topology identification of weighted complex dynamical networks abstract recently various papers investigated the geometry features synchronization and control of complex network provided with certain topology while the exact topology of a network is sometimes unknown or uncertain using lyapunov theory we propose an adaptive feedback controlling method to identify the exact topology of a rather general weighted complex dynamical network model by receiving the network nodes evolution the topology of such kind of network with identical or different nodes or even with switching topology can be monitored experiments show that the methods presented in this paper are of high accuracy with good performance

multiscale statistical behaviors for ising financial dynamics with continuum percolation jump abstract a financial dynamics of interaction and jump is developed and investigated by two statistical physics systems ising model and continuum percolation this proposed model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price in an attempt to describe interacting micromechanism and sudden jump for stock price changes further the corresponding fluctuation behaviors and various complexity properties of logarithmic returns for the financial model are investigated by some statistical and complex analyses then p order multiscale autocorrelation function and q order multiscale entropy are also introduced to study the financial model with scaled analysis methods moreover the real stock market indexes are used to compare with the simulation returns from the financial model the empirical research shows that the simulation time series exhibits the similar fluctuation patterns with real time series

accuracy of approximations of solutions to fredholm equations by kernel methods approximate solutions to inhomogeneous fredholm integral equations of the second kind by radial and kernel networks are investigated upper bounds are derived on errors in approximation of solutions of these equations by networks with increasing model complexity the bounds are obtained using results from nonlinear approximation theory the results are applied to networks with gaussian and kernel units and illustrated by numerical simulations

multifractal detrended cross correlation analysis on benchmark cryptocurrencies and crude oil prices abstract in this paper we investigate the cross correlations between three benchmark cryptocurrencies including bitcoin ethereum and ripple and some of the well known crude oils west texas intermediate and brent the data of the study spans from 7 august 2015 to 10 june 2019 we utilized the multifractal detrending moving average cross correlation analysis mf x dma method to examine the multifractal features among data we find that the cross correlations between each pair of time series are significant by using the cross correlation test statistic q c c m analysis and detrended moving average cross correlation analysis dmca coefficient also the cross correlation coefficients d m c a show that the data are positively correlated but the degree of correlation has been elevated by increasing the window intervals v the observed results obtained through the mf x dma method infer the existence of multifractal cross correlations on ten bivariate time series in the study and that the strength of multifractality between ethereum and ripple is the highest followed by the strength of multifractality between wti crude oil and ethereum

the russo seymour welsh theorem and the equality of critical densities and the dual critical densities for continuum percolation on mathbb r 2 a russo seymour welsh rsw theorem is established for continuum percolation on mathbb r 2 the equality of various definitions of critical densities for the continuum percolation on mathbb r 2 is deduced as an application of the rsw theorem it is also shown that various notions of the size of a cluster yield the same notion of critical density

fluctuation behavior analysis of stochastic exclusion financial dynamics with random jump abstract a novel financial price model combining stochastic exclusion system and compound poisson process with lattice fractal sierpinski carpet percolation jumps is established to reflect fluctuation behaviors of energy markets the exclusion system one of statistical physics systems is applied in implementing interaction behaviors of traders and the percolation theory is used to implement gusty jumps of price volatilities further the actual market data and the simulation data are combined to analyze statistical properties and complex characteristics by applying autocorrelation analysis detrended fluctuation analysis method and fractional fuzzy entropy moreover a new synchronization measurement method named the cross cid fuzzyen which is composed of cross fuzzy entropy and complexity invariant distance is firstly proposed in this work empirical results show that the analog returns and the actual returns have parallel characteristics and strong synchronicity which displays that the proposed model is rational and can effectively reflect the internal mechanism of real energy markets to some extent

