on the ramanujan conjecture over number fields we extend to an arbitrary number eld the best known bounds towards ramanujan for the group gln n 2 3 4 in particular we present a technique which overcomes the analytic obstacles posed by the presence of an innite group of units

analysis of moments based methods for fractional gaussian noise estimation fractional gaussian noise given as the increment of fractional brownian motion is a stationary gaussian process characterized by the hurst parameter in the paper moments based estimators of the hurst parameter are presented and analyzed with respect to asymptotic variance

triple product p adic l functions for balanced weights we construct p adic triple product l functions that interpolate square roots of central critical l values in the balanced region thus our construction complements that of harris and tilouine there are four central critical regions for the triple product l functions and two opposite settings according to the sign of the functional equation in the first case three of these regions are of interpolation having positive sign they are called the unbalanced regions and one gets three p adic l functions one for each region of interpolation this is the harris tilouine setting in the other setting there is only one region of interpolation called the balanced region we produce the corresponding p adic l function our triple product p adic l function arises as p adic period integrals interpolating normalizations of the local archimedean period integrals the latter encode information about classical representation theoretic branching laws the main step in our construction of p adic period integrals is showing that these branching laws vary in a p adic analytic fashion this relies crucially on the ash stevens theory of highest weight representations over affinoid algebras

ml parameter estimation of a multiscale stochastic process using the em algorithm an algorithm for estimation of the parameters of a multiscale stochastic process based on scale recursive dynamics on trees is presented the expectation maximization algorithm is used to provide maximum likelihood estimates for the general case of a nonhomogeneous tree with no fixed structure for the process dynamics experimental results are presented using synthetic data

bounds for rankin selberg integrals and quantum unique ergodicity for powerful levels reference epfl article 202508doi 10 1090 s0894 0347 2013 00779 1view record in web of science record created on 2014 10 23 modified on 2017 12 10

local e factors and characters of gl 2 introduction the representation theory of gl 2 k for k a nonarchimedean local field is somewhat more complicated than the corresponding theory for gl 2 r in particular the formulas for the characters of discrete series representation of gl 2 r have a concise closed form while the published character formulas for supercuspidal representations of gl 2 k occupy several pages 10 14 the purpose of this paper is to give a concise formula for the character of certain infinite dimensional representations of gl 2 k the representations considered are admissible in the sense that the stabilizer of a vector in the representation space is open in gl 2 k and the subspace stabilized by an open compact subgroup of gl 2 k is finite dimensional irreducible admissible representations ir of gl 2 k satisfy schur s lemma so that the center k of gl 2 k acts by multiplication by a quasicharacter there exists a locally constant character function ch defined on a dense open subgroup of gl 2 k which determines the isomorphism class of ir 7 section 7 jacquet and langlands 7 section 2 introduced factors e 10 x attached to the twist of ir by quasicharacters x of k which describe the action of r in a specific model for each separable quadratic extension l of k there exists an irreducible admissible representation bcl k 1r of gl 2 l the base change of ir to l 9 section 2 this representation of gl 2 l enters into the expression for the character the main result of this paper is the following formula recall that conjugacy classes of nonsplit cartan subgroups are parameterized by quadratic separable field extensions l of k via embeddings of l in gl 2 k

equidistribution of cusp forms in the level aspect let f traverse a sequence of classical holomorphic newforms of fixed weight and increasing square free level q infinity we prove that the pushforward of the mass off to the modular curve of level 1 equidistributes with respect to the poincare measure

estimation of fractal signals from noisy measurements using wavelets the role of the wavelet transformation as a whitening filter for 1 f processes is exploited to address problems of parameter and signal estimations for 1 f processes embedded in white background noise robust computationally efficient and consistent iterative parameter estimation algorithms are derived based on the method of maximum likelihood and cramer rao bounds are obtained included among these algorithms are optimal fractal dimension estimators for noisy data algorithms for obtaining bayesian minimum mean square signal estimates are also derived together with an explicit formula for the resulting error these smoothing algorithms find application in signal enhancement and restoration the parameter estimation algorithms find application in signal enhancement and restoration the parameter estimation algorithms in addition to solving the spectrum estimation problem and to providing parameters for the smoothing process are useful in problems of signal detection and classification results from simulations are presented to demonstrated the viability of the algorithms

