gromov witten classes quantum cohomology and enumerative geometry the paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry in particular it contains an axiomatic treatment of gromov witten classes and a discussion of their properties for fano varieties cohomological field theories are defined and it is proved that tree level theories are determined by their correlation functions application to counting rational curves on del pezzo surfaces and projective spaces are given

the undersampled discrete gabor transform conventional studies on discrete gabor transforms have generally been confined to the cases of critical sampling and oversampling in which the gabor families span the whole signal space in this paper we investigate undersampled discrete gabor transforms for an undersampled gabor triple g a b i e a spl middot b n we show that the associated generalized dual gabor window gdgw function is the same as the one associated with the oversampled g n b n a except for the constant factor ab n computations of undersampled gabor transforms are made possible by applying the methods algorithms developed in oversampled settings the undersampled gdgw is determined then we are able to obtain the best approximation of a signal x by linear combinations of vectors in the gabor family

harmonic wavelet analysis a new harmonic wavelet is suggested unlike wavelets generated by discrete dilation equations whose shape cannot be expressed in functional form harmonic wavelets have the simple structure w x exp i4 pi x exp i2 pi x i2 pi x this function w x is concentrated locally around x 0 and is orthogonal to its own unit translations and octave dilations its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency domain rather than in the x domain an efficient implementation of a discrete transform using this wavelet is based on the fast fourier transform fft fourier coefficients are processed in octave bands to generate wavelet coefficients by an orthogonal transformation which is implemented by the fft the same process works backwards for the inverse transform

functions analytic on the half plane as quantum mechanical states a transform between the state space of one dimensional quantum mechanical systems and a direct sum of two spaces of square integrable functions analytic on the open upper half plane is constructed it gives a representation of usual quantum mechanics on which the free evolution is trivial and the representation of canonical transformation very simple generalizations to higher dimensions are also discussed

double series representation of bounded signals series representations of the form f t approximately sigma sub n infinity sup infinity sigma sub k infinity sup infinity a sub n k nu t n sub e sup 2 pi kts for bounded signals f t are studied as are conditions on the unit function nu t such that coefficients a sub n k reveal the energy content of f t in the time interval n 1 2

time frequency localization operators a geometric phase space approach the author defines a set of operators which localize in both time and frequency these operators are similar to but different from the low pass time limiting operator the singular functions of which are the prolate spheroidal wave functions the author s construction differs from the usual approach in that she treats the time frequency plane as one geometric whole phase space rather than as two separate spaces for disk shaped or ellipse shaped domains in time frequency plane the associated localization operators are remarkably simple their eigenfunctions are hermite functions and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions

the effective cone of the space of parametrized rational curves in a grassmannian we determine the effective cone of the quot scheme parametrizing all rank r degree d quotient sheaves of the trivial bundle of rank n on mathbb p 1 more specifically we explicitly construct two effective divisors which span the effective cone and we also express their classes in the picard group in terms of a known basis

linear systems in gabor time frequency space a new approach for the description and operation of linear time varying systems is presented the proposed formalism implements the superposition integral describing a general linear operation in gabor time frequency space enabling the use of its joint properties the method is based on transforming both the input and the time varying impulse response function into the gabor space the 2 and 4 d arrays corresponding to the gabor spectra of the input signal and the impulse response respectively are multiplied yielding a 2 d array corresponding to the output gabor spectrum from which the output time signal is subsequently reconstructed unlike other time varying operation methods carried out in different mixed time frequency spaces e g wigner space the suggested approach when employing the critically sampled gabor expansion generates a legal output spectrum and eliminates the need to resort to cumbersome and numerically taxing approximate synthesis techniques the proposed formalism can be implemented in the areas of time variant filtering speech scrambling and any other linear operations that vary their characterizations in time

analytical footprints compact representation of elementary singularities in wavelet bases we introduce a family of elementary singularities that are point holder regular these singularities are self similar and are the green functions of fractional derivative operators i e by suitable fractional differentiation one retrieves a dirac function at the exact location of the singularity we propose to use fractional operator like wavelets that act as a multiscale version of the derivative in order to characterize and localize singularities in the wavelet domain we show that the characteristic signature when the wavelet interacts with an elementary singularity has an asymptotic closed form expression termed the analytical footprint practically this means that the dictionary of wavelet footprints is embodied in a single analytical form we show that the wavelet coefficients of the nonredundant decomposition can be fitted in a multiscale fashion to retrieve the parameters of the underlying singularity we propose an algorithm based on stepwise parametric fitting and the feasibility of the approach to recover singular signal representations

two dimensional filter bank design for optimal reconstruction using limited subband information in this correspondence we propose design techniques for analysis and synthesis filters of 2 d perfect reconstruction filter banks prfb s that perform optimal reconstruction when a reduced number of subband signals is used based on the minimization of the squared error between the original signal and some low resolution representation of it the 2 d filters are optimally adjusted to the statistics of the input images so that most of the signal s energy is concentrated in the first few subband components this property makes the optimal prfb s efficient for image compression and pattern representations at lower resolutions for classification purposes by extending recently introduced ideas from frequency domain principal component analysis to two dimensions we present results for general 2 d discrete nonstationary and stationary second order processes showing that the optimal filters are nonseparable particular attention is paid to separable random fields proving that only the first and last filters of the optimal prfb are separable in this case simulation results that illustrate the theoretical achievements are presented

