some small unipotent representations of indefinite orthogonal groups abstract we study a family of small unitary representations of indefinite orthogonal groups these representations arise as analytic continuations of the discrete series and were studied extensively by knapp in k3 we complete knapp s analysis by proving that they are irreducible in order to do so we prove that the representations are unipotent and have irreducible associated cycles in which all multiplicities are exactly one moreover we prove that the k type structure of each representation matches up to a shift the k type structure of the ring of functions on the closure a nilpotent k c orbit on p

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

on certain distinguished unitary representations supported on null cones let inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i or inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i and let g u p q inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i be the isometry group of a inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 05i hermitian form of signature p q for 2 n min p q we consider the action of g on v n the direct sum of n copies of the standard module v inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 06i and the associated action of g on the regular part of the null cone denoted by x 00 we show that there is a commuting set of g invariant differential operators acting on the space of c functions on x 00 which transform according to a distinguished gl n inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 07i character and the resulting kernel is an irreducible unitary representation of g our result can be interpreted as providing a geometric construction of the theta lift of the characters from the group g u n n or o 4 n the construction and approach here follow a previous work of zhu and huang representation theory 1 1997 where the group concerned is g o p q with p q even

special prehomogeneous vector spaces associated to f4 e6 e7 e8 and simple jordan algebras of rank 3 abstract a simple complex lie algebra has a natural grading g g 2 g 1 g 0 g 1 g 2 associated to the highest root it is related to the quaternionic real form of g the real rank of the associated symmetric space is shown to be at most 4 when the rank is equal to 4 i e g a n c n g 2 the semi simple lie algebra m g 0 g 0 is shown to be the conformal algebra of a rank 3 semi simple jordan algebra v if g is one of the four exceptional lie algebras f4 e6 e7 e8 then v is simple the vector space g 1 is a prehomogeneous vector space under the action of m c where m int m is the adjoint group of m it admits a non zero m invariant polynomial of degree 4 conversely to any simple jordan algebra v of rank 3 is naturally associated a representation of a twofold covering of its conformal group co v on a vector space w such that w is a prehomogeneous vector space under the action of co v c an invariant polynomial of degree 4 is explicitly constructed a geometric description of all the orbits of co v in w is given

on twistor transformations and invariant differential operator of simple lie group g2 2 the twistor transformations associated to the simple lie group g2 are described explicitly we consider the double fibration g2 p2 g2 b g2 p1 where p1 and p2 are two parabolic subgroups of g2 and b is a borel subgroup and its local version h2 f h1 where h1 is the heisenberg group of dimension 5 embedded in the coset space g2 p1 f cp1 h1 and h2 contains the nilpotent lie group h2 of step three the baker campbell hausdorff formula is used to parametrize the coset spaces coordinates charts their transition functions and the fibers of the projection as complex curves we write down the relative de rham sequence on f along the fibers and push it down to h1 to get a family of matrix valued differential operators dk then we establish a kind of penrose correspondence for g2 the kernel of dk is isomorphic to the first cohomology of the sheaf o k over h2 we also give the penrose type integral transformation u pf for f o k which gives solutions to equations dku 0 when restricted to the re

detection of stellate distortions in mammograms malignant densities in mammograms have an irregular appearance and frequently are surrounded by a radiating pattern of linear spicules in this paper a method is described to detect such stellate patterns this method is based on statistical analysis of a map of pixel orientations if an increase of pixels pointing to a region is found this region is marked as suspicious especially if such an increase is found in many directions orientations of the image intensity map are determined at each pixel using a multiscale approach at a given scale accurate line based orientation estimates are obtained from the output of three directional second order gaussian derivative operators the orientation at the scale at which these operators have maximum response is selected if a line like structure is present at a given site this method provides an estimate of the orientation of this structure whereas in other cases the image noise will generate a random orientation the pixel orientation map is used to construct two operators which are sensitive to radial patterns of straight lines combination of the output of these operators using a classifier allows for detection of stellate patterns different classification methods have been compared and results obtained on a common database are presented around 90 of the malignant cases were detected at rate of one false positive fp per image

