determining the first order perturbation of a polyharmonic operator on admissible manifolds abstract we consider the inverse boundary value problem for the first order perturbation of the polyharmonic operator l g x q with x being a w 1 vector field and q being an l function on compact riemannian manifolds with boundary which are conformally embedded in a product of the euclidean line and a simple manifold we show that the knowledge of the dirichlet to neumann map determines x and q uniquely the method is based on the construction of complex geometrical optics solutions using the carleman estimate for the laplace beltrami operator due to dos santos ferreira kenig salo and uhlmann notice that the corresponding uniqueness result does not hold for the first order perturbation of the laplace beltrami operator

the calderon problem with partial data in this paper we improve an earlier result by bukhgeim and uhlmann 1 by showing that in dimension n 3 the knowledge of the cauchy data for the schr nodinger equation measured on possibly very small subsets of the boundary determines uniquely the potential we follow the general strategy of 1 but use a richer set of solutions to the dirichlet problem this implies a similar result for the problem of electrical impedance tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary

hybrid be zier patches on sphere like surfaces abstract we develop a method for interpolating scattered data on sphere like based on a local triangular patch which is constructed from a blend of certain spherical bernstein bezier polynomials introduced recently by alfeld neamtu and schumaker 1996 the method produces a c1 interpolant which matches values and derivatives and is a natural analog of a planar method of foley and opitz 1992 and goodman and said 1991 we also show how the same approach can be used to construct a c2 quintic hybrid patch matching second derivative information as an analog of a planar method of chang and said 1995

locating a changed segment in a sequence of bernoulli variables the theory underlying inferences about a single change point in a sequence of independent bernoulli variables is extended to the two change points problem where the distance between the two change points is known namely a changed segment both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations the distribution of the maximum likelihood estimator of the location of the changed segment is derived

bootstrap confidence intervals and bootstrap approximations abstract the bca bootstrap procedure efron 1987 for constructing parametric and nonparametric confidence intervals is considered like the bootstrap this procedure can be applied to complicated problems in a wide range of situations for models indexed by a scalar parameter with efficient estimator the bca procedure relies on the existence of a transformation g such that is approximately normally distributed with standard deviation 1 ag although explicit knowledge of g is not required in this article we show how to construct this transformation by generalizing the one given by efron 1987 sec 10 for translation families this construction consists of the composition of a variance stabilizing transformation and a skewness reducing transformation it produces a new interval the bca interval that is asymptotically equivalent to the bca interval and can be computed without bootstrap sampling we also derive from this construction an accurate approximation to the bootstrap distribu

an inverse boundary value problem for schrodinger operators with vector potentials we consider the schrodinger operator for a magnetic potential a and an electric potential q which are supported in a bounded domain in r n with n 3 we prove that knowledge of the dirichlet to neumann map associated to the schrodinger operator determines the magnetic field rot a and the electric potential 4 simultaneously provided rot a is small in the l topology

power of the scan statistic in detecting a changed segment in a bernoulli sequence summary fu curnow 1990 derive recursive equations to find the level of significance and power of a likelihood ratio test for a changed segment of specified length based on the scan statistic the maximum number of successes within the specified length their method is computationally feasible for segment lengths of 20 or less we present and evaluate highly accurate approximations as well as bounds for the power function of this test that are computationally feasible even for very large segment lengths we also evaluate power when the duration of the increased length used in the test statistic does not correspond to the actual length scientists dealing with data sequences modelled by independent bernoulli trials frequently seek criteria to detect changes in the underlying process certain criteria have been developed to be sensitive to situations in which the probability of success on an individual trial changes at a point in the sequence fu curnow 1990 consider a version of a two change point problem with known distance m between the change points and with the trial probability of success at the two ends being equal they give recurrence relations for the probability of type i error and the power computational difficulties arise on even large computers when the number of trials is large in the present paper we derive highly accurate approximations that allow computation of power for all segment lengths consider a sequence of n independent 0 1 random variables x1 x2 xn let 1 denote success with pr x 1 i t we wish to test the null hypothesis of a constant probability of success ho i t i t 1 n against the alternative that some contiguous sequence of m events starting at an unknown trial z has a higher probability of success fu curnow 1990 note that the generalized likelihood ratio test for this alternative rejects ho for large values of the scan statistic

