pairwise rotation invariant co occurrence local binary pattern designing effective features is a fundamental problem in computer vision however it is usually difficult to achieve a great tradeoff between discriminative power and robustness previous works shown that spatial co occurrence can boost the discriminative power of features however the current existing co occurrence features are taking few considerations to the robustness and hence suffering from sensitivity to geometric and photometric variations in this work we study the transform invariance ti of co occurrence features concretely we formally introduce a pairwise transform invariance pti principle and then propose a novel pairwise rotation invariant co occurrence local binary pattern pricolbp feature and further extend it to incorporate multi scale multi orientation and multi channel information different from other lbp variants pricolbp can not only capture the spatial context co occurrence information effectively but also possess rotation invariance we evaluate pricolbp comprehensively on nine benchmark data sets from five different perspectives e g encoding strategy rotation invariance the number of templates speed and discriminative power compared to other lbp variants furthermore we apply pricolbp to six different but related applications texture material flower leaf food and scene classification and demonstrate that pricolbp is efficient effective and of a well balanced tradeoff between the discriminative power and robustness

texture information in run length matrices we use a multilevel dominant eigenvector estimation algorithm to develop a new run length texture feature extraction algorithm that preserves much of the texture information in run length matrices and significantly improves image classification accuracy over traditional run length techniques the advantage of this approach is demonstrated experimentally by the classification of two texture data sets comparisons with other methods demonstrate that the run length matrices contain great discriminatory information and that a good method of extracting such information is of paramount importance to successful classification

nekhoroshev theorem for small amplitude solutions in nonlinear schrodinger equations we prove a nekhoroshev type result 26 27 for the nonlinear schrodinger equation with vanishing or periodic boundary conditions on 0 pi here m in mathbb r is a parameter and varphi mathbb r to mathbb r is a function analytic in a neighborhood of the origin and such that varphi 0 0 varphi 0 not 0 more precisely we consider the cauchy problem for 0 1 with initial data which extend to analytic entire functions of finite order and prove that all the actions of the linearized system are approximate constants of motion up to times growing faster than any negative power of the size of the initial datum the proof is obtained by a method which applies to hamiltonian perturbations of linear pde s with the following properties i the linear dynamics is periodic ii there exists a finite order birkhoff normal form which is integrable and quasi convex as a function of the action variables eq 0 1 satisfies i and ii when restricted to a level surface of left vert u l 2 right vert which is an integral of motion the main technical tool used in the proof is a normal form lemma for systems with symmetry which is also proved here

an averaging theorem for hamiltonian dynamical systems in the thermodynamic limit it is shown how to perform some steps of perturbation theory if one assumes a measure theoretic point of view i e if one renounces to control the evolution of the single trajectories and the attention is restricted to controlling the evolution of the measure of some meaningful subsets of phase space for a system of coupled rotators estimates uniform in n for finite specific energy can be obtained in quite a direct way this is achieved by making reference not to the sup norm but rather following koopman and von neumann to the much weaker l2 norm

recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable on the lattice x s q 2 abstract we give explicitly recurrence relations satisfied by the connection coefficients between two families of the classical orthogonal polynomials of a discrete variable on a non uniform lattice x s q2s i e the q analogues of charlier meixner krawtchouk and hahn polynomials in terms of the coefficients and of the pearson equation satisfied by the weight function and the coefficients of the three term recurrence relation and of two structure relations obeyed by these polynomials

fisher tensors for classifying human epithelial cells analyzing and classifying human epithelial type 2 hep 2 cells using indirect immunofluorescence protocol has been the golden standard for detecting connective tissue diseases such as rheumatoid arthritis however this suffers from numerous shortcomings such as being subjective as well as time and labor intensive recently several studies explore the advantages of artificial systems to automate the process not only to reduce the test turn around time but also to deliver more consistent results in this paper we extend the conventional bag of word models from euclidean space to non euclidean riemannian manifolds and utilize them to classify the hep 2 cells the main motivation comes from the observation that hep 2 cells can be efficiently described by symmetric positive definite matrices which lie on a riemannian manifold with this motivation we first discuss an intrinsic bag of riemannian words model we then propose fisher tensors which can in turn encode additional information about the distribution of the signatures in a bag of word model experiments on two challenging hep 2 images datasets namely icprcontest and snphep 2 show that the proposed methods obtain notable improvements in discrimination accuracy in comparison to baseline and several state of the art methods the proposed framework while hand crafted towards cell classification is a generic framework for object recognition this is supported by assessing the performance of our proposal on a challenging texture classification task