multifractal analysis of managed and independent float exchange rates abstract we investigate multifractal properties of daily price changes in currency rates using the multifractal detrended fluctuation analysis mf dfa we analyze managed and independent floating currency rates in eight countries and determine the changes in multifractal spectrum when transitioning between the two regimes we find that after the transition from managed to independent float regime the changes in multifractal spectrum position of maximum and width indicate an increase in market efficiency the observed changes are more pronounced for developed countries that have a well established trading market after shuffling the series we find that the multifractality is due to both probability density function and long term correlations for managed float regime while for independent float regime multifractality is in most cases caused by broad probability density function

complex and composite entropy fluctuation behaviors of statistical physics interacting financial model abstract in an attempt to investigate and reproduce the fluctuation dynamics of price changes in financial markets a novel complex random interacting financial price model is developed by combining voter interacting system with compound poisson process in this model the dissemination of investors investment attitudes can simulate normal and frequent small price fluctuations of financial markets while the random drastic jumps can capture undue and rare large price fluctuations as results of sudden economic events and political events in the markets in order to verify the rationality of the model some statistical characteristics of the model returns including fat tail power law scaling complexity and multifractal are compared with real returns by probability density functions composite distance fuzzy entropy c fuzzyen matching energy and multifractal detrended fluctuation analysis the c fuzzyen is a new entropy based approach based on fuzzy entropy and complexity invariant to measure the complexity behaviors of return series the effectiveness analysis of c fuzzyen indicates that it has a higher estimation accuracy and stronger robustness than fuzzy entropy the empirical results show that the price model is able to reproduce some important statistical properties of financial markets to a certain extent and the complexity of returns for the proposed model increases when infection intensity or jump intensity increases

nonlinear complexity of random visibility graph and lempel ziv on multitype range intensity interacting financial dynamics abstract in an attempt to investigate the nonlinear complex evolution of financial dynamics a new financial price model the multitype range intensity contact mric financial model is developed based on the multitype range intensity interacting contact system in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading two new random visibility graph vg based analyses and lempel ziv complexity lzc are applied to study the complex behaviors of return time series and the corresponding random sorted series the vg method is the complex network theory and the lzc is a non parametric measure of complexity reflecting the rate of new pattern generation of a series in this work the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further the numerical empirical study shows the similar complexity behaviors between the model and the real markets the research confirms that the financial model is reasonable to some extent

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

modeling stock price dynamics by continuum percolation system and relevant complex systems analysis abstract the continuum percolation system is developed to model a random stock price process in this work recent empirical research has demonstrated various statistical features of stock price changes the financial model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price in an attempt to reproduce and explain this set of empirical facts the continuum percolation model is usually referred to as a random coverage process or a boolean model the local interaction or influence among traders is constructed by the continuum percolation and a cluster of continuum percolation is applied to define the cluster of traders sharing the same opinion about the market we investigate and analyze the statistical behaviors of normalized returns of the price model by some analysis methods including power law tail distribution analysis chaotic behavior analysis and zipf analysis moreover we consider the daily returns of shanghai stock exchange composite index from january 1997 to july 2011 and the comparisons of return behaviors between the actual data and the simulation data are exhibited

nonlinear stochastic exclusion financial dynamics modeling and time dependent intrinsic detrended cross correlation abstract in attempt to reproduce price dynamics of financial markets a stochastic agent based financial price model is proposed and investigated by stochastic exclusion process the exclusion process one of interacting particle systems is usually thought of as modeling particle motion with the conserved number of particles in a continuous time markov process in this work the process is utilized to imitate the trading interactions among the investing agents in order to explain some stylized facts found in financial time series dynamics to better understand the correlation behaviors of the proposed model a new time dependent intrinsic detrended cross correlation tdi dcc is introduced and performed also the autocorrelation analyses are applied in the empirical research furthermore to verify the rationality of the financial price model the actual return series are also considered to be comparatively studied with the simulation ones the comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets

multiscale multifractal dcca and complexity behaviors of return intervals for potts price model abstract to investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events we use a potts dynamic system to construct a random financial time series model of the attitudes of market traders we use multiscale multifractal detrended cross correlation analysis mm dcca and lempel ziv complexity lzc perform numerical research of the return intervals for two significant china s stock market indices and for the proposed model the new mm dcca method is based on the hurst surface and provides more interpretable cross correlations of the dynamic mechanism between different return interval series we scale the lzc method with different exponents to illustrate the complexity of return intervals in different scales empirical studies indicate that the proposed return intervals from the potts system and the real stock market indices hold similar statistical properties

multi scaling in the cont bouchaud microscopic stock market model abstract the cont bouchaud percolation model is one of the simplest microsimulation models yet able to account for the main stylized fact of financial markets e g fat tails of the histogram of log returns in the present paper we show that for a certain range of the parameters it is possible to generate price time series that cannot be described in terms of a unique scaling exponent

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

intermittency in an interacting generalization of the geometric brownian motion model we propose a minimal interacting generalization of the geometric brownian motion model which turns out to be formally equivalent to a model describing the dynamics of networks of analogue neurons for sufficiently strong interactions such systems may have many meta stable states transitions between meta stable states are associated with macroscopic reorganizations of the system which can be triggered by random external forcing such a system will exhibit intermittent dynamics within a large part of its parameter space we propose market dynamics as a possible application of this model in which case random external forcing would correspond to the arrival of important information the emergence of a model of interacting prices of the type considered here can be argued to follow naturally from a general argument based on integrating out all non price degrees of freedom from the dynamics of a hypothetical complete description of economic dependences

error estimates for a numerical method for an ill posed cauchy problem for the heat equation logarithmic convexity type continuous dependence results for discrete solutions of the heat equation are proved using these results error estimates for a least squares penalty method for approximating a noncharacteristic cauchy problem for the heat equation are obtained numerical results are presented

volatility behavior of visibility graph emd financial time series from ising interacting system abstract a financial market dynamics model is developed and investigated by stochastic ising system where the ising model is the most popular ferromagnetic model in statistical physics systems applying two graph based analysis and multiscale entropy method we investigate and compare the statistical volatility behavior of return time series and the corresponding imf series derived from the empirical mode decomposition emd method and the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further we find that the degree distribution of visibility graph for the simulation series has the power law tails and the assortative network exhibits the mixing pattern property all these features are in agreement with the real market data the research confirms that the financial model established by the ising system is reasonable

a method for the numerical solution of the one dimensional inverse stefan problem in this paper we suggest the use of complete families of solutions of the heat equation for the numerical solution of the inverse stefan problem our approach leads to linear optimization problems which can be established and solved easily convergence results are proved in a final section the method is applied to some examples

complexity and multifractal behaviors of multiscale continuum percolation financial system for chinese stock markets abstract a new financial agent based time series model is developed and investigated by multiscale continuum percolation system which can be viewed as an extended version of continuum percolation system in this financial model for different parameters of proportion and density two poisson point processes where the radii of points represent the ability of receiving or transmitting information among investors are applied to model a random stock price process in an attempt to investigate the fluctuation dynamics of the financial market to validate its effectiveness and rationality we compare the statistical behaviors and the multifractal behaviors of the simulated data derived from the proposed model with those of the real stock markets further the multiscale sample entropy analysis is employed to study the complexity of the returns and the cross sample entropy analysis is applied to measure the degree of asynchrony of return autocorrelation time series the empirical results indicate that the proposed financial model can simulate and reproduce some significant characteristics of the real stock markets to a certain extent

volatility aggregation intensity energy futures series on stochastic finite range exclusion dynamics abstract the stochastic finite range exclusion process one of statistical physics systems is introduced to construct a new agent based financial price model to study the mechanism of market dynamics a novel volatility aggregation intensity vai time series describing the fluctuation aggregation intensity of the volatility series is developed for further investigating the nonlinear volatility behaviors in energy markets for studying the proposed vai series and the proposed price model the new york mercantile exchange energy futures data is selected and analyzed further cross correlation analysis auto correlation analysis with multiscale and multifractal detrended fluctuation analysis are applied to analyze the correlation volatility clustering and multifractal natures of the vai time series the empirical results show that the proposed model has the parallel behaviors with the authentic markets indicating that it is rational and available the new concept of vai series is of great value and can enrich the study of volatility behaviors in energy markets to some extent

