inverse halftoning algorithm using edge based lookup table approach the inverse halftoning algorithm is used to reconstruct a gray image from an input halftone image based on the recently published lookup table lut technique this paper presents a novel edge based lut method for inverse halftoning which improves the quality of the reconstructed gray image the proposed method first uses the lut based inverse halftoning method as a preprocessing step to transform the given halftone image to a base gray image and then the edges are extracted and classified from the base gray image according to these classified edges a novel edge based lut is built up to reconstruct the gray image based on a set of 30 real training images with both low and high frequency contents experimental results demonstrated that the proposed method achieves a better image quality when compared to the currently published two methods by chang et al and mes 80e and vaidyanathan

retarding subdiffusion and accelerating superdiffusion governed by distributed order fractional diffusion equations we propose diffusionlike equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena whose diffusion exponent varies with time and which correspondingly cannot be viewed as self affine random processes possessing a unique hurst exponent we prove the positivity of the solutions of the proposed equations and establish their relation to the continuous time random walk theory we show that the distributed order time fractional diffusion equation describes the subdiffusion random process that is subordinated to the wiener process and whose diffusion exponent decreases in time retarding subdiffusion this process may lead to superslow diffusion with the mean square displacement growing logarithmically in time we also demonstrate that the distributed order space fractional diffusion equation describes superdiffusion phenomena with the diffusion exponent increasing in time accelerating superdiffusion

towards deterministic equations for levy walks the fractional material derivative levy walks are random processes with an underlying spatiotemporal coupling this coupling penalizes long jumps and therefore levy walks give a proper stochastic description for a particle s motion with broad jump length distribution we derive a generalized dynamical formulation for levy walks in which the fractional equivalent of the material derivative occurs our approach is expected to be useful for the dynamical formulation of levy walks in an external force field or in phase space for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited

econophysics scaling and its breakdown in finance we discuss recent empirical results obtained by analyzing high frequency data of a stock market index the standard and poor s 500 we focus on the scaling properties and on its breakdown of the index dynamics a simple stochastic model the truncated levy flight is illustrated successes and limitations of this model are presented a discussion about similarities and differences between the scaling properties observed in financial markets and in fully developed turbulence is also provided

tempered fractional sturm liouville eigenproblems continuum time random walk is a general model for particle kinetics which allows for incorporating waiting times and or non gaussian jump distributions with divergent second moments to account for levy flights exponentially tempering the probability distribution of the waiting times and the anomalously large displacements results in tempered stable levy processes with finite moments where the fluid continuous limit leads to the tempered fractional diffusion equation the development of fast and accurate numerical schemes for such nonlocal problems requires a new spectral theory and suitable choice of basis functions in this study we introduce two classes of regular and singular tempered fractional sturm liouville problems of two kinds tfslp i and tfslp ii of order nu in 0 2 in the regular case the corresponding tempered differential operators are associated with tempering functions p i x exp 2 tau and p ii x exp 2 tau tau geq 0 respectively in the regular tfslp i

fluctuations in multiplicative systems with jumps fluctuation properties of the langevin equation including a multiplicative power law noise and a quadratic potential are discussed the noise has the l evy stable distribution if this distribution is truncated the covariance can be derived in the limit of large time it falls exponentially covariance in the stable case studied for the cauchy distribution exhibits a weakly stretched exponential shape and can be approximated by the simple exponential the dependence of that function on system parameters is determined then we consider a dynamics which involves the above process and obeys the generalized langevin equation the same as for the gaussian case the resulting distributions possess power law tails which fall similarly to those for the driving noise whereas central parts can assume the gaussian shape moreover a process with the covariance 1 t at large time is constructed and the corresponding dynamical equation is solved diffusion properties of systems for both covariances are discussed

new multi parametric analytical approximations of exponential distribution with power law tails for new cars sells and other applications abstract a multi parametric family of exponential distributions with various power law tails is introduced and is shown to describe adequately the known distributions of incomes and wealth as well as the recently measured distributions of new car sales the three or four parametric families are characterized by effective temperature in the exponential part the power exponent in the power law asymptotic part the coefficient for the transition between the above two parts and the starting value if it is not equal to zero since the new car sales distributions are found to correspond to known distributions of incomes the latter may be inferred from the former

analytical representation of stock and stock indexes returns non gaussian random walks with various jump laws abstract empirical data for stock and stock indexes returns that is available for international markets as well as for the russian stock market is introduced and discussed random walk process with a specific law of an elementary independent increment jump in some random walk space is proposed for a proper basic description an analytical representation of a random walk distribution law is derived from a general conception of stochastic elementary jumps this representation covers classic s chandrasekhar s results for gauss random walks with limited jumps and jumps having distributions with all moments as well as p levy flights with jump distributions without moments starting from the second one finally it describes truncated levy random walks for jumps having distributions with at least the second moment the natural generalization of truncated levy walks is done the random walk process is compared with known empirical data for the above discussed return fluctuations of international assets and stock indexes there is a very good agreement of the elaborated theory with empirical data

