entanglement entropy from corner transfer matrix in forrester baxter non unitary rsos models using a corner transfer matrix approach we compute the bipartite entanglement renyi entropy in the off critical perturbations of non unitary conformal minimal models realised by lattice spin chains hamiltonians related to the forrester baxter rsos models bianchini et al 2015 j stat mech p03010 in regime iii this allows to show on a set of explicit examples that the renyi entropies for non unitary theories rescale near criticality as the logarithm of the correlation length with a coefficient proportional to the effective central charge this complements a similar result recently established for the size rescaling at the critical point bianchini et al 2015 j phys a math theor 48 04ft01 showing the expected agreement of the two behaviours we also compute the first subleading unusual correction to the scaling behaviour showing that it is expressible in terms of expansions of various fractional powers of the correlation length related to the differences between the conformal dimensions of fields in the theory and the minimal conformal dimension finally a few observations on the limit leading to the off critical logarithmic minimal models of pearce and seaton 2012 j stat mech p09014 are put forward

stability and convergence of the peaceman rachford adi method for initial boundary value problems etude des proprietes de stabilite et de convergence de la methode des directions alternees implicite losrsqu elle est appliquee aux problemes aux valeurs initiales dans un espace bidimensionnel

rigorous rg algorithms and area laws for low energy eigenstates in 1d one of the central challenges in the study of quantum many body systems is the complexity of simulating them on a classical computer a recent advance landau et al in nat phys 2015 gave a polynomial time algorithm to compute a succinct classical description for unique ground states of gapped 1d quantum systems despite this progress many questions remained unsolved including whether there exist efficient algorithms when the ground space is degenerate and of polynomial dimension in the system size or for the polynomially many lowest energy states or even whether such states admit succinct classical descriptions or area laws in this paper we give a new algorithm based on a rigorously justified rg type transformation for finding low energy states for 1d hamiltonians acting on a chain of nparticles in the process we resolve some of the aforementioned open questions including giving a polynomial time algorithm for poly n degenerate ground spaces and an n o log n algorithm for the poly n lowest energy states under a mild density condition for these classes of systems the existence of a succinct classical description and area laws were not rigorously proved before this work the algorithms are natural and efficient and for the case of finding unique ground states for frustration free hamiltonians the running time is o nm n where m n is the time required to multiply two n n matrices

nonlinear network description for many body quantum systems in continuous space we show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units using this wave function in variational monte carlo simulations of liquid 4 mathrm he in two and three dimensions we typically find a tenfold increase in accuracy over currently used wave functions furthermore subsequent stages of the iteration procedure define a set of increasingly good wave functions each with its own variational energy and variance of the local energy extrapolation to zero variance gives energies in close agreement with the exact values for two dimensional 4 mathrm he we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form a feature shared with the shadow wave function but now joined by much higher accuracy we also achieve significant progress for liquid 3 mathrm he in three dimensions improving previous variational and fixed node energies

tracking deformable objects in the plane using an active contour model the problems of segmenting a noisy intensity image and tracking a nonrigid object in the plane are discussed in evaluating these problems a technique based on an active contour model commonly called a snake is examined the technique is applied to cell locomotion and tracking studies the snake permits both the segmentation and tracking problems to be simultaneously solved in constrained cases a detailed analysis of the snake model emphasizing its limitations and shortcomings is presented and improvements to the original description of the model are proposed problems of convergence of the optimization scheme are considered in particular an improved terminating criterion for the optimization scheme that is based on topographic features of the graph of the intensity image is proposed hierarchical filtering methods as well as a continuation method based on a discrete sale space representation are discussed results for both segmentation and tracking are presented possible failures of the method are discussed

diagrammatics for su 2 invariant matrix product states we report on a systematic implementation of su 2 invariance for matrix product states mps with concrete computations cast in a diagrammatic language as an application we present a variational mps study of a spin 1 2 quantum chain for efficient computations we make systematic use of the su 2 symmetry at all steps of the calculations i the matrix space is set up as a direct sum of irreducible representations ii the local matrices with state valued entries are set up as superposition of su 2 singlet operators iii products of operators are evaluated algebraically by making use of identities for 3j and 6j symbols the remaining numerical computations like the diagonalization of the associated transfer matrix and the minimization of the energy expectation value are done in spaces free of symmetry degeneracies the energy expectation value is a strict upper bound of the true ground state energy and yields definite conclusions about the accuracy of density matrix renormalization group results reported in the literature furthermore we present explicit results with accuracy better than 10 4 for nearest and next nearest neighbour spin correlators and for general dimer dimer correlators in the thermodynamical limit of the spin heisenberg chain with frustration

the spectral gap for some spin chains with discrete symmetry breaking we prove that for any finite set of generalized valence bond solid gvbs states of a quantum spin chain there exists a translation invariant finite range hamiltonian for which this set is the set of ground states this result implies that there are gvbs models with arbitrary broken discrete symmetries that are described as combinations of lattice translations lattice reflections and local unitary or anti unitary transformations we also show that all gvbs models that satisfy some natural conditions have a spectral gap the existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics this general scheme is interesting in its own right and threfore although the basic idea is not new we present it in a system independent setting the results are illustrated with a number of examples