a statistical approach to texture classification from single images we investigate texture classification from single images obtained under unknown viewpoint and illumination a statistical approach is developed where textures are modelled by the joint probability distribution of filter responses this distribution is represented by the frequency histogram of filter response cluster centres textons recognition proceeds from single uncalibrated images and the novelty here is that rotationally invariant filters are used and the filter response space is low dimensional classification performance is compared with the filter banks and methods of leung and malik ijcv 2001 schmid cvpr 2001 and cula and dana ijcv 2004 and it is demonstrated that superior performance is achieved here classification results are presented for all 61 materials in the columbia utrecht texture database we also discuss the effects of various parameters on our classification algorithm such as the choice of filter bank and rotational invariance the size of the texton dictionary as well as the number of training images used finally we present a method of reliably measuring relative orientation co occurrence statistics in a rotationally invariant manner and discuss whether incorporating such information can enhance the classifier s performance

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

on the computation of fourier transforms of singular functions abstract in this paper we consider a method for the computation of finite fourier transforms of functions having endpoint singularities of algebraic or logarithmic type this method may be considered as a modification of clenshaw curtis quadrature the nonoscillatory and nonsingular part of the integrand is replaced by a truncated chebyshev series approximation and the integral is then evaluated using recurrence relations the numerical stability of these recurrence relations is investigated

the abc of hyper recursions each member of the family of gauss hypergeometric functions fn 2f1 a e1n b e2n c e3n z where a b c and z do not depend on n and ej 0 1 not all ej equal to zero satisfies a second order linear difference equation of the form anfn 1 bnfn cnfn 1 0 because of symmetry relations and functional relations for the gauss functions the set of 26 cases for different ej values can be reduced to a set of 5 basic forms of difference equations in this paper the coefficients an bn and cn of these basic forms are given in addition domains in the complex z plane are given where a pair of minimal and dominant solutions of the difference equation have to be identified the determination of such a pair asks for a detailed study of the asymptotic properties of the gauss functions fn for large values of n and of other gauss functions outside this group this will be done in a later paper

nekhoroshev type stability results for hamiltonian systems with an additional transversal component abstract we prove exponential stability theorems of nekhoroshev type for motion in the neighbourhood of an elliptic fixed point in hamiltonian systems having an additional transverse component of arbitrary dimension under certain conditions on this transverse component we consider both the cases i of a strongly constrained motion and ii of a weak perturbation

exponentially small splitting of separatrices under fast quasiperiodic forcing we consider fast quasiperiodic perturbations with two frequencies 1 epsiv of a pendulum where is the golden mean number the complete system has a two dimensional invariant torus in a neighbourhood of the saddle point we study the splitting of the three dimensional invariant manifolds associated to this torus provided that the perturbation amplitude is small enough with respect to and some of its fourier coefficients the ones associated to fibonacci numbers are separated from zero it is proved that the invariant manifolds split and that the value of the splitting which turns out to be exponentially small with respect to is correctly predicted by the melnikov function

error bounds for linear recurrence relations etude des relations de recurrence lineaires pour les systemes oscillatoires et monotones estimations des bornes d erreurs

computation of jacobi functions of the second kind for use in nearside farside scattering theory abstract the nearside farside decomposition of a partial wave series is currently being used to understand the angular scattering of atom diatom collision systems in this theory it is necessary to compute jacobi functions of the second kind on the cut these functions are denoted by q n cos where n may be large positive integers the q n cos can be computed from a three term linear recurrence relation provided the initial values corresponding to n 0 and 1 are known we derive explicit formulas for q 0 cos q 1 cos in terms of elementary transcendental functions a new generating function for jacobi functions of nonintegral degree off the cut is obtained a special case of which yields a generating function for q n cos this is used to check the numerical results as is a casoratian relation we show that the recurrence for q n cos is stable in the forward direction with errors growing like o n we also present some numerics demonstrating the success of the method

on the hill determinant method the conditions of applicability of the hill determinant method to the potentials v r v1r v2r2 and v x x2 lambda x2 1 gx2 are investigated it is shown that the procedure leads to the actual eigenvalues in the former case provided the ansatz is properly chosen but it completely fails to yield the right answer in the latter one

