3 d image denoising by local smoothing and nonparametric regression three dimensional 3 d images are becoming increasingly popular in image applications such as magnetic resonance imaging mri functional mri fmri and other image applications observed 3 d images often contain noise that should be removed beforehand for improving the reliability of subsequent image analyses in the literature most existing image denoising methods are for 2 d images their direct extensions to 3 d cases generally cannot handle 3 d images efficiently because the structure of 3 d images is often substantially more complicated than that of 2 d images for instance edge locations are surfaces in 3 d cases which are much more challenging to handle compared to edge curves in 2 d cases in this article we propose a novel 3 d image denoising procedure based on nonparametric estimation of a 3 d jump surface from noisy data one important feature of this method is its ability to preserve edges and major edge structures such as intersections of two edge surfaces pyramids pointed corn

bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

jump and sharp cusp detection by wavelets summary a method is proposed to detect jumps and sharp cusps in a function which is observed with noise by checking if the wavelet transformation of the data has significantly large absolute values across fine scale levels asymptotic theory is established and practical implementation is discussed the method is tested on simulated examples and applied to stock market return data the analysis of change points which describe sudden localised changes has recently found increasing interest change points can be used to model practical problems arising in fields such as quality control economics medicine signal and image processing and physical sciences for example in electroencephalogram signals sharp cusps exhibit the accelerations and decelerations in the beating of the hearts many practical problems like this involve functions which have jumps and sharp cusps the recently developed theory of wavelets has drawn much attention from both math ematicians statisticians and engineers in the seminal work of donoho 1993 donoho johnstone 1994 1995a b and donoho johnstone et al 1995 orthonormal bases of compactly supported wavelets have been used to estimate functions the theory of wavelets permits decomposition of functions into localised oscillating components this is an ideal tool to study localised changes such as jumps and sharp cusps in one dimension as well as several dimensions unlike traditional smoothing methods based on a fixed spatial scale the wavelet method is a multiresolution approach and has local adaptivity in this

propagation separation approach for local likelihood estimation the paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models including e g the regression density poisson and binary response model the method extends the adaptive weights smoothing aws procedure introduced in polzehl and spokoiny 2000 in context of image denoising the main idea of the method is to describe a greatest possible local neighborhood of every design point x i in which the local parametric assumption is justified by the data the method is especially powerful for model functions having large homogeneous regions and sharp discontinuities the performance of the proposed procedure is illustrated by numerical examples for density estimation and classification we also establish some remarkable theoretical nonasymptotic results on properties of the new algorithm this includes the propagation property which particularly yields the root n consistency of the resulting estimate in the homogeneous case we also state an oracle result which implies rate optimality of the estimate under usual smoothness conditions and a separation result which explains the sensitivity of the method to structural changes

the local piecewisely linear kernel smoothing procedure for fitting jump regression surfaces it is known that a surface fitted by conventional local smoothing procedures is not statistically consistent at the jump locations of the true regression surface this article suggests a procedure for modifying conventional local smoothing procedures such that the modified procedures fit the surface with jumps preserved automatically taking the local linear kernel smoothing procedure as an example in a neighborhood of a given point a bivariate piecewisely linear function is fitted with possible jumps along the boundaries of four quadrants the fitted function provides four estimators of the surface at the given point which are constructed from observations in the four quadrants when the difference among the four estimators is smaller than a threshold value the given point is most likely a continuous point and the surface at that point is then estimated by the average of the four estimators when the difference is larger than the threshold value the given point is likely a jump point and at least

change point estimation using nonparametric regression we consider a regression model in which the mean function may have a discontinuity at an unknown point we propose an estimate of the location of the discontinuity based on one side nonparametric regression estimates of the mean function the change point estimate is shown to converge in probability at rate 0 n 1 and to have the same asymptotic distribution as maximum likelihood estimates considered by other authors under parametric regression models confidence regions for the location and size of the change are also discussed

edge preserving and peak preserving smoothing an alternative procedure is developed to the smoothed linear fitting method of mcdonald and owen the procedure is based on the detection of discontinuities by comparing at any given position three smooth fits diagnostics are used to detect discontinuities in the regression function itself edge detection or in its first derivative peak detection an application in electron microscopy is discussed

