atmospheric data analysis with the i variability diagram method hint to fractional brownian motion like phenomena for the inner structure of clouds abstract a method to sort out short range correlations and decorrelations in meteorology physical data is introduced an i variability diagram statistical method is used on liquid water cloud content taken from the astex 92 program data set the i 1 2 cases are treated here the subsequent points are found to be embedded in polygons for which the inertial axes are calculated and are shown to have non trivial values such findings are similar to those found in biological and financial data sequences this suggests ways of modeling inner cloud structure and possibly alter meteorological fields using fractional brownian motion type constraints

structure and perimeters of percolation clusters site percolation clusters are simulated at the percolation threshold on the square lattice an algorithm for walks around each cluster is used to obtain information on its fractal geometry the fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it if the vacant perimeter sites have only nearest neighbour connectivity then the perimeter has dimension de 1 37 or 0 03 instead of that of the hull dh 1 75 the authors also measured the mass of internal dangling sites surrounded by the backbone s blobs singly and doubly connected sites the number of blobs and the average linear distance between entry into the exit from a blob

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

a new class of incremental gradient methods for least squares problems the least mean squares lms method for linear least squares problems differs from the steepest descent method in that it processes data blocks one by one with intermediate adjustment of the parameter vector under optimization this mode of operation often leads to faster convergence when far from the eventual limit and to slower sublinear convergence when close to the optimal solution we embed both lms and steepest descent as well as other intermediate methods within a one parameter class of algorithms and we propose a hybrid class of methods that combine the faster early convergence rate of lms with the faster ultimate linear convergence rate of steepest descent these methods are well suited for neural network training problems with large data sets furthermore these methods allow the effective use of scaling based for example on diagonal or other approximations of the hessian matrix

bounded cascade models as nonstationary multifractals we investigate a class of bounded random cascade models which are multiplicative by construction yet additive with respect to some but not all of their properties we assume the multiplicative weights go to unity as the cascade proceeds then the resulting field has upper and lower bounds two largely complementary multifractal statistical methods of analysis are used singular measures and structure functions yielding respectively the exponent hierarchies ital d sub ital q and ital h sub ital q we study in more detail a specific subclass of one dimensional models with weights 1 plus minus 1 minus 2 ital p ital r sub ital n minus 1 sup ital h at relative scale ital r sub ital n 2 sup minus ital n after ital n cascade steps the parameter ital h gt 0 regulates the degree of nonstationarity at ital h 0 stationarity prevails and singular ital p model cascades meneveau and sreenivasan phys rev lett 59 1424 1987 are retrieved our model has at once large scale stationarity and small scale nonstationarity with stationary increments due to the boundedness the ital d sub ital q all converge to unity with increasing ital n the rate of convergence is estimated and the results are discussed in terms of residual multifractality a spurious singularity spectrum due to finite size effects the structure function exponents are moremore interesting ital h sub ital q min l brace ital h 1 ital q r brace in the limit ital n r arrow infinity we further focus on the cases ital q 1 related to the fractal structure of the graph ital q 2 related to the energy spectrum and ital q 1 ital h the critical order beyond which our multiplicative and multiscaling bounded cascade model can be statistically distinguished from fractional brownian motion the corresponding additive and monoscaling model less

distributed parameter estimation in sensor networks nonlinear observation models and imperfect communication the paper studies distributed static parameter vector estimation in sensor networks with nonlinear observation models and noisy intersensor communication it introduces separably estimable observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation it studies two distributed estimation algorithms in separably estimable models the nu with its linear counterpart lu and the nlu their update rule combines a consensus step where each sensor updates the state by weight averaging it with its neighbors states and an innovation step where each sensor processes its local current observation this makes the three algorithms of the consensus innovations type very different from traditional consensus this paper proves consistency all sensors reach consensus almost surely and converge to the true parameter value efficiency and asymptotic unbiasedness for lu and nu it proves asymptotic normality and provides convergence rate guarantees the three algorithms are characterized by appropriately chosen decaying weight sequences algorithms lu and nu are analyzed in the framework of stochastic approximation theory algorithm nlu exhibits mixed time scale behavior and biased perturbations and its analysis requires a different approach that is developed in this paper