asymptotic analysis of a class of three degree of freedom hamiltonian systems near stable equilibria abstract a conservative near integrable hamiltonian dynamical system is examined which to leading order consists of three uncoupled harmonic oscillators with constant frequencies in the ratio 1 2 for certain rational formally the problem considered can arise by perturbing any three degree of freedom hamiltonian near a stable equilibrium point so that the hamiltonian consists of a power series expansion in a small parameter where successive terms are homogeneous polynomials of increasing degree in the coordinates and the momenta the special case of two exact simultaneous resonances one in the first perturbation term and one in the second is examined and explicit asymptotic solutions are obtained the solution procedure involves reducing the original hamiltonian to two degrees of freedom using one integral of the motion then transforming to standard form to find two additional adiabatic invariants by near identity averaging canonical transformations a specific example is studied numerically to verify the asymptotic validity of the results over long times

on the problem of energy equipartition for large systems of the fermi pasta ulam type analytical and numerical estimates abstract we report on some analytical and numerical results on the exchanges of energy in systems of the fermi pasta ulam type in the light of nekhoroshev s theorem with particular attention to the dependence of the estimates on the number n of degrees of freedom for the ordinary fpu problem we look for a control of the single normal mode energies and we find both the analytical and numerical estimates to agree in predicting that the energy exchanges of the single modes cannot be controlled in the thermodynamic limit we consider then a modified fpu model with alternating light and heavy particles which appears as composed of two subsystems of low acoustic frequency and of high optical frequency respectively we try to control the exchange of the total energy of the high frequency modes up to times increasing exponentially with the frequency in this case the numerical estimates are stronger than the available analytical ones and give indications for nonequipartition with constants essentially independent of the number n of degrees of freedom

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

an averaging technique for highly oscillatory hamiltonian problems in this paper we are concerned with the numerical solution of highly oscillatory hamiltonian systems with a stiff linear part we construct an averaged system whose solution remains close to the exact one over bounded time intervals possesses the same adiabatic and hamiltonian invariants as the original system and is nonstiff we then investigate its numerical approximation through a method which combines a symplectic integration scheme and an acceleration technique for the evaluation of time averages developed in e cances et al numer math 100 2005 pp 211 232 eventually we demonstrate the efficiency of our approach on two test problems with one or several frequencies

extensive adiabatic invariants for nonlinear chains we look for extensive adiabatic invariants in nonlinear chains in the thermodynamic limit considering the quadratic part of the klein gordon hamiltonian by a linear change of variables we transform it into a sum of two parts in involution at variance with the usual method of introducing normal modes our constructive procedure allows us to exploit the complete resonance while keeping the extensive nature of the system next we construct a nonlinear approximation of an extensive adiabatic invariant for a perturbation of the discrete nonlinear schrodinger model the fluctuations of this quantity are controlled via gibbs measure estimates independent of the system size for a large set of initial data at low specific energy finally by numerical calculations we show that our adiabatic invariant is well conserved for times much longer than predicted by our first order theory with fluctuation much smaller than expected according to standard statistical estimates

classical freezing of plane rotations a proof of the boltzmann jeans conjecture using simple known methods and results of classical perturbation theory especially those due to nekhoroshev and neishtadt we study the energy exchanges between the rotational and the translational degrees of freedom in a particular model representing the planar motion of a rigid body in a bounded analytic potential we prove that if the angular velocity co is initially large then the energy exchanges are small o co 1 for times growing exponentially with co ill exp co we also deduce that in a scattering process from a smooth potential barrier the overall change in the rotational energy of the incoming body is exponentially small in co g exp co the results are interpreted in the light of an old conjecture by boltzmann and jeans on the existence of very large time scales for equilibrium in statistical systems containing high frequency degrees of freedom purely classical freezing of the high frequency degrees of freedom the rotating object is in this interpretation a classical molecule which moves in an external field or collides with the wall of a container two different limits of large co are considered namely the limit of large rotational energy and as is interesting for the molecular interpretation the limit of point mass at finite rotational energy