amplitude frequency relationship obtained using hamiltonian approach for oscillators with sum of non integer order nonlinearities in this paper the hamiltonian approximate analytical approach is extended for solving vibrations of conservative oscillators with the sum of integer and or non integer order strong nonlinearities solution of the nonlinear differential equation is assumed in the form of a trigonometric function with unknown frequency the frequency equation is obtained based on the hypothesis that the derivative of the hamiltonian in amplitude of vibration is zero the accuracy of the approximate solution is treated with two different approaches comparing the analytical value for period of vibration with the period obtained numerically and developing an error estimation method based on the ratio between the averaged residual function and the total constant energy of system the procedures given in the paper are applied for two types of examples an oscillator with a strong nonlinear term and an oscillator where the nonlinearity is of polynomial type

restrictions of quaternionic representations in a paper by gross and wallach 1996 j reine angew math 481 73 123 the k types of the continuations of the quaternionic discrete series of a quaternionic lie group g are associated with projective orbits o of certain subgroups in g c in this paper we will show that the restrictions of the representations to quaternionic subgroups are closely related with the intersection of the zariski closure of o with hyperplanes we apply this to the minimal representations of the exceptional groups of real rank 4 and investigate the correspondences of certain compact dual pairs

comments on the method of harmonic balance the advantages and limitations of the harmonic balance or describing function approximation scheme for solving nonlinear ordinary differential equations of oscillatory motion are discussed advantages include appicability to equations of any order and with large degrees of nonlinearity ease of determining limit cycle behavior and its stability and overall speed and efficiency the limitation rules are essentially those described by mickens 1983 it is pointed out that perturbation procedures provide better results when the degree of nonlinearity is small

hypotheses for image features icons and textons we review ideas about the relationship between qualitative description of local image structure and quantitative description based on responses to a family of linear filters we propose a sequence of three linking hypotheses the first the feature hypothesis is that qualitative descriptions arise from a category system on filter response space the second the icon hypothesis is that the partitioning into categories of filter response space is determined by a system of iconic images one associated with each point of the space the third the texton hypothesis is that the correct images to play the role of icons are those that are the most likely explanations of a vector of filter responses we present results in support of these three hypotheses including new results on 2 d 1st order structure

classification of minimal representations of real simple lie groups based on an idea by gan and savin represent theory 9 46 93 2005 we give a classification of minimal representations of connected simple real lie groups not of type a actually we prove that there exist no new minimal representations up to infinitesimal equivalence

the structure of locally orderless images we propose a representation of images in which a global but not a local topology is defined the topology is restricted to resolutions up to the extent of the local region of interest roi although the roi s may contain many pixels there is no spatial order on the pixels within the roi the only information preserved is the histogram of pixel values within the roi s this can be considered as an extreme case of a textel texture element image the histogram is the limit of texture where the spatial order has been completely disregarded we argue that locally orderless images are ubiquitous in perception and the visual arts formally the orderless images are most aptly described by three mutually intertwined scale spaces the scale parameters correspond to the pixellation inner scale the extent of the roi s outer scale and the resolution in the histogram tonal scale we describe how to construct locally orderless images how to render them and how to use them in a variety of local and global image processing operations

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

realization of quaternionic discrete series on the unit ball in h d abstract we give a realization for the quaternionic discrete series for the group sp 1 d as the kernel of certain elementary cauchy riemann fueter operator and we compute the corresponding reproducing kernels

quasi conformal actions quaternionic discrete series and twistors su 2 1 and g 2 2 quasi conformal actions were introduced in the physics literature as a generalization of the familiar fractional linear action on the upper half plane to hermitian symmetric tube domains based on arbitrary jordan algebras and further to arbitrary freudenthal triple systems in the mathematics literature quaternionic discrete series unitary representations of real reductive groups in their quaternionic real form were constructed as degree 1 cohomology on the twistor spaces of symmetric quaternionic kahler spaces these two constructions are essentially identical as we show explicitly for the two rank 2 cases su 2 1 and g2 2 we obtain explicit results for certain principal series quaternionic discrete series and minimal representations of these groups including formulas for the lowest k types in various polarizations we expect our results to have applications to topological strings black hole micro state counting and to the theory of automorphic forms

