measures for oscillatory sequences abstract the classical concept of oscillation is not sufficient to fully describe the oscillatory behavior of a real sequence by introducing the concepts of frequency measures of subsets of integers and investigating their properties we are able to strengthen the original concept of an oscillatory sequence and thus new oscillation criteria for difference equations can be derived these criteria differ from the classical ones in that they are described by means of the measures of the level sets of the involved parameter sequences a brief description of the theory of frequency measures for multiple sequences is also given

morphisms of f isocrystals and the finite monodromy theorem for unit root f isocrystals we discuss tate type problems for f isocrystals that is the full faithfulness of the natural restriction functors between categories of overconvergent f isocrystals on schemes of positive characteristic we prove it in the cases of unit root f isocrystals using this result we prove that an overconvergent unit root f isocrystal has a finite monodromy

asymptotic stability of linear non autonomous difference equations with fixed delay abstract this paper studies the asymptotic stability of the linear non autonomous difference equations with fixed delay it is shown that the difference system is asymptotically stable if and only if the norm of the limit for the coefficient matrix is less than 1 under some conditions furthermore the discretization of the pantograph equation by runge kutta methods with variable stepsize is analyzed finally some numerical experiments are made to demonstrate the main conclusions

oscillation for difference equations with continuous variable consider the delay difference equation y t y t p t h y t t t 0 where 0 0 and p c r r f c r r h c r r some oscillation criteria for this equation are obtained

oscillation criteria of first order linear difference equations with delay argument abstract this paper presents new sufficient conditions for the oscillation of all proper solutions of the first order linear difference equation with delay argument u k p k u k 0 k n where u k u k 1 u k p n r n n and lim k k examples illustrating the results are given it is to be pointed out that this is the first paper dealing with the oscillatory behaviour of the equation in the case of a general delay argument k

the iwasawa main conjecture for semistable abelian varieties over function fields we prove the iwasawa main conjecture over the arithmetic mathbb z p extension for semistable abelian varieties over function fields of characteristic p 0

asymptotic stability for a linear difference equation with variable delay we shall obtain sufficient conditions for the uniform stability and the global asymptotic stability of the linear difference equation with variable delay xn 1 xn pnxn kn 0 n n where pn is a sequence of nonnegative real numbers kn is a sequence of nonnegative integers and there exists a nonnegative integer k such that kn k for n n

oscillations of delay difference equations with oscillating coefficients abstract in this paper we establish sufficient conditions for the oscillation of all solutions of the delay difference equation y n 1 y n p n y n k 0 n 0 1 2 where pn is a sequence of real numbers and k is a positive integer an open problem in ladas in international conference on differential equations stability and control dekker new york 1990 is solved

permanence contractivity and global stability in logistic equations with general delays abstract we obtain new conditions of the permanence and contractivity of solutions and the global asymptotic stability for the positive equilibrium x 1 a j 0 m b j of the following logistic equation with general delays 0 1 dx t dt x t r t 1 ax t j 0 m b j x j t t t 0 x t t 0 t t 0 and t 0 0 where r t is a nonnegative continuous function on t0 a b 0 or a b 0 and b j 0mmin 0 bj each j t is piecewise continuous on t0 j t t for 0 j m and t min 1 j m j t as t the results improve that of j w h so and j s yu hokkaido math j 24 1995 269 286 for a logistic equation with nonlinear delay terms a similar result is obtained

asymptotic behavior of solutions for neutral difference equations the boundedness and asymptotic behavior of all solutions of the neutral delay difference equation of the form d x n c nx n m p nx n k q nx n l 0 n 0 1 2 are investigated where k l m are positive integers c n q n and p n are three sequences of real numbers the obtained sufficient conditions extend and improve the existing results in the literature

