topological interactions in systems of mutually interlinked polymer rings topological interaction that arises in interlinked polymeric rings such as dna catenanes is considered more specifically the free energy for a pair of linked random walk rings is derived where the distance r between two segments each of which is part of a different ring is kept constant topology conservation is imposed by the gauss invariant a previous approach otto and vilgis 1998 phys rev lett 80 881 to the problem is refined in several ways it is confirmed that asymptotically i e for large r rg where rg is the average size of a single random walk ring the effective topological interaction free energy scales r4

the direct link model for polymer rings using topological field theory and the second topological moment in dense systems polymer rings in solution are either permanently entangled or are not permanent topological restrictions give rise to additional entropic interactions apart from the ones arising due to mere chain flexibility or excluded volume conversely entangled polymer rings systems may be formed by closing randomly entangled flexible linear chains the dependence of linking numbers between randomly entangled rings on the chain length more specifically the second topological moment n2 i e the average squared linking number may be determined in this paper an approach recently discussed in mathematical physics and called abelian bf theory is presented which allows one to express the linking constraint in its simplest form the gauss integral in terms of two gauge fields the model of brereton and shah for a single ring entangled with many other surrounding rings is rederived the latter model is finally used to calculate the second topological moment in agreement with a recent result by ferrari kleinert and lazzizzera obtained using n component 4 theory for the limit n 0

accurate estimation of the hurst parameter of long range dependent traffic using modified allan and hadamard variances internet traffic exhibits self similarity and longrange dependence lrd on various time scales in this paper we propose to use the modified allan variance mavar and a modified hadamard variance mhvar to estimate the hurst parameter h of the lrd traffic series or more generally the exponent alpha of data with 1 falpha alpha ges 0 power law spectrum mhvar generalizes the principle of mavar a time domain quantity widely used for frequency stability characterization to higher order differences of input data in our knowledge this mhvar has been mentioned in literature only few times and with little detail so far the behaviour of mavar and mhvar with power law random processes and some common deter ministic signals viz drifts sine waves steps is studied by analysis and simulation the mavar and mhvar accuracy in estimating h is evaluated and compared to that of wavelet logscale diagram ld extensive simulations show that mavar and mhvar achieve significantly better confidence and no bias in h estimation moreover mavar and mhvar feature a number of other advantages which make them valuable to complement other established techniques such as ld finally mhvar and ld are also applied to a real ip traffic trace

wigner ville spectral analysis of nonstationary processes the wigner ville spectrum has been recently introduced as the unique generalized spectrum for time varying spectral analysis its properties are revised with emphasis on its central role in the analysis of second order properties of nonstationary random signals we propose here a general class of spectral estimators of the wigner ville spectrum this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time frequency representations of deterministic signals with finite energy classical estimators like short time periodograms and the recently introduced pseudo wigner estimators are shown to be special cases of the general class the generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo wigner estimators the effective numerical implementation by an n point fft of pseudo wigner estimators of 2n points is indicated and various examples are given

tightness of slip linked polymer chains we study the interplay between entropy and topological constraints for a polymer chain in which sliding rings slip links enforce pair contacts between monomers these slip links divide a closed ring polymer into a number of subloops which can exchange length among each other in the ideal chain limit we find the joint probability density function for the sizes of segments within such a slip linked polymer chain paraknot a particular segment is tight small in size or loose of the order of the overall size of the paraknot depending on both the number of slip links it incorporates and its competition with other segments when self avoiding interactions are included scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations

characterization of gaussian self similar stochastic processes using wavelet based informational tools efficient tools to characterize stochastic processes are discussed quantifiers originally proposed within the framework of information theory like entropy and statistical complexity are translated into wavelet language which renders the above quantifiers into tools that exhibit the important localization advantages provided by wavelet theory two important and popular stochastic processes fractional brownian motion and fractional gaussian noise are studied using these wavelet based informational tools exact analytical expressions are obtained for the wavelet probability distribution finally numerical simulations are used to validate our analytical results