crossover in the cont bouchaud percolation model for market fluctuations abstract monte carlo simulations of the cont bouchaud herding model for stock market traders show power law distributions for short times and exponential truncation for longer time intervals if they are made at the percolation threshold in two to seven dimensions

time evolution of stochastic processes with correlations in the variance stability in power law tails of distributions abstract we model the time series of the s p500 index by a combined process the ar garch process where ar denotes the autoregressive process which we use to account for the short range correlations in the index changes and garch denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long range correlations in the variance we study the ar garch process with an initial distribution of truncated levy form we find that this process generates a new probability distribution with a crossover from a levy stable power law to a power law with an exponent outside the levy range beyond the truncation cutoff we analyze the sum of n variables of the ar garch process and find that due to the correlations the ar garch process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n a feature which is observed in the probability distribution of the s p500 index we find that this power law stability depends on the characteristic scale in the correlations we also find that inclusion of short range correlations through the ar process is needed to obtain convergence to a limiting gaussian distribution for large n as observed in the data

econophysics financial time series from a statistical physics point of view in recent years physicists have started applying concepts and methods of statistical physics to study economic problems the word econophysics is sometimes used to refer to this work much recent work is focused on understanding the statistical properties of nancial time series one reason for this interest is that nancial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that nancial time series viewed from a dierent perspective might yield new results this article reviews the results of three recent phenomenological studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as eight orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by three orders of magnitude from 1 min up to approximately 10 d ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law and persist for several months iii correlations among dierent companies the third result bears on the application of random matrix theory to understand the correlations among price uctuations of any two dierent stocks from a study of the eigenvalue statistics of the cross correlation matrix constructed from price uctuations of the leading 1000 stocks we nd that the largest 1 of the eigenvalues and the corresponding eigenvectors show systematic deviations from the predictions for a random matrix whereas the rest of the eigenvalues conform to random matrix behavior suggesting that these 1 of the eigenvalues contain system specic information about correlated time evolution of dierent companies c 2000 published by elsevier science b v all rights reserved

an approximation technique for the numerical solution of a stefan problem a nonlinear approximation technique for the numerical solution of certain free boundary problems is proposed the method is shown for a degenerate one dimensional stefan problem for this problem an error estimate which is independent of the used algorithm is derived numerical examples are discussed

statistical volatility duration and complexity of financial dynamics on sierpinski gasket lattice percolation abstract a novel agent based financial dynamics is established based on the percolation system on sierpinski gasket lattice to reproduce the statistical characteristics of financial markets sierpinski gasket lattice is a fractal like graph which corresponds to the fractal well known sierpinski gasket modeling a financial dynamics on sierpinski gasket lattice is a new approach in financial micro mechanism construction in an attempt to investigate the statistical properties of returns and prove the feasibility of the proposed model two new nonlinear statistics maximum and average monotonous volatility duration are introduced in this work for the first time which describe the trend of volatility of return time series in financial markets furthermore a new method cmcid is proposed to measure the synchronization and similarity behaviors of return volatility duration in multiscale the results show that the pairs of real data and simulated data have synchronization and the synchronization becomes stronger when the scale increases and the power law distribution is employed to investigate the corresponding statistical properties which shows that the proposed model shares a common power law distribution with regard to monotonous volatility duration the empirical results show that the simulated series from the financial model and the historical data share common statistical properties which indicate that the proposed model is reasonable in terms of volatility behavior