random walk model with waiting times depending on the preceding jump length in the present paper the generalized continuous time random walk model with a coupled transition kernel is considered the coupling occurs through the dependence of the waiting time probability distribution on the preceding jump length for the description of this model a method is suggested that includes the details of the microscopic distribution over the waiting times and arrival distances at a given point a close analogy to the problem of a random walk with finite velocity is demonstrated for the particular case of coupling when a waiting time is a simple function of a preceding jump length with its help an analytical solution for the generalized random walk model is found including both effects finite velocity and jump dependent waiting times simultaneously

the ctrw in finance direct and inverse problems with some generalizations and extensions we study financial distributions within the framework of the continuous time random walk ctrw we review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies a non markovian formulation of the ctrw aimed to account for correlated increments of the return

on the error estimation for a mixed type of interpolation we analyse the error induced by the approximation of a function by an interpolation function which is a combination of algebraic and first order trigonometric polynomials we prove that under certain conditions this error can be expressed in a similar form as in the purely polynomial case as an application we establish in closed form the local truncation error for a class of extended linear multistep methods of the adams type

stretched gaussian asymptotics of the truncated levy flights for the diffusion in nonhomogeneous media abstract the levy jumping process defined in terms of the jumping size distribution and the waiting time distribution is considered the jumping rate depends on the process value the fractional diffusion equation which contains the variable diffusion coefficient is solved in the diffusion limit that solution resolves itself to the stretched gaussian when the order parameter 2 the truncation of the levy flights in the exponential and power law form is introduced and the corresponding random walk process is simulated by the monte carlo method the stretched gaussian tails are found in both cases the time which is needed to reach the limiting distribution strongly depends on the jumping rate parameter when the cutoff function falls slowly the tail of the distribution appears to be algebraic

anomalous diffusion for a correlated process with long jumps abstract we discuss diffusion properties of a dynamical system which is characterised by long tail distributions and finite correlations the particle velocity has the stable levy distribution it is assumed as a jumping process the kangaroo process with a variable jumping rate both the exponential and the algebraic form of the covariance defined for the truncated distribution are considered it is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power law correlations decays with time but a simple modification of the process makes the tails stable the main result of the paper is a finding that in contrast to the velocity fluctuations the position variance may be finite it rises with time faster than linearly the diffusion is anomalously enhanced on the other hand a process which follows from a superposition of the ornstein uhlenbeck levy processes always leads to position distributions with a divergent variance which means accelerated diffusion

analytic approach to the problem of convergence of truncated levy flights towards the gaussian stochastic process an analytic expression for characteristic function defining a truncated l evy flight is derived it is shown that the characteristic function yields results in agreement with recent simulations of truncated l evy flights by mantegna and stanley phys rev lett 73 2946 1994 with the analytic expression for the characteristic function the convergence of the l evy process towards the gaussian is demonstrated without simulations in the calculation of first return probability the simulations are replaced by numerical integration using simple quadratures

calibration of the subdiffusive arithmetic brownian motion with tempered stable waiting times in the classical analysis many models used to real data description are based on the standard brownian diffusion type processes however some real data exhibit characteristic periods of constant values in such cases the popular systems seem not to be applicable therefore we propose an alternative approach based on the combination of the popular brownian motion with drift called also the arithmetic brownian motion and tempered stable subordinator the probability density function of the proposed model can be described by a fokker planck type equation and therefore it has many similar properties as the popular brownian motion with drift in this paper we propose the estimation procedure for the considered tempered stable subdiffusive arithmetic brownian motion and calibrate the analyzed process to the real financial data

moments for tempered fractional advection diffusion equations this paper develops moment formulas for exponentially tempered fractional advection diffusion equations tfades that transition from anomalous to asymptotic diffusion limits over time exact analytical expressions or series representations for spatial moments up to the fourth order are derived by integral transform or asymptotic expansion approach a fully lagrangian solver cross verified by an implicit eulerian approach is also developed to calculate numerically the complete evolution of moments for the tfades with complex initial and boundary conditions moment analysis identifies the diffusion equation that attracts the tempered anomalous diffusion in the long time limit fitting of moments measured at two end members of alluvial systems checks the applicability of moment analysis in understanding real diffusion

first passage time moments of asymmetric levy flights we investigate the first passage dynamics of symmetric and asymmetric l evy flights in a semi infinite and bounded intervals by solving the space fractional diffusion equation we analyse the fractional order moments of the first passage time probability density function for different values of the index of stability and the skewness parameter a comparison with results using the langevin approach to l evy flights is presented for the semi infinite domain in certain special cases analytic results are derived explicitly and in bounded intervals a general analytical expression for the mean first passage time of l evy flights with arbitrary skewness is presented these results are complemented with extensive numerical analyses

