preconditioning for dual time stepping simulations of the shallow water equations including coriolis and bed friction effects diagonal preconditioners for implicit unsteady and steady discretizations of the shallow water equations at low and high rossby and drag number limits are analyzed for each case sub and supercritical flow conditions are also considered based on the analysis a preconditioner is derived for use with a multigrid cycle that performs as well as possible under all conditions in addition a streamwise upwind petrov galerkin discretization of the system is presented that is derived from the preconditioned system using this discretization it is demonstrated that for most conditions the preconditioner gives rapid convergence that is independent of the grid resolution and the flow parameters practical tests including an equatorial rossby soliton and tide propagation over variable bathymetry are simulated to demonstrate the performance of this approach

estimation of object location from wideband scattering data we present a time domain algorithm for computation of the maximum likelihood estimate of the location of a known scattering object from wide band scattering data acquired in a suite of scattering experiments the algorithm consists of a three step procedure 1 data filtering 2 time domain backpropagation and 3 coherent summation and is implemented via a number of forward and inverse radon transforms integrated into a tomographic scheme a computer simulation is included for illustration purposes

polygonal and polyhedral contour reconstruction in computed tomography this paper is about three dimensional 3 d reconstruction of a binary image from its x ray tomographic data we study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation we formulate this problem as a nonlinear inverse problem using the bayesian framework vertice estimation is done without using a voxel approximation of the 3 d image it is based on the construction and optimization of a regularized criterion that accounts for surface smoothness we investigate original deterministic local algorithms based on the exact computation of the line projections their update and their derivatives with respect to the vertice coordinates results are first derived in the two dimensional 2 d case which consists of reconstructing a 2 d object of deformable polygonal contour from its tomographic data then we investigate the 3 d extension that requires technical adaptations simulation results illustrate the performance of polygonal and polyhedral reconstruction algorithms in terms of quality and computation time

estimation of object location from diffraction tomographic intensity data it is shown that an image of the log likelihood function for estimating the location of a known weakly inhomogeneous object can be generated directly from noisy intensity distributions measured in a set of scattering experiments this image is a close approximation to the exact log likelihood function generated from complete data i e from both the magnitude and phase of the transmitted wavefields as long as the measurements are performed sufficiently far from the object the performance of the procedure is measured through calculation of the cramer rao bound for the estimation error and is illustrated by a computer simulation study

reconstruction from projections based on detection and estimation of objects parts i and ii performance analysis and robustness analysis the problem of reconstructing a multidimensional field from noisy limited projection measurements is approached using an object based stochastic field model objects within a cross section are characterized by a finite dimensional set of parameters which are estimated directly from limited noisy projection measurements using maximum likelihood estimation in part i the computational structure and performance of the ml estimation procedure are investigated for the problem of locating a single object in a deterministic background simulations are also presented in part ii the issue of robustness to modeling errors is addressed

markov random field modeling for three dimensional reconstruction of the left ventricle in cardiac angiography this paper reports on a method for left ventricle three dimensional 3 d reconstruction from two orthogonal ventriculograms the proposed algorithm is voxel based and takes into account the conical projection geometry associated with the biplane image acquisition equipment the reconstruction process starts with an initial ellipsoidal approximation derived from the input ventriculograms this model is subsequently deformed in such a way as to match the input projections to this end the object is modeled as a 3 d markov gibbs random field and an energy function is defined so that it includes one term that models the projections compatibility and another one that includes the space time regularity constraints the performance of this reconstruction method is evaluated by considering the reconstruction of mathematically synthesized phantoms and two 3 d binary databases from two orthogonal synthesized projections the method is also tested using real biplane ventriculograms in this case the performance of the reconstruction is expressed in terms of the projection error which attains values between 9 50 and 11 78 for two biplane sequences including a total of 55 images

a velocity pressure streamline diffusion finite element method for navier stokes equations a streamline diffusion finite element method is introduced for the time dependent incompressible navier stokes equations in a bounded domain in r squared and r cubed in the case of a flow with a high reynolds number an error estimate is proved and numerical results are given the method is based on a mixed velocity pressure formulation using the same finite element discretization of space time for the velocity and the pressure spaces which consist of piecewise linear functions together with certain least squares modifications of the galerkin variational formulation giving added stability without sacrificing accuracy

