stability and error estimates of local discontinuous galerkin methods with implicit explicit time marching for advection diffusion problems the main purpose of this paper is to analyze the stability and error estimates of the local discontinuous galerkin ldg methods coupled with carefully chosen implicit explicit imex runge kutta time discretization up to third order accuracy for solving one dimensional linear advection diffusion equations in the time discretization the advection term is treated explicitly and the diffusion term implicitly there are three highlights of this work the first is that we establish an important relationship between the gradient and interface jump of the numerical solution with the independent numerical solution of the gradient in the ldg methods the second is that by aid of the aforementioned relationship and the energy method we show that the imex ldg schemes are unconditionally stable for the linear problems in the sense that the time step tau is only required to be upper bounded by a constant which depends on the ratio of the diffusion and the square of the advection coefficients and is independent

adapted numerical methods for advection reaction diffusion problems generating periodic wavefronts abstract the paper presents an adapted numerical integration for advection reaction diffusion problems the numerical scheme exploiting the a priori knowledge of the qualitative behaviour of the solution gains advantages in terms of efficiency and accuracy with respect to classic schemes already known in literature the adaptation is here carried out through the so called trigonometrical fitting technique for the discretization in space giving rise to a system of odes whose vector field contains both stiff and non stiff terms due to this mixed nature of the vector field an implicit explicit imex method is here employed for the integration in time based on the first order forward backward euler method the coefficients of the method here introduced rely on unknown parameters which have to be properly estimated in this work such an estimate is performed by minimizing the leading term of the local truncation error the effectiveness of this problem oriented approach is shown through a rigorous theoretical analysis and some numerical experiments

using angular dispersion of gradient direction for detecting edge ribbons edges in a scene generally project to smooth continuous curves nearly everywhere in the image which results in low angular deviation of the intensity gradients in small neighborhoods straddling edges angular deviation is shown to be a measure of snr a theoretical analysis of angular deviation arising due to independent and identically distributed n 0 sigma sup 2 random noise is presented angular deviation thresholds for neighborhood sizes from 3 3 to 11 11 pixels are determined both from this analysis and numerical examples the proposed gradient angular dispersion detection algorithm detects edge elements by comparing the measured angular deviation with values computed for the minimum acceptable snr low values of deviation violate the no edge hypothesis the algorithm is shown to make good use of the limited dynamic range of the imaging system the sensitivity and selectivity of the strategy are both shown to be high

on the evolution of periodic plane waves in reaction diffusion systems of l w type lambda omega systems are a class of simple reaction diffusion equations with a limit cycle in the reaction kinetics the author considers the solution of the system given by lambda r lambda 0 r p omega r omega 0 r p on a semi infinite spatial domain with initial data decaying exponentially across the domain numerical evidence is presented showing that this initial condition induces a wave front moving across the domain with periodic plane waves behind the front these periodic waves can move in either direction depending on the parameter values the author uses intuitive criteria to derive an expression for the speed of the advancing front and by reducing the system to ordinary differential equations for similarity solutions the amplitude and speed of the periodic plane waves are determined the speed of these periodic waves varies continuously with the initial data perturbation theory is then used to obtain an analytical approximation to the solutions these anal

stein s method and birth death processes barbour introduced a probabilistic view of stein s method for estimating the error in probability approximations however in the case of approximations by general distributions on the integers there have been no purely probabilistic proofs of stein s bounds till this paper furthermore the methods introduced here apply to a very large class of approximating distributions on the non negative integers among which there is a natural class for higher order approximations by probability distributions rather than signed measures as previously the methods also produce stein magic factors for process approximations which do not increase with the window of observation and which are simpler to apply than those in brown weinberg and xia

stein s method palm theory and poisson process approximation the framework of stein s method for poisson process approximation is presented from the point of view of palm theory which is used to construct stein identities and define local dependence a general result theorem 2 3 in poisson process approximation is proved by taking the local approach it is obtained without reference to any particular metric thereby allowing wider applicability a wasserstein pseudometric is introduced for measuring the accuracy of point process approximation the pseudometric provides a generalization of many metrics used so far including the total variation distance for random variables and the wasserstein metric for processes as in barbour and brown stochastic process appl 43 1992 9 31 also through the pseudometric approximation for certain point processes on a given carrier space is carried out by lifting it to one on a larger space extending an idea of arratia goldstein and gordon statist sci 5 1990 403 434 the error bound in the general result is similar in form to that for poisson approximation as it yields the stein factor 1 as in poisson approximation it provides good approximation particularly in cases where is large the general result is applied to a number of problems including poisson process modeling of rare words in a dna sequence

exponentially fitted two step hybrid methods for y f x y it is the purpose of this paper to derive two step hybrid methods for y f x y with oscillatory or periodic solutions specially tuned to the behaviour of the solution through the usage of the exponential fitting technique the construction of two step exponentially fitted hybrid methods is shown and their properties are discussed some numerical experiments confirming the theoretical expectations are provided