estimation of 1 f noise several models have emerged for describing 1 f sup spl gamma noise processes based on these various techniques for estimating the properties of such processes have been developed this paper provides theoretical analysis of a new wavelet based approach which has the advantages of having low computational complexity and being able to handle the case where the 1 f sup spl gamma noise might be embedded in a further white noise process however the analysis conducted here shows that these advantages are balanced by the fact that the wavelet based scheme is only consistent for spectral exponents spl gamma in the range spl gamma spl isin 0 1 this is in contradiction to the results suggested in previous empirical studies when spl gamma spl isin 0 1 this paper also establishes that wavelet based maximum likelihood methods are asymptotically gaussian and efficient finally the asymptotic rate of mean square convergence of the parameter estimates is established and is shown to slow as spl gamma approaches one combined with a survey of non wavelet based methods these new results give a perspective on the various tradeoffs to be considered when modeling and estimating 1 f sup spl gamma noise processes

establishing a direct connection between detrended fluctuation analysis and fourier analysis to understand methodological features of the detrended fluctuation analysis dfa using a higher order polynomial fitting we establish the direct connection between dfa and fourier analysis based on an exact calculation of the single frequency response of the dfa the following facts are shown analytically 1 in the analysis of stochastic processes exhibiting a power law scaling of the power spectral density psd s f f a higher order detrending in the dfa has no adverse effect in the estimation of the dfa scaling exponent which satisfies the scaling relation 1 2 2 the upper limit of the scaling exponents detectable by the dfa depends on the order of polynomial fit used in the dfa and is bounded by m 1 where m is the order of the polynomial fit 3 the relation between the time scale in the dfa and the corresponding frequency in the psd are distorted depending on both the order of the dfa and the frequency dependence of the psd we can improve the scale distortion by introducing the corrected time scale in the dfa corresponding to the inverse of the frequency scale in the psd in addition our analytical approach makes it possible to characterize variants of the dfa using different types of detrending as an application properties of the detrending moving average algorithm are discussed

on 1 f noise and other distributions with long tails abstract it is shown following shockley shockley w 1957 proc ire 45 279 290 that when a population is engaged in tasks whose completion requires the successful conclusion of many independent subtasks the distribution function for successes in the primary task is log normal it is also shown that when the dispersion of the log normal distribution is large the distribution is mimicked by a 1 x distribution over a wide range of x this argument provides a generic set of processes that yields the much observed 1 x distribution and will also lead to a 1 f noise spectrum it is commonly found that distributions that seem to be log normal over a broad range say to the 95th percentile of a population change to an inverse fractional power pareto distribution for the last few percentile annual income distributions are examples with this structure the very wealthy generally achieve their superwealth through amplification processes that are not available to most we have introduced a simple amplification model to characterize the transition from a log normal distribution to an inverse power pareto tail

signal detection in fractional gaussian noise several results related to the reproducing kernel hilbert space of fractional brownian motion are presented to facilitate the study of signal detection in additive fractional gaussian noise this hilbert space is completely characterized and an alternative characterization for the restriction of this class of functions to a compact interval 0 t is given infinite and finite interval whitening filters for fractional brownian motion are also developed the application of these results to the signal detection problem yields necessary and sufficient conditions for a deterministic or stochastic signal to produce a nonsingular shift when embedded in additive fractional gaussian noise a formula for the likelihood ratio corresponding to any deterministic nonsingular shift is developed

eigenvalue problems of the model from nonlocal continuum mechanics this article studies the eigenvalue problem of a fractional differential equation which is a foundation model of a bar of finite length with long range interactions arising from non local continuum mechanics we show that this problem has countable simple real eigenvalues and the corresponding eigenfunctions form a complete orthogonal system in the hilbert space l2 furthermore the asymptotic behavior of eigenvalues and the numbers of zeros of eigenfunctions are studied by using the analytic perturbation theory