simple dynamical system with discrete bound states we study numerically the dynamical system of a two electron atom with the darwin interaction as a model to investigate scale dependent effects of the relativistic action at a distance electrodynamics this dynamical system consists of a small perturbation of the coulomb dynamics for energies in the atomic range the key properties of the coulomb dynamics are i a peculiar mixed type phase space with sparse families of stable nonionizing orbits and ii scale invariance symmetry with all orbits defined by an arbitrary scale parameter the combination of this peculiar chaotic dynamics i and ii with the scale dependent relativistic corrections darwin interaction generates the phenomenon of scale dependent stability we find numerical evidence that stable nonionizing orbits can exist only for a discrete set of resonant energies the fourier transform of these nonionizing orbits is a set of sharp frequencies the energies and sharp frequencies of the nonionizing orbits we study are in the quantum atomic range

on convergence properties of the em algorithm for gaussian mixtures we build up the mathematical connection between the expectation maximization em algorithm and gradient based approaches for maximum likelihood learning of finite gaussian mixtures we show that the em step in parameter space is obtained from the gradient via a projection matrix p and we provide an explicit expression for the matrix we then analyze the convergence of em in terms of special properties of p and provide new results analyzing the effect that p has on the likelihood surface based on these mathematical results we present a comparative discussion of the advantages and disadvantages of em and other algorithms for the learning of gaussian mixture models

smoothed langevin dynamics of highly oscillatory systems abstract we consider hamiltonian systems containing a strong constraining potential such systems were first investigated by rubin and ungar who derived the corresponding reduced equations of motion for the slow degree of freedom the purpose of this paper is two fold i we transform the highly oscillatory degree of freedom to action angle variables and use recent results on the truncation error of the corresponding normal form transformations to derive an estimate on the lifespan of the underlying adiabatic invariant ii we investigate thermally embedded hamiltonian systems i e langevin dynamics containing a strong constraining potential using again a transformation to action angle variables and applying the principle of averaging we derive reduced equations of motion for the slowly varying degrees of freedom this includes in particular the derivation of a correcting force term that stands for the coupling of the slow and fast degrees of motion in case of strong thermal coupling our reduced equations of motion suggest that the correcting force term can be approximated by the gradient of the fixman potential as used in statistical mechanics we also discuss smoothing in the context of constant temperature molecular dynamics and provide a numerical example

numerical computation of the incomplete lipschitz hankel integral je o a z abstract two factorial neumann series expansions are derived for the incomplete lipschitz hankel integral je 0 a z these expansions are used together with the neumann series expansion given by agrest in an algorithm which efficiently computes je 0 a z to a user defined number of significant digits other expansions for je 0 a z which are found in the literature are also discussed but these expansions are found to offer no significant computational advantages when compared with the expansions used in the algorithm

numerical evaluation of airy functions with complex arguments abstract we present two methods for the evaluation of airy functions of complex argument the first method is accurate to any desired precision but is slow and unsuitable for fixed precision languages the second method is accurate to double precision 12 digits and is suitable for programming in a fixed precision language such as fortran the first method uses the symbolic manipulation language maple to evaluate either the taylor series expansion or an asymptotic expansion of each function the second method extends an idea of j c p miller to the complex plane it uses the first method to obtain a grid of points in the complex plane where the functions are known to high precision and then uses taylor series from these base points the resulting algorithm is accurate and efficient

construction of analytic kam surfaces and effective stability bounds a class of analytic possibly time dependent hamiltonian systems withd degrees of freedom and the corresponding class of area preserving twist diffeomorphisms of the plane are considered implementing a recent scheme due to moser salamon and zehnder we provide a method that allows us to construct explicitly kam surfaces and hence to give lower bounds on their breakdown thresholds we then apply this method to the hamiltonianh y2 2 e cosx cos x t and to the map y x y e sinx x y e sinx obtaining with the aid of computer assisted estimations explicit approximations within an error of 10 5 of the golden mean kam surfaces for complex values of e with e less or equal than respectively 0 015 and 0 65 the experimental numerical values at which such surfaces are expected to disappear are about respectively 0 027 and 0 97 a possible connection between break down thresholds and singularities in the complex e plane is pointed out

hep 2 cell classification using shape index histograms with donut shaped spatial pooling we present a new method for automatic classification of indirect immunoflourescence images of hep 2 cells into different staining pattern classes our method is based on a new texture measure called shape index histograms that captures second order image structure at multiple scales moreover we introduce a spatial decomposition scheme which is radially symmetric and suitable for cell images the spatial decomposition is performed using donut shaped pooling regions of varying sizes when gathering histogram contributions we evaluate our method using both the icip 2013 and the icpr 2012 competition datasets our results show that shape index histograms are superior to other popular texture descriptors for hep 2 cell classification moreover when comparing to other automated systems for hep 2 cell classification we show that shape index histograms are very competitive especially considering the relatively low complexity of the method

