on the p and hp extension of nedelec s curl conforming elements abstract we establish interpolation error estimates for the hp extension of nedelec s curl and divergence conforming three dimensional finite elements using these interpolation estimates we investigate the use of higher order edge finite elements for the linear three dimensional magnetostatic problem our estimates show that the standard mixed method for the magnetostatic problem can be approximated to optimal order in both h and p

a robust watermarking scheme using phase shift keying with the combination of amplitude boost and low amplitude block selection watermarking is a potential method for copyright protection and authentication of multimedia data in the internet the watermarking process can be viewed as a communication task where the watermark acting like information is embedded into a host image acting like noise in a communication channel which is susceptible to all kinds of attacks acting like jamming in a previous paper we proposed a robust watermarking scheme using frequency shift keying fsk in the scheme high variance block selection hvbs is employed to enhance robustness in this paper a novel watermarking scheme using phase shift keying psk modulation with amplitude boost ab and low amplitude block selection labs is proposed ab is hired to increase the robustness while labs is employed to improve the imperceptibility with proper combination of ab and labs the proposed scheme achieves superior performance in terms of robustness and imperceptibility in order to demonstrate the effectiveness of the proposed scheme simulations under various conditions were conducted the empirical results showed that qpsk is the best choice among other psks and the proposed scheme can sustain most common attacks including jpeg compression rotating resizing cropping painting noising and blurring etc the empirical results also showed that the scheme with ab and labs properly combined outperforms the scheme without the gain of the former over the latter is more significant for host images with smooth characteristics than those with high frequency characteristics simulation comparison with two other schemes the hsu s scheme and the chen s scheme showed that the proposed scheme is the most robust among the three

efficient preconditioning for the p version finite element method in two dimensions parallel preconditioners are formulated and analyzed for systems of equations arising from the p version finite element method applied to second order self adjoint elliptic boundary value problems in two dimensions by using new theoretical results for polynomial spaces it is proved that the condition number of the preconditioned system grows as log 2 p where p is the degree of the polynomial space numerical results are presented showing that the condition number indeed grows very slowly with p

an hp error analysis of mitc plate elements we give an hp error analysis of several rectangular families of finite elements for the reissner mindlin plate bending equations we consider both the original mitc families k j bathe f brezzi and m fortin internat j numer methods engrg 28 1989 pp 1787 1801 and some new ones introduced in this paper for the deflection and rotation we give error estimates which are optimal with respect to the mesh size h and optimal up to ordo p varepsilon varepsilon 0 arbitrary with respect to the polynomial degree p we also obtain estimates for the error in the shear force calculated via two different methods our analysis utilizes some recent results of ours for the mixed method for the stokes problem as well as hp interpolation estimates for mixed methods for second order elliptic equations in this regard we derive new hp results in this paper for the brezzi douglas fortin marini spaces and improve upon previous estimates for the brezzi douglas marini spaces

constrained least absolute deviation neural networks it is well known that least absolute deviation lad criterion or norm used for estimation of parameters is characterized by robustness i e the estimated parameters are totally resistant insensitive to large changes in the sampled data this is an extremely useful feature especially when the sampled data are known to be contaminated by occasionally occurring outliers or by spiky noise in our previous works we have proposed the least absolute deviation neural network ladnn to solve unconstrained lad problems the theoretical proofs and numerical simulations have shown that the ladnn is lyapunov stable and it can globally converge to the exact solution to a given unconstrained lad problem we have also demonstrated its excellent application value in time delay estimation more generally a practical lad application problem may contain some linear constraints such as a set of equalities and or inequalities which is called constrained lad problem whereas the unconstrained lad can be considered as a special form of the constrained lad in this paper we present a new neural network called constrained least absolute deviation neural network cladnn to solve general constrained lad problems theoretical proofs and numerical simulations demonstrate that the proposed cladnn is lyapunov stable and globally converges to the exact solution to a given constrained lad problem independent of initial values the numerical simulations have also illustrated that the proposed cladnn can be used to robustly estimate parameters for nonlinear curve fitting which is extensively used in signal and image processing

