Expansion Of Representation Research Articles

Wave-atoms-based multipurpose scheme via perceptual image hashing and watermarking

This paper presents a novel multipurpose scheme for content-based image authentication and copyright protection using a perceptual image hashing and watermarking strategy based on a wave atom transform. The wave atom transform is expected to outperform other transforms because it gains sparser expansion and better representation for texture than other traditional transforms, such as wavelet and curvelet transforms. Images are decomposed into multiscale bands with a number of tilings using the wave atom transform. Perceptual hashes are then extracted from the features of tiling in the third scale band for the purpose of content-based authentication; simultaneously, part of the selected hashes are designed as watermarks, which are embedded into the original images for the purpose of copyright protection. The experimental results demonstrate that the proposed scheme shows great performance in content-based authentication by distinguishing the maliciously attacked images from the nonmaliciously attacked images. Moreover, watermarks extracted from the proposed scheme also achieve high robustness against common malicious and nonmalicious image-processing attacks, which provides excellent copyright protection for images.

The Digital Edition and the Digital Humanities

The legacy of early digital editions and their related scholarship reveals the textual foundation of digital literary studies, a foundation that emphasized form and materiality, in effect a representational rather than interpretative view of text. Early digital editions were formed out of a whole text approach, a cohesive print-to-digital model that features interrelated textual materials, often in print book form, rather than an expansive and fragmented representation of text, as is increasingly the case with data-based practices. This article examines the ways in which the digital edition privileges the structure of the book, which is viewed as a self-contained entity with a naturalized means for displaying knowledge and replicated in most aspects of creating digital editions, from display to data treatment.

Iris recognition by fusing different representations of multi-scale Taylor expansion

The random distribution of features in an iris image texture allows to perform iris-based personal authentication with high confidence. We propose three new iris representations that are based on a multi-scale Taylor expansion of the iris texture. The first one is a phase-based representation that is based on binarized first and second order multi-scale Taylor coefficient. The second one is based on the most significant local extremum points of the first two Taylor expansion coefficients. The third method is a combination of the first two representations. Furthermore, we provide efficient similarity measures for the three representations that are robust to moderate inaccuracies in iris segmentation. In a thorough validation using the three iris data-sets Casia 2.0 (device 1), ICE-1 and MBGC-3l, we show that the first two representations perform very well while the third one, i.e., the combination of the first two, significantly outperforms state-of-art iris recognition approaches.

(Semi-)Analytic Gaussian Mixture Filter

AbstractIn nonlinear filtering, special types of Gaussian mixture filters are a straightforward extension of Gaussian filters, where linearizing the system model is performed individually for each Gaussian component. In this paper, two novel types of linearization are combined with Gaussian mixture filters. The first linearization is called analytic stochastic linearization, where the linearization is performed analytically and exactly, i.e., without Taylor-series expansion or approximate sample-based density representation. In cases where a full analytical linearization is not possible, the second approach decomposes the nonlinear system into a set of nonlinear subsystems that are conditionally integrable in closed form. These approaches are more accurate than fully applying classical linearization.

Two-Dimensional Microwave Imaging Based on Hybrid Scatterer Representation and Differential Evolution

A hybrid method for solving two-dimensional inverse scattering problems is proposed. The method utilizes differential evolution as a global optimizer and is based on two alternative representations of the unknown scatterer. Initially, the scatterer properties are represented by means of truncated cosine Fourier series expansion that involves limited number of unknown expansion coefficients. Then, the reconstructed profile obtained is used as an initial estimate and the differential evolution is further applied to a scatterer representation based on pulse function expansion. In this representation, the scatterer region is subdivided by a fine grid and the scatterer properties are considered constant within each cell. When the truncated cosine Fourier expansion representation is adopted, the dimension of the solution space can be reduced and the instabilities caused by the ill-posedness of the problem are suppressed. In the second step of the hybrid method, where the pulse functions representation is considered, the scatterer reconstruction is finer and more accurate due to its quite accurate initial estimate. Numerical results show that the hybrid method results in lower reconstruction error compared to above-mentioned representations. Also, the hybrid method outperforms the other two representations, even in the presence of noisy field measurements.

