mammographic feature enhancement by multiscale analysis introduces a novel approach for accomplishing mammographic feature analysis by overcomplete multiresolution representations the authors show that efficient representations may be identified within a continuum of scale space and used to enhance features of importance to mammography methods of contrast enhancement are described based on three overcomplete multiscale representations 1 the dyadic wavelet transform separable 2 the spl phi transform nonseparable nonorthogonal and 3 the hexagonal wavelet transform nonseparable multiscale edges identified within distinct levels of transform space provide local support for image enhancement mammograms are reconstructed from wavelet coefficients modified at one or more levels by local and global nonlinear operators in each case edges and gain parameters are identified adaptively by a measure of energy within each level of scale space the authors show quantitatively that transform coefficients modified by adaptive nonlinear operators can make more obvious unseen or barely seen features of mammography without requiring additional radiation the authors results are compared with traditional image enhancement techniques by measuring the local contrast of known mammographic features they demonstrate that features extracted from multiresolution representations can provide an adaptive mechanism for accomplishing local contrast enhancement by improving the visualization of breast pathology one can improve chances of early detection while requiring less time to evaluate mammograms for most patients

an mhd stokes eigenvalue problem and its approximation by a spectral collocation method abstract an eigenvalue problem is introduced for the magnetohydrodynamic mhd stokes equations describing the flow of a viscous and electrically conducting fluid in a duct under the influence of a uniform magnetic field the solution of the eigenproblem is approximated by using a spectral collocation method that is based on vanishing the residual equation at the collocation points on the physical domain which are chosen to be the chebyshev gauss lobatto points as the solutions are sought in the physical space the approximations to the derivatives of the unknowns are directly evaluated the equations are formulated in the primitive variables and hence with inclusion of the continuity equation the discretization of the operator results in a generalized eigenproblem with zero diagonal entries therefore a penalty method is applied to circumvent the degeneracy where a perturbed form of the problem is considered and a zero mean pressure value is introduced the numerical prospects of the algorithm are investigated and demonstrated by a number of characteristic tests the key features of interest are the effects of introducing a magnetic field on the eigenspectrum focusing mainly on the change of the fundamental eigenpairs and the consequential variation of the eigenstructure with the magnetic field the mechanisms that underlie these effects are examined by the numerical model proposed the implications of these effects are presented and it is shown that the flow field is considerably affected with the introduction of a magnetic field into the physical model

a well conditioned collocation method using a pseudospectral integration matrix in this paper a well conditioned collocation method is constructed for solving general p th order linear differential equations with various types of boundary conditions based on a suitable birkhoff interpolation we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features the condition number of the linear system is independent of the number of collocation points and the underlying boundary conditions are imposed exactly moreover the new basis leads to an exact inverse of the pseudospectral differentiation matrix of the highest derivative at interior collocation points which is therefore called the pseudospectral integration matrix psim we show that psim produces the optimal integration preconditioner and stable collocation solutions with even thousands of points

on techniques for detecting circumscribed masses in mammograms a method for detecting one type of breast tumor circumscribed masses in mammograms is presented it relies on a combination of criteria used by experts including the shape brightness contrast and uniform density of tumor areas the method uses modified median filtering to enhance mammogram images and template matching to detect the tumors in the template matching step suspicious areas are identified by thresholding the cross correlation values and a percentile method is used to determine a threshold for each film in addition two tests are used to remove false alarms from the resulting candidates the results obtained by applying these techniques to a set of test images are described they are judged encouraging

the screening of species in a darwinistic tree like model of evolution abstract numerical and theoretical investigations of a tree like model of self organized critical evolution are presented the screening of species from the evolution process is numerically studied critical exponents for i the avalanche distribution ii the correlation function iii the order parameter and iv the fraction of unscreened species are given a mean field approximation is developed this theory is quite accurate for describing the critical state but is not able to describe the transient regimes i e the self organized slowing down of both order parameter and fraction of unscreened species towards the critical state