a measure theoretic approach to the theory of dense hypergraphs in this paper we develop a measure theoretic method to treat problems in hypergraph theory our central theorem is a correspondence principle between three objects an increasing hypergraph sequence a measurable set in an ultraproduct space and a measurable set in a finite dimensional lebesgue space using this correspondence principle we build up the theory of dense hypergraphs from scratch along these lines we give new proofs for the hypergraph removal lemma the hypergraph regularity lemma the counting lemma and the testability of hereditary hypergraph properties we prove various new results including a strengthening of the regularity lemma and an inverse counting lemma we also prove the equivalence of various notions for convergence of hypergraphs and we construct limit objects for such sequences we prove that the limit objects are unique up to a certain family of measure preserving transformations as our main tool we study the integral and measure theory on the ultraproduct of finite measure spaces which is interesting on its own right

differential quadrature layerwise modeling technique for three dimensional analysis of cross ply laminated plates of various edge supports abstract in this paper a differential quadrature model is proposed which is established within a layerwise framework for the bending analysis of composite laminates three dimensional theory of elasticity is implemented and all physical governing equations are satisfied including characteristics of the continuity and discontinuity of interfacial transverse and in plane displacements strains and stresses along interfaces of the composite laminates thus delivering highly accurate numerical solutions variation in boundary conditions plate aspect and thickness ratios and loading conditions are examined demonstrating the applicability accuracy and stability of the present methodology numerical examples for rectangular cross ply laminated plates subjected to a uniform load sinusoidal load or uniformly distributed moment are studied selected results from these examples are compared with those available in existing published literature

discontinuous regression surfaces fitting we suggest a three stage procedure to recover discontinuous regression surfaces when noisy data are present in the first stage jump candidate points are detected using a jump detection criterion a local principal component line is then fitted through these points in a neighborhood of a design point this line provides a first order approximation to the true jump location curve in that neighborhood in the third stage observations on the same side of the line as the given point are combined using a weighted average procedure to fit the surface at that point if there are no jump candidate points in the neighborhood then all observations in that neighborhood are used in the surface fitting if however the center of the neighborhood is on a jump location curve only those observations on one side of the line are used thus blurring is automatically avoided around the jump locations this methodology requires o n k 2 computation where n is the sample size and k is the window width its assumptions on the model are flexible some numerical results are presented to evaluate the surface fit and to discuss the selection of the window widths

application of the boundary integral equation method to reissner s plate model numerical solution of reissner s model for the bending of elastic plates by an advanced boundary integral equation method is outlined construction of fundamental solutions and computational strategy is fully described implementation of the resulting one dimensional model is illustrated by two test problems including comparison to analytical solutions

a two stage algorithm for discontinuity preserving surface reconstruction a two stage algorithm for visual surface reconstruction from scattered data while preserving discontinuities is presented the first stage consists of a robust local approximation algorithm the moving least median of squares mlms of error to clean the data and create a grid from the original scattered data points this process is discontinuity preserving the second stage introduces a weighted bicubic spline wbs as a surface descriptor the wbs has a factor in the regularizing term that adapts the behavior of the spline across discontinuities the weighted bicubic approximating spline can approximate data with step discontinuities with no discernible distortion in the approximating surface the combination of robust surface fitting and wbss removes outliers and reduces gaussian noise either stage by itself would not effectively remove both kinds of noise experimental results with the two stage algorithm are presented

generalized differential quadrature method for the free vibration of truncated conical panels abstract this paper presents an improved generalized differential quadrature gdq method for the investigation of the effects of boundary conditions on the free vibration characteristics of truncated conical panels the truncated conical panel is an important geometrical shape in the fields of aerospace marine and structural engineering however despite this importance few works in free vibration analysis have dealt with this particular geometry in this work the vibration characteristics of clamped and simply supported truncated conical shells are obtained for various circumferential wave numbers further the effects of the vertex and subtended angles on the frequency parameters are also examined in detail due to limited published results in the open literature results for a range of cases are compared with those generated from the commercial finite element solver mcneal schwendler corporation nastran and excellent agreement is observed