transfer matrix renormalization group method for general markov random fields abstract we seek the numerical calculation of partition functions of general markov random fields mrfs on an infinitely long twisted cylindrical lattice by using the transfer matrix renormalization group tmrg method the tmrg is a variant of the density matrix renormalization group dmrg which automatically truncates the hilbert space so that the properties of large systems can be precisely calculated while the dimension of the renormalized hilbert space remains constant we apply the tmrg to the decimation of the fundamental transfer matrix that we have proposed previously for general mrfs instead of the standard s e scheme for tmrg we propose a new e s e scheme and propose an alternative method for selecting the renormalized basis specifically the new e s e scheme keeps those singular value decomposition svd components of the fundamental transfer matrix that are relevant for the perron state and truncates the other irrelevant ones results for the ising model show that our method exhibits very impressive accuracy under a rather restricted computational resource simulations for another four general mrfs demonstrate that our tmrg method is superior to the classical monte carlo method in accuracy computational speed and in the possibility of treating a much larger system

an orthogonal spline collocation alternating direction implicit crank nicolson method for linear parabolic problems on rectangles we formulate an alternating direction implicit crank nicolson scheme for solving a general linear variable coefficient parabolic problem in nondivergence form on a rectangle with the solution subject to nonhomogeneous dirichlet boundary condition orthogonal spline collocation with piecewise hermite bicubics is used for spatial discretization we show that for sufficiently small time stepsize the scheme is stable and of optimal order accuracy in time and the h1 norm in space we also describe an efficient implementation of the scheme and present numerical results demonstrating the accuracy and convergence rates in various norms

thermodynamic model of social influence on two dimensional square lattice case for two features abstract we propose a thermodynamic multi state spin model in order to describe equilibrial behavior of a society our model is inspired by the axelrod model used in social network studies in the framework of the statistical mechanics language we analyze phase transitions of our model in which the spin interaction j is interpreted as a mutual communication among individuals forming a society the thermal fluctuations introduce a noise t into the communication which suppresses long range correlations below a certain phase transition point t t large scale clusters of the individuals who share a specific dominant property are formed the measure of the cluster sizes is an order parameter after spontaneous symmetry breaking by means of the corner transfer matrix renormalization group algorithm we treat our model in the thermodynamic limit and classify the phase transitions with respect to inherent degrees of freedom each individual is chosen to possess two independent features f 2 and each feature can assume one of q traits e g interests hence each individual is described by q 2 degrees of freedom a single first order phase transition is detected in our model if q 2 whereas two distinct continuous phase transitions are found if q 2 only evaluating the free energy order parameters specific heat and the entanglement von neumann entropy we classify the phase transitions t t q in detail the permanent existence of the ordered phase the large scale cluster formation with a non zero order parameter is conjectured below a non zero transition point t t q 0 5 in the asymptotic regime q

feature guided gaussian mixture model with semi supervised em and local geometric constraint for retinal image registration abstract retinal image registration which can be formulated by matching two sets of sparse features extracted from two observed retinal images is a crucial step in the diagnosis and treatment of various eye diseases existing methods suffer from missing true correspondences or do not fully consider local appearance information which causes difficulty in matching low quality retinal images due to insufficient reliable features in addition the relationships between retinal image pairs are usually modeled by linear transformation such as affine transformation which cannot generate accurate alignments in large viewpoint changes due to the nonplanar eyeball surface to address these issues a feature guided gaussian mixture model gmm is proposed for the non rigid registration of retinal images we formulate the problem as an estimation of a feature guided mixture of densities a gmm is fitted to one point set in which the centers of the gaussian densities characterized by spatial positions associated with local appearance descriptors are constrained to coincide with the other point set the problem is solved under a maximum likelihood framework and semi supervised expectation maximization is used to iteratively estimate the feature correspondence and spatial transformation which is initialized by a set of confidential feature matches obtained previously non rigid transformation is specified in a reproducing kernel hilbert space and a local geometric constraint is imposed to establish the transformation estimation for obtaining a meaningful solution a fast implementation based on sparse approximation is also provided and reduces the time complexity from cubic to quadratic moreover we use the edge map which can extract more reliable features as a uniform representation of retinal images experimental results on publicly available retinal images show that our approach is robust in different registration tasks and outperforms several competing approaches especially when data is severely degraded

retinal artery vein classification via topology estimation we propose a novel graph theoretic framework for distinguishing arteries from veins in a fundus image we make use of the underlying vessel topology to better classify small and midsized vessels we extend our previously proposed tree topology estimation framework by incorporating expert domain specific features to construct a simple yet powerful global likelihood model we efficiently maximize this model by iteratively exploring the space of possible solutions consistent with the projected vessels we tested our method on four retinal datasets and achieved classification accuracies of 91 0 93 5 91 7 and 90 9 outperforming existing methods our results show the effectiveness of our approach which is capable of analyzing the entire vasculature including peripheral vessels in wide field of view fundus photographs this topology based method is a potentially important tool for diagnosing diseases with retinal vascular manifestation

probabilistic low rank factorization accelerates tensor network simulations of critical quantum many body ground states we provide evidence that randomized low rank factorization is a powerful tool for the determination of the ground state properties of low dimensional lattice hamiltonians through tensor network techniques in particular we show that randomized matrix factorization outperforms truncated singular value decomposition based on state of the art deterministic routines in time evolving block decimation tebd and density matrix renormalization group dmrg style simulations even when the system under study gets close to a phase transition we report linear speedups in the bond or local dimension of up to 24 times in quasi two dimensional cylindrical systems