mass lesion detection with a fuzzy neural network abstract this paper presents a novel fuzzy neural network fnn approach to detect malignant mass lesions on mammograms the fnn is a self adjusting and adaptive system it is simple in structure and easy to incorporate experts knowledge and fuzzified factors in the detection of malignant mass lesions on mammograms the fnn has four layers the first layer is the input layer consisting of 4 fuzzy neurons the second layer has 4 ordinary neurons the third layer consists of n maximum fuzzy neurons the number of fuzzy neurons n in the third layer is determined during the training process and varies with the network parameters and data distribution the fourth layer has 2 maximum fuzzy neurons and one competitive fuzzy neuron mammograms were obtained from the digital database for screening mammography ddsm six hundred and seventy regions of interest rois were extracted from 100 mammograms all extracted rois were randomly divided into two sets training and testing sets the co occurrence matrix of each roi was computed textural features were calculated at sizes of 256 256 and 768 768 respectively the feature differences at these two image sizes were computed for each feature these feature differences are very discriminant in differentiating between malignant masses and normal tissues regardless of lesion shape size and subtlety after training the fnn can correctly detect all malignant masses on mammograms in the testing group the true positive fraction tpf is 0 92 when the number of false positives fp is 1 33 per mammogram and 1 0 when the fp is 2 15 per mammogram the proposed approach will be very useful for breast cancer control

markov random field for tumor detection in digital mammography a technique is proposed for the detection of tumors in digital mammography detection is performed in two steps segmentation and classification in segmentation regions of interest are first extracted from the images by adaptive thresholding a further reliable segmentation is achieved by a modified markov random field mrf model based method in classification the mrf segmented regions are classified into suspicious and normal by a fuzzy binary decision tree based on a series of radiographic density related features a set of normal 50 and abnormal 45 screen film mammograms were tested the latter contained 48 biopsy proven malignant masses of various types and subtlety the detection accuracy of the algorithm was evaluated by means of a free response receiver operating characteristic curve which shows the relationship between the detection of true positive masses and the number of false positive alarms per image the results indicated that a 90 sensitivity can be achieved in the detection of different types of masses at the expense of two falsely detected signals per image the algorithm was notably successful in the detection of minimal cancers manifested by masses spl les 10 mm in size for the 16 such cases in the authors dataset a 94 sensitivity was observed with 1 5 false alarms per image an extensive study of the effects of the algorithm s parameters on its sensitivity and specificity was also performed in order to optimize the method for a clinical observer performance study

on inhomogeneous eigenvalue problems i abstract in studying stability of solutions of linear differential equations one naturally encounters liapunov equations in a suitable setting they can be interpreted as equations for the normalized directions of these solutions when applying discretizations to the liapunov equations one is led to a problem which in its most elementary form can be stated as given a matrix a and a vector b determine a vector x with xtx 1 and a scalar such that ax b x here is called the inhomogeneous eigenvalue we consider the question of how many solution pairs x of this problem exist we also give some numerical methods to compute such a pair they are based on generalizations of shifted power iterations finally we consider the case that b is small so that the inhomogeneous eigenvalues can be viewed as perturbations of the homogeneous ones i e b 0

a theoretical analysis of the properties of median filters necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived these conditions state that a signal must be locally monotone to pass through a median filter unchanged it is proven that the form of successive median filtering of a signal i e the filtered output is itself again filtered eventually reduces the original signal to an invariant signal called a root signal for a signal of length l samples a maximum of frac 1 2 l 2 repeated filterings produces a root signal

auxiliary fields for treating two time lagrangian quantum mechanics functional integrals over complex and real auxiliary fields for propagators relating to two time memory actions are constructed the integrals over fields result from partial replacement of the path variable via functional integration in the path integral form of the propagator by a field variable in a way that allows the remaining path integration to be performed thus leaving a functional integral two new cases of actions involving memory a quadratic and a quartic are treated explicitly a functional integral identity is also developed furthermore the method of coupling an auxiliary dynamical field for generating memory actions is also employed and formulae are developed in the case of certain quadratic actions giving the propagator exactly the method is flexible enough embracing all explicitly known cases of two time quadratic actions and in addition enabling further cases to be treated an example of this nature is given explicitly

on second moment properties of median filtered sequences of independent data in this paper we present the derivation of the bivariate distribution function for median filtered sequences of independent arbitrary second order random variables this result is then used to qualitatively analyze second moment properties of median filtered data the results hint towards a low pass characteristic of the median filters and a low dependency of the output spectrum on input alphabet size and distribution

diffusion and reaction in random media and models of evolution processes a diffusion equation including source terms representing randomly distributed sources and sinks is considered for quasilinear growth rates the eigenvalue problem is equivalent to that of the quantum mechanical motion of electrons in random fields correspondingly there exist localized and extended density distributions dependent on the statistics of the random field and on the dimension of the space besides applications in physics nonequilibrium processes in pumped disordered solid materials a new evolution model is discussed which considers evolution as hill climbing in a random landscape

