an autoregressive growth model for longitudinal item analysis a first order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits specifically the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time or the lagged response an initial conditions problem arises because there is no lagged response at the initial time period we handle this problem by adapting solutions proposed for dynamic models in panel data econometrics asymptotic and finite sample power for the autoregressive parameters are investigated the consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first order autoregressive growth model the proposed methods are applied to longitudinal data on korean students self esteem

a fast sinc function gridding algorithm for fourier inversion in computer tomography the fourier inversion method for reconstruction of images in computerized tomography has not been widely used owing to the perceived difficulty of interpolating from polar or other measurement grids to the cartesian grid required for fast numerical fourier inversion although the fourier inversion method is recognized as being computationally faster than the back projection method for parallel ray projection data the artifacts resulting from inaccurate interpolation have generally limited application of the method this paper presents a computationally efficient gridding algorithm which can be used with direct fourier transformation to achieve arbitrarily small artifact levels the method has potential for application to other measurement geometries such as fan beam projections and diffraction tomography and nmr imaging

on the symmetric doubly stochastic inverse eigenvalue problem abstract let 1 2 n be a list of real numbers the symmetric doubly stochastic inverse eigenvalue problem hereafter sdiep is to determine the list which can occur as the spectrum of an n n symmetric doubly stochastic matrix a if the matrix a is positive we can necessarily obtain a subproblem symmetric positive doubly stochastic inverse eigenvalue problem hereafter spdiep of the sdiep in this paper we give some sufficient conditions for the sdiep and spdiep and prove that the set formed by the spectra of all n n symmetric positive doubly stochastic matrices is non convex for n 4

direct inversion of the nonequispaced fast fourier transform abstract various applications such as mri solution of pdes etc need to perform an inverse nonequispaced fast fourier transform nfft i e compute m fourier coefficients from given n nonequispaced data in the present paper we consider direct methods for the inversion of the nfft we introduce algorithms for the setting m n as well as for the underdetermined and overdetermined cases for the setting m n a direct method of complexity o n log n is presented which utilizes lagrange interpolation and the fast summation for the remaining cases we use the matrix representation of the nfft to deduce our algorithms thereby we are able to compute an inverse nfft up to a certain accuracy by means of a modified adjoint nfft in o m log m n arithmetic operations finally we show that these approaches can also be explained by means of frame approximation

a stable and accurate butterfly sparse fourier transform recently the butterfly approximation scheme was proposed for computing fourier transforms with sparse and smooth sampling in the frequency and spatial domains we present a rigorous error analysis which shows how the local expansion degree depends on the target accuracy and the nonharmonic bandwidth moreover we show that the original scheme becomes numerically unstable if a large local expansion degree is used this problem is removed by representing all approximations in a lagrange type basis instead of the previously used monomial basis all theoretical results are illustrated by numerical experiments

spectrally accurate fast summation for periodic stokes potentials a spectrally accurate method for the fast evaluation of n particle sums of the periodic stokeslet is presented two different decomposition methods leading to one sum in real space and one in reciprocal space are considered an fft based method is applied to the reciprocal part of the sum invoking the equivalence of multiplications in reciprocal space to convolutions in real space thus using convolutions with a gaussian function to place the point sources on a grid due to the spectral accuracy of the method the grid size needed is low and also in practice for a fixed domain size independent of n the leading cost which is linear in n arises from the to grid and from grid operations combining this fft based method for the reciprocal sum with the direct evaluation of the real space sum a spectrally accurate algorithm with a total complexity of o nlogn is obtained this has been shown numerically as the system is scaled up at constant density

marginal maximum likelihood estimation for the one parameter logistic model two algorithms are described for marginal maximum likelihood estimation for the one parameter logistic model the more efficient of the two algorithms is extended to estimation for the linear logistic model numerical examples of both procedures are presented

efficient thermal field computation in phase field models we solve the phase field equations in two dimensions to simulate crystal growth in the low undercooling regime the novelty is the use of a fast solver for the free space heat equation to compute the thermal field this solver is based on the efficient direct evaluation of the integral representation of the solution to the constant coefficient free space heat equation with a smooth source term the computational cost and memory requirements of the new solver are reasonable and no artificial boundary conditions are needed this allows one to solve for the thermal field in a computational domain whose size depends only on the size of the growing crystal and not on the extent of the thermal field which can result in significant computational savings in the low undercooling regime

a reconstruction algorithm for photoacoustic imaging based on the nonuniform fft fourier reconstruction algorithms significantly outperform conventional backprojection algorithms in terms of computation time in photoacoustic imaging these methods require interpolation in the fourier space domain which creates artifacts in reconstructed images we propose a novel reconstruction algorithm that applies the one dimensional nonuniform fast fourier transform to photoacoustic imaging it is shown theoretically and numerically that our algorithm avoids artifacts while preserving the computational effectiveness of fourier reconstruction

loglinear rasch model tests existing statistical tests for the fit of the rasch model have been criticized because they are only sensitive to specific violations of its assumptions contingency table methods using loglinear models have been used to test various psychometric models in this paper the assumptions of the rasch model are discussed and the rasch model is reformulated as a quasi independence model the model is a quasi loglinear model for the incomplete subgroup score item 1 item 2 itemk contingency table using ordinary contingency table methods the rasch model can be tested generally or against less restrictive quasi loglinear models to investigate specific violations of its assumptions

fast tomographic reconstruction via rotation based hierarchical backprojection we introduce a family of fast algorithms for tomographic backprojection in the parallel beam geometry the algorithms reduce the computational cost of backprojecting p projections onto an n times n pixel image from the conventional o n 2 p to o n 2 log p the new algorithms aggregate the projections in a hierarchical structure with images in the hierarchy formed by the rotation and addition of other images made up of fewer projections while these algorithms are related to existing fast algorithms this work places them within the signal processing framework providing a systematic means to optimize and adjust the trade off between computational cost and accuracy rotations are performed separably in order that higher order interpolators may be used with low computational cost the same ideas are applied to create a tomographic projection algorithm which computes projections of an n times n pixel image onto p view angles at a cost of o n 2 log p