three dimensional motion tracking of coronary arteries in biplane cineangiograms a three dimensional 3 d method for tracking the coronary arteries through a temporal sequence of biplane x ray angiography images is presented a 3 d centerline model of the coronary vasculature is reconstructed from a biplane image pair at one time frame and its motion is tracked using a coarse to fine hierarchy of motion models three dimensional constraints on the length of the arteries and on the spatial regularity of the motion field are used to overcome limitations of classical two dimensional vessel tracking methods such as tracking vessels through projective occlusions this algorithm was clinically validated in five patients by tracking the motion of the left coronary tree over one cardiac cycle the root mean square reprojection errors were found to be submillimeter in 93 54 58 of the image pairs the performance of the tracking algorithm was quantified in three dimensions using a deforming vascular phantom rms 3 d distance errors were computed between centerline models tracked in the x ray images and gold standard centerline models of the phantom generated from a gated 3 d magnetic resonance image acquisition the mean error was 0 69 spl plusmn 0 06 mm over eight temporal phases and four different biplane orientations

solving the master equation without kinetic monte carlo in multiscale modeling of heterogeneous catalytic processes one crucial point is the solution of a markovian master equation describing the stochastic reaction kinetics usually this is too high dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic monte carlo method in this study we break the curse of dimensionality for the direct solution of the markovian master equation by exploiting the tensor train format for this purpose the performance of the approach is demonstrated on a first principles based reduced model for the co oxidation on the ruo2 110 surface we investigate the complexity for increasing system size and for various reaction conditions the advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness

a generalization of peaceman rachford fractional step method in this paper we develop a set of time integrators of type fractional step runge kutta methods which generalize the time integrator involved in the classical peaceman rachford scheme combining a time semidiscretization of this type with a standard spatial discretization we obtain a totally discrete algorithm capable of discretizing efficiently a general parabolic problem if suitable splittings of the elliptic operator are considered we prove that our proposal is second order consistent and stable even for an operator splitting in m terms which do not necessarily commute finally we illustrate the theoretical results with various applications such as alternating directions or evolutionary domain decomposition

edge detection with embedded confidence computing the weighted average of the pixel values in a window is a basic module in many computer vision operators the process is reformulated in a linear vector space and the role of the different subspaces is emphasized within this framework wellknown artifacts of the gradient based edge detectors such as large spurious responses can be explained quantitatively it is also shown that template matching with a template derived from the input data is meaningful since it provides an independent measure of confidence in the presence of the employed edge model the widely used three step edge detection procedure gradient estimation non maxima suppression hysteresis thresholding is generalized to include the information provided by the confidence measure the additional amount of computation is minimal and experiments with several standard test images show the ability of the new procedure to detect weak edges

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

a computational method for segmenting topological point sets and application to image analysis we propose a computational method for segmenting topological subdimensional point sets in scalar images of arbitrary spatial dimensions the technique is based on calculating the homotopy class defined by the gradient vector in a subdimensional neighborhood around every image point this neighborhood is defined as the linear envelope spawned over a given subdimensional vector frame in the simplest case where the rank of this frame is maximal we obtain a technique for localizing the critical points we consider in particular the important case of frames formed by an arbitrary number of the first largest by absolute value principal directions of the hessian the method then segments positive and and negative ridges as well as other types of critical surfaces of different dimensionalities the signs of the eigenvalues associated to the principal directions provide a natural labeling of the critical subsets the result in general is a constructive definition of a hierarchy of point sets of different dimensionalities linked by inclusion relations because of its explicit computational nature the method gives a fast way to segment height ridges or edges in different applications the defined topological point sets are connected manifolds and therefore our method provides a tool for geometrical grouping using only local measurements we have demonstrated the grouping properties of our construction by presenting two different cases where an extra image coordinate is introduced

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

a finite tame wild trichotomy theorem for tensor diagrams abstract in this paper we consider the problem of determining when two tensor networks are equivalent under a heterogeneous change of basis in particular to a tensor or string diagram in a certain monoidal category which we call tensor diagrams we formulate an associated abelian category of representations each representation corresponds to a tensor network on that diagram we then classify which tensor diagrams give rise to categories that are finite tame or wild in the traditional sense of representation theory for those tensor diagrams of finite and tame type we classify the indecomposable representations our main result is that a tensor diagram is wild if and only if it contains a vertex of degree at least three otherwise it is of tame or finite type

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

construction of coarse grained order parameters in nonequilibrium systems we develop a renormalization group rg procedure that includes important system specific features the key ingredient is to systematize the coarse graining procedure that generates the rg flow the coarse graining technology comes from the control and operator theoretic model reduction the resulting generalized rg is a consistent generalization of the wilsonian rg we apply the procedure to a deterministic nonlinear wave equation nlwe with probabilistic initial conditions we derive the form of the projection operator from the dynamics of the nlwe and then use it to generate the rg flow for the distribution of initial conditions the probability density of the initial conditions is chosen to be a boltzmann weight that is quartic in the field variables in our calculation we find that in contrast to conventional implementations of the rg naive power counting breaks down we also show that the resulting rg equations are different from those derived from the conventional rg

a non perturbative real space renormalization group scheme based on the original idea of the density matrix renormalization group dmrg i e to include the missing boundary conditions between adjacent blocks of the blocked quantum system we present a rigorous and non perturbative mathematical formulation for the real space renormalization group idea conceived by kadanoff and further developed by wilson this is achieved by using additional hilbert spaces called auxiliary spaces in the construction of each single isolated block which is then termed a superblock in accordance with the original nomenclature on this superblock we define two maps called embedding and truncation for successively integrating out the small scale structure our method overcomes the known difficulties of the numerical dmrg i e the limitation to zero temperature and one space dimension

generalization of the tensor renormalization group approach to 3 d or higher dimensions abstract in this paper a way of generalizing the tensor renormalization group trg is proposed mathematically the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is discovered a theoretical contraction framework is therefore proposed furthermore the canonical polyadic decomposition is introduced to tensor network theory a numerical verification of this method on the 3 d ising model is carried out