determining the first order perturbation of a bi harmonic operator on bounded and unbounded domains from partial data abstract in this paper we study inverse boundary value problems with partial data for the bi harmonic operator with first order perturbation we consider two types of subsets of r n n 3 one is an infinite slab the other is a bounded domain in the case of a slab we show that from dirichlet and neumann data given either on the different boundary hyperplanes of the slab or on the same boundary hyperplane one can uniquely determine the magnetic potential and the electric potential in the case of a bounded domain we show the unique determination of the magnetic potential and the electric potential from partial dirichlet and neumann data under two different assumptions the first assumption is that the magnetic and electric potentials are known in a neighborhood of the boundary in this situation we obtain the uniqueness result when the dirichlet and neumann data are only given on two arbitrary open subsets of the boundary the second assumption is that the dirichlet and neumann data are known on the same part of the boundary whose complement is a part of a hyperplane we also establish the unique determination result in this local data case

the regularizing properties of anisotropic radial basis functions in the present work we consider the problem of interpolating scattered data using radial basis functions rbf in general it is well known that this leads to a discrete linear inverse problem that needs to be regularized in order to provide a meaningful solution the work focuses on a metric regularization approach based on a new class of rbf called anisotropic rbf the work provides theoretical justifications for the regularization approach and it considers a suitable proposal for the metric supporting it by numerical examples

minimally selected p and other tests for a single abrupt changepoint in a binary sequence summary a novel changepoint statistic based on the minimum value over possible changepoint locations of fisher s exact test is introduced specific points in the exact distribution of the minimally selected fisher s value may be rapidly calculated as a lattice path counting problem via known recurrence methods the test is compared to the kolmogorov smirnov two sample test the maximally selected chi square and a likelihood ratio test the tests are applied to assessing recombination in genetic sequences of hiv

vertical fault detection from scattered data the purpose of this paper is to study the problem of detection of vertical faults in explicit surfaces first we establish a characterization of jump discontinuities for bivariate functions next we derive a detection method of vertical faults in surfaces which takes as input a set of scattered data points finally some numerical and graphical examples are given

reconstructing discontinuities using complex geometrical optics solutions in this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the laplacian as the leading order term we apply these special solutions to the problem of reconstructing inclusions inside a domain filled with known conductivity from local boundary measurements computational results demonstrate the versatility of these solutions to determine electrical inclusions

the complex variable interpolating moving least squares method abstract in this paper a new method for deriving the moving least squares mls approximation is presented first considering the unclear physical meaning of the functional in the existing complex variable moving least squares cvmls approximation an improved cvmls approximation is presented by constructing a new functional with an explicit physical meaning based on the improved cvmls approximation the complex variable interpolating moving least squares cvimls method is presented and the interpolating property of the corresponding shape function of the cvimls method is proved

approximations for the tail probabilities and moments of the scan statistic the scan statistic is used to test the hypothesis that the observed events occur at random uniformly distributed in time or space versus the hypothesis that they cluster within a moving window of size w to implement the testing procedure based on the scan statistic its tail probabilities have to be effectively evaluated in this article a survey of results on the approximations of the distribution of the scan statistic and its moments is presented numerical results comparing these approximations are also given numerous references with applications in epidemiological studies using the scan statistics are mentioned related scan statistics that have been used in many other interesting applications are listed in the reference section the article concludes with the presentation of unsolved problems related to the scan statistic

unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets abstract we consider a restricted dirichlet to neumann map s r t associated with the operator t 2 g a q where g is the laplace beltrami operator of a riemannian manifold m g and a and q are a vector field and a function on m the restriction s r t corresponds to the case where the dirichlet traces are supported on 0 t s and the neumann traces are restricted on 0 t r here s and r are open sets which may be disjoint on the boundary of m we show that s r t determines uniquely up the natural gauge invariance the lower order terms a and q in a neighborhood of the set r assuming that r is strictly convex and that the wave equation is exactly controllable from s in time t 2 we give also a global result under a convex foliation condition the main novelty is the recovery of a and q when the sets r and s are disjoint we allow a and q to be non self adjoint and in particular the corresponding physical system may have dissipation of energy