on the numerical solution of the heat equation i we describe a fast solver for the inhomogeneous heat equation in free space following the time evolution of the solution in the fourier domain it relies on a recently developed spectral approximation of the free space heat kernel coupled with the non uniform fast fourier transform unlike finite difference and finite element techniques there is no need for artificial boundary conditions on a finite computational domain the method is explicit unconditionally stable and requires an amount of work of the order o nm log n where n is the number of discretization points in physical space and m is the number of time steps we refer to the approach as the fast recursive marching frm method

estimating latent distributions consider vectors of item responses obtained from a sample of subjects from a population in which ability is distributed with densityg where the are unknown parameters assuming the responses depend on through a fully specified item response model this paper presents maximum likelihood equations for the estimation of the population parameters directly from the observed responses i e without estimating an ability parameter for each subject also provided are asymptotic standard errors and tests of fit computing approximations and details of four special cases a non parametric approximation a normal solution a resolution of normal components and a beta binomial solution

some neglected problems in irt the paper addresses three neglected questions from irt in section 1 the properties of the measurement of ability or trait parameters and item difficulty parameters in the rasch model are discussed it is shown that the solution to this problem is rather complex and depends both on general assumptions about properties of the item response functions and on assumptions about the available item universe section 2 deals with the measurement of individual change or modifiability based on a rasch test a conditional likelihood approach is presented that yields a an ml estimator of modifiability for given item parameters b allows one to test hypotheses about change by means of a clopper pearson confidence interval for the modifiability parameter or c to estimate modifiability jointly with the item parameters uniqueness results for all three methods are also presented in section 3 the mantel haenszel method for detecting dif is discussed under a novel perspective what is the most general framework within which the mantel haenszel method correctly detects dif of a studied item the answer is that this is a 2pl model where however all discrimination parameters are known and the studied item has the same discrimination in both populations since these requirements would hardly be satisfied in practical applications the case of constant discrimination parameters that is the rasch model is the only realistic framework a simple pearsonx2 test for dif of one studied item is proposed as an alternative to the mantel haenszel test moreover this test is generalized to the case of two items simultaneously studied for dif

fast fourier transforms of piecewise polynomials abstract we introduce an efficient algorithm for evaluating the fourier transform of piecewise polynomial data on d dimensional simplices in d dimensional euclidean space r d it generalizes butterfly algorithms for pointwise d 0 nonuniform fast fourier transforms with new dimensional recurrences for exponential polynomial moments error analysis and numerical comparisons with direct evaluation validate the efficiency and accuracy of the algorithm

a multilevel matrix decomposition algorithm for analyzing scattering from large structures a multilevel algorithm is presented for analyzing scattering from electrically large surfaces the algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics the algorithm permits a fast matrix vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks with each describing the interaction between distant scatterers the multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast fourier transform fft and that only relies on well known algebraic techniques the computational complexity and the memory requirements of the proposed algorithm are o n log sup 2 n

fast computation of fourier integral operators we introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation general hyperbolic equations and curvilinear tomography the problem is to numerically evaluate a so called fourier integral operator fio of the form int e 2 pi i phi x xi a x xi hat f xi d xi at points given on a cartesian grid here xi is a frequency variable hat f xi is the fourier transform of the input f a x xi is an amplitude and phi x xi is a phase function which is typically as large as xi hence the integral is highly oscillatory because a fio is a dense matrix a naive matrix vector product with an input given on a cartesian grid of size n by n would require o n 4 operations this paper develops a new numerical algorithm which requires o n 2 5 log n operations and as low as o sqrt n in storage space the constants in front of these estimates are small it operates by localizing the integral over polar wedges with small angular aperture in the frequency plane on each wedge the algorithm factorizes the kernel e 2 pi i phi x xi a x xi into two components 1 a diffeomorphism which is handled by means of a nonuniform fft and 2 a residual factor which is handled by numerical separation of the spatial and frequency variables the key to the complexity and accuracy estimates is the fact that the separation rank of the residual kernel is provably independent of the problem size several numerical examples demonstrate the numerical accuracy and low computational complexity of the proposed methodology we also discuss the potential of our ideas for various applications such as reflection seismology

solving inverse eigenvalue problems via householder and rank one matrices abstract a brief and practical algorithm is introduced to solve symmetric inverse eigenvalue problems which we call hrou algorithm the algorithm is based on householder transformations and rank one updating we give some basic properties and the computational amount and develop sensitivity analysis of hrou algorithm furthermore we develop hrou algorithm into a multi level and adaptive one named mlahrou to solve symmetric nonnegative inverse eigenvalue problems new sufficient conditions to ensure symmetric nonnegative matrices and symmetric m matrices are given many numerical examples are given to verify our theory compare with existing results and show the efficiency of our algorithms

kaiser bessel basis for particle mesh interpolation in this work we introduce the kaiser bessel interpolation basis for the particle mesh interpolation in the fast ewald method a reliable a priori error estimate is developed to measure the accuracy of the force computation in correlated charge systems and is shown to be effective in optimizing the shape parameter of the kaiser bessel basis in terms of accuracy by comparing the optimized kaiser bessel basis with the traditional b spline basis we demonstrate that the former is more accurate than the latter in part of the working parameter space say a relatively small real space cutoff a relatively small reciprocal space mesh and a relatively large truncation of basis in some cases the kaiser bessel basis is found to be more than one order of magnitude more accurate

data driven optimal transport the problem of optimal transport between two distributions x and y is extended to situations where the distributions are only known through a finite number of samples xi and yj a weak formulation is proposed based on the dual of the kantorovich formulation with two main modifications replacing the expected values in the objective function by their empirical means over the xi and yj and restricting the dual variables u x and v y to a suitable set of test functions adapted to the local availability of sample points a procedure is proposed and tested for the numerical solution of this problem based on a fluidlike flow in phase space where the sample points play the role of active lagrangian markers 2016 wiley periodicals inc