analogue p adique du theoreme de turrittin et le theoreme de la monodromie p adique 1 rappel de quelques resultats sur la structure p adique d un point singulier d une equation differentielle 322 2 cas d une pente entiere 327 3 cas d une pente fractionnaire premiere a p 333 4 cas d un rang premier a p 335 5 cas general 339 6 l exemple mx 1 3 343 7 la theorie des modules et l implication dr pst 346

oscillation criteria for first order nonlinear delay difference equations in this paper two interesting oscillation criteria are obtained for all solutions of the nonlinear delay difference equation of the formx n 1 x n p nf x n l 1 x n l 2 x n l m 0 n 0 1 2 the results extend some well known results in the literature and two examples are given to demonstrate the advantage of our results

an oscillation criterion for a delay difference equation by using the method of yu zhang and qian in j s yu b g zhang x z qian oscillation of delay difference equations with oscillating coefficients j math anal appl 177 1993 432 444 we prove another oscillation criterion for all solutions of the following linear delay difference equation x n 1 x n p nx n k 0 n 0 1 2 where p n is a sequence of real numbers and k is a positive integer

an oscillation criterion for linear difference equations with oscilling coefficients abstract relatively few oscillation criteria have been established for delay difference equations of the form yn 1 yn qnyn 0 where qn is an oscillatory sequence in this note we make use of the convexity property of the function x ln x to obtain such a criterion which complements some of the existing results even when qn is nonnegative

periodic orbits on discrete dynamical systems abstract in this paper we discuss the discrete dynamical system x n 1 x n g x n n 0 1 arising as a discrete time network of single neuron where is the internal decay rate g is a signal function first we consider the case where g is of mcculloch pitts nonlinearity periodic orbits are discussed according to different range of moreover we can construct periodic orbits then we consider the case where g is a sigmoid function sufficient conditions are obtained for has periodic orbits of arbitrary periods and an example is also given to illustrate the theorem

new oscillation criteria for delay difference equations abstract this paper is concerned with the oscillation of all solutions of the delay difference equations and where pn and pi n are sequences of nonnegative real numbers an k and ki are positive integers new oscillation criteria of the forms for equation and for equation are obtained where lim infn 1 k n 1i n k pi and c is the the best possible function of in some sense

green functions and positive solutions for boundary value problems of third order difference equations in this paper we investigate the boundary value problems for the third order nonlinear difference equation d 3u t 2 a t f u t 0 t 2 t 2 satisfying five kinds of different boundary value conditions the green functions are constructed carefully and their bounds are evaluated some verifiable criteria for the existence of at least one positive solution and two positive solutions are obtained by using the green functions and the evaluations of bounds some examples are given to demonstrate the applications of the theorems obtained

coherence enhancing diffusion filtering the completion of interrupted lines or the enhancement of flow like structures is a challenging task in computer vision human vision and image processing we address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so called interest operator second moment matrix structure tensor an m dimensional formulation of this method is analysed with respect to its well posedness and scale space properties an efficient scheme is presented which uses a stabilization by a semi implicit additive operator splitting aos and the scale space behaviour of this method is illustrated by applying it to both 2 d and 3 d images

filtrations de type hasse arf et monodromie p adique one proves the crew tsuzuki p adic local monodromy conjecture for local fields of characteristic p 0

asymptotic behavior of delay difference systems this paper is concerned with a delay difference system where k is a positive integer and f is a signal transmission function of mcculloch pitts type the difference system can be regarded as the discrete analog of the artificial neural network of two neurons with mcculloch pitts nonlinearity some interesting results are obtained for the asymptotic behavior of the system

cohomology of arithmetic families of γ modules we prove the niteness of the cohomology and the iwasawa cohomology of arithmetic families of modules using this niteness theorem we show that a family of galois representations that is densely pointwise rened in the sense of mazur is actually trianguline as a family over a large subspace in the case of the colemanmazur eigencurve we determine the behavior at all classical points