multivariate scattered data fitting during the week of 2 8 march 1995 a meeting entitled international conference on scattered data fitting was held in cancun mexico the meeting was attented by 42 researchers from europe and the americas and 34 lectures were presented this special issue of journal of computational and applied mathematics includes 14 papers based on presentations at the conference

homogeneous simplex splines homogeneous simplex splines also known as cone splines or multivariate truncated power functions are discussed from a perspective of homogeneous divided differences and polar forms this makes it possible to derive the basic properties of these splines in a simple and economic way in addition a construction of spaces of homogeneous simplex splines is considered which in the nonhomogeneous setting is due to dahmen micchelli and seidel a proof for this construction is presented based on knot insertion restricting the homogeneous splines to a sphere gives rise to spaces of spherical simplex splines

multiple changepoint testing for an alternating segments model of a binary sequence summary a binary sequence may give the appearance of being composed of alternating segments with relatively high and relatively low probability of success determining whether such an alternating pattern is significant is a multiple changepoint problem where the number of segments and their success probabilities are unknown with the added constraint of segment alternation a dynamic programming method for determining the optimal segmentation into a given number of segments is provided given this a variation on the simulation method of venter and steel 1996 computational statistics and data analysis22 481 504 may be employed t o test the null hypothesis of a homogeneous sequence as well as to estimate the number and location of changepoints a sample application the assessment of the possibility of genetic recombination in hiv sequences is presented

inverse problem for schrodinger equations with yang mills potentials in a slab abstract in this work we consider the inverse boundary value problem for schrodinger equations with yang mills potentials in the domain of infinite slab type we prove that the potentials can be determined uniquely up to a gauge equivalent class assuming that only partial measurements are known on the boundary hyperplanes

a mathematical model of controlling the growth of tissue in pigs a mathematical model of controlling the growth of tissues in pigs is described in this paper in that sense a method is given by which it is possible to periodically and very accurately estimate live pig weight of backfat based upon measurements done by ultrasound these estimations will be used for the purpose of predicting growth of backfat in live pigs backfat weight is estimated on the basis of measurements done by using the moving total least squares method whereas estimation of live pig backfat growth is done by using a generalized logistic function whose parameters are estimated by means of the least squares method since thereby the hessian of the corresponding minimizing function is very close to a singular matrix an additional problem analysis was necessary

approximate interpolation with applications to selecting smoothing parameters in this paper we study the global behavior of a function that is known to be small at a given discrete data set such a function might be interpreted as the error function between an unknown function and a given approximant we will show that a small error on the discrete data set leads under mild assumptions automatically to a small error on a larger region we will apply these results to spline smoothing and show that a specific a priori choice of the smoothing parameter is possible and leads to the same approximation order as the classical interpolant this has also a surprising application in stabilizing the interpolation process by splines and positive definite kernels

a trust region algorithm for parametric curve and surface fitting abstract let a family of curves or surfaces be given in parametric form via the model equation x s where x rn r m and s s rd d such that the manifold m s s s is a best fit toscattered data zi i 1y rn in the sense that for some s i i 1 n the sum of the squared least distances i 1 n z i s i 2 2 from the data points to the manifold m is minimal among all such manifolds for robustness our algorithm uses a globally convergent trust region approach in which at each iteration an approximation to the objective function is minimized in a given neighborhood of the current iterate the set s may be all of rd or a closed convex subset in particular it may be chosen so that our theory is applicable to splines