oscillation threshold of a clarinet model a numerical continuation approach this paper focuses on the oscillation threshold of single reed instruments several characteristics such as blowing pressure at threshold regime selection and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion previous works have shown interesting tendencies using analytical expressions with simplified models in the present study a more elaborated physical model is considered the influence of several parameters depending on the reed properties the design of the instrument or the control operated by the player are studied previous results on the influence of the reed resonance frequency are confirmed new results concerning the simultaneous influence of two model parameters on oscillation threshold regime selection and playing frequency are presented and discussed the authors use a numerical continuation approach numerical continuation consists in following a given solution of a set of equations when a parameter varies considering the instrument as a dynamical system the oscillation threshold problem is formulated as a path following of hopf bifurcations generalizing the usual approach of the characteristic equation as used in previous works the proposed numerical approach proves to be useful for the study of musical instruments it is complementary to analytical analysis and direct time domain or frequency domain simulations since it allows to derive information that is hardly reachable through simulation without the approximations needed for analytical approach

gabor representation of generalized functions this paper deals with gabor representation of generalized functions by this we mean that a given function is to be expanded in a series involving gabor functions that are located in the points of a given lattice in the time frequency plane we shall mainly consider lattices in which the area of the elementary cells of the lattice equals 1 in 1946 gabor used these expansions for the simultaneous analysis of signals in time and frequency cf 181 gabor stated that the above mentioned expansions exist for every reasonable signal and that the coefficients in the expansion are uniquely determined by the signal this statement is true when interpreted carefully and the aim of this paper is to find out what kind of generalized functions are sufficiently well behaved to allow a development in a gabor series we shall also consider the question of the uniqueness of the coefficients in the expansions as well as questions concerning convergence it turns out that the uniqueness questions can be handled with the aid of the main results of io in particular 2 12 and 2 13 the questions on the existence of expansions are harder to answer and require special care depending on the particular function we consider lpfunctions 1 p 2 in detail and show existence of gabor representation for tempered distribution in general

the analysis and design of windowed fourier frame based multiple description source coding schemes in this paper the windowed fourier encoding decoding scheme applied to the multiple description compression problem is analyzed in the general case four window functions are needed to define the encoder and decoder although this number can be reduced to three or two by using time shift or frequency shift division schemes the encoding coefficients are next divided into two groups according to the eveness of either the modulation or translation index the distortion on each channel is analyzed using the zak transform for the optimal windows explicit representation formulas are obtained and nonlocalization results are proved asymptotic formulas of the total distortion and transmission rate are established and the redundancy is shown to trade off between these two

theory of regular m band wavelet bases orthonormal m band wavelet bases have been constructed and applied by several authors this paper makes three main contributions first it generalizes the minimal length k regular 2 band wavelets of daubechies 1988 to the m band case by deriving explicit formulas for k regular m band scaling filters several equivalent characterizations of k regularity are given and their significance explained second two approaches to the construction of the m 1 wavelet filters and associated wavelet bases are described one relies on a state space characterization with a novel technique to obtain the unitary wavelet filters the other uses a factorization approach third this paper gives a set of necessary and sufficient condition on the m band scaling filter for it to generate an orthonormal wavelet basis the conditions are very similar to those obtained by cohen 1990 and lawton 1990 for 2 band wavelets

a general description of linear time frequency transforms and formulation of a fast invertible transform that samples the continuous s transform spectrum nonredundantly examining the frequency content of signals is critical in many applications from neuroscience to astronomy many techniques have been proposed to accomplish this one of these the s transform provides simultaneous time and frequency information similar to the wavelet transform but uses sinusoidal basis functions to produce frequency and globally referenced phase measurements it has shown promise in many medical imaging applications but has high computational requirements this paper presents a general transform that describes fourier family transforms including the fourier short time fourier and s transforms a discrete nonredundant formulation of this transform as well as algorithms for calculating the forward and inverse transforms are also developed these utilize efficient sampling of the time frequency plane and have the same computational complexity as the fast fourier transform when configured appropriately this new algorithm samples the continuous s transform spectrum efficiently and nonredundantly allowing signals to be transformed in milliseconds rather than days as compared to the original s transform algorithm the new and efficient algorithms make practical many existing signal and image processing techniques both in biomedical and other applications

improved impedance matrix localization method em problems moment method calculations have the well known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems the impedance matrix localization iml method was introduced as a modification to standard moment method calculations to ease these limitations it utilizes a matrix transformation which effectively changes the basis testing functions into ones resembling traveling waves an improved method that uses an orthogonal transformation to generate standing wave like basis functions is presented here remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers furthermore the correspondence of the large elements in this matrix to geometrical theory of diffraction gtd terms is strengthened as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements

the weyl correspondence and time frequency analysis describes the weyl correspondence and its properties showing how it gives a window independent definition of time frequency concentration for use in models in signal detection the definition of concentration is justified by showing that it gives reasonable answers in certain intuitive cases the weyl correspondence expresses a linear transformation as a weighted superposition of time frequency shifts of the signal and then authors explain why this is not the same as transforming a signal into the time frequency domain multiplying by a weight in the transform domain and taking the inverse the investigation into time frequency concentration and the weyl correspondence is justified by a new result the authors show that convolving the wigner distribution with a general smoothing function is equivalent to evaluating a weighted sum of spectrograms this is a new interpretation of the process of smoothing the wigner distribution to reduce cross terms it relates smoothing of the wigner distribution to the multiple window technique pioneered by thomson 1982

transforms associated to square integrable group representations i general results let g be a locally compact group which need not be unimodular let x u x x g be an irreducible unitary representation of g in a hilbert space h u assume that u is square integrable i e that there exists in h u at least one nonzero vector g such that u x g g 2 dx we give here a reasonably self contained analysis of the correspondence associating to every vector f h u the function u x g f on g discussing its isometry characterization of the range inversion and simplest interpolation properties this correspondence underlies many properties of generalized coherent states

frame theoretic analysis of oversampled filter banks we provide a frame theoretic analysis of oversampled finite impulse response fir and infinite impulse response fir uniform filter banks fbs our analysis is based on a new relationship between the fbs polyphase matrices and the frame operator corresponding to an fb for a given oversampled analysis fb we present a parameterization of all synthesis fbs providing perfect reconstruction we find necessary and sufficient conditions for an oversampled fb to provide a frame expansion a new frame theoretic procedure for the design of paraunitary fbs from given nonparaunitary fbs is formulated we show that the frame bounds of an fb can be obtained by an eigen analysis of the polyphase matrices the relevance of the frame bounds as a characterization of important numerical properties of an fb is assessed by means of a stochastic sensitivity analysis we consider special cases in which the calculation of the frame bounds and synthesis filters is simplified finally simulation results are presented

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

two characteristic numbers for smooth plane curves of any degree we use a sequence of blow ups over the projective space parametrizing plane curves of degree d to obtain some enumerative results concerning smooth plane curves of arbitrary degree for d 4 this gives a first modern verification of results of h g zeuthen

l stability for linear multiresolution algorithms a new explicit approach part ii the cases of symlets coiflets biorthogonal wavelets and supercompact multiwavelets abstract in amat and moncayo s amat m moncayo l stability for linear multiresolution algorithms a new explicit approach part i the basic rules and the daubechies case appl math comput 206 1 2008 74 91 was introduced a direct procedure to obtain an explicit computation of the error bounds for the mallat s multiresolution transform associated to orthogonal wavelet filters the general stability framework was applied to the specific case of daubechies filters in this paper we extend our approach giving the bounds related to others well known and used wavelet families as symlets coiflets biorthogonal wavelets and supercompact multiwavelets

image reconstruction from projections under wavelet constraints first the authors discuss how the wavelet transform can be used to perform spatially varying filtering of an image suppressing noise locally in smooth regions of the image and discuss detection of such regions in a noise corrupted image second they show how to compute the minimum mean square estimate of an image given 1 noisy projections of the image 2 statistics of additive noise in the projections and 3 constraints on wavelet coefficients of the image examples illustrate the resulting procedure

wavelet frames and admissibility in higher dimensions this paper is concerned with the relations between discrete and continuous wavelet transforms on k dimensional euclidean space we start with the construction of continuous wavelet transforms with the help of square integrable representations of certain semidirect products thereby generalizing results of bernier and taylor we then turn to frames of l2 rk and to the question when the functions occurring in a given frame are admissible for a given continuous wavelet transform for certain frames we give a characterization which generalizes a result of daubechies to higher dimensions

discriminative wavelet shape descriptors for recognition of 2 d patterns in this paper we present a set of wavelet moment invariants together with a discriminative feature selection method for the classification of seemingly similar objects with subtle di erences these invariant features are selected automatically based on the discrimination measures defined for the invariant features using a minimum distance classifier our wavelet moment invariants achieved the highest classification rate for all four di erent sets tested compared with zernike s moment invariants and li s moment invariants for a test set consisting of 26 upper cased english letters wavelet moment invariants could obtain 100 classification rate when applied to 26 30 randomly generated noisy and scaled letters whereas zernike s moment invariants and li s moment invariants obtained only 98 7 and 75 3 respectively the theoretical and experimental analyses in this paper prove that the proposed method has the ability to classify many types of image objects and is particularly suitable for classifying seemingly similar objects with subtle di erences 1999 pattern recognition society published by elsevier science ltd all rights reserved

a composite fourier wavelet transform and square integrable group representations a formula for a composite fourier wavelet transform is suggested from which the noncommutative fourier and wavelet transforms can be obtained as particular examples as well as several other fourier type transforms it is shown how this composite transform can be used to extend certain results originally obtained for square integrable group representations to more general measures arising in quantum probability theory

the degree of the variety of rational ruled surfaces and gromov witten invariants we compute the degree of the variety parametrizing rational ruled surfaces of degree d in p 3 by relating the problem to gromov witten invariants and quantum cohomology