object based 3 d reconstruction of arterial trees from magnetic resonance angiograms by exploiting a priori knowledge of arterial shape and smoothness subpixel accuracy reconstructions are achieved from only four noisy projection images the method incorporates a priori knowledge of the structure of branching arteries into a natural optimality criterion that encompasses the entire arterial tree an efficient optimization algorithm for object estimation is presented and its performance on simulated phantom and in vivo magnetic resonance angiograms is demonstrated it is shown that accurate reconstruction of bifurcations is achievable with parametric models

adaptive tetrahedral meshing in free surface flow an unstructured three dimensional moving mesh algorithm is developed for free surface flows with the capability of simulating large deformation a robust edge swapping algorithm and an optimization based mesh smoothing algorithm are used to improve mesh quality as the interface deforms the edge swapping algorithm uses an optimal swap sequence to transform configurations with several tetrahedra sharing a common edge the optimization based mesh smoothing relocates vertex position so that the minimum quality of the incident cells is maximized also edge contraction and bisection are used to adjust the mesh resolution according to surface curvature these local refinements effectively maintain good mesh quality and appropriate mesh size while avoiding global re meshing this scheme s robustness and accuracy are demonstrated with deforming liquid ligaments periodic jets and colliding droplets

cramer rao bounds for parametric shape estimation in inverse problems we address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems when the boundaries are parameterized by a finite number of unknown variables our model applies to multiple unknown objects each with its own unknown gray level or color and boundary parameterization on an arbitrary known background while such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the cramer rao lower bounds very few results have been reported due to the difficulty of computing the derivatives of a functional with respect to shape deformation we provide a general formula for computing cramer rao lower bounds in inverse problems where the observations are related to the object by a general linear transform followed by a possibly nonlinear and noisy measurement system as an illustration we derive explicit formulas for computed tomography fourier imaging and deconvolution problems the bounds reveal that highly accurate parametric reconstructions are possible in these examples using severely limited and noisy data

a two fluid spectral element method abstract a spectral element formulation for two fluid flows is presented which uses arbitrary lagrangian eulerian mesh movement with an unstructured mesh the main advantage of this approach is that the spectral elements provide a high order of accuracy while the unstructured mesh allows geometric flexibility the accuracy of this approach is demonstrated for several relatively simple configurations with and without moving interfaces another unique feature of the formulation as compared to previous single fluid spectral element methods is that a fully implicit time advancement scheme is used this is made possible by the development of a spectral multigrid iteration which solves the implicit governing equations in a fixed number of iterations insensitive to both the polynomial degree of the spectral elements and the number of elements in the mesh by using this approach solutions for both stiff unsteady problems and steady state problems can be obtained efficiently

p 2 continuous finite elements on tetrahedra with local mass matrix inversion abstract when using continuous finite element methods for unsteady simulations one must invert a global mass matrix even for an explicit time advancement scheme in this paper we develop a local mass matrix inversion procedure for p 2 c 0 tetrahedral elements and also show that unlike on triangles b t helenbrook siam j numer anal 47 2009 1304 1318 this procedure does not generalize to higher order for the p 2 basis it is demonstrated that the accuracy of the local inversion is better than any previous mass lumping scheme this allows the development of fast and low memory iterative algorithms as well as accurate explicit computations to be performed the efficiency of using the approach as an iterative relaxation scheme for solving the helmholtz equation is shown by comparing to more standard approaches such as p multigrid with jacobi relaxation lastly the local mass matrix inversion is used to march the unsteady heat equation explicitly with third order spatial accuracy

exploitation of symmetries for image reconstruction in linearized variable density diffraction tomography the problem of reconstructing an object s weakly varying compressibility and density distributions in three dimensional 3d acoustic diffraction tomography is studied based on the fourier diffraction projection theorem for acoustic media it is demonstrated that the 3d fourier components of an object s compressibility and density distributions can be decoupled algebraically thereby providing a method for separately reconstructing the distributions this is facilitated by the identification and exploitation of tomographic symmetries and the rotational invariance of the imaging model the developed reconstruction methods are investigated by use of computer simulation studies the application of the proposed image reconstruction strategy to other tomography problems is discussed

combining and updating of local estimates and regional maps along sets of one dimensional tracks in this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates generated at different times of the same process sample path the first of these cases has applications in decentralized estimation while the second has applications in updating maps of spatially distributed random quantities given measurements along several tracks the method of solution for the second problem uses the result of the first and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields

three dimensional reconstruction from projections with incomplete and noisy data by object estimation an estimation approach to three dimensional reconstruction from parallel ray projections with incomplete and very noisy data is described using a stochastic dynamic model for an object of interest in a probed domain of known background density the reconstruction problem is reformulated as a n onlinear state estimation problem an approximate minimum mean square error globally optimal algorithm for the solution of this problem is presented the algorithm which is recursive in a hybrid frequency space domain operates directly on the fourier transformed projection data eliminating altogether the attempt to invert the projection integral equation the simulation example considered in this paper demonstrates that good object estimates may be obtained with as few as five views in a limited sector of 90 and at a signal to noise ratio as low as 0 db

solving discontinuous galerkin formulations of poisson s equation using geometric and p multigrid methods for solving discontinuous galerkin formulations of the poisson equation by coupling p multigrid to geometric multigrid are investigated the simple approach of performing iterative relaxation on solution approximations of decreasing polynomial degree p down to p 0 and then applying geometric multigrid is ineffective the transition from p 1 top 0 causes the performance of the entire iteration to degrade because the long wavelength eigenfunctions of the p 1 discontinuous system are not represented well in thep 0 space a new approach is proposed that coarsens from thep 1 discontinuous space to thep 1 continuous space this approach eliminates the problems caused by the p 1 to p 0 transition furthermore the p 1 continuous space is a standard finite element space for which geometric multigrid is well defined in addition when the discontinuous galerkin equations are restricted to a continuous space one recovers the galerkin formulation of continuous finite elements thus applying geometric multigrid to this system is straightforward and effective numerical tests agree well with the analysis and confirm that the new approach gives rapid convergence rates that are grid independent and only weakly sensitive to the polynomial order

a triangular spectral element method applications to the incompressible navier stokes equations abstract encouraged by the success of spectral elements methods in computational fluid dynamics and p type finite element methods in structural mechanics we wish to extend these ideas to solving high order polynomial approximations on triangular domains as the next generation of spectral element solvers we introduce here a complete formulation using a modal basis which has been implemented in a new code ne t r the new basis has the following properties jacobi polynomials of mixed weights semi orthogonality hierarchical structure generalized tensor warped product variable order and a new apex co ordinate system allowing automated integration with gaussian quadrature we have discussed the formulation using a matrix notation which allows for an easy interpretation of the forward and backward transformations we use this notation to formulate the linear advection and helmholtz equations in an efficient manner and show that we recover the following properties well conditioned matrices asymptotic operation count of o n 3 scaling o n 2 of the spectral radius of the weak convective operator and exponential convergence using polynomials up to 40 having constructed and numerically analysed these equations we are then able to solve the incompressible navier stokes equations using a high order splitting scheme we demonstrate a variety of results showing exponential convergence using both deformed and straight triangular subdomains for both the stokes and navier stokes problems

application of a maximum likelihood estimator in an experimental study in ultrasonic diffraction tomography a recently proposed approach to the inverse problem of detecting the presence and estimating the location of a known object from data collected in a set of diffraction tomographic experiments is evaluated experimental data are used to validate of the filtered backpropagation algorithms used and their robustness to modeling errors and to severe limitations in the angular coverage of the tomographic data is demonstrated a potential application to medical imaging of soft tissue is illustrated

regular article free surface flow simulation using hp spectral elements computational instabilities inherent in the solution of inviscid incompressible free surface flow have been apparent for some time and different techniques have been used to overcome them in this paper we attempt to explain why these instabilities occur and in doing so a method is developed to study the spatially semi discrete eigenvalues and eigenvectors which govern the stability of the system it is found that the asymmetric spatial discretisation of the fluid domain causes the instabilities after mechanisms for stability are recognised and implemented unsteady inviscid incompressible linear and non linear free surface flow is simulated using a hp spectral element code ensuring fast convergence which incorporates arbitrary lagrangian eulerian ale techniques to decrease deformation of the computational mesh