complexity regularized image denoising we study a new approach to image denoising based on complexity regularization this technique presents a flexible alternative to the more conventional l sup 2 l sup 1 and besov regularization methods different complexity measures are considered in particular those induced by state of the art image coders we focus on a gaussian denoising problem and derive a connection between complexity regularized denoising and operational rate distortion optimization this connection suggests the use of efficient algorithms for computing complexity regularized estimates bounds on denoising performance are derived in terms of an index of resolvability that characterizes the compressibility of the true image comparisons with state of the art denoising algorithms are given

fourier jacobi expansion of automorphic forms on sp 1 q generating quaternionic discrete series abstract the aim of this paper is to develop the notion of the fourier expansion of automorphic forms on sp 1 q generating quaternionic discrete series which are non holomorphic forms there is such an expansion given by tsuneo arakawa assuming the boundedness of the forms and the integrability of the discrete series we study these automorphic forms without such assumptions when q 1 we prove the koecher principle for such automorphic forms whose validity is known for holomorphic automorphic forms except elliptic modular forms

the sextonions and e712 we fill in the hole in the exceptional series of lie algebras that was observed by cvitanovic deligne cohen and deman more precisely we show that the intermediate lie algebra between e7 and e8 satisfies some of the decomposition and dimension formulas of the exceptional simple lie algebras a key role is played by the sextonions a six dimensional algebra between the quaternions and octonions using the sextonions we show similar results hold for the rows of an expanded freudenthal magic chart we also obtain new interpretations of the adjoint variety of the exceptional group g2

maximum likelihood orientation estimation of 1 d patterns in laguerre gauss subspaces a method for measuring the orientation of linear 1 d patterns based on a local expansion with laguerre gauss circular harmonic lg ch functions is presented it lies on the property that the polar separable lg ch functions span the same space as the 2 d cartesian separable hermite gauss 2 d hg functions exploiting the simple steerability of the lg ch functions and the peculiar block linear relationship among the two expansion coefficients sets maximum likelihood ml estimates of orientation and cross section parameters of 1 d patterns are obtained projecting them in a proper subspace of the 2 d hg family it is shown in this paper that the conditional ml solution derived by elimination of the cross section parameters surprisingly yields the same asymptotic accuracy as the ml solution for known cross section parameters the accuracy of the conditional ml estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials a thorough proof of the key relationship between the lg ch and the 2 d hg expansions is also provided

asymptotic methods for vibrations of the pure non integer order oscillator in this paper oscillators with a restoring force which is the function of a non integer power exponent of deflection are considered the oscillatory motion is described by a differential equation with a rational power term the equation is first analyzed qualitatively the new analytical methods are developed for solving the differential equation with a non integer order term the methods are based on the assumption that the vibration of the non integer oscillator has to be close to that of integer order one the new perturbation method based on variation of the order of the non linearity is developed the unperturbed system is the integer order non linear oscillator one of the methods uses the perturbation of the amplitude and phase and the following two techniques introduce the straightforward expansion using the known values for the pure integer order oscillators the first order approximate solutions are obtained their accuracy is checked on several examples the results obtained are compared with the exact numerical solution showing good agreement the vibrations are widely discussed

nilpotent orbits and some small unitary representations of indefinite orthogonal groups abstract for 2 m l 2 let g be a simply connected lie group with g 0 so 2m 2l 2m as lie algebra let g k p be the complexification of the usual cartan decomposition let k be the analytic subgroup with lie algebra k g 0 and let u g be the universal enveloping algebra of g this work examines the unitarity and k spectrum of representations in the analytic continuation of discrete series of g relating these properties to orbits in the nilpotent radical of a certain parabolic subalgebra of g the roots with respect to the usual compact cartan subalgebra are all ei ej with 1 i q l u be the parabolic subalgebra of g for which em em 1 contributes to u and the other simple roots contribute to l let l be the analytic subgroup of g with lie algebra l g 0 let l c int g l let 2 u be the sum of the roots contributing to u and let q l u be the parabolic subalgebra opposite to q the members of u p are nilpotent members of g the group l c acts on u p with finitely many orbits and the topological closure of each orbit is an irreducible algebraic variety if y is one of these varieties let r y be the dual coordinate ring of y this is a quotient of the algebra of symmetric tensors on u p that carries a fully reducible representation of l c for s z let s k 1 m l s 2 e k then s defines a one dimensional l l module c s extend this to a q l module by having u act by 0 and define n s 2 u u g q c s 2 u let n s 2 u be the unique irreducible quotient of n s 2 u the representations under study are s s n s 2 u and s s n s 2 u where s dim u k and s is the sth derived bernstein functor for s 2l 2 it is known that s s and that s is in the discrete series enright parthsarathy wallach and wolf showed for m s 2l 2 that s s and that s is still unitary the present paper shows that s is unitary for 0 s m 1 even though s s and it relates the k spectrum of the representations s to the representation of l c on a suitable r y with y depending on s use of a branching formula of d e littlewood allows one to obtain an explicit multiplicity formula for each k type in s the variety y is indispensable in the proof the chief tools involved are an idea of b gross and wallach a geometric interpretation of littlewood s theorem and some estimates of norms it is shown further that the natural invariant hermitian form on s does not make s unitary for s l c on any r y a final section of the paper treats in similar fashion the simply connected lie group with lie algebra g 0 so 2m 2l 2m 1 2 m l 2

