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

treatment of a sloping fluid solid interface and sediment layering with the seismo acoustic parabolic equation the parabolic equation method is extended to handle problems in seismo acoustics that have multiple fluid and solid layers continuous depth dependence within layers and sloping interfaces between layers the medium is approximated in terms of a series of range independent regions and a single scattering approximation is used to compute transmitted fields across the vertical interfaces between regions the approach is implemented in terms of a set of dependent variables that is well suited to piecewise continuous depth dependence in the elastic parameters but one of the fluid solid interface conditions in that formulation involves a second derivative that complicates the treatment of sloping interfaces this issue is resolved by using a non centered four point difference formula for the second derivative the approach is implemented using a matrix decomposition that is efficient when the parameters of the medium have a general dependence within the upper layers of the sediment but only depend on depth in the water column and deep within the sediment

dynamical systems disjoint from any minimal system furstenberg showed that if two topological systems x t and y s are disjoint then one of them say y s is minimal when y s is nontrivial we prove that x t must have dense recurrent points and there are countably many maximal transitive subsystems of x t such that their union is dense and each of them is disjoint from y s showing that a weakly mixing system with dense periodic points is in m the collection of all systems disjoint from any minimal system furstenberg asked the question to characterize the systems in m we show that a weakly mixing system with dense regular minimal points is in m and each system in m has dense minimal points and it is weakly mixing if it is transitive transitive systems in m and having no periodic points are constructed moreover we show that there is a distal system in m recently weiss showed that a system is weakly disjoint from all weakly mixing systems iff it is topologically ergodic we construct an example which is weakly disjoint from all topologically ergodic systems and is not weakly mixing

generalized bremmer series with rational approximation for the scattering of waves in inhomogeneous media the bremmer series solution of the wave equation in generally inhomogeneous media requires the introduction of pseudodifferential operators in this paper sparse matrix representations of these pseudodifferential operators are derived the authors focus on designing sparse matrices keeping the accuracy high at the cost of ignoring any critical scattering angle phenomena such matrix representations follow from rational approximations of the vertical slowness and the transverse laplace operator symbols and of the vertical derivative as they appear in the parabolic equation method sparse matrix representations lead to a fast algorithm an optimization procedure is followed to minimize the errors in the high frequency limit for a given discretization rate the bremmer series solver consists of three steps directional decomposition into up and downgoing waves one way propagation and interaction of the counterpropagating constituents each of these steps is represented by a sparse matrix equation the resulting algorithm provides an improvement of the parabolic equation method in particular for transient wave phenomena and extends the latter method systematically for backscattered waves

a wide angle on surface radiation condition applied to scattering by spheroids a rational approximation of the pseudo differential dirichlet to neumann operator for a circular cylinder is made using zero placement for an acoustically hard circular cylinder this zero corresponds to the dominant creeping wave singularity in the residue series for the time harmonic free space surface green s function based on this operator a wide angle on surface radiation condition osrc is developed first for two dimensional slender convex bodies for the object scattering problem this osrc is accurate for wide scattering angles relative to the surface normal the notion of creeping waves is then used to develop a wide angle three dimensional osrc applicable to smooth convex bodies application to both hard and soft prolate and oblate spheroids is presented and excellent agreement is found in comparison with a more costly technique

radial structure of the internet the structure of the internet at the autonomous system as level has been studied by the physics mathematics and computer science communities we extend this work to include features of the core and the periphery taking a radial perspective on as network structure new methods for plotting as data are described and they are used to analyse datasets that have been extended to contain edges missing from earlier collections the average distance from one vertex to the rest of the network is used as the baseline metric for investigating radial structure common vertex specific quantities are plotted against this metric to reveal distinctive characteristics of central and peripheral vertices two datasets are analysed

parabolic control problems in measure spaces with sparse solutions optimal control problems in measure spaces lead to controls that have small support which is desirable e g in the context of optimal actuator placement for problems governed by parabolic partial differential equations well posedness is guaranteed in the space of square integrable measure valued functions which leads to controls with a spatial sparsity structure a conforming approximation framework allows one to derive numerically accessible optimality conditions as well as convergence rates in particular although the state is discretized the control problem can still be formulated and solved in the measure space numerical examples illustrate the structural features of the optimal controls

application of the detrended fluctuation analysis dfa method for describing cloud breaking abstract a method to sort out correlations and decorrelations in stratus cloud formation persistence and breakup is introduced the detrended fluctuation analysis dfa statistical method is applied to microwave radiometer data the existence of long range power law correlations in stratus cloud liquid water content fluctuations is demonstrated over a 2 h period moreover using a finite size time interval window a change from brownian to non brownian fluctuation regimes is clearly shown to define the cloud structure changes such findings are similar to those found in dna and financial data sequences when mosaics of persistent and antipersistent patches are present the occurrence of these statistics in stratus cloud liquid water content suggests the usefulness of similar studies on cloud resolving model output and for better meteorological predictability

