quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

on continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument abstract bounded continuous solutions on r of a class of systems of nonlinear functional difference equations with a complicated nonlinear deviation of the argument that depends on unknown functions are studied here

a confidence limit for the empirical mode decomposition and hilbert spectral analysis the confidence limit is a standard measure of the accuracy of the result in any statistical analysis most of the confidence limits are derived as follows the data are first divided into subsections and then under the ergodic assumption the temporal mean is substituted for the ensemble mean next the confidence limit is defined as a range of standard deviations from this mean however such a confidence limit is valid only for linear and stationary processes furthermore in order for the ergodic assumption to be valid the subsections have to be statistically independent for non stationary and nonlinear processes such an analysis is no longer valid the confidence limit of the method here termed emd hsa for empirical mode decomposition hilbert spectral analysis is introduced by using various adjustable stopping criteria in the sifting processes of the emd step to generate a sample set of intrinsic mode functions imfs the emd technique acts as a pre processor for hsa on the original data producing a set of components imfs from the original data that equal the original data when added back together each imf represents a scale in the data from smallest to largest the ensemble mean and standard deviation of the imf sample sets obtained with different stopping criteria are calculated and these form a simple random sample set the confidence limit for emd hsa is then defined as a range of standard deviations from the ensemble mean without evoking the ergodic assumption subdivision of the data stream into short sections is unnecessary hence the results and the confidence limit retain the full frequency resolution of the full dataset this new confidence limit can be applied to the analysis of nonlinear and non stationary processes by these new techniques data from length of day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied by providing a confidence limit for this new approach a stable range of stopping criteria for the decomposition or sifting phase emd has been established making the results of the final processing with hsa and the entire emd hsa method more definitive

forecasting interval time series using a fully complex valued rbf neural network with dpso and pso algorithms we propose a novel interval time series its forecasting approach a fully complex valued rbf neural network is extended to address its forecasting dpso pso are used to jointly optimize the structure and parameters of the model results on simulated and real world its data confirm the efficacy of the approach interval time series prediction is one of the most challenging research topics in the field of time series modeling and prediction in view of the remarkable function approximation capability of fully complex valued radial basis function neural networks fcrbfnns we set out to investigate the possibility of forecasting interval time series by denoting the lower and upper bounds of the interval as real and imaginary parts of a complex number respectively this results in a complex valued interval we then model the resulted complex valued interval time series via a fcrbfnn furthermore we propose to evolve the fcrbfnn by using particle swarm optimization pso and discrete pso for joint optimization of the structure and parameters finally the proposed interval time series prediction approach is tested with simulated interval time series data as well as real interval stock price time series data from the new york stock exchange our experimental results indicate that it is a promising alternative for interval time series forecasting

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

one or two frequencies the empirical mode decomposition answers this paper investigates how the empirical mode decomposition emd a fully data driven technique recently introduced for decomposing any oscillatory waveform into zero mean components behaves in the case of a composite two tones signal essentially two regimes are shown to exist depending on whether the amplitude ratio of the tones is greater or smaller than unity and the corresponding resolution properties of the emd turn out to be in good agreement with intuition and physical interpretation a refined analysis is provided for quantifying the observed behaviors and theoretical claims are supported by numerical experiments the analysis is then extended to a nonlinear model where the same two regimes are shown to exist and the resolution properties of the emd are assessed

effect of nonlinear filters on detrended fluctuation analysis when investigating the dynamical properties of complex multiple component physical and physiological systems it is often the case that the measurable system s output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms instead the output signal is often a linear or nonlinear function of the quantity of interest here we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal using the detrended fluctuation analysis dfa which has been shown to accurately quantify power law correlations in nonstationary signals specifically we study the effect of three types of transforms i linear y i a x i b ii nonlinear polynomial y i a x k i and iii nonlinear logarithmic y i log x i delta filters we compare the correlation and scaling properties of signals before and after the transform we find that linear filters do not change the correlation properties while the effect of nonlinear polynomial and logarithmic filters strongly depends on a the strength of correlations in the original signal b the power k of the polynomial filter and c the offset delta in the logarithmic filter we further apply the dfa method to investigate the apparent scaling of three analytic functions i exponential exp x a ii logarithmic log x a and iii power law x a lambda which are often encountered as trends in physical and biological processes while these three functions have different characteristics we find that there is a broad range of values for parameter a common for all three functions where the slope of the dfa curves is identical we further note that the dfa results obtained for a class of other analytic functions can be reduced to these three typical cases we systematically test the performance of the dfa method when estimating long range power law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider

bounded solutions of some systems of nonlinear functional differential equations with iterated deviating argument abstract for a class of systems of nonlinear functional differential equations with iterated deviating arguments dependent of unknown functions are given some conditions for the existence of bounded solutions on the real line satisfying some additional conditions

