a practical guide to heavy tails statistical techniques and applications part 1 applications heavy tailed probability distributions in the world wide web m e crovella et al self similarity and heavy tails structural modelling of network traffic w willinger et al heavy tails in high frequency financial data u a muller et al stable paretian modelling in finance some empirical and theoretical aspects s mittnik et al risk management and quantile estimation f bassi et al part 2 time series analyzing stable time series r j adler et al inference for linear processes with stable noise m calder r a davis on estimating the intensity of long range dependence in finite and infinite variance time series m s taqqu v teverovsky why non linearities can ruin the heavy tailed modeller s day s i resnick periodogram estimates from heavy tailed data t mikosch bayesian inference for time series with infinite variance stable innovations n ravishanker z qiou part 3 heavy tail estimation hill bootstrap and jackknife estimators for heavy tails o v pictet et al characteristic function based estimation of stable distribution parameters s m kogan d b williams part 4 regression bootstrapping signs and permutations for regression with heavy tailed errors a robust resampling r lepage et al linear regression with stable disturbances j h mcculloch part 5 signal processing deviation from normality in statistical signal processing parameter estimation with alpha stable distributions p tsakalides c l nikias statistical modelling and receiver design for multi user communication networks g a tsihrintzis part 6 model structures subexponential distributions c m goldie c kluppelberg structure of stationary stable processes j rosinski tail behaviour of some shot noise processes g samorodnitsky part 7 numerical procedures numerical approximation of the symmetric stable distribution and density j h mcculloch table of the maximally skewed stable distributions j h mcculloch d b panton multivariate stable distributions approximation estimation simulation and identification j p nolan univariate stable distributions parametrizations and software j p nolan

dct domain watermarking techniques for still images detector performance analysis and a new structure a spread spectrum like discrete cosine transform dct domain watermarking technique for copyright protection of still digital images is analyzed the dct is applied in blocks of 8 spl times 8 pixels as in the jpeg algorithm the watermark can encode information to track illegal misuses for flexibility purposes the original image is not necessary during the ownership verification process so it must be modeled by noise two tests are involved in the ownership verification stage watermark decoding in which the message carried by the watermark is extracted and watermark detection which decides whether a given image contains a watermark generated with a certain key we apply generalized gaussian distributions to statistically model the dct coefficients of the original image and show how the resulting detector structures lead to considerable improvements in performance with respect to the correlation receiver which has been widely considered in the literature and makes use of the gaussian noise assumption as a result of our work analytical expressions for performance measures such as the probability of errors in watermark decoding and the probabilities of false alarms and of detection in watermark detection are derived and contrasted with experimental results

a pyramid vector quantizer the geometric properties of a memoryless laplacian source are presented and used to establish a source coding theorem motivated by this geometric structure a pyramid vector quantizer pvq is developed for arbitrary vector dimension the pvq is based on the cubic lattice points that lie on the surface of an l dimensional pyramid and has simple encoding and decoding algorithms a product code version of the pvq is developed and generalized to apply to a variety of sources analytical expressions are derived for the pvq mean square error mse and simulation results are presented for pvq encoding of several memoryless sources for large rate and dimension pvq encoding of memoryless laplacian gamma and gaussian sources provides rose improvements of 5 64 8 40 and 2 39 db respectively over the corresponding optimum scalar quantizer although suboptimum in a rate distortion sense because the pvq can encode large dimensional vectors it offers significant reduction in rose distortion compared with the optimum lloyd max scalar quantizer and provides an attractive alternative to currently available vector quantizers

spatial structure of time periodic solutions of the ginzburg landau equation abstract we study solutions of the form a x t a x ei t of the complex ginzburg landau equation i a t a xx a a 2 a near those of the integrable limit the nonlinear schrodinger equation i a t a xx a 2 a real we show that spatially periodic and quasiperiodic solutions as well as heteroclinic orbits to them exist in addition to the spatially decaying homoclinic solitions found by hocking and stewartson 1972 we speculate briefly on spatially chaotic solutions