stability estimates for the calderon problem with partial data this is a follow up of a previous article where we proved local stability estimates for a potential in a schr odinger equation on an open bounded set in dimension n 3 from the dirichlet to neumann map with partial data the region under control was the penumbra delimited by a source of light outside of the convex hull of the open set these local estimates provided stability of log log type corresponding to the uniqueness results in calder on s inverse problem with partial data proved by kenig sj ostrand and uhlmann in this article we prove the corresponding global estimates in all dimensions higher than three the estimates are based on the construction of solutions of the schr odinger equation by complex geometrical optics developed in the anisotropic setting by dos santos ferreira kenig salo and uhlmann to solve the calder on problem in certain admissible geometries

operators on radial functions a general theory is provided that allows to write multi variate fourier transforms or convolutions of radial functions as very simple univariate operations as a byproduct an interesting group of operators i x r with i i i i i is defined it contains the classical derivatives as i1 d dr and is intimately connected to the fourier transform applications to the construction of new positive definite radial and to new identities for special functions are included

the power of likelihood ratio and cumulative sum tests for a change in a binomial probability summary a simple iterative procedure is found for the exact null and alternative distributions of likelihood ratio cumulative sum and related statistics for testing for a change in probability of a sequence of independent binomial random variables it is concluded that the likelihood ratio test is slightly less powerful than the cumulative sum test near the middle of the sequence but that the likelihood ratio test is much more powerful near the ends an example from epidemiology is used to illustrate the results under certain conditions the cumulative sum test is identical to a two sample kolmogorov smirnov test and so the iterative procedure can be used to find the null distribution of kolmogorov smirnov and related statistics

testing for co integration in vector autoregressions with non stationary volatility abstract many key macroeconomic and financial variables are characterized by permanent changes in unconditional volatility in this paper we analyse vector autoregressions with non stationary unconditional volatility of a very general form which includes single and multiple volatility breaks as special cases we show that the conventional rank statistics computed as in johansen 1988 johansen 1991 are potentially unreliable in particular their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co integration tests as we demonstrate numerically a solution to the identified inference problem is provided by considering wild bootstrap based implementations of the rank tests these do not require the practitioner to specify a parametric model for volatility or to assume that the pattern of volatility is common to or independent across the vector of series under analysis the bootstrap is shown to perform very well in practice

capacity of reproducing kernel spaces in learning theory the capacity of reproducing kernel hilbert spaces rkhs plays an essential role in the analysis of learning theory covering numbers and packing numbers of balls of these reproducing kernel spaces are important measurements of this capacity we first present lower bound estimates for the packing numbers by means of nodal functions then we show that if a mercer kernel is c sup s for some s 0 being not an even integer the rkhs associated with this kernel can be embedded into c sup s 2 this gives upper bound estimates for the covering number concerning sobolev smooth kernels examples and applications to v sub spl gamma dimension and tikhonov 1977 regularization are presented to illustrate the upper and lower bound estimates

adaptive interpolation based on polya frequency functions translation invariant interpolation of frequency domain functions by means of fourier transforms of polya frequency functions which belong to the bochner class of interpolation kernels is presented for the implementation we use an adaptive interpolation process which is a variant of the recently introduced adaptive residual subsampling method moreover it is shown that adaptive residual subsampling with polya interpolation kernels is an excellent preprocessing interface when used in conjunction with the well known vector fitting vf rational modeling algorithm

a useful upper bound for the tail probabilities of the scan statistic when the sample size is large abstract although a number of approximations to the distribution under uniformity of the scan statistic are known they are when the sample size is large either difficult to compute or numerically unstable a simple upper bound for the upper tail of the distribution based on a result of hunter 1976 is derived it is found that for large sample sizes and a reasonably wide range of window widths this bound gives a numerically stable approximation that is sufficiently accurate for hypothesis testing purposes