spectral representation of fractional brownian motion in n dimensions and its properties fractional brownian motion fbm provides a useful model for processes with strong long term dependence such as 1 f sup spl beta spectral behavior however fbm s are nonstationary processes so that the interpretation of such a spectrum is still a matter of speculation to facilitate the study of this problem another model is provided for the construction of fbm from a white noise like process by means of a stochastic or ito integral in frequency of a stationary uncorrelated random process also a generalized power spectrum of the nonstationary fbm process is defined this new approach to fbm can be used to compute all of the correlations power spectra and other properties of fbm in this paper a number of these fbm properties are developed from this model such as the t sup h law of scaling the power law of fractional order the correlation of two arbitrary fbm s and the evaluation of the fractal dimension under various transformations this new treatment of fbm using a spectral representation is extended also for the first time to two or more topological dimensions in order to analyze the features of isotropic n dimensional fbm

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

on the wavelet transform of fractional brownian motion a theorem characterizing fractional brownian motion by the covariance structure of its wavelet transform is established the authors examine whether there are alternate gaussian processes whose wavelet transforms have a natural covariance structure in addition the authors examine if there are any gaussian processes whose wavelet transform is stationary with respect to the affine group i e the statistics of the wavelet transform do not depend on translations and dilations of the process

the spectra and periodograms of anti correlated discrete fractional gaussian noise discrete fractional gaussian noise dfgn has been proposed as a model for interpreting a wide variety of physiological data the form of actual spectra of dfgn for frequencies near zero varies as f 1 2h where 0 h 1 is the hurst coefficient however this form for the spectra need not be a good approximation at other frequencies when h approaches zero dfgn spectra exhibit the 1 2h power law behavior only over a range of low frequencies that is vanishingly small when dealing with a time series of finite length drawn from a dfgn process with unknown h practitioners must deal with estimated spectra in lieu of actual spectra the most basic spectral estimator is the periodogram the expected value of the periodogram for dfgn with small h also exhibits non power law behavior at the lowest fourier frequencies associated with a time series of n values sampled from a dfgn process the expected value of the periodogram for h approaching zero varies as f 0 rather than f 1 2h for finite n and small h the expected value of the periodogram can in fact exhibit a local power law behavior with a spectral exponent of 1 2h at only two distinct frequencies

analysis and synthesis of 1 f processes via shannon wavelets 1 f processes can be very useful in modeling processes with long term correlation we propose analysis and synthesis procedures to express these processes in terms of the shannon wavelet unlike previous techniques our analysis procedure generates uncorrelated decomposition coefficients for the 1 f process this is done by taking onto account and then removing the residual correlation between the wavelet components the analysis procedure is the major contribution of this work the proposed synthesis algorithm which is a byproduct of the proposed analysis algorithm is competitive with other techniques

correlation structure of the discrete wavelet coefficients of fractional brownian motion it is shown that the discrete wavelet coefficients of fractional brownian motion at different scales are correlated and that their auto and cross correlation functions decay hyperbolically fast at a rate much faster than that of the autocorrelation of the fractional brownian motion itself the rate of decay of the correlation function in the wavelet domain is primarily determined by the number of vanishing moments of the analyzing wavelet

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

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

the ergodicity analysis of two dimensional discrete wavelet based fbm fields the article explores the ergodicity property of the two dimensional 2 d discrete wavelet transform for a fractional brownian motion fbm field that consists of one approximation image and three detail images the decorrelation and ergodicity of the three detail images of fbm fields are shown to be achieved

wavelet based representations for a class of self similar signals with application to fractal modulation a potentially important family of self similar signals based upon a deterministic scale invariance characterization is introduced these signals which are referred to as dy homogeneous signals because they generalize the well known homogeneous functions have highly convenient representations in terms of orthonormal wavelet bases in particular wavelet representations can be exploited to construct orthonormal self similar bases for these signals the spectral and fractal characteristics of dy homogeneous signals make them appealing candidates for use in a number of applications as one potential example their use in a communications based context is considered specifically a strategy for embedding information into a dy homogeneous waveform on multiple time scales is developed this multirate modulation strategy called fractal modulation is potentially well suited for use with noisy channels of simultaneously unknown duration and bandwidth