fractional differential models for anomalous diffusion abstract in this study we investigate three kinds of fractional differential models distributed order model variable order model and random order model for characterization of anomalous diffusion the characteristics physical advantages and potential applications of each model are highlighted the numerical simulations also validate our analytical and comparison results furthermore a generalized distributed variable order model and a more generalized distributed variable random order model are proposed to combine the advantages of distributed order model variable order model and random order model

bifurcation bimodality and finite variance in confined levy flights we investigate the statistical behavior of levy flights confined in a symmetric quartic potential well u x proportional variant x 4 at stationarity the probability density function features a distinct bimodal shape and decays with power law tails which are steep enough to give rise to a finite variance in contrast to free levy flights from a delta initial condition a bifurcation of the unimodal state is observed at t c 0 the nonlinear oscillator with potential u x ax 2 2 bx 4 4 a b 0 shows a crossover from unimodal to bimodal behavior at stationarity depending on the ratio a b

fractional diffusion equation for a power law truncated levy process abstract truncated levy flights are stochastic processes which display a crossover from a heavy tailed levy behavior to a faster decaying probability distribution function pdf putting less weight on long flights overcomes the divergence of the levy distribution second moment we introduce a fractional generalization of the diffusion equation whose solution defines a process in which a levy flight of exponent is truncated by a power law of exponent 5 a closed form for the characteristic function of the process is derived the pdf of the displacement slowly converges to a gaussian in its central part showing however a power law far tail possible applications are discussed

anomalous diffusion in stochastic systems with nonhomogeneously distributed traps the stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed the particle is subjected to a stochastic stimulation obeying a general levy stable statistics and experiences long rests due to nonhomogeneously distributed traps the memory is taken into account by subordination of that process to a random time then the subordination equation is position dependent the problem is approximated by a decoupling of the medium structure and memory and exactly solved for a power law position dependence of the memory in the case of the gaussian statistics the density distribution and moments are derived depending on geometry and memory parameters the system may reveal both the subdiffusion and enhanced diffusion the similar analysis is performed for the levy flights where the finiteness of the variance follows from a variable noise intensity near a boundary two diffusion regimes are found in the bulk and near the surface the anomalous diffusion exponent as a function of the system parameters is derived

high order numerical approximation formulas for riemann liouville riesz tempered fractional derivatives construction and application i abstract in this paper we develop a new numerical algorithm for solving the riesz tempered space fractional diffusion equation the stability and convergence of the numerical scheme are discussed via the technique of matrix analysis finally numerical experiments are performed to confirm the effectiveness of our numerical algorithm

generalized langevin equation with tempered memory kernel abstract we study a generalized langevin equation for a free particle in presence of a truncated power law and mittag leffler memory kernel it is shown that in presence of truncation the particle from subdiffusive behavior in the short time limit turns to normal diffusion in the long time limit the case of harmonic oscillator is considered as well and the relaxation functions and the normalized displacement correlation function are represented in an exact form by considering external time dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement additionally the double peak phenomenon in the imaginary part of the complex susceptibility is observed it is obtained that the truncation parameter has a huge influence on the behavior of these quantities and it is shown how the truncation parameter changes the critical frequencies the normalized displacement correlation function for a fractional generalized langevin equation is investigated as well all the results are exact and given in terms of the three parameter mittag leffler function and the prabhakar generalized integral operator which in the kernel contains a three parameter mittag leffler function such kind of truncated langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes

levy flights from a continuous time process l evy flight dynamics can stem from simple random walks in a system whose operational time number of steps n typically grows superlinearly with physical time t thus this process is a kind of continuous time random walk ctrw dual to the typical scher montroll model in which n grows sublinearly with t models in which l evy flights emerge due to a temporal subordination allow one easily to discuss the response of a random walker to a weak outer force which is shown to be nonlinear on the other hand the relaxation of an ensemble of such walkers in a harmonic potential follows a simple exponential pattern and leads to a normal boltzmann distribution mixed models describing normal ctrw s in superlinear operational time and l evy flights under the operational time of subdiffusive ctrw s lead to a paradoxical diffusive behavior similar to the one found in transport on polymer chains the relaxation to the boltzmann distribution in such models is slow and asymptotically follows a power law

numerical method for solving diffusion wave phenomena we find solutions for the diffusion wave problem in 1d with n term time fractional derivatives whose orders belong to the intervals 0 1 1 2 and 0 2 respectively using the method of the approximation of the convolution by laguerre polynomials in the space of tempered distributions this method transfers the diffusion wave problem into the corresponding infinite system of linear algebraic equations through the coefficients which are uniquely solvable under some relations between the coefficients with index zero the method is applicable for nonlinear problems too