optimization algorithms on subspaces revisiting missing data problem in low rank matrix low rank matrix approximation has applications in many fields such as 3d reconstruction from an image sequence and 2d filter design in this paper one issue with low rank matrix approximation is re investigated the missing data problem much effort was devoted to this problem and the wiberg algorithm or the damped newton algorithm were recommended in previous studies however the wiberg or damped newton algorithms do not suit for large especially long matrices because one needs to solve a large linear system in every iteration in this paper we revitalize the usage of the levenberg marquardt algorithm for solving the missing data problem by utilizing the property that low rank approximation is a minimization problem on subspaces in two proposed implementations of the levenberg marquardt algorithm one only needs to solve a much smaller linear system in every iteration especially for long matrices simulations and experiments on real data show the superiority of the proposed algorithms though the proposed algorithms achieve a high success rate in estimating the optimal solution by random initialization as illustrated by real examples it still remains an open issue how to properly do the initialization in a severe situation that is a large amount of data is missing and with high level noise

heteroscedastic low rank matrix approximation by the wiberg algorithm low rank matrix approximation has applications in many fields such as 2 d filter design and 3 d reconstruction from an image sequence in this paper one issue with low rank matrix approximation is investigated heteroscedastic noise in most of previous research the covariance matrix of the heteroscedastic noise is assumed to be positive definite this requirement restricts the usefulness of results derived from such research in this paper we extend the wiberg algorithm which originally deals with the missing data problem with low rank approximation to the cases where the heteroscedastic noise has a singular covariance matrix experiments show that the proposed wiberg algorithm converges much faster than the bilinear approach and consequently avoids many nonconvergent cases in the bilinear approach experiments also show that to some extent the wiberg algorithm can tolerate outliers and is not sensitive to parameter variation

l_ 1 norm low rank matrix decomposition by neural networks and mollifiers the l 1 norm cost function of the low rank approximation of the matrix with missing entries is not smooth and also cannot be transformed into a standard linear or quadratic programming problem and thus the optimization of this cost function is still not well solved to tackle this problem first a mollifier is used to smooth the cost function high closeness of the smoothed function to the original one can be obtained by tuning the parameters contained in the mollifier next a recurrent neural network is proposed to optimize the mollified function which will converge to a local minimum in addition to boost the speed of the system the mollifying process is implemented by a filtering procedure the influence of two mollifier parameters is theoretically analyzed and experimentally confirmed showing that one of the parameters is critical to computational efficiency and accuracy while the other not a large number of experiments on synthetic data show that the proposed method is competitive to the state of the art methods in particular the experiments on large matrices and a real application in the structure from motion indicate that the memory requirement of the proposed algorithm is mild making it suitable for real applications that often involve large scale matrix decomposition

a paraperspective factorization method for shape and motion recovery the factorization method first developed by tomasi and kanade 1992 recovers both the shape of an object and its motion from a sequence of images using many images and tracking many feature points to obtain highly redundant feature position information the method robustly processes the feature trajectory information using singular value decomposition svd taking advantage of the linear algebraic properties of orthographic projection however an orthographic formulation limits the range of motions the method can accommodate paraperspective projection first introduced by ohta et al 1981 is a projection model that closely approximates perspective projection by modeling several effects not modeled under orthographic projection while retaining linear algebraic properties our paraperspective factorization method can be applied to a much wider range of motion scenarios including image sequences containing motion toward the camera and aerial image sequences of terrain taken from a low altitude airplane

rank 1 weighted factorization for 3d structure recovery algorithms and performance analysis the paper describes the rank 1 weighted factorization solution to the structure from motion problem this method recovers the 3d structure from the factorization of a data matrix that is rank 1 rather than rank 3 this matrix collects the estimates of the 2d motions of a set of feature points of the rigid object these estimates are weighted by the inverse of the estimates error standard deviation so that the 2d motion estimates for sharper features which are usually well estimated are given more weight while the noisier motion estimates for smoother features are weighted less we analyze the performance of the rank 1 weighted factorization algorithm to determine what are the most suitable 3d shapes or the best 3d motions to recover the 3d structure of a rigid object from the 2d motions of the features our approach is developed for the orthographic camera model it avoids expensive singular value decompositions by using the power method and is suitable to handle dense sets of feature points and long video sequences experimental studies with synthetic and real data illustrate the good performance of our approach