discontinuity preserving and viewpoint invariant reconstruction of visible surfaces using a first order regularization this paper describes the application of a first order regularization technique to the reconstruction of visible surfaces our approach is a computationally efficient first order method that simultaneously achieves approximate invariance and preservation of discontinuities it is also robust with respect to the smoothing parameter spl lambda the robustness property to spl lambda allows a free choice of spl lambda without struggling to determine an optimal spl lambda that provides the best reconstruction a new approximately invariant first order stabilizing function for surface reconstruction is obtained by employing a first order taylor expansion of a nonconvex invariant stabilizing function that is expanded at the estimated value of the squared gradient instead of at zero the data compatibility measure is the squared perpendicular distance between the reconstructed surface and the constraint surface this combination of stabilizing function and data compatibility measure is necessary to achieve invariance with respect to rotations and translations sharp preservation of discontinuities is achieved by a weighted sum of adjacent pixels the results indicate that the proposed methods perform well on sparse noisy range data in addition the volume between two surfaces normalized by the surface area interpreted as average distance between two surfaces is proposed as an invariant measure for the comparison of reconstruction results

an edge detection technique using genetic algorithm based optimization abstract in this paper we present a genetic algorithm based optimization technique for edge detection the problem of edge detection is formulated as one of choosing a minimum cost edge configuration the edge configurations are viewed as two dimensional chromosomes with fitness values inversely proportional to their costs the design of the crossover and the mutation operators in the context of the two dimensional chromosomal representation is described the knowledge augmented mutation operator which exploits knowledge of the local edge structure is shown to result in rapid convergence the incorporation of meta level operators and strategies such as the elitism strategy the engineered conditioning operator and adaptation of mutation and crossover rates in the context of edge detection are discussed and are shown to improve the convergence rate the genetic algorithm with various combinations of meta level operators is tested on synthetic and natural images the performance of the genetic algorithm based cost minimization technique is compared both qualitatively and quantitatively with local search based and simulated annealing based cost minimization approaches the genetic algorithm based technique is shown to perform very well in terms of robustness to noise rate of convergence and quality of the final edge image

the koiter newton approach using von karman kinematics for buckling analyses of imperfection sensitive structures the koiter newton approach is a reduced basis method for nonlinear structural analyses the method combines koiter s approach as a predictor step and the newton arc length technique as a corrector step to trace the entire load displacement equilibrium path of a structure in a step by step manner this computationally highly efficient and accurate solution method has recently demonstrated a superior performance in nonlinear analyses compared to standard techniques in this paper we propose an extension to buckling imperfection sensitivity analyses exploiting the method s stability and reliability we present two different modeling techniques for imperfection loads that both profit from the koiter newton approach reducing the initial computation steps to a small fraction thereof we introduce von karman kinematics which neglect some nonlinear terms of the green strain displacement relations to further increase the computational efficiency of the analysis by an essential reduction of the computation effort required to obtain higher order derivatives of the strain energy using various numerical examples and benchmark tests we demonstrate the overall high quality and performance of the proposed method

uniqueness of banach space valued graphons abstract a banach space valued graphon is a function w a 2 z from a probability space to a banach space with a separable predual measurable in a suitable sense and lying in appropriate l p spaces as such we may consider w x y as a two variable random element of the banach space a two dimensional analogue of moments can be defined with the help of graphs and weak evaluations and a natural question that then arises is whether these generalized moments determine the function w uniquely up to measure preserving transformations the main motivation comes from the theory of multigraph limits where these graphons arise as the natural limit objects for convergence in a generalized homomorphism sense our main result is that this holds true under some carleman type condition but fails in general even with z r for reasons related to the classical moment problem in particular limits of multigraph sequences are uniquely determined up to measure preserving transformations whenever the tails of the edge distributions stay small enough

non linear bending analysis of plates and shells by using a mixed spline boundary element and finite element method in this paper a mixed spline boundary element and finite element method is suggested to analyse non linear bending of plates and shells only the fundamental solutions for plates are required in order to establish the boundary integral equations a quadratic rectangular spline element is adopted to deal with the membrane effects of plates and shells numerical examples show that the approach developed in this paper is very effective and especially promising for the non linear analysis of plates and shells