physical limitations on antennas of arbitrary shape in this paper physical limitations on bandwidth realized gain q factor and directivity are derived for antennas of arbitrary shape the product of bandwidth and realizable gain is shown to be bounded from above by the eigenvalues of the long wavelength high contrast polarizability dyadics these dyadics are proportional to the antenna volume and are easily determined for an arbitrary geometry ellipsoidal antenna volumes are analysed in detail and numerical results for some generic geometries are presented the theory is verified against the classical chu limitations for spherical geometries and shown to yield sharper bounds for the ratio of the directivity and the q factor for non spherical geometries

optimality of operator like wavelets for representing sparse ar 1 processes the discrete cosine transform dct is known to be asymptotically equivalent to the karhunen loeve transform klt of gaussian first order auto regressive ar 1 processes since being uncorrelated under the gaussian hypothesis is synonymous with independence it also yields an independent component analysis ica of such signals in this paper we present a constructive non gaussian generalization of this result the characterization of the optimal orthogonal transform ica for the family of symmetric alpha stable ar 1 processes the degree of sparsity of these processes is controlled by the stability parameter 0 with the only non sparse member of the family being the classical gaussian ar 1 process with alpha 2 specifically we prove that for alpha a fixed family of operator like wavelet bases systematically outperforms the dct in terms of compression and denoising ability the effect is quantified with the help of two performance criteria one based on the kullback leibler divergence and the other on stein s formula for the minimum estimation error that can also be viewed as statistical measures of independence finally we observe that for the sparser kind of processes with 0 the operator like wavelet basis as dictated by linear system theory is undistinguishable from the ica solution obtained through numerical optimization our framework offers a unified view that encompasses sinusoidal transforms such as the dct and a family of orthogonal haar like wavelets that is linked analytically to the underlying signal model

phase modulated resonances modeled as self similar processes with application to turbulent sounds in this paper we propose a nonlinear stochastic model for time varying resonances where the instantaneous phase and frequency of a sinusoidal oscillation is allowed to vary proportionally to an spl alpha stable self similar stochastic processes the main motivation of our work stems from previous experimental and theoretical evidence that speech resonances in fricative sounds can be modeled phenomenologically as am fm signals with randomly varying instantaneous frequencies and that several signal classes related to turbulent phenomena are self similar 1 f processes our general approach is to model the instantaneous phase of an am fm resonance as a self similar spl alpha stable process as a special case this random phase model includes the class of random fractal signals known as fractional brownian motion we theoretically explore this random modulation model and analytically derive its autocorrelation and power spectrum we also propose an algorithm to fit this model to arbitrary resonances with random phase modulation further we apply the above ideas to real speech data and demonstrate that this model is suitable for resonances of fricative sounds

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

some distributional properties of the continuous wavelet transform of random processes without finite moment conditions some properties of random processes such as stationarity and self similarity are characterized via corresponding properties of their wavelet transform anyone of these distributional properties of the wavelet transform characterizes the corresponding property of the increments of the random process of order equal to the order of regularity of the analyzing wavelet extensions of these results to random fields are then indicated

on the spectrum of fractional brownian motions fractional brownian motions fbms provide useful models for a number of physical phenomena whose empirical spectra obey power laws of fractional order however due to the nonstationary nature of these processes the precise meaning of such spectra remains generally unclear two complementary approaches are proposed which are intended to clarify this point the first one based on a time frequency analysis takes into account the nonstationary nature of fbm and puts emphasis on time averaged measurements the second one based on a time scale analysis is matched to self similarity properties of fbm and reveals an underlying stationary structure relative to each time scaling