reduction of nonlinear embedded boundary models for problems with evolving interfaces embedded boundary methods alleviate many computational challenges including those associated with meshing complex geometries and solving problems with evolving domains and interfaces developing model reduction methods for computational frameworks based on such methods seems however to be challenging indeed most popular model reduction techniques are projection based and rely on basis functions obtained from the compression of simulation snapshots in a traditional interface fitted computational framework the computation of such basis functions is straightforward primarily because the computational domain does not contain in this case a fictitious region this is not the case however for an embedded computational framework because the computational domain typically contains in this case both real and ghost regions whose definitions complicate the collection and compression of simulation snapshots the problem is exacerbated when the interface separating both regions evolves in time this paper addresses this issue by formulating the snapshot compression problem as a weighted low rank approximation problem where the binary weighting identifies the evolving component of the individual simulation snapshots the proposed approach is application independent and therefore comprehensive it is successfully demonstrated for the model reduction of several two dimensional vortex dominated fluid structure interaction problems

the arctic circle boundary and the airy process we prove that the appropriately rescaled boundary of the north polar region in the aztec diamond converges to the airy process the proof uses certain determinantal point processes given by the extended krawtchouk kernel we also prove a version of propp s conjecture concerning the structure of the tiling at the center of the aztec diamond 1 introduction and results domino tilings of the aztec diamond were introduced in 8 9 asymptotic properties of random domino tilings of the aztec diamond have been studied in 5 12 15 in particular in 12 the existence of the so called arctic circle was proved the arctic circle is the asymptotic boundary of the disordered so called temperate region of the tiling outside this boundary the tiling forms a completely regular brick wall pattern the methods in 12 combined with the results in 13 show that the fluctuations of the point of intersection of the boundary of the temperate region with a line converge to the tracy widom distribution of random matrix theory in this paper we extend this result to show that the fluctuations of the boundary around the arctic circle converges to the airy process introduced in 23 the paper is a continuation of the approach used in 14 and 15 where certain point processes with determinantal correlation functions 24 and the krawtchouk ensemble were used we will use the general techniques developed in 16 and investigate an extended point process which also has determinantal correlation functions given by a kernel which we call the extended krawtchouk kernel the aztec diamond an of order n is the union of all lattice squares m m 1 l l 1 m l 2 z that lie inside the region x1 y1 x1 y1

improved incompressible smoothed particle hydrodynamics method for simulating flow around bluff bodies in this article we present numerical solutions for flow over an airfoil and a square obstacle using incompressible smoothed particle hydrodynamics isph method with an improved solid boundary treatment approach referred to as the multiple boundary tangents mbt method it was shown that the mbt boundary treatment technique is very effective for tackling boundaries of complex shapes also we have proposed the usage of the repulsive component of the lennard jones potential ljp in the advection equation to repair particle fractures occurring in the sph method due to the tendency of sph particles to follow the stream line trajectory this approach is named as the artificial particle displacement method numerical results suggest that the improved isph method which is consisting of the mbt method artificial particle displacement and the corrective sph discretization scheme enables one to obtain very stable and robust sph simulations the square obstacle and naca airfoil geometry with the angle of attacks between 0 and 15 were simulated in a laminar flow field with relatively high reynolds numbers we illustrated that the improved isph method is able to capture the complex physics of bluff body flows naturally such as the flow separation wake formation at the trailing edge and the vortex shedding the sph results are validated with a mesh dependent finite element method fem and excellent agreements among the results were observed

an arbitrary boundary with ghost particles incorporated in coupled fem sph model for fsi problems abstract it is important to treat the arbitrary boundary of fluid structure interaction fsi problems in computational mechanics in order to ensure complete support condition and restore the first order consistency near the boundary of smoothed particle hydrodynamics sph method for coupling finite element method fem with sph model a new ghost particle method is proposed by dividing the interceptive area of kernel support domain into subareas corresponding to boundary segments of structure the ghost particles are produced automatically for every fluid particle at each time step and the properties of ghost particles such as density mass and velocity are defined by using the subareas to satisfy the boundary condition in the coupled fem sph model the normal and shear forces from a boundary segment of structure to a fluid particle are calculated through the corresponding ghost particles and its opposite forces are exerted on the corresponding boundary segment then the momentum of the present method is conservation and there is no matching requirements between the size of elements and the size of particles the performance of the present method is discussed and validated by several fsi problems with complex geometry boundary and moving boundary