a distance measure and a feature likelihood map concept for scale invariant model matching this paper presents two approaches for evaluating multi scale feature based object models within the first approach a scale invariant distance measure is proposed for comparing two image representations in terms of multi scale features based on this measure the maximisation of the likelihood of parameterised feature models allows for simultaneous model selection and parameter estimation the idea of the second approach is to avoid an explicit feature extraction step and to evaluate models using a function defined directly from the image data for this purpose we propose the concept of a feature likelihood map which is a function normalised to the interval 0 1 and that approximates the likelihood of image features at all points in scale space to illustrate the applicability of both methods we consider the area of hand gesture analysis and show how the proposed evaluation schemes can be integrated within a particle filtering approach for performing simultaneous tracking and recognition of hand models under variations in the position orientation size and posture of the hand the experiments demonstrate the feasibility of the approach and that real time performance can be obtained by pyramid implementations of the proposed concepts

a notion of rank for unitary representations of reductive groups based on kirillov s orbit method we introduce a new notion of rank for unitary representations of semisimple groups over a local field of characteristic zero the theory is based on kirillov s method of orbits for nilpotent groups over local fields when the semisimple group is a classical group we prove that the new theory is essentially equivalent to howe s theory of n rank see ho4 l2 sc therefore our results provide a systematic generalization of the notion of a small representation in the sense of howe to exceptional groups however unlike previous works that used ad hoc methods to study different types of classical groups and some exceptional ones see we ls our definition is simultaneously applicable to both classical and exceptional groups the most important result of this article is a general purity result for unitary representations which demonstrates how similar partial results in these authors works should be formulated and proved for an arbitrary semisimple group in the language of kirillov s theory the purity result is a crucial step toward studying small representations of exceptional groups new results concerning small unitary representations of exceptional groups will be published in a forthcoming paper s

computerized radiographic mass detection i lesion site selection by morphological enhancement and contextual segmentation this paper presents a statistical model supported approach for enhanced segmentation and extraction of suspicious mass areas from mammographic images with an appropriate statistical description of various discriminate characteristics of both true and false candidates from the localized areas an improved mass detection may be achieved in computer assisted diagnosis cad in this study one type of morphological operation is derived to enhance disease patterns of suspected masses by cleaning up unrelated background clutters and a model based image segmentation is performed to localize the suspected mass areas using a stochastic relaxation labeling scheme we discuss the importance of model selection when a finite generalized gaussian mixture is employed and use the information theoretic criteria to determine the optimal model structure and parameters examples are presented to show the effectiveness of the proposed methods on mass lesion enhancement and segmentation when applied to mammographical images experimental results demonstrate that the proposed method achieves a very satisfactory performance as a preprocessing procedure for mass detection in cad