"Sioux Yells" in the Dawes Era: Lakota "Indian Play," the Wild West, and the Literatures of Luther Standing Bear

In 1902, in an era when the federal government endeavored to immobilize, disband, and assimilate the Lakota into the national body, Buffalo Bill Cody's Wild West enabled Luther Standing Bear to leave Pine Ridge and, consequently, transformed his life and his life's work. Ultimately Standing Bear's literature, in particular his autobiography My People the Sioux (1928), was dynamically conversant with both Cody's and cinematic representations of American expansion that featured Lakota violence. While dismantling accounts, such as the Battle of Little Big Horn, central to Cody's narrative, Standing Bear grounded the veracity of My People in a Cody-esque rhetoric of "authenticity." The Lakota writer also engaged the rhetoric of white liberal reformers who equated racial "uplift" with private-property-owning American citizenship. In Land of the Spotted Eagle (1933) he blasted "progressives" whose beliefs threatened to destroy, because they failed to understand, the sophistication and value of Lakota society.

Corrected Article: “An error-controlled fast multipole method” [J. Chem. Phys. 131, 244102 (2009)

We present a two-stage error estimation scheme for the fast multipole method (FMM). This scheme can be applied to any particle system. It incorporates homogeneous as well as inhomogeneous distributions. The FMM error as a consequence of the finite representation of the multipole expansions and the operator error is correlated with an absolute or relative user-requested energy threshold. Such a reliable error control is the basis for making reliable simulations in computational physics. Our FMM program on the basis of the two-stage error estimation scheme is available on request.

An error-controlled fast multipole method

We present a two-stage error estimation scheme for the fast multipole method (FMM). This scheme can be applied to any particle system. It incorporates homogeneous as well as inhomogeneous distributions. The FMM error as a consequence of the finite representation of the multipole expansions and the operator error is correlated with an absolute or relative user-requested energy threshold. Such a reliable error control is the basis for making reliable simulations in computational physics. Our FMM program on the basis of the two-stage error estimation scheme is available on request.

Low-energy-electron-diatomic molecule scattering

Recent developments in traditional close-coupling methods as applied to electron-molecule scattering are described. The choice of coordinate frame of expansion, single-center versus two-center representation, and inclusion of exchange and polarization effects are discussed.

Orthogonality relations for fluid-structural waves in a three-dimensional, rectangular duct with flexible walls

An exact expression for the fluid-coupled structural waves that propagate in a three-dimensional, rectangular waveguide with elastic walls is presented in terms of the non-separable eigenfunctions ψ n ( y , z ). It is proved that these eigenfunctions are linearly dependent and that an eigenfunction expansion representation of a suitably smooth function f ( y , z ) converges point-wise to that function. Orthogonality results for the derivatives ψ n y ( a , z ) are derived which, together with a partial orthogonality relation for ψ n ( y , z ), enable the solution of a wide range of acoustic scattering problems. Two prototype problems, of the type typically encountered in two-part scattering problems, are solved, and numerical results showing the displacement of the elastic walls are presented.

Path-independent integrals to identify localized plastic events in two dimensions

We use a power expansion representation of plane-elasticity complex potentials due to Kolossov and Muskhelishvili to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant contributions correspond to first-order singularities of quadrupolar and dipolar symmetry which can be associated, respectively, with pure deviatoric and pure volumetric plastic strain of an equivalent circular inclusion. By construction of holomorphic functions from the displacement field and its derivatives, it is possible to define path-independent Cauchy integrals which capture the amplitudes of these singularities. Analytical expressions and numerical tests on simple finite-element data are presented. The development of such numerical tools is of direct interest for the identification of local structural reorganizations, which are believed to be the key mechanisms for plasticity of amorphous materials.