accuracy and stability in incompressible sph isph based on the projection method and a new approach the stability and accuracy of three methods which enforce either a divergence free velocity field density invariance or their combination are tested here through the standard taylor green and spin down vortex problems while various approaches to incompressible sph isph have been proposed in the past decade the present paper is restricted to the projection method for the pressure and velocity coupling it is shown that the divergence free isph method cannot maintain stability in certain situations although it is accurate before instability sets in the density invariant isph method is stable but inaccurate with random noise like disturbances the combined isph combining advantages in divergence free isph and density invariant isph can maintain accuracy and stability although at a higher computational cost redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh free method is lost a new divergence free isph approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative this avoids the highly anisotropic particle spacing which eventually triggers instability importantly pressure fields are free from spurious oscillations up to the highest reynolds numbers tested

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

quasi perspective projection model theory and application to structure and motion factorization from uncalibrated image sequences this paper addresses the problem of factorization based 3d reconstruction from uncalibrated image sequences previous studies on structure and motion factorization are either based on simplified affine assumption or general perspective projection the affine approximation is widely adopted due to its simplicity whereas the extension to perspective model suffers from recovering projective depths to fill the gap between simplicity of affine and accuracy of perspective model we propose a quasi perspective projection model for structure and motion recovery of rigid and nonrigid objects based on factorization framework the novelty and contribution of this paper are as follows firstly under the assumption that the camera is far away from the object with small lateral rotations we prove that the imaging process can be modeled by quasi perspective projection which is more accurate than affine model from both geometrical error analysis and experimental studies secondly we apply the model to establish a framework of rigid and nonrigid factorization under quasi perspective assumption finally we propose an extended cholesky decomposition to recover the rotation part of the euclidean upgrading matrix we also prove that the last column of the upgrading matrix corresponds to a global scale and translation of the camera thus may be set freely the proposed method is validated and evaluated extensively on synthetic and real image sequences and improved results over existing schemes are observed

factorization with uncertainty factorization using singular value decomposition svd is often used for recovering 3d shape and motion from feature correspondences across multiple views svd is powerful at finding the global solution to the associated least square error minimization problem however this is the correct error to minimize only when the x and y positional errors in the features are uncorrelated and identically distributed but this is rarely the case in real data uncertainty in feature position depends on the underlying spatial intensity structure in the image which has strong directionality to it hence the proper measure to minimize is covariance weighted squared error or the mahalanobis distance in this paper we describe a new approach to covariance weighted factorization which can factor noisy feature correspondences with high degree of directional uncertainty into structure and motion our approach is based on transforming the raw data into a covariance weighted data space where the components of noise in the different directions are uncorrelated and identically distributed applying svd to the transformed data now minimizes a meaningful objective function in this new data space this is followed by a linear but suboptimal second step to recover the shape and motion in the original data space we empirically show that our algorithm gives very good results for varying degrees of directional uncertainty in particular we show that unlike other svd based factorization algorithms our method does not degrade with increase in directionality of uncertainty even in the extreme when only normal flow data is available it thus provides a unified approach for treating corner like points together with points along linear structures in the image

the pearcey process the extended airy kernel describes the space time correlation functions for the airy process which is the limiting process for a polynuclear growth model the airy functions themselves are given by integrals in which the exponents have a cubic singularity arising from the coalescence of two saddle points in an asymptotic analysis pearcey functions are given by integrals in which the exponents have a quartic singularity arising from the coalescence of three saddle points a corresponding pearcey kernel appears in a random matrix model and a brownian motion model for a fixed time this paper derives an extended pearcey kernel by scaling the brownian motion model at several times and a system of partial differential equations whose solution determines associated distribution functions we expect there to be a limiting nonstationary process consisting of infinitely many paths which we call the pearcey process whose space time correlation functions are expressible in terms of this extended kernel

variational and momentum preservation aspects of smooth particle hydrodynamic formulations this paper presents a new variational framework for various existing smooth particle hydrodynamic sph techniques and presents a new corrected sph formulation the linear and angular momentum preserving properties of sph formulations are also discussed the paper will show that in general in order to preserve angular momentum the sph equations must correctly evaluate the gradient of a linear velocity field a corrected algorithm that combines kernel correction with gradient correction is presented the paper will illustrate the theory presented with several examples relating to simple free surface flows