the homotopy theory of dg categories and derived morita theory the main purpose of this work is to study the homotopy theory of dg categories up to quasi equivalences our main result is a description of the mapping spaces between two dg categories c and d in terms of the nerve of a certain category of c d bimodules we also prove that the homotopy category ho dg cat possesses internal hom s relative to the derived tensor product of dg categories we use these two results in order to prove a derived version of morita theory describing the morphisms between dg categories of modules over two dg categories c and d as the dg category of c d bi modules finally we give three applications of our results the first one expresses hochschild cohomology as endomorphisms of the identity functor as well as higher homotopy groups of the classifying space of dg categories i e the nerve of the category of dg categories and quasi equivalences between them the second application is the existence of a good theory of localization for dg categories defined in terms of a natural universal property our last application states that the dg category of continuous morphisms between the dg categories of quasi coherent resp perfect complexes on two schemes resp smooth and proper schemes is quasi equivalent to the dg category of quasi coherent resp perfect complexes on their product

element diameter free stability parameters for stabilized methods applied to fluids abstract stability parameters for stabilized methods in fluids are suggested the computation of the largest eigenvalue of a generalized eigenvalue problem replaces controversial definitions of element diameters and inverse estimate constants used heretofore to compute these stability parameters the design is employed in the advective diffusive model incompressible navier stokes equations and the stokes problem

cramer rao bounds for 2 d target shape estimation in nonlinear inverse scattering problems with application to passive radar we present new methods for computing fundamental performance limits for two dimensional 2 d parametric shape estimation in nonlinear inverse scattering problems with an application to passive radar imaging we evaluate cramer rao lower bounds crb on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory the crb provides an unbeatable performance limit for any unbiased estimator and under fairly mild regularity conditions is asymptotically achieved by the maximum likelihood estimator mle the resultant crbs are used to define an asymptotic global confidence region centered around the true boundary in which the boundary estimate lies with a prescribed probability these global confidence regions conveniently display the uncertainty in various geometric parameters such as shape size orientation and position of the estimated target and facilitate geometric inferences numerical simulations are performed using the layer approach and the nystrom method for computation of domain derivatives and using fourier descriptors for target shape parameterization this analysis demonstrates the accuracy and generality of the proposed methods

a fast spectral element solver combining static condensation and multigrid techniques we propose a spectral element multigrid method for the two dimensional helmholtz equation discretized on regular grids combining p multigrid with static condensation the method achieves nearly linear complexity with an order independent convergence rate for solving the condensed equations for smoothing we consider two groups of edge based relaxation schemes the best of which attains a multigrid convergence rate of 0 014 to 0 028 numerical experiments have been carried out that demonstrate the robustness of the approach for orders up to 32 and a total of 109 degrees of freedom in comparison with a fast finite difference solver the latter is clearly outperformed already for errors of one percent or lower

associative yang baxter equation and fukaya categories of square tiled surfaces abstract we show that all strongly non degenerate trigonometric solutions of the associative yang baxter equation aybe can be obtained from triple massey products in the fukaya categories of square tiled surfaces along the way we give a classification result for cyclic a algebra structures on a certain frobenius algebra associated with a pair of 1 spherical objects in terms of the equivalence classes of the corresponding solutions of the aybe as an application combining our results with homological mirror symmetry for punctured tori cf 17 we prove that any two simple vector bundles on a cycle of projective lines are related by a sequence of 1 spherical twists and their inverses

a quasi elliptic transformation for moving boundary problems with large anisotropic deformations we have developed a quasi elliptic set of equations for generating a discretization mesh that optimally conforms to an entire domain that undergoes large deformations in primarily one direction we have applied this method to the axisymmetric problem of the transient displacement of a viscous liquid by a high pressure gas the liquid initially fills completely a tube the diameter of which may be constant or change smoothly suddenly or periodically along its finite length key ingredients for the success of the proposed transformation are limiting the orthogonality requirements on the mesh and employing an improved node distribution function along the deforming boundary the retained orthogonal term along with the penalty method for the imposition of the boundary conditions overcome the inherent restrictions of a conformal transformation producing meshes of high quality this term also eliminates the discontinuous slopes of the coordinate lines that are normal to the free surface these usually arise due to the harmonic transformation around highly deforming surfaces the mathematical anisotropy in the mesh generating equations directly corresponds to the physical one when the initially straight and normal to the axis of symmetry air fluid interface at the tube entrance develops mostly along the axial direction generating a long open bubble moreover the generalized node distribution imposes an optimal discretization of the bubble surface itself combining this scheme with the mixed finite element method produces a powerful tool with extended robustness and accuracy in order to reduce the computational cost the resulting set of equations is solved with a non linear gauss seidel technique and a variable time step specific applications of the proposed scheme are presented