automatic joint classification and segmentation of whole cell 3d images we present a machine learning tool for automatic texton based joint classification and segmentation of mitochondria in mnt 1 cells imaged using ion abrasion scanning electron microscopy ia sem for diagnosing signatures that may be unique to cellular states such as cancer automatic tools with minimal user intervention need to be developed for analysis and mining of high throughput data from these large volume data sets typically 2gb cell challenges for such a tool in 3d electron microscopy arise due to low contrast and signal to noise ratios snr inherent to biological imaging our approach is based on block wise classification of images into a trained list of regions given manually labeled images our goal is to learn models that can localize novel instances of the regions in test datasets since datasets obtained using electron microscopes are intrinsically noisy we improve the snr of the data for automatic segmentation by implementing a 2d texture preserving filter on each slice of the 3d dataset we investigate texton based region features in this work classification is performed by k nearest neighbor k nn classifier support vector machines svms adaptive boosting adaboost and histogram matching using a nn classifier in addition we study the computational complexity vs segmentation accuracy tradeoff of these classifiers segmentation results demonstrate that our approach using minimal training data performs close to semi automatic methods using the variational level set method and manual segmentation carried out by an experienced user using our method which we show to have minimal user intervention and high classification accuracy we investigate quantitative parameters such as volume of the cytoplasm occupied by mitochondria differences between the surface area of inner and outer membranes and mean mitochondrial width which are quantities potentially relevant to distinguishing cancer cells from normal cells to test the accuracy of our approach these quantities are compared against manually computed counterparts we also demonstrate extension of these methods to segment 3d images obtained using electron tomography

new contractivity condition in a population model with piecewise constant arguments abstract in this paper we improve contractivity conditions of solutions for the positive equilibrium n 1 a i 0 m b i of the following differential equation with piecewise constant arguments d n t d t n t r t 1 a n t i 0 m b i n n i n t n 1 n 0 1 2 n 0 n 0 0 and n j n j 0 j 1 2 m where r t is a nonnegative continuous function on 0 r t 0 i 0 m b i 0 b i 0 i 0 1 2 m and a b 0 i 1 m b i in particular for the case a 0 and m 1 we really improve the known three type conditions of the contractivity for solutions of this model see for example y muroya a sufficient condition on global stability in a logistic equation with piecewise constant arguments hokkaido math j 32 2003 75 83 for the other case a 0 and m 1 under the condition j 1 m b j 2 b 0 a j 1 m b j 1 b 0 j 0 m b j the obtained result partially improves the known results on the contractivity of solutions for the positive equilibrium of this model given by the author y muroya persistence contractivity and global stability in logistic equations with piecewise constant delays j math anal appl 270 2002 602 635 and others

some oscillation criteria for difference equations abstract consider the difference equation x n 1 x n p n x n k 0 where p n is a sequence of nonnegative real numbers and k is a positive integer it is proved that all solutions oscillate if there exists some positive integer l such that lim sup n i 0 k pn i i 0 k j 1 k pn i j m 0 l 1 i 0 k j 0 m 1 pn jk 1 1 or lim sup n i 1 k pn i i 1 k j 1 k pn i j m 0 l 1 i 0 k j 0 m 1 pn jk 1 1

a further result on the oscillation of delay difference equations in this paper we are concerned with the delay difference equations of the form yn 1 yn pnyn k 0 n 0 1 2 where pn 0 and k is a positive integer we prove by using a new technique that n 0 i nn kpi ln i nn k pi 1 sign i nn k pi i n 1n k pi ln i n 1n k pi 1 sign i n 1n k pi guarantees that all solutions of equation oscillate which improves many previous well known results in particular our theorems also fit the case where n 1i n kpi kk 1 k 1 k 1 in addition we present a nonoscillation sufficient condition for equation

a p adic local monodromy theorem we produce a canonical filtration for locally free sheaves on an open p adic annulus equipped with a frobenius structure using this filtration we deduce a conjecture of crew on p adic differential equations analogous to grothendieck s local monodromy theorem also a consequence of results of andre and of mebkhout namely given a finite locally free sheaf on an open p adic annulus with a connection and a compatible frobenius structure the module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix

asymptotic behavior results for nonlinear neutral delay difference equations abstract this paper is concerned with the nonlinear neutral delay difference equation x n c n x n m p n f x n k 0 n n n 0 where is the forward difference operator defined by x n x n 1 x n c n is a sequence of real numbers p n is a positive sequence f c r r m and k are positive integers n 0 is a nonnegative integer and n n 0 n 0 n 0 1 n 0 2 sufficient conditions are obtained under which every solution of equation is bounded and tends to a constant as n our results improve and extend some known results one example is given to illustrate our results

oscillation of nonlinear delay difference equations abstract in this paper two interesting oscillation criteria are obtained for all solutions of the nonlinear delay difference equations of the form yn 1 yn pnf yn k 0 n 0 1 2 some applications are given to demonstrate the advantage of results obtained in this paper our results also improve the existing results in the literature even when applying them to the linear delay difference equation

slic superpixels compared to state of the art superpixel methods computer vision applications have come to rely increasingly on superpixels in recent years but it is not always clear what constitutes a good superpixel algorithm in an effort to understand the benefits and drawbacks of existing methods we empirically compare five state of the art superpixel algorithms for their ability to adhere to image boundaries speed memory efficiency and their impact on segmentation performance we then introduce a new superpixel algorithm simple linear iterative clustering slic which adapts a k means clustering approach to efficiently generate superpixels despite its simplicity slic adheres to boundaries as well as or better than previous methods at the same time it is faster and more memory efficient improves segmentation performance and is straightforward to extend to supervoxel generation

oscillation of delay difference equation we introduce some new techniques to analyze generalized characteristic equations to obtain several infinite sum sharp conditions for oscillation of the following delay difference equation xn 1 xn i 1mpi n xn ki 0 n 0 1 2 where pi n 0 and ki are positive integers

oscillation of delay difference equations with several delays abstract in this paper we obtain some new oscillation criteria for the difference equation with several delays x n 1 x n i 1 m p i n x n k i 0 n 0 1 2 which improve the existing results in the literature the mistakes in comput math appl 44 2002 817 821 are pointed out

turbopixels fast superpixels using geometric flows we describe a geometric flow based algorithm for computing a dense oversegmentation of an image often referred to as superpixels it produces segments that on one hand respect local image boundaries while on the other hand limiting undersegmentation through a compactness constraint it is very fast with complexity that is approximately linear in image size and can be applied to megapixel sized images with high superpixel densities in a matter of minutes we show qualitative demonstrations of high quality results on several complex images the berkeley database is used to quantitatively compare its performance to a number of oversegmentation algorithms showing that it yields less undersegmentation than algorithms that lack a compactness constraint while offering a significant speedup over n cuts which does enforce compactness

global stability for separable nonlinear delay differential systems abstract in this paper we consider separable nonlinear delay differential systems and we establish conditions for global asymptotic stability of the zero solution applying these we offer improved 3 2 type criteria for global asymptotic stability of nonautonomous lotka volterra systems with delays

new results for oscillation of delay difference equations in this paper we consider the delay difference equation xn 1 xn pnxn k 0 n 0 1 2 where pn is a sequence of nonnegative real numbers and k is a positive integer some new results for the oscillation of this equation are obtained our theorems improve all known results in the literature

global asymptotic stability for nonlinear difference equations in this paper some sufficient conditions are established for the asymptotic stability of solutions of the nonlinear difference equationx n 1 x n a nx n k b nf x n l n 0 which generalize and improve some exist results in the literature

global stability for separable nonlinear delay differential equations consider the following separable nonlinear delay differential equation dy t dt i 0ma i t g i y t i t t t 0y t f t t t 0 where we assume that there is a strictly monotone increasing function f x on such that f 0 0 00 0 i m andiff x x thenlim x f x orlim x f x isfinite in this paper to the above separable nonlinear delay differential equation we establish conditions of global asymptotic stability for the zero solution in particular for a special wide class of f x which contains a case of f x e x 1 we give more explicit conditions applying these we offer conditions of global asymptotic stability for solutions of nonautonomous logistic equations with delays