the geometry of weighted low rank approximations the low rank approximation problem is to approximate optimally with respect to some norm a matrix by one of the same dimension but smaller rank it is known that under the frobenius norm the best low rank approximation can be found by using the singular value decomposition svd although this is no longer true under weighted norms in general it is demonstrated here that the weighted low rank approximation problem can be solved by finding the subspace that minimizes a particular cost function a number of advantages of this parameterization over the traditional parameterization are elucidated finding the minimizing subspace is equivalent to minimizing a cost function on the grassmann manifold a general framework for constructing optimization algorithms on manifolds is presented and it is shown that existing algorithms in the literature are special cases of this framework within this framework two novel algorithms a steepest descent algorithm and a newton like algorithm are derived for solving the weighted low rank approximation problem they are compared with other algorithms for low rank approximation as well as with other algorithms for minimizing a cost function on a grassmann manifold

experimental studies of separation on a two dimensional airfoil at low reynolds numbers the laminar separation transition and turbulent reattachment near the leading edge of a two dimensional naca 663 018 airfoil were investigated using a low speed smoke visualization wind tunnel lift and drag force measurements were made using an external strain gage balance for a chord reynolds number range of 40 goo400 000 an extensive flow visualization study was performed and correlated with the force measurements experiments were also conducted with distributed surface roughness at the leading edge and external acoustic excitation to influence the development of the airfoil boundary layer this study delineates the effects of angle of attack and chord reynolds number on the separation characteristics and airfoil performance nomenclature c model chord cd section profile drag coefficient uncorrected cf section lift coefficient uncorrected cp pressure coefficient acoustic frequency hz r reattachment location rc reynolds number based on chord length u civ s separation location t location of approximate end of transition freestream velocity x c nondimensional distance along chord a angle of attack v kinematic viscosity

random skew plane partitions and the pearcey process we study random skew 3d partitions weighted by qvol and specifically the q 1 asymptotics of local correlations near various points of the limit shape we obtain sine kernel asymptotics for correlations in the bulk of the disordered region airy kernel asymptotics near a general point of the frozen boundary and a pearcey kernel asymptotics near a cusp of the frozen boundary

variable resolution for sph a dynamic particle coalescing and splitting scheme abstract in this paper a novel variable resolution method using particle splitting and coalescing for the sph numerical solution of the navier stokes equations is presented the key idea of the scheme is to modify dynamically the particle sizes by means of splitting and coalescing merging individual particles to provide good resolution only where it is needed the sph scheme adopted is derived using the variational principle guaranteeing that both mass and momentum are conserved for particles with different smoothing lengths a particle shifting procedure is used to prevent unacceptable anisotropic distributions of the particles and is further generalized for treating domains with variable mass particles the algorithm has been tested against analytical solutions for poiseuille and taylor green flows showing that the shifting algorithm is effective in increasing the accuracy and that error introduced by the splitting and coalescing is negligible the capability of the numerical scheme for increasing efficiency is shown for more general problems the simulations of a moving square in a box and flow past a cylinder have shown that the particle refinement procedure is able to increase the efficiency while maintaining the same level of accuracy as a uniform distribution with the most refined resolution

on the wiberg algorithm for matrix factorization in the presence of missing components this paper considers the problem of factorizing a matrix with missing components into a product of two smaller matrices also known as principal component analysis with missing data pcamd the wiberg algorithm is a numerical algorithm developed for the problem in the community of applied mathematics we argue that the algorithm has not been correctly understood in the computer vision community although there are many studies in our community almost every one of which refers to the wiberg study as far as we know there is no literature in which the performance of the wiberg algorithm is investigated or the detail of the algorithm is presented in this paper we present derivation of the algorithm along with a problem in its implementation that needs to be carefully considered and then examine its performance the experimental results demonstrate that the wiberg algorithm shows a considerably good performance which should contradict the conventional view in our community namely that minimization based algorithms tend to fail to converge to a global minimum relatively frequently the performance of the wiberg algorithm is such that even starting with random initial values it converges in most cases to a correct solution even when the matrix has many missing components and the data are contaminated with very strong noise our conclusion is that the wiberg algorithm can also be used as a standard algorithm for the problems of computer vision

mixed enrichment for the finite element method in heterogeneous media summary problems of multiple scales of interest or of locally nonsmooth solutions may often involve heterogeneous media these problems are usually very demanding in terms of computations with the conventional finite element method on the other hand different enriched finite element methods such as the partition of unity which proved to be very successful in treating similar problems are developed and studied for homogeneous media in this work we present a new idea to extend the partition of unity finite element method to treat heterogeneous materials the idea is studied in applications to wave scattering and heat transfer problems where significant advantages are noted over the standard finite element method although presented within the partition of unity context the same enrichment idea can also be extended to other enriched methods to deal with heterogeneous materials copyright 2014 john wiley sons ltd