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

retina verification system based on biometric graph matching this paper presents an automatic retina verification framework based on the biometric graph matching bgm algorithm the retinal vasculature is extracted using a family of matched filters in the frequency domain and morphological operators then retinal templates are defined as formal spatial graphs derived from the retinal vasculature the bgm algorithm a noisy graph matching algorithm robust to translation non linear distortion and small rotations is used to compare retinal templates the bgm algorithm uses graph topology to define three distance measures between a pair of graphs two of which are new a support vector machine svm classifier is used to distinguish between genuine and imposter comparisons using single as well as multiple graph measures the classifier achieves complete separation on a training set of images from the varia database 60 of the data equaling the state of the art for retina verification because the available data set is small kernel density estimation kde of the genuine and imposter score distributions of the training set are used to measure performance of the bgm algorithm in the one dimensional case the kde model is validated with the testing set a 0 eer on testing shows that the kde model is a good fit for the empirical distribution for the multiple graph measures a novel combination of the svm boundary and the kde model is used to obtain a fair comparison with the kde model for the single measure a clear benefit in using multiple graph measures over a single measure to distinguish genuine and imposter comparisons is demonstrated by a drop in theoretical error of between 60 and more than two orders of magnitude

density matrix renormalization group study of the correlation function of the bilinear biquadratic spin 1 chain using the recently developed density matrix renormalization group approach we study the correlation function of the spin 1 chain with quadratic and biquadratic interactions this allows us to define and calculate the periodicity of the ground state which differs markedly from that in the classical analogue combining our results with other studies we predict three phases in the region where the quadratic and biquadratic terms are both positive

spectral chebyshev fourier collocation for the helmholtz and variable coefficient equations in a disk the paper is concerned with the spectral collocation solution of the helmholtz equation in a disk in the polar coordinates r and q we use spectral chebyshev collocation in r spectral fourier collocation in q and a simple integral condition to specify the value of the approximate solution at the center of the disk the scheme is solved at a quasi optimal cost using the idea of superposition a matrix decomposition algorithm and fast fourier transforms both the dirichlet and neumann boundary conditions are considered and extensions to equations with variable coefficients are discussed numerical results confirm the spectral convergence of the method

extrapolation cam theory for critical exponents we propose and test a new method for generating canonical sequences for analysis by the coherent anomaly method cam from non mean field approximations by intentionally underestimating the rate of convergence of exact diagonalization values for the mass or energy gaps of finite systems we form families of sequences of gap estimates the gap estimates cross zero with generically nonzero linear terms in their taylor expansions so that for each member of these sequences of estimates thus the cam can be used to determine our freedom in deciding exactly how to underestimate the convergence allows us to choose the sequence that displays the clearest coherent anomaly we demonstrate this approach on the two dimensional ferromagnetic ising model for which we also use it on the three dimensional ferromagnetic ising model finding in good agreement with other estimates finally we apply it to an antiferromagnetic spin 1 heisenberg chain finding at the phase transition between the haldane phase and the dimerized phase in agreement with the field theoretic prediction although the specific systems used to test the extrapolation cam procedure involve finite system sizes the method could be applied to other finite approximations such as systematic variational approximations

the dual bootstrap iterative closest point algorithm with application to retinal image registration motivated by the problem of retinal image registration this paper introduces and analyzes a new registration algorithm called dual bootstrap iterative closest point dual bootstrap icp the approach is to start from one or more initial low order estimates that are only accurate in small image regions called bootstrap regions in each bootstrap region the algorithm iteratively 1 refines the transformation estimate using constraints only from within the bootstrap region 2 expands the bootstrap region and 3 tests to see if a higher order transformation model can be used stopping when the region expands to cover the overlap between images steps 1 and 3 the bootstrap steps are governed by the covariance matrix of the estimated transformation estimation refinement step 2 uses a novel robust version of the icp algorithm in registering retinal image pairs dual bootstrap icp is initialized by automatically matching individual vascular landmarks and it aligns images based on detected blood vessel centerlines the resulting quadratic transformations are accurate to less than a pixel on tests involving approximately 6000 image pairs it successfully registered 99 5 of the pairs containing at least one common landmark and 100 of the pairs containing at least one common landmark and at least 35 image overlap

statistical edge detection learning and evaluating edge cues we formulate edge detection as statistical inference this statistical edge detection is data driven unlike standard methods for edge detection which are model based for any set of edge detection filters implementing local edge cues we use presegmented images to learn the probability distributions of filter responses conditioned on whether they are evaluated on or off an edge edge detection is formulated as a discrimination task specified by a likelihood ratio test on the filter responses this approach emphasizes the necessity of modeling the image background the off edges we represent the conditional probability distributions nonparametrically and illustrate them on two different data sets of 100 sowerby and 50 south florida images multiple edges cues including chrominance and multiple scale are combined by using their joint distributions hence this cue combination is optimal in the statistical sense we evaluate the effectiveness of different visual cues using the chernoff information and receiver operator characteristic roc curves this shows that our approach gives quantitatively better results than the canny edge detector when the image background contains significant clutter in addition it enables us to determine the effectiveness of different edge cues and gives quantitative measures for the advantages of multilevel processing for the use of chrominance and for the relative effectiveness of different detectors furthermore we show that we can learn these conditional distributions on one data set and adapt them to the other with only slight degradation of performance without knowing the ground truth on the second data set this shows that our results are not purely domain specific we apply the same approach to the spatial grouping of edge cues and obtain analogies to nonmaximal suppression and hysteresis