flute like musical instruments a toy model investigated through numerical continuation abstract self sustained musical instruments bowed string woodwind and brass instruments can be modelled by nonlinear lumped dynamical systems among these instruments flutes and flue organ pipes present the particularity to be modelled as a delay dynamical system in this paper such a system a toy model of flute like instruments is studied using numerical continuation equilibrium and periodic solutions are explored with respect to the blowing pressure with focus on amplitude and frequency evolutions along the different solution branches as well as jumps between periodic solution branches the influence of a second model parameter namely the inharmonicity on the behaviour of the system is addressed it is shown that harmonicity plays a key role in the presence of hysteresis or quasiperiodic regime throughout the paper experimental results on a real instrument are presented to illustrate various phenomena and allow some qualitative comparisons with numerical results

wavelet transforms associated with finite cyclic groups multiresolution analysis via decomposition on wavelet bases has emerged as an important tool in the analysis of signals and images when these objects are viewed as sequences of complex or real numbers an important class of multiresolution decompositions are the laplacian pyramid schemes in which the resolution is successively halved by recursively low pass filtering the signal under analysis and decimating it by a factor of two in general the principal framework within which multiresolution techniques have been studied and applied is the same as that used in the discrete time fourier analysis of sequences of complex numbers an analogous framework is developed for the multiresolution analysis of finite length sequences of elements from arbitrary fields attention is restricted to sequences of length 2 sup n for n a positive integer so that the resolution may be recursively halved to completion as in finite length fourier analysis a cyclic group structure of the index set of such sequences is exploited to characterize the transforms of interest for the particular cases of complex and finite fields

harmonic wavelet based data filtering for enhanced machine defect identification a filter construction technique is presented for enhanced defect identification in rotary machine systems based on the generalized harmonic wavelet transform a series of sub frequency band wavelet coefficients are constructed by choosing different harmonic wavelet parameter pairs the energy and entropy associated with each sub frequency band are then calculated the filtered signal is obtained by choosing the wavelet coefficients whose corresponding sub frequency band has the maximum energy to entropy ratio experimental studies using rolling bearings that contain different types of structural defects have confirmed that the developed new technique enables high signal to noise ratio for effective machine defect identification

wavelets associated with representations of the affine weyl heisenberg group the affine weyl heisenberg group generated by time and frequency translations and time dilations is considered and some associated resolutions of the identity are derived as a result it will be shown that they can all be obtained from those associated with the affine group and the weyl heisenberg group by frequency translations of the analyzed function and the analyzing and reconstructing wavelets

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

frames in generalized fock spaces let a denote a real linear transformation on cn which is symmetric and positive definite relative to the real inner product re z w z w cn let fa cn denote the fock space consisting of holomorphic functions on cn which are square integrable with respect to the gaussian measure d a z detra ne re az z for w cn let ewa z ea z w e 12re aw w ka z w z cn where ka is the reproducing kernel for fa cn the main aim of this paper is to show that there exist a b 0 such that the set of functions ema inba m n zn forms a frame in fa

the growth of bargmann functions and the completeness of sequences of coherent states the growth of bargmann functions is intimately connected to the density of the zeros of these functions and to the completeness of sequences of coherent states using these ideas we find the least density that a sequence of coherent states must have in order to be overcomplete within the space of bargmann functions of an order not exceeding and of a type not exceeding if of order these results generalize known results on the completeness of von neumann lattices the practical significance of this formalism in the context of quantum optics is also discussed

the wavelet transform of stochastic processes with stationary increments and its application to fractional brownian motion the wavelet transform of random processes with wide sense stationary increments is shown to be a wide sense stationary process whose correlation function and spectral distribution are determined the second order properties of the coefficients in the wavelet orthonormal series expansion of such processes is obtained applications to the spectral analysis and to the synthesis of fractional brownian motion are given

a four parameter atomic decomposition of chirplets a new four parameter atomic decomposition of chirplets is developed for compact and precise representation of signals with chirp components the four parameter chirplet atom is obtained from the unit gaussian function by successive applications of scaling fractional fourier transform frft and time shift and frequency shift operators the application of the frft operator results in a rotation of the wigner distribution of the gaussian in the time frequency plane by a specified angle the decomposition is realized by using the matching pursuit algorithm for this purpose the four parameter space is discretized to obtain a small but complete subset in the hilbert space a time frequency distribution tfd is developed for clear and readable visualization of the signal components it is observed that the chirplet decomposition and the related tfd provide more compact and precise representation of signal inner structures compared with the commonly used time frequency representations

enhanced frequency analysis using wavelets an enhanced frequency analysis method is introduced using a phase shift wavelet representation to analyse individual frequency components and to reveal features of a given signal the frequency representation provides details at each time location without the loss caused by local orthogonality between the wavelet basis functions and the given signal which occurs when a normal wavelet decomposition is employed movement of the local orthogonality locations corresponding to the phase shift of the wavelet basis functions are studied and it is shown that these movements are important and can be used to reveal features of the signal in the frequency domain such as continuities smoothness and trends several examples are presented to illustrate the method and an application to a permanent magnet synchronous drive system is provided to demonstrate the approach

triangular wavelet based finite elements via multivalued scaling equations this paper develops a class of triangular finite elements based on l2 rn orthonormal compactly supported wavelets as in the case of recently derived tensor product wavelet elements the triangular elements are defined by deriving an algebraic eigenvalue problem characterizing the entries of the elemental matrices these entries are uniquely defined by normalization conditions derived from the polynomial reproducing properties of the wavelet scaling functions the work herein generalizes the development of the tensor product wavelet elements in that the geometry of the triangular elemental domain is characterized using a multivalued scaling equation the multivalued scaling function is used to represent the self similar tiling of rn onto itself by triangular domains