signal modeling with filtered discrete fractional noise processes filtered versions of fractionally differenced gaussian noise fdgn processes are studied fractionally differenced gaussian noise is a discrete time equivalent of fractional brownian motion filtered versions of such processes are ideally suited for modeling signals with different short term and long term correlation structure two iterative algorithms for estimating the parameters of filtered fdgn processes are described the first technique is based on the expectation maximization algorithm it converges to a stationary point of the log likelihood function corresponding to the parameters of the model the second technique is a computationally efficient approximate approach it is found to converge experimentally but no proof of its convergence is given the usefulness of filtered fdgn models and the performance of the proposed iterative algorithms are illustrated by fitting filtered fdgn models to speech waveforms and other data corresponding to natural phenomena

texture roughness analysis and synthesis via extended self similar ess model the 2d fractional brownian motion fbm model provides a useful tool to model textured surfaces whose roughness is scale invariant to represent textures whose roughness is scale dependent we generalize the fbm model to the extended self similar ess model in this research we present an estimation algorithm to extract the model parameters from real texture data furthermore a new incremental fourier synthesis algorithm is proposed to generate the 2d realizations of the ess model finally the estimation and rendering methods are combined to synthesize real textured surfaces

fractal estimation using models on multiscale trees we estimate the hurst parameter h of fractional brownian motion or by extension the fractal exponent spl phi of stochastic processes having 1 f sup spl phi like spectra by applying a multiresolution framework this framework admits an efficient likelihood function evaluation allowing us to compute the maximum likelihood estimate of this fractal parameter with relative ease in addition to yielding results that compare well with other proposed methods and in contrast with other approaches our method is directly applicable with at most very simple modification in a variety of other contexts including fractal estimation given irregularly sampled data or nonstationary measurement noise and the estimation of fractal parameters for 2 d random fields

piecewise fractional brownian motion starting from fractional brownian motion fbm of unique parameter h a piecewise fractional brownian motion pfbm of parameters h sub o h sub i and spl gamma is defined this new process has two spectral regimes it behaves like an fbm of parameter h sub o for low frequencies spl omega spl gamma and like an fbm of parameter h sub i for high frequencies spl omega spl ges spl gamma when h sub o h sub i or for limit cases spl gamma spl rarr 0 and spl gamma spl rarr spl infin pfbm becomes classical fbm it is shown that pfbm is a continuous gaussian and nonstationary process having continuous gaussian and stationary increments namely piecewise fractional gaussian noises the asymptotic self similarity of pfbm is shown according to the considered regime at large scale the process is self similar with parameter h sub o and with parameter h sub i at low scale

a multifractal wavelet model with application to network traffic we develop a new multiscale modeling framework for characterizing positive valued data with long range dependent correlations 1 f noise using the haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results the model provides a rapid o n cascade algorithm for synthesizing n point data sets we study both the second order and multifractal properties of the model the latter after a tutorial overview of multifractal analysis we derive a scheme for matching the model to real data observations and to demonstrate its effectiveness apply the model to network traffic synthesis the flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics variance time plots and moment scaling and queuing behavior although for illustrative purposes we focus on applications in network traffic modeling the multifractal wavelet model could be useful in a number of other areas involving positive data including image processing finance and geophysics

multiscale representations of markov random fields recently a framework for multiscale stochastic modeling was introduced based on coarse to fine scale recursive dynamics defined on trees this model class has some attractive characteristics which lead to extremely efficient statistically optimal signal and image processing algorithms the authors show that this model class is also quite rich in particular they describe how 1 d markov processes and 2 d markov random fields mrfs can be represented within this framework the recursive structure of 1 d markov processes makes them simple to analyze and generally leads to computationally efficient algorithms for statistical inference on the other hand 2 d mrfs are well known to be very difficult to analyze due to their noncausal structure and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification in contrast their multiscale representations are based on scale recursive models and thus lead naturally to scale recursive algorithms which can be substantially more efficient computationally than those associated with mrf models in 1 d the multiscale representation is a generalization of the midpoint deflection construction of brownian motion the representation of 2 d mrfs is based on a further generalization to a midline deflection construction the exact representations of 2 d mrfs are used to motivate a class of multiscale approximate mrf models based on one dimensional wavelet transforms they demonstrate the use of these latter models in the context of texture representation and in particular they show how they can be used as approximations for or alternatives to well known mrf texture models

fractal estimation from noisy data via discrete fractional gaussian noise dfgn and the haar basis the authors show that the application of the discrete wavelet transform dwt using the haar basis to the increments of fractional brownian motion fbm also known as discrete fractional gaussian noise dfgn yields coefficients which are weakly correlated and have a variance that is exponentially related to scale similar results were derived by flandrin 1989 tewfik and kim for a continuous time fbm going through a continuous wavelet transform cwt the new theoretical results justify an improvement to a fractal estimation algorithm recently proposed by wornell and oppenheim the performance of the new algorithm is compared with that of wornell and oppenheim s see ieee trans signal processing vol 40 p 611 623 mar 1992 algorithm in numerical simulation