a property of exponential stability in nonlinear wave equations near the fundamental linear mode abstract we consider the nonlinear wave equation utt c2uxx u u t 0 u t 0 where is an analytic function satisfying 0 0 and 00 0 for each value of the harmonic energy e i e energy when 0 we consider the closed curve e which is the phase space trajectory of the linear mode with lowest frequency if the perturbation parameter and the harmonic energy e are small enough then near e we construct by means of a suitable simplified equation a closed curve e with the following property provided the distance between the initial datum and such a curve is small enough the corresponding solution remains close to e up to times exponentially long with 1 eve cannot expect the curves e to be trajectories of solutions of such curves depend smoothly on the parameters e and the above result is deduced from a general theorem on generic hamiltonian perturbations of completely resonant linear systems

computation of multiple eigenvalues of infinite tridiagonal matrices in this paper it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues the computation of such double eigenvalues is enabled by the newton method of two variables the three term recurrence relations obtained from its eigenvalue problem evp subsume the well known relations of a the zeros of j v z b the zeros of zj f v z hj v z c the evp of the mathieu differential equation and d the evp of the spheroidal wave equation the results of experiments are shown for the three cases a c for the computation of their double pairs

explicit bounds for second order difference equations and a solution to a question of stevic this note gives explicit applicable bounds for solutions of a wide class of second order difference equations with nonconstant coefficients among the applications is an affirmative answer to a recent question of stevic

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

long time energy conservation of numerical methods for oscillatory differential equations we consider second order differential systems where high frequency oscillations are generated by a linear part we present a frequency expansion of the solution and we discuss two invariants of the system that determine the coefficients of the frequency expansion these invariants are related to the total energy and the oscillatory harmonic energy of the original system for the numerical solution we study a class of symmetric methods that discretize the linear part without error we are interested in the case where the product of the step size with the highest frequency can be large in the sense of backward error analysis we represent the numerical solution by a frequency expansion where the coefficients are the solution of a modified system this allows us to prove the near conservation of the total and the oscillatory energy over very long time intervals

on the conservation of adiabatic invariants for a system of coupled rotators abstract we study the accuracy of the conservation of adiabatic invariants in a model of n weakly coupled rotators most attention is devoted to n 2 and frequency 1 2 with 2 1 quadratic irrational we apply a heuristic approximation scheme going back to jeans and to landau and teller and perform a very accurate numerical check of the result observing a quite remarkable agreement

resurrecting the asymptotics of linear recurrences abstract once on the forefront of mathematical research in america the asymptotics of the solutions of linear recurrence equations is now almost forgotten especially by the people who need it most namely combinatorists and computer scientists here we present this theory in a concise form and give a number of examples that should enable the practicing combinatorist and computer scientist to include this important technique in her or his asymptotics tool kit

hep 2 staining pattern recognition using stacked fisher network for encoding weber local descriptor abstract this study addresses the recognition problem of the hep 2 cell using indirect immunofluorescent iif image analysis which can indicate the presence of autoimmune diseases by finding antibodies in the patient serum generally the method used for iif analysis remains subjective and depends too heavily on the experience and expertise of the physician this study aims to explore an automatic hep 2 cell recognition system in which how to extract highly discriminate visual features plays a key role in this recognition application in order to realize this purpose our main efforts include 1 a simple but robust local descriptor without any quantization for local patch representation 2 a transformation of the difference values between the surrounding pixels and the center one to the perception degree which is based on the fact that human perception for disguising a pattern depends not only on the absolute intensity of the stimulus but also on the relative variance of the stimulus called as weber local descriptor wld 3 a data driven coding strategy with a parametric probability process and the extraction of not only low but also high order statistics for image representation called as fisher vector 4 the stacking of the fisher network into multi layer framework for more discriminate feature experiments using the open hep 2 cell dataset released in the icip2013 contest validate that the proposed strategy can achieve a much better performance than the state of the art approaches and that the achieved recognition error rate is even very significantly below the observed intra laboratory variability