computing the ground state and dynamics of the nonlinear schrodinger equation with nonlocal interactions via the nonuniform fft we present efficient and accurate numerical methods for computing the ground state and dynamics of the nonlinear schrodinger equation nlse with nonlocal interactions based on a fast and accurate evaluation of the long range interactions via the nonuniform fast fourier transform nufft we begin with a review of the fast and accurate nufft based method in 29 for nonlocal interactions where the singularity of the fourier symbol of the interaction kernel at the origin can be canceled by switching to spherical or polar coordinates we then extend the method to compute other nonlocal interactions whose fourier symbols have stronger singularity at the origin that cannot be canceled by the coordinate transform many of these interactions do not decay at infinity in the physical space which adds another layer of complexity since it is more difficult to impose the correct artificial boundary conditions for the truncated bounded computational domain the performance of our method against other existing methods is illustrated numerically with particular attention on the effect of the size of the computational domain in the physical space finally to study the ground state and dynamics of the nlse we propose efficient and accurate numerical methods by combining the nufft method for potential evaluation with the normalized gradient flow using backward euler fourier pseudospectral discretization and time splitting fourier pseudospectral method respectively extensive numerical comparisons are carried out between these methods and other existing methods for computing the ground state and dynamics of the nlse with various nonlocal interactions numerical results show that our scheme performs much better than those existing methods in terms of both accuracy and efficiency

accelerated boundary integral method for multiphase flow in non periodic geometries an accelerated boundary integral method for stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry the computational complexity of the algorithm scales as o n or o n log n where n is proportional to the product of number of particles and the number of elements employed to discretize the particle this technique is enabled by the use of an alternative boundary integral formulation in which the velocity field is expressed in terms of a single layer integral alone even in problems with non matched viscosities the density of the single layer integral is obtained from a fredholm integral equation of the second kind involving the double layer integral acceleration in this implementation is provided by the use of general geometry ewald like method ggem for computing the velocity and stress fields driven by a set of point forces in the geometry of interest for the particular case of the slit geometry a fourier chebyshev spectral discretization of ggem is developed efficient implementations employing the ggem methodology are presented for the resulting single and the double layer integrals the implementation is validated with test problems on the velocity of rigid particles and drops between parallel walls in pressure driven flow the taylor deformation parameter of capsules in simple shear flow and the particle trajectories in pair collisions of capsules in simple shear flow the computational complexity of the algorithm is verified with results from several large scale multiparticle simulations

a map of sufficient conditions for the real nonnegative inverse eigenvalue problem abstract the real nonnegative inverse eigenvalue problem rniep is the problem of determining necessary and sufficient conditions for a list of real numbers to be the spectrum of an entrywise nonnegative matrix a number of sufficient conditions for the existence of such a matrix are known in this paper in order to construct a map of sufficient conditions we compare these conditions and establish inclusion relations or independency relations between them

robust exponential convergence of hp fem in balanced norms for singularly perturbed reaction diffusion problems corner domains abstract the h p version of the finite element method is applied to singularly perturbed reaction diffusion type equations on polygonal domains the solution exhibits boundary layers as well as corner layers on a class of meshes that are suitably refined near the boundary and the corners robust exponential convergence in the polynomial degree is shown in both a balanced norm and the maximum norm

computing steerable principal components of a large set of images and their rotations we present here an efficient algorithm to compute the principal component analysis pca of a large image set consisting of images and for each image the set of its uniform rotations in the plane we do this by pointing out the block circulant structure of the covariance matrix and utilizing that structure to compute its eigenvectors we also demonstrate the advantages of this algorithm over similar ones with numerical experiments although it is useful in many settings we illustrate the specific application of the algorithm to the problem of cryo electron microscopy

a parallel butterfly algorithm the butterfly algorithm is a fast algorithm which approximately evaluates a discrete analogue of the integral transform int mathbb r d k x y g y dy at large numbers of target points when the kernel k x y is approximately low rank when restricted to subdomains satisfying a certain simple geometric condition in d dimensions with o n d quasi uniformly distributed source and target points when each appropriate submatrix of k is approximately rank r the running time of the algorithm is at most o r 2 n d log n a parallelization of the butterfly algorithm is introduced which assuming a message latency of alpha and per process inverse bandwidth of beta executes in at most o r 2 frac n d p log n beta r frac n d p alpha log p time using p processes this parallel algorithm was then instantiated in the form of the open source textttdistbutterfly library for the special case where k x y exp i phi x y where phi x y is a black box sufficiently smooth

fast ewald summation based on nfft with mixed periodicity in this paper we develop new fast fourier based methods for the coulomb problem we combine the ewald summation formulas and the fast summation approach based on the nonequispaced fast fourier transform nfft in order to develop efficient methods for calculating the coulomb energies as well as the acting forces in charged particle systems subject to mixed periodic boundary conditions therewith we extend the applicability of nfft based methods which already exist for open as well as for 3d periodic boundary conditions to arbitrary combinations of periodic and open boundary conditions we reconsider the derivation of the ewald formulas for 2d and 1d periodic systems introduce the new algorithms and present high precision numerical results

realizability criterion for the symmetric nonnegative inverse eigenvalue problem abstract let 1 2 n a set of real numbers the real nonnegative inverse eigenvalue problem rniep is the problem of determining necessary and sufficient conditions in order that be the spectrum of an entrywise nonnegative n n matrix if there exists a nonnegative matrix a with spectrum we say that is realized by a many realizability criteria for the existence of such a matrix a are known this paper shows that a realizability criterion given by the author which contains both kellogg s realizability criterion and borobia s realizability criterion is sufficient for the existence of an n n symmetric nonnegative matrix with prescribed spectrum

an inversion formula and fast algorithms for cauchy vandermonde matrices abstract matrices of composed type consisting of a vandermonde and a cauchy part and their connection to rational interpolation are investigated an inversion formula is presented and fast solution algorithms with o n log2 n complexity for cauchy vandermonde systems are developed

fast approximate fourier transforms for irregularly spaced data several algorithms for efficiently evaluating trigonometric polynomials at irregularly spaced points are presented and analyzed the algorithms can be viewed as approximate generalizations of the fast fourier transform fft and they are compared with regard to their accuracy and their computational efficiency