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

a local polynomial jump detection algorithm in nonparametric regression we suggest a one dimensional jump detection algorithm based on local polynomial fitting for jumps in regression functions zero order jumps or jumps in derivatives first order or higherorder jumps if jumps exist in the mth order derivative of the underlying regression function then an m 1 order polynomial is fitted in a neighborhood of each design point we then characterize the jump information in the coefficients of the highest order terms of the fitted polynomials and suggest an algorithm for jump detection this method is introduced briefly for the general setup and then presented in detail for zero order and first order jumps several simulation examples are discussed we apply this method to the bombay india sea level pressure data

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

local likelihood tracking of fault lines and boundaries summary we suggest locally parametric methods for estimating curves such as boundaries of density supports or fault lines in response surfaces in a variety of spatial problems the methods are based on spatial approximations to the local likelihood that the curve passes through a given point in the plane as a function of that point the local likelihood might be a regular likelihood computed locally with kernel weights e g in the case of support boundary estimation or a local version of a likelihood ratio statistic e g in fault line estimation in either case the local likelihood surface represents a function which is relatively large near the target curve and relatively small elsewhere therefore the curve may be estimated as a ridge line of the surface we require only a numerical algorithm for tracking the projection of a ridge into the plane this approach offers several potential advantages over alternative methods first the local log likelihood surface can be graphed and the degree of ridginess assessed visually to determine how the level of local smoothing should be varied in different spatial locations in order to emphasize the ridge and hence the curve adequately secondly the local likelihood surface does not need to be computed in anything like its entirety once we have a reasonable approximation to a point on the curve we may track it by numerically walking along the ridge line thirdly the method is appropriate without change for many different types of spatial explanatory vanables gridded stochastic or otherwise three examples are explored in detail fault lines in response surfaces and in intensity or density surfaces and boundaries of supports of probability densities

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

the direct boundary element method in plate bending the direct boundary element method based on the rayleigh green identity is employed for the static analysis of kirchhoff plates the starting point is a slightly modified version of stern s equations the focus is on the implementation of the method for linear elements and a hermitian interpolation for the deflection w the concept of element matrices is developed and the cauchy principal values of the singular integrals are given in detail the treatment of domain integrals the handling of internal supports the properties of the solution and the effect of singularities are discused numerical examples illustrate the various techniques in the appendix the influence functions for the second and third derivatives of the deflection w are given

on discontinuity adaptive smoothness priors in computer vision a variety of analytic and probabilistic models in connection with markov random fields mrfs have been proposed in the last decade for solving low level vision problems involving discontinuities this paper presents a systematic study of these models and defines a general discontinuity adaptive da mrf model by analyzing the euler equation associated with the energy minimization it shows that the fundamental difference between different models lies in the behavior of interaction between neighboring points which is determined by the a priori smoothness constraint encoded into the energy function an important necessary condition is derived for the interaction to be adaptive to discontinuities to avoid oversmoothing this forms the basis on which a class of adaptive interaction functions aifs is defined the da model is defined in terms of the euler equation constrained by this class of aifs its solution is c sup 1 continuous and allows arbitrarily large but bounded slopes in dealing with discontinuities because of the continuous nature it is stable to changes in parameters and data a good property for regularizing ill posed problems experimental results are shown

maximal meaningful events and applications to image analysis we discuss the mathematical properties of a recently introduced method for computing geometric structures in a digital image without any a priori information this method is based on a basic principle of perception which we call the helmholtz principle according to this principle an observed geometric structure is perceptually meaningful if the expectation of its number of occurrences in other words its number of false alarms nf is very small in a random image it is maximal meaningful if its nf is minimal among the meaningful structures of the same kind which it contains or is contained in this definition meets the gestalt theory requirement that parts of a whole are not perceived we explain by large deviation estimates why this definition leads to an a priori knowledge free method compatible with phenomenology we state a principle according to which maximal structures do not meet we prove this principle in the large deviations framework in the case of alignments in a digital image we show why these results make maximal meaningful structures computable and display several applications