direct search methods then and now we discuss direct search methods for unconstrained optimization we give a modern perspective on this classical family of derivative free algorithms focusing on the development of direct search methods during their golden age from 1960 to 1971 we discuss how direct search methods are characterized by the absence of the construction of a model of the objective we then consider a number of the classical direct search methods and discuss what research in the intervening years has uncovered about these algorithms in particular while the original direct search methods were consciously based on straightforward heuristics more recent analysis has shown that in most but not all cases these heuristics actually suffice to ensure global convergence of at least one subsequence of the sequence of iterates to a first order stationary point of the objective function

goal oriented adaptivity using unconventional error representations for the multidimensional helmholtz equation in goal oriented adaptivity goa the error in the quantity of interest qoi is represented using the error functions of the direct and adjoint problems this error representation is subsequently bounded above by element wise error indicators that are used to drive optimal refinements in this work we propose to replace in the error representation the adjoint problem by an alternative operator the main advantage of the proposed approach is that when judiciously selecting such alternative operator the corresponding upper bound of the error representation becomes sharper leading to a more efficient goa while the method can be applied to a variety of problems we focus here on two and threedimensional 2d and 3d helmholtz problems we show via extensive numerical experimentation that the upper bounds provided by the alternative error representations are sharper than the classical ones and lead to a more robust p adaptive process we also provide guidelines for finding operators delivering sharp error representation upper bounds we further extend the results to a convectiondominated diffusion problem as well as to problems with discontinuous material coefficients finally we consider a sonic logging while drilling lwd problem to illustrate the applicability of the proposed method

combinational image watermarking in the spatial and frequency domains in order to provide more watermarks and to minimize the distortion of the watermarked image a novel technique using the combinational spatial and frequency domains is presented in this paper the splitting of the watermark image into two parts respectively for spatial and frequency insertion relies on the user s preference and data importance experimental results provide the comparisons when different sized watermarks are embedded into a grayscale image the proposed combinational image watermarking possesses the following advantages more watermark data can be inserted into the host image so that the capacity is increased the splitting of the watermark into two parts makes the degree of protection double the splitting strategy can be designed even more complicated to be unable to compose furthermore to enhance robustness a random permutation of the watermark is used to defeat the attacks of signal processing such as image crops

de rham diagram for hp finite element spaces abstract we prove that the hp finite elements for h curl spaces introduced in 1 fit into a general de rham diagram involving hp approximations the corresponding interpolation operators generalize the notion of hp interpolation introduced in 2 and are different from the classical operators of nedelec and raviart thomas

the optimal convergence rate of the p version of the finite element method optimal error estimates for the p version of the finite element method in two dimensions are proven for the case when u in h k omega or u has singularities induced by the corners of the domain the case of nonhomogenous essential boundary conditions is also analyzed

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

wavelet tree quantization for copyright protection watermarking this paper proposes a wavelet tree based blind watermarking scheme for copyright protection the wavelet coefficients of the host image are grouped into so called super trees the watermark is embedded by quantizing super trees the trees are so quantized that they exhibit a large enough statistical difference which will later be used for watermark extraction each watermark bit is embedded in perceptually important frequency bands which renders the mark more resistant to frequency based attacks also the watermark is spread throughout large spatial regions this yields more robustness against time domain geometric attacks examples of various attacks will be given to demonstrate the robustness of the proposed technique

a novel image watermarking scheme based on amplitude attack this paper presents a novel image watermark scheme based on the characteristics of amplitude attacks first of all the analysis of amplitude attacks is performed then the amplitude attacks are categorized into three types positive attack negative attack and random attack finally based on these attack types we design three corresponding detectors the detectors remove the unreliable discrete cosine transform dct coefficients in the attacked image so that only reliable coefficients are used for the extraction of the watermark embedded the experimental results indicate that the proposed technique improves robustness significantly without sacrificing the false alarm rate