continuous integral kernels for unbounded schrodinger semigroups and their spectral projections abstract by suitably extending a feynman kac formula of simon canad math soc conf proc 28 2000 317 we study one parameter semigroups generated by the negative of rather general schrodinger operators which may be unbounded from below and include a magnetic vector potential in particular a common domain of essential self adjointness for such a semigroup is specified moreover each member of the semigroup is proven to be a maximal carleman operator with a continuous integral kernel given by a brownian bridge expectation the results are used to show that the spectral projections of the generating schrodinger operator also act as carleman operators with continuous integral kernels applications to schrodinger operators with rather general random scalar potentials include a rigorous justification of an integral kernel representation of their integrated density of states a relation frequently used in the physics literature on disordered solids

classifying mammographic lesions using computerized image analysis the classification of 3 common breast lesions fibroadenomas cysts and cancers was achieved using computerized image analysis of tumor shape in conjunction with patient age the process involved the digitization of 69 mammographic images using a video camera and a commercial frame grabber on a pc based computer system an interactive segmentation procedure identified the tumor boundary using a thresholding technique which successfully segmented 57 of the lesions several features were chosen based on the gross and fine shape describing properties of the tumor boundaries as seen on the radiographs patient age was included as a significant feature in determining whether the tumor was a cyst fibroadenoma or cancer and was the only patient history information available for this study the concept of a radial length measure provided a basis from which 6 of the 7 shape describing features were chosen the seventh being tumor circularity the feature selection process was accomplished using linear discriminant analysis and a euclidean distance metric determined group membership the effectiveness of the classification scheme was tested using both the apparent and the leaving one out test methods the best results using the apparent test method resulted in correctly classifying 82 of the tumors segmented using the entire feature space and the highest classification rate using the leaving one out test method was 69 using a subset of the feature space the results using only the shape descriptors and excluding patient age resulted in correctly classifying 72 using the entire feature space except age and 51 using a subset of the feature space

measures of acutance and shape for classification of breast tumors most benign breast tumors possess well defined sharp boundaries that delineate them from surrounding tissues as opposed to malignant tumors computer techniques proposed to date for tumor analysis have concentrated on shape factors of tumor regions and texture measures while shape measures based on contours of tumor regions can indicate differences in shape complexities between circumscribed and spiculated tumors they are not designed to characterize the density variations across the boundary of a tumor here the authors propose a region based measure of image edge profile acutance which characterizes the transition in density of a region of interest roi along normals to the roi at every boundary pixel the authors investigate the potential of acutance in quantifying the sharpness of the boundaries of tumors and propose its application to discriminate between benign and malignant mammographic tumors in addition they study the complementary use of various shape factors based upon the shape of the roi such as compactness fourier descriptors moments and chord length statistics to distinguish between circumscribed and spiculated tumors thirty nine images from the mammographic image analysis society mias database and an additional set of 15 local cases were selected for this study the cases included 16 circumscribed benign 7 circumscribed malignant 12 spiculated benign and 19 spiculated malignant lesions all diagnoses were proven by pathologic examinations of resected tissue the contours of the lesions were first marked by an expert radiologist using x paint and x windows on a sun sparcstation 2 workstation for computation of acutance the roi boundaries were iteratively approximated using a split merge and end point adjustment technique to obtain the best fitting polygonal approximation the jackknife method using the mahalanobis distance measure in the bmdp biomedical programs package was used for classification of the lesions using acutance and the shape factors as features in various combinations acutance alone resulted in a benign malignant classification accuracy of 95 the mias cases compactness alone gave a circumscribed spiculated classification rate of 92 3 with the mias cases acutance in combination with a moment based shape measure and a fourier descriptor based measure gave four group classification rate of 95 with the mias cases the results indicate the importance of including lesion edge definition with shape information for classification of tumors and that the proposed measure of acutance fills this need

a fast and well conditioned spectral method a spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients and general boundary conditions the method leads to matrices that are al

arnold winther mixed finite elements for stokes eigenvalue problems this paper is devoted to study the arnold winther mixed finite element method for two dimensional stokes eigenvalue problems using the stress velocity formulation a priori error estimates for the eigenvalue and eigenfunction errors are presented to improve the approximation for both eigenvalues and eigenfunctions we propose a local post processing with the help of the local post processing we derive a reliable a posteriori error estimator which is shown to be empirically efficient we confirm numerically the proven higher order convergence of the post processed eigenvalues for convex domains with smooth eigenfunctions on adaptively refined meshes we obtain numerically optimal higher orders of convergence of the post processed eigenvalues even on nonconvex domains