precision edge contrast and orientation estimation the contrast and orientation estimation accuracy of several edge operators that have been proposed in the literature is examined both for the noiseless case and in the presence of additive gaussian noise the test image is an ideal step edge that has been sampled with a square aperture grid the effects of subpixel translations and rotations of the edge on the performance of the operators are studied it is shown that the effect of subpixel translations of an edge can generate more error than moderate noise levels methods with improved results are presented for sobel angle estimates and the nevatia babu operator and theoretical noise performance evaluations are also provided an edge operator based on two dimensional spatial moments is presented all methods are compared according to worst case and rms error in an ideal noiseless situation and rms error under various noise levels

robust and efficient image alignment based on relative gradient matching in this paper we present a robust image alignment algorithm based on matching of relative gradient maps this algorithm consists of two stages namely a learning based approximate pattern search and an iterative energy minimization procedure for matching relative image gradient the first stage finds some candidate poses of the pattern from the image through a fast nearest neighbor search of the best match of the relative gradient features computed from training database of feature vectors which are obtained from the synthesis of the geometrically transformed template image with the transformation parameters uniformly sampled from a given transformation parameter space subsequently the candidate poses are further verified and refined by matching the relative gradient images through an iterative energy minimization procedure this approach based on the matching of relative gradients is robust against nonuniform illumination variations experimental results on both simulated and real images are shown to demonstrate superior efficiency and robustness of the proposed algorithm over the conventional normalized correlation method

robust fft based scale invariant image registration with image gradients we present a robust fft based approach to scale invariant image registration our method relies on fft based correlation twice once in the log polar fourier domain to estimate the scaling and rotation and once in the spatial domain to recover the residual translation previous methods based on the same principles are not robust to equip our scheme with robustness and accuracy we introduce modifications which tailor the method to the nature of images first we derive efficient log polar fourier representations by replacing image functions with complex gray level edge maps we show that this representation both captures the structure of salient image features and circumvents problems related to the low pass nature of images interpolation errors border effects and aliasing second to recover the unknown parameters we introduce the normalized gradient correlation we show that using image gradients to perform correlation the errors induced by outliers are mapped to a uniform distribution for which our normalized gradient correlation features robust performance exhaustive experimentation with real images showed that unlike any other fourier based correlation techniques the proposed method was able to estimate translations arbitrary rotations and scale factors up to 6

implicit explicit methods for time dependent partial differential equations implicit explicit imex schemes have been widely used especially in conjunction with spectral methods for the time integration of spatially discretized partial differential equations pdes of diffusion convection type typically an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term reaction diffusion problems can also be approximated in this manner in this work we systematically analyze the performance of such schemes propose improved new schemes and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods for the prototype linear advection diffusion equation a stability analysis for first second third and fourth order multistep imex schemes is performed stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified numerical experiments demonstrate that weak decay

numerical solution of reaction diffusion systems of λ ω type by trigonometrically fitted methods the numerical solution of reaction diffusion equations of type which are known to possess a one parameter family of periodic plane wave solutions is object of this paper due to the periodic character of such solutions a special purpose numerical integration is here proposed based on adapted finite differences the adaptation occurs at the level of the problem by a suitable spatial semi discretization based on trigonometrically fitted finite differences numerical experiments confirming the effectiveness of the approach are given

zero biasing and a discrete central limit theorem we introduce a new family of distributions to approximate p w a for a 2 1 0 1 2 and w a sum of independent integer valued random variables 1 2 n with finite second moments where with large probability w is not concentrated on a lattice of span greater than i the well known berry esseen theorem states that for z a normal random variable with mean e w and variance var w p z e a provides a good approximation to p w a for a of the form 00 x however for more general a such as the set of all even numbers the normal approximation becomes unsatisfactory and it is desirable to have an appropriate discrete non normal distribution which approximates w in total variation and a discrete version of the berry esseen theorem to bound the error in this paper using the concept of zero biasing for discrete random variables cf goldstein and reinert j theoret probab 18 2005 237 260 we introduce a new family of discrete distributions and provide a discrete version of the berry esseen theorem showing how members of the family approximate the distribution of a sum w of integer valued variables in total variation

exponentially fitted methods applied to fourth order boundary value problems fourth order boundary value problems are solved by means of exponentially fitted methods of different orders these methods which depend on a parameter can be constructed following a six step flow chart of ixaru and vanden berghe special attention is paid to the expression for the error term and to the choice of the parameter in order to make the error as small as possible some numerical examples are given to illustrate the practical implementation issues of these methods

exponentially fitted two step runge kutta methods construction and parameter selection abstract we derive exponentially fitted two step runge kutta methods for the numerical solution of y f x y specially tuned to the behaviour of the solution such methods have nonconstant coefficients which depend on a parameter to be suitably estimated the construction of the methods is shown and a strategy of parameter selection is presented some numerical experiments are provided to confirm the theoretical expectations

