are possible and preferences are quasilinear. We offer an explicit description of the individually rational mechanisms which are Pareto-optimal in the class of feasible, strategy-proof, anonymous and envy-free mechanisms. These mechanisms form a one-parameter infinite family; the Vickrey mechanism is the only Groves mechanism in that family.

On Some Infinite Convex Invariants

The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions

Strategies for Inverse Profiling of Two Dimensional Dielectric Scatterers Using Electromagnetic Illumination

Electromagnetic tomography has been applied to problems in nondestructive evolution, ground-penetrating radar, synthetic aperture radar, target identification, electrical well logging, medical imaging etc. The problem of electromagnetic tomography involves the estimation of cross sectional distribution dielectric permittivity, conductivity etc based on measurement of the scattered fields. The inverse scattering problem of electromagnetic imaging is highly non linear and ill posed, and is liable to get trapped in local minima. The iterative solution techniques employed for computing the inverse scattering problem of electromagnetic imaging are highly computation intensive. Thus the solution to electromagnetic imaging problem is beset with convergence and computational issues. The attempt of this thesis is to develop methods suitable for improving the convergence and reduce the total computations for tomographic imaging of two dimensional dielectric cylinders illuminated by TM polarized waves, where the scattering problem is defmed using scalar equations. A multi resolution frequency hopping approach was proposed as opposed to the conventional frequency hopping approach employed to image large inhomogeneous scatterers. The strategy was tested on both synthetic and experimental data and gave results that were better localized and also accelerated the iterative procedure employed for the imaging. A Degree of Symmetry formulation was introduced to locate the scatterer in the investigation domain when the scatterer cross section was circular. The investigation domain could thus be reduced which reduced the degrees of freedom of the inverse scattering process. Thus the entire measured scattered data was available for the optimization of fewer numbers of pixels. This resulted in better and more robust reconstructions of the scatterer cross sectional profile. The Degree of Symmetry formulation could also be applied to the practical problem of limited angle tomography, as in the case of a buried pipeline, where the ill posedness is much larger. The formulation was also tested using experimental data generated from an experimental setup that was designed. The experimental results confirmed the practical applicability of the formulation.

Exploring Bit-Difference for Approximate KNN Search in High-dimensional Databases

In this paper, we develop a novel index structure to support efficient approximate k-nearest neighbor (KNN) query in high-dimensional databases. In high-dimensional spaces, the computational cost of the distance (e.g., Euclidean distance) between two points contributes a dominant portion of the overall query response time for memory processing. To reduce the distance computation, we first propose a structure (BID) using BIt-Difference to answer approximate KNN query. The BID employs one bit to represent each feature vector of point and the number of bit-difference is used to prune the further points. To facilitate real dataset which is typically skewed, we enhance the BID mechanism with clustering, cluster adapted bitcoder and dimensional weight, named the BID⁺. Extensive experiments are conducted to show that our proposed method yields significant performance advantages over the existing index structures on both real life and synthetic high-dimensional datasets.

A three-dimensional magnetometer for motion sensing of a balloon-carried atmospheric measurement package

An instrument is described which carries three orthogonal geomagnetic field sensors on a standard meteorological balloon package, to sense rapid motion and position changes during ascent through the atmosphere. Because of the finite data bandwidth available over the UHF radio link, a burst sampling strategy is adopted. Bursts of 9s of measurements at 3.6Hz are interleaved with periods of slow data telemetry lasting 25s. Calculation of the variability in each channel is used to determine position changes, a method robust to periods of poor radio signals. During three balloon ascents, variability was found repeatedly at similar altitudes, simultaneously in each of three orthogonal sensors carried. This variability is attributed to atmospheric motions. It is found that the vertical sensor is least prone to stray motions, and that the use of two horizontal sensors provides no additional information over a single horizontal sensor

Catena-Poly[bis(ethane-1,2-diammonium) [manganese(II)-di-mu-phosphato-kappa O-4 : O ']]: a one-dimensional manganese phosphate

The title compound,{(C2H10N2)(2)[Mn(PO4)(2)]}(n), contains anionic square-twisted chains of formula [Mn(PO4)(2)](4-) constructed from corner-sharing four-membered rings of alternating MnO4 and PO4 units. The Mn and P atoms have distorted tetrahedral coordination and the Mn atom lies on a twofold axis. The linear manganese-phosphate chains are held together by hydrogen-bonding interactions involving the framework O atoms and the H atoms of the ethane-1,2-diammonium cations, which lie in the interchain spaces.

FACSGen 2.0 animation software: generating three-dimensional FACS-valid facial expressions for emotion research

In this article, we present FACSGen 2.0, new animation software for creating static and dynamic threedimensional facial expressions on the basis of the Facial Action Coding System (FACS). FACSGen permits total control over the action units (AUs), which can be animated at all levels of intensity and applied alone or in combination to an infinite number of faces. In two studies, we tested the validity of the software for the AU appearance defined in the FACS manual and the conveyed emotionality of FACSGen expressions. In Experiment 1, four FACS-certified coders evaluated the complete set of 35 single AUs and 54 AU combinations for AU presence or absence, appearance quality, intensity, and asymmetry. In Experiment 2, lay participants performed a recognition task on emotional expressions created with FACSGen software and rated the similarity of expressions displayed by human and FACSGen faces. Results showed good to excellent classification levels for all AUs by the four FACS coders, suggesting that the AUs are valid exemplars of FACS specifications. Lay participants’ recognition rates for nine emotions were high, and comparisons of human and FACSGen expressions were very similar. The findings demonstrate the effectiveness of the software in producing reliable and emotionally valid expressions, and suggest its application in numerous scientific areas, including perception, emotion, and clinical and euroscience research.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.

A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

The STRATADAPT scale: a measure of marketing strategy adaptation to international business markets

Purpose – The development of marketing strategies optimally adjusted to export markets has been a vitally important topic for both managers and academics for about five decades. However, there is no agreement in the literature about which elements integrate marketing strategy and which components of domestic strategies should be adapted to export markets. The purpose of this paper is to develop a new scale – STRATADAPT. Design/methodology/approach – Results from a sample of small and medium-sized industrial exporting firms support a four-dimensional scale – product, promotion, price, and distribution strategies – of 30 items. The scale presents evidence of composite reliability as well as discriminant and nomological validity. Findings – Findings reveal that all four dimensions of marketing strategy adaptation are positively associated with the amount of the firm's financial resources allocated to export activity. Practical implications – The STRATADAPT scale may assist managers in developing better international marketing strategies as well as in planning more accurate and efficient marketing programs across markets. Originality/value – This study develops a new scale, the STRATADAPT scale, which is a broad measure of export marketing strategy adaptation.

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.