higher order nonlinear diffraction tomography inversion of the rytov series nonlinear tomographic reconstruction algorithms are developed for inversion of data measured in scattering experiments in which the complex phase of the wavefields is modeled by an arbitrarily large possibly infinite number of terms in the rytov series the algorithms attain the form of a volterra series of nonlinear operators with the usual filtered backpropagation algorithm of diffraction tomography as the leading linear term a computer simulation study is included to illustrate the performance of the algorithms for the case of scattering objects with cylindrical symmetry

two dimensional prony modeling and parameter estimation a new method for estimating the two dimensional 2d exponential modes and amplitude coefficients in a prony model is presented this method involves two parts each utilizing a 1d singular value decomposition based technique and is capable of locating frequencies anywhere in the 2d frequency plane simulations are shown which demonstrate the performance of the algorithm

non bayesian detection and detectability of anomalies from a few noisy tomographic projections the detection of an anomaly from a few noisy tomographic projections is addressed from the statistical point of view an unknown scene is composed of a background considered as a deterministic nuisance parameter with a possibly hidden anomaly because the full pixel by pixel reconstruction is impossible a parametric non bayesian approach is proposed to fill up the gap in the missing data an optimal statistical test which eliminates the background and detects the anomaly is designed the potential advantage of such an approach is its capacity to detect an anomaly target hidden in background designed by an adversary to mask the anomaly a key issue in the non bayesian anomaly detection i e the problem of anomaly detectability is stated and solved in this paper in the case of a bivariate polynomial background defined on an unknown rectangular support the size of detectable anomaly reaches its maximum defined by the number of elementary cells of x ray detector and degree of the polynomial function

braid group actions on derived categories of coherent sheaves this paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety x the motivation for this is m kontsevich s homological mirror conjecture together with the occurrence of certain braid group actions in symplectic geometry one of the main results is that when dim x geq 2 our braid group actions are always faithful we describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities relations with the mckay correspondence and with exceptional sheaves on fano manifolds are given moreover the case of an elliptic curve is worked out in some detail

mesh deformation using the biharmonic operator the use of the biharmonic operator for deforming a mesh in an arbitrary lagrangian eulerian simulation is investigated the biharmonic operator has the advantage that two conditions can be specified on each boundary of the mesh this allows both the position and the normal mesh spacing along a boundary to be controlled which is important for two fluid interfaces and periodic boundaries at these boundaries we can simultaneously fix the position of the boundary and ensure that the normal mesh spacing is continuous across the boundary in addition results for deforming surfaces show that greater surface deformation can be tolerated when using biharmonic equations compared to approaches using second order partial differential equations a final advantage is that with the biharmonic operator the integrity of a grid in a moving boundary layer can be preserved as the boundary moves the main disadvantage of the approach is its increased computational expense

estimation of dynamically evolving ellipsoids with applications to medical imaging the estimation of dynamically evolving ellipsoids from noisy lower dimensional projections is examined in particular this work describes a model based approach using geometric reconstruction and recursive estimation techniques to obtain a dynamic estimate of left ventricular ejection fraction from a gated set of planar myocardial perfusion images the proposed approach differs from current ejection fraction estimation techniques both in the imaging modality used and in the subsequent processing which yields a dynamic ejection fraction estimate for this work the left ventricle is modeled as a dynamically evolving three dimensional 3 d ellipsoid the left ventricular outline observed in the myocardial perfusion images is then modeled as a dynamic two dimensional 2 d ellipsoid obtained as the projection of the former 3 d ellipsoid this data is processed in two ways first as a 3 d dynamic ellipsoid reconstruction problem second each view is considered as a 2 d dynamic ellipse estimation problem and then the 3 d ejection fraction is obtained by combining the effective 2 d ejection fractions of each view the approximating ellipsoids are reconstructed using a rauch tung striebel smoothing filter which produces an ejection fraction estimate that is more robust to noise since it is based on the entire data set in contrast traditional ejection fraction estimates are based only on true frames of data further numerical studies of the sensitivity of this approach to unknown dynamics and projection geometry are presented providing a rational basis for specifying system parameters this investigation includes estimation of ejection fraction from both simulated and real data