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

unique existence of bounded continuous solutions on the real line of a class of nonlinear functional equations with complicated deviations abstract the existence and uniqueness of bounded continuous solutions on the real line of a general class of nonlinear functional equations with quite complicated deviations dependent of unknown functions are established in this paper

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

time series and dependent variables we present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series the method is particularly suited to series with broad band spectra such as chaotic series with or without noise we derive quantities j e based on conditional probabilities whose magnitude roughly speaking is an indicator of the extent to which the kth element in the series is a deterministic function of the k j th element to within a measurement uncertainty e we apply our method to a number of deterministic time series generated by chaotic processes such as the tent logistic and h non maps as well as to sequences of quasi random numbers in all cases the 6j correctly indicate the expected dependencies we also show that the j are robust to the addition of substantial noise in a deterministic process in addition we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance e finally we discuss the behavior of the 6i as e approaches zero

existence of solutions bounded together with their first derivatives of some systems of nonlinear functional differential equations we give sufficient conditions for the system of nonlinear functional differential equations of the formx t 1 ax t f t x t x v 1 t x v k t x g 1 t x g l t where a is a matrix deta 0 v j t email protected j 1 t x f j 2 x f j m j t x t j 1 email protected and functions f r x r n k l 1 r n g j r r j 1 email protected f j i r xr n r j 1 email protected i 1 m email protected are continuous for the unique existence of continuously differentiable solutions x t which are bounded together with their first derivatives on r 0 and satisfy the condition lim t x t 1 ax t 0

gray scale morphological associative memories neural models of associative memories are usually concerned with the storage and the retrieval of binary or bipolar patterns thus far the emphasis in research on morphological associative memory systems has been on binary models although a number of notable features of autoassociative morphological memories amms such as optimal absolute storage capacity and one step convergence have been shown to hold in the general gray scale setting in this paper we make extensive use of minimax algebra to analyze gray scale autoassociative morphological memories specifically we provide a complete characterization of the fixed points and basins of attractions which allows us to describe the storage and recall mechanisms of gray scale amms computer simulations using gray scale images illustrate our rigorous mathematical results on the storage capacity and the noise tolerance of gray scale morphological associative memories mams finally we introduce a modified gray scale amm model that yields a fixed point which is closest to the input pattern with respect to the chebyshev distance and show how gray scale amms can be used as classifiers

estimation of flexible fuzzy garch models for conditional density estimation in this work we introduce a new flexible fuzzy garch model for conditional density estimation the model combines two different types of uncertainty namely fuzziness or linguistic vagueness and probabilistic uncertainty the probabilistic uncertainty is modeled through a garch model while the fuzziness or linguistic vagueness is presented in the antecedent and combination of the rule base system the fuzzy garch model under study allows for a linguistic interpretation of the gradual changes in the output density providing a simple understanding of the process such a system can capture different properties of data such as fat tails skewness and multimodality in one single model this type of models can be useful in many fields such as macroeconomic analysis quantitative finance and risk management the relation to existing similar models is discussed while the properties interpretation and estimation of the proposed are provided the model performance is illustrated in simulated time series data exhibiting complex behavior and a real data application of volatility forecasting for the s p 500 daily returns series

a representation theory for morphological image and signal processing a unifying theory for many concepts and operations encountered in or related to morphological image and signal analysis is presented the unification requires a set theoretic methodology where signals are modeled as sets systems signal transformations are viewed as set mappings and translational invariant systems are uniquely characterized by special collections of input signals this approach leads to a general representation theory in which any translation invariant increasing upper semicontinuous system can be presented exactly as a minimal nonlinear superposition of morphological erosions or dilations the theory is used to analyze some special cases of image signal analysis systems such as morphological filters median and order statistic filters linear filters and shape recognition transforms although the developed theory is algebraic its prototype operations are well suited for shape analysis hence the results also apply to systems that extract information about the geometrical structure of signals