a feature based robust digital image watermarking scheme a robust digital image watermarking scheme that combines image feature extraction and image normalization is proposed the goal is to resist both geometric distortion and signal processing attacks we adopt a feature extraction method called mexican hat wavelet scale interaction the extracted feature points can survive a variety of attacks and be used as reference points for both watermark embedding and detection the normalized image of an image object is nearly invariant with respect to rotations as a result the watermark detection task can be much simplified when it is applied to the normalized image however because image normalization is sensitive to image local variation we apply image normalization to nonoverlapped image disks separately the disks are centered at the extracted feature points several copies of a 16 bit watermark sequence are embedded in the original image to improve the robustness of watermarks simulation results show that our scheme can survive low quality jpeg compression color reduction sharpening gaussian filtering median filtering row or column removal shearing rotation local warping cropping and linear geometric transformations

maxwell eigenvalues and discrete compactness in two dimensions abstract we present an elementary proof of the discrete compactness result for a general class of hp finite elements introduced in 1 2 we discuss h convergence of 2d elements only and in this context the results are not new as the analysis of h curl conforming elements for maxwell s equations can be reduced to the long known results for raviart thomas elements 3 the work is based on the result of kikuchi 4 5 for nedelec s edge triangular elements of the lowest order and presents an alternative to techniques presented in 3 6 in particular the present version does not use an inverse inequality argument and therefore is valid for h adaptive meshes we conclude the presentation with a number of 2d computational experiments including nonconvex domains

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

a two dimensional self adaptive hp finite element method for the characterization of waveguide discontinuities part i energy norm based automatic hp adaptivity abstract the accurate analysis and characterization of waveguide discontinuities is an important issue in microwave engineering in some cases the discontinuities are an unavoidable result of mechanical or electric transitions which effects have to be minimized in other cases the discontinuities are deliberately introduced into the waveguide to perform a certain electric function this is the first of two papers analyzing different types of rectangular waveguide discontinuities by using a fully automatic hp adaptive finite element method in this paper a fully automatic energy norm based hp adaptive finite element fe strategy applied to a number of relevant waveguide structures is presented the methodology produces exponential convergence rates in terms of the energy norm error of the solution against the problem size number of degrees of freedom extensive numerical results demonstrate the suitability of the hp method for solving different rectangular waveguide discontinuities these results illustrate the flexibility reliability and high accuracy of the method the self adaptive hp fem provides similar sometimes more accurate results than those obtained with semi analytical techniques such as the mode matching method for problems where semi analytical methods can be applied at the same time the hp fem provides the flexibility of modeling more complex waveguide structures and including the effects of dielectrics metallic screws round corners etc which cannot be easily considered when using semi analytical techniques in the second part the work is extended by presenting a fully automatic goal oriented hp adaptive fe in terms of the scattering or s parameters which are widely used in microwave engineering for the characterization of microwave devices

on orthogonal linear approximation the problem is considered of orthogonal l1 fitting of discrete data local best approximations are characterized and the question of the robustness of these solutions is considered an algorithm for the problem is presented along with numerical results of its application to some data sets

geometric invariance in image watermarking surviving geometric attacks in image watermarking is considered to be of great importance in this paper the watermark is used in an authentication context two solutions are being proposed for such a problem both geometric and invariant moments are used in the proposed techniques an invariant watermark is designed and tested against attacks performed by stirmark using the invariant moments on the other hand an image normalization technique is also proposed which creates a normalized environment for watermark embedding and detection the proposed algorithms have the advantage of being robust computationally efficient and no overhead needs to be transmitted to the decoder side the proposed techniques have proven to be highly robust to all geometric manipulations filtering compression and slight cropping which are performed as part of stirmark attacks as well as noise addition both gaussian and salt pepper

three points method for searching the best least absolute deviations plane in this paper a new method for estimation of optimal parameters of a best least absolute deviations plane is proposed which is based on the fact that there always exists a best least absolute deviations plane passing through at least three different data points the proposed method leads to a solution in finitely many steps moreover a modification of the aforementioned method is proposed that is especially adjusted to the case of a large number of data and the need to estimate parameters in real time both methods are illustrated by numerical examples on the basis of simulated data and by one practical example from the field of robotics