multilevel algorithm for obtaining the proper orthogonal decomposition a multilevel proper orthogonal decomposition mpod is introduced for obtaining the proper orthogonal decomposition pod of data sets with a large number of snapshots without requiring the solutio

a semi implicit augmented iim for navier stokes equations with open traction or free boundary conditions in this paper a new navier stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open traction and free boundary conditions which can be applied to simulations of fluid structure interaction implicit solvent model for biomolecular applications and other free boundary or interface problems for some problems of this type the projection method and the augmented immersed interface method iim do not work well or does not work at all the proposed new navier stokes solver is based on the local pressure boundary method and a semi implicit augmented iim a fast poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future the time discretization is based on a second order multi step method numerical tests with exact solutions are presented to validate the accuracy of the method application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented

a computational study of reconstruction algorithms for diffraction tomography interpolation versus filtered backpropagation from the standpoint of reporting a new contribution this paper shows that by using bilinear interpolation followed by direct two dimensional fourier inversion one can obtain reconstructions of quality which is comparable to that produced by the filtered backpropagation algorithm proposed recently by devaney for an n n image reconstructed from n diffracted projections the former approach requires approximately 4n fft s whereas the backpropagation technique requires approximately n2fft s we have also taken this opportunity to present the reader with a tutorial introduction to diffraction tomography an area that is becoming increasingly important not only in medical imaging but also in underwater and seismic mapping with microwaves and sound the main feature of the tutorial part is the statement of the fourier diffraction projection theorem which is an extension of the traditional fourier slice theorem to the case of image formation with diffracting illumination

detection of edges from projections in a number of applications of computerized tomography the ultimate goal is to detect and characterize objects within a cross section detection of edges of different contrast regions yields the required information the problem of detecting edges from projection data is addressed it is shown that the class of linear edge detection operators used on images can be used for detection of edges directly from projection data this not only reduces the computational burden but also avoids the difficulties of postprocessing a reconstructed image this is accomplished by a convolution backprojection operation for example with the marr hildreth edge detection operator the filtering function that is to be used on the projection data is the radon transform of the laplacian of the 2 d gaussian function which is combined with the reconstruction filter simulation results showing the efficacy of the proposed method and a comparison with edges detected from the reconstructed image are presented

direct fourier reconstruction in computer tomography direct fourier transform ft reconstruction of images in computerized tomography ct is not widely used because of the difficulty of precisely interpolating from polar to cartesian samples in this paper an exact interpolation scheme is proposed which in practice can be approached with arbitrary accuracy using well conditioned algorithms several features of the direct ft method are discussed a method that allows angular band limiting of the data before processing to avoid angular aliasing artifacts in the reconstructed image is discussed and experimentally verified the experimental results demonstrate the feasibility of direct ft reconstruction of ct data

maximum likelihood estimation of object location in diffraction tomography the problem is formulated within the context of diffraction tomography where the complex phase of the diffracted wavefield is modeled using the rytov approximation and the measurements consist of noisy renditions of this complex phase at a single frequency the log likelihood function is computed for the case of additive zero mean gaussian white noise and shown to be expressible in the form of the filtered backpropagation algorithm of diffraction tomography in this form however the filter function is no longer the rho filter appropriate to least square reconstruction but is now the generalized projection propagation of the object centered at the origin onto the line s parallel to the measurement line s but passing through the origin this result allows the estimation problem to be solved via a diffraction tomographic imaging procedure where the noisy data is filtered and backpropagated in a first step and the point of maximum value of the resulting image is then the maximum likelihood ml estimate of the object s location the authors include a calculation of the cramer rao bound for the estimation error and a computer simulation study illustrating the estimation procedure

on the fukaya categories of higher genus surfaces abstract we construct the fukaya category of a closed surface equipped with an area form using only elementary essentially combinatorial methods we also compute the grothendieck group of its derived category

nonparametric fixed interval smoothing of nonlinear vector valued measurements the problem of estimating a smooth vector valued function given noisy nonlinear vector valued measurements of that function is addressed a nonparametric optimality criterion for this estimation problem is presented and a computationally efficient iterative algorithm for its solution is developed the criterion is the natural generalization of previously published work on vector splines with linear measurement models the algorithm provides an alternative to the extended kalman filter as it does not require a parametric state space model an automatic procedure that uses the measurements to determine how much to smooth is presented the algorithm s subpixel estimation accuracy is demonstrated on the estimation of a curved edge in a noisy image and on a biomedical image processing application