multifractal description of wind power fluctuations using arbitrary order hilbert spectral analysis a b s t r a c t the objectives are to study and model the aggregate wind power fluctuations dynamics in the multifractal framework we present here the analysis of aggregate power output sampled at 1 hz during three years we decompose the data into several intrinsic mode functions imfs using empirical mode decomposition emd we use a new approach ar bitrary order hilbert spectral analysis a combination of the emd approach with hilbert spectral analysis or hilbert huang transform and the classical structure function anal ysis to extract the scaling exponents or multifractal spectrum q this function provides a full characterization of a process at all intensities and all scales the application of both methods i e structure function and arbitrary order hilbert spectral analyses gives similar results indicating that the aggregate power output from a wind farm possesses intermit tent and multifractal properties in order to check this result we generate stochastic simu lations of a multifractal random walk mrw using a log normal stochastic equation we show that the simulation results are fully compatible with the experimental results

multifractal random walk in copepod behavior abstract a 3d copepod trajectory is recorded in the laboratory using two digital cameras the copepod undergoes a very structured type of trajectory with successive moves displaying intermittent amplitudes we perform a statistical analysis of this 3d trajectory using statistical tools developed in the field of turbulence and anomalous diffusion in natural sciences we show that the walk belongs to multifractal random walks characterized by a nonlinear moment scaling function for the distance versus time to our knowledge this is the first experimental study of multifractal anomalous diffusion in natural sciences we then propose a new type of stochastic process reproducing these multifractal scaling properties this can be directly used for stochastic numerical simulations and is thus of important potential applications in the field of animal movement study and more generally of anomalous diffusion studies

estimating the active demension of the dynamics in a time series based on an information criterion abstract we describe a method for estimating the active dimension of the dynamics generating a time series from the observed time series the active dimension is the minimum number of variables needed to describe the essential part of the dynamics behind the time series and is equal to the minimal embedding dimension at which the delay coordinate reconstruction becomes a local embedding the achievement of embedding was examined based on the results of time series prediction with the optimal metric to bring further objectivity to the estimation we introduced an information criterion the minimum description length criterion we demonstrated the effectiveness of the method by applying it to chaotic time series obtained from numerical calculations and from an electrochemical experiment the advantages of the proposed method are the transparency of its parameter settings and its applicability to relatively short time series

multifractal detrending moving average cross correlation analysis there are a number of situations in which several signals are simultaneously recorded in complex systems which exhibit long term power law cross correlations the multifractal detrended cross correlation analysis mfdcca approaches can be used to quantify such cross correlations such as the mfdcca based on the detrended fluctuation analysis mfxdfa method we develop in this work a class of mfdcca algorithms based on the detrending moving average analysis called mfxdma the performances of the proposed mfxdma algorithms are compared with the mfxdfa method by extensive numerical experiments on pairs of time series generated from bivariate fractional brownian motions two component autoregressive fractionally integrated moving average processes and binomial measures which have theoretical expressions of the multifractal nature in all cases the scaling exponents h xy extracted from the mfxdma and mfxdfa algorithms are very close to the theoretical values for bivariate fractional brownian motions the scaling exponent of the cross correlation is independent of the cross correlation coefficient between two time series and the mfxdfa and centered mfxdma algorithms have comparative performances which outperform the forward and backward mfxdma algorithms for two component autoregressive fractionally integrated moving average processes we also find that the mfxdfa and centered mfxdma algorithms have comparative performances while the forward and backward mfxdma algorithms perform slightly worse for binomial measures the forward mfxdma algorithm exhibits the best performance the centered mfxdma algorithms performs worst and the backward mfxdma algorithm outperforms the mfxdfa algorithm when the moment order q 0 we apply these algorithms to the return time series of two stock market indexes and to their volatilities for the returns the centered mfxdma algorithm gives the best estimates of h xy q since its h xy 2 is closest to 0 5 as expected and the mfxdfa algorithm has the second best performance for the volatilities the forward and backward mfxdma algorithms give similar results while the centered mfxdma and the mfxdfa algorithms fail to extract rational multifractal nature

a general framework for fuzzy morphological associative memories fuzzy associative memories fams can be used as a powerful tool for implementing fuzzy rule based systems the insight that fams are closely related to mathematical morphology mm has recently led to the development of new fuzzy morphological associative memories fmams in particular implicative fuzzy associative memories ifams as the name fmam indicates these models belong to the class of fuzzy morphological neural networks fmnns thus each node of an fmam performs an elementary operation of fuzzy mm clarifying several misconceptions about fmams that have recently appeared in the literature we provide a general framework for fmams within the class of fmnn we show that many well known fam models fit within this framework and can therefore be classified as fmams moreover we employ certain concepts of duality that are defined in the general theory of mm in order to derive a large class of strategies for learning and recall in fmams