periodic and quasi periodic solutions of degenerate modulation equations abstract in some circumstances degenerations it is essential to add higher order nonlinear coefficients to a ginzburg landau type modulation equation which only has one cubic nonlinearity in this paper we study these degenerate modulation equations we consider the important situation in which the equation has real coefficients and the case of coefficients with small imaginary parts first we determine the stability of periodic solutions the stationary problem is like in the non degenerate case integrable there exist families of quasi periodic and homoclinic solutions this system is perturbed by considering modulation equations with coefficients with small imaginary parts we establish that there exists an unbounded domain in parameter space in which the modulation equation has quasi periodic solutions moreover we show that there is a manifold of codimension 1 in parameter space on which the homoclinic solutions survive the perturbation

symmetric trellis coded vector quantization we present here design techniques for trellis coded vector quantizers with symmetric codebooks that facilitate low complexity quantization as well as partitioning into equiprobable sets for trellis coding the quantization performance of this coder on the independently identically distributed i i d laplacian source matches the performance of trellis based scalar vector quantization tb svq but requires less computational complexity

neutral einstein metrics in four dimensions in matsushita j math phys 22 979 982 1981 ibid 24 36 40 1983 for curvature endomorphisms for the pseudo euclidean space r2 2 an analog of the petrov classification as a basis for applications to neutral einstein metrics on compact orientable four dimensional manifolds is provided this paper points out flaws in matsushita s classification and moreover that an error in chern s pseudo riemannian geometry and the gauss bonnet formula acad brasileira ciencias 35 17 26 1963 and shiing shen chern selected papers springer verlag new york 1978 gauss bonnet formula for pseudo riemannian geometry was incorporated in matsushita s subsequent analysis a self contained account of the subject of the title is presented to correct these errors including a discussion of the validity of an appropriate analog of the thorpe hitchin inequality of the riemannian case when the inequality obtains in the neutral case the euler characteristic is nonpositive in contradistinction to matsushita

analysis of multiresolution image denoising schemes using generalized gaussian and complexity priors research on universal and minimax wavelet shrinkage and thresholding methods has demonstrated near ideal estimation performance in various asymptotic frameworks however image processing practice has shown that universal thresholding methods are outperformed by simple bayesian estimators assuming independent wavelet coefficients and heavy tailed priors such as generalized gaussian distributions ggds in this paper we investigate various connections between shrinkage methods and maximum a posteriori map estimation using such priors in particular we state a simple condition under which map estimates are sparse we also introduce a new family of complexity priors based upon rissanen s universal prior on integers one particular estimator in this class outperforms conventional estimators based on earlier applications of the minimum description length mdl principle we develop analytical expressions for the shrinkage rules implied by ggd and complexity priors this allows us to show the equivalence between universal hard thresholding map estimation using a very heavy tailed ggd and mdl estimation using one of the new complexity priors theoretical analysis supported by numerous practical experiments shows the robustness of some of these estimates against mis specifications of the prior a basic concern in image processing applications

high resolution quantization theory and the vector quantizer advantage the authors consider how much performance advantage a fixed dimensional vector quantizer can gain over a scalar quantizer they collect several results from high resolution or asymptotic in rate quantization theory and use them to identify source and system characteristics that contribute to the vector quantizer advantage one well known advantage is due to improvement in the space filling properties of polytopes as the dimension increases others depend on the source s memory and marginal density shape the advantages are used to gain insight into product transform lattice predictive pyramid and universal quantizers although numerical prediction consistently overestimated gains in low rate 1 bit sample experiments the theoretical insights may be useful even at these rates

sources sinks and wavenumber selection in coupled cgl equations and experimental implications for counter propagating wave systems we study the coupled complex ginzburg landau cgl equations for traveling wave systems and show that sources and sinks are the important coherent structures that organize much of the dynamical properties of traveling wave systems we focus on the regime in which sources and sinks separate patches of left and right traveling waves i e the case that these modes suppress each other we present in detail the framework to analyze these coherent structures and show that the theory predicts a number of general properties which can be tested directly in experiments our counting arguments for the multiplicities of these structures show that independently of the precise values of the coefficients in the equations there generally exists a symmetric stationary source solution which sends out waves with a unique frequency and wave number sinks on the other hand occur in two parameter families and play an essentially passive role being sandwiched between the sources these simple but general results imply that sources are important in organizing the dynamics of the coupled cgl equations simulations show that the consequences of the wavenumber selection by the sources is reminiscent of a similar selection by spirals in the 2d complex ginzburg landau equations sources can send out stable waves convectively unstable waves or absolutely unstable waves we show that there exists an additional dynamical regime where both single and bimodal states are unstable the ensuing chaotic states have no counterpart in single amplitude equations a third dynamical mechanism is associated with the fact that the width of the sources does not show simple scaling with the growth rate e this is related to the fact that the standard coupled cgl equations are not uniform in e in particular when the group velocity term dominates over the linear growth term no stationary source can exist however sources displaying nontrivial dynamics can often survive here our results for the existence multiplicity wavelength selection dynamics and scaling of sources and sinks and the patterns they generate are easily accessible by experiments we therefore advocate a study of the sources and sinks as a means to probe traveling wave systems and compare theory and experiment in addition they bring up a large number of new research issues and open problems which are listed explicitly in the concluding section