optimal reduced rank estimation and filtering this paper provides a unified view of and a further insight into a class of optimal reduced rank estimators and filters an alternating power ap method for computing the optimal reduced rank estimators and filters is derived and analyzed the ap method is a generalization of the conventional power method for subspace computation which is shown to be globally and exponentially convergent under weak conditions when the rank reduction is relatively large the ap method is computationally more efficient than the conventional methods the ap method is useful for adaptive computation of the canonical components of a desired reduced rank estimate which in turn facilitates the detection of a time varying rank the study shown in this paper is particularly useful for applications that involve a large number of sources and a large number of receivers where rank reduction is either inherent in the multivariate system or required to reduce the model complexity and or the computational load

recovering the missing components in a large noisy low rank matrix application to sfm in computer vision it is common to require operations on matrices with missing data for example because of occlusion or tracking failures in the structure from motion sfm problem such a problem can be tackled allowing the recovery of the missing values if the matrix should be of low rank when noise free the filling in of missing values is known as imputation imputation can also be applied in the various subspace techniques for face and shape classification online recommender systems and a wide variety of other applications however iterative imputation can lead to the recovery of data that is seriously in error in this paper we provide a method to recover the most reliable imputation in terms of deciding when the inclusion of extra rows or columns containing significant numbers of missing entries is likely to lead to poor recovery of the missing parts although the proposed approach can be equally applied to a wide range of imputation methods this paper addresses only the sfm problem the performance of the proposed method is compared with jacobs and shum s methods for sfm

principal component analysis with missing data and its application to polyhedral object modeling observation based object modeling often requires integration of shape descriptions from different views to overcome the problems of errors and their accumulation we have developed a weighted least squares wls approach which simultaneously recovers object shape and transformation among different views without recovering interframe motion we show that object modeling from a range image sequence is a problem of principal component analysis with missing data pcamd which can be generalized as a wls minimization problem an efficient algorithm is devised after we have segmented planar surface regions in each view and tracked them over the image sequence we construct a normal measurement matrix of surface normals and a distance measurement matrix of normal distances to the origin for all visible regions over the whole sequence of views respectively these two matrices which have many missing elements due to noise occlusion and mismatching enable us to formulate multiple view merging as a combination of two wls problems a two step algorithm is presented after surface equations are extracted spatial connectivity among the surfaces is established to enable the polyhedral object model to be constructed experiments using synthetic data and real range images show that our approach is robust against noise and mismatching and generates accurate polyhedral object models

an incompressible multi phase sph method an incompressible multi phase sph method is proposed in this method a fractional time step method is introduced to enforce both the zero density variation condition and the velocity divergence free condition at each full time step to obtain sharp density and viscosity discontinuities in an incompressible multi phase flow a new multi phase projection formulation in which the discretized gradient and divergence operators do not require a differentiable density or viscosity field is proposed numerical examples for taylor green flow capillary waves drop deformation in shear flows and for rayleigh taylor instability are presented and compared to theoretical solutions or references from literature the results suggest good accuracy and convergence properties of the proposed method

discrete polynuclear growth and determinantal processes we consider a discrete polynuclear growth png process and prove a functional limit theorem for its convergence to the airy process this generalizes previous results by prahofer and spohn the result enables us to express the f1 goe tracy widom distribution in terms of the airy process we also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem furthermore we discuss a rather general class of measures given by products of determinants and show that these measures have determinantal correlation functions

computing smooth time trajectories for camera and deformable shape in structure from motion with occlusion we address the classical computer vision problems of rigid and nonrigid structure from motion sfm with occlusion we assume that the columns of the input observation matrix w describe smooth 2d point trajectories over time we then derive a family of efficient methods that estimate the column space of w using compact parameterizations in the discrete cosine transform dct domain our methods tolerate high percentages of missing data and incorporate new models for the smooth time trajectories of 2d points affine and weak perspective cameras and 3d deformable shape we solve a rigid sfm problem by estimating the smooth time trajectory of a single camera moving around the structure of interest by considering a weak perspective camera model from the outset we directly compute euclidean 3d shape reconstructions without requiring postprocessing steps such as euclidean upgrade and bundle adjustment our results on real sfm data sets with high percentages of missing data compared positively to those in the literature in nonrigid sfm we propose a novel 3d shape trajectory approach that solves for the deformable structure as the smooth time trajectory of a single point in a linear shape space a key result shows that compared to state of the art algorithms our nonrigid sfm method can better model complex articulated deformation with higher frequency dct components while still maintaining the low rank factorization constraint finally we also offer an approach for nonrigid sfm when w is presented with missing data