boundedness character of a class of difference equations abstract a complete picture regarding the boundedness character of positive solutions to the following difference equation x n max a x n 1 p x n k p n n 0 where k 2 and the parameters a and p are positive real numbers is given in particular for the case p k 1 0 k k k 1 k 1 we prove that all solutions to the equation are bounded we also present corresponding results concerning the following closely related difference equation x n a x n 1 p x n k p n n 0

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

on stability results for φ strongly pseudocontractive mappings abstract we study the stability problems of the following unified iterative scheme involving a strongly pseudocontractive mapping or hemicontractive mapping t x n 1 f t v n x n n x n n tv n n u n in arbitrary banach spaces we apply our results to obtain stability of an iterative scheme for a family of k selfmappings

existence of bounded solutions of some systems of nonlinear functional differential equations with complicated deviating argument abstract sufficient conditions for the existence of bounded solutions on the real line satisfying lipschitz s condition of a class of systems of nonlinear functional differential equations with complicated deviating argument dependent of unknown functions are given in this paper

arbitrary order hilbert spectral analysis for time series possessing scaling statistics comparison study with detrended fluctuation analysis and wavelet leaders in this paper we present an extended version of hilbert huang transform namely arbitrary order hilbert spectral analysis to characterize the scale invariant properties of a time series directly in an amplitude frequency space we first show numerically that due to a nonlinear distortion traditional methods require high order harmonic components to represent nonlinear processes except for the hilbert based method this will lead to an artificial energy flux from the low frequency large scale to the high frequency small scale part thus the power law if it exists is contaminated we then compare the hilbert method with structure functions sf detrended fluctuation analysis dfa and wavelet leader wl by analyzing fractional brownian motion and synthesized multifractal time series for the former simulation we find that all methods provide comparable results for the latter simulation we perform simulations with an intermittent parameter 0 15 we find that the sf underestimates scaling exponent when q 3 the hilbert method provides a slight underestimation when q 5 however both dfa and wl overestimate the scaling exponents when q 5 it seems that hilbert and dfa methods provide better singularity spectra than sf and wl we finally apply all methods to a passive scalar temperature data obtained from a jet experiment with a taylor s microscale reynolds number re 250 due to the presence of strong ramp cliff structures the sf fails to detect the power law behavior for the traditional method the ramp cliff structure causes a serious artificial energy flux from the low frequency large scale to the high frequency small scale part thus dfa and wl underestimate the scaling exponents however the hilbert method provides scaling exponents q quite close to the one for longitudinal velocity indicating a less intermittent passive scalar field than what was believed before 2011 american physical society

multifractal stationary random measures and multifractal random walks with log infinitely divisible scaling laws we define a large class of continuous time multifractal random measures and processes with arbitrary log infinitely divisible exact or asymptotic scaling law these processes generalize within a unified framework both the recently defined log normal multifractal random walk j f muzy j delour and e bacry eur j phys b 17 537 2000 e bacry j delour and j f muzy phys rev e 64 026103 2001 and the log poisson product of cylindrical pulses j barral and b b mandelbrot cowles foundation discussion paper no 1287 2001 unpublished our construction is based on some continuous stochastic multiplication as introduced in f schmitt and d marsan eur j phys b 20 3 2001 from coarse to fine scales that can be seen as a continuous interpolation of discrete multiplicative cascades we prove the stochastic convergence of the defined processes and study their main statistical properties the question of genericity universality of limit multifractal processes is addressed within this new framework we finally provide a method for numerical simulations and discuss some specific examples

second order structure function in fully developed turbulence we relate the second order structure function of a time series with the power spectrum of the original variable taking an assumption of statistical stationarity with this approach we find that the structure function is strongly influenced by the large scales the large scale contribution and the contribution range are respectively 79 and 1 4 decades for a kolmogorov ensuremath 5 3 power spectrum we show numerically that a single scale influence range over smaller scales is about 2 decades we argue that the structure function is not a good method to extract the scaling exponents when the data possess large energetic scales an alternative methodology the arbitrary order hilbert spectral analysis which may constrain this influence within 0 3 decade is proposed to characterize the scaling property directly in an amplitude frequency space an analysis of passive scalar temperature turbulence time series is presented to show the influence of large scale structures in real turbulence and the efficiency of the hilbert based methodology the corresponding scaling exponents ensuremath zeta ensuremath theta q provided by the hilbert based approach indicate that the passive scalar turbulence field may be less intermittent than what was previously believed