on the inverse eigenvalue problem for matrices atomic corrections the inverse eigenvalue problem for matrices is studied with the objective of obtaining an efficient method for correcting energy levels in atomic systems though the results are applicable to any eigenvalue problem the approach is a development of earlier work by s friedland 1977 the diagonal elements of a real symmetric matrix with given off diagonal elements are adjusted to yield a given spectrum the authors discuss cases where there are real solutions and no real solutions with particular emphasis on the latter problems of slow convergence arise they demonstrate the cause of this slow convergence give a geometrical interpretation of the problem and show how it can be avoided also the matrices encountered arise from complex calculations and are subject to error they develop an error analysis that permits us among other things to judge whether corrections in any particular case are justified in view of anticipated errors in the given computed off diagonal matrix elements finally the method is demonstrated in an application to certain sets of levels in 12 times ionized neon like titanium

fast potential theory ii layer potentials and discrete sums we present three new families of fast algorithms for classical potential theory based on ewald summation and fast transforms of gaussians and fourier series ewald summation separates the green function for a cube into a high frequency localized part and a rapidly converging fourier series each part can then be evaluated efficiently with appropriate fast transform algorithms our algorithms are naturally suited to the use of green functions with boundary conditions imposed on the boundary of a cube rather than free space green functions our first algorithm evaluates classical layer potentials on the boundary of a d dimensional domain with d equal to two or three the quadrature error is o hm e where h is the mesh size on the boundary and m is the order of quadrature used the algorithm evaluates the discretized potential using n elements at o n points in o n log n arithmetic operations the constant in o n log n depends logarithmically on the desired error tolerance our second scheme evaluates a layer potential on the domain itself with the same accuracy it produces md values using n boundary elements in o n md log m arithmetic operations our third method evaluates a discrete sum of values of the green function of the type which occur in particle methods it attains error at a cost o na log n where a 2 1 dd and d is the hausdorff dimension of the set where the sources concentrate in the limit n thus it is o n log n when the sources do not cluster too much and close to o n log n in the important practical case when the points are uniformly distributed over a hypersurface we also sketch an o n log n algorithm based on special functions two dimensional numerical results are presented for all three algorithms layer potentials are evaluated to second order accuracy in times which exhibit considerable speedups even over a reasonably sophisticated direct calculation discrete sum calculations are speeded up astronomically our algorithm reduces the cpu time required for a calculation with 40 000 points from six months to one hour

nonlinear approximation by sums of exponentials and translates in this paper we discuss the numerical solution of two nonlinear approximation problems many applications in electrical engineering signal processing and mathematical physics lead to the following problem let h be a linear combination of exponentials with real frequencies determine all frequencies all coefficients and the number of summands if finitely many perturbed uniformly sampled data of h are given we solve this problem by an approximate prony method apm and prove the stability of the solution in the square and uniform norm further an apm for nonuniformly sampled data is proposed too the second approximation problem is related to the first one and reads as follows let varphi be a given 1 periodic window function as defined in section 4 further let f be a linear combination of translates of varphi determine all shift parameters all coefficients and the number of translates if finitely many perturbed uniformly sampled data of f are given using fourier technique this problem is transferred into the above parameter estimation problem for an exponential sum which is solved by apm the stability of the solution is discussed in the square and uniform norm too numerical experiments show the performance of our approximation methods

locally dependent latent trait model and the dutch identity revisited in this paper we propose a class of locally dependent latent trait models for responses to psychological and educational tests typically item response models treat an individual s multiple response to stimuli as conditional independent given the individual s latent trait in this paper instead the focus is on models based on a family of conditional distributions or kernel that describes joint multiple item responses as a function of student latent trait not assuming conditional independence specifically we examine a hybrid kernel which comprises a component for one way item response functions and a component for conditional associations between items given latent traits the class of models allows the extension of item response theory to cover some new and innovative applications in psychological and educational research an em algorithm for marginal maximum likelihood of the hybrid kernel model is proposed furthermore we delineate the relationship of the class of locally dependent models and the log linear model by revisiting the dutch identity holland 1990

spectral ewald acceleration of stokesian dynamics for polydisperse suspensions in this work we develop the spectral ewald accelerated stokesian dynamics seasd a novel computational method for dynamic simulations of polydisperse colloidal suspensions with full hydrodynamic interactions seasd is based on the framework of stokesian dynamics sd with extension to compressible solvents and uses the spectral ewald se method lindbo and tornberg 2010 29 for the wave space mobility computation to meet the performance requirement of dynamic simulations we use graphic processing units gpu to evaluate the suspension mobility and achieve an order of magnitude speedup compared to a cpu implementation for further speedup we develop a novel far field block diagonal preconditioner to reduce the far field evaluations in the iterative solver and seasd nf a polydisperse extension of the mean field brownian approximation of banchio and brady 2003 39 we extensively discuss implementation and parameter selection strategies in seasd and demonstrate the spectral accuracy in the mobility evaluation and the overall o n log n computation scaling we present three computational examples to further validate seasd and seasd nf in monodisperse and bidisperse suspensions the short time transport properties the equilibrium osmotic pressure and viscoelastic moduli and the steady shear brownian rheology our validation results show that the agreement between seasd and seasd nf is satisfactory over a wide range of parameters and also provide significant insight into the dynamics of polydisperse colloidal suspensions

a matrix inverse eigenvalue problem and its application the problem of generating a matrix a with specified eigenvalues which maps a given set of vectors of another given set is presented an existence theorem is given and proved a stable algorithm for producing the matrix a is discussed the relation between this problem and the pole assignment problem in control theory is investigated the application of this problem in the design of neural networks is discussed

generalized latent trait models in this paper we discuss a general model framework within which manifest variables with different distributions in the exponential family can be analyzed with a latent trait model a unified maximum likelihood method for estimating the parameters of the generalized latent trait model will be presented we discuss in addition the scoring of individuals on the latent dimensions the general framework presented allows not only the analysis of manifest variables all of one type but also the simultaneous analysis of a collection of variables with different distributions the approach used analyzes the data as they are by making assumptions about the distribution of the manifest variables directly