a structured fixed rate vector quantizer derived from a variable length scalar quantizer i memoryless sources for pt i see ibid vol 39 no 3 p 851 67 1993 the fixed rate scalar vector quantizer svq for quantizing stationary memoryless sources is extended to a specific type of vector source in which each component is a stationary memoryless scalar subsource independent of the other components algorithms for the design and implementation of the original svq are modified to apply to this case the resulting svq referred to as the extended svq esvq is then used to quantize stationary sources with memory with known autocorrelation function numerical results are presented for the quantization of first order gauss markov sources using this scheme it is shown that the esvq based scheme performs very close to entropy coded transform quantization while maintaining a fixed rate output and outperforms the fixed rate scheme that uses scalar lloyd max quantization of the transform coefficients it is also shown that this scheme performs better than implementable vector quantizers especially at high rates

solutions of neutral delay differential equations using a generalized lambert w function abstract the lambert w function is defined by w a e w a a 0 one of the many applications of the lambert w function is in solving delay differential equations ddes in 2003 asl and ulsoy provided a solution of some ddes in terms of the lambert w functions asl et al 2003 1 however the solutions are limited to differential equations with delay in the state variable scott et al 2006 2 introduced a generalized lambert function which was further studied by mez and baricz 2017 3 in our work we show that this generalization of the lambert w function provides an analytical solution to neutral delay differential equations nddes nddes are ddes with time delay not only in the state variables but also in the derivative terms this analytical solution is advantageous such that it is similar to the general solutions of linear odes also one can identify how the parameters affect the solution of the equation since our proposed solution is written in terms of these parameters we then propose a new numerical method to solve linear nddes using the generalized lambert w function we test our method to examples with known solutions we also provide a real world application by solving an ndde model of the population growth of an e coli culture using our proposed approach

pulses in a complex ginzburg landau system persistence under coupling with slow diffusion abstract the ginzburg landau gl equation is essential for understanding the dynamics of patterns in a wide variety of physical contexts it governs the evolutions of small amplitude instabilities near criticality if the instabilities are however driven by two coupled instability mechanisms of which one corresponds with a neutrally stable mode their evolution is described by a gl equation coupled to a diffusion equation in this paper we study the influence of an additional diffusion equation on the existence of pulse solutions in the complex gl equation in light of recently developed insights into the effect of slow diffusion on the stability of pulses we consider the case of slow diffusion i e in which the additional diffusion equation acts on a long spatial scale in previous work a doelman g hek n valkhoff stabilization by slow diffusion in a real ginzburg landau system j nonlinear sci 14 2004 237 278 a doelman g hek n j m valkhoff algebraically decaying pulses in a ginzburg landau system with a neutrally stable mode nonlinearity 20 2007 357 389 we restricted ourselves to a model with both real coefficients and more importantly a real amplitude a rather than the complex valued a that is needed to completely describe the pattern formation near criticality in this simpler setting we proved that pulse solutions of the gl equation can both persist and be stabilized under coupling with a slow diffusion equation in the current work we no longer make these restrictions so that the problem is higher dimensional and intrinsically harder by a combination of a geometrical approach and explicit perturbation analysis we consider the persistence of the solitary pulse solution of the gl equation under coupling with the additional diffusion equation in the two limiting situations of the nearly real gl equation and the near nonlinear schrodinger equation we show that the pulse solutions can indeed persist under this coupling