tensor least angle regression for sparse representations of multidimensional signals sparse signal representations have gained much interest recently in both signal processing and statistical communities compared to orthogonal matching pursuit omp and basis pursuit which solve

structural health monitoring using empirical mode decomposition and the hilbert phase abstract this paper discusses a new signal processing tool involving the use of empirical mode decomposition and its application to health monitoring of structures empirical mode decomposition is a time series analysis method that extracts a custom set of basis functions to describe the vibratory response of a system in conjunction with the hilbert transform the empirical mode decomposition method provides some unique information about the nature of the vibratory response in this paper the method is used to process time series data from a variety of 1 d structures with and without structural damage empirically derived basis functions are processed through the hilbert huang transform to obtain magnitude phase and damping information this magnitude phase and damping information is later processed to extract the underlying incident energy propagating through the structure this incident energy is also referred to as the dereverberated response of a structure using simple physics based models of 1 d structures it is possible to determine the location and extent of damage by tracking phase properties between successive degrees of freedom this paper also presents experimental validation of this approach using a civil building model results illustrate that this new time series method is a powerful signal processing tool that tracks unique features in the vibratory response of structures

a maximum likelihood digital receiver using coordinate ascent and the discrete wavelet transform in this paper a maximum likelihood ml method is presented for joint estimation of amplitude phase time delay and data symbols in a single user direct sequence spread spectrum communication system since maximization of the likelihood function is analytically intractable a novel coordinate ascent algorithm is used to obtain sequential updates of the data symbols and all unknown nuisance parameters the novelty of the algorithm is due to the use of a multiresolution expansion of the received signal and the use of polynomial rooting in the complex plane in place of a line search over the signal delay parameter the multiresolution structure of the algorithm is exploited to reduce sensitivity to impulsive noise via wavelet thresholding computer simulations of the single user system show that the algorithm has fast convergence and comparison with theoretical lower bounds establishes that the algorithm achieves nearly optimal error performance

oversampling in the gabor scheme a method for calculating the coefficients of the gabor expansion in the case of oversampling is presented the method is based on the concept of frames and utilizes the zak transform as such the zak transform highlights the meaning and importance of frames in the context of oversampling and other aspects of signal representation by means of nonorthogonal bases

bargmann transform zak transform and coherent states it is well known that completeness properties of sets of coherent states associated with lattices in the phase plane can be proved by using the bargmann representation or by using the kq representation which was introduced by j zak in this paper both methods are considered in particular in connection with expansions of generalized functions in what are called gabor series the setting consists of two spaces of generalized functions tempered distributions and elements of the class s which appear in a natural way in the context of the bargmann transform also a thorough mathematical investigation of the zak transform is given this paper contains many comments and complements on existing literature in particular connections with the theory of interpolation of entire functions over the gaussian integers are given

on the cohomology of brill noether loci over quot schemes abstract let c be a smooth projective irreducible curve over an algebraic closed field k of characteristic 0 we consider brill noether loci over the moduli space of morphisms from c to a grassmannian g m n of m planes in k n and the corresponding quot schemes of quotients of a trivial vector bundle on c compactifying the spaces of morphisms we study in detail the case in which m 2 n 4 we prove results on the irreducibility and dimension of these brill noether loci and we address explicit formulas for their cohomology classes we study the existence problem of these spaces which is closely related with the problem of classification of vector bundles over curves

explicit mapping of acoustic regimes for wind instruments this paper proposes a methodology to map the various acoustic regimes of wind instruments the maps can be generated in a multidimensional space consisting of design control parameters and initial conditions the boundaries of the maps are obtained explicitly in terms of the parameters using a support vector machine svm classifier as well as a dedicated adaptive sampling scheme the approach is demonstrated on a simplified clarinet model for which several maps are generated based on different criteria examples of computation of the probability of occurrence of a specific acoustic regime are also provided in addition the approach is demonstrated on a design optimization example for optimal intonation

an improved image compression algorithm using binary space partition scheme and geometric wavelets geometric wavelet is a recent development in the field of multivariate nonlinear piecewise polynomials approximation the present study improves the geometric wavelet gw image coding method by using the slope intercept representation of the straight line in the binary space partition scheme the performance of the proposed algorithm is compared with the wavelet transform based compression methods such as the embedded zerotree wavelet ezw the set partitioning in hierarchical trees spiht and the embedded block coding with optimized truncation ebcot and other recently developed sparse geometric representation based compression algorithms the proposed image compression algorithm outperforms the ezw the bandelets and the gw algorithm the presented algorithm reports a gain of 0 22 db over the gw method at the compression ratio of 64 for the cameraman test image

a high order purely frequency based harmonic balance formulation for continuation of periodic solutions combining the harmonic balance method hbm and a continuation method is a well known technique to follow the periodic solutions of dynamical systems when a control parameter is varied however since deriving the algebraic system containing the fourier coefficients can be a highly cumbersome procedure the classical hbm is often limited to polynomial quadratic and cubic nonlinearities and or a few harmonics several variations on the classical hbm such as the incremental hbm or the alternating frequency time domain hbm have been presented in the literature to overcome this shortcoming here we present an alternative approach that can be applied to a very large class of dynamical systems autonomous or forced with smooth equations the main idea is to systematically recast the dynamical system in quadratic polynomial form before applying the hbm once the equations have been rendered quadratic it becomes obvious to derive the algebraic system and solve it by the so called asymptotic numerical method anm continuation technique several classical examples are presented to illustrate the use of this numerical approach