rescaling entropy and divergence rates based on rescaling by some suitable sequence instead of the number of time units the usual notion of divergence rate is here extended to define and determine meaningful generalized divergence rates rescaling entropy rates appears as a special case suitable rescaling is naturally induced by the asymptotic behavior of the marginal divergences closed form formulas are obtained as soon as the marginal divergences behave like powers of some analytical functions a wide class of countable markov chains is proved to satisfy this property most divergence and entropy functionals defined in the literature are concerned e g the classical shannon kullback leibler renyi and tsallis for illustration purposes ferreri or basu harris hjort jones among others are also considered

detrended cross correlation analysis consistently extended to multifractality we propose an algorithm multifractal cross correlation analysis mfcca which constitutes a consistent extension of the detrended cross correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross correlations between two time series our motivation for introducing this algorithm is that the already existing methods like multifractal extension have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross correlations when there are none the principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments furthermore we present a broad analysis of the model fractal stochastic processes as well as of the real world signals and show that mfcca is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross correlative structure of analyzed processes in particular it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized hurst exponent and the multifractal scaling parameter ensuremath lambda q this relation provides information about the character of potential multifractality in cross correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far by using examples of time series from the stock market we show that financial fluctuations typically cross correlate multifractally only for relatively large fluctuations whereas small fluctuations remain mutually independent even at maximum of such cross correlations finally we indicate possible utility of mfcca to study effects of the time lagged cross correlations

a mapping approach for handling sloping interfaces a mapping approach for handling sloping interfaces in parabolic equation solutions is developed and tested at each range the medium is rigidly translated vertically so that a sloping interface becomes horizontal to simplify the approach the slope is assumed to be small and the extra terms that arise in the wave equation under the mapping are neglected the effects of these terms can be approximately accounted for by applying a leading order correction to the phase the mapping introduces variations in topography which are relatively easy to handle for the case of a pressure release boundary condition the accuracy of the approach is demonstrated for problems involving fluid sediments the approach should also be accurate for problems involving elastic sediments and should be useful for solving three dimensional problems involving variable topography

oceanographic inverse problems abstract oceanographic inverse problems are generalizations of the concept of linear regression to encompass the fitting of numerical models based on the partial diffential equations of fluid dynamics to oceanic data by adjusting surface fluxes initial conditions and or transport parameters the limited resolution of the data requires some sort of regularizing assumptions similar to those needed for spatial interpolation computationally they are nonlinear least squares problems involving very many variables these problems can be ill conditioned due to the indirect nature of the observations to the way the dynamics enter and to the effect of the regularizing assumptions solving such large optimization problems requires efficient computation of derivatives of functions defined by computational codes the adjoint method provides derivatives with respect to all the code s many adjustable inputs for roughly the same cost as computing a single model simulation although computationally difficult model fitting offers the promise of dynamically consistent multivariate analyses of oceanographic data

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

independence in topological and c dynamics we develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods one of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing properties we also reframe our theory of dynamical independence in terms of tensor products and thereby expand its scope to c dynamics

multifractal detrended cross correlation analysis of sunspot numbers and river flow fluctuations abstract we use the detrended cross correlation analysis dcca to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators specifically rivers represented by river flow fluctuation for daugava holston nolichucky and french broad rivers the multifractal detrended cross correlation analysis mf dxa shows that there exist some crossovers in the cross correlation fluctuation function versus time scale of the river flow and sunspot series one of these crossovers corresponds to the well known cycle of solar activity demonstrating a universal property of the mentioned rivers the scaling exponent given by dcca for original series at intermediate time scale 12 24 s 130 months is 1 17 0 04 which is almost similar for all underlying rivers at 1 confidence interval showing the second universal behavior of river runoffs to remove the sinusoidal trends embedded in data sets we apply the singular value decomposition svd method our results show that there exists a long range cross correlation between the sunspot numbers and the underlying streamflow records the magnitude of the scaling exponent and the corresponding cross correlation exponent are 0 76 0 85 and 0 30 0 48 respectively different values for scaling and cross correlation exponents may be related to local and external factors such as topography drainage network morphology human activity and so on multifractal cross correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series in addition the empirical relation between scaling exponent derived by dcca and detrended fluctuation analysis dfa h sun h river 2 is confirmed

rational square root approximations for parabolic equation algorithms in this article stable pade approximations to the function 1 z are derived by choosing a branch cut in the negative half plane the pade coefficients are complex and may be derived analytically to arbitrary order from the corresponding real coefficients associated with the principal branch defined by z 1 i z 0 i z denotes the imaginary part of z the characteristics of the corresponding square root approximation are illustrated for various segments of the complex plane in particular for waveguide problems it is shown that an increasingly accurate representation may be obtained of both the evanescent part of the mode spectrum for the acoustic case and the complex mode spectrum for the elastic case an elastic parabolic equation algorithm is used to illustrate the application of the new pade approximations to a realistic ocean environment including elasticity in the ocean bottom