the chebyshev fast gauss and nonuniform fast fourier transforms and their application to the evaluation of distributed heat potentials we present a method for the fast and accurate computation of distributed heat potentials in two dimensions the distributed source is assumed to be given in terms of piecewise space time chebyshev polynomials we discretize uniformly in time whereas in space the polynomials are defined on the leaf nodes of a quadtree the quadtree can vary at each time step we combine a product integration rule with fast algorithms fast heat potentials nonuniform fft fast gauss transform to obtain a high order accurate method with optimal complexity if n is the number of time steps m is the maximum number of leaf nodes over all the time steps and the input contains a qth order polynomial representation of f then our method requires o q 3mnlogm work to evaluate the heat potential at arbitrary mn space time target locations the overall convergence rate of the method is of order q we present numerical experiments for q 4 8 and 16 and we verify the theoretical convergence rate of the method when the solution is sufficiently smooth the 16th order variant results in significant computational savings even in the case in which we require only a few digits of accuracy

a boundary mixture approach to violations of conditional independence conditional independence is a fundamental principle in latent variable modeling and item response theory violations of this principle commonly known as local item dependencies are put in a test information perspective and sharp bounds on these violations are defined a modeling approach is proposed that makes use of a mixture representation of these boundaries to account for the local dependence problem by finding a balance between independence on the one side and absolute dependence on the other side in contrast to alternative approaches the nature of the proposed boundary mixture model does not necessitate a change in formulation of the typical item characteristic curves used in item response theory this has attractive interpretational advantages and may be useful for general test construction purposes

non uniform fft for the finite element computation of the micromagnetic scalar potential we present a quasi linearly scaling first order polynomial finite element method for the solution of the magnetostatic open boundary problem by splitting the magnetic scalar potential the potential is determined by solving a dirichlet problem and evaluation of the single layer potential by a fast approximation technique based on fourier approximation of the kernel function the latter approximation leads to a generalization of the well known convolution theorem used in finite difference methods we address it by a non uniform fft approach overall our method scales o m n nlogn for n nodes and m surface triangles we confirm our approach by several numerical tests

fast direct methods for gaussian processes a number of problems in probability and statistics can be addressed using the multivariate normal gaussian distribution in the one dimensional case computing the probability for a given mean and variance simply requires the evaluation of the corresponding gaussian density in the n dimensional setting however it requires the inversion of an n times n covariance matrix c as well as the evaluation of its determinant det c in many cases such as regression using gaussian processes the covariance matrix is of the form c sigma 2 i k where k is computed using a specified covariance kernel which depends on the data and additional parameters hyperparameters the matrix c is typically dense causing standard direct methods for inversion and determinant evaluation to require mathcal o n 3 work this cost is prohibitive for large scale modeling here we show that for the most commonly used covariance functions the matrix c can be hierarchically factored into a product of block low rank updates of the identity matrix yielding an mathcal o n log 2 n algorithm for inversion more importantly we show that this factorization enables the evaluation of the determinant det c permitting the direct calculation of probabilities in high dimensions under fairly broad assumptions on the kernel defining k our fast algorithm brings many problems in marginalization and the adaptation of hyperparameters within practical reach using a single cpu core the combination of nearly optimal scaling in terms of problem size with high performance computing resources will permit the modeling of previously intractable problems we illustrate the performance of the scheme on standard covariance kernels

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

rapid computation of the discrete fourier transform algorithms for the rapid computation of the forward and inverse discrete fourier transform for points which are nonequispaced or whose number is unrestricted are presented the computational procedure is based on approximation using a local taylor series expansion and the fast fourier transform fft the forward transform for nonequispaced points is computed as the solution of a linear system involving the inverse fourier transform this latter system is solved using the iterative method gmres with preconditioning numerical results are given to confirm the efficiency of the algorithms

fast and accurate evaluation of nonlocal coulomb and dipole dipole interactions via the nonuniform fft we present a fast and accurate algorithm for the evaluation of nonlocal long range coulomb and dipole dipole interactions in free space the governing potential is simply the convolution of an interaction kernel u mathbf x and a density function rho mathbf x psi mathbf x 2 for some complex valued wave function psi mathbf x permitting the formal use of fourier methods these are hampered by the fact that the fourier transform of the interaction kernel widehat u mathbf k has a singularity and or widehat rho mathbf k ne0 at the origin mathbf k bf 0 in fourier phase space thus accuracy is lost when using a uniform cartesian grid in mathbf k which would otherwise permit the use of the fft for evaluating the convolution here we make use of a high order discretization of the fourier integral accelerated by the nonuniform fast fourier transform nufft by adopting spherical and polar phase space discretizations in three and two dimensions respectively

fast elliptic solvers in cylindrical coordinates and the coulomb collision operator in this paper we describe a new class of fast solvers for separable elliptic partial differential equations in cylindrical coordinates r q z with free space radiation conditions by combining integral equation methods in the radial variable r with fourier methods in q and z we show that high order accuracy can be achieved in both the governing potential and its derivatives a weak singularity arises in the fourier transform with respect to z that is handled with special purpose quadratures we show how these solvers can be applied to the evaluation of the coulomb collision operator in kinetic models of ionized gases

a fluctuating boundary integral method for brownian suspensions abstract we present a fluctuating boundary integral method fbim for overdamped brownian dynamics bd of two dimensional periodic suspensions of rigid particles of complex shape immersed in a stokes fluid we develop a novel approach for generating brownian displacements that arise in response to the thermal fluctuations in the fluid our approach relies on a first kind boundary integral formulation of a mobility problem in which a random surface velocity is prescribed on the particle surface with zero mean and covariance proportional to the green s function for stokes flow stokeslet this approach yields an algorithm that scales linearly in the number of particles for both deterministic and stochastic dynamics handles particles of complex shape achieves high order of accuracy and can be generalized to three dimensions and other boundary conditions we show that brownian displacements generated by our method obey the discrete fluctuation dissipation balance relation dfdb based on a recently developed positively split ewald method fiore et al 2017 24 near field contributions to the brownian displacements are efficiently approximated by iterative methods in real space while far field contributions are rapidly generated by fast fourier space methods based on fluctuating hydrodynamics fbim provides the key ingredient for time integration of the overdamped langevin equations for brownian suspensions of rigid particles we demonstrate that fbim obeys dfdb by performing equilibrium bd simulations of suspensions of starfish shaped bodies using a random finite difference temporal integrator