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

steerable wedge filters for local orientation analysis steerable filters have been used to analyze local orientation patterns in imagery such filters are typically based on directional derivatives whose symmetry produces orientation responses that are periodic with period spl pi independent of image structure we present a more general set of steerable filters that alleviate this problem

elucidating reaction mechanisms on quantum computers with rapid recent advances in quantum technology we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers here we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems using the open problem of biological nitrogen fixation in nitrogenase as an example we discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms to significantly increase their accuracy and enable hitherto intractable simulations our resource estimates show that even when taking into account the substantial overhead of quantum error correction and the need to compile into discrete gate sets the necessary computations can be performed in reasonable time on small quantum computers our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources

detection of blood vessels in retinal images using two dimensional matched filters blood vessels usually have poor local contrast and the application of existing edge detection algorithms yield results which are not satisfactory an operator for feature extraction based on the optical and spatial properties of objects to be recognized is introduced the gray level profile of the cross section of a blood vessel is approximated by a gaussian shaped curve the concept of matched filter detection of signals is used to detect piecewise linear segments of blood vessels in these images twelve different templates that are used to search for vessel segments along all possible directions are constructed various issues related to the implementation of these matched filters are discussed the results are compared to those obtained with other methods

a new method for linear feature and junction enhancement in 2d images based on morphological operation oriented anisotropic gaussian function and hessian information abstract feature enhancement is an important preprocessing step in many image processing tasks it is the process of adjusting image intensities so that the enhanced results are more suitable for analysis good enhancement results for linear structures such as vessels or neurites can be used as inputs for segmentation and other operations in this paper a novel linear feature enhancement filter an adaptive multi scale morpho gaussian filter which can enhance and smooth linear features is proposed based on morphological operation anisotropic gaussian function and hessian information this filter can enhance and smooth along the local orientation of the linear structures and the hessian measurement is used to further enhance the linear features we utilize the hessian matrix to calculate the orientation information for our directional morphological operation and the oriented anisotropic gaussian smoothing we also propose a novel method for junction enhancement which can solve the problem of junction suppression we decompose the junctions and enhance along each linear structure within a junction region we present the test results of our algorithm on images of different types and compare our method with three existing methods the experimental results show that the proposed approach can achieve better results

gapped and gapless phases of frustration free spin 1 2 chains we consider a family of translation invariant quantum spin chains with nearest neighbor interactions and derive necessary and sufficient conditions for these systems to be gapped in the thermodynamic limit more precisely let be an arbitrary two qubit state we consider a chain of n qubits with open boundary conditions and hamiltonian h n which is defined as the sum of rank 1 projectors onto applied to consecutive pairs of qubits we show that the spectral gap of h n is upper bounded by 1 n 1 if the eigenvalues of a certain 2 2 matrix simply related to have equal non zero absolute value otherwise the spectral gap is lower bounded by a positive constant independent of n depending only on a key ingredient in the proof is a new operator inequality for the ground space projector which expresses a monotonicity under the partial trace this monotonicity property appears to be very general and might be interesting in its own right as an extension of our main result we obtain a complete classification of gapped and gapless phases of frustration free translation invariant spin 1 2 chains with nearest neighbor interactions

parallelization strategies for density matrix renormalization group algorithms on shared memory systems shared memory smp parallelization strategies for density matrix renormalization group dmrg algorithms enable the treatment of complex systems in solid state physics we present two different approaches by which parallelization of the standard dmrg algorithm can be accomplished in an efficient way the methods are illustrated with dmrg calculations of the two dimensional hubbard model and the one dimensional holstein hubbard model on contemporary smp architectures the parallelized code shows good scalability up to at least eight processors and allows us to solve problems which exceed the capability of sequential dmrg calculations

an adi extrapolated crank nicolson orthogonal spline collocation method for nonlinear reaction diffusion systems an alternating direction implicit adi orthogonal spline collocation osc method is described for the approximate solution of a class of nonlinear reaction diffusion systems its efficacy is demonstrated on the solution of well known examples of such systems specifically the brusselator gray scott gierer meinhardt and schnakenberg models and comparisons are made with other numerical techniques considered in the literature the new adi method is based on an extrapolated crank nicolson osc method and is algebraically linear it is efficient requiring at each time level only o n operations where n is the number of unknowns moreover it is shown to produce approximations which are of optimal global accuracy in various norms and to possess superconvergence properties

symmetry respecting real space renormalization for the quantum ashkin teller model we use a simple real space renormalization group approach to investigate the critical behavior of the quantum ashkin teller model a one dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously this approach which is based on exploiting the on site symmetry of the model has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse field ising model our investigation explores this approach in more generality in a model in which the critical behavior has a richer structure but which reduces to the simpler ising case at a special point we demonstrate that the correlation length critical exponent as predicted from this real space renormalization group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality near the ising special point the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods although the accuracy decreases away from the decoupled ising model point

locality at the boundary implies gap in the bulk for 2d peps proving that the parent hamiltonian of a projected entangled pair state peps is gapped remains an important open problem we take a step forward in solving this problem by showing two results first we identify an approximate factorization condition on the boundary state of rectangular subregions that is sufficient to prove that the parent hamiltonian of the bulk 2d peps has a constant gap in the thermodynamic limit second we then show that gibbs state of a local finite range hamiltonian satisfy such condition the proof applies to the case of injective and mpo injective peps employs the martingale method of nearly commuting projectors and exploits a result of araki commun math phys 14 2 120 157 1969 on the robustness of one dimensional gibbs states our result provides one of the first rigorous connections between boundary theories and dynamical properties in an interacting many body system