an hp adaptive finite element method for electromagnetics part 1 data structure and constrained approximation abstract this is the first of papers describing an implementation of the hp adaptive mixed finite element fe method for the solution of steady state maxwell s equations proposed in l demkowicz and l vardapetyan modeling of electromagnetic absoption scattering problems using hp adaptive finite elements computer methods in applied mechanics and engineering 152 1998 103 124 the discretization is defined on a hybrid grid consisting of both triangles and quads and allows for both h and p refinements of the mesh the paper focuses on the data structure and constrained approximation issues and provides a number of illustrative examples

approximating surfaces by moving total least squares method we suggest a method for generating a surface approximating the given data x i y i z i e r 3 i 1 m assuming that the errors can occur both in the independent variables x and y as well as in the dependent variable z our approach is based on the moving total least squares method where the local approximants local planes are determined in the sense of total least squares the parameters of the local approximants are obtained by finding the eigenvector corresponding to the smallest eigenvalue of a certain symmetric matrix to this end we develop a procedure based on the inverse power method the method is tested on several examples

generalized finite element systems for smooth differential forms and stokes problem we provide both a general framework for discretizing de rham sequences of differential forms of high regularity and some examples of finite element spaces that fit in the framework the general framework is an extension of the previously introduced notion of finite element systems and the examples include conforming mixed finite elements for stokes equation in dimension 2 we detail four low order finite element complexes and one infinite family of highorder finite element complexes in dimension 3 we define one low order complex which may be branched into whitney forms at a chosen index stokes pairs with continuous or discontinuous pressure are provided in arbitrary dimension the finite element spaces all consist of composite polynomials the framework guarantees some nice properties of the spaces in particular the existence of commuting interpolators it also shows that some of the examples are minimal spaces

dealing with the multiplicity of solutions of the l1 and l regression models abstract it is well known that the least absolute value l and the least sum of absolute deviations l1 algorithms produce estimators that are not necessarily unique in this paper it is shown how the set of all solutions of the l1 and l regression problems for moderately large sample sizes can be obtained in addition if the multiplicity of solutions wants to be avoided two new methods giving the same optimal l1 and l values but supplying unique solutions are proposed the idea consists of using two steps in the first step the optimal values of the l1 and l errors are calculated and in the second step in case of non uniqueness of solutions one of the multiple solutions is selected according to a different criterion for the l the procedure is used sequentially but removing in each iteration the data points with maximum absolute residual and adding the corresponding constraints for keeping these residuals and this process is repeated until no change in the solution is obtained in this way not only the maximum absolute residual values are minimized in the modified method but also the maximum absolute residual values of the remaining points sequentially until no further improvement is possible in the l1 case a least squares criterion is used but restricted to the l1 residual condition thus in the modified l1 method not only the l1 residual is minimized but also the sum of squared residuals subject to the l1 residual the methods are illustrated by their application to some well known examples and their performances are tested by some simulations which show that the lack of uniqueness problem cannot be corrected for some experimental designs by increasing the sample size

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

integration of hp adaptivity and a two grid solver for electromagnetic problems we present implementation details and analyze convergence of a two grid solver forming the core of a fully automatic hp adaptive strategy for electromagnetic problems the solver delivers a solution for a fine grid obtained from an arbitrary coarse hp grid by a global hp refinement the classical v cycle algorithm combines an overlapping block jacobi smoother with optimal relaxation and a direct solve on the coarse grid a theoretical analysis of the two grid solver is illustrated with numerical experiments several electromagnetic applications show the efficiency of combining the fully automatic hp adaptive strategy with the two grid solver

on the stability and convergence of higher order mixed finite element methods for second order elliptic problems we investigate the use of higher order mixed methods for second order elliptic problems by establishing refined stability and convergence estimates which take into account both the mesh size h and polynomial degree p our estimates yield asymptotic convergence rates for the p and h p versions of the finite element method they also describe more accurately than previously proved estimates the increased rate of convergence expected when the h version is used with higher order polynomials