hole solutions in the 1d complex ginzburg landau equation abstract the cubic complex ginzburg landau equation cgle has a one parameter family of traveling localized source solutions these so called nozaki bekki holes are dynamically stable in some parameter range but always structurally unstable a perturbation of the equation in general leads to a positive or negative monotonic acceleration or an oscillation of the holes this confirms that the cubic cgle has an inner symmetry as a consequence small perturbations change some of the qualitative dynamics of the cubic cgle and enhance or suppress spatio temporal intermittency in some parameter range an analytic stability analysis of holes in the cubic cgle and a semianalytical treatment of the acceleration instability in the perturbed equation is performed by using matching and perturbation methods furthermore we treat the asymptotic hole shock interaction the results which can be obtained fully analytically in the nonlinear schro dinger limit are also used for the quantitative description of modulated solutions made up of periodic arrangements of traveling holes and shocks

interval type 2 relative entropy fuzzy c means clustering fuzzy set theory especially type 2 fuzzy set theory provides an efficient tool for handling uncertainties and vagueness in real world observations among various clustering techniques type 2 fuzzy clustering methods are the most effective methods in the case of having no prior knowledge about observations while uncertainties in type 2 fuzzy clustering parameters are investigated by researchers uncertainties associated with membership degrees are not very well discussed in the literature in this paper investigating the latter uncertainties is our concern and interval type 2 relative entropy fuzzy c means it2 refcm clustering method is proposed the computational complexity of the proposed method is discussed and its performance is examined using several experiments the obtained results show that the proposed method has a very good ability in detecting noises and assignment of suitable membership degrees to observations

breaking the hidden symmetry in the ginzburg landau equation in this paper we study localised traveling solutions to a ginzburg landau equation to which we have added a small o e 0 e 1 quintic term we consider this term as a model for the higher order nonlinearities which appear in the derivation of the ginzburg landau equation by a combination of a geometrical approach and an explicit perturbation analysis we are able to relate the family of bekki nozaki solutions of the cubic equation n bekki and b nozaki 1985 phys lett a 110 133 135 to a curve of co dimension 2 homoclinic bifurcations in parameter space thus we are able to interpret the hidden symmetry which has been conjectured to explain the existence of the bekki nozaki solutions from the point of view of bifurcation theory we show that the quintic term breaks this hidden symmetry and that the one parameter family of bekki nozaki solutions is embedded in a two parameter family of homoclinic solutions which exist at a co dimension 1 homoclinic bifurcation furthermore we show mainly by geometrical arguments that the addition of the small quintic term can create large families of traveling localised structures that cannot exist in the cubic case these solutions exist in open subsets of the parameter space and correspond to structurally stable multi or n circuit heteroclinic orbits in an ode reduction and have a monotonically decreasing increasing amplitude except for a number n of relatively fast jumps

optimum quantizer performance for a class of non gaussian memoryless sources the performance of optimum quantizers subject to an entropy constraint is studied for a wide class of memoryless sources for a general distortion criterion necessary conditions are developed for optimality and a recursive algorithm is described for obtaining the optimum quantizer under a mean square error criterion the performance of entropy encoded uniform quantization of memoryless gaussian sources is well known to be within 0 255 bits sample of the rate distortion bound at relatively high rates despite claims to the contrary it is demonstrated that similar performance can be expected for a wide range of memoryless sources indeed for the cases considered the worst case performance is observed to be less than 0 3 bits sample from the rate distortion bound and in most cases this disparity is less at iow rates

relative entropy collaborative fuzzy clustering method the main task of clustering methods especially fuzzy methods is to find whether natural grouping exists in data and to impose identity on them in some situations data are stored in several data sites and to discover the global structures clustering methods have to be aware of dependencies in all data sites collaborative fuzzy clustering methods have been proposed and widely studied to answer such need in this paper a novel collaborative fuzzy clustering method is proposed in this method relative entropy concept is used as the communication method a new approach is applied to calculate the interaction coefficient between data sites and horizontal and vertical modes of the proposed method are discussed performance of the proposed method is evaluated using several experiments and the results show that it has the highest quality of collaboration and could classify data more efficiently in many clustering methods it is assumed that the data are stored in one data site ways of communication between data sites effects the clustering results a new communication method based on relative entropy is proposed it minimizes the divergence of membership degrees of kth data in ith cluster in all data sites recfc and its two modes could efficiently classify data stored in several data sites