compact moving least squares an optimization framework for generating high order compact meshless discretizations abstract a generalization of the optimization framework typically used in moving least squares is presented that provides high order approximation while maintaining compact stencils and a consistent treatment of boundaries the approach which we refer to as compact moving least squares resembles the capabilities of compact finite differences but requires no structure in the underlying set of nodes an efficient collocation scheme is used to demonstrate the capabilities of the method to solve elliptic boundary value problems in strong form stably without the need for an expensive weak form the flexibility of the approach is demonstrated by using the same framework to both solve a variety of elliptic problems and to generate implicit approximations to derivatives finally an efficient preconditioner is presented for the steady stokes equations and the approach s efficiency and high order of accuracy is demonstrated for domains with curvi linear boundaries

riemann hilbert approach to multi time processes the airy and the pearcey cases we prove that matrix fredholm determinants related to multi time processes can be expressed in terms of determinants of integrable kernels a la its izergin korepin slavnov iiks and hence related to suitable riemann hilbert problems thus extending the known results for the single time case we focus on the airy and pearcey processes as an example of applications we re deduce a third order pde found by adler and van moerbeke for the two time airy process

practical matrix completion and corruption recovery using proximal alternating robust subspace minimization low rank matrix completion is a problem of immense practical importance recent works on the subject often use nuclear norm as a convex surrogate of the rank function despite its solid theoretical foundation the convex version of the problem often fails to work satisfactorily in real life applications real data often suffer from very few observations with support not meeting the randomness requirements ubiquitous presence of noise and potentially gross corruptions sometimes with these simultaneously occurring this paper proposes a proximal alternating robust subspace minimization method to tackle the three problems the proximal alternating scheme explicitly exploits the rank constraint on the completed matrix and uses the ell 0 l 0 pseudo norm directly in the corruption recovery step we show that the proposed method for the non convex and non smooth model converges to a stationary point although it is not guaranteed to find the global optimal solution in practice we find that our algorithm can typically arrive at a good local minimizer when it is supplied with a reasonably good starting point based on convex optimization extensive experiments with challenging synthetic and real data demonstrate that our algorithm succeeds in a much larger range of practical problems where convex optimization fails and it also outperforms various state of the art algorithms

sph with the multiple boundary tangent method in this article we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics sph method benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries as well current sph boundary approaches do not properly treat curved boundaries in complicated flow domains these drawbacks have been remedied in a new boundary treatment method presented in this article called the multiple boundary tangent mbt approach in this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions the two benchmark problems chosen are the lid driven cavity problem and flow over a cylinder the sph solutions using the mbt approach and the results from literature are in very good agreement these solutions involved solid boundaries but the approach presented herein should be extendable to time evolving free surface boundaries copyright 2008 john wiley sons ltd

affine structure and motion from points lines and conics in this paper several new methods for estimating scene structure and camera motion from an image sequence taken by affine cameras are presented all methods can incorporate both point line and conic features in a unified manner the correspondence between features in different images is assumed to be known three new tensor representations are introduced describing the viewing geometry for two and three cameras the centred affine epipoles can be used to constrain the location of corresponding points and conics in two images the third order or alternatively the reduced third order centred affine tensors can be used to constrain the locations of corresponding points lines and conics in three images the reduced third order tensors contain only 12 components compared to the 16 components obtained when reducing the trifocal tensor to affine cameras a new factorization method is presented the novelty lies in the ability to handle not only point features but also line and conic features concurrently another complementary method based on the so called closure constraints is also presented the advantage of this method is the ability to handle missing data in a simple and uniform manner finally experiments performed on both simulated and real data are given including a comparison with other methods