a generalization of the injectivity condition for projected entangled pair states we introduce a family of tensor network states that we term semi injective projected entangled pair states pepss they extend the class of injective pepss and include other states like the ground states of the aklt and the czx models in square lattices we construct parent hamiltonians for which semi injective pepss are unique ground states we also determine the necessary and sufficient conditions for two tensors to generate the same family of such states in two spatial dimensions using this result we show that the third cohomology labeling of symmetry protected topological phases extends to semi injective pepss

modeling analysis and visualization of left ventricle shape and motion by hierarchical decomposition this paper presents an approach to the modeling analysis and visualization of left ventricle motion and deformation the authors modeling of left ventricle shape and motion as a hierarchical representation enables them to develop a promising noninvasive technique for monitoring heart dynamics where both image analysis and image synthesis are involved the proposed hierarchical motion model of left ventricle is constructed by combining several existing simple models and is able to capture major motion and deformation components of the left ventricle the hierarchical decomposition characterizes the left ventricle motion and deformation in a coarse to fine fashion and leads to computationally efficient estimation algorithms the authors estimate the global rigid motion of the left ventricle by establishing a time varying object centered coordinate system the global deformations of the left ventricle are obtained by fitting the given data to superquadric modeling primitives the local deformations are estimated by a tensor description approach that is based on the locally deformable surface obtained by constructing spherical harmonic local surface from the residues of global shape estimation the authors also describe in this paper methods of image synthesis and dynamic animation for visualizing the estimated results of the time varying left ventricle shape motion and deformations these animation results are consistent with the apparent motion pattern of the left ventricle and therefore show the success of the authors hierarchical decomposition based approach

three dimensional tracking of coronary arteries from biplane angiographic sequences using parametrically deformable models a new method for coronary artery tracking in biplane digital subtraction is presented the dynamic tracking of nonrigid objects from two views is achieved using a generalization of parametrically deformable models three dimensional 3 d fourier descriptors used for shape representation are obtained from the two dimensional 2 d descriptors of the projections a new constraint inferred from epipolar geometry is applied to the contour model direct 3 d tracking is compared with the classical approach in two steps independent 2 d tracking in each of the two projection planes 3 d reconstruction using the epipolar constraint convergence quality and accuracy of the 3 d reconstruction are analyzed for several sequences showing different displacement amplitudes deformation rates and image contrasts

low rank tensor recovery via iterative hard thresholding abstract we study extensions of compressive sensing and low rank matrix recovery matrix completion to the recovery of low rank tensors of higher order from a small number of linear measurements while the theoretical understanding of low rank matrix recovery is already well developed only few contributions on the low rank tensor recovery problem are available so far in this paper we introduce versions of the iterative hard thresholding algorithm for several tensor decompositions namely the higher order singular value decomposition hosvd the tensor train format tt and the general hierarchical tucker decomposition ht we provide a partial convergence result for these algorithms which is based on a variant of the restricted isometry property of the measurement operator adapted to the tensor decomposition at hand that induces a corresponding notion of tensor rank we show that subgaussian measurement ensembles satisfy the tensor restricted isometry property with high probability under a certain almost optimal bound on the number of measurements which depends on the corresponding tensor format these bounds are extended to partial fourier maps combined with random sign flips of the tensor entries finally we illustrate the performance of iterative hard thresholding methods for tensor recovery via numerical experiments where we consider recovery from gaussian random measurements tensor completion recovery of missing entries and fourier measurements for third order tensors

relaxation times in the asep model using a dmrg method we compute the largest relaxation times for the totally asymmetric exclusion process tasep with open boundary conditions with a dmrg method this allows us to reach much larger system sizes than in previous numerical studies we are then able to show that the phenomenological theory of the domain wall indeed predicts correctly the largest relaxation time for large systems besides we can obtain results even when the domain wall approach breaks down and show that the kpz dynamical exponent z 3 2 is recovered in the whole maximal current phase

joint volumetric extraction and enhancement of vasculature from low snr 3 d fluorescence microscopy images abstract to simultaneously overcome the challenges imposed by the nature of optical imaging characterized by a range of artifacts including space varying signal to noise ratio snr scattered light and non uniform illumination we developed a novel method that segments the 3 d vasculature directly from original fluorescence microscopy images eliminating the need for employing pre and post processing steps such as noise removal and segmentation refinement as used with the majority of segmentation techniques our method comprises two initialization and constrained recovery and enhancement stages the initialization approach is fully automated using features derived from bi scale statistical measures and produces seed points robust to non uniform illumination low snr and local structural variations this algorithm achieves the goal of segmentation via design of an iterative approach that extracts the structure through voting of feature vectors formed by distance local intensity gradient and median measures qualitative and quantitative analysis of the experimental results obtained from synthetic and real data prove the efficacy of this method in comparison to the state of the art enhancing segmenting methods the algorithmic simplicity freedom from having a priori probabilistic information about the noise and structural definition gives this algorithm a wide potential range of applications where i e structural complexity significantly complicates the segmentation problem