fractional brownian motion a maximum likelihood estimator and its application to image texture fractals have been shown to be useful in characterizing texture in a variety of contexts use of this methodology normally involves measurement of a parameter h which is directly related to fractal dimension in this work the basic theory of fractional brownian motion is extended to the discrete case it is shown that the power spectral density of such a discrete process is only approximately proportional to f a instead of in direct proportion as in the continuous case an asymptotic cramer rao bound is derived for the variance of an estimate of h subsequently a maximum likelihood estimator mle is developed to estimate h it is shown that the variance of this estimator nearly achieves the minimum bound a generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the mle when the discrete fractional brownian process is contaminated with additive gaussian noise the results show that even at signal to noise ratios of 30 db significant errors in estimation of h can result when noise is present the mle is then applied to x ray images of the human calcaneus to demonstrate how the line to line formulation can be applied to the two dimensional case these results indicate that it has strong potential for quantifying texture

extended self similarity in turbulent flows we report on the existence of a hitherto undetected form of self similarity which we call extended self similarity ess ess holds at high as well as at low reynolds number and it is characterized by the same scaling exponents of the velocity differences of fully developed turbulence

trilinear forms and the central values of triple product l functions we give an explicit formula for certain global trilinear forms that appear in jacquet s conjecture in terms of local trilinear forms and the central values of triple product l functions

stochastic models that separate fractal dimension and the hurst effect fractal behavior and long range dependence have been observed in an astonishing number of physical biological geological and socioeconomic systems time series profiles and surfaces have been characterized by their fractal dimension a measure of roughness and by the hurst coefficient a measure of long memory dependence both phenomena have been modeled and explained by self affine random functions such as fractional gaussian noise and fractional brownian motion the assumption of statistical self affinity implies a linear relationship between fractal dimension and hurst coefficient and thereby links the two phenomena this article introduces stochastic models that allow for any combination of fractal dimension and hurst coefficient associated software for the synthesis of images with arbitrary prespecified fractal properties and power law correlations is available the new models suggest a test for self affinity that assesses coupling and decoupling of local and global behavior

nth order fractional brownian motion and fractional gaussian noises a generalization of fractional brownian motion fbm of parameter h in 0 1 is proposed more precisely this work leads to nth order fbm n fbm of h parameter in n 1 n where n is any strictly positive integer they include fbm for the special case n 1 properties of these new processes are investigated their covariance function are given and it is shown that they are self similar in addition their spectral shape is assessed as 1 f sup spl alpha with spl alpha belonging to 1 spl infin providing a larger framework than classical fbm special interest is given to their nth order stationary increments which extend fractional gaussian noises the covariance function and power spectral densities are calculated the properties and signal processing tasks such as a cholesky type synthesis technique and a maximum likelihood estimation method of the h parameter are presented the results show that the estimator is efficient unbiased and reaches the cramer rao lower bound for a large majority of tested values

extending self similarity for fractional brownian motion the fractional brownian motion fbm model has proven to be valuable in modeling many natural processes because of its persistence for large time lags however the model is characterized by one single parameter that cannot distinguish between short and long term correlation effects this article investigates the idea of extending self similarity to create a correlation model that generalizes discrete fbm referred to as asymptotic fbm afbm namely afbm is parameterized by variables controlling short and long term correlation effects it proposes a fast parameter estimation algorithm for afbm based on the haar transform and demonstrates the performance of this parameter estimation algorithm with numerical simulations

quantitatively investigating the locally weak stationarity of modified multifractional gaussian noise a b s t r a c t we suggest that there exists a critical point h 0 70 of the local holder exponent h t for describing the weak stationary stationary for short property of the modified multifractional gaussian noise mmgn from the point of view of engineering more precisely when h t 0 70 for t 0 the stationarity of mmgn is conditional relying on the variation ranges of h t when h t 0 70 on the other side mmgn is unconditionally stationary yielding a consequence that short memory mmgn is stationary in addition for h t 0 70 we introduce the concept of stationary range denoted by hmin hmax it means that corr r h t1 r h t2 0 70 if h t1 h t2 hmin hmax where r h t1 and r h t2 are the autocorrelation functions of mmgn with h t1 and h t2 for t1 t2 respectively and corr r h t1 r h t2 is the correlation coefficient between r h t1 and r h t2 we present a set of stationary ranges which may be used for a quantitative description of the local stationarity of mmgn a case study is demonstrated for applying the present method to testing the stationarity of a real traffic trace