nonuniform fast fourier transforms using min max interpolation the fast fourier transform fft is used widely in signal processing for efficient computation of the ft of finite length signals over a set of uniformly spaced frequency locations however in many applications one requires nonuniform sampling in the frequency domain i e a nonuniform ft several papers have described fast approximations for the nonuniform ft based on interpolating an oversampled fft this paper presents an interpolation method for the nonuniform ft that is optimal in the min max sense of minimizing the worst case approximation error over all signals of unit norm the proposed method easily generalizes to multidimensional signals numerical results show that the min max approach provides substantially lower approximation errors than conventional interpolation methods the min max criterion is also useful for optimizing the parameters of interpolation kernels such as the kaiser bessel function

sparse fourier transform via butterfly algorithm this paper introduces a fast algorithm for computing sparse fourier transforms with spatial and fourier data supported on curves or surfaces this problem appears naturally in several important applications of wave scattering digital signal processing and reflection seismology the main idea of the algorithm is that the interaction between a frequency region and a spatial region is approximately low rank if the product of their widths are bounded by the maximum frequency based on this property we can approximate the interaction between these two boxes accurately and compactly using a small number of equivalent sources the overall structure of the algorithm follows the butterfly algorithm the computation is further accelerated by exploiting the tensor product property of the fourier kernel in two and three dimensions the proposed algorithm is accurate and has the optimal complexity we present numerical results in both two and three dimensions

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

an irt model with a parameter driven process for change an irt model with a parameter driven process for change is proposed quantitative differences between persons are taken into account by a continuous latent variable as in common irt models in addition qualitative interindividual differences and autodependencies are accounted for by assuming within subject variability with respect to the parameters of the irt model in particular the parameters of the irt model are governed by an unobserved or hidden homogeneous markov process the model includes the mixture linear logistic test model mislevy verhelst 1990 the mixture rasch model rost 1990 and the saltus model wilson 1989 as specific instances the model is applied to a longitudinal experiment on discontinuity in conservation acquisition van der maas 1993

the regular fourier matrices and nonuniform fast fourier transforms for any triple of positive integers m n q the matrix f m n q called the m n q regular fourier matrix is defined the regular fourier matrices f m n q are then applied to set up new algorithms for nonuniform fast fourier transforms numerical results show that the accuracies obtained by our algorithms are much better than previously reported results with the same computation complexity the algorithms require o n cdot log 2n arithmetic operations where n is the number of data points

constructing symmetric nonnegative matrices via the fast fourier transform abstract we derive an algorithm based on the fast fourier transform to construct a real symmetric matrix s with eigenvalues 1 2 n with eigenvector e 1 1 1 t belonging to the eigenvalue 1 we find simple conditions on the eigenvalues such that the algorithm constructs an irreducible matrix s 1 e where e is a symmetric doubly stochastic matrix

granger causality analysis with nonuniform sampling and its application to pulse coupled nonlinear dynamics the granger causality gc analysis is an effective approach to infer causal relations for time series however for data obtained by uniform sampling i e with an equal sampling time interval it is known that gc can yield unreliable causal inference due to aliasing if the sampling rate is not sufficiently high to solve this unreliability issue we consider the nonuniform sampling scheme as it can mitigate against aliasing by developing an unbiased estimation of power spectral density of nonuniformly sampled time series we establish a framework of spectrum based nonparametric gc analysis applying this framework to a general class of pulse coupled nonlinear networks and utilizing some particular spectral structure possessed by these nonlinear network data we demonstrate that for such nonlinear networks with nonuniformly sampled data reliable gc inference can be achieved at a low nonuniform mean sampling rate at which the traditional uniform sampling gc may lead to spurious causal inference

high order boundary integral equation solution of high frequency wave scattering from obstacles in an unbounded linearly stratified medium we apply boundary integral equations for the first time to the two dimensional scattering of time harmonic waves from a smooth obstacle embedded in a continuously graded unbounded medium in the case we solve the square of the wavenumber refractive index varies linearly in one coordinate i e e x 2 u x 1 x 2 0 where e is a constant this models quantum particles of fixed energy in a uniform gravitational field and has broader applications to stratified media in acoustics optics and seismology we evaluate the fundamental solution efficiently with exponential accuracy via numerical saddle point integration using the truncated trapezoid rule with typically 102 nodes with an effort that is independent of the frequency parameter e by combining with a high order nystrom quadrature we are able to solve the scattering from obstacles 50 wavelengths across to 11 digits of accuracy in under a minute on a desktop or laptop

short note the type 3 nonuniform fft and its applications the nonequispaced or nonuniform fast fourier transform nufft arises in a variety of application areas including imaging processing and the numerical solution of partial differential equations in its most general form it takes as input an irregular sampling of a function and seeks to compute its fourier transform at a nonuniform sampling of frequency locations this is sometimes referred to as the nufft of type 3 like the fast fourier transform the amount of work required is of the order o nlogn where n denotes the number of sampling points in both the physical and spectral domains in this short note we present the essential ideas underlying the algorithm in simple terms we also illustrate its utility with application to problems in magnetic resonance imagin and heat flow

copula functions for residual dependency most item response theory models are not robust to violations of conditional independence however several modeling approaches e g conditioning on other responses additional random effects exist that try to incorporate local item dependencies but they have some drawbacks such as the nonreproducibility of marginal probabilities and resulting interpretation problems in this paper a new class of models making use of copulas to deal with local item dependencies is introduced these models belong to the bigger class of marginal models in which margins and association structure are modeled separately it is shown how this approach overcomes some of the problems associated with other local item dependency models