precise and fast computation of lambert w functions without transcendental function evaluations we have developed a new method to compute the real valued lambert w functions w 0 z and w 1 z the method is a composite of 1 the series expansions around the branch point w 1 and around zero w 0 and 2 the numerical solution of the modified defining equation w ze w in the latter process we 1 repeatedly duplicate a test interval until it brackets the solution 2 conduct bisections to find an approximate solution and 3 improve it by a single application of the fifth order formula of schroder s method the first two steps are accelerated by preparing auxiliary numerical constants beforehand and utilizing the addition theorem of the exponential function as a result the new method requires no call of transcendental functions such as the exponential function or the logarithm this makes it around twice as fast as existing methods 1 7 and 2 0 times faster than the methods of fritsch et al 1973 and veberic 2012 16 14 for w 0 z and 1 8 and 2 0 times faster than the methods of veberic 2012 14 and chapeau blondeau and monir 2002 13 for w 1 z

numerical evaluation of the lambert w function and application to generation of generalized gaussian noise with exponent 1 2 we address the problem of synthesizing a generalized gaussian noise with exponent 1 2 by means of a nonlinear memoryless transformation applied to a uniform noise we show that this transformation is expressable in terms of a special function known under the name of the lambert w function we review the main methods for numerical evaluation of the relevant branch of the multivalued lambert w function with controlled accuracy and complement them with an original rational function approximation based on these methods synthesis of the generalized gaussian noise can be performed with arbitrary accuracy we construct a simple and fast evaluation algorithm with prescribed accuracy which is especially suited for monte carlo simulation requiring large numbers of realizations of the generalized gaussian noise

pseudo chern classes of an almost pseudo hermitian manifold pour une variete presque pseudo hermitienne on definit des classes pseudo chern sur son fibre tangent complexifiee avec la structure pseudo hermitienne representee par certaines formes ad jcp q invariantes sur la variete

slow time periodic solutions of the ginzburg landau equation in this paper we study the behaviour of solutions of the form if z t q z e i wt e 1 of the rescaled ginzburg landau equation k 1 1 ib l kl2 k 1 ia kzz for a ca b eb w plays the role of free parameter this leads to a perturbation analysis on a complex duffing equation similar to the analysis of holmes physica d 23 1986 84 we show that the spatial quasiperiodic solutions of the unperturbed e 0 case disappear due to the perturbation and prove the existence of degenerated periodic solutions which oscillate through the origin we also establish the existence of several types of heteroclinic orbits connecting counterrotating periodic patterns

lattice and trellis quantization with lattice and trellis bounded codebooks high rate theory for memoryless sources high rate lattice and trellis quantizers for nonuniform sources are introduced and analyzed the performance of these quantizers is determined by two separable quantities the granular gain and the boundary gain which are determined by the shapes of the granular cells and of the support region respectively the granular gain and boundary gain are the duals of shaping and coding gain in data transmission applications using this duality it is shown for gaussian sources that the ultimate achievable boundary gain with high rate lattice bounded lattice codebooks is the same as the ultimate gain that can be obtained from variable rate entropy coding it is observed that if lattice codebooks can achieve the ultimate granular gain of 0 255 b per dimension then lattice bounded lattice codebooks can approach the rate distortion limit the performance of lattice quantizers is compared to that of optimum vector quantizers

geometric source coding and vector quantization a geometric formulation is presented for source coding and vector quantizer design motivated by the asymptotic equipartition principle the authors consider two broad classes of source codes and vector quantizers elliptical codes and quantizers based on the gaussian density function and pyramid codes and quantizers based on the laplacian density function elliptical and weighted pyramid vector quantizers are developed by selecting codewords as points in a lattice that lie on or near a specified ellipse or pyramid the combination of geometric structure and lattice basis allows simple encoding and decoding algorithms

relative entropy fuzzy c means clustering pattern recognition is a collection of computer techniques to classify various observations into different clusters of similar attributes in either supervised or unsupervised manner application of fuzzy logic to unsupervised classification or clustering methods has resulted in many wildly used techniques such as fuzzy c means fcm method however when the observations are too noisy the performance of such methods might be reduced thus in this paper a new fuzzy clustering method based on fcm is presented and the relative entropy is added to its objective function as a regularization function to maximize the dissimilarity between clusters several examples are provided to examine the performance of the proposed clustering method the obtained results show that the proposed method has a very good ability in detecting noises and assignment of suitable membership degrees to the observations

numerical computation of inverse complete elliptic integrals of first and second kinds we developed the numerical procedures to evaluate the inverse functions of the complete elliptic integrals of the first and the second kind k m and e m with respect to the parameter m the evaluation is executed by inverting eight sets of the truncated taylor series expansions of the integrals in terms of m or of log 1 m the developed procedures are 1 so precise that the maximum absolute errors are less than 3 5 machine epsilons and 2 30 40 faster than the evaluation of the integrals themselves by the fastest procedures fukushima 2009a 2011