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

multiple changepoint fitting via quasilikelihood with application to dna sequence segmentation summary we consider situations where a step function with a variable number of steps provides an adequate model for a regression relationship while the variance of the observations depends on their mean this model provides for discontinuous jumps at changepoints and for constant means and error variances in between changepoints the basic statistical problem consists of identification of the number of changepoints their locations and the levels the function assumes in between we embed this problem into a quasilikelihood formulation and utilise the minimum deviance criterion to fit the model for the choice of the number of changepoints we discuss a modified schwarz criterion a dynamic programming algorithm makes the segmentation feasible for sequences of moderate length the performance of the segmentation method is demonstrated in an application to the segmentation of the bacteriophage l sequence

a numerical scheme for solving a class of logarithmic integral equations arisen from two dimensional helmholtz equations using local thin plate splines abstract this paper presents a numerical method for solving logarithmic fredholm integral equations which occur as a reformulation of two dimensional helmholtz equations over the unit circle with the robin boundary conditions the method approximates the solution utilizing the discrete collocation method based on the locally supported thin plate splines as a type of free shape parameter radial basis functions the local thin plate splines establish an efficient and stable technique to estimate an unknown function by a small set of nodes instead of all points over the solution domain to compute logarithm like singular integrals appeared in the method we use a particular nonuniform gauss legendre quadrature rule since the scheme does not require any mesh generations on the domain it can be identified as a meshless method the error estimate of the proposed method is presented numerical results are included to show the validity and efficiency of the new technique these results also confirm that the proposed method uses much less computer memory in comparison with the method established on the globally supported thin plate splines moreover it seems that the algorithm of the presented approach is attractive and easy to implement on computers

total least squares state of the art regression in numerical analysis total least squares regression tls fits a line to data where errors may occur in both the dependent and independent variables in higher dimensions tls fits a hyperplane to such data the elementary algorithm presented here fits readily in a first course in numerical linear algebra

a method to test for a recent increase in hiv 1 seroconversion incidence results from the multicenter aids cohort study macs we have formulated the problem of determining whether there has been an upturn in hiv 1 seroconversion incidence over the first five years of follow up in the multicenter aids cohort study macs as that of locating the minimum of a quadratic regression or examination of two knot piecewise spline models under a quadratic model we propose a method to obtain a direct estimate and a bootstrap estimate for the location of the temporal turning point local minimum for hiv 1 seroconversion incidence and three methods to estimate confidence intervals for the location of the turning point for hiv seroconversion incidence 1 wald confidence interval estimate with or without log transformation assuming the asymptotic normality and applying the delta method 2 asymmetric confidence intervals using fieller s theorem and its modification and 3 bootstrapping confidence intervals inferences for the temporal turning point based on wald tests for a single regression term in a non linear regression model were not reliable compared to inferences based on confidence intervals placed on calendar time we present results using these different methods applied to the macs data and we obtain power estimates to illustrate the performances of different methods

the calderon problem with partial data for conductivities with 3 2 derivatives we extend a global uniqueness result for the calderon problem with partial data due to kenig sjostrand uhlmann ann math 2 165 567 591 2007 to the case of less regular conductivities specifically we show that in dimensions n ge 3 the knowledge of the diricihlet to neumann map measured on possibly very small subsets of the boundary determines uniquely a conductivity having essentially 3 2 derivatives in an l2 sense

stability estimate for an inverse problem for the magnetic schrodinger equation from the dirichlet to neumann map abstract we consider the problem of stability estimate of the inverse problem of determining the magnetic field entering the magnetic schrodinger equation in a bounded smooth domain of r n with input dirichlet data from measured neumann boundary observations this information is enclosed in the dynamical dirichlet to neumann map associated to the solutions of the magnetic schrodinger equation we prove in dimension n 2 that the knowledge of the dirichlet to neumann map for the magnetic schrodinger equation measured on the boundary determines uniquely the magnetic field and we prove a holder type stability in determining the magnetic field induced by the magnetic potential