the thermodynamics of fractals revisited with wavelets abstract the multifractal formalism originally introduced to describe statistically the scaling properties of singular measures is revisited using the wavelet transform this new approach is based on the definition of partition functions from the wavelet transform modulus maxima we demonstrate that very much like thermodynamic functions the generalized fractal dimensions d q and the f singularity spectrum can be readily determined from the scaling behavior of these partition functions we show that this method provides a natural generalization of the classical box counting techniques to fractal signals the wavelets playing the role of generalized boxes we illustrate our theoretical considerations on pedagogical examples e g devil s staircases and fractional brownian motions we also report the results of some recent application of the wavelet transform modulus maxima method to fully developed turbulence data that we emphasize the wavelet transform as a mathematical microscope that can be further used to extract microscopic informations about the scaling properties of fractal objects in particular we show that a dynamical system which leaves invariant such an object can be uncovered form the space scale arrangement of its wavelet transform modulus maxima we elaborate on a wavelet based tree matching algorithm that provides a very promising tool for solving the inverse fractal problem this step towards a statistical mechanics of fractals is illustrated on discrete period doubling dynamical systems where the wavelet transform is shown to reveal the renormalization operation which is essential to the understanding of the universal properties of this transition to chaos finally we apply our technique to analyze the fractal hierarchy of dla azimuthal cantor sets defined by intersecting the inner frozen region of large mass off lattice diffusion limited aggregates dla wit a circle this study clearly lets out the existence of an underlying multiplicative process that is likely to account for the fibonacci structural ordering recently discovered in the apparently disordered arborescent dla morphology

information driven distributed maximum likelihood estimation based on gauss newton method in wireless sensor networks in this paper we develop an energy efficient distributed estimation method that can be used in applications such as the estimation of a diffusive source and the localization and tracking of an acoustic target in wireless sensor networks we first propose a statistical measurement model in which we separate the linear and nonlinear parameters this modeling strategy reduce the processing complexity we then study the distributed implementation of the gauss newton method in the maximum likelihood estimation after that we propose a fully distributed estimation approach based on an incremental realization of the gauss newton method we derive three modifications of the basic algorithm to improve the distributed processing performance while still considering the energy restriction we implement the idea of information driven collaborative signal processing and provide a sensor node scheduling scheme in which the cramer rao bound crb is used as the performance and information utility measure to select the next sensor node numerical examples are used to study the performance of the distributed estimation and we show that of the methods considered here the proposed multiple iteration kalman filtering method has the most advantages for wireless sensor networks

incremental subgradient methods for nondifferentiable optimization we consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions this type of minimization arises in a dual context from lagrangian relaxation of the coupling constraints of large scale separable problems the idea is to perform the subgradient iteration incrementally by sequentially taking steps along the subgradients of the component functions with intermediate adjustment of the variables after processing each component function this incremental approach has been very successful in solving large differentiable least squares problems such as those arising in the training of neural networks and it has resulted in a much better practical rate of convergence than the steepest descent method in this paper we establish the convergence properties of a number of variants of incremental subgradient methods including some that are stochastic based on the analysis and computational experiments the methods appear very promising and effective for important classes of large problems a particularly interesting discovery is that by randomizing the order of selection of component functions for iteration the convergence rate is substantially improved

self organizing criticality in cloud formation abstract starting from the phenomenology of cloud formation we derive a cellular automaton model which turns out to have a strong resemblance to percolation based growth models projections of thereby produced clusters show a realistic fractal dimension of the perimeter but only at or near the critical percolation threshold pc a mechanism based on the continuity equation is proposed and numerically tested which possibly explains why the atmosphere acts in fact near its critical threshold during cloud formation self organizing criticality numerically this is achieved by a feedback of the number of active sites on the occupation concentration p

three dimensional turbulent diffusion versus critical phenomena the critical exponent nu of the correlated or coherent length of a turbulent cluster has been related to the minimal fractal dimension dmin of multifractal isotropic turbulence the relationship has turned out to be nu dmin 3 2 for the homogeneous case dmin 3 and hence nu 1 2 the so called mean field approach of the theory of critical phenomena for dmin approximately 2 36 the well known turbulent value nu approximately 0 63 this result allows one to classify this case as the critical phenomenon of the so called thermal class of universality transition to the percolation class of universality nu approximately 0 9 is determined by the boundary conditions

spreading of percolation in three and four dimensions the authors present monte carlo simulations of the spreading of bond percolation on three and four dimensional simple hyper cubic lattices the algorithm is the same as that applied previously in two dimensions with the spreading proceeding from a hyperplane they find the spreading dimension to be d 1 82 or 0 02 three dimensional and d 1 88 or 0 03 four dimensional also they obtain values of the percolation probability and of the static exponents with errors at least comparable to the best values from the literature