an explicit analytical solution for sound propagation in a three dimensional penetrable wedge with small apex angle a problem of sound propagation in a shallow water waveguide with a weakly sloping penetrable bottom is considered the adiabatic mode parabolic equations are used to approximate the solution of the three dimensional 3d helmholtz equation by modal decomposition of the acoustic pressure field the mode amplitudes satisfy parabolic equations that admit analytical solutions in the special case of the 3d wedge using the analytical formula for modal amplitudes an explicit and remarkably simple expression for the acoustic pressure in the wedge is obtained the proposed solution is validated by the comparison with a solution of the 3d penetrable wedge problem obtained using a fully 3d parabolic equation that includes a leading order cross term correction

treatment of ice cover and other thin elastic layers with the parabolic equation method the parabolic equation method is extended to handle problems involving ice cover and other thin elastic layers parabolic equation solutions are based on rational approximations that are designed using accuracy constraints to ensure that the propagating modes are handled properly and stability constrains to ensure that the non propagating modes are annihilated the non propagating modes are especially problematic for problems involving thin elastic layers it is demonstrated that stable results may be obtained for such problems by using rotated rational approximations milinazzo zala and brooke j acoust soc am 101 760 766 1997 and generalizations of these approximations the approach is applied to problems involving ice cover with variable thickness and sediment layers that taper to zero thickness

spike controls for elliptic and parabolic pdes abstract we analyze the use of measures of the minimal norm to control elliptic and parabolic equations we prove the sparsity of the optimal control in the parabolic case we prove that the solution of the optimization problem is a borel measure supported in a set of lebesgue measure zero in both cases the approximate controllability can be achieved efficiently by means of controls that are activated in some finite number of pointwise locations we also analyze the corresponding dual problem

illusion of persistence in nba 1995 2018 regular season data abstract among the sports fans beliefs about hot hands and winning streaks are widely spread while the scientific debate about these effects is still ongoing recently in a paper by ferreira 2018 detrended fluctuation analysis was applied to the nba teams win records it was shown that 28 considered nba teams exhibit persistence in the win record time series in this paper we take the same data set and compare the obtained results against various random models we find that the empirical results are consistent with the results obtained from various simple random models

combinatorial lemmas and applications to dynamics abstract the well known combinatorial lemma of karpovsky milman and alon and a very recent one of kerr and li are extended the obtained lemmas are applied to study the maximal pattern entropy introduced in the paper it turns out that the maximal pattern entropy is equal to the supremum of sequence entropies over all sequences both in topological and measure theoretical settings moreover it is shown the maximal pattern entropy of any topological system is log k for some k n with k the maximal length of intrinsic sequence entropy tuples and a zero dimensional system has zero sequence entropy for any sequence if and only if the maximal pattern with respect to any open cover is of polynomial order

on match lengths zero entropy and large deviations with application to sliding window lempel ziv algorithm the sliding window lempel ziv swlz algorithm that makes use of recurrence times and match lengths has been studied from various perspectives in information theory literature in this paper we undertake a finer study of these quantities under two different scenarios 1 zero entropy sources that are characterized by strong long term memory and 2 the processes with weak memory as described through various mixing conditions for zero entropy sources a general statement on match length is obtained it is used in the proof of almost sure optimality of fixed shift variant of lempel ziv fslz and swlz algorithms given in literature through an example of stationary and ergodic processes generated by an irrational rotation we establish that for a window of size n w a compression ratio given by o log n w n w a where a depends on n w and approaches 1 as n w is obtained under the application of fslz and swlz algorithms in addition we give a general expression for the compression ratio for a class of stationary and ergodic processes with zero entropy next we extend the study of ornstein and weiss on the asymptotic behavior of the normalized version of recurrence times and establish the large deviation property for a class of mixing processes in addition an estimator of entropy based on recurrence times is proposed for which large deviation principle is proved for sources satisfying similar mixing conditions

higher order pade approximations for accurate and stable elastic parabolic equations with application to interface wave propagation higher order pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover accuracy is achieved by placing constraints on the derivatives of the pade approximations at the point corresponding to the reference wave number stability is achieved by requiring that the pade approximations map part of the lower left quadrant of the complex plane into the upper half of the complex plane elastic parabolic equations based on these pade series can handle problems involving compressional shear and interface waves very wide propagation angles and large depth variations and weak range variations in the seismoacoustic parameters a finite difference spectral solution is developed for generating reference solutions and starting fields the rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range dependent problems