the semicycles of solutions of delay difference equations in this paper we study the semicycles of oscillatory solutions of the delay difference equation yn 1 yn pnyn k 0 where pn is is a sequence of nonnegative real numbers and k is a positive integer upper bound of numbers of terms of semicycles are determined

oscillation results for difference equations with several oscillating coefficients this paper presents a new sufficient condition for the oscillation of all solutions of difference equations with several deviating arguments and oscillating coefficients corresponding difference equations of both retarded and advanced type are studied examples illustrating the results are also given

global attractivity for a nonlinear difference equation with variable delay abstract in this paper we give sufficient conditions under which every solution of the nonlinear difference equation with variable delay x n 1 x n p n f x g n 0 n 0 1 2 tends to zero as n here p n is a nonnegative sequence f r r is a continuous function with xf x 0 if x 0 and g n z is nondecreasing and satisfies g n n for n 0 and lim n g n

semicycles of solutions of nonlinear difference equations with several delays abstract in this paper we study the semicycles of oscillatory solutions of nonlinear difference equation with several delays where pi n is a real sequence with pi n 0 for all large n l mi kij are positive integers ij i 1 2 l j 1 2 mi are nonnegative real numbers with mij 1 ij 1 i 1 2 l upper bound of numbers of terms of semicycles are determined

an estimate of numbers of terms of semicycles of delay difference equations in this paper we study the semicycles of oscillatory solutions of the delay difference equation yn 1 yn pnyn k 0 where pn is a sequence of nonnegative real numbers and k is a positive integer upper bound of numbers of terms of semicycles are determined in the case when our results improve and complement known results in literature

asymptotic stability in perturbed delay difference systems abstract consider the delay difference system x i n 1 x i n b i x i n l i n j 1 m d i j n x j n h i j n i j 1 2 m where 0 l i n l i 0 h i j n h i j d i j n d i j l i h i j are nonnegative integers b i 0 d i j 0 are real constants it is shown that the trivial solution of the above system is asymptotically stable if b i l i 1 3 2 1 2 l i 1 i 1 2 m and a certain matrix derived from the coefficient matrix is a nonsingular m matrix

uniform stability of nonlinear difference systems abstract we offer sufficient conditions for the uniform stability and uniformly asymptotic stability of the zero solution of the nonlinear difference system formula where 0 1 f n s r sis the set of all functions n k 0 rfor somek n andxn sis defined byxn m x n m form n k 0

persistence contractivity and global stability in logistic equations with piecewise constant delays abstract we establish sufficient conditions for the persistence and the contractivity of solutions and the global asymptotic stability for the positive equilibrium n 1 a i 0 m b i of the following differential equation with piecewise constant arguments dn t dt n t r t 1 an t i 0 m b i n n i n t n 0 1 2 n 0 n 0 0 and n j n j 0 j 1 2 m where r t is a nonnegative continuous function on 0 r t 0 i 0mbi 0 bi 0 i 0 1 2 m and a i 0mbi 0 these new conditions depend on a b0 and i 1mbi and hence these are other type conditions than those given by so and yu hokkaido math j 24 1995 269 286 and others in particular in the case m 0 and r t r 0 we offer necessary and sufficient conditions for the persistence and contractivity of solutions we also investigate the following differential equation with nonlinear delay terms dx t dt x t r t 1 ax t g x t x t 1 x t m t 0 x k k 0 0 k m and 0 0 where r t is a nonnegative continuous function on 0 r t 0 1 ax g x x x 0 has a unique solution x 0 and g x0 x1 xm c1 0 0 0

oscillation of parabolic neutral delay difference equations with several positive and negative coefficients we obtain some oscillation criteria for the parabolic neutral delay difference equations with several positive and negative coefficients