linear modal stability analysis of bowed strings linearised models are often invoked as a starting point to study complex dynamical systems besides their attractive mathematical simplicity they have a central role for determining the stability properties of static or dynamical states and can often shed light on the influence of the control parameters on the system dynamical behaviour while the bowed string dynamics has been thoroughly studied from a number of points of view mainly by time domain computer simulations this paper proposes to explore its dynamical behaviour adopting a linear framework linearising the friction force near an equilibrium state in steady sliding conditions and using a modal representation of the string dynamics starting from the simplest idealisation of the friction force given by coulomb s law with a velocity dependent friction coefficient the linearised modal equations of the bowed string are presented and the dynamical changes of the system as a function of the bowing parameters are studied using linear stability

on some identities and inequalities for frames in hilbert spaces we give new parseval type identities and inequalities for frames in hilbert spaces our results generalize the remarkable results obtained recently by r balan p g casazza d edidin and g kutyniok

balian low type theorems in finite dimensions we formulate and prove finite dimensional analogs for the classical balian low theorem and for a quantitative balian low type theorem that in the case of the real line we obtained in a previous work moreover we show that these results imply their counter parts on the real line

on the sensitivity of elastic waves due to structural damages time frequency based indexing method time frequency analysis of various simulated and experimental signals due to elastic wave scattering from damage are performed using wavelet transform wt and hilbert huang transform hht and their performances are compared in context of quantifying the damages spectral finite element method is employed for numerical simulation of wave scattering an analytical study is carried out to study the effects of higher order damage parameters on the reflected wave from a damage based on this study error bounds are computed for the signals in the spectral and also on the time frequency domains it is shown how such an error bound can provide an estimate of error in the modelling of wave propagation in structure with damage measures of damage based on wt and hht is derived to quantify the damage information hidden in the signal the aim of this study is to obtain detailed insights into the problem of 1 identifying localised damages 2 dispersion of multifrequency non stationary signals after they interact with various types of damage and 3 quantifying the damages sensitivity analysis of the signal due to scattered wave based on time frequency representation helps to correlate the variation of damage index measures with respect to the damage parameters like damage size and material degradation factors

wave propagation and sampling theory part ii sampling theory and complex waves morlet et al 1982 this issue showed the advantages of using complex values for both waves and characteristics of the media we simulated the theoretical tools we present here using the goupillaud kunetz algorithm now we present sampling methods for complex signals or traces corresponding to received waves and sampling methods for complex characterization of multilayered or heterogeneous media regarding the complex signals we present a twodimecsional 2 d method of sampling in the time frequency domain using a special or extended gabor expansion on a set of basic wavelets adapted to phase preservation such a 2 d expansion permits us to handle in a proper manner instantaneous frequency spectra we show the differences between wavelet resolution and sampling grid resolution we also show the importance of phase preservation in high resolution seismic regarding the media we show how analytical studies of wave propagation in periodic structured layers could help when trying to characterize the physical properties of the layers and their large scale granularity as a result of complex deconvolution analytical studies of wave propagation in periodic structures are well known in solid state physics and lead to the so called bloch waves the introduction of complex waves leads to replacing the classical wave equation by a schriidinger equation finally we show that complex wave equations gabor expansion and bloch waves are three different ways of introducing the tools of quantum mechanics in highresolution seismic gabor 1946 kittel 1976 morlet 1975 and conversely the goupillaud kunetz algorithm and an extended gabor expansion may be of some use in solid state physics

wavelet transform of multifractals we present the wavelet transform as a mathematical microscope which is well suited for studying the local scaling properties of fractal objects we apply this technique to probability measures on self similar cantor sets and to the golden mean trajectories on two tori at the onset of chaos

ondelettes and phase cell cluster expansions a vindication y meyer has recently developed a particularly useful o n basis forl2 r d expansions using this basis i e expansions into ondelettes or wavelets have yielded important new results in soft and hard analysis the expansion into ondelettes of a boson scalar field naturally leads to phase cell cluster expansions a formalism already developed by the authors using other related bases adoption of ondelettes expansions into the phase cell program gives improvements of some extant results and excises an early error

