layer solutions in a half space for boundary reactions r n 1 are denoted by y y1 yn 1 our main goal is to study bounded solutions of 1 1 that are monotone increasing say from 1 to 1 in one of the y variables we call them layer solutions of 1 1 and we study their existence uniqueness symmetry and variational properties as well as their asymptotic behavior the interest in such increasing solutions comes from some models of boundary phase transitions when the nonlinearity f is given by f u sin cu for some constant c problem 1 1 in a half plane is called the peierls nabarro problem and it appears as a model of dislocations in crystals see 21 36 the peierls nabarro problem is also central to the analysis of boundary vortices in the paper 28 which studies a model for soft thin films in micromagnetism recently derived by kohn and slastikov 26 see also 27 our main result theorem 1 2 characterizes the nonlinearities f for which there exists a layer solution of 1 1 in dimension n 2 we prove that the necessary and sufficient condition is that the potential g defined by g f has two and only two absolute minima in the interval 1 1 located at 1 under the additional hypothesis g 1 0 we also establish the uniqueness of a layer solution up to translations in the y variable the proofs of both the necessity and the sufficiency of the condition on g for existence use new ingredients which we develop in this article a first one is a nonlocal estimate as well as a conserved or hamiltonian quantity satisfied by every layer solution in dimension 2 see theorem 1 3 the estimate can be seen as

image based lens geometric distortion correction using minimization of average bicoherence index in this paper a lens geometric distortion correction method for low cost digital cameras is described the lens distortion coefficient is estimated by the value minimizing average bicoherence index which denotes image dependent higher order correlations in the frequency domain in order to formulate the minimization of the average bicoherence index in terms of the lens distortion coefficient alone the feasibility of a square pixel assumption and the effect of the image center bias on the image quality are shown experimentally at the same time a computationally efficient method for calculating the bicoherence index is proposed which comprises an approximation of coordinate resampling and development of a relationship between the lens distortion coefficients of the original and its reduced image depending on the spatial distribution of image features the performance of the proposed method can be made comparable to that of precision camera calibration

numerical solution of nonlinear hypersingular integral equations of the peierls type in dislocation theory in this paper we analyze hypersingular integral equations of the peierls type specified on the whole real axis the method of approximate approximations maz ya proceedings of the eighth conference on the mathematics of finite elements and applications viii mafelap 1993 brunel university 1994 pp 107 104 is employed in order to produce numerical solutions of high accuracy and the results are applied to problems in the theory of dislocations the critical peierls stress is evaluated for different configurations of dislocations and for different types of the interatomic force law

on stable solutions for boundary reactions a de giorgi type result in dimension 4 1 we prove that every bounded stable solution of begin aligned delta 1 2 u f u 0 qquad text in mathbb r 3 end aligned is a 1d profile i e u x phi e cdot x for some e in mathbb s 2 where phi mathbb r rightarrow mathbb r is a nondecreasing bounded stable solution in dimension one equivalently stable critical points of boundary reaction problems in mathbb r d 1 mathbb r d 1 cap x d 1 ge 0 of the form begin aligned int x d 1 ge 0 frac 1 2 nabla u 2 dx dx d 1 int x d 1 0 f u dx end aligned are 1d when d 3 these equations have been studied since the 1940 s in crystal dislocations also as it happens for the allen cahn equation the associated energies enjoy a gamma convergence result to the perimeter functional in particular when f u u 3 u or equivalently when f u frac 1 4 1 u 2 2 our result implies the analogue of the de giorgi conjecture for the half laplacian in dimension 4 namely that monotone solutions are 1d note that our result is a pde version of the fact that stable embedded minimal surfaces in mathbb r 3 are planes it is interesting to observe that the corresponding statement about stable solutions to the allen cahn equation namely when the half laplacian is replaced by the classical laplacian is still unknown for d 3

prediction intervals for screening using a measured correlated variate at least i units are required whose values of a performance variable y fall below the upper specification limit u they are obtained by screening units on a correlated variable x until m units are obtained whose values of x meet the threshold w the numbers i and m are specified in advance of screening and w needs to be determined two cases are discussed one with all parameters known and one with all parameters unknown the analysis in this paper amounts to the application of a binomial model in addition to the bivariate normal screening model previously discussed in owen mclntire and seymour 1975 and in owen and su 1977 when the bivariate distribution parameters are unknown finding w is similar to the prediction interval problem discussed in the literature some illustrative tables and examples are included