on statistical data analysis based on the l1 norm and related methods an introduction to statistical data analysis l 1 norm based y dodge the place of the l 1 norm in robust estimation p j huber i historical development the historical development of the l 1 and l estimation procedures r w farebrother bounded influence inference in regression a review e ronchetti ii computational algorithms and computer packages algorithms for unconstrained l 1 linear regression j e gentle s c narula v a sposito the reduced gradient algorithm m r osborne the l 1 estimate as limiting case of an l p or huber estimate h ekblom a review of computational methods for solving the nonlinear l 1 norm estimation problem r gonin a h money fitting data through homotopy methods j p schellhorn blinwdr a fortran program for robust and bounded influence regression r dutter solving bounded influence regression problems with robsys a marazzi xplore a computing environment for exploratory regression w hardle iii estimation characterization properties and selection of variables l 1 distances in statistical inference comparison of topological functional and statistical properties i vajda the role played by l 1 in data analysis b fichet l 1 embeddings of a data structure i d g le calve assessing the accuracy of the sample median estimated standard errors vs interpolated confidence intervals s j sheather the median of a finite measure on a banach space j h b kemperman variable selection in linear model based on trimmed least squares estimator j antoch numerical techniques for finding estimates which minimize the upper bound of the absolute deviation a gaivoronski asymptotic properties of restricted l 1 estimates of regression j dupacova adaptive combination of least squares and least absolute deviations estimators y dodge j jureckova iv statistical inference procedures a comparison of asymptotic testing methods for l 1 regression r koenker least absolute errors analysis of variance j w mckean r m schrader small sample properties of least absolute errors analysis of variance r m schrader j w mckean bootstrap and inference procedures for l 1 regression g stangenhaus invariant tests in bivariate models and the l 1 criterion b m brown t p hettmansperger using regression fractiles to identify outliers s portnoy various discrepancy measures in model testing two competing regression models v v fedorov v nonparametric analysis kernel estimates of the sparsity function a h welsh what does optimal bandwidth selection mean for nonparametric regression estimation j s marron density estimation from dependent sample l gyorfi vi cluster analysis clustering by means of medoids l kaufman p j rousseeuw l 1 in fuzzy clustering e trauwaert using the l 1 norm within cluster analysis h spath vii applications an application of l 1 to astronomy p j rousseeuw

geometrically invariant watermarking using feature points this paper presents a new approach for watermarking of digital images providing robustness to geometrical distortions the weaknesses of classical watermarking methods to geometrical distortions are outlined first geometrical distortions can be decomposed into two classes global transformations such as rotations and translations and local transformations such as the stirmark attack an overview of existing self synchronizing schemes is then presented theses schemes can use periodical properties of the mark invariant properties of transforms template insertion or information provided by the original image to counter geometrical distortions thereafter a new class of watermarking schemes using the image content is presented we propose an embedding and detection scheme where the mark is bound with a content descriptor defined by salient points three different types of feature points are studied and their robustness to geometrical transformations is evaluated to develop an enhanced detector the embedding of the signature is done by extracting feature points of the image and performing a delaunay tessellation on the set of points the mark is embedded using a classical additive scheme inside each triangle of the tessellation the detection is done using correlation properties on the different triangles the performance of the presented scheme is evaluated after jpeg compression geometrical attack and transformations results show that the fact that the scheme is robust to these different manipulations finally in our concluding remarks we analyze the different perspectives of such content based watermarking scheme

approximating surfaces by the moving least absolute deviations method in this paper we are going to consider the problem of global data approximation on the basis of data containing outliers for that purpose a new method entitled the moving least absolute deviations method is proposed in the region of data in the network of knots weighted least absolute deviations local planes are constructed by means of which a global approximant is defined the method is tested on the well known franke s function an application in gridding of sonar data is also shown