strong selection or rejection of spatially periodic patterns in degenerate bifurcations abstract when studying bifurcating space periodic solutions one often has a situation common in many problems of fluid dynamics in which in the r k plane r a control parameter such as reynolds number k wave number the passage from linear stability to instability is characterized by a parabola like curve having a minimum at r c k c we analyse classes of problems in which the coefficients of nonlinear terms in the amplitude equation go through zero near k c various examples of such degenerate problems can be found in the literature but have not been studied yet we give an extensive classification of bifurcation pictures which display rather unusual behaviour we further study the stability of these periodic solutions subject to quite general perturbation we find as a general result that all bifurcating solutions are unstable except for a small neighbourhood of a curve in the r k plane there is hence a strong selection mechanism of periodic patterns which fixes for each value of r with a very small uncertainty the wave number of the stable bifurcating periodic solution for one class of problems the curve continues to exist for all values of r for which our theory is consistent for another class the curve stops at a value r r c for r r all bifurcating periodic solutions are unstable in this case instability provides a mechanism of rejection of all periodic patterns in the last section we analyse the particular case of the blasius boundary layer flow

thorpe hitchin inequality for compact einstein 4 manifolds of metric signature and the generalized hirzebruch index formula it is proved that the euler characteristic and the hirzebruch index of a compact oriented einstein 4 manifold of metric signature satisfy an inequality which is well known as the thorpe hitchin inequality for the case of a riemannian metric to derive the inequality a generalized hirzebruch formula relating the index to the first pseudo pontrjagin number of the manifold is proved this formula may be contrasted with chern s generalized gauss bonnet formula for a pseudo riemannian manifold

lattice vector quantization of generalized gaussian sources many important sources of data including sub band image and speech coefficients are highly peaked and can be well modeled by the family of generalized gaussian gg pdfs parameterized by a shape parameter spl nu we present here algorithms for defining and quantizing to a z lattice in which the boundary is optimized to the characteristics of gg sources and show that these techniques lead to high performance and low complexity for bit rates and dimensions that are of interest in a number of practical coding applications we derive an analytical description of the granular and overload distortion valid for low and moderate bit rates and also provide a description of quantizer performance in the limit of high rate and dimension

on the structure of the solution set of a generalized euler lambert equation abstract the transcendental equation x e x z and its solutions described by the lambert w function often occur in physics and mathematics in the last decades it turned out that the study of similar but more general equations is necessary in molecular physics in the theory of general relativity and also in the description of bose fermi mixtures as well as in some combinatorial problems in this paper we offer a full description for the solution set of a one parameter generalization of the above mentioned equation

noise enhanced performance for an optimal bayesian estimator a novel instance of a stochastic resonance effect under the form of a noise improved performance is shown to be possible for an optimal bayesian estimator estimation of the frequency of a periodic signal corrupted by a phase noise is considered the optimal bayesian estimator achieving the minimum of the mean square estimation error is explicitly derived conditions are exhibited where this minimal error is reduced when the noise level is raised over some ranges where this occurs essentially with non gaussian noise in the tested configurations these results contribute a new step in the exploration of stochastic resonance and its potentialities for signal processing

on the modeling of dct and subband image data for compression image subband and discrete cosine transform coefficients are modeled for efficient quantization and noiseless coding quantizers and codes are selected based on laplacian fixed generalized gaussian and adaptive generalized gaussian models the quantizers and codes based on the adaptive generalized gaussian models are always superior in mean squared error distortion performance but generally by no more than 0 08 bit pixel compared with the much simpler laplacian model based quantizers and noiseless codes this provides strong motivation for the selection of pyramid codes for transform and subband image coding

singular heteroclinic orbits for degenerate modulation equations the problem of finding heteroclinic orbits for the quintic ginzburg landau equation in the case that the imaginary parts of the coefficients are o with 0 1 is considered when c where is a distinguished parameter in the equation and 0 there exists a singular heteroclinic orbit connecting a stable finite amplitude state to the stable zero state it is shown that for a certain region of parameter space this orbit persists for small with a wave speed c which is o furthermore using an approach reminiscent of the melnikov method the sign of c 0 is calculated this calculation is crucial in settling the persistence question finally it is shown that for this wave speed it is possible for additional heteroclinic orbits to exist these additional orbits connect two finite amplitude states