Primitive recursive real numbers

AbstractIn mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure – Dedekind‐complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computable real numbers. Although the computable real numbers can be defined in various equivalent ways, if “computable” is replaced by “primitive recursive” (p. r., for short), these definitions lead to a number of different concepts, which we compare in this article. We summarize the known results and add new ones. In particular we show that there is a proper hierarchy among p. r. real numbers by nested interval representation, Cauchy representation, b ‐adic expansion representation, Dedekind cut representation, and continued fraction expansion representation. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On eigenfunction expansions associated with wave propagation along ducts with wave-bearing boundaries

A class of boundary value problems, that has application in the propagation of waves along ducts in which the boundaries are wave-bearing, is considered. This class of problems is characterised by the presence of high order derivatives of the dependent variable(s) in the duct boundary conditions. It is demonstrated that the underlying eigenfunctions are linearly dependent and, most signiflcantly, that an eigenfunction expansion representation of a suitably smooth function, say f(y), converges point-wise to that function. Two physical examples are presented. It is demonstrated that, in both cases, the eigenfunction representation of the solution is rendered unique via the application of suitable edge conditions. Within the context of these two examples, a detailed discussion of the issue of completeness is presented.

An Improved Algorithm for the Fourier Integral of the KWW Function and Its Application to Neutron Scattering and Dielectric Data

The Kohlrausch–Williams–Watts (KWW) function is widely used to describe relaxation behavior in glass‐forming polymers and other condensed systems. The application of this time domain function to frequency domain spectroscopy is, in principle, possible through its Fourier transform. Unfortunately analytical forms for the transform exist only in limited cases, and a number of methods, which circumvent this limitation, are described in the literature. Here we have revisited the problem of evaluating the Fourier integral in the general case, but with the specific aim of producing a fast and accurate algorithm suitable for use within common spreadsheet applications available on personal computers. Two methods were examined, a corrected discrete Fourier transform and, more successfully, a two‐series expansion representation. A previous problem associated with the use of complementary series, that they may not adequately cover the whole range of evaluation of the transform, was overcome by the substitution of a Padé approximant for one of the series. This was found to provide the basis for a robust and effective algorithm whose accuracy was tested against both symbolic mathematical expressions and standard tabulated values. The use of this algorithm in iterative nonlinear least squares curve fitting routines is illustrated by reference to quasi‐elastic neutron scattering data and dielectric relaxation spectra. The former involves a convolution of the real part of the integral with the instrumental resolution function; very satisfactory fits to scattering spectra for poly(vinyl acetate) and poly(isobutylene), at temperatures above their glass transitions, was achieved and the KWW characteristic relaxation parameters established. The dielectric spectrum due to the α‐relaxation of poly(vinyl acetate) is similarly well‐described, here using both the real and the imaginary parts of the integral. The KWW description of the PVAc relaxation is compared with that using the Havriliak–Negami equation and was found to provide an equally acceptable description of the data, and by using one less adjustable parameter.

Development of bilinear power system representations for small signal stability analysis

In this paper, a new analysis technique for predicting and characterizing nonlinear behavior of stressed power networks is proposed. Making use of an analytical approximation of the system nonlinear model via the use of a truncated Carleman linearization technique, a bilinear state-space model of the power system is developed in which the second and higher order nonlinear terms are explicitly incorporated in the series expansion representation of the system model. The proposed framework enables the study of the dynamic behavior of nonlinear systems, both analytically and numerically, and can be used to represent a wide class of non-linear systems and oscillatory processes. Analytical criteria are developed based on the structural properties of the bilinear state-space model matrices, which predict the existence and stability character of modal interaction in terms of the eigenstructure of the linear system representation. The properties and behavior of the bilinear model are then investigated, and a number of useful results are derived. The present method is quite general and extends readily to higher-dimensional systems. A simplified 2-area, 4-machine system is used to illustrate the proposed procedure. Detailed nonlinear time-domain simulations are conducted to identify the strength of nonlinear behavior arising from interaction of the fundamental modes of oscillation, as well as to check the validity of the analysis.