a boundary element analysis of symmetric laminated composite shallow shells this paper presents a boundary element formulation for the analysis of symmetric laminated composite shallow shells where only the boundary is discretized classical plate bending and plane elasticity formulations are coupled and effects of curvature are treated as body forces fundamental solutions for elastostatic formulations are used and body forces are written as a sum of approximation functions multiplied by unknown coefficients two approximation functions are used domain integrals which arise in the formulation are transformed into boundary integrals by the radial integration method results for the approximation functions are compared and the accuracy of the proposed formulation is assessed by results from literature it was shown that results obtained with the approximation function called augmented thin plate spline present very good agreement with literature even for shells that are not so shallow

kernel type estimators of jump points and values of a regression function in the fixed design nonparametric regression model kernel type estimators of the locations of jump points and the corresponding sizes of jump values of the regression function are proposed these kernel type estimators are analyzed with almost sure results and limiting distributions using the limiting distributions we are able to test the number of jump points and give asymptotic confidence intervals for the sizes of jump values of the regression function simulation studies demonstrate that the asymptotic results hold for reasonable sample sizes

nonlinear stability analysis of thin doubly curved orthotropic shallow shells by the differential quadrature method the geometric nonlinear buckling problem of a thin doubly curved shallow shell with all edges hinged is complicated and difficult to obtain an exact analytical solution thus differential equations are solved incrementally by using the differential quadrature method in this paper detailed formulations are worked out convergence study is performed several examples with various material properties curvatures and dimensions are investigated comparisons are made with existing semi analytical data or finite element data it is shown that the critical loads are lower than the data obtained by either so called adjacent equilibrium method or partitioned solution method the possible reasons to cause the difference are discussed

on optimal selection of interior points for applying discretized boundary conditions in dq vibration analysis of beams and plates the direct implementation of derivative boundary conditions at edge points was demonstrated to be simple flexible and computationally efficient in the vibration analysis of beams and plates by using the differential quadrature dq method in the approach the discretized governing equations at certain interior points need to be replaced by the discretized boundary conditions naturally one may have questions as to whether the replacement points can be selected arbitrarily and how to choose the optimal replacement points this paper tries to answer these questions and its focus is to investigate systematically the effect of the replacement location on the accuracy of the numerical solution from the error distribution analysis of derivative approximation it is found that the optimal position for the replacement is the interior point just adjacent to the boundary this conclusion is confirmed by the numerical experiments of free vibration analysis for beams and plates with various boundary conditions

likelihood based confidence bands for fault lines in response surfaces we consider the problem of constructing asymptotic confidence bands both pointwise and simultaneous for a smooth fault line in a response surface when the design is represented by a point process either deterministic or stochastic with intensity n diverging to infinity the estimator of the fault line is defined as the ridge line on the likelihood surface which arises from locally fitting a model that employs a linear approximation to the fault line to a kernel smooth of the data the construction is based on analysis of the limiting behaviour of perpendicular distance from a point on the true fault line to the nearest point on the ridge we derive asymptotic properties of bias and the limiting distribution of stochastic error this distribution is given by the location of the maximum of a gaussian process with quadratic drift although the majority of attention is focused on the regression problem the limiting distribution is shown to have wider relevance to local likelihood approaches to fault line estimation for density or intensity surfaces

unscented transformation based estimation of parameters of nonlinear models using heteroscedastic data this paper addresses the issue of estimating the parameters of nonlinear models using heteroscedastic data a weighted least squares problem formulation where the sum of the mahalanobis distance for all measurements is minimized forms the framework of this paper determining the mahalanobis distance requires the gradient of the cost function with respect to the noisy measurements which can be computationally expensive and infeasible for model which are discontinuous a derivative free approach to determine the mahalanobis distance as an error metric is proposed using the unscented transformation the advantages of using the proposed approach include a black box approach to evaluate the gradient weighted objective function precluding the need for analytical gradients and an improved estimation of the covariance numerical results for various applications such as triangulation using radar measurements ellipse and super ellipse fitting demonstrate the benefits of the proposed approach heteroscedastic data resulting from real x ray images are also used to illustrate the potential of the proposed approach highlightsderivative free approach of solving gradient weighted least squares problems improved approximation of the geometric distance for curve fitting improved performance of proposed technique demonstrated on three benchmarks monte carlo used to benchmark the reduction in bias in estimated parameters relevant to model fitting problems with heteroscedastic data