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

local orientation analysis in images by means of the hermite transform we introduce new theoretical results on how the local differential structure in images can be described processed and coded efficiently by means of the hermite transform it is shown that the hermite transform can take many alternative forms all of which have their specific advantages the various forms of the hermite transform correspond to different ways of coding the local orientation in the image and we describe a systematic theory based on well known principles from vector spaces for deriving such alternative forms one specific case called the sampled hermite transform is shown to be especially interesting for adaptive image processing and coding an application in the field of adaptive noise reduction is included by way of illustration

shape from focus using fast discrete curvelet transform a new method for focus measure computation is proposed to reconstruct 3d shape using image sequence acquired under varying focus plane adaptive histogram equalization is applied to enhance varying contrast across different image regions for better detection of sharp intensity variations fast discrete curvelet transform fdct is employed for enhanced representation of singularities along curves in an input image followed by noise removal using bivariate shrinkage scheme based on locally estimated variance the fdct coefficients with high activity are exploited to detect high frequency variations of pixel intensities in a sequence of images finally focus measure is computed utilizing neighborhood support of these coefficients to reconstruct the shape and a well focused image of the scene being probed

minimal unitary representation of su 2 2 and its deformations as massless conformal fields and their supersymmetric extensions we study the minimal unitary representation minrep of so 4 2 over a hilbert space of functions of three variables obtained by quantizing its quasiconformal action on a five dimensional space the minrep of so 4 2 which coincides with the minrep of su 2 2 similarly constructed corresponds to a massless conformal scalar in four space time dimensions there exists a one parameter family of deformations of the minrep of su 2 2 for positive negative integer values of the deformation parameter one obtains positive energy unitary irreducible representations corresponding to massless conformal fields transforming in 0 2 2 0 representation of the sl 2 c subgroup we construct the supersymmetric extensions of the minrep of su 2 2 and its deformations to those of su 2 2 n the minimal unitary supermultiplet of su 2 2 4 in the undeformed case simply corresponds to the massless n 4 yang mills supermultiplet in four dimensions for each given nonzero integer value of one obtains a uniq

the improbability of harris interest points an elementary characterization of the map underlying harris corners also known as harris interest points or key points is provided two principal and basic assumptions made are 1 local image structure is captured in an uncommitted way simply using weighted raw image values around every image location to describe the local image information and 2 the lower the probability of observing the image structure present in a particular point the more salient or interesting this position is i e saliency is related to how uncommon it is to see a certain image structure how surprising it is through the latter assumption the axiomatization proposed makes a sound link between image saliency in computer vision on the one hand and on the other computational models of preattentive human visual perception where exactly the same definition of saliency has been proposed because of this link the characterization provides a compelling case in favor of harris interest points over other approaches

multiresolution detection of spiculated lesions in digital mammograms we present a novel multiresolution scheme for the detection of spiculated lesions in digital mammograms first a multiresolution representation of the original mammogram is obtained using a linear phase nonseparable two dimensional 2 d wavelet transform a set of features is then extracted at each resolution in the wavelet pyramid for every pixel this approach addresses the difficulty of predetermining the neighborhood size for feature extraction to characterize objects that may appear in different sizes detection is performed from the coarsest resolution to the finest resolution using a binary tree classifier this top down approach requires less computation by starting with the least amount of data and propagating detection results to finer resolutions experimental results using the mias image database have shown that this algorithm is capable of detecting spiculated lesions of very different sizes at low false positive rates

d4 modular forms in this paper we study modular forms on two simply connected groups of type d 4 over q one group g s is a globally split group of type d 4 viewed as the group of isotopies of the split rational octonions the other g c is the isotopy group of the rational nonsplit octonions we study automorphic forms on g s in analogy to the work of gross gan and savin on g 2 namely we study automorphic forms whose component at infinity corresponds to a quaternionic discrete series representation we study automorphic forms on g c using gross s formalism of algebraic modular forms finally we follow work of gan savin gross rallis and others to study an exceptional theta correspondence connecting modular forms on g c and g s this can be thought of as an octonionic generalization of the jacquet langlands correspondence