statistical texture characterization from discrete wavelet representations we conjecture that texture can be characterized by the statistics of the wavelet detail coefficients and therefore introduce two feature sets 1 the wavelet histogram signatures which capture all first order statistics using a model based approach and 2 the wavelet co occurrence signatures which reflect the coefficients second order statistics the introduced feature sets outperform the traditionally used energy best performance is achieved by combining histogram and co occurrence signatures

exact solutions of the one dimensional quintic complex ginzburg landau equation abstract exact solitary wave solutions of the one dimensional quintic complex ginzburg landau equations are obtained using a method derived from the painleve test for integrability these solutions are expressed in terms of hyperbolic functions and include the pulses and fronts found by van saarloos and hohenberg we also find previously unknown sources and sinks the emphasis is put on the systematic character of the method which breaks away from approaches involving somewhat ad hoc ansatze

the time dependent amplitude equation for the swift hohenberg problem precise estimates for the validity of the amplitude approximation for the swift hohenberg equation are given in a fully time dependent framework it is shown that small solutions of ordero which are modulated like stationary solutions have an evolution which is well described in the amplitude approximation for a time of ordero 2 for the proofs we use techniques for nonlinear semigroups and oscillatory integrals

multipulse like orbits for a singularly perturbed nearly integrable system abstract we use topological shooting arguments to study the existence of multipulse like orbits for a singularly perturbed 3 dimensional dynamical system established as a model problem for the 1 dimensional complex ginzburg landau equations our main result improves an earlier result obtained by doelman and hek

lattice codebook enumeration for generalized gaussian source the goal of this correspondence is to propose a low complexity enumeration algorithm for lattice vectors based on a geometrical interpretation and valid for different source distributions i e for different l sub p norms in the range 0 p spl les 2 as a particular case we obtain the laplacian enumeration formula of fischer this point of view offers various advantages and particularly it enables one to make the link with the generalized theta series and to reduce the algorithm to the calculation of a few convolutional products in the special cases p 1 and p 2 using a dedicated digital signal processing dsp architecture convolutional products are easy to implement and require few arithmetic operations our algorithm developed for the z sup n lattice can be generalized to other lattices like the d sub n

uniform and piecewise uniform lattice vector quantization for memoryless gaussian and laplacian sources lattice vector quantizer design procedures for nonuniform sources are presented the procedures yield lattice vector quantizers with excellent performance and retaining the structure required for fast quantization analytical methods for truncating and scaling lattices to be used in vector quantizations are given and their utility is demonstrated for independent and identically distributed i i d gaussian and laplacian sources an analytical technique for piecewise linear multidimensional compandor designs is evaluated for i i d gaussian and laplacian sources by comparing its performance to that of the other vector quantizers

elliptic solutions of the quintic complex one dimensional ginzburg landau equation the conte musette method has been modified for the search of only elliptic solutions to systems of differential equations a key idea of this a prior restriction is to simplify calculations by means of the use of a few laurent series solutions instead of one and the use of the residue theorem the application of this approach to the quintic complex one dimensional ginzburg landau equation cgle5 allows us to find elliptic solutions in the wave form restrictions on coefficients which are necessary conditions for the existence of elliptic solutions for the cgle5 have been found as well we demonstrate that to find elliptic solutions the analysis of a system of differential equations is preferable to the analysis of the equivalent single differential equation

bifurcation of homoclinic orbits to a saddle focus in reversible systems with so 2 symmetry we study reversible so 2 invariant vector fields in r4 depending on a real parameter e which possess for e 0 a primary family of homoclinic orbits t h0 s1 under a transversality condition with respect to e the existence of homoclinic n pulse solutions is demonstrated for a sequence of parameter values e n k 0 for k the existence of cascades of 2l3m pulse solutions follows by showing their transversality and then using induction the method relies on the construction of an so 2 equivariant poincare map which after factorization is a composition of two involutions a logarithmic twist map and a smooth global map reversible periodic orbits of this map corresponds to reversible periodic or homoclinic solutions of the original problem as an application we treat the steady complex ginzburg landau equation for which a primary homoclinic solution is known explicitly