hydrological natural inflow and climate variables time and frequency causality analysis numbers of studies have proved the significant influence of climate variables on hydrologicalseries considering the pivotal role of the hydroelectric power plants play in the electricity production in brazil this paper considers the natural hydrological inflow data from 15 major basins and 8 climate variables containing 7 el ni no southern oscillation proxies and the sunspot numbers the causal relationships between hydrological natural inflows and climate variables are investigated by adopting and comparing 5 different causality detection methods granger causality test frequency domain causality test convergent cross mapping causality test single spectrum analysis ssa causality test and periodic autoregressive model causality test that cover both well established and novel empirical approaches both time domain and frequency domain causality tests gain valid evidences of unidirectional causality for a group of series ccm achieved unidirectional causality for 18 of pairs and overwhelmingly indicated the opposite direction of causality a mixture of results are concluded by ssa causality test par based causality test obtained six unidirectional causality but only one is really significant

a single scattering correction for large contrasts in elastic layers the single scattering solution is implemented in a formulation that makes it possible to accurately handle solid solid interfaces with the parabolic equation method problems involving large contrasts across sloping stratigraphy can be handled by subdividing a vertical interface into a series of two or more scattering problems the approach can handle complex layering and is applicable to a large class of seismic problems the solution of the scattering problem is based on an iteration formula which has improved convergence in the new formulation and the transverse operator of the parabolic wave equation which is implemented efficiently in terms of banded matrices accurate solutions can often be obtained by using only one iteration

arbitrarily wide angle wave equations for complex media by combining various ideas related to one way wave equations owwes half space stiffness relation special finite element discretization and complex coordinate stretching a systematic procedure is developed for deriving a series of highly accurate space domain versions of owwes the resulting procedure is applicable to complex media where the governing equation full wave equation is a second order differential system making the procedure applicable for general heterogeneous anisotropic porous viscoelastic media owing to their high accuracy in representing waves propagating in an arbitrarily wide range of angles the resulting equations are named arbitrarily wide angle wave equations awwes in order to illustrate the proposed procedure awwes are derived for one way propagation in acoustic as well as elastic media while acoustic awwes can be considered as modified versions of well known space domain owwes based on rational approximations of the square root operator the elastic awwes are significantly different from the existing elastic owwes unlike the existing elastic owwes elastic awwes are displacement based and are applicable to general anisotropic media furthermore awwes are simple in their form and appear amenable to easy numerical implementation

leading order cross term correction of three dimensional parabolic equation models the issue of handling a leading order cross multiplied term in three dimensional 3d parabolic equation pe based models is addressed in particular numerical results obtained incorporating a leading order cross term correction in an existing 3d pe model written in cylindrical coordinates based on higher order pade approximations in both depth and azimuth and a splitting operator technique are reported note that the numerical algorithm proposed in this paper could be used in the future to update any 3d pe codes that neglect cross terms and use a splitting numerical technique the 3d penetrable wedge benchmark problem is chosen to illustrate the accuracy of the now fully wide angle enhanced 3d pe model the comparisons with a 3d reference solution based on the image source clearly show that handling the leading order cross term in the 3d pe computation is sufficient to remove the phase errors inherent to any 3d pe models that neglect cross terms in their formulations

entropy dimension of shift spaces on monoids we consider the entropy dimension of g shifts of finite type for the case where g is a non abelian monoid entropy dimension tells us whether a shift space has zero topological entropy suppose the cayley graph cg of g has a finite representation that is cgg g g is a finite set up to graph isomorphism and relations among generators of g are determined by a matrix a we reveal an association between the characteristic polynomial of a and the finite representation of the cayley graph after introducing an algorithm for the computation of the entropy dimension the set of entropy dimensions is related to a collection of matrices in which the sum of each row of every matrix is bounded by the number of leaves of the graph furthermore the algorithm extends to g having finitely many free followers

a comparison of forward boundary integral and parabolic wave equation propagation models the parabolic wave equation and its variants have provided the theoretical framework for most practical forward propagation models split step integration generates an easily obtained robust solution for most applications irregular boundaries can be incorporated by using a conformal mapping technique introduced by beilis and tappert 1979 and refined by donohue and kuttler see ibid vol 48 p 260 77 2000 in an earlier paper we demonstrated an alternative method that incorporates a numerical solution to the forward boundary integral equation within each split step cycle this paper compares predictions of forward propagation obtained by these two distinctly different methods the results confirm that the pwe based method is very accurate for smoothly varying surfaces and that it captures the primary forward structure even in the presence of unresolved surface detail the moderate loss of fidelity is often an acceptable trade for increased computational efficiency there are situations however where the details of the surface structure are important furthermore the induced surface currents are unique to the forward boundary integral method we illustrate their use by calculating the bistatic scatter that would he measured from an isolated surface segment we show that the scattered field measured in this way can be normalized to form a bistatic scatter function only when the illuminating beam is tilted slightly toward the surface we interpret this disparity as a breakdown in concept that underlies a local scattering function