detection of architectural distortion in prior mammograms we present methods for the detection of sites of architectural distortion in prior mammograms of interval cancer cases we hypothesize that screening mammograms obtained prior to the detection of cancer could contain subtle signs of early stages of breast cancer in particular architectural distortion the methods are based upon gabor filters phase portrait analysis a novel method for the analysis of the angular spread of power fractal analysis laws texture energy measures derived from geometrically transformed regions of interest rois and haralick s texture features with gabor filters and phase portrait analysis 4224 rois were automatically obtained from 106 prior mammograms of 56 interval cancer cases including 301 true positive rois related to architectural distortion and from 52 mammograms of 13 normal cases for each roi the fractal dimension the entropy of the angular spread of power 10 laws measures and haralick s 14 features were computed the areas under the receiver operating characteristic curves obtained using the features selected by stepwise logistic regression and the leave one roi out method are 0 76 with the bayesian classifier 0 75 with fisher linear discriminant analysis and 0 78 with a single layer feed forward neural network free response receiver operating characteristics indicated sensitivities of 0 80 and 0 90 at 5 8 and 8 1 false positives per image respectively with the bayesian classifier and the leave one image out method

global error minimization method for solving strongly nonlinear oscillator differential equations a modified variational approach called global error minimization gem method is developed for obtaining an approximate closed form analytical solution for nonlinear oscillator differential equations the proposed method converts the nonlinear differential equation to an equivalent minimization problem a trial solution is selected with unknown parameters next the gem method is used to solve the minimization problem and to obtain the unknown parameters this will yield the approximate analytical solution of the nonlinear ordinary differential equations odes this approach is simple accurate and straightforward to use in identifying the solution to illustrate the effectiveness and convenience of the suggested procedure a cubic duffing equation with strong nonlinearity is considered comparisons are made between results obtained by the proposed gem method the exact solution and results from five recently published methods for addressing duffing oscillators the maximal relative error for the frequency obtained by the gem method compared with the exact solution is 0 0004 which indicates the remarkable precision of the gem method

jordan algebras exceptional groups and bhargava composition abstract we consider an integral version of the freudenthal construction relating jordan algebras and exceptional algebraic groups we show how this construction is related to higher composition laws of m bhargava in number theory we propose an algorithmic approach to studying orbit spaces of groups underlying bhargava s higher composition laws using this method we discover two new examples of spaces sharing similar properties and indicate several more examples of spaces where such composition laws may be introduced

theta lifting from elliptic cusp forms to automorphic forms on sp 1 q tsuneo arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on sp 1 q in his unpublished note which was inspired by kudla lifting i e a theta lifting from elliptic modular forms to holomorphic automorphic forms on su 1 q we prove that the images of arakawa s theta lifting belong to the space of bounded automorphic forms generating quaternionic discrete series which are non holomorphic forms in the appendix we provide the construction of eisenstein series and poincare series generating such discrete series

improved lindstedt poincare method for the solution of nonlinear problems abstract we apply the linear delta expansion lde to the lindstedt poincare distorted time method to find improved approximate solutions to nonlinear problems we find that our method works very well for a wide range of parameters in the case of the anharmonic oscillator duffing equation of the non linear pendulum and of more general anharmonic potentials the approximate solutions found with this method converge more rapidly to the exact ones than in the simple lindstedt poincare method

on the truly nonlinear oscillator with positive and negative damping in this paper the oscillator with a restoring force of rational order of nonlinearity named truly nonlinear oscillators and damping positive and negative is considered the mathematical model of the oscillator is a second order differential equation with nonlinear terms of integer or noninteger and also linear and nonlinear damping terms the approximate solution of the generating differential equation only the nonlinear deflection and linear viscous damping terms exist in the form of the ateb function is obtained using the harmonic balance method based on the generating solution the vibrations of the oscillator with damping are obtained by extending the method of time variable amplitude frequency and phase the special attention is given to the truly nonlinear damped van der pol oscillator the interaction of the viscous and van der pol damping on the motion of the truly nonlinear oscillator is investigated the boundary for the limit cycle motion depending on the order of nonlinearity is analyzed the interactive influence of the damping coefficients positive and negative and the order of nonlinearity on the frequency and the period of the vibration is also analyzed two numerical examples are considered the approximate analytical solutions are compared with numerically calculated ones the obtained results are in a good agreement