topological loop intermittency in the three dimensional turbulence a new topological or loop type of intermittency is studied in three dimensional turbulence the spectral or fracton dimension ds 7 4 7 1 95 for this turbulence i e all states are localized this intermittency is different both from kolmogorov type unlocalized since ds 2 and from alexander orbach type strong localized helical fractons with ds 43 the corresponding energy spectral exponent is obtained to be equal to 1 7 1 65 these results are in good agreement with recent numerical spectral dimension and laboratory turbulent energy spectrum data the anomaly in the experimentally observed fractal dimension of clouds surface d 2 35 can be also explained in the framework of this intermittency phenomenon the results have been obtained by a renormalization of the noise like 1k energy spectrum in isotropic incompressible turbulence with taking into account of spontaneous parity breaking by virtual pairs of helical excitations

stability and performance limits of adaptive primal dual networks this paper studies distributed primal dual strategies for adaptation and learning over networks from streaming data two first order methods are considered based on the arrow hurwicz ah and augmented lagrangian al techniques several revealing results are discovered in relation to the performance and stability of these strategies when employed over adaptive networks the conclusions establish that the advantages that these methods exhibit for deterministic optimization problems do not necessarily carry over to stochastic optimization problems it is found that they have narrower stability ranges and worse steady state mean square error performance than primal methods of the consensus and diffusion type it is also found that the ah technique can become unstable under a partial observation model while the other techniques are able to recover the unknown under this scenario a method to enhance the performance of al strategies is proposed by tying the selection of the step size to their regularization parameter it is shown that this method allows the al algorithm to approach the performance of consensus and diffusion strategies but that it remains less stable than these other strategies

precise m k zipf diagram analysis of mathematical and financial time series when m 6 k 2 for studying short range time correlations in nancial signals we have envisaged to combine the zipf method and the i variability diagrams vd as useful tools the 2 vd describes the local curvature short range correlations we have resulted into ranking the 2 vd data according to their frequency of occurrence after having tested the ideas and estimated the error bars on a brownian motion signal we have examined two stocks i e sgp and oxhp closing price and volume of transaction long series a precise m k zipf diagram analysis when m 6 k 2 has been shown to lead to a non immediate information on the signal behavior even taking into account error bars the set of curvatures translated into words indicates a brownian motion like set for the closing price local curvature of such signals over a 6 day span moreover it has been shown that the conjecture about a simple relationship between the hurst exponent h and the exponent of zipf plots does not seem to be substantiated here c 1999 elsevier science b v all rights reserved

the iterated kalman filter update as a gauss newton method it is shown that the iterated kalman filter ikf update is an application of the gauss newton method for approximating a maximum likelihood estimate an example is presented in which the iterated kalman filter update and maximum likelihood estimate show correct convergence behavior as the observation becomes more accurate whereas the extended kalman filter update does not

toward a phase diagram for stocks abstract a display of the tentatively basic parameters of stocks i e the daily closing price and the daily transaction volume is presented eliminating the time variable between them the phase diagram looks like a triangular region similar to the two phase region of traffic diagrams the data is taken for two companies sgp and oxhp which present different long range correlations in the closing price value as examined by the linearly detrended fluctuation analysis dfa statistical method substructures are observed in the phase diagram as due to changes in management policy e g stock splits

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

thermodynamics of fractal signals based on wavelet analysis application to fully developed turbulence data and dna sequences we use the continuous wavelet transform to generalize the multifractal formalism to fractal functions we report the results of recent applications of the so called wavelet transform modulus maxima wtmm method to fully developed turbulence data and dna sequences we conclude by briey describing some works currently under progress which are likely to be the guidelines for future research c 1998 elsevier science b v all rights reserved

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

convergence and applications of a gossip based gauss newton algorithm the gauss newton algorithm is a popular and efficient centralized method for solving non linear least squares nlls problems in this paper a multi agent distributed version of this algorithm is proposed to solve general nlls problems in a network named gossip based gauss newton ggn algorithm furthermore we analyze and present sufficient conditions for its convergence and show numerically that the ggn algorithm achieves performance comparable to the centralized algorithm with graceful degradation in case of network failures more importantly the ggn algorithm provides significant performance gains compared to other distributed first order methods

illumination a new method for studying 3d percolation fronts in a concentration gradient a new method of studying percolation fronts is introduced in situations where the concentration is not constant gradient percolation approach it consists in an efficient way of determining subsets of the percolation cluster which are exactly at the percolation threshold the method is applied to both lattice and continuum percolation in order to determine the percolation threshold in 3d more accurately two variations of this method illumination and projection seem to give a similar scaling behaviour at low gradients for the cubic lattice case leading to a new estimate for the percolation threshold pc 0 31173 or 0 00007 for continuum percolation of overlapping spheres the new estimate for the critical volume fraction is 0 291 or 0 002 and the value of the critical exponent alpha sigma for the width of the front scaled with the concentration gradient is very close to the one for the lattice case