normal approximation for associated point processes via stein s method with applications to determinantal point processes abstract we use stein s method to provide non asymptotic l 1 bounds also known as wasserstein bounds to the normal for functionals of associated point processes as for supporting tools we use the connection between association and mixing properties that was recently uncovered by 29 we apply our main results to determinantal point processes which are known to be negatively associated a potential application to determinantal point processes in the laguerre gaussian family is also presented

error analysis of imex runge kutta methods derived from differential algebraic systems in this paper we present an error analysis of the imex runge kutta methods when applied to stiff problems containing a nonstiff term and a stiff term characterized by a small stiffness parameter varepsilon in this analysis we expand the global error in powers of varepsilon and show that the coefficients of the error are the global errors of the imex runge kutta method applied to a differential algebraic system interesting convergence results of these errors and of the remainder of the expansion allow us to determine sharp error bounds for stiff problems as a representative example of stiff problems we have chosen the van der pol equation we illustrate that the theoretical prediction is confirmed by the numerical test specifically an order reduction phenomenon is observed when the problem becomes increasingly stiff in particular making several assumptions we try to improve global error estimates of several imex runge kutta methods existing in the literature

functional poisson approximation in kantorovich rubinstein distance with applications to u statistics and stochastic geometry a poisson or a binomial process on an abstract state space and a symmetric function f acting on k tuples of its points are considered they induce a point process on the target space of f the main result is a functional limit theorem which provides an upper bound for an optimal transportation distance between the image process and a poisson process on the target space the technical background are a version of stein s method for poisson process approximation a glauber dynamics representation for the poisson process and the malliavin formalism as applications of the main result error bounds for approximations of u statistics by poisson compound poisson and stable random variables are derived and examples from stochastic geometry are investigated

the effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction diffusion systems abstract many oscillatory biological systems show periodic travelling waves these are often modelled using coupled reaction diffusion equations however the effects of different movement rates diffusion coefficients of the interacting components on the predictions of these equations are largely unknown here we investigate the ways in which varying the diffusion coefficients in such equations alters the wave speed time period wavelength amplitude and stability of periodic wave solutions we focus on two sets of kinetics that are commonly used in ecological applications lambda omega equations which are the normal form of an oscillatory coupled reaction diffusion system close to a supercritical hopf bifurcation and a standard predator prey model our results show that changing the ratio of the diffusion coefficients can significantly alter the shape of the one parameter family of periodic travelling wave solutions the position of the boundary between stable and unstable waves also depends on the ratio of the diffusion coefficients in all cases stability changes through an eckhaus sideband instability these effects are always symmetrical in the two diffusion coefficients for the lambda omega equations but are asymmetric in the predator prey equations especially when the limit cycle of the kinetics is of large amplitude in particular there are two separate regions of stable waves in the travelling wave family for some parameter values in the predator prey scenario our results also show the existence of a one parameter family of travelling waves but not necessarily a hopf bifurcation for all values of the diffusion coefficients simulations of the full partial differential equations reveals that varying the ratio of the diffusion coefficients can significantly change the properties of periodic travelling waves that arise from particular wave generation mechanisms and our analysis of the travelling wave families assists in the understanding of these effects

compound poisson process approximation compound poisson processes are often useful as approximate models when describing the occurrence of rare events in this paper we develop a method for showing how close such approximations are our approach is to use stein s method directly rather than by way of declumping and a marked poisson process this has conceptual advantages but entails technical difficulties several applications are given to illustrate the procedure

gradient orientation pattern matching with the hamming distance abstract this paper presents a novel pattern matching technique that is robust to illumination changes and the occlusion problem the technique is based on the matching of gradient orientations in place of traditional image features such as intensities or gradients gradient orientations depend on the texture in an image they are known to be insensitive to changes of image intensities that are often caused by time varying illuminations or the auto gain control agc function of the camera moreover the proposed method employs a voting strategy in the process of matching gradient orientations the method works remarkably well even when a large part of the pattern is occluded with a foreign object consequently the proposed method is robust to both irregular lighting conditions and the occlusion problem

hybrid image matching combining hausdorff distance with normalized gradient matching image matching has been a central problem in computer vision and image processing for decades most of the previous approaches to image matching can be categorized into the intensity based and edge based comparison hausdorff distance has been widely used for comparing point sets or edge maps since it does not require point correspondences in this paper we propose a new image similarity measure combining the hausdorff distance with a normalized gradient consistency score for image matching the normalized gradient consistency score is designed to compare the normalized image gradient fields between two images to alleviate the illumination variation problem in image matching by combining the edge based and intensity based information for image matching we are able to achieve robust image matching under different lighting conditions we show the superior robustness property of the proposed image matching technique through experiments on face recognition under different lighting conditions