nonparametric simultaneous testing for structural breaks in this paper we consider a regression model with errors that are martingale differences this modeling includes the regression of both independent and time series data the aim is to study the appearance of structural breaks in both the mean and the variance functions assuming that such breaks may occur simultaneously in both the functions we develop nonparametric testing procedures that simultaneously test for structural breaks in the conditional mean and the conditional variance the asymptotic distribution of an adaptive test statistic is established as well as its asymptotic consistency and efficiency simulations illustrate the performance of the adaptive testing procedure an application to the analysis of financial time series also demonstrates the usefulness of the proposed adaptive test in practice

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

an accurate and efficient implementation of initial geometrical imperfections in the predictor corrector reduced order modeling method abstract a predictor corrector reduced order modeling method based on koiter theory is proposed for nonlinear buckling analysis of thin walled structures with initial geometric imperfections the imperfections are implemented into the von karman kinematics and are considered using an a priori and a posteriori manners respectively in buckling analysis since the nonlinear predictor obtained from the reduced order model with imperfections provides a fairly large step size in path tracing the a priori account of imperfections still shows advantages in computational efficiency the advantages are more significant when considering a posteriori the effects of imperfections in the reduced order model of the structure without imperfections which means building once and for all by simply adding some independent imperfection terms in the reduced system the a posteriori accounts of imperfections with the first second order accuracies are developed respectively to deal with the linear nonlinear prebuckling behaviors and small large imperfection amplitudes the good performance of the proposed method in terms of reliability accuracy and computational effort is demonstrated with several examples using the linear buckling modes or measured geometric shapes as whole field geometric imperfections

free vibration analysis of functionally graded conical cylindrical shell and annular plate structures with a four parameter power law distribution based on the first order shear deformation theory fsdt this paper focuses on the dynamic behavior of moderately thick functionally graded conical cylindrical shells and annular plates the last two structures are obtained as special cases of the conical shell formulation the treatment is developed within the theory of linear elasticity when materials are assumed to be isotropic and inhomogeneous through the thickness direction the two constituent functionally graded shell consists of ceramic and metal these constituents are graded through the thickness from one surface of the shell to the other a generalization of the power law distribution presented in literature is proposed two different four parameter power law distributions are considered for the ceramic volume fraction some material profiles through the functionally graded shell thickness are illustrated by varying the four parameters of power law distributions for the first power law distribution the bottom surface of the structure is ceramic rich whereas the top surface can be metal rich ceramic rich or made of a mixture of the two constituents and on the contrary for the second one symmetric and asymmetric volume fraction profiles are presented in this paper the homogeneous isotropic material can be inferred as a special case of functionally graded materials fgm the governing equations of motion are expressed as functions of five kinematic parameters by using the constitutive and kinematic relationships the solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell the discretization of the system equations by means of the generalized differential quadrature gdq method leads to a standard linear eigenvalue problem where two independent variables are involved without using the fourier modal expansion methodology numerical results concerning six types of shell structures illustrate the influence of the power law exponent of the power law distribution and of the choice of the four parameters on the mechanical behaviour of shell structures considered

difference detection between two images for image monitoring abstractin manufacturing industries images are commonly used for quality control purposes in such applications if the quality of the products is good then their images should be all similar to the image of a good quality product therefore comparison of images is a fundamental task in image based quality control this problem however is complicated in the sense that 1 observed images often contain noise and 2 the related images need to be geometrically matched up first because images of different products could be geometrically mismatched because the relative positions between a camera and different products are often not exactly the same the first issue requires a statistical method that can remove noise and the second issue is related to the so called image registration problem in the image processing literature in this article we propose effective methods for detecting difference between two images of products and our proposed methods can accommodate both noise and geometric mismatch m