tumor detection in nonstationary backgrounds the authors introduce two detectors which they use to locate simulated tumors of fixed size in clinical gamma ray images the first method was conceived when it was observed that small tumors possess an identifiable signature in curvature feature space where curvature is the local curvature of the image data when viewed as a relief map computed curvature values are mapped to a normalized significance space using a windowed statistic the resulting test statistic is thresholded at a chosen level of significance to give a positive detection nonuniform anatomic background activity is effectively suppressed the second detector is an adaptive prewhitening matched filter which uses a form of preprocessing known as statistical scaling to adaptively prewhiten the background tests are performed using simulated gaussian shaped tumors superimposed on twelve clinical gamma ray images when the tumors to be detected are small less than 3 pixels in diameter the curvature detector out performs the matched filter in true positive false positive tests a mean true positive rate of 95 at one false positive per image is achieved when the local signal to noise ratio of the tumor background is spl ges 2 at larger tumor sizes the best performance is displayed by a different form of matched filter namely the statistical correlation function proposed by pratt 1991

the mini mixed finite element for the stokes problem an experimental investigation abstract o h 3 2 superconvergence in pressure and velocity has been experimentally investigated for the two dimensional stokes problem discretized with the mini mixed finite element even though the classic mixed finite element theory for the mini element guarantees linear convergence for the total error recent theoretical results indicate that superconvergence of order o h 3 2 in pressure and of the linear part of the computed velocity to the piecewise linear nodal interpolation of the exact velocity is in fact possible with structured three directional triangular meshes the numerical experiments presented here suggest a more general validity of o h 3 2 superconvergence possibly to automatically generated and unstructured triangulations in addition the approximating properties of the complete computed velocity have been compared with the approximating properties of the piecewise linear part of the computed velocity finding that the former is generally closer to the exact velocity whereas the latter conserves mass better

a generalization of median filtering using linear combinations of order statistics we consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence assuming a constant signal in white noise the coefficients in the linear combination are chosen to minimize the output mse for several noise distributions it is shown that the optimal order statistic filter osf tends toward the median filter as the noise becomes more impulsive the optimal osf is applied to an actual noisy image and is shown to perform well combining properties of both the averaging and median filters a more general design scheme for applications involving nonconstant signals is also given

a stabilized finite element method for the two field and three field stokes eigenvalue problems in this paper the stabilized finite element approximation of the stokes eigenvalue problems is considered for both the two field displacement pressure and the three field stress displacement pressure formulations the method presented is based on a subgrid scale concept and depends on the approximation of the unresolvable scales of the continuous solution in general subgrid scale techniques consist in the addition of a residual based term to the basic galerkin formulation the application of a standard residual based stabilization method to a linear eigenvalue problem leads to a quadratic eigenvalue problem in discrete form which is physically inconvenient as a distinguished feature of the present study we take the space of the unresolved subscales orthogonal to the finite element space which promises a remedy to the above mentioned complication in essence we put forward that only if the orthogonal projection is used the residual is simplified and the use of term by term stabilization is allowed thus we do not need to put the whole residual in the formulation and the linear eigenproblem form is recovered properly we prove that the method applied is convergent and present the error estimates for the eigenvalues and the eigenfunctions we report several numerical tests in order to illustrate that the theoretical results are validated

long time asymptotics of diffusion in random media and related problems for n dimensional diffusion in gaussian random fields with continuous and singular covariances the leading long time behaviour of the averaged population is derived by estimating brownian motion expectations it is shown how these results are related to the leading low energy behaviour of the density of states for a particle in a corresponding random potential and to the strong coupling limit of the free energy of the pekar frolich polaron

partition function of a particle subject to gaussian noise we study the averaged partition function for a quantum particle subjected to gaussian noise using the path integral representation the noise is characterized by a covariance function with a strength and a range it falls off rapidly with distance but the analytic form at short distances and the dimensionality are important the remaining parameter is the thermal length of the particle for a finite range we study the behavior of the partition function over the entire domain of strengths and thermal lengths the techniques used are successively more accurate upper and lower bounds that include contributions from configurations involving traps particular attention is paid to a self consistent field analysis lower bound and to a nonlocal quadratic action bound we also study the white noise limit i e vanishing range with finite values of the other parameters in one dimension the white noise limit leads to convergent results in three or higher dimensions the divergent terms can be isolated and computed in two dimensions the degree of divergences changes at a finite value of the product of the strength and thermal length squared