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

a statistical method for geometry inspection from point clouds abstract this paper introduces a statistical methodology for geometry inspection from point clouds obtained with a laser scanner or other measuring systems the null hypothesis of interest is that the real surface of an object fits the theoretical shape and dimensions of the object an algorithm based on bivariate kernel smoothers is used to nonparametrically estimate the surface of the object and bootstrap based procedures are proposed for testing the null hypothesis in order to validate the methodology a simulated study was conducted finally the proposed methodology was applied to the inspection of a parabolic dish antenna

the calderon problem with partial data in two dimensions we prove for a two dimensional bounded domain that the cauchy data for the schrodinger equation measured on an arbitrary open subset of the boundary determines uniquely the potential this implies for the conductivity equation that if we measure the current fluxes at the boundary on an arbitrary open subset of the boundary produced by voltage potentials supported in the same subset we can determine uniquely the conductivity we use carleman estimates with degenerate weight functions to construct appropriate complex geometrical optics solutions to prove the results

composite exponential approximations the composite exponential approximations cea arise in a natural way when one investigates the stability and order properties of a combination of several methods for the numerical solution of ordinary differential equations sequentially implemented with different step lengths some general results on the order acceptability and exponential fitting properties of cea are derived the composite pade approximations and tv approximations are explored in detail

carleman estimate for the schrodinger equation and application to magnetic inverse problems abstract in this paper we prove lipschitz stable determination of the complex valued electric potential and the direction of the magnetic field appearing in the dynamic schrodinger equation with static coefficients by finitely many partial boundary measurements of the solution this is by means of the bukhgeim klibanov method based on an appropriate carleman estimate since the time symmetrization of the static magnetic schrodinger equation around t 0 is not possible we preliminarily establish a carleman inequality specifically designed for this problem

a method for solving the parameter identification problem for ordinary differential equations of the second order we give a method for solving the parameter identification problem for ordinary differential equations of the second order using a noninterpolated moving least squares method the method is tested in two practical examples

unit root tests with a break in innovation variance abstract it is shown that an abrupt change in the innovation variance of an integrated process can generate spurious rejections of the unit root null hypothesis in routine applications of dickey fuller tests we develop and investigate modified test statistics based on unit root tests of perron for a time series with a changing level or changing intercept and slope which are applicable when there is a change in innovation variance of an unknown magnitude at an unknown location

on uniqueness in the general inverse transmisson problem in this paper we demonstrate uniqueness of a transparent obstacle of coefficients of rather general boundary transmission condition and of a potential coefficient inside obstacle from partial dirichlet to neumann map or from complete scattering data at fixed frequency the proposed transmission problem includes in particular the isotropic elliptic equation with discontinuous conductivity coefficient uniqueness results are shown to be optimal hence the considered form can be viewed as a canonical form of isotropic elliptic transmission problems proofs use singular solutions of elliptic equations and complex geometrical optics determining an obstacle and boundary conditions i e reflecting and transmitting properties of its boundary and interior is of interest for acoustical and electromagnetic inverse scattering for modeling fluid structure interaction and for defects detection

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

stability estimates for the radon transform with restricted data and applications in this article we prove a stability estimate going from the radon transform of a function with limited angle distance data to the l p norm of the function itself under some conditions on the support of the function we apply this theorem to obtain stability estimates for an inverse boundary value problem with partial data

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

on c 2 quintic spline functions over triangulations of powell sabin s type abstract given a triangulation of a polygonal domain we find a refinemet of of by choosing t in a neighborhood of the center of the inscribed circle of each triangle of t connecting t to the vertices of the triangle t and connecting t to t if t shares an interior edge with t or to the midpoint e of any boundary edge e of t the resulting triangulation is a triangulation of powell sabin s type we investigate a c 2 quintic spline space s 5 2 whose elements are c 3 only at t s we give a dimension formula for this spline space show how to construct a locally supported basis display an interpolation scheme and prove that this spline space has the full approximation order

limiting carleman weights and anisotropic inverse problems in this article we consider the anisotropic calderon problem and related inverse problems the approach is based on limiting carleman weights introduced in kenig et al ann math 165 567 591 2007 in the euclidean case we characterize those riemannian manifolds which admit limiting carleman weights and give a complex geometrical optics construction for a class of such manifolds this is used to prove uniqueness results for anisotropic inverse problems via the attenuated geodesic ray transform earlier results in dimension n 3 were restricted to real analytic metrics