edge structure preserving 3d image denoising by local surface approximation in various applications including magnetic resonance imaging mri and functional mri fmri 3d images are becoming increasingly popular to improve the reliability of subsequent image analyses 3d image denoising is often a necessary preprocessing step which is the focus of the current paper in the literature most existing image denoising procedures are for 2d images their direct extensions to 3d cases generally cannot handle 3d images efficiently because the structure of a typical 3d image is substantially more complicated than that of a typical 2d image for instance edge locations are surfaces in 3d cases which would be much more challenging to handle compared to edge curves in 2d cases we propose a novel 3d image denoising procedure in this paper based on local approximation of the edge surfaces using a set of surface templates an important property of this method is that it can preserve edges and major edge structures e g intersections of two edge surfaces and pointed corners numerical studies show that it works well in various applications

a boundary element formulation for geometrically nonlinear analysis of shear deformable shells abstract a new boundary element method to solve geometrically nonlinear deflection problems of shear deformable shallow shells having quadratic mid surface is presented the displacement integral equations have been derived to obtain five integral equations in term of displacements two rotations one out of plane displacement and two in plane displacements the boundary is discretised into quadratic isoparametric elements and the domain is transferred to the boundary using the dual reciprocity technique a simple yet efficient load incremental technique is developed to solve the nonlinear problem several examples are presented and the results are in good agreement with the finite element method

image denoising pointwise adaptive approach a new method of pointwise adaptation has been proposed and studied in spokoiny 1998 ann statist 26 1356 1378 in the context of estimation of piecewise smooth univariate functions the present paper extends that method to estimation of bivariate grey scale images composed of large homogeneous regions with smooth edges and observed with noise on a gridded design the proposed estimator hat f x at a point x is simply the average of observations over a window widehat u x selected in a data driven way the theoretical properties of the procedure are studied for the case of piecewise constant images we present a nonasymptotic bound for the accuracy of estimation at a specific grid point x as a function of the number of pixels n of the distance from the point of estimation to the closest boundary and of smoothness properties and orientation of this boundary it is also shown that the proposed method provides a near optimal rate of estimation near edges and inside homogeneous regions we briefly discuss algorithmic aspects and the complexity of the procedure the numerical examples demonstrate a reasonable performance of the method and they are in agreement with the theoretical issues an example from satellite sar imaging illustrates the applicability of the method

general anisotropic doubly curved shell theory a differential quadrature solution for free vibrations of shells and panels of revolution with a free form meridian abstract the generalized differential quadrature gdq method is applied to study the dynamic behavior of anisotropic doubly curved shells and panels of revolution with a free form meridian the first order shear deformation theory fsdt is used to analyze the above mentioned moderately thick structural elements in order to include the effect of the initial curvature in the evaluation of the stress resultants three different approaches specifically qatu approach toorani lakis approach and reissner mindlin approach are considered and compared an improvement of the classical reissner mindlin theory crmt using a different kinematical model is considered by so doing a generalization of the theory of anisotropic doubly curved shells and panels of revolution is proposed four different anisotropic shell theories namely general first order shear deformation theory by qatu gfsdtq general first order shear deformation theory by toorani lakis gfsdttl general first order shear deformation theory by reissner mindlin gfsdtrm and classical reissner mindlin theory crmt are compared in order to show the differences and the accuracy of these theories the solution is given in terms of generalized displacement components of points lying on the middle surface of the shell simple rational bezier curves are used to define the meridian curve of the revolution structures results are obtained taking the meridian and circumferential coordinates into account without using the fourier modal expansion methodology furthermore gdq results are compared with those obtained by using commercial programs such as abaqus ansys nastran straus and pro mechanica very good agreement is observed

nonparametric estimation of a regression function consider the regression model y i g x i e i i 1 2 n where x i s denote unordered design variables and g is an unknown function defined on the interval 0 1 assume e i are iid random variables with zero mean and finite variance priestley and chao 1972 and clark 1977 proposed estimators g 2n and g 3n respectively for g in this paper the asymptotic behavior of g 2n and g 3n is studied utilizing the properties of the new estimator g 1n it is shown that g 1n g 2n g 3n are asymptotically equivalent in various senses moreover consistency results are established and rates of uniform convergence obtained for example if e e 3 if g is lipschitz of order 1 and if n is any sequence of constants tending to as n then for all 0 a leqq b 1 n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 mathord left vphantom n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 right kern nulldelimiterspace beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 as n finally when g is monotone a strong consistent isotonic estimator g n is considered