level spacing of random matrices in an external source in an earlier work we had considered a gaussian ensemble of random matrices in the presence of a given external matrix source the measure is no longer unitary invariant and the usual techniques based on orthogonal polynomials or on the coulomb gas representation are not available nevertheless the n point correlation functions are still given in terms of the determinant of a kernel known through an explicit integral representation this kernel is no longer symmetric though and is not readily accessible to standard methods in particular finding the level spacing probability is always a delicate problem in fredholm theory and we have to reconsider the problem within our model we find a new class of universality for the level spacing distribution when the spectrum of the source is ajusted to produce a vanishing gap in the density of the state the problem is solved through coupled non linear differential equations which turn out to form a hamiltonian system as a result we find that the level spacing probability p s behaves like exp c s 8 over 3 for large spacing s this is consistent with the asymptotic behavior exp c s 2 beta 2 whenever the density of state behaves near the edge as rho lambda sim lambda beta

comparisons of weakly compressible and truly incompressible algorithms for the sph mesh free particle method in the smoothed particle hydrodynamics sph discretisation method for the navier stokes equations the most widespread method to solve for pressure and mass conservation is the weakly compressible assumption wcsph this includes hydraulics applications and leads to some drawbacks such as severe artificial pressure fluctuations and a limitation to very small time steps related to the wcsph mach number and explicit method this paper presents comparisons of a semi implicit and truly incompressible sph isph algorithm with the classical wcsph method showing how some of the problems encountered in wcsph have been resolved by using isph to simulate incompressible flows mathematical models are presented before describing sph formalism several standard boundary conditions are introduced and special attention is given to tracking the surface particles the lid driven cavity flow re 400 and 1000 is performed as a benchmarking test a bluff body test case a square cylinder in a closed channel re d 20 and 100 based on the cylinder diameter shows that pressure fields extracted from wcsph are very unreliable whereas isph predict pressures and forces in closer agreement with classical finite volume cfd methods dam breaking cases with dry or wet beds downstream are then presented to highlight free surface flow and rapid dynamics effects the wcsph and isph results are generally verified with reference data from experiment and or another numerical method all the comparisons show improvement with isph and good agreement in general

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

bilinear modeling via augmented lagrange multipliers balm this paper presents a unified approach to solve different bilinear factorization problems in computer vision in the presence of missing data in the measurements the problem is formulated as a constrained optimization where one of the factors must lie on a specific manifold to achieve this we introduce an equivalent reformulation of the bilinear factorization problem that decouples the core bilinear aspect from the manifold specificity we then tackle the resulting constrained optimization problem via augmented lagrange multipliers the strength and the novelty of our approach is that this framework can seamlessly handle different computer vision problems the algorithm is such that only a projector onto the manifold constraint is needed we present experiments and results for some popular factorization problems in computer vision such as rigid non rigid and articulated structure from motion photometric stereo and 2d 3d non rigid registration

a partitioned fully explicit lagrangian finite element method for highly nonlinear fluid structure interaction problems summary in this work a fully explicit partitioned method for the simulation of fluid structure interaction fsi problems is presented the fluid domain is modelled with an explicit particle finite element method pfem based on the hypothesis of weak compressibility the lagrangian description of the fluid is particularly effective in the simulation of fsi problems with free surface flows and large structural displacements since the fluid boundaries are automatically defined by the position of the mesh nodes a distinctive feature of the proposed fsi strategy is that the solid domain is modelled using the explicit integration finite element method fem in a off the shelf commercial software abaqus explicit this allows to perform simulations with a complete and advanced description on the structural domain including advanced structural material models and contact the structure to fluid coupling algorithm is based on a technique derived from the domain decomposition methods namely the gravouil and combescure gc algorithm the method allows for arbitrarily large interface displacements using different time incrementation and non conforming meshes in the different domains which is an essential feature for the efficiency of an explicit solver involving different materials the resulting fully explicit and fully lagrangian finite element approach is particularly appealing for the possibility of its efficient application in a large variety of highly nonlinear engineering problems this article is protected by copyright all rights reserved

a robust weakly compressible sph method and its comparison with an incompressible sph summary this paper presents a comparative study for the weakly compressible wcsph and incompressible isph smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle improved wcsph and isph techniques are used to solve these two bluff body flow problems it is shown that both approaches can handle complex geometries using the multiple boundary tangents mbt method and eliminate particle clustering induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected sph discretization scheme wcsph and isph simulation results are compared and validated with those of a finite element method fem the quantitative comparisons of wcsph isph and fem results in terms of strouhal number for the square obstacle test case and the pressure envelope surface traction forces and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the wcsph method with the suggested implementation produces numerical results as accurate and reliable as those of the isph and fem methods copyright 2011 john wiley sons ltd