hep 2 cell image classification with multiple linear descriptors abstract the automatic classification of the hep 2 cell stain patterns from indirect immunofluorescence images has attracted much attention recently as an image classification problem it can be well solved by the state of the art bag of features bof model as long as a suitable local descriptor is known unfortunately for this special task we have very limited knowledge of such a descriptor in this paper we explore the possibility of automatically learning the descriptor from the image data itself specifically we assume that a local patch can be well described by a set of linear projections performed on its pixel values based on this assumption both unsupervised and supervised approaches are explored for learning the projections more importantly we propose a multi projection multi codebook scheme which creates multiple linear projection descriptors and multiple image representation channels with each channel corresponding to one descriptor through our analysis we show that the image representation obtained by combining these different channels can be more discriminative than that obtained from a single projection scheme this analysis is further verified by our experimental study we evaluate the proposed approach by strictly following the protocol suggested by the organizer of the 2012 hep 2 cell classification contest which is hosted to compare the state of the art methods for hep 2 cell classification in this paper our system achieves 66 6 cell level classification accuracy which is just slightly lower than the best performance achieved in the hep 2 cell classification contest this result is impressive and promising considering that we only utilize a single type of feature namely linear projection coefficients of patch pixel values which is learned from the image data

stability of motions near resonances in quasi integrable hamiltonian systems nekhoroshev s theorem on the stability of motions in quasi integrable hamiltonian systems is revisited at variance with the proofs already available in the literature we explicitly consider the case of weakly perturbed harmonic oscillators furthermore we prove the confinement of orbits in resonant regions in the general case of nonisochronous systems by using the elementary idea of energy conservation instead of more complicated mechanisms an application of nekhoroshev s theorem to the study of perturbed motions inside resonances is also provided

homogenization of hamiltonian systems with a strong constraining potential abstract the paper studies hamiltonian systems with a strong potential forcing the solutions to oscillate on a very small time scale in particular we are interested in the limit situation where the size of this small time scale tends to zero but the velocity components remain oscillating with an amplitude variation of the order o 1 the process of establishing an effective initial value problem for the limit positions will be called homogenization of the hamiltonian system this problem occurs in mechanics as the problem of realization of holonomic constraints as various singular limits in fluid flow problems in plasma physics as the problem of guiding center motion and in the simulation of biomolecules as the so called smoothing problem we suggest the systematic use of the notion of weak convergence in order to approach this problem this methodology helps to establish unified and short proofs of many known results which throw light on the inherent structure of the problem moreover we give a careful and critical review of the literature

efficient k nn based hep 2 cells classifier human epithelial hep 2 cells are commonly used in the indirect immunofluorescence iif tests to detect autoimmune diseases the diagnosis consists of searching and classification to specific patterns created by anti nuclear antibodies anas in the patient serum evaluation of the iif test is mostly done by humans which means that it is highly dependent on the experience and expertise of the physician therefore a significant amount of research has been focused on the development of computer aided diagnostic systems which could help with the analysis of images from microscopes this work deals with the design and development of hep 2 cells classifier the classifier is able to categorize pre segmented images of hep 2 cells into 6 classes the core of this engine consists of the following image descriptors haralick features local binary patterns sift surface description and a granulometry based descriptor these descriptors produce vectors that form metric spaces k nn classification is based on aggregated distance function which combines several features together an extensive set of evaluations was performed on the publicly available mivia hep 2 images dataset which allows a direct comparison of our approach with other solutions the results show that our approach is one of the leading classifiers when comparing with other participants in the hep 2 cells classification contest

asymptotic expansions for second order linear difference equations abstract formal series solutions are obtained for the difference equation y n 2 a n y n 1 b n y n 0 where a n and b n have asymptotic expansions of the form a n s 0 a s n s and b n s 0 b s n s for large values of n and b0 0 these solutions are characterized by the roots of the characteristic equation 2 a0 b0 0 our discussion is divided into three cases according to whether the roots are distinct or equal and do not satisfy the auxiliary equation a1 b1 0 or equal and do satisfy the auxiliary equation the last case is further divided into three subcases according to whether the roots of the indicial equation 1 2 a1 a2 b2 0 do not differ by a nonnegative integer or differ by a positive integer or are equal in all cases the formal series solutions will be shown to be asymptotic our approach is based on the method of successive approximations

realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory part ii the so called problem of the realization of the holonomic constraints of classical mechanics is here revisited in the light of nekhoroshev like classical perturbation theory precisely if constraints are physically represented by very steep potential wells with associated high frequency transversal vibrations then one shows that within suitable assumptions the vibrational energy and the energy associated to the constrained motion are separately almost constant for a very long time scale growing exponentially with the frequency i e with the rigidity of the constraint one aims to realize this result can also be applied to microscopic physics providing a possible entirely classical mechanism for the freezing of the high frequency degrees of freedom in terms of non equilibrium statistical mechanics according to some ideas expressed by boltzmann and jeans at the turn of the century in this part i we introduce the problem and prove a first theorem concerning the realization of a single constraint within a system of any number of degrees of freedom the problem of the realization of many constraints will be considered in a forthcoming part ii

a new algorithm for computing orthogonal polynomials the aim of this paper is to present an algorithm for computing orthogonal polynomials the fast fourier transform completes the connection given by draux between the three term recurrence relationship and the euclidian algorithm applications to hankel systems and numerical examples illustrate our purpose

using basic image features for texture classification representing texture images statistically as histograms over a discrete vocabulary of local features has proven widely effective for texture classification tasks images are described locally by vectors of for example responses to some filter bank and a visual vocabulary is defined as a partition of this descriptor response space typically based on clustering in this paper we investigate the performance of an approach which represents textures as histograms over a visual vocabulary which is defined geometrically based on the basic image features of griffin and lillholm proc spie 6492 09 1 11 2007 rather than by clustering bifs provide a natural mathematical quantisation of a filter response space into qualitatively distinct types of local image structure we also extend our approach to deal with intra class variations in scale our algorithm is simple there is no need for a pre training step to learn a visual dictionary as in methods based on clustering and no tuning of parameters is required to deal with different datasets we have tested our implementation on three popular and challenging texture datasets and find that it produces consistently good classification results on each including what we believe to be the best reported for the kth tips and equal best reported for the uiuctex databases

improving bag of features for large scale image search this article improves recent methods for large scale image search we first analyze the bag of features approach in the framework of approximate nearest neighbor search this leads us to derive a more precise representation based on hamming embedding he and weak geometric consistency constraints wgc he provides binary signatures that refine the matching based on visual words wgc filters matching descriptors that are not consistent in terms of angle and scale he and wgc are integrated within an inverted file and are efficiently exploited for all images in the dataset we then introduce a graph structured quantizer which significantly speeds up the assignment of the descriptors to visual words a comparison with the state of the art shows the interest of our approach when high accuracy is needed experiments performed on three reference datasets and a dataset of one million of images show a significant improvement due to the binary signature and the weak geometric consistency constraints as well as their efficiency estimation of the full geometric transformation i e a re ranking step on a short list of images is shown to be complementary to our weak geometric consistency constraints our approach is shown to outperform the state of the art on the three datasets

a user friendly method for computing indefinite integrals of oscillatory functions for indefinite integrals q f x 1 x f t e i t d t x 1 1 torii and the first author hasegawa and torii 1987 developed a quadrature method of clenshaw curtis c c type its improvement was made and combined with sidi s m w transformation by sidi and the first author hasegawa and sidi 1996 to compute infinite oscillatory integrals the improved method per se however has not been elucidated in its attractive features which here we reveal with new results and its detailed algorithm a comparison with a method of c c type for definite integrals q f 1 due to dominguez et al 2011 suggests that a smaller number of computations is required in our method this is achieved by exploiting recurrence and normalization relations and their associated linear system we show their convergence and stability properties and give a verified truncation error bound for a result computed from the linear system with finite dimension for f z analytic on and inside an ellipse in the complex plane z the error of the approximation to q f x of the improved method is shown to be bounded uniformly numerical examples illustrate the stability and performance of the method

slow dynamics via degenerate variational asymptotics we introduce the method of degenerate variational asymptotics for a class of singularly perturbed ordinary differential equations in the limit of strong gyroscopic forces such systems exhibit dyna

on the hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms we reconsider the problem of the hamiltonian interpolation of symplectic mappings following moser s scheme we prove that for any mapping e analytic and e close to the identity there exists an analytic autonomous hamiltonian system he such that its time one mapping he differs from e by a quantity exponentially small in 1 e this result is applied in particular to the problem of numerical integration of hamiltonian systems by symplectic algorithms it turns out that when using an analytic symplectic algorithm of orders to integrate a hamiltonian systemk one actually follows exactly namely within the computer roundoff error the trajectories of the interpolating hamiltonian he or equivalently of the rescaled hamiltonian ke e 1he which differs fromk but turns out to be e5 close to it special attention is devoted to numerical integration for scattering problems