implicative fuzzy associative memories associative neural memories are models of biological phenomena that allow for the storage of pattern associations and the retrieval of the desired output pattern upon presentation of a possibly noisy or incomplete version of an input pattern in this paper we introduce implicative fuzzy associative memories ifams a class of associative neural memories based on fuzzy set theory an ifam consists of a network of completely interconnected pedrycz logic neurons with threshold whose connection weights are determined by the minimum of implications of presynaptic and postsynaptic activations we present a series of results for autoassociative models including one pass convergence unlimited storage capacity and tolerance with respect to eroded patterns finally we present some results on fixed points and discuss the relationship between implicative fuzzy associative memories and morphological associative memories

eventually constant solutions of a rational difference equation we describe all the solutions of a rational difference equation from putnam s mathematical competition which are eventually equal to its positive equilibrium email protected 1 as a consequence we give a new elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one moreover we show that almost all solutions of the equation are not eventually equal to one

on q difference asymptotic solutions of a system of nonlinear functional differential equations the asymptotic behavior and the existence of a continuously differentiable solution bounded together with its first derivative of a system of nonlinear functional differential equations is studied here

finding the embedding dimension and variable dependencies in time series we present a general method the test which establishes functional dependencies given a sequence of measurements the approach is based on calculating conditional probabilities from vector component distances imposing the requirement of continuity of the underlying function the obtained values of the conditional probabilities carry information on the embedding dimension and variable dependencies the power of the method is illustrated on synthetic time series with different time lag dependencies and noise levels and on the sunspot data the virtue of the method for preprocessing data in the context of feedforward neural networks is demonstrated also its applicability for tracking residual errors in output units is stressed

morphological perceptrons with competitive learning lattice theoretical framework and constructive learning algorithm a morphological neural network is generally defined as a type of artificial neural network that performs an elementary operation of mathematical morphology at every node possibly followed by the application of an activation function the underlying framework of mathematical morphology can be found in lattice theory with the advent of granular computing lattice based neurocomputing models such as morphological neural networks and fuzzy lattice neurocomputing models are becoming increasingly important since many information granules such as fuzzy sets and their extensions intervals and rough sets are lattice ordered in this paper we present the lattice theoretical background and the learning algorithms for morphological perceptrons with competitive learning which arise by incorporating a winner take all output layer into the original morphological perceptron model several well known classification problems that are available on the internet are used to compare our new model with a range of classifiers such as conventional multi layer perceptrons fuzzy lattice neurocomputing models k nearest neighbors and decision trees

a study of the characteristics of white noise using the empirical mode decomposition method based on numerical experiments on white noise using the empirical mode decomposition emd method we find empirically that the emd is effectively a dyadic filter the intrinsic mode function imf components are all normally distributed and the fourier spectra of the imf components are all identical and cover the same area on a semi logarithmic period scale expanding from these empirical findings we further deduce that the product of the energy density of imf and its corresponding averaged period is a constant and that the energy density function is chi squared distributed furthermore we derive the energy density spread function of the imf components through these results we establish a method of assigning statistical significance of information content for imf components from any noisy data southern oscillation index data are used to illustrate the methodology developed here

on a nonlinear generalized max type difference equation abstract the boundedness character of positive solutions of the following max type difference equation x n max a x n 1 p x n k r n n 0 where k n 1 the parameters a and r are positive and p is a nonnegative real number is studied in this paper our main results considerably improve results appearing in the literature

globally bounded solutions of a system of nonlinear functional differential equations with iterated deviating argument abstract some sufficient conditions which guarantee the existence of a bounded solution together with its first derivative on the whole real line of a system of nonlinear functional differential equations with an iterated deviating argument dependent of unknown function are given

on the max type equation xn 1 max axn xn 2 abstract we show that every well defined solution of the difference equation x n 1 max a x n x n 2 n n 0 where a r is eventually periodic with period three