differential equations for dyson processes we call a dyson process any process on ensembles of matrices in which the entries undergo diffusion we are interested in the distribution of the eigenvalues or singular values of such matrices in the original dyson process it was the ensemble of n n hermitian matrices and the eigenvalues describe n curves given sets x1 xm the probability that for each k no curve passes through xk at time k is given by the fredholm determinant of a certain matrix kernel the extended hermite kernel for this reason we call this dyson process the hermite process similarly when the entries of a complex matrix undergo diffusion we call the evolution of its singular values the laguerre process for which there is a corresponding extended laguerre kernel scaling the hermite process at the edge leads to the airy process which was introduced by prahofer and spohn as the limiting stationary process for a polynuclear growth model and in the bulk to the sine process scaling the laguerre process at the edge leads to the bessel process

numerical investigation of newtonian and non newtonian multiphase flows using isph method we have presented a multiphase incompressible smoothed particle hydrodynamics method with an improved interface treatment procedure to demonstrate the effectiveness of the interface treatment which can handle multiphase flow problems with high density and viscosity ratios we have modeled several challenging two phase flow problems namely single vortex flow square droplet deformation droplet deformation in shear flow and finally the newtonian bubble rising in viscous and viscoelastic liquids the proposed interface treatment includes the usage of i different smoothing functions in this work cubic spline kernel function for discretizing equations associated with the calculation of the surface tension force while the quintic spline for the discretization of governing equations and the relevant boundary conditions and ii a new discretization scheme for calculating the pressure gradient it is shown that with the application of the improved interface treatment it becomes possible to model multiphase flow problems with the density and viscosity ratios up to 1000 and 100 respectively while using standard projection method the utilization of cubic spline for the continuum surface force model significantly improves the quality of the calculated interface thereby eliminating the interphase particle penetrations and in turn leading to the calculation of more accurate velocity and pressure fields

a consistent multi resolution smoothed particle hydrodynamics method abstract we seek to accelerate and increase the size of simulations for fluid structure interactions fsi by using multiple resolutions in the spatial discretization of the equations governing the time evolution of systems displaying two way fluid solid coupling to this end we propose a multi resolution smoothed particle hydrodynamics sph approach in which subdomains of different resolutions are directly coupled without any overlap region the second order consistent discretization of spatial differential operators is employed to ensure the accuracy of the proposed method as sph particles advect with the flow a dynamic sph particle refinement coarsening is employed via splitting merging to maintain a predefined multi resolution configuration particle regularity is enforced via a particle shifting technique to ensure accuracy and stability of the lagrangian particle based method embraced the convergence accuracy and efficiency attributes of the new method are assessed by simulating four different flows in this process the numerical results are compared to the analytical finite element and consistent sph single resolution solutions we anticipate that the proposed multi resolution method will enlarge the class of sph tractable fsi applications

multilinear factorizations for multi camera rigid structure from motion problems camera networks have gained increased importance in recent years existing approaches mostly use point correspondences between different camera views to calibrate such systems however it is often difficult or even impossible to establish such correspondences but even without feature point correspondences between different camera views if the cameras are temporally synchronized then the data from the cameras are strongly linked together by the motion correspondence all the cameras observe the same motion the present article therefore develops the necessary theory to use this motion correspondence for general rigid as well as planar rigid motions given multiple static affine cameras which observe a rigidly moving object and track feature points located on this object what can be said about the resulting point trajectories are there any useful algebraic constraints hidden in the data is a 3d reconstruction of the scene possible even if there are no point correspondences between the different cameras and if so how many points are sufficient is there an algorithm which warrants finding the correct solution to this highly non convex problem this article addresses these questions and thereby introduces the concept of low dimensional motion subspaces the constraints provided by these motion subspaces enable an algorithm which ensures finding the correct solution to this non convex reconstruction problem the algorithm is based on multilinear analysis matrix and tensor factorizations our new approach can handle extreme configurations e g a camera in a camera network tracking only one single point results on synthetic as well as on real data sequences act as a proof of concept for the presented insights

universality of correlation functions of hermitian random matrices in an external field the behavior of correlation functions is studied in a class of matrix models characterized by a measure exp s containing a potential term and an external source term s n tr v m ma in the large n limit the short distance behavior is found to be identical to the one obtained in previously studied matrix models thus extending the universality of the level spacing distribution the calculation of correlation functions involves finite n determinant formulae reducing the problem to the large n asymptotic analysis of a single kernel k this is performed by an appropriate matrix integral formulation of k multi matrix generalizations of these results are discussed

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state