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

a block spin construction of ondelettes part i lemarie functions using block spin assignments we construct anl2 orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions these functions have exponential localization and for even values of a construction parameterm one can make them classcm 1 with vanishing moments up to orderm inclusive such a basis has an important application to phase cell cluster expansions in quantum field theory

reconstruction from projections under time frequency constraints low pass filtering computed tomography ct images to reduce noise may smooth or modify image features which are very important to the physician image features are often more easily identified and processed in the time frequency plane the authors use time frequency distributions for spatially varying filtering of noisy ct images constraining time frequency representation coefficients of the projection data or of the reconstructed image to be zero in certain regions of the time frequency plane the authors consider two different applications 1 filtering the projection data and then performing image reconstruction and 2 filtering the reconstructed image directly criteria minimized subject to constraints may be either a deterministic minimum weighted perturbation of the given projection data or a stochastic minimum mean square error in colored gaussian noise results show improvement over processing the image with a linear spatially invariant filter

oversampled gabor representation for transient signals considers the gabor representation that uses a one sided exponential window for detection and analysis of transient signals earlier results on the critically sampled case are extended to the more practically useful oversampled case for oversampling by an integer factor the authors derive an explicit analytical expression for the dual window dual frame function required for computing the gabor representation based on this expression they develop an efficient procedure for computing the gabor coefficients finally they demonstrate the performance of the method by numerical examples

frame vector multipliers for finite group representations abstract a frame vector or generator for a group representation of a countable or finite group g on a hilbert space h is a vector h such that g g g is a parseval frame for h frame vector multipliers are the unitary operators on h that map frame vectors to frame vectors based on a characterization of frame vectors with respect to the standard decomposition of a group representation as the direct sums of irreducible subrepresentations with multiplicity we obtain explicit characterizations of frame generator multipliers for two basic cases for finite group representations with the help of these characterizations we obtain some necessary conditions of frame vector multipliers for general frame representations and present several examples to demonstrate how these results can be used to get explicit characterizations for frame vector multipliers

acceleration of the frame algorithm shows how polynomial acceleration techniques which have been developed for the solution of large linear systems can be employed to improve and accelerate the frame algorithm these methods permit a reduction in the number of necessary iterations by an order of magnitude when the frame algorithm is slow the author gives several examples from the theory of irregular sampling from wavelet theory and from gabor theory where these methods are probably mandatory for efficient reconstruction

frames in the bargmann space of entire functions we look at the decomposition of arbitrary f in l2 r in terms of the family of functions cp x w exp iimnab iman i x nb 2 with a b 0 we derive bounds and explicit formulas for the minimal expansion coefficients in the case where ab 2w n n an integer 2 2 transported to the hilbert space f of entire functions introduced by v bargmann these results are expressed as inequalities of the form

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

orthogonalization of circular stationary vector sequences and its application to the gabor decomposition certain vector sequences in hermitian or in hilbert spaces can be orthogonalized by a fourier transform in the finite dimensional case the discrete fourier transform dft accomplishes the orthogonalization the property of a vector sequence which allows the orthogonalization of the sequence by the dft called circular stationarity cs is discussed in this paper applying the dft to a given cs vector sequence results in an orthogonal vector sequence which has the same span as the original one in order to obtain coefficients of the decomposition of a vector upon a particular nonorthogonal cs vector sequence the decomposition is first found upon the equivalent dft orthogonalized one and then the required coefficients are found through the dft it is shown that the sequence of discrete gabor 1946 basis functions with periodic kernel and with a certain inner product on the space of n periodic discrete functions satisfies the cs condition the theory of decomposition upon cs vector sequences is then applied to the gabor basis functions to produce a fast algorithm for calculation of the gabor coefficients

degree of the generalized plucker embedding of a quot scheme and quantum cohomology we compute the degree of the generalized plucker embedding kappa of a quot scheme x over pp 1 the space x can also be considered as a compactification of the space of algebraic maps of a fixed degree from pp 1 to the grassmanian rm grass m n then the degree of the embedded variety kappa x can be interpreted as an intersection product of pullbacks of cohomology classes from rm grass m n through the map psi that evaluates a map from pp 1 at a point x in pp 1 we show that our formula for the degree verifies the formula for these intersection products predicted by physicists through quantum cohomology cite va92 cite in91 cite wi94 we arrive at the degree by proving a version of the classical pieri s formula on the variety x using a cell decomposition of a space that lies in between x and kappa x

black holes bandwidths and beethoven it is usually believed that a function t whose fourier spectrum is bounded can vary at most as fast as its highest frequency component max this is in fact not the case as aharonov berry and others drastically demonstrated with explicit counterexamples so called superoscillations it has been claimed that even the recording of an entire beethoven symphony can occur as part of a signal with a 1 hz bandwidth bandlimited functions also occur as ultraviolet regularized fields their superoscillations have been suggested for example to resolve the trans planckian frequencies problem of black hole radiation here we give an exact proof for generic superoscillations namely we show that for every fixed bandwidth there exist functions that pass through any finite number of arbitrarily prespecified points further we show that in spite of the presence of superoscillations the behavior of bandlimited functions can be characterized reliably namely through an uncertainty relation the standard devi

pattern analysis with two dimensional spectral localisation applications of two dimensional s transforms abstract an image is a function f x y of the independent space variables x and y the global fourier spectrum of the image is a complex function f k x k y of the wave numbers k x and k y the global spectrum may be viewed as a construct of the spectra of an arbitrary number of segments of f x y leading to the concept of a local spectrum at every point of f x y the two dimensional s transform is introduced here as a method of computation of the local spectrum at every point of an image in addition to the variables x and y the 2 d s transform retains the variables k x and k y being a complex function of four variables visualisation of a function of four variables is difficult we skirt around this by removing one degree of freedom through examination of slices each slice of the 2 d s transform would then be a complex function of three variables with separate amplitude and phase components by ranging through judiciously chosen slice locations the entire s transform can be examined images with strictly periodic patterns are best analysed with a global fourier spectrum on the other hand the 2 d s transform would be more useful in spectral characterisation of aperiodic or random patterns