screening on correlated variables a bayesian approach let x and y be two correlated variables where the measurement of x is easier or less expensive to make than the one on y suppose that the y measurement is required to meet a certain specification limit given that the joint distribution of x y is bivariate normal and given the sufficient statistics from a random sample from this distribution we propose a bayesian method for determining a cutoff limit on x so that with a guaranteed probability y meets its specification limit monte carlo simulations are used to evaluate the bayesian procedure it is seen to be less conservative than the method of owen li and chou 1981 and it is fairly robust under nonnormality an example using data from one time point to predict results at another time point illustrates the application of the method

the extended domain eigenfunction method for solving elliptic boundary value problems with annular domains standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely if ever obtainable in this paper we propose a solution technique wherein we embed the original

screening in a normal model on presente une approche bayesienne a travers l utilisation de probabilites predictives et on l applique a un modele parametrique dans lequel y x a une distribution normale bivariable

the peierls nabarro and benjamin ono equations abstract an intimate connection between the peierls nabarro equation in crystal dislocation theory and the travelling wave form of the benjamin ono equation in hydro dynamics is uncovered it is used to prove the essential uniqueness of peierls solution of the peierls nabarro equation and to give in closed form all solutions of the analogous periodic problem the latter problem is shown to be an example of global bifurcation with no secondary symmetry breaking bifurcations for a nonlinear neumann boundary value problem or equivalently for an equation involving the conjugate operator which is the hilbert transform of functions on the unit circle

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

high accuracy periodic solutions to the sivashinsky equation the aim of this work is the accurate calculation of periodic solutions to the sivashinsky equation which models dynamics of the long wave instability of laminar premixed flame a highly accurate computational algorithm was developed in both one and two spatial dimensions and its crucial implementation details are presented the algorithm is based on the concept of saturated asymptotic approximations and can be straightforwardly extended to a wide variety of nonlinear integro differential equations the development of such an algorithm was motivated by difficulties in interpretation of the results of numerical experiments with the sivashinsky equation using spectral methods the computations carried out by the algorithm in question are in good agreement with the results obtained earlier by spectral methods analysis of the accuracy of obtained numerical solutions and of their stabilization to steady states supports the idea of the instability of the steady coalescent pole solutions with maximal possible number of poles to the sivashinsky equation in large domains through huge linear transient amplification of nonmodal perturbations of small but finite amplitudes

diagnostic and sampling models in screening summary screening methods are developed which raise the proportion of successes in the retained population to a predetermined level specification regions for the screening variables are derived within both the diagnostic and sampling paradigms dawid 1976 logistic and normal models are used for the two frameworks and the results are illustrated by an example of screening for malnourishment

nonlinear fractional laplacian problems with nonlocal gradient terms let n 2 be a smooth bounded domain for s 1 2 1 we consider a problem of the form where 0 is a real parameter f belongs to a suitable lebesgue space and is a nonlocal gradient square term given by depending on the real parameter 0 we derive existence and non existence results the proof of our existence result relies on sharp calderon zygmund type regularity results for the fractional poisson equation with low integrability data we also obtain existence results for related problems involving different nonlocal diffusion terms

numerical implementation of the edem for modified helmholtz bvps on annular domains in a recent paper by the current authors a new methodology called the extended domain eigenfunction method edem was proposed for solving elliptic boundary value problems on annular like domains in this paper we present and investigate one possible numerical algorithm to implement the edem this algorithm is used to solve modified helmholtz bvps on annular like domains two examples of annular like domains are studied the results and performance are compared with those of the well known boundary element method bem the high accuracy of the edem solutions and the superior efficiency of the edem over the bem make edem an excellent alternate candidate to use in the animation industry where speed is a predominant requirement and by the scientific community where accuracy is the paramount objective

extended domain eigenfunction method edem a study of ill posedness and regularization the extended domain eigenfunction method edem proposed for solving elliptic boundary value problems on annular like domains requires an inversion process the procedure thus represents an ill posed problem whose numerical solution involves an ill conditioned system of equations in this paper the ill posed nature of edem is studied and numerical solutions based on regularization schemes are considered it is shown that the edem solution methodology lends itself naturally to a formulation in terms of the well known iterative landweber method and the more general and faster converging semi iterative regularization schemes theoretical details and numerical results of the regularization schemes are presented for the case of the two dimensional laplace operator on annular domains

a few remarks about the hilbert transform a generalized integral similar to integrability b is used to study the hilbert transform onx 1 p lp r with a view to obtaining i a mollifier which commutes with the hilbert transform onxand coincides with the friedrichs mollifier onlloc1 r ii estimates for nonlinear equations iii an integral representation for the hilbert transform of a regular schwartz distribution iv a generalized multiplier representation of the hilbert transform onl1 r v an elementary proof of the injectivity of h onx