swarm based translation invariant morphological prediction method for financial time series forecasting in this paper we present a method to overcome the random walk rw dilemma for financial time series forecasting called swarm based translation invariant morphological prediction stmp method it consists of a hybrid model composed of a modular morphological neural network mmnn combined with a particle swarm optimizer pso which searches for the best time lags to optimally describe the time series phenomenon as well as estimates the initial sub optimal parameters of the mmnn weights architecture and number of modules an additional optimization is performed with each particle of the pso population a distinct mmnn using the back propagation bp algorithm after the mmnn parameters adjustment we use a behavioral statistical test and a phase fix procedure to adjust time phase distortions observed in financial time series finally we conduct an experimental analysis with the proposed method using four real world stock market time series where five well known performance metrics and a fitness function are used to assess the prediction performance the obtained results are compared with those generated by classical models presented in the literature

morphological regularization neural networks abstract in this paper we establish a relationship between regularization theory and morphological shared weight neural networks msnn we show that a certain class of morphological shared weight neural networks with no hidden units can be viewed as regularization neural networks this relationship is established by showing that this class of msnns are solutions of regularization problems this requires deriving the fourier transforms of the min and max operators the fourier transforms of min and max operators are derived using generalized functions because they are only defined in that sense

multifractal random walk we introduce a class of multifractal processes referred to as multifractal random walks mrws to our knowledge it is the first multifractal process with continuous dilation invariance properties and stationary increments mrws are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio the mrws are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments we briefly explain how in the same way one can build stationary multifractal processes or positive random measures

periodicity of a class of nonautonomous max type difference equations abstract in this note we prove several general and easily applicable results regarding the periodicity of positive solutions of the following difference equations x n max f 1 x n k 1 n f m x n k m n x n s n n 0 and x n min f 1 x n k 1 n f m x n k m n x n s n n 0 where 1 k 1 k m m s n and where the functions f i 0 n 0 0 1 i m satisfy some additional conditions these results considerably extend and unify numerous results on max type difference equations existing in the literature

hilbert huang transform based multifractal analysis of china stock market national natural science foundation of china nsfc 11202122 11301433 11332006 pu jiang project of shanghai 12pj1403500 social science foundation of fujian 2013c056

generalized scaling in fully developed turbulence in this paper we report numerical and experimental results on the scaling properties of the velocity turbulent fields in several flows the limits of a new form of scaling named extended self similarity ess are discussed we show that when a mean shear is absent the self scaling exponents are universal and they do not depend on the specific flow 3d homogeneous turbulence thermal convection mhd in contrast ess is not observed when a strong shear is present we propose a generalized version of self scaling which extends down to the smallest resolvable scales even in cases where ess is not present this new scaling is checked in several laboratory and numerical experiments a possible theoretical interpretation is also proposed a synthetic turbulent signal having most of the properties of a real one has been generated

fuzzy forecasting based on automatic clustering and axiomatic fuzzy set classification the method can generate clustering based intervals the method can predict the fuzzy trend of forecasted data in advance the afs classification is exploited to yield the semantic interpretation of each fuzzy trend with the proposed method the horizon of prediction can be as long as desired the method has both good interpretability and superior accuracy in spite of the impressive diversity of models of fuzzy forecasting there is still a burning need to arrive at models that are both accurate and highly interpretable this study proposes a new fuzzy forecasting model designed with the use of the two key techniques namely clustering and axiomatic fuzzy set afs classification first clustering algorithm is utilized to generate clustering based intervals second the fuzzy trend labeled training data set is constructed based on fuzzy logic relationships and fuzzy trends of historical samples then the afs classification is exploited to yield the semantic interpretation of each fuzzy trend the main novelty is that the proposed model not only predicts the value but can also capture the trend prevailing in the time series and obtain its semantic interpretation the taiwan stock exchange capitalization weighted stock index taiex inventory demand and spanish electricity prices are used in a series of experiments the results show that the proposed model has both good interpretability and accuracy

stochastic numerical treatment for solving troesch s problem abstract in this article the numerical techniques are presented for the solution of troesch s problem based on neural networks optimized with three different methods including particle swarm optimization pso active set as and pso hybridized with as pso as algorithms the variable transformation is applied in order to convert the original problem to a transformed problem which is relatively less stiff to solve feed forward artificial neural networks are used to model the transformed problem learning of adjustable parameters is made with pso as and pso as algorithms the proposed methodologies are applied to a number of cases for stiff and non stiff boundary value problems the comparative analyses are carried out with other standard numerical solutions as well as approximate analytical solver