multiscale synchrony behaviors of paired financial time series by 3d multi continuum percolation abstract multiscale synchrony behaviors and nonlinear dynamics of paired financial time series are investigated in an attempt to study the cross correlation relationships between two stock markets a random stock price model is developed by a new system called three dimensional 3d multi continuum percolation system which is utilized to imitate the formation mechanism of price dynamics and explain the nonlinear behaviors found in financial time series we assume that the price fluctuations are caused by the spread of investment information the cluster of 3d multi continuum percolation represents the cluster of investors who share the same investment attitude in this paper we focus on the paired return series the paired volatility series and the paired intrinsic mode functions which are decomposed by empirical mode decomposition a new cross recurrence quantification analysis is put forward combining with multiscale cross sample entropy to investigate the multiscale synchrony of these paired series from the proposed model the corresponding research is also carried out for two china stock markets as comparison

detecting long range correlations with detrended fluctuation analysis abstract we examine the detrended fluctuation analysis dfa which is a well established method for the detection of long range correlations in time series we show that deviations from scaling which appear at small time scales become stronger in higher orders of dfa and suggest a modified dfa method to remove them the improvement is necessary especially for short records that are affected by non stationarities furthermore we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of dfa

1 f noise from nonlinear stochastic differential equations we consider a class of nonlinear stochastic differential equations giving the power law behavior of the power spectral density in any desirably wide range of frequency such equations were obtained starting from the point process models of 1 fbeta noise in this article the power law behavior of spectrum is derived directly from the stochastic differential equations without using the point process models the analysis reveals that the power spectrum may be represented as a sum of the lorentzian spectra such a derivation provides additional justification of equations expands the class of equations generating 1 fbeta noise and provides further insights into the origin of 1 fbeta noise

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

a new collocation type method for hammerstein integral equations on presente une methode du type de collocation pour la resolution numerique des equations integrales d hammerstein on etablit la convergence de l approximation desiree vers la solution exacte

persistence probabilities of the german dax and shanghai index abstract we present a relatively detailed analysis of the persistence probability distributions in financial dynamics compared with the auto correlation function the persistence probability distributions describe dynamic correlations nonlocal in time universal and non universal behaviors of the german dax and shanghai index are analyzed and numerical simulations of some microscopic models are also performed around the fixed point z 0 0 the interacting herding model produces the scaling behavior of the real markets

control of stefan problems by means of linear quadratic defect minimization we investigate the following problem to influence a heat conduction process in such a way that the conductor melts in a prescribed manner since we treat a linear auxiliary problem it suffices to deal with a linear quadratic defect minimization problem with linear restrictions where we use splines or polynomials as approximation spaces in case of exact controllability we derive various order of convergence estimates which we discuss for some numerical examples

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

adomian s method for hammerstein integral equations arising from chemical reactor theory an ordinary differential equation with a parameter in the boundary conditions describes the steady state in an adiabatic tubular chemical reactor in this paper the problem is considered as a hammerstein integral equation and solutions are obtained using adomian s decomposition method

a generalized dynamic herding model with feed back interactions abstract a dynamic feed back interaction is introduced to the eguiluz zimmermann model phys rev lett 85 2000 5659 in application to financial dynamics transmission of information at time t is supposed to depend on the variation of the financial index at t 1 the generated time series is strongly correlated in time at criticality both static and dynamic behavior are investigated

inverse stefan problem tracking of the interface position from measurements on the solid phase this study presents a sequential algorithm for the identification of the position s of the moving boundary of a variable one dimensional or two dimensional domain from discrete measurements temperatures and fluxes collected at the fixed boundary the inverse problem is solved by minimization with respect to s of a penalized output least square criterion defined on a sliding time horizon of length at every time step several iterations are performed to estimate the unknown s each iteration consists in a guess of s a computation of the corresponding value of the output y direct model and the criterion j and a step towards a new estimation of s the impact of the different parameters space and time discretization intervals regularization coefficient dimension of the unknown parameter s length of the observation horizon choice of the observed output temperature or flux and choice of the direct model is thoroughly analysed for an analytical test case