global stability for nonlinear difference equations with variable coefficients abstract consider the following nonlinear difference equation with variable coefficients x n 1 x n j 0 m a j n f j x n j n 0 1 2 x j x j m j 0 where a j n 0 0 j m j 0 m a j n 0 and n 0 j 0 m a j n we assume that there exists a strictly monotone increasing function f x on such that f 0 0 0 f j x f x 1 x 0 0 j m and lim x f x is finite if f x x in this paper we establish sufficient conditions for the zero solution of the above equation to be globally asymptotically stable applying these conditions to some special cases we improve the 3 2 criteria type stability conditions for linear and nonlinear difference equations

global attractivity of neutral difference equations abstract in this paper we discuss the global attractivity of the neutral difference equation n c n k p n n l 0 n 0 1 2 where is the forward difference operator c 1 1 k l and pn is a sequence of nonnegative real numbers

automatic segmentation of mitochondria in em data using pairwise affinity factorization and graph based contour searching in this paper we investigate the segmentation of closed contours in subcellular data using a framework that primarily combines the pairwise affinity grouping principles with a graph partitioning contour searching approach one salient problem that precluded the application of these methods to large scale segmentation problems is the onerous computational complexity required to generate comprehensive representations that include all pairwise relationships between all pixels in the input data to compensate for this problem a practical solution is to reduce the complexity of the input data by applying an over segmentation technique prior to the application of the computationally demanding strands of the segmentation process this approach opens the opportunity to build specific shape and intensity models that can be successfully employed to extract the salient structures in the input image which are further processed to identify the cycles in an undirected graph the proposed framework has been applied to the segmentation of mitochondria membranes in electron microscopy data which are characterized by low contrast and low signal to noise ratio the algorithm has been quantitatively evaluated using two datasets where the segmentation results have been compared with the corresponding manual annotations the performance of the proposed algorithm has been measured using standard metrics such as precision and recall and the experimental results indicate a high level of segmentation accuracy

the asymptotic stability of xn 1 axn bxn k 0 we obtain necessary and sufficient conditions for the asymptotic stability of the difference equation xn 1 axn bxn k 0 n 0 1 2 where the coefficients a and b are real numbers and the delay k is a nonnegative integer

oscillation for even order delay difference equations with unstable type in this paper we first prove the even odd delay difference equation with unstable type d mx email protected i 1 np i n x n k i n 0 1 2 has always a positive solution which tends infinity as n then we obtain some oscillation criteria for all bounded solutions of eq

oscillations of difference equations with several delays abstract consider the first order delay difference equation where lim infn pi n pi 0 ki 0 i 1 2 sufficient conditions for the oscillation of all solutions of the above equation are established in the case when the corresponding limiting equation admits nonoscillatory solutions oscillation criteria for the nonlinear difference equation are also derived as applications

nonexistence and existence of positive solutions for difference equations with unbounded delay consider the delay difference equation xn 1 xn pnx n 0 0 1 2 where n z n n for n n and limn n pn r some existence results of positive solutions and oscillation criteria for this equation are obtained

graph based tools for microscopic cellular image segmentation we propose a framework of graph based tools for the segmentation of microscopic cellular images this framework is based on an object oriented analysis of imaging problems in pathology our graph tools rely on a general formulation of discrete functional regularization on weighted graphs of arbitrary topology it leads to a set of useful tools which can be combined together to address various image segmentation problems in pathology to provide fast image segmentation algorithms we also propose an image simplification based on graphs as a pre processing step the abilities of this set of image processing discrete tools are illustrated through automatic and interactive segmentation schemes for color cytological and histological images segmentation problems

oscillation criteria for difference equations with unbounded delay consider the delay difference equation n 1 n pn n 0 n 0 1 2 where n z is nondecreasing n n for n n and limn n pn is a nonnegative sequence some oscillation criteria for this equation are obtained

stability for first order delay dynamic equations on time scales in this paper we establish some sufficient conditions for the uniform stability and the uniformly asymptotical stability of the first order delay dynamic equation x d t p t x t t t 0 t t where t is a time scale p is rd continuous and positive the delay function t t 0 r our results unify the corresponding ones for differential and difference equations to the best of our knowledge this is the first time to discuss the asymptotical behavior of delay dynamic equations on time scales

sufficient conditions for the oscillation of linear delay difference equations with oscillating coefficients abstract in this paper sufficient conditions for the oscillation of all solutions of the delay difference equation xn 1 xn pnxn k 0 n 0 1 2 are established where the coefficient pn itself may be allowed to be oscillatory we also give an example to demonstrate the advantage of our results

classicality for small slope overconvergent automorphic forms on some compact pel shimura varieties of type c we study the rigid cohomology of the ordinary locus in some compact pel shimura varieties of type c with values in automorphic local systems and use it to prove a small slope criterion for classicality of overconvergent hecke eigenforms this generalises work of coleman and is a first step in an ongoing project to extend the cohomological approach to classicality to higher dimensional shimura varieties

a global stability criterion in nonautonomous delay differential equations abstract consider the following nonautonomous nonlinear delay differential equation d y t d t a t y t i 0 m a i t g i y i t t t 0 y t t t t 0 where we assume that there is a strictly monotone increasing function f x on such that f 0 0 0 g i x f x 1 x 0 0 i m and if f x x then lim x f x or lim x f x is finite in this paper to the above nonautonomous nonlinear delay differential equation we establish conditions of global asymptotic stability for the zero solution in particular for a special wide class of f x which contains two cases f x e x 1 and f x x we give more explicit conditions which are some extension of the 3 2 type criterion applying these to discrete models of nonautonomous delay differential equations we also obtain new sufficient conditions of the global asymptotic stability of the zero solution

finite local monodromy of overconvergent unit root f isocrystals on a curve we prove that the category of p adic continuous representations of a fundamental group of a curve over a perfect field of a positive characteristic p with finite local monodromy is equivalent to that of overconvergent unit root f isocrystals on the curve to show the equivalence of categories we study the local theory and apply it to the global case

distance regularized level set evolution and its application to image segmentation level set methods have been widely used in image processing and computer vision in conventional level set formulations the level set function typically develops irregularities during its evolution which may cause numerical errors and eventually destroy the stability of the evolution therefore a numerical remedy called reinitialization is typically applied to periodically replace the degraded level set function with a signed distance function however the practice of reinitialization not only raises serious problems as when and how it should be performed but also affects numerical accuracy in an undesirable way this paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution the level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations the distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward and backward fab diffusion effect which is able to maintain a desired shape of the level set function particularly a signed distance profile near the zero level set this yields a new type of level set evolution called distance regularized level set evolution drlse the distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors in contrast to complicated implementations of conventional level set formulations a simpler and more efficient finite difference scheme can be used to implement the drlse formulation drlse also allows the use of more general and efficient initialization of the level set function in its numerical implementation relatively large time steps can be used in the finite difference scheme to reduce the number of iterations while ensuring sufficient numerical accuracy to demonstrate the effectiveness of the drlse formulation we apply it to an edge based active contour model for image segmentation and provide a simple narrowband implementation to greatly reduce computational cost

new oscillation criteria for delay difference equations abstract this paper considers the delay difference equation x n 1 x n p n x n k 0 n 0 1 2 where pn is a sequence of nonnegative real numbers and k is a positive integer some new oscillation criteria for this equation are obtained our theorems improve all known results in the literature

on exponential dichotomy bohl perron type theorems and stability of difference equations abstract for a delay difference equation x n 1 k d n a n k x k f n in a banach space the following result is proved if for any f l p the solution is x l p then the solution of the homogeneous equation f 0 is exponentially stable this result is applied to obtain new explicit conditions for exponential stability of a scalar nonautonomous delay difference equation