on some simple estimates of an exponent of regular variation summary we present a class of simple estimates of an exponent of regular variation unlike those proposed recently by de haan and resnick 1980 ours converge at an algebraic rather than a logarithmic rate and unlike those considered by teugels 1980 their form does not depend on the unknown exponent

generalization of the rotated parabolic equation to variable slopes the rotated parabolic equation j acoust soc am 87 1035 1037 1990 is generalized to problems involving ocean sediment interfaces of variable slope the approach is based on approximating a variable slope in terms of a series of constant slope regions the original rotated parabolic equation algorithm is used to march the field through each region an interpolation extrapolation approach is used to generate a starting field at the beginning of each region beyond the one containing the source for the elastic case a series of operators is applied to rotate the dependent variable vector along with the coordinate system the variable rotated parabolic equation should provide accurate solutions to a large class of range dependent seismo acoustics problems for the fluid case the accuracy of the approach is confirmed through comparisons with reference solutions for the elastic case variable rotated parabolic equation solutions are compared with energy conserving and mapping solutions

scaled entropy for dynamical systems in order to characterize the complexity of a system with zero entropy we introduce the notions of scaled topological and metric entropies we allow asymptotic rates of the general form e alpha a n determined by an arbitrary monotonically increasing scaling sequence a n this covers the standard case of exponential scale corresponding to a n n as well as the cases of zero and infinite entropy we describe some basic properties of the scaled entropy including the inverse variational principle for the scaled metric entropy furthermore we present some examples from symbolic and smooth dynamics that illustrate that systems with zero entropy may still exhibit various levels of complexity

topological entropy dimension for nonautonomous dynamical systems abstract in this paper the topological entropy dimension for nonautonomous dynamical systems is studied this entropy dimension measures the complexity of the systems with zero entropy via the subexponential growth rate of orbits some basic properties of this topological entropy dimension are developed moreover we construct concrete nonautonomous dynamical systems with zero entropy such that their topological entropy dimension can attain any real number between 0 and 1

generating synthetic time series from bak sneppen co evolution model mixtures abstract the bak sneppen model of co evolution is used to derive synthetic time series with a priori specified fractal dimension or hurst exponent through a mixing of processes in various lattice dimensions both theoretical and numerical analyses concern the avalanches at the critical threshold and provide a model for time series reconstruction that can be tested as an alternative to the classical fractional brownian motion fbm because of differences in properties new results on critical threshold and avalanche structure are obtained up to euclidean dimension d 6 the method involves a lattice based structure and therefore is suitable for the application of parallel computing

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

approximation of elliptic control problems in measure spaces with sparse solutions optimal control problems in measure spaces governed by elliptic equations are considered for distributed and neumann boundary control which are known to promote sparse solutions optimality conditions are derived and some of the structural properties of their solutions in particular sparsity are discussed a framework for their approximation is proposed which is efficient for numerical computations and for which we prove convergence and provide error estimates

alternating proximal algorithms for linearly constrained variational inequalities application to domain decomposition for pde s abstract let x y z be real hilbert spaces let f x r g y r be closed convex functions and let a x z b y z be linear continuous operators let us consider the constrained minimization problem p min f x g y a x b y given a sequence n which tends toward 0 as n we study the following alternating proximal algorithm a x n 1 argmin n 1 f 1 2 a b y n z 2 2 x n x 2 x y n 1 argmin n 1 g 1 2 a x n 1 b z 2 2 y n y 2 y where and are positive parameters it is shown that if the sequence n tends moderately slowly toward 0 then the iterates of a weakly converge toward a solution of p the study is extended to the setting of maximal monotone operators for which a general ergodic convergence result is obtained applications are given in the area of domain decomposition for pde s

single scattering parabolic equation solutions for elastic media propagation including rayleigh waves the parabolic equation method with a single scattering correction allows for accurate modeling of range dependent environments in elastic layered media for problems with large contrasts accuracy and efficiency are gained by subdividing vertical interfaces into a series of two or more single scattering problems this approach generates several computational parameters such as the number of interface slices an iteration convergence parameter and the number of iterations n for convergence using a narrow angle approximation the choices of n 1 and 2 give accurate solutions analogous results from the narrow angle approximation extend to environments with larger variations when slices are used as needed at vertical interfaces the approach is applied to a generic ocean waveguide that includes the generation of a rayleigh interface wave results are presented in both frequency and time domains