nystrom method for fredholm integral equations of the second kind in two variables on a triangle the paper deals with the approximation of the solution of the following bivariate fredholm integral equationf y email protected dk x y f x w x dx g y email protected d where the domain d is a triangle the proposed procedure by a suitable transformation is essentially the nystrom method based on the zeros of univariate jacobi orthogonal polynomials convergence stability and well conditioning of the method are proved in order to illustrate the efficiency of the proposed method some numerical tests are given

multifractal analysis of the wti crude oil market us stock market and epu abstract this paper adopts multifractal methods to analyze the nonlinear correlations among economic policy uncertainty epu the crude oil market and the stock market first using multifractal detrended fluctuation analysis mf dfa we find that each of the three series shows multifractality and the sources of multifractality are all from long range correlations and fat tailed distributions however for the stock and oil price series the long range correlation has a greater impact while the fat tailed distribution contributes more to epu multifractality furthermore we apply multifractal detrended cross correlation analysis mf dcca to analyze the cross correlation multifractal features among the three series the generalized hurst exponents of any two series are significantly greater than 0 5 and the stock and oil price series have the strongest cross correlation values coupling detrended fluctuation cdfa analysis of the three series shows that the coupling correlation among the three sequences is also multifractal the chi squared statistic reveals that the contribution of the stock market to the multifractality of the coupling correlation is greater than that of other series and epu has the smallest influence on the coupling correlation finally we employ multiscale multifractal analysis mma to visualize the dynamic behaviors of the correlations among the series the results show that the cross correlation of stock with the oil price has some symmetry at small and large scale fluctuations additionally the influence of epu on the overall coupling features is mainly reflected under small scale fluctuations and at large scales the coupling correlation of the three series remains similar to the hurst surface of stock with the oil price these results are useful for building predictive models

the numerical solution of the inverse stefan problem in two space variables a method is given for solving the inverse stefan problem for the heat equation in two space variables the approach is based on using a complete family of solutions to the heat equation thus reducing the dimensionality of the problem by one and minimizing the maximal defect in the initial boundary data subject to regularizing constraints thus making the problem well posed in the sense that the solution now depends continuously on the data two numerical examples are given which make use of a linear semi infinite programming method recently developed by hettich and zencke

using the swarm intelligence algorithms in solution of the two dimensional inverse stefan problem in the paper a procedure for solving the two dimensional inverse stefan problem is presented in considered problem the heat transfer coefficient is identified with the aid of known measurements of temperature in selected points of the region as the additional information direct stefan problem is solved by using the alternating phase truncation method goal of the paper is to compare two swarm intelligence algorithms the ant colony optimization algorithm and the artificial bee colony algorithm applied for minimizing a functional expressing the error of approximate solution

a spline collocation method for fredholm hammerstein integral equations of the second kind in two variables we consider fredholm hammerstein integral equations of the second kind over a rectangular region in plane as in kumar and sloan 1987 5 we reformulate it into an equivalent integral equation for the alternative equation we triangulate the rectangular domain and on each triangle use a collocation method based on constant spline approximation we discuss the convergence of the approximate solutions and conclude the paper with numerical examples

modeling and complexity of stochastic interacting levy type financial price dynamics abstract in attempt to reproduce and investigate nonlinear dynamics of security markets a novel nonlinear random interacting price dynamics which is considered as a levy type process is developed and investigated by the combination of lattice oriented percolation and potts dynamics which concerns with the instinctive random fluctuation and the fluctuation caused by the spread of the investors trading attitudes respectively to better understand the fluctuation complexity properties of the proposed model the complexity analyses of random logarithmic price return and corresponding volatility series are preformed including power law distribution lempel ziv complexity and fractional sample entropy in order to verify the rationality of the proposed model the corresponding studies of actual security market datasets are also implemented for comparison the empirical results reveal that this financial price model can reproduce some important complexity features of actual security markets to some extent the complexity of returns decreases with the increase of parameters 1 and respectively furthermore the volatility series exhibit lower complexity than the return series