frustration free gapless hamiltonians for matrix product states for every matrix product state mps one can always construct a so called parent hamiltonian this is a local frustration free hamiltonian which has the mps as ground state and is gapped whenever that parent hamiltonian has a degenerate ground state space the so called non injective case we construct another uncle hamiltonian which is also local and frustration free has the same ground state space but is gapless and its spectrum is mathbb r the construction is obtained by linearly perturbing the matrices building up the state in a random direction and then taking the limit where the perturbation goes to zero for mps where the parent hamiltonian has a unique ground state the so called injective case we also build such uncle hamiltonian with the same properties in the thermodynamic limit

on manifolds of tensors of fixed tt rank recently the format of tt tensors hackbusch and kuhn in j fourier anal appl 15 706 722 2009 oseledets in siam j sci comput 2009 submitted oseledets and tyrtyshnikov in siam j sci comput 31 5 2009 oseledets and tyrtyshnikov in linear algebra appl 2009 submitted has turned out to be a promising new format for the approximation of solutions of high dimensional problems in this paper we prove some new results for the tt representation of a tensor u in mathbb r n 1 times cdots times n d and for the manifold of tensors of tt rank underline r as a first result we prove that the tt or compression ranks r i of a tensor u are unique and equal to the respective separation ranks of u if the components of the tt decomposition are required to fulfil a certain maximal rank condition we then show that the set mathbb t of tt tensors of fixed rank underline r locally forms an embedded manifold in mathbb r n 1 times cdots times n d therefore preserving the essential theoretical properties of the tucker format but often showing an improved scaling behaviour extending a similar approach for matrices conte and lubich in m2an 44 759 2010 we introduce certain gauge conditions to obtain a unique representation of the tangent space mathcal t u mathbb t of mathbb t and deduce a local parametrization of the tt manifold the parametrisation of mathcal t u mathbb t is often crucial for an algorithmic treatment of high dimensional time dependent pdes and minimisation problems lubich in from quantum to classical molecular dynamics reduced methods and numerical analysis 2008 we conclude with remarks on those applications and present some numerical examples

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

segmentation of vessel like patterns using mathematical morphology and curvature evaluation this paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel like patterns in a noisy environment such patterns are very common in medical images vessel detection is interesting for the computation of parameters related to blood flow its tree like geometry makes it a usable feature for registration between images that can be of a different nature in order to define vessel like patterns segmentation is performed with respect to a precise model we define a vessel as a bright pattern piece wise connected and locally linear mathematical morphology is very well adapted to this description however other patterns fit such a morphological description in order to differentiate vessels from analogous background patterns a cross curvature evaluation is performed they are separated out as they have a specific gaussian like profile whose curvature varies smoothly along the vessel the detection algorithm that derives directly from this modeling is based on four steps 1 noise reduction 2 linear pattern with gaussian like profile improvement 3 cross curvature evaluation 4 linear filtering we present its theoretical background and illustrate it on real images of various natures then evaluate its robustness and its accuracy with respect to noise

shape discrimination using fourier descriptors description or discrimination of boundary curves shapes is an important problem in picture processing and pattern recognition fourier descriptors fd s have interesting properties in this respect first a critical review is given of two kinds of fd s some properties of the fd s are given and a distance measure is proposed in terms of fd s that measures the difference between two boundarv curves it is shown how fd s can be used for obtaining skeletons fobjects finally experimental results are given in character recognition and machine parts recognition

a renormalization group theory of cultural evolution abstract we present a theory of cultural evolution based upon a renormalization group scheme we consider rational but cognitively limited agents who optimize their decision making process by iteratively updating and refining the mental representation of their natural and social environment these representations are built around the most important degrees of freedom of their world cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequate order parameter as the importance of social interactions increases or agents become more intelligent we observe and quantify a series of dynamic phase transitions by which cultural coherence advances in the society a similar phase transition may explain the so called cultural explosion in human evolution some 50 000 years ago

general retinal vessel segmentation using regularization based multiconcavity modeling detecting blood vessels in retinal images with the presence of bright and dark lesions is a challenging unsolved problem in this paper a novel multiconcavity modeling approach is proposed to handle both healthy and unhealthy retinas simultaneously the differentiable concavity measure is proposed to handle bright lesions in a perceptive space the line shape concavity measure is proposed to remove dark lesions which have an intensity structure different from the line shaped vessels in a retina the locally normalized concavity measure is designed to deal with unevenly distributed noise due to the spherical intensity variation in a retinal image these concavity measures are combined together according to their statistical distributions to detect vessels in general retinal images very encouraging experimental results demonstrate that the proposed method consistently yields the best performance over existing state of the art methods on the abnormal retinas and its accuracy outperforms the human observer which has not been achieved by any of the state of the art benchmark methods most importantly unlike existing methods the proposed method shows very attractive performances not only on healthy retinas but also on a mixture of healthy and pathological retinas

spectral gap and exponential decay of correlations we study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short range interactions on a wide class of lattices we prove that if two observables anticommute with each other at large distance then the nonvanishing spectral gap implies exponential decay of the corresponding correlation when two observables commute with each other at large distance the connected correlation function decays exponentially under the gap assumption if the observables behave as a vector under the u 1 rotation of a global symmetry of the system we use previous results on the large distance decay of the correlation function to show the stronger statement that the correlation function itself rather than just the connected correlation function decays exponentially under the gap assumption on a lattice with a certain self similarity in fractal dimensions d 2 in particular if the system is translationally invariant in one of the spatial directions then this self similarity condition is automatically satisfied we also treat systems with long range power law decaying interactions