Numerical simulation of solitary waves on plane slopes

In this paper, we present a numerical method for the computation of surface water waves over bottom topography. It is based on a series expansion representation of the Dirichlet–Neumann operator in terms of the surface and bottom variations. This method is computationally very efficient using the fast Fourier transform. As an application, we perform computations of solitary waves propagating over plane slopes and compare the results with those obtained from a boundary element method. A good agreement is found between the two methods.

A Two-Dimensional Nonlinear Nonlocal Feed-Forward Cochlear Model and Time Domain Computation of Multitone Interactions

A two-dimensional cochlear model is presented, which couples the classical second order partial differential equations of the basilar membrane (BM) with a discrete feed-forward (FF) outer hair cell (OHC) model for enhanced sensitivity. The enhancement (gain) factor in the model depends on BM displacement in a nonlinear nonlocal manner in order to capture multifrequency sound interactions and compression effects in a time-dependent simulation. The FF mechanism is based on the longitudinal tilt of the OHCs in feeding the mechanical energy onto the BM. A numerical method of second order accuracy in space and time is formulated by reducing the unknown variables to the BM with the representation of eigenfunction expansions. Though the nonlinear coupling with OHCs created an implicit algebraic problem at each time step, the structure of the FF mass matrix is found to permit a decomposition into a sum of a time-independent symmetric positive definite part and the remaining time-dependent part. A fast iterative m...

Weak computability and representation of reals

AbstractThe computability of reals was introduced by Alan Turing [20] by means of decimal representations. But the equivalent notion can also be introduced accordingly if the binary expansion, Dedekind cut or Cauchy sequence representations are considered instead. In other words, the computability of reals is independent of their representations. However, as it is shown by Specker [19] and Ko [9], the primitive recursiveness and polynomial time computability of the reals do depend on the representation. In this paper, we explore how the weak computability of reals depends on the representation. To this end, we introduce three notions of weak computability in a way similar to the Ershov's hierarchy of Δ02‐sets of natural numbers based on the binary expansion, Dedekind cut and Cauchy sequence, respectively. This leads to a series of classes of reals with different levels of computability. We investigate systematically questions as on which level these notions are equivalent. We also compare them with other known classes of reals like c. e. and d‐c. e. reals. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Wave reflection and transmission from a thin film with one-dimensional disorder

This paper deals with a TE plane wave reflection and transmission from a thin film with one-dimensional disorder by means of the stochastic functional approach. The relative permittivity of the thin film is written by a Gaussian random field in the horizontal direction with infinite extent, and is uniform in the vertical direction with finite thickness. Arandomwavefield is obtained in terms of a Wiener–Hermite expansion representation with approximate expansion coefficients (Wiener kernels) under a small fluctuation case. For a SiC thin film and a glass thin film having one-dimensional disorder with Gaussian correlation or an exponential correlation, numerical examples of the first-order incoherent scattering cross section and the optical theorem are illustrated in the figures. It is then found that ripples and four major peaks appear in angular distributions of the incoherent scattering. Such four peaks may occur in the directions of forward scattering, specular reflection, backscattering and in the symmetrical direction of forward scattering with respect to the normal to surface of the thin film. Physical processes that yield such ripples and peaks are discussed.

Calculation of binding energy for muonic three-body systems in the hyperspherical approach

Muonic three-body bound states are investigated within a hyperspherical adiabatic expansion representation. We have used a method for determining the basis functions of the expansion, which consists of decomposing these functions into Faddeev-type components and an equivalent treatment of all two-body contributions. Through this approach, and using partial waves for components, the binding energy of the ground state and the lowest eigenpotentials for the muonic molecules $(pd\ensuremath{\mu},pt\ensuremath{\mu},dt\ensuremath{\mu})$ are calculated in extreme and uncoupled adiabatic approximation. The obtained results are very close to variational calculations.