edge and line feature extraction based on covariance models image segmentation based on contour extraction usually involves three stages of image operations feature extraction edge detection and edge linking this paper is devoted to the first stage a method to design feature extractors used to detect edges from noisy and or blurred images the method relies on a model that describes the existence of image discontinuities e g edges in terms of covariance functions the feature extractor transforms the input image into a log likelihood ratio image such an image is a good starting point of the edge detection stage since it represents a balanced trade off between signal to noise ratio and the ability to resolve detailed structures for 1 d signals the performance of the edge detector based on this feature extractor is quantitatively assessed by the so called average risk measure the results are compared with the performances of 1 d edge detectors known from literature generalizations to 2 d operators are given applications on real world images are presented showing the capability of the covariance model to build edge and line feature extractors finally it is shown that the covariance model can be coupled to a mrf model of edge configurations so as to arrive at a maximum a posteriori estimate of the edges or lines in the image

generic neighborhood operators a method that treats linear neighborhood operators within a unified framework that enables linear combinations concatenations resolution changes or rotations of operators to be treated in a canonical manner is presented various families of operators with special kinds of symmetries such as translation rotation magnification are explicitly constructed in 1 d 2 d and 3 d a concept of order is defined and finite orthonormal bases of functions closely connected with the operators of various orders are constructed linear transformations between the various representations are considered the method is based on two fundamental assumptions a decrease of resolution should not introduce spurious detail and the local operators should be self similar under changes of resolution these assumptions merely sum up the even more general need for homogeneity isotropy scale invariance and separability of independent dimensions of front end processing in the absence of a priori information

a hitherto unnoticed singularity of scale space a hitherto unnoticed singularity of scale space occurs only at isolated points in scale space thus it does not generically occur for single images but it can occur occasionally in members of time sequences say it occurs at those critical points of the image at which the laplacean of the illuminance vanishes a nongeneric condition the structure of scale space in an infinitesimal neighborhood of such a singularity is explored the effect of the singularity of mappings between copies of an image at different levels of resolution is evaluated and checked with a numerical calculation

oscillator with fraction order restoring force abstract in this paper a new analytical method for solving the differential equations which describe the motion of the oscillator with fraction order elastic force is introduced using the first integral of motion the exact period of vibration in the form of the euler beta function is obtained based on that value the approximate solution of the strong nonlinear fraction order differential equation is formed the suggested procedure is applied for various fraction values but also for the pure quadratic cubic and quintic oscillators the advantage of the suggested method is that is valid for all fraction values 1 the accuracy of the approximate solution is very high as the period of vibration is exactly analytically determined and is independent on the time in the paper the fraction order differential equation with small linear and nonlinear terms is also considered the krylov bogolubov method is extended due to the fact that frequency of vibration depends on the amplitude of vibration the approximate solution is with time variable amplitude phase and frequency the linear damped fraction order oscillator is widely discussed the approximate solution of the differential equation which describes the vibrations of such oscillator is compared with exact numerical one and shows a good agreement

a differential model of the complex cell the receptive fields of simple cells in the visual cortex can be understood as linear filters these filters can be modeled by gabor functions or gaussian derivatives gabor functions can also be combined in an energy model of the complex cell response this letter proposes an alternative model of the complex cell based on gaussian derivatives it is most important to account for the insensitivity of the complex response to small shifts of the image the new model uses a linear combination of the first few derivative filters at a single position to approximate the first derivative filter at a series of adjacent positions the maximum response over all positions gives a signal that is insensitive to small shifts of the image this model unlike previous approaches is based on the scale space theory of visual processing in particular the complex cell is built from filters that respond to the 2d differential structure of the image the computational aspects of the new model are studied in one and two dimensions using the steerability of the gaussian derivatives the response of the model to basic images such as edges and gratings is derived formally the response to natural images is also evaluated using statistical measures of shift insensitivity the neural implementation and predictions of the model are discussed

accurate analytical solutions to oscillators with discontinuities and fractional power restoring force by means of the optimal homotopy asymptotic method in this paper a new approach combining the features of the homotopy concept with an efficient computational algorithm which provides a simple and rigorous procedure to control the convergence of the solution is proposed to find accurate analytical explicit solutions for some oscillators with discontinuities and a fractional power restoring force which is proportional to sign x a very fast convergence to the exact solution was proved since the second order approximation lead to very accurate results comparisons with numerical results are presented to show the effectiveness of this method four numerical applications prove the accuracy of the method which works very well for the whole range of initial amplitudes the obtained results prove the validity and efficiency of the method which can be easily extended to other strongly nonlinear problems