refined saddle point preconditioners for discretized stokes problems this paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints we establish theory which shows that including a simple scaling within well established block diagonal preconditioners for stokes problems can result in significantly faster convergence when applying the preconditioned minres method the codes used in the numerical studies are available online

statistical mechanics of eigen s evolution model the correspondence between eigen s model of macromolecular evolution and the equilibrium statistical mechanics of an inhomogeneous ising system is developed the free energy landscape of random ising systems with the hopfield hamiltonian as a special example is applied to the replication rate coefficient landscape the coupling constants are scaled with 1 l since the maxima of any landscape must not increase with the length of the macromolecules the calculated error threshold relation then agrees with eigen s expression which was derived in a different way it gives an explicit expression for the superiority parameter in terms of the parameters of the landscape the dynamics of selection and evolution is discussed

explicit evaluation of a path integral with memory kernel an explicit expression is presented for the path integral of an harmonic oscillator interacting with itself in the past the time dependence of the memory kernel is assumed to be exponential the relation with the feynman trial action for the variational calculation of the polaron ground state energy is discussed

functional integral approach for diffusion in a random media the authors present a local functional integral representation for the random diffusion equation studied by kardar parisi and zhang 1986

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

the automatic solution of partial differential equations using a global spectral method a spectral method for solving linear partial differential equations pdes with variable coefficients and general boundary conditions defined on rectangular domains is described based on separable representations of partial differential operators and the one dimensional ultraspherical spectral method if a partial differential operator is of splitting rank 2 such as the operator associated with poisson or helmholtz the corresponding pde is solved via a generalized sylvester matrix equation and a bivariate polynomial approximation of the solution of degree n x n y is computed in o n x n y 3 2 operations partial differential operators of splitting rank 3 are solved via a linear system involving a block banded matrix in o min n x 3 n y n x n y 3 operations numerical examples demonstrate the applicability of our 2d spectral method to a broad class of pdes which includes elliptic and dispersive time evolution equations the resulting pde solver is written in matlab and is publicly available as part of chebfun it can resolve solutions requiring over a million degrees of freedom in under 60 seconds an experimental implementation in the julia language can currently perform the same solve in 10 seconds

explicit evaluation of certain gaussian functional integrals arising in problems of statistical physics an explicit formula is presented for a conditional wiener integral the integrand of which is an exponential of a general quadratic functional of the path the functional integrals arising in non markovian gaussian approximations to various problems of statistical physics e g theory of the large polaron theory of disordered systems are easily recovered as special cases

path integration of a two time quadratic action path integration of a general two time quadratic action characterising memory effects is performed within the framework of feynman s polygonal path approach explicit evaluation of the propagator in exact analytical form is further carried out for the specific kernel used by feynman in the polaron problem

spectral differencing with a twist spectral collocation methods have become very useful in providing highly accurate solutions to differential equations a straightforward implementation of these methods involves the use of spectral differentiation matrices to obtain optimal accuracy these matrices must be computed carefully we demonstrate that naive algorithms for computing these matrices suffer from severe loss of accuracy due to roundoff errors several improvements are analyzed and compared a number of numerical examples are provided demonstrating significant differences between the sensitivity of the forward problem and the inverse problem

unbiased monte carlo evaluation of certain functional integrals abstract a monte carlo algorithm for the evaluation of certain functional integrals is introduced this algorithm is not based on the approximation of the functional integral by a finite dimensional integral unbiased estimators for the functional integrals are constructed and corresponding variance reduction techniques are considered numerical results of simulation studies are presented

multi space reduced basis preconditioners for parametrized stokes equations abstract we introduce a two level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element fe discretization of parametrized stokes equations this preconditioner extends the multi space reduced basis msrb preconditioning method proposed in dal santo et al 2018 it combines an approximated block fine grid preconditioner with a reduced basis rb solver which plays the role of coarse component a sequence of rb spaces constructed either with an enriched velocity formulation or a petrov galerkin projection is built each rb coarse component is defined to perform a single iteration of the iterative method at hand the flexible gmres fgmres algorithm is employed to solve the resulting preconditioned system and targets small tolerances with a very small iteration count and in a very short time numerical test cases for stokes flows in three dimensional parameter dependent geometries are considered to assess the numerical properties of the proposed technique in different large scale computational settings