a single scattering correction for the seismo acoustic parabolic equation an efficient single scattering correction that does not require iterations is derived and tested for the seismo acoustic parabolic equation the approach is applicable to problems involving gradual range dependence in a waveguide with fluid and solid layers including the key case of a sloping fluid solid interface the single scattering correction is asymptotically equivalent to a special case of a single scattering correction for problems that only have solid layers kusel et al j acoust soc am 121 808 813 2007 the single scattering correction has a simple interpretation conservation of interface conditions in an average sense that facilitated its generalization to problems involving fluid layers promising results are obtained for problems in which the ocean bottom interface has a small slope

rational operators for filtering the parabolic equation pe method has been applied to approximate the wave equation construct radiation conditions solve scattering problems construct initial conditions and derive energy flux conditions a new application of the pe method filters based on rational approximations of depth operators is described and tested the rational approximation is designed to act as the identity operator on the desired part of the spectrum of the depth separated wave equation and to annihilate other parts of the spectrum this approach does not require explicit knowledge of the spectrum the applications of the filter include directly solving eigenvalue problems annihilating components of the wave number spectrum generating initial conditions at the source range and eliminating gibbs oscillations that arise in energy conserving pe solutions

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

frequency of frequencies distributions and size dependent exchangeable random partitions abstractmotivated by the fundamental problem of modeling the frequency of frequencies fof distribution this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random count and its exchangeable random partitions a cluster structure naturally arising from a completely random measure mixed poisson process allows the probability distribution of the random partitions of a subset of a population to be dependent on the population size a distinct and motivated feature that makes it more flexible than a partition structure this allows it to model an entire fof distribution whose structural properties change as the population size varies a fof vector can be simulated by drawing an infinite number of poisson random variables or by a stick breaking construction with a finite random number of steps a generalized negative binomial process model is proposed to generate a cluster structure where in the prior the number of clusters is f

transparent boundary conditions for split step pade approximations of the one way helmholtz equation in this paper we generalize the nonlocal discrete transparent boundary condition introduced by f schmidt and p deuflhard 1995 comput math appl 29 53 76 and by f schmidt and d yevick 1997 j comput phys 134 96 107 to propagation methods based on arbitrary pade approximations of the two dimensional one way helmholtz equation our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition which then yields an unconditionally stable propagation method

exact discrete nonlocal boundary conditions for high order pade parabolic equations the nonlocal boundary conditions nlbcs for high order finite difference parabolic equations pes are obtained by z transformation of the discrete pe in a homogeneous medium the considered nlbcs include the free space radiation condition possibly with a density jump at the nlbc interface the nlbc at an arbitrary impedance interface and the nlbcs for sources and the starting field beyond the nlbc interface the derivation is presented for the multiterm pade pe model owwe one way wave equation but the developed technique is applicable to a broad class of finite difference pes the obtained nlbcs are exact for the given finite difference scheme they are not limited by the order of pade approximation or by the pe steps in range and depth the nlbc convolution coefficients are calculated by the numerical inverse z transformation the accuracy and performance of the algorithm are analyzed for several benchmark problems the solution is robust for the range steps over 25 wavelengths and or the approximations up to the tenth order the nlbcs are faster and more accurate for large steps because fewer previous range steps contribute to the convolution precomputation of the nlbc coefficients may be required in time demanding applications the results are compared with earlier proposed nlbcs for high order pes

growing networks of overlapping communities with internal structure we introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks the model comprises two complementary mechanisms one mechanism accounts for the evolution of the internal link structure of a single community and the second mechanism coordinates the growth of multiple overlapping communities the first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates we demonstrate that this simple mechanism gives rise to an effective maximal degree within communities this observation is related to the anthropological theory known as dunbar s number i e the empirical observation of a maximal number of ties which an average individual can sustain within its social groups the second mechanism is based on a recently proposed generalization of preferential attachment to community structure appropriately called structural preferential attachment spa the combination of these two mechanisms into a single model spa allows us to reproduce a number of the global statistics of real networks the distribution of community sizes of node memberships and of degrees the spa model also predicts a three qualitative regimes for the degree distribution within overlapping communities and b strong correlations between the number of communities to which a node belongs and its number of connections within each community we present empirical evidence that support our findings in real complex networks

zero entropy systems this paper introduces the notion of entropy dimension to measure the complexity of zero entropy dynamical systems including the probabilistic and the topological versions these notions are isomorphism invariants for measure preserving transformation and continuity we discuss basic propositions for entropy dimension and construct some examples to show that the topological entropy dimension attains any value between 0 and 1 this paper also gives a symbolic subspace to achieve zero topological entropy but with full entropy dimension