regression by local fitting methods properties and computational algorithms abstract local regression is a procedure for estimating regression surfaces by the local fitting of linear or quadratic functions of the independent variables in a moving fashion that is analogous to how a moving average is computed for a time series the advantage of the methodology over the global fitting of parametric functions of the independent variables by least squares the current paradigm in regression studies is that a much wider class of regression functions can be estimated without distortion in this paper we discuss the methods their statistical properties and computational algorithms

reconstruction of a penetrable obstacle by complex spherical waves we consider an inverse acoustic scattering problem for identifying a non convex penetrable obstacle in three dimensions in a homogeneous medium we apply the complex geometrical optics solutions with logarithmic phase which is called complex spherical waves to reconstruction problem the reconstruction schemes will be demonstrated in the last section

multistep scattered data interpolation using compactly supported radial basis functions a hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support a nested sequence of subsets of the data is computed efficiently using successive delaunay triangulations the scale of the basis function at each level is determined from the current density of the points using information from the triangulation the method is rotationally invariant and has good reproduction properties moreover the solution can be calculated and evaluated in acceptable computing time

spurious rejections by dickey fuller tests in the presence of a break under the null abstract it is well known that if a series is generated by a process that is stationary around a broken trend conventional dickey fuller tests can have very low power in this paper the converse phenomenon is studied and illustrated suppose that the true generating process is integrated of order one but with a break then it is shown that if the break occurs early in the series routine application of standard dickey fuller tests can lead to a very serious problem of spurious rejection of the unit root null hypothesis

an approximation for the distribution of the scan statistic the scan statistic evaluates whether an apparent cluster of disease in time is due to chance the statistic employs a moving window of length w and finds the maximum number of cases revealed through the window as it scans or slides over the entire time period t computation of the probability of observing a certain size cluster under the hypothesis of a uniform distribution is infeasible when n the total number of events is large and w is of moderate or small size relative to t we give an approximation that is an asymptotic upper bound easy to compute and for the purposes of hypothesis testing more accurate than other approximations presented in the literature the approximation applies both when n is fixed and when n has a poisson distribution we illustrate the procedure on a data set of trisomic spontaneous abortions observed in a two year period in new york city

on condition numbers associated with radial function interpolation abstract estimates on spectral condition numbers for scattered data interpolation matrices associated with a certain class of conditionally positive definite radial functions of order 0 including the gaussians are provided in addition lp condition number estimates with 1 p are discussed the estimates on the spectral condition numbers lead to necessary and sufficient conditions for such condition numbers to be independent of the number of data sites

localization of multivariate interpolation and smoothing methods multivariate smoothing or interpolation methods for scattered data are frequently localized by computing the value of the required function at a point from data in some small neighborhood of the point we describe the piecewise nature of the resulting function and show how a smoothing of the usually discontinuous function can be carried out by a convolution which preserves interpolation

inverse boundary value problems for the perturbed polyharmonic operator author s krupchyk k lassas m uhlmann g abstract we show that a first order perturbation a x d q x of the polyharmonic operator m m 2 can be determined uniquely from the set of the cauchy data for the perturbed polyharmonic operator on a bounded domain in n n 3 notice that the corresponding result does not hold in general when m 1 2013 american mathematical society

uniqueness in an inverse boundary problem for a magnetic schrodinger operator with a bounded magnetic potential we show that the knowledge of the set of the cauchy data on the boundary of a bounded open set in mathbb r n n geq 3 for the magnetic schrodinger operator with l magnetic and electric potentials determines the magnetic field and electric potential inside the set uniquely the proof is based on a carleman estimate for the magnetic schrodinger operator with a gain of two derivatives

integrated multiquadric radial basis function approximation methods promising numerical results using once and twice integrated radial basis functions have been recently presented in this work we investigate the integrated radial basis function irbf concept in greater detail connect to the existing rbf theory and make conjectures about the properties of irbf approximation methods the irbf methods are used to solve pdes