dual pair correspondences for non linear covers of orthogonal groups abstract in this paper we study compact dual pair correspondences arising from smallest representations of non linear covers of odd orthogonal groups we identify representations appearing in these correspondences with subquotients of cohomologically induced representations

local variance controlled forward and backward diffusion for image enhancement and noise reduction in order to improve signal to noise ratio snr and contrast to noise ratio this paper introduces a local variance controlled forward and backward lvcfab diffusion algorithm for edge enhancement and noise reduction in our algorithm an alternative fab diffusion algorithm is proposed the results for the alternative fab algorithm show better algorithm behavior than other existing diffusion fab approaches furthermore two distinct discontinuity measures and the alternative fab diffusion are incorporated into a lvcfab diffusion algorithm where the joint use of the two measures leads to a complementary effect for preserving edge features in digital images this lvc mechanism adaptively modifies the degree of diffusion at any image location and is dependent on both local gradient and inhomogeneity qualitative experiments based on general digital images and magnetic resonance images show significant improvements when the lvcfab diffusion algorithm is used versus the existing anisotropic diffusion and the previous fab diffusion algorithms for enhancing edge features and improving image contrast quantitative analyses based on peak snr confirm the superiority of the proposed lvcfab diffusion algorithm

mammographic mass segmentation embedding multiple features in vector valued level set in ambiguous regions mammographic mass segmentation plays an important role in computer aided diagnosis systems it is very challenging because masses are always of low contrast with ambiguous margins connected with the normal tissues and of various scales and complex shapes to effectively detect true boundaries of mass regions we propose a feature embedded vector valued contour based level set method with relaxed shape constraint in particular we initially use the contour based level set method to obtain the initial boundaries on the smoothed mammogram as the shape constraint to prevent the contour leaking and meanwhile preserve the radiative characteristics of specific malignant masses afterward we relax the obtained shape constraint by analyzing possible valid regions around the initial boundaries the relaxed shape constraint is then used to design a novel stopping function for subsequent vector valued level set method since texture maps gradient maps and the original intensity map can reflect different characteristics of the mammogram we integrate them together to obtain more accurate segmentation by incorporating the new stopping function into the newly proposed feature embedded vector valued contour based level set method the experimental results suggest that the proposed feature embedded vector valued contour based level set method with relaxed shape constraint can effectively find ambiguous margins of the mass regions comparing against existing active contours methods the new scheme is more effective and robust in detecting complex masses

the generic bilinear calibration estimation problem we identify a very general recurring pattern in a number of well known problems in biological and machine vision many problems are of a peculiar double sided nature one attempts to estimate certain properties of the environment using a certain type of equipment and simultaneously one attempts to calibrate the same equipment on the structure of the environment at first sight this appears the kind of the chicken and the egg problem that might well prove to be insoluble however due to basic constraints that universally apply e g the world is only three dimensional a solution up to a certain class of ambiguity transformations often exists the more complicated the problem is the less important the remaining ambiguity will be at least in a relative sense many well known problems are special in that they can be cast in bilinear form sometimes after transformation or the introduction of dummy variables instances include photometric stereo photometric estimations e g of lightness local differential image operators a variety of photogrammetric problems etc it turns out that many of these problems and together these make up a large fraction of the generic problems in machine vision today can be cast in a simple universal framework this framework enables one to handle arbitrarily large that is not minimal consistent configurations noisy thus inconsistent date sets automatically the level at which prior information either of a deterministic or a statistical nature is used assumptions such as constant albedo rigidity uniform distributions etc is clearly separated as an additional typically nonlinear stage

a non simultaneous variational approach for the oscillators with fractional order power nonlinearities abstract this paper is concerned with a class of conservative oscillators the restitution force of which is of a power form which includes positive non integer exponents it is shown how an approximate lagrangian and hamilton s variational principle can be used to obtain a second order approximate solution for their free vibrations due to the fact that in a general case when the restoring force is multi term the period cannot be obtained from the energy conservation law in a closed form the problem is formulated as a one point boundary value problem and a non simultaneous variation is introduced the explicit expressions for the amplitudes and frequency of oscillations are derived in which there are no restrictions on the values of the non integer powers the analytically obtained results are compared with numerical results as well as with some approximate analytical results from the literature