poset limits can be totally ordered s janson poset limits and exchangeable random posets combinatorica 31 2011 529 563 defined limits of finite posets in parallel to the emerging theory of limits of dense graphs we prove that each poset limit can be represented as a kernel on the unit interval with the standard order thus answering an open question of janson we provide two proofs real analytic and combinatorial the combinatorial proof is based on a szemeredi type regularity lemma for posets which may be of independent interest also as a by product of the analytic proof we show that every atomless ordered probability space admits a measure preserving and almost order preserving map to the unit interval

edge preserving image denoising and estimation of discontinuous surfaces in this paper we are interested in the problem of estimating a discontinuous surface from noisy data a novel procedure for this problem is proposed based on local linear kernel smoothing in which local neighborhoods are adapted to the local smoothness of the surface measured by the observed data the procedure can therefore remove noise correctly in continuity regions of the surface and preserve discontinuities at the same time since an image can be regarded as a surface of the image intensity function and such a surface has discontinuities at the outlines of objects this procedure can be applied directly to image denoising numerical studies show that it works well in applications compared to some existing procedures

jump surface estimation edge detection and image restoration surface estimation is important in many applications when conventional smoothing procedures e g running averages local polynomial kernel smoothing procedures smoothing spline procedures are used for estimating jump surfaces from noisy data jumps are blurred at the same time when noise is removed in recent years new smoothing methodologies have been proposed in the statistical literature for detecting jumps in surfaces and for estimating jump surfaces with jumps preserved we provide a review of these methodologies because a monochrome image can be considered a jump surface of the image intensity function with jumps at the outlines of objects edge detection and image restoration problems in image processing are closely related to the jump surface estimation problem in statistics we also review major methodologies on edge detection and image restoration and discuss connections and differences among these methods and related methods in the statistical literature

change points in nonparametric regression analysis an otherwise smooth regression model are proposed the assumptions needed are much weaker than those made in parametric models the proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change points of slope and of higher order curvature the proposed estimators are based on a comparison of left and right one sided kernel smoothers weak convergence of a stochastic process in local differences to a gaussian process is established for properly scaled versions of estimators of the location of a change point the continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change point estimators these rates are typically faster than n 1 2 rates of global lp convergence of curve estimates with appropriate kernel modifications adapting to estimated change points are derived as a consequence it is shown that these rates of convergence are the same as if the location of the change point was known the methods are illustrated by means of the well known data on the annual flow volume of the nile river between 1871 and 1970 1 introduction nonparametric regression methods are usually applied in order to obtain a smooth fit of a regression curve without having to specify a parametric class of regression functions sometimes a generally smooth curve might contain an isolated discontinuity or change point in the curve or in a possibly higher order derivative and in many cases interest focuses on the occurrence of such change points in parametric approaches to the regression change point problem simple linear regressions before and after a possible change point are assumed and then the possibility of a discontinuity in the form of a jump or of a jump in the first derivative or equivalently a slope change is incorporated into the model see for instance hinkley 1969 and brown durbin and evans 1975 the analysis of change points which describe sudden localized changes typically occurring in economics medicine and the physical sciences has recently found increasing interest general smoothness assumptions allowing for a large class of regression functions to be considered seem to be more appropriate in a variety of applied problems than parametric modelling an

smoothing with split linear fits we introduce a family of smoothing algorithms that can produce discontinuous output unlike most commonly used smoothers that tend to blur discontinuities in the data this smoother can be used for smoothing with edge detection we cite examples of other approaches to two dimensional smoothing with edge detection in image processing and apply our one dimensional smoother to sea surface temperature data where the discontinuities arise from changes in ocean currents

static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method a new version of the differential quadrature method is presented in this paper to overcome the difficulty existing in the ordinary differential quadrature method for applying multi boundary conditions in two dimensional problems since the weighting coefficients of the first derivative are the same as for the ordinary differential quadrature method even with the introduction of multi degree of freedom at the boundary points the method is easier to extend to two or three dimensional problems a new version of the differential quadrature plate element has been established for demonstration the essential difference from the existing old version of the differential quadrature plate element is the way the weighting coefficients are determined the methodology is worked out in detail and some numerical examples are given to show the efficiency of the present method