combined complex ridgelet shrinkage and total variation minimization a new algorithm for the characterization of engineering surface topographies with line singularities is proposed it is based on thresholding complex ridgelet coefficients combined with total variation tv minimization the discrete ridgelet transform is designed by first using a discrete radon transform based on the nonequispaced fast fourier transform nfft and then applying a dual tree complex wavelet transform dt cwt the nfft based approach of the radon transform completely avoids linear interpolations of the cartesian to polar grid and requires only o n2 log n arithmetic operations for n by n arrays while its inverse preserves the good reconstruction quality of the filtered backprojection the dt cwt in the second step of the ridgelet transform provides approximate shift invariance on the projections of the radon transform after hard thresholding the ridgelet coefficients they are restored using tv minimization to eliminate the pseudo gibbs artifacts near the discontinuities numerical experiments demonstrate the remarkable ability of the methodology to extract line scratches

fast fourier transforms for nonequispaced data a group of algorithms is presented generalizing the fast fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval pi pi the schemes of this paper are based on a combination of certain analytical considerations with the classical fast fourier transform and generalize both the forward and backward ffts each of the algorithms requires o n cdot log n n cdot log 1 varepsilon arithmetic operations where varepsilon is the precision of computations and n is the number of nodes the efficiency of the approach is illustrated by several numerical examples

construction of nonnegative symmetric matrices with given spectrum abstract let 1 n be the spectrum of a nonnegative symmetric matrix a with the perron eigenvalue 1 a diagonal entry c and let 1 m be the spectrum of a nonnegative symmetric matrix b with the perron eigenvalue 1 we show how to construct a nonnegative symmetric matrix c with the spectrum 1 max 0 1 c 2 n 2 m

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

an inverse eigenvalue problem for nonnegative matrices abstract this paper gives a solution to an inverse eigenvalue problem of nonnegative matrices which was proposed by miroslav fiedler

a sparse data fast fourier transform sdfft a multilevel algorithm that efficiently fourier transforms sparse spatial data to sparse spectral data with controllable error is presented the algorithm termed sparse data fast fourier transform sdfft is particularly useful for signal processing applications where only part of the k space is to be computed regardless of whether it is a regular region like an angular section of the ewald sphere or it consists of completely arbitrary points scattered in the k space in addition like the various nonuniform fast fourier transforms the o nlogn algorithm can deal with a sparse nonuniform spatial domain in this paper the parabolic reflector antenna problem is studied as an example to demonstrate its use in the computation of far field patterns due to arbitrary aperture antennas and antenna arrays the algorithm is also promising for various applications such as backprojection tomography diffraction tomography and synthetic aperture radar imaging

inverse problems for symmetric doubly stochastic matrices whose suleĭmanova spectra are bounded below by 1 2 abstract a new sufficient condition for a list of real numbers to be the spectrum of a symmetric doubly stochastic matrix is presented this is a contribution to the classical spectral inverse problem for symmetric doubly stochastic matrices that is still open in its full generality it is proved that whenever 2 n are non positive real numbers with 1 2 n 1 2 then there exists a symmetric doubly stochastic matrix whose spectrum is precisely 1 2 n we point out that this criterion is incomparable to the classical sufficient conditions due to perfect mirsky soules and their modern refinements due to nader et al we also provide some examples and applications of our results

approximation of the high frequency helmholtz kernel by nested directional interpolation error analysis we present and analyze an approximation scheme for a class of highly oscillatory kernel functions taking the 2d and 3d helmholtz kernels as examples the scheme is based on polynomial interpolation combined with suitable pre and post multiplication by plane waves it is shown to converge exponentially in the polynomial degree and supports multilevel approximation techniques our convergence analysis may be employed to establish exponential convergence of certain classes of fast methods for discretizations of the helmholtz integral operator that feature polylogarithmic linear complexity

logistic latent trait models with linear constraints two linearly constrained logistic models which are based on the well known dichotomous rasch model the linear logistic test model lltm and the linear logistic model with relaxed assumptions llra are discussed necessary and sufficient conditions for the existence of unique conditional maximum likelihood estimates of the structural model parameters are derived methods for testing composite hypotheses within the framework of these models and a number of typical applications to real data are mentioned

on the existence and uniqueness of maximum likelihood estimates in the rasch model necessary and sufficient conditions for the existence and uniqueness of a solution of the so called unconditional uml and the conditional cml maximum likelihood estimation equations in the dichotomous rasch model are given the basic critical condition is essentially the same for uml and cml estimation for complete data matricesa it is formulated both as a structural property ofa and in terms of the sufficient marginal sums in case of incomplete data the condition is equivalent to complete connectedness of a certain directed graph it is shown how to apply the results in practical uses of the rasch model

extensions of the partial credit model the partial credit model developed by masters 1982 is a unidimensional latent trait model for responses scored in two or more ordered categories in the present paper some extensions of the model are presented first a marginal maximum likelihood estimation procedure is developed which allows for incomplete data and linear restrictions on both the item and the population parameters secondly two statistical tests for evaluating model fit are presented the former test has power against violation of the assumption about the ability distribution the latter test offers the possibility of identifying specific items that do not fit the model

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

selection of a convolution function for fourier inversion using gridding computerised tomography application in the technique known as gridding the data samples are weighted for sampling density and convolved with a finite kernel then resampled on a grid preparatory to a fast fourier transform the authors compare the artifact introduced into the image for various convolving functions of different sizes including the kaiser bessel window and the zero order prolate spheroidal wave function pswf they also show a convolving function that improves upon the pswf in some circumstances

accelerating the nonuniform fast fourier transform the nonequispaced fourier transform arises in a variety of application areas from medical imaging to radio astronomy to the numerical solution of partial differential equations in a typical problem one is given an irregular sampling of n data in the frequency domain and one is interested in reconstructing the corresponding function in the physical domain when the sampling is uniform the fast fourier transform fft allows this calculation to be computed in o n log n operations rather than o n 2 operations unfortunately when the sampling is nonuniform the fft does not apply over the last few years a number of algorithms have been developed to overcome this limitation and are often referred to as nonuniform ffts nuffts these rely on a mixture of interpolation and the judicious use of the fft on an oversampled grid a dutt and v rokhlin siam j sci comput 14 1993 pp 1368 1383 in this paper we observe that one of the standard interpolation or gridding schemes based on gaussians can be accelerated by a significant factor without precomputation and storage of the interpolation weights this is of particular value in two and three dimensional settings saving either 10 d n in storage in d dimensions or a factor of about 5 10 in cputime independent of dimension