on the bias of traceroute sampling or power law degree distributions in regular graphs understanding the graph structure of the internet is a crucial step for building accurate network models and designing efficient algorithms for internet applications yet obtaining this graph structure can be a surprisingly difficult task as edges cannot be explicitly queried for instance empirical studies of the network of internet protocol ip addresses typically rely on indirect methods like traceroute to build what are approximately single source all destinations shortest path trees these trees only sample a fraction of the network s edges and a paper by lakhina et al 2003 found empirically that the resulting sample is intrinsically biased further in simulations they observed that the degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is poisson in this article we study the bias of traceroute sampling mathematically and for a very general class of underlying degree distributions explicitly calculate the distribution that will be observed as example applications of our machinery we prove that traceroute sampling finds power law degree distributions in both regular and poisson distributed random graphs thus our work puts the observations of lakhina et al on a rigorous footing and extends them to nearly arbitrary degree distributions

complex pade approximants for wide angle acoustic propagators procedures for constructing wide angle propagators that attenuate evanescent modes in parabolic equation pe models of underwater sound propagation are examined in this context two new split step pade approximations to exponentiated square root operators are proposed the first method involves a propagator derived from a pade approximant of a square root operator that has been rotated in the complex plane while the propagator of the second method is obtained from a complex coefficient rational approximation of the square root operator numerical evidence confirms that these proposed methods yield improved behavior compared to previously suggested techniques in selected areas of the spectral domain

an admm numerical approach to linear parabolic state constrained optimal control problems optimal control problems arising from systems modeled by linear parabolic equations may be difficult for both theoretical analysis and algorithmic design for the case where there are additional constraints on the state variables restrictive regularity assumptions are usually required to guarantee the existence of the associated lagrange multiplier and thus some regularization type methods such as the moreau yosida and lavrentiev methods have been discussed in the literature in this article we study the application of the alternating direction method of multipliers admm to linear parabolic state constrained optimal control problems and propose an admm numerical approach we prove the convergence of the admm algorithm without any existence or regularity assumption on the lagrange multiplier and estimate its worst case convergence rate in both the ergodic and nonergodic senses an important feature of the admm approach is that it decouples the state constraints and the parabolic optimal control problems inside each iteration we show the efficiency of the admm approach by testing some control problems in two space dimensions

inverse scattering from arbitrary two dimensional objects in stratified environments via a green s operator an important problem in geophysics medical imaging and nondestructive imaging today is the construction of a practical accurate and efficient means of imaging geophysical anomalies tumours or material defects in layered media this paper discusses such a method the use of a stratified green s function for the solution of the forward problem is detailed this forward problem is then incorporated into an efficient and accurate inversion algorithm based on optimization the method is nonperturbative unlike diffraction tomography which relies on linearization to make the problem tractable in the inversion a pair of lippmann schwinger like integral equations are solved simultaneously via the galerkin procedure for the unknown total internal fields and speed distribution the computational burden is high but made manageable by utilizing biconjugate gradients fast fourier transforms and sinc basis functions to speed up the solution of the forward problem the size and contrasts for which the me

coherent and random sequences in financial fluctuations abstract the detrended fluctuation analysis dfa is used to sort out temporal correlations in financial data its usefulness for the investigations of long range power law correlations in economic sequences is shown our findings of persistent and antipersistent sequences are suprisingly similar to those for dna sequences which appeared as a mosaic of coding and non coding patches

sparse source identification of linear diffusion advection equations by adjoint methods abstract we present an algorithm for the time inversion of diffusion advection equations based on the adjoint methodology given a final state distribution our main aim is to recover sparse initial conditions constituted by a finite combination of kronecker deltas identifying their location and mass we discuss the strengths of the adjoint machinery and the difficulties that are to be faced in particular when the diffusivity coefficient or the time horizon is large

modeling rayleigh and stoneley waves and other interface and boundary effects with the parabolic equation an improved approach for handling boundaries interfaces and continuous depth dependence with the elastic parabolic equation is derived and benchmarked the approach is applied to model the propagation of rayleigh and stoneley waves depending on the choice of dependent variables the operator in the elastic wave equation may not factor or the treatment of interfaces may be difficult these problems are resolved by using a formulation in terms of the vertical displacement and the range derivative of the horizontal displacement these quantities are continuous across horizontal interfaces which permits the use of galerkin s method to discretize in depth this implementation extends the capability of the elastic parabolic equation to handle arbitrary depth dependence and should lead to improvements for range dependent problems

energy conserving and reciprocal solutions for higher order parabolic equations conservation of sound energy in nonabsorbing media and acoustical reciprocity in stationary fluids at rest are the fundamental properties of the acoustic field preserving these properties in parabolic approximations is essential for accurate modeling of sound propagation in shallow water environments recently godin proposed a family of wide angle parabolic equations pe s for motionless fluid which are energy conserving reciprocal and allow improved description of mode coupling without adversely affecting phase accuracy for moving media a generalized claerbout pe was also derived its solutions preserve the acoustic energy in the absence of dissipation and satisfy the flow reversal theorem frt which is an extension of reciprocity principle to moving media the report presents a numerical scheme for solving the proposed pe s the algorithm preserves the conservational properties of the original pseudo differential equations implicit finite difference solutions satisfy discrete analogs of the e