hep 2 cell classification using rotation invariant co occurrence among local binary patterns abstract this paper proposes a novel method for classifying six categories of patterns of fluorescence staining of a hep 2 cell the proposed method is constructed as a combination of the powerful rotation invariant co occurrence among adjacent local binary pattern ric lbp image feature and a linear support vector machine svm ric lbp provides high descriptive ability and robustness against local rotations of an input cell image to further deal with global rotation we synthesize many training images by rotating the original training images and constructing the svm using both the original and synthesized images the proposed method has the following advantages 1 robustness against uniform changes in intensity of an input cell image 2 invariance under local and global rotation of the image 3 low computational cost and 4 easy implementation the proposed method was demonstrated to be effective through evaluation experiments using the mivia hep 2 images dataset and comparison with typical state of the art methods

towards a rigorous treatment of the jeans landau teller method for the energy exchanges of harmonic oscillators for classical hamiltonian systems containing an harmonic oscillator of high frequency one has the problem of controlling the energy exchange between the oscillator and the remaining slow degrees of freedom under very general conditions such an exchange turns out to be exponentially small with the fre quency of the oscillator in the jeans landau teller method one aims to prove the exponential dependence and to estimate the coefficient of the exponential by exploiting the analyticity properties of the solution of the differential equations describing the motion of the system however in practice since the exact solution is not known such properties are inferred from those of an approximate solution with no control of the difference this fact might a priori even invalidate the exponential dependence itself in the present paper a rigorous treatment is given for a particular model of interest in the domain of atomic collisions by keeping control of the difference between the exact and the approximate solution

exploring illumination robust descriptors for human epithelial type 2 cell classification strong illumination variation is a key challenge in the human epithelial type 2 hep 2 cell classification task aiming to improve the robustness of the hep 2 classification system to the illumination variation this paper deeply explores discriminative and illumination robust descriptors specifically we propose a novel spatial shape index descriptor ssid to capture spatial layout information of the second order structures and utilize a local orientation adaptive descriptor load which was originally designed for texture classification to the hep 2 cell classification task both ssid and load show strong discrimination and great complementarity to each other four different sets of experiments were carried out to evaluate ssid load and their combination our two submissions achieved superior performance on the new executable thematic of pattern recognition techniques for indirect immunofluorescence images analysis compared to the rank 1st method in the icpr 2014 hep 2 cell classification contest both of our submissions achieved a better performance when only using the provided training data our approaches also demonstrated superior performance on a newly compiled large scale hep 2 data set with 63 445 cell images highlightstwo introduced features achieve superior performance on the hep 2 cell classification task we propose a novel spatial shape index descriptor ssid to capture spatial layout of the second order texture structures we utilize a multi scale local orientation adaptive descriptor load to the hep 2 cell classification task we introduce a new large scale hep 2 data set that contains 63 445 cell images from the i3a task 2 data set

an algorithm for nondominant solutions of linear second order inhomogeneous difference equations an algorithm is given for computing a weighted sum of a nondominant solution of a linear second order inhomogeneous difference equation to a prescribed accuracy by estimating the truncation error the present method is an extension of both the stable numerical method due to olver and sookne and a summation technique due to deuflhard for computing minimal solutions of a homogeneous difference equation the method is illustrated by numerical examples

converting approximate error bounds into exact ones in order to produce error bounds quickly and easily people often apply to error bounds linearized propagation rules this is done instead of a precise error analysis the payoff estimates so produced are not guaranteed to be true bounds one can at most hope that they are good approximations of true bounds this paper discusses a way to convert such approximate error bounds into true bounds this is done by dividing the approximate bound by 1 with a small both the approximate bound and are produced by the same linearized error analysis this method makes it possible both to simplify the error analyses and to sharpen the bounds in an interesting class of numerical algorithms in particular it seems to be ideal for the derivation of tight true error bounds for simple and accurate algorithms like those used in subroutines for the evaluation of elementary mathematical functions exp log sin etc for instance the main subject of this paper is forward a priori error analysis however the method may be fitted to other types of error analysis too in fact the outlines of a forward a posteriori error analysis theory and of running error analysis are given also in the course of proofs a new methodology is applied for the representation of propagated error bounds this methodology promotes easy derivation of sharp helpful inequalities several examples of forward a priori error analysis and one of a posteriori error analysis and running error analysis are included