simplified model for fractal dimension of clouds abstract projections of three dimensional random percolation clusters onto a two dimensional plane give roughly the same fractal dimension 1 3 for the perimeter versus area relation as lovejoy s observation of real clouds and cellular automata simulations of nagel and raschke

low order variability diagrams for short range correlation evidence in financial data bgl usd exchange rate dow jones industrial average gold ounce price a method to sort out short range correlations and decorrelations in financial data is tested on three typical sets the bulgarian lev usa dollar bgl usd exchange rate the dow jones industrial average the gold ounce price the method makes use of the so called variability diagram technique three toys are used as models in order to understand features our findings indicate that some predictability can be found at short range time intervals c 1999 elsevier science b v all rights reserved

concentration gradient approach to continuum percolation in two dimensions the author has investigated percolation properties of a system of overlapping discs randomly distributed with a gradient of concentration fractal properties and critical exponents of this system appear to be identical to their counterparts on a lattice this is in agreement with the universality of critical exponents of percolation the concentration gradient approach permits a precise calculation of the percolation threshold corresponding to a critical area fraction of 0 6766 or 0 0005 he has investigated the part of the external perimeter of the percolation cluster which is accessible to discs of various sizes the fractal dimension of this accessible perimeter is found to decrease abruptly as a function of the radius of invading discs from 1 75 or 0 02 to 1 35 or 0 02

modeling of financial data comparison of the truncated levy flight and the arch 1 and garch 1 1 processes we compare our results on empirical analysis of nancia l data with simulations of two stochastic models of the dynamics of stock market prices the two models are i the truncated l evy igh t recently introduced by us and ii the arch 1 and garch 1 1 processes we n d that the tlf well describes the scaling and its breakdown observed in empirical data while it is not able to properly describe the uctuation s of volatility empirically detected the arch 1 and garch 1 1 models are able to describe the probability density function of price changes at a given time horizon but both fail to describe the scaling properties of the pdfs for short time horizons c 1998 elsevier science b v all rights reserved

critical couplings of mixed spin 1 2 spin s ising model a free fermion approximation a free fermion approximation procedure is applied to the mixed spin 1 2 spin s ising models the author s results for the critical coupling kc are in very satisfactory agreement with the high temperature series results of yousif and bowers 1984

thermodynamical properties of the random field mixed spin ising model abstract a theoretical study of a mixed spin ising system consisting of spin 1 2 and spin 1 with a random field is studied by the use of the finite cluster approximation within the framework of a single site cluster theory in this approach the phase diagrams and magnetizations are investigated for the simple cubic lattice when the random field is bimodally and trimodally distributed the internal energy specific heat and susceptibility are also calculated for both kinds of the probability distributions

generalized transformation for decorated spin models abstract the paper discusses the transformation of decorated ising models into an effective undecorated spin model using the most general hamiltonian for interacting ising models including a long range and high order interactions the inverse of a vandermonde matrix with equidistant nodes s s is used to obtain an analytical expression of the transformation this kind of transformation is very useful to obtain the partition function of decorated systems the method presented by fisher is also extended in order to obtain the correlation functions of the decorated ising models transforming into an effective undecorated ising model we apply this transformation to a particular mixed spin 1 2 1 and 1 2 2 square lattice with only nearest site interaction this model could be transformed into an effective uniform spin s square lattice with nearest and next nearest interaction furthermore the effective hamiltonian also includes combinations of three body and four body interactions in particular we considered spin 1 and 2

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

estimating the hausdorff besicovitch dimension of boundary of basin of attraction in helicopter trim helicopter trim involves solution of nonlinear force equilibrium equations as in many nonlinear dynamic systems helicopter trim problem can show chaotic behavior this chaotic behavior is found in the basin of attraction of the nonlinear trim equations which have to be solved to determine the main rotor control inputs given by the pilot this study focuses on the boundary of the basin of attraction obtained for a set of control inputs we analyze the boundary by considering it at different magnification levels the magnified views reveal intricate geometries it is also found that the basin boundary exhibits the characteristic of statistical self similarity which is an essential property of fractal geometries these results led the authors to investigate the fractal dimension of the basin boundary it is found that this dimension is indeed greater than the topological dimension from all the observations it is evident that the boundary of the basin of attraction for helicopter trim problem is fractal in nature c 2012 elsevier inc all rights reserved

mixed spin 1 2 and spin 1 ising model in transverse random fields abstract we investigate the critical properties of a mixed spin 1 2 and spin 1 ising model in a transverse random field in this study we use two approaches the pair approximation and the mean field renormalization group each combined with the discretized path integral representation it is found that both methods predict quantitatively the same phase diagram critical exponents of the system are also calculated