wave number sampling at short range the self starter is an efficient approach for solving geoacoustic inverse problems involving a vertical array of receivers located on the order of ten wavelengths from a source r j cederberg and m d collins j acoust soc am 22 102 109 1997 with this approach accurate solutions can be obtained by sampling the wave number spectrum at approximately ten points there have been unsubstantiated claims that the spectral solution provides similar efficiency when implemented with an approach that involves perturbing the integration contour off the real line f b jensen et al computational ocean acoustics american institute of physics new york 1994 pp 231 240 it is demonstrated that this quadrature scheme breaks down at short ranges and that the self starter solution is about an order of magnitude faster these conclusions are based on comparisons of the rational approximations associated with the self starter and the quadrature scheme comparisons of acoustic fields for particular proble

a parabolic approximation method with application to global wave propagation motivated by the difficulty in using the splitting matrix method to obtain parabolic approximations to complicated wave equations we have developed an alternative method it is three dimensional does not a priori assume a preferred direction or path of propagation in the horizontal determines spreading factors and results in equations that are energy conserving it is an extension of previous work by several authors relating parabolic equations to the horizontal ray acoustics approximation unlike previous work it applies the horizontal ray acoustics approximation to the propagator rather than to the green s function or the homogenous field the propagator is related to the green s function by an integral over the famous fifth parameter of fock and feynman methods for evaluating this integral are equivalent to narrow angle approximations and their wide angle improvements when this new method is applied to simple problems it gives the standard results in this paper it is described by applying it to a problem of current interest the development of a parabolic approximation for modeling global underwater and atmospheric acoustic propagation the oceanic or atmospheric waveguide is on an earth that is modeled as an arbitrary convex solid of revolution the method results in a parabolic equation that is energy conserving and has a spreading factor that describes field intensification for antipodal propagation significantly it does not have the singularities in its range sliced version possessed by many parabolic equations developed for global propagation we then discuss two extensions of the method first to propagation along refracted geodesics and second to a description involving discrete local normal modes

applications of statistical physics to economic and financial topics abstract problems in economy and finance have started to attract the interest of statistical physicists fundamental problems pertain to the existence or not of long medium short range power law correlations in economic systems as well as to the presence of financial cycles methods like the extended detrended fluctuation analysis and the multi affine analysis are recalled emphasizing their value in sorting out correlation ranges and predictability among spectacular results the possibility of crash predictions is indicated the well known financial analyst technique the so called moving average is shown to raise questions about fractional brownian motion properties finally the m k zipf method and the i variability diagram technique are presented for sorting out short range correlations analogies with other fields of modern applied statistical physics are also presented in view of some universal openess

hurst exponent of very long birth time series in xx century romania social and religious aspects abstract the hurst exponent of very long birth time series in romania has been extracted from official daily records i e over 97 years between 1905 and 2001 included the series result from distinguishing between families located in urban u or rural r areas and belonging ox or not nox to the orthodox religion four time series combining both criteria u r and ox nox are also examined a statistical information is given on these sub populations measuring their xx th century state as a snapshot however the main goal is to investigate whether the daily production of babies is purely noisy or is fluctuating according to some non trivial fractional brownian motion in the four types of populations characterized by either their habitat or their religious attitude yet living within the same political regime one of the goals was also to find whether combined criteria implied a different behavior moreover we wish to observe whether some seasonal periodicity exists the detrended fluctuation analysis technique is used for finding the fractal correlation dimension of such 9 signals it has been first necessary due to two periodic tendencies to define the range regime in which the hurst exponent is meaningfully defined it results that the birth of babies in all cases is a very strongly persistent signal it is found that the signal fractal correlation dimension is weaker i for nox than for ox and ii or u with respect to r moreover it is observed that the combination of u or r with nox or ox enhances the unox uox and rox fluctuations but smoothens the rnox signal thereby suggesting a stronger conditioning on religiosity rituals or rules

estimating heavy tail exponents through max self similarity in this paper a novel approach to the problem of estimating the heavy tail exponent 0 of a distribution is proposed it is based on the fact that block maxima of size m scale at a rate m1 for independent as well as for a number of dependent data this scaling rate can be captured well by the max spectrum plot of the data that leads to regression based estimators for consistency and asymptotic normality of these estimators is established for independent data under mild conditions on the behavior of the tail of the distribution the proposed estimators have an important computational advantage over existing methods namely they can be calculated and updated sequentially in an on line fashion without having to store the entire data set practical issues on the automatic selection of tuning parameters for the estimators and corresponding confidence intervals are also addressed extensive numerical simulations show that the proposed method is competitive for both small and large sample sizes robust to contaminants and continues to work under the presence of substantial amount of dependence the proposed estimators are used to illustrate the close connection between long range dependence and heavy tails over an internet traffic trace