scattered data interpolation subject to piecewise quadratic range restrictions abstract the constriction of range restricted univariate and bivariate c1 interpolants to scattered data is considered in particular we deal with quadratic spline interpolation on a refined univariate grid respectively on a powell sabin refinement of a triangulation of the data sites subject to piecewise quadratic lower and upper obstacles to the values of the interpolant the derived sufficient conditions for the fulfillment of the range restrictions result in a system of linear inequalities for the slopes respectively gradients as parameters which is separated with respect to the data sites this system is shown to be always solvable for important special forms of the obstacles if at all in general there exist an infinite number of spline interpolants meeting the constraints the selection of a visually pleasant one is based on the minimization of a suitable choice functional

fieller s theorem the likelihood and the delta method this note discusses the direct likelihood estimation of ratio parameters the method is based on the use of nonlinear regression models from the exponential family the variances of the maximum likelihood estimates are identical with values obtained from the corresponding generalized linear models and the delta method bishop fienberg and holland discrete multivariate analysis theory and practice cambridge massachusetts mit press 1975 but are easier to calculate the approach is illustrated by means of a number of examples including a rather complex logistic regression model we also discuss the connection between confidence intervals obtained from fieller s theorem and large sample intervals obtained from the information matrix we conclude from this comparison and from the examples that direct maximum likelihood estimation of ratios offers a useful alternative to traditional methods based on linear models especially for complex data sets

determining a first order perturbation of the biharmonic operator by partial boundary measurements abstract we consider an operator 2 a x d q x with the navier boundary conditions on a bounded domain in r n n 3 we show that a first order perturbation a x d q can be determined uniquely by measuring the dirichlet to neumann map on possibly very small subsets of the boundary of the domain notice that the corresponding result does not hold in general for a first order perturbation of the laplacian

the reflection principle and calderon problems with partial data we propose a geometric approach towards for solving the partial data calderon problem for the magnetic schrodinger operator in dimension two this allowed us to clarify some of the ideas in the previous works while simultaneously consider the problem on general riemann surfaces with boundary

semi orthogonal wavelet packet bases for parallel least squares approximation a generalization to the wavelet packet case of the semi orthogonal wavelets given by c k chui is presented and a simple numerical algorithm for their practical evaluation is developed to provide a motivation it is shown how using these new bases the least squares approximation problem in a multiresolution space can easily be solved by means of an efficient parallel algorithm

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

determining a magnetic schrodinger operator from partial cauchy data in this paper we show in dimension n 3 that knowledge of the cauchy data for the schrodinger equation in the presence of a magnetic potential measured on possibly very small subsets of the boundary determines uniquely the magnetic field and the electric potential we follow the general strategy of 7 using a richer set of solutions to the dirichlet problem that has been used in previous works on this problem

a recursive algorithm for hermite interpolation over a triangular grid a recursive algorithm for hermite interpolation of bivariate data over triangular grids is presented this interpolation algorithm has a dynamic programming flavor and it computes a single polynomial that interpolates the full set of data the data we interpolate are partial derivatives and mixed partials up to some fixed order at the nodes of the grid the interpolant is a polynomial with minimal degree bound when the order is identical for all nodes the proposed interpolation algorithm is affinely invariant has at least linear precision is symmetric with respect to the grid directions and can reuse existing computations if points are added to the grid

a meshless method for solving nonlinear two dimensional integral equations of the second kind on non rectangular domains using radial basis functions with error analysis in this paper we present a numerical method for solving two dimensional nonlinear fredholm integral equations of the second kind on a non rectangular domain the method utilizes radial basis functions rbfs constructed on scattered points as a basis in the discrete collocation method the proposed scheme is meshless since it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional nonlinear integral equation to the solution of a nonlinear system of algebraic equations error analysis is presented for this method finally numerical examples are included to show the validity and efficiency of the new technique

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

maximum likelihood estimation of multiple change points summary maximum likelihood estimation of the locations of changes in sequences of independent categorical random variables when there are known lower bounds on the lengths of the sub sequences between the change points is discussed a method is developed which finds one of the maximum likelihood solutions the problem of estimating the number of changed segments is discussed and some numerical results about the precision of the estimates of the locations of changes are presented the method also allows the boundary distributions for the changed segments to be different from the distribution for the central region of the changed segments an application to the prediction of protein helical regions is presented