correlation measure to detect time series distances whence economy globalization abstract an instantaneous time series distance is defined through the equal time correlation coefficient the idea is applied to the gross domestic product gdp yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation some data discussion is first presented to decide what eks gk or derived gdp series should be studied distances are then calculated from the correlation coefficient values between pairs of series the role of time averaging of the distances over finite size windows is discussed three network structures are next constructed based on the hierarchy of distances it is shown that the mean distance between the most developed countries on several networks actually decreases in time which we consider as a proof of globalization an empirical law is found for the evolution after 1990 similar to that found in flux creep the optimal observation time window size is found 15 years

regular article a fast spectral algorithm for nonlinear wave equations with linear dispersion spectral algorithms offer very high spatial resolution for a wide range of nonlinear wave equations on periodic domains including well known cases such as the korteweg de vries and nonlinear schrodinger equations for the best computational efficiency one needs also to use high order methods in time while somehow bypassing the usual severe stability restrictions we use linearly implicit multistep methods with the innovation of choosing different methods for different ranges in fourier space high accuracy at low wavenumbers and a stability at high wavenumbers this new approach compares favorably to alternatives such as split step and integrating factor or linearly exact methods

hybrid cluster identification i present a hybrid method for the labelling of clusters in two dimensional lattices which combines the recursive approach with iterative scanning to reduce the stack size required by the pure recursive technique while keeping its benefits single pass and straightforward cluster characterization and percolation detection parallel to the labelling while the capacity to hold the entire lattice in memory is usually regarded as the major constraint for the applicability of the recursive technique the required stack size is the real limiting factor resorting to recursion only for the transverse direction greatly reduces the recursion depth and therefore the required stack it also enhances the overall performance of the recursive technique as is shown by results on a set of uniform random binary lattices and on a set of samples of the ising model i also show how this technique may replace the recursive technique in wolff s cluster algorithm decreasing the risk of stack overflow and increasing its speed and the hoshen kopelman algorithm in the swendsen wang cluster algorithm allowing effortless characterization during generation of the samples and increasing its speed

the pseudospectral method for third order differential equations generalized quadrature rules are derived which assist in the selection of collocation points for the pseudospectral solution of differential equations in particular it is shown that for an nth order differential equation in one space dimension with two point derivative boundary conditions an ideal choice of interior collocation points is the set of zeros of a jacobi polynomial the pseudospectral solution of a third order initial boundary value problem is considered and accuracy is assessed by examining how well the discrete eigenproblem approximates the continuous one convergence is established for a special choice of collocation points and numerical results are included to demonstrate the viability of the approach

a small time solutions for the korteweg de vries equation using spline approximation in this paper the one dimensional nonlinear korteweg de vries kdv equation is numerically solved using second order spline approximation the test problems concerning the propagation of a solution and two solution interaction are used to validate the proposal scheme and it is found to be both accurate and efficient at small times also it is shown that the second order spline approximation may be used effectively at small times when the exact solution of the kdv equation is not known

eventual periodicity of the forced oscillations for a korteweg de vries type equation on a bounded domain using a sinc collocation method abstract we demonstrate numerically the eventual time periodicity of solutions u t to the korteweg de vries type equation with periodic forcing at one end using the sinc collocation method this method approximates the space dimension of the solution with a cardinal expansion of sinc functions thus allowing the avoidance of a costly finite difference grid for a third order boundary value problem the first order time derivative is approximated with a weighted finite difference method the sinc collocation method was found to be more robust and more efficient than other numerical schemes when applied to this problem

the galerkin method for the kdv equation using a new basis of smooth piecewise cubic polynomials abstract in this paper we introduce the galerkin method using a new basis of smooth piecewise cubic polynomials for the one dimensional nonlinear kdv equation the stability analysis shows that the present method is unconditionally stable in l 2 norm numerical experiments show that the proposed method preserves the conservation laws and is effective for simulating the motions and the interactions of solitary waves

critical percolation clusters in seven dimensions and on a complete graph we study critical bond percolation on a seven dimensional hypercubic lattice with periodic boundary conditions 7d and on the complete graph cg of finite volume number of vertices v we numerically confirm that for both cases the critical number density n s v of clusters of size s obeys a scaling form n s v s n over s v d f with identical volume fractal dimension d f 2 3 and exponent 1 1 d f 5 2 we then classify occupied bonds into bridge bonds which includes branch and junction bonds and nonbridge bonds a bridge bond is a branch bond if and only if its deletion produces at least one tree deleting branch bonds from percolation configurations produces leaf free configurations whereas deleting all bridge bonds leads to bridge free configurations composed of blobs it is shown that the fraction of nonbridge biconnected bonds vanishes n cg 0 for large cgs but converges to a finite value n 7d 0 0061931 7 for the 7d hypercube further we observe that while the bridge free dimension d bf 1 3 holds for both the cg and 7d cases the volume fractal dimensions of the leaf free clusters are different d lf 7d 0 669 9 2 3 and d lf cg 0 3337 17 1 3 on the cg and in 7d the whole leaf free and bridge free clusters all have the shortest path volume fractal dimension d min 1 3 characterizing their graph diameters we also study the behavior of the number and the size distribution of leaf free and bridge free clusters for the number of clusters we numerically find the number of leaf free and bridge free clusters on the cg scale as lnv while for 7d they scale as v for the size distribution we find the behavior on the cg is governed by a modified fisher exponent 1 while for leaf free clusters in 7d it is governed by fisher exponent 5 2 the size distribution of bridge free clusters in 7d displays two scaling behavior with exponents 4 and 1 the probability distribution p c 1 v dc 1 of the largest cluster of size c 1 for whole percolation configurations is observed to follow a single variable function p over x dx with x c 1 v d f for both cg and 7d up to a rescaling factor for the variable x the probability functions for cg and 7d collapse on top of each other within the entire range of x the analytical expressions in