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

eigenvalue problems for fractional differential equations with right and left fractional derivatives this paper studies the eigenvalue problem of a class of fractional differential equations with right and left fractional derivatives with the aid of the spectral theory of compact self adjoint operators in hilbert spaces we show that the spectrum of this problem consists of only countable real eigenvalues with finite multiplicity and the corresponding eigenfunctions form a complete orthogonal system furthermore the lower bound of the eigenvalues is obtained

a note on the discrete wavelet transform of second order processes some properties of second order random processes such as stationarity and scaling are characterized via corresponding multiscale properties of their discrete wavelet transform the single scale characterizations valid in the continuous setting do not extend to the discrete setting some extensions of these results are also indicated

the statistical mechanics of a concatenated polymer chain the elastic and configurational properties of mesoscopic structures which have been formed by linking a finite number of polymer loops to each other are considered for simplicity it is assumed that the linking numbers between pairs of loops provides a sufficient description of the topological structure to conserve the topology the statistical mechanical calculation of the partition sum is restricted to the configuration space labelled by the specified linking numbers an expansion of the partition sum is proposed where the linking numbers corresponding to a particular structure select a sub set of terms from the expansion the case of a linear concatenated chain of loops is studied and it is shown that the first non zero contribution from this expansion is already able to describe the chain as a re scaled gaussian chain capable of supporting stress this confirms that the approximation maintains the structural integrity of the chain the effective step length and step length distribution function are also identified together with the elastic properties the relationship of linking numbers to the abelian chern simons gauge field theory is used to illustrate essential parts of the calculation the relevant term in the partition sum is represented in terms of feynman diagrams describing the two particle scattering amplitude for vector gauge bosons it is shown that the expected re scaled gaussian chain result comes from the dominance in the s channel of a massive scalar boson representing the structure of an individual loop in the chain

characteristics of natural scenes related to the fractal dimension many objects in images of natural scenes are so complex and erratic that describing them by the familiar models of classical geometry is inadequate in this paper we exploit the power of fractal geometry to generate global characteristics of natural scenes in particular we are concerned with the following two questions 1 can we develop a measure which can distinguish between different global backgrounds e g mountains and trees and 2 can we develop a measure that is sensitive to change in distance or scale we present a model based on fractional brownian motion which will allow us to recover two characteristics related to the fractal dimension from silhouettes the first characteristic is an estimate of the fractal dimension based on a least squares linear fit we show that this feature is stable under a variety of real image conditions and use it to distinguish silhouettes of trees from silhouettes of mountains next we introduce a new theoretical concept called the average holder constant and relate it mathematically to the fractal dimension it is shown that this measurement is sensitive to scale in a predictable manner and hence provides the potential for use as a range indicator corroborating experimental results are presented

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

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

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

statistical analysis of dwt coefficients of fgn processes using arfima p d q models abstract fractional gaussian noise fgn provides an important parametric representation for the data recorded from long memory processes also it has been well established in literature that the orthogonal wavelet transforms prove to be the optimal bases to represent the data as fgn or fbm fractional brownian motion models this paper highlights the statistical properties of discrete wavelet transform dwt coefficients in the wavelet expansion of fgn statistical analysis was carried out by analyzing the inter scale and intra scale correlations of the dwt coefficients for wavelets with varying vanishing moments two types of auto regressive moving average arma models were fit to the wavelet coefficients of fgn namely i arma p q and ii arfima p d q models the latter represents the arma models with fractional differencing using the akaike information criteria aic and the bayesian information criteria bic it has been shown that arfima models best represent the wavelet coefficients of fgn the above observation holds good when wavelets with increasing number of vanishing moments are used for obtaining dwt coefficients after estimating the optimal model and its parameters different properties pertaining to the inter scale and intra scale correlations were verified using these models

time domain approach to the forward scattering sum rule the forward scattering sum rule relates the extinction cross section integrated over all wavelengths with the polarizability dyadics it is useful for deriving bounds on the interaction between scatterers and electromagnetic fields antenna bandwidth and directivity and energy transmission through sub wavelength apertures the sum rule is valid for linearly polarized plane waves impinging on linear passive and time translational invariant scattering objects in free space here a time domain approach is used to clarify the derivation and the used assumptions the time domain forward scattered field defines an impulse response energy conservation shows that this impulse response is the kernel of a passive convolution operator which implies that the fourier transform of the impulse response is a herglotz function the forward scattering sum rule is finally constructed from integral identities for herglotz functions

on the correlation structure of the wavelet coefficients of fractional brownian motion shows that the interdependence of the discrete wavelet coefficients of fractional brownian motion defined by normalized correlation decays exponentially fast across scales and hyperbolically fast along time