computation of gauss kronrod of quadrature rules recently laurie presented a new algorithm for the computation of 2n 1 point gauss kronrod quadrature rules with real nodes and positive weights this algorithm first determines a symmetric tridiagonal matrix of order 2n 1 from certain mixed moments and then computes a partial spectral factorization we describe a new algorithm that does not require the entries of the tridiagonal matrix to be determined and thereby avoids computations that can be sensitive to perturbations our algorithm uses the consolidation phase of a divide and conquer algorithm for the symmetric tridiagonal eigenproblem we also discuss how the algorithm can be applied to compute kronrod extensions of gauss radau and gauss lobatto quadrature rules throughout the paper we emphasize how the structure of the algorithm makes efficient implementation on parallel computers possible numerical examples illustrate the performance of the algorithm

a dynamic generalization of the rasch model in the present paper a model for describing dynamic processes is constructed by combining the common rasch model with the concept of structurally incomplete designs this is accomplished by mapping each item on a collection of virtual items one of which is assumed to be presented to the respondent dependent on the preceding responses and or the feedback obtained it is shown that in the case of subject control no unique conditional maximum likelihood cml estimates exist whereas marginal maximum likelihood mml proves a suitable estimation procedure a hierarchical family of dynamic models is presented and it is shown how to test special cases against more general ones furthermore it is shown that the model presented is a generalization of a class of mathematical learning models known as luce s beta model

a framework for discrete integral transformations i the pseudopolar fourier transform the fourier transform of a continuous function evaluated at frequencies expressed in polar coordinates is an important conceptual tool for understanding physical continuum phenomena an analogous tool suitable for computations on discrete grids could be very useful however no exact analogue exists in the discrete case in this paper we present the notion of pseudopolar grid pp grid and the pseudopolar fourier transform ppft which evaluates the discrete fourier transform at points of the pp grid the pp grid is a type of concentric squares grid in which the radial density of squares is twice as high as usual the pp grid consists of equally spaced samples along rays where different rays are equally spaced in slope rather than angle we develop a fast algorithm for the ppft with the same complexity order as the cartesian fast fourier transform the algorithm is stable invertible requires only one dimensional operations and uses no approximate interpolations we prove that the ppft is invertible and develop two algorithms for its inversion iterative and direct both with complexity o n 2 log n where n times n is the size of the reconstructed image the iterative algorithm applies conjugate gradients to the gram operator of the ppft since the transform is ill conditioned we introduce a preconditioner which significantly accelerates the convergence the direct inversion algorithm utilizes the special frequency domain structure of the transform in two steps first it resamples the pp grid to a cartesian frequency grid and then recovers the image from the cartesian frequency grid

conjunctive item response theory kernels conjunctive item response models are introduced such that a sufficient statistics for latent traits are not necessarily additive in item scores b items are not necessarily locally independent and c existing compensatory additive item response models including the binomial rasch logistic and general locally independent model are special cases simple estimates and hypothesis tests for conjunctive models are introduced and evaluated as well conjunctive models are also identified with cognitive models that assume the existence of several individually necessary component processes for a global ability it is concluded that conjunctive models and methods may show promise for constructing improved tests and uncovering conjunctive cognitive structure it is also concluded that conjunctive item response theory may help to clarify the relationships between local dependence multidimensionality and item response function form

applications of a brauer theorem in the nonnegative inverse eigenvalue problem abstract a result by brauer which shows how to modify one single eigenvalue of a matrix without changing any of the remaining eigenvalues plays a relevant role in the study of the nonnegative inverse eigenvalue problem niep perfect in a long time ignored paper 1955 presents an extension of this result which shows how to modify r eigenvalues of a matrix of order n r n via a rank r perturbation without changing any of the n r remaining eigenvalues by using this extension perfect gives a realizability criterion for the real niep which is not contained in soto s realizability criterion in this work by extending perfect s result we give a new realizability criterion for the real niep which contains soto s criterion thus this new realizability criterion appears to be the most general sufficient condition for the real niep so far we also contribute to the solution of the symmetric niep for n 5

an exact and fast computation of discrete fourier transform for polar and spherical grid numerous applied problems of two dimensional 2 d and 3 d imaging are formulated in continuous domain they place great emphasis on obtaining and manipulating the fourier transform in polar and spherical coordinates however the translation of continuum ideas with the discrete sampled data on a cartesian grid is problematic there exists no exact and fast solution to the problem of obtaining discrete fourier transform for polar and spherical grids in the literature in this paper we develop exact algorithms to the above problem for 2 d and 3 d which involve only 1 d equispaced fast fourier transform with no interpolation or approximation at any stage the result of the proposed approach leads to a fast solution with very high accuracy we describe the computational procedure to obtain the solution in both 2 d and 3 d which includes fast forward and inverse transforms we find the nested multilevel matrix structure of the inverse process and we propose a hybrid grid and use a preconditioned conjugate gradient method that exhibits a drastic improvement in the condition number

consistent estimation in the rasch model based on nonparametric margins consider the class of two parameter marginal logistic rasch models for a test ofm true false items where the latent ability is assumed to be bounded using results of karlin and studen we show that this class of nonparametric marginal logistic nml models is equivalent to the class of marginal logistic models where the latent ability assumes at most m 2 2 values this equivalence has two implications first estimation for the nml model is accomplished by estimating the parameters of a discrete marginal logistic model second consistency for the maximum likelihood estimates of the nml model can be shown whenm is odd using the results of kiefer and wolfowitz an example is presented which demonstrates the estimation strategy and contrasts the nml model with a normal marginal logistic model