fast exact synthesis of gaussian and nongaussian long range dependent processes 1 f noise and statistically self similar random processes such as fractional brownian motion fbm and fractional gaussian noise fgn are fundamental models for a host of real world phenomena from network traffic to dna to the stock market synthesis algorithms play a key role by providing the feedstock of data necessary for running complex simulations and accurately evaluating analysis techniques unfortunately current algorithms to correctly synthesize these long range dependent lrd processes are either abstruse or prohibitively costly which has spurred the wide use of inexact approximations to fill the gap we develop a simple fast o n log n operations for a length n signal framework for exactly synthesizing a range of gaussian and nongaussian lrd processes as a bonus we introduce and study a new bi scaling fbm process featuring a kinked correlation function that exhibits distinct scaling laws at coarse and fine scales

multiscale systems kalman filters and riccati equations an algorithm analogous to the rauch tung striebel algorithm spl minus consisting of a fine to coarse kalman filter like sweep followed by a coarse to fine smoothing step spl minus was developed previously by the authors ibid vol 39 no 3 p 464 78 1994 in this paper they present a detailed system theoretic analysis of this filter and of the new scale recursive riccati equation associated with it while this analysis is similar in spirit to that for standard kalman filters the structure of the dyadic tree leads to several significant differences in particular the structure of the kalman filter error dynamics leads to the formulation of an ml version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the hamiltonian for the smoothing problem in addition the notion of stability for dynamics requires some care as do the concepts of reachability and observability using these system theoretic constructs the stability and steady state behavior of the fine to coarse kalman filter and its riccati equation are analysed

scaling properties of image textures a detrending fluctuation analysis approach abstract the aim of this paper is to explore the application of detrended fluctuation analysis dfa to study roughness features of images unidimensional sequences at different image orientations are extracted and their average scaling exponent is estimated in this form the existence of anisotropies can be detected when considerable variations in the scaling exponent at different image orientation are observed different images from grass to solar granulation are analyzed and the underlying physics of such results is briefly commented

wavelet analysis and synthesis of fractional brownian motion fractional brownian motion fbm offers a convenient modeling for nonstationary stochastic processes with long term dependencies and 1 f type spectral behavior over wide ranges of frequencies statistical self similarity is an essential feature of fbm and makes natural the use of wavelets for both its analysis and its synthesis a detailed second order analysis is carried out for wavelet coefficients of fbm it reveals a stationary structure at each scale and a power law behavior of the coefficients variance from which the fractal dimension of fbm can be estimated conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed consequences of discretization are considered and some connections between the wavelet point of view and previous approaches based on length measurements analysis or dyadic interpolation synthesis are briefly pointed out

fast positive definite linear system solvers the authors show that the m band wavelet transforms of a wide class of covariance matrices consist of subblocks that are essentially banded furthermore they prove that the cholesky factors of the transformed covariance matrices also consist of subblocks that are essentially banded they combine these two observations to construct a fast o n sup 2 algorithm for solving the n spl times n linear positive definite systems of equations that arise in statistical signal processing finally they provide an error analysis of the proposed linear positive definite system solver

sparse equidistribution problems period bounds and subconvexity we introduce a geometric method to bound periods of automorphic forms the key features of this method are the use of equidistribution results in place of mean value theorems and the systematic use of mixing and the spectral gap applications are given to equidistribution of sparse subsets of horocycles and to equidistribution of cm points to subconvexity of the triple product period in the level aspect over number fields which implies subconvexity for certain standard and rankin selberg l functions and to bounding fourier coefficients of automorphic forms

triple product formula and the subconvexity bound of triple product l function in level aspect in this paper we derive a nice general formula for the local integrals of triple product formula whenever one of the representations has sufficiently higher level than the other two as an application we generalize venkatesh and woodbury s work on the subconvexity bound of triple product l function in level aspect allowing joint ramifications higher ramifications general unitary central characters and general special values of local epsilon factors

wavelet packet decompositions for the analysis of 2 d fields with stationary fractional increments nonstationary two dimensional random fields with wide sense stationary fractional increments are introduced using a fractional order for their increments in two directions of space some of their properties are studied and their value in modeling nonstationary possibly anisotropic fields is shown via examples a separable wavelet packet analysis proves to be a useful tool in analyzing this kind of texture as it leads to stationary wavelet packet coefficients

subconvexity bounds for triple l functions and representation theory we describe a new method to estimate the trilinear period on automorphic representations of pgl 2 such a period gives rise to a special value of the triple l function we prove a bound for the triple period which amounts to a subconvexity bound for the corresponding special value of the triple l function our method is based on the study of the analytic structure of the corresponding unique trilinear functional on unitary representations of pgl 2