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

the bremmer series for a multi dimensional acoustic scattering problem the bremmer series is used to reduce a complex scattering problem to a sequence of simpler single scattering problems in the bremmer series the wave equation is first decomposed into a coupled system of one way wave equations the system is then decoupled into a sequence of one way wave equations with a fixed point iteration in this paper a left symbol representation of the decomposition operator and the vertical propagation operator are used time domain convergence of the bremmer series is shown for a set of dispersive medium models the non dispersive case is treated with an approximation procedure

linking topology of tethered polymer rings with applications to chromosome segregation and estimation of the knotting length the gauss linking number ca of two flexible polymer rings which are tethered to one another is investigated for ideal random walks mean linking squared varies with the square root of polymer length while for self avoiding walks linking squared increases logarithmically with polymer length the free energy cost of linking of polymer rings is therefore strongly dependent on degree of self avoidance i e on intersegment excluded volume scaling arguments and numerical data are used to determine the free energy cost of fixed linking number in both the fluctuation and large ca regimes for ideal random walks for ca n 1 4 the free energy of catenation is found to grow proportional variant ca n 1 4 4 3 when excluded volume interactions between segments are present the free energy rapidly approaches a linear dependence on gauss linking df dca approximately 3 7k b t suggestive of a novel catenation condensation effect these results are used to show that condensation of long entangled polymers along their length so as to increase excluded volume while decreasing number of statistical segments can drive disentanglement if a mechanism is present to permit topology change for chromosomal dna molecules lengthwise condensation is therefore an effective means to bias topoisomerases to eliminate catenations between replicated chromatids the results for mean square catenation are also used to provide a simple approximate estimate for the knotting length or number of segments required to have a knot along a single circular polymer explaining why the knotting length ranges from approximately 300 for an ideal random walk to 10 6 for a self avoiding walk

on the non uniqueness of the electromagnetic instantaneous response the instantaneous response models the rapid part of the interaction between electromagnetic fields and materials from a physical point of view the instantaneous response is non observable and from a mathematical point of view it constitutes the principal part of the maxwell equations in this paper it is shown that the instantaneous response is not uniquely determined from a given set of values of the constitutive map the given values only give an upper bound on the size of the instantaneous response a numerical example illustrates the non uniqueness of the instantaneous response

wavelet representations of stochastic processes and multiresolution stochastic models deterministic signal analysis in a multiresolution framework through the use of wavelets has been extensively studied very successfully in recent years in the context of stochastic processes the use of wavelet bases has not yet been fully investigated we use compactly supported wavelets to obtain multiresolution representations of stochastic processes with paths in l sup 2 defined in the time domain we derive the correlation structure of the discrete wavelet coefficients of a stochastic process and give new results on how and when to obtain strong decay in correlation along time as well as across scales we study the relation between the wavelet representation of a stochastic process and multiresolution stochastic models on trees proposed by basseville et al see ieee trans inform theory vol 38 p 766 784 mar 1992 we propose multiresolution stochastic models of the discrete wavelet coefficients as approximations to the original time process these models are simple due to the strong decorrelation of the wavelet transform experiments show that these models significantly improve the approximation in comparison with the often used assumption that the wavelet coefficients are completely uncorrelated

a wiener wintner theorem for 1 f power spectra abstract wiener s generalized harmonic analysis gha provides a theory of harmonic analysis for subspaces of tempered functions not accessible to the l 1 l 2 and fourier series theories and it does it in a way that is usually more quantitative than that provided by the theory of distributions on the other hand gha does not yield an adequate spectral analysis of large classes of functions including nonstationary processes and in particular 1 f noise in this paper we adapt gha to deal with 1 f noise by extending the wiener wintner theorem to the case of 1 f power spectra