product code vector quantizers for waveform and voice coding memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding lpc one approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy such shape gain vector quantizers can be applied both to waveform coding using a quadratic error distortion measure and to voice coding using an itakura saito distortion measure in each case the minimum distortion reproduction vector can be found by first selecting a shape code word and then based on that choice selecting a gain codeword several algorithms are presented for the design of shape gain vector quantizers based on a traning sequence of data or a probabilistic model the algorithms are used to design shape gain vector quantizers for both the waveform coding and voice coding application the quantizers are simulated and their performance is compared to that of previously reported vector quantization systems

fast quantizing and decoding and algorithms for lattice quantizers and codes for each of the lattices a n n geq 1 d n n geq 2 e 6 e 7 e 8 and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point if these lattices are used for vector quantizing of uniformly distributed data the algorithm finds the minimum distortion lattice point if the lattices are used as codes for a gaussian channel the algorithm performs maximum likelihood decoding

fronts pulses sources and sinks in generalized complex ginzberg landau equations an important clement in the long time dynamics of pattern forming systems is a class of solutions we will call coherent structures these are states that are either themselves localized or that consist of domains of regular patterns connected by localized defects or interfaces this paper summarizes and extends recent work on such coherent structures in the one dimensional complex ginzburg landau equation and its generalizations for which rather complete information can be obtained on the existence and competition of fronts pulses sources and sinks for the special subclass of uniformly translating structures the solutions are derived from a set of ordinary differential equations that can be interpreted as a flow in a three dimensional phase space fixed points of the flow correspond to the two basic building blocks of coherent structures uniform amplitude states and evanescent waves whose amplitude decreases smoothly to zero a study of the stability of the fixed points under the flow leads to results on the existence and multiplicity of the different coherent structures the dynamical analysis of the original partial differential equation focusses on the competition between pulses and fronts and is expressed in terms of a set of conjectures for front propagation that generalize the marginal stability and pinch point approaches of earlier authors these rules together with an exact front solution whose dynamics plays an important role in the selection of patterns yield an analytic expression for the upper limit of the range of existence of pulse solutions as well as a determination of the regions of parameter space where uniformly translating fron t solutions can exist extensive numerical simulations show consistency with these rules and conjectures for the existence of fronts and pulses in the parameter ranges where no uniformly translating fronts can exist examples are shown of irregularly spreading fronts that generate strongly chaotic regions as well as nonuniformly translating fronts that lead to uniform amplitude states recent perturbative treatments based on expansions about the nonlinear schr6dinger equation are generalized to perturbations of the cubic quintic and derivative schr idinger equations for which both pulses and fronts exist in the unperturbed system comparison of the results with the exact solutions shows that the perturbation theory only yields a subset of the relevant solutions nevertheless those that are obtained are found to be consistent with the general conjectures and in particular they provide an analytic demonstration of front pulse competition while the discussion of the competition between fronts and pulses focusses on the complex ginzburg landau equation with quintic terms and a subcritical bifurcation a number of results are also presented for the cubic equation in particular the existence of a family of moving source solutions derived by bekki and nozaki for this equation contradicts the naive counting arguments we attribute this contradiction to a hidden symmetry of the solution but have not been able to show explicitly how this symmetry affects the phase space orbits

homoclinic saddle node bifurcations and subshifts in a three dimensional flow we study a two parameter family of three dimensional vector fields that are small perturbations of an integrable system possessing a line of degenerate saddle points connected by a manifold of homoclinic loops under perturbation this manifold splits and undergoes a quadratic homoclinic tangency perturbation methods followed by geometrical analyses reveal the presence of countably infinite sets of homoclinic orbits to and a non wandering set topologically conjugate to a shift on two symbols a smale horseshoe we use the symbolic description to identify and partially order bifurcation sequences in which the homoclinic orbits appear and we formally derive an explicit two dimensional poincare return map to further illustrate our results the problem was motivated by the search for travelling structures such as fronts and domain walls in partial differential equations

on euler characteristics of compact einstein 4 manifolds of metric signature in the present paper the euler characteristic is studied for a compact oriented einstein 4 manifold of signature for such a manifold there are three types of normal forms of the curvature tensor it is shown that for each type the euler characteristic is nonnegative and even several new inequalities are obtained concerning the euler characteristic and the volume of the manifold the second betti number is even and if it is zero then the first betti number also vanishes the arguments developed here are based upon the famous work of chern about the gauss bonnet formula for a pseudo riemannian manifold