analysis of a streamline diffusion finite element method for the stokes and navier stokes equations for the stokes equations with convection and the incompressible navier stokes equations the authors analyze a streamline diffusion finite element method that is capable of balancing both the convection and the pressure thus allowing the use of arbitrary pairs of velocity pressure spaces for the linear problem the authors obtain for all mesh peclet numbers optimal error estimates in natural norms including in particular the l 2 norm of the pressure the same holds for the nonlinear problem which close to a regular branch of solutions i e the linearized operator is an isomorphism of the norm of the inverse of which still depends on the reynolds number consequently the dependence of the error constants on the reynolds number is not completely resolved in this case

application of p multigrid to discontinuous galerkin formulations of the poisson equation we investigate p multigrid as a solution method for several different discontinuous galerkin dg formulations of the poisson equation different combinations of relaxation schemes and basis sets have been combined with the dg formulations to find the best performing combination the damping factors of the schemes have been determined using fourier analysis for both one and two dimensional problems one important finding is that when using dg formulations the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable to ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques of the relaxation schemes we find that the combination of jacobi relaxation with the spectral element basis is fairly effective the results using this combination are p sensitive in both one and two dimensions but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes a competitive alternative is a block gauss seidel relaxation this actually out performs a more expensive line relaxation when the mesh is isotropic when the mesh becomes highly anisotropic the implicit line method and the gauss seidel implicit line method are the only effective schemes adding the gauss seidel terms to the implicit line method gives a significant improvement over the line relaxation method

classical yang baxter equation and the a constraint abstract we show that elliptic solutions of classical yang baxter equation cybe can be obtained from triple massey products on an elliptic curve we introduce the associative version of this equation which has two spectral parameters and construct its elliptic solutions we also study some degenerations of these solutions

preconditioning for incompressible flows with free surfaces and two fluid interfaces we investigate preconditioners for solving steady or implicit unsteady arbitrary lagrangian eulerian moving mesh formulations of incompressible free surface and interfacial flow problems the solution for the flow is obtained using the artificial compressibility method combined with a multigrid cycle to find the surface positions in a free surface problem we use an iteration that is quasi physical with the position of the free surface driven by the kinematic condition by modifying the fluxes through the free surface and also using an iterative free surface time step that is different from the flow time step we are able to obtain convergence rates that are almost indistinguishable from those of a flow without a free surface this is true in the limits of both large and small surface stresses such as gravity or surface tension and also for all flow conditions high or low reynolds number or small implicit courant friedrichs lewy number for interfacial flows the free surface preconditioner is extended by using a mass averaging technique the iterative flow time step at the interface is a mass average of the time step for the flow conditions on either side of the interface and the iterative time step for the kinematic condition is also based on mass average quantities we verify that this technique produces the correct results in the limits of identical fluids or a free surface flow we also verify that it produces well conditioned results when the characteristic time scales of the two fluids are very different

two filter formulae for discrete time non linear bayesian smoothing two filler formulae for the bayes solution of the fixed interval discrete time nonlinear smoothing problem are obtained the smoothed a posteriori density is computed under the assumptions of a general markov signal observed through a general memoryless noisy channel the case where there is feedback from the observation to the signal is also considered the derived algorithms complement a two pass algorithm obtained under somewhat more restrictive assumptions by askar and derin 1981 known smoothing results for the linear gaussian case are interpreted in the light of the general bayesian results

a bayesian approach to reconstruction from incomplete projections of a multiple object 3d domain an estimation approach is described for three dimensional reconstruction from line integral projections using incomplete and very noisy data generalized cylinders parameterized by stochastic dynamic models are used to represent prior knowledge about the properties of objects of interest in the probed domain the object models a statistical measurement model and the maximum a posteriori probability performance criterion are combined to reformulate the reconstruction problem as a computationally challenging nonlinear estimation problem for computational feasibility a suboptimal hierarchical algorithm is described whose individual steps are locally optimal and are combined to satisfy a global optimality criterion the formulation and algorithm are restricted to objects whose center axis is a single valued function of a fixed spatial coordinate simulation examples demonstrate accurate reconstructions with as few as four views in a 135 degrees sector at an average signal to noise ratio of 3 3