compensated optimal grids for elliptic boundary value problems a method is proposed which allows to efficiently treat elliptic problems on unbounded domains in two and three spatial dimensions in which one is only interested in obtaining accurate solutions at the domain boundary the method is an extension of the optimal grid approach for elliptic problems based on optimal rational approximation of the associated neumann to dirichlet map in fourier space it is shown that using certain types of boundary discretization one can go from second order accurate schemes to essentially spectrally accurate schemes in two dimensional problems and to fourth order accurate schemes in three dimensional problems without any increase in the computational complexity the main idea of the method is to modify the impedance function being approximated to compensate for the numerical dispersion introduced by a small finite difference stencil discretizing the differential operator on the boundary we illustrate how the method can be efficiently applied to nonlinear problems arising in modeling of cell communication

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

penalized maximum likelihood estimation in logistic regression and discrimination summary maximum likelihood estimation of the parameters of the binary logistic regression model for pr h i x is discussed with separate discussion of sampling from i the conditional distribution of h given x ii the joint distribution of h and x and iii the conditional distribution of x given h difficulties associated with continuous x in the latter sampling scheme are discussed to avoid these penalized maximum likelihood estimates are introduced which give estimates of the logistic parameters and a nonparametric spline estimate of the marginal distribution of x extensions to multinomial logistic regression are outlined

camera calibration with distortion models and accuracy evaluation a camera model that accounts for major sources of camera distortion namely radial decentering and thin prism distortions is presented the proposed calibration procedure consists of two steps 1 the calibration parameters are estimated using a closed form solution based on a distribution free camera model and 2 the parameters estimated in the first step are improved iteratively through a nonlinear optimization taking into account camera distortions according to minimum variance estimation the objective function to be minimized is the mean square discrepancy between the observed image points and their inferred image projections computed with the estimated calibration parameters the authors introduce a type of measure that can be used to directly evaluate the performance of calibration and compare calibrations among different systems the validity and performance of the calibration procedure are tested with both synthetic data and real images taken by tele and wide angle lenses

the influence of variables in a logistic model summary the influence of explanatory variables in a logistic model is considered when the goal is to determine the predictive probability of a future observation in a bayesian approach we consider whether the predictive distribution will change greatly when subsets of the explanatory variables are omitted from the data set or from the future observation several authors have considered the problem of the influence of observations in a logistic regression model in particular pregibon 1981 cook weisberg 1982 ch 2 and johnson 1985 have developed measures of influence for identifying observations in the data which are influential relative to the estimation of the regression coefficients the determination of predictive probabilities and the classification of future observations our aim is to consider the influence of explanatory variables in a logistic regression model this has been studied extensively in regression analysis but usually for the estimation or testing of the regression parameters the novelty of the approach suggested here stems from the goal being to determine the effect on the predictive probability of a future observation of the omission of subsets of the explanatory variables

time marching algorithms for nonlocal evolution equations based upon approximate approximations new time marching algorithms for solving initial value problems for nonlocal evolution equations are described with respect to the space variable the discretization is based on a method of approximate approximation proposed by the second author in time the algorithms are finite difference schemes of either the first or the second approximation order whereas with respect to the space variables we use approximate approximations of an arbitrary high order the algorithms are stable under mild restrictions to the time step which come from the nonlinear part of the equation some computational results and hints on crucial implementation issues are provided

practical ways to calculate camera lens distortion for real time camera calibration in this paper we address practical methods for calculating camera lens distortion for real time applications although the lens distortion problem can be easily ignored for constant parameter lenses it becomes important in the eld of real time camera calibrations particularly for zoom lenses tsai s camera calibration method which is adopted in this paper for real time application consists of two stages while some camera parameters can be calculated algebraically in the rst stage a nonlinear optimization process is involved in the second stage for calculating other parameters including lens distortion which requires a large number of calculations however if the lens distortion can be calculated independently of the other camera parameters we can easily calibrate a camera with a linear method without a computational burden we propose two di erent methods for calculating lens distortion independently these methods are so simple and require so few calculations that the lens distortion can be rapidly calculated even in real time applications the rst one uses a look up table lut of focal length and lens distortion which can be constructed in the initialization process the second one is a feature based method using the relationship between the feature points found in an image experiments were carried out for both methods results of which show that the proposed methods are favorably comparable in performance with the non real time full optimization method 2001 pattern recognition society published by elsevier science ltd all rights reserved