adi spectral collocation methods for parabolic problems we discuss the crank nicolson and laplace modified alternating direction implicit legendre and chebyshev spectral collocation methods for a linear variable coefficient parabolic initial boundary value problem on a rectangular domain with the solution subject to non zero dirichlet boundary conditions the discretization of the problems by the above methods yields matrices which possess banded structures this along with the use of fast fourier transforms makes the cost of one step of each of the chebyshev spectral collocation methods proportional except for a logarithmic term to the number of the unknowns we present the convergence analysis for the legendre spectral collocation methods in the special case of the heat equation using numerical tests we demonstrate the second order accuracy in time of the chebyshev spectral collocation methods for general linear variable coefficient parabolic problems

quasioptimality of maximum volume cross interpolation of tensors we consider a cross interpolation of high dimensional arrays in the tensor train format we prove that the maximum volume choice of the interpolation sets provides the quasioptimal interpolation accuracy that differs from the best possible accuracy by the factor which does not grow exponentially with dimension for nested interpolation sets we prove the interpolation property and propose greedy cross interpolation algorithms we justify the theoretical results and measure speed and accuracy of the proposed algorithm with numerical experiments

spectral fractional step runge kutta discretizations for initial boundary value problems with time dependent boundary conditions in this paper we develop a technique for avoiding the order reduction caused by nonconstant boundary conditions in the methods called splitting alternating direction or more generally fractional step methods such methods can be viewed as the combination of a semidiscrete in time procedure with a special type of additive runge kutta method which is called the fractional step runge kutta method and a standard space discretization which can be of type finite differences finite elements or spectral methods among others spectral methods have been chosen here to complete the analysis of convergence of a totally discrete scheme of this type of improved fractionary steps the numerical experiences performed also show the increase of accuracy that this technique provides

on local convergence of alternating schemes for optimization of convex problems in the tensor train format alternating linear schemes als with the alternating least squares algorithm a notable special case provide one of the simplest and most popular choices for the treatment of optimization tasks by tensor methods an according adaptation of als for the recent tt tensor train format i v oseledets siam j sci comput 33 2011 pp 2295 2317 known in quantum computations as matrix product states has recently been investigated in s holtz t rohwedder and r schneider siam j sci comput 34 2012 pp a683 a713 with the present work the positive practical experience with tt als is backed up with an according local linear convergence theory for the optimization of convex functionals j the main assumption entering the proof is that the redundancy introduced by the tt parametrization tau matches the null space of the hessian of the induced functional j j circ tau and we give conditions under which this assumption can be expected to hold in particular this is the case if

a novel vessel segmentation algorithm for pathological retina images based on the divergence of vector fields in this paper a method is proposed for detecting blood vessels in pathological retina images in the proposed method blood vessel like objects are extracted using the laplacian operator and noisy objects are pruned according to the centerlines which are detected using the normalized gradient vector field the method has been tested with all the pathological retina images in the publicly available stare database experiment results show that the method can avoid detecting false vessels in pathological regions and can produce reliable results for healthy regions

efficient spectral galerkin method i direct solvers of second and fourth order equations using legendre polynomials this paper presents some efficient algorithms based on the legendre galerkin approximations for the direct solution of the second and fourth order elliptic equations the key to the efficiency of these algorithms is to construct appropriate base functions which lead to systems with sparse matrices for the discrete variational formulations the complexities of the algorithms are a small multiple of n d 1 operations for a d dimensional domain with n 1 d unknowns while the convergence rates of the algorithms are exponential for problems with smooth solutions in addition the algorithms can be effectively parallelized since the bottlenecks of the algorithms are matrix matrix multiplications

an alternating direction implicit orthogonal spline collocation scheme for nonlinear parabolic problems on rectangular polygons we consider a nonlinear parabolic initial boundary value problem on a rectangular polygon with the solution satisfying robin boundary conditions with variable coefficients an approximation to the solution at the desired time value is obtained using an alternating direction implicit extrapolated crank nicolson scheme in which orthogonal spline collocation with piecewise polynomials of an arbitrary degree is used for spatial discretization at each time level the scheme determines the intermediate solution along horizontal lines and the approximate solution along vertical lines passing through the gauss points only at the last time level is the approximate solution along vertical lines converted into the approximate solution defined on the entire rectangular polygon this property of our approach leads to its efficient implementation and its applicability to rectangular polygons

dynamic feature extraction of coronary artery motion using dsa image sequences this paper aims to define and describe features of the motion of coronary arteries in two and three dimensions presented as geometrical parameters that identify motion patterns the main left coronary artery centerlines obtained from digital subtraction angiography dsa image sequences are first reconstructed thereafter global and local motion features are evaluated along the sequence the global attributes are centerline and point trajectory lengths displacement amplitude and virtual reference point while local attributes are displacement direction perpendicular radial components rotation direction and curvature and torsion these kinetic features allow the authors to obtain a detailed quantitative description of the displacements of arteries centerlines as well as associated epicardium deformations the authors modeling of local attributes as quasi homogeneous on a segment analysis enables them to propose a novel numeric to symbolic image transformation which provides the required facts for knowledge based motion interpretation experimental results using real data are consistent with cardiac dynamic behavior

boundary finding with parametrically deformable models segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model based global shape information the authors apply flexible constraints in the form of a probabilistic deformable model to the problem of segmenting natural 2 d objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form the parametric model is based on the elliptic fourier decomposition of the boundary probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations boundary finding is formulated as an optimization problem using a maximum a posteriori objective function results of the method applied to real and synthetic images are presented including an evaluation of the dependence of the method on prior information and image quality