hierarchical active shape models using the wavelet transform active shape models asms are often limited by the inability of relatively few eigenvectors to capture the full range of biological shape variability this paper presents a method that overcomes this limitation by using a hierarchical formulation of active shape models using the wavelet transform the statistical properties of the wavelet transform of a deformable contour are analyzed via principal component analysis and used as priors in the contour s deformation some of these priors reflect relatively global shape characteristics of the object boundaries whereas some of them capture local and high frequency shape characteristics and thus serve as local smoothness constraints this formulation achieves two objectives first it is robust when only a limited number of training samples is available second by using local statistics as smoothness constraints it eliminates the need for adopting ad hoc physical models such as elasticity or other smoothness models which do not necessarily reflect true biological variability examples on magnetic resonance images of the corpus callosum and hand contours demonstrate that good and fully automated segmentations can be achieved even with as few as five training samples

generalized gabor expansions of discrete time signals in l sup 2 z via biorthogonal like sequences in this paper a biorthogonal like sequences bls theory and its application to the generalized gabor expansions equivalently the generalized short time fourier transform filterbank summation are presented a pair of bls s are defined to be two sequences satisfying a biorthogonal like condition blc which is a moment equation and equivalent to a linear difference equation we show that two collections in a hilbert space generated by a pair of bls s in the joint time frequency domain are complete either can be used as an analysis filter and the other can be used as a synthesis filter for a generalized gabor expansion of discrete time signals a sufficient and necessary condition on the existence of bls s based on the moment equation is presented which is simpler to use than frame theory given a filter generating a frame its bls s also generate frames the dual frame is one of them given a fir analysis synthesis filter there is a fir synthesis analysis filter if bls s exist the algorithm to compute fir analysis and synthesis filters based on the linear difference equation is presented in this paper which is simpler than frame operator

rational von neumann lattices a rational von neumann lattice is defined as a lattice in phase space with the constants a and b in the x and p directions given by a ratio of integers zeros of harmonic oscillator functions in the kq representation on such lattices are found it is shown that the number of zeros of the kq function determines the number of states by which a set on a von neumann lattice is overcomplete interesting relations between theta functions are derived on the basis of their connection with the harmonic oscillator states in the kq representation

adaptive learning for event modeling and characterization adaptive learning of specific patterns or events of interest has been an area of significant research for various applications in the last two decades in developing diagnostic evaluation and safety monitoring applications of a propulsion system it is critical to detect characterize and model events of interest it is a challenging task since the detection system should allow adaptive characterization of potential events of interest and correlate them to learn new models for future detection for online health monitoring and diagnostic evaluation in this paper a novel framework is established using a hierarchical adaptive clustering approach with fuzzy membership functions to characterize specific events of interest from the measured and processed features raw engine measurement data is first analyzed using the wavelet transform to provide features for localization of frequency information for use in the classification system a method combining hierarchical and fuzzy k means clustering is then applied to a set of selected measurements and computed features to determine the events of interest during engine operations experimental results have shown that the proposed approach is effective and computationally efficient to detect characterize and model new events of interest from data collected through continuous operations

weyl heisenberg frames and balian low theorem in l2 z this paper focuses on the reconstruction of digital signals in multirate digital signal processing we study the discrete time weyl heisenberg dtwh system for oversampling schemes and describe the frame operator of dtwh frames as the composition of the sampling operator and interpolation operator using discrete time zak transform we characterize the dual discrete time weyl heisenberg tight frames dtwh frames and tight dtwh frames based on oversampling schemes in addition we discuss the applications of dtwh frames to the reconstruction of weyl heisenberg systems in periodic space l2 0 1 finally we give balian low theorem for an orthonormal basis formed by dtwh systems and weak balian low theorem for exact dtwh frames in sequence space l2 z

collocation methods for the computation of periodic solutions of delay differential equations in this paper we investigate collocation methods for the computation of periodic solutions of autonomous delay differential equations ddes periodic solutions are found by solving a periodic two point boundary value problem which is an infinite dimensional problem for ddes in contrast to the case of ordinary differential equations we investigate three collocation methods based on piecewise polynomials we discuss computational issues and show numerical orders of convergence using an extensive number of tests we compare our numerical results with known theoretical convergence results for initial value problems for ddes in particular we show how superconvergence at the mesh points can be lost or recovered depending on the dde model under consideration and on the choice of collocation discretization we end with a brief discussion of adaptive mesh selection

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

multiscale autoregressive processes i schur levinson parametrizations in many applications it is of interest to analyze and recognize phenomena occurring at different scales the recently introduced wavelet transforms provide a time and scale decomposition of signals that offers the possibility of such analysis a corresponding statistical framework to support the development of optimal multiscale statistical signal processing algorithms is described the theory of multiscale signal representation leads naturally to models of signals on trees and this provides the framework for investigation in particular the class of isotropic processes on homogeneous trees is described and a theory of autoregressive models is developed in this context this leads to generalizations of schur and levinson recursions associated properties of the resulting reflection coefficients and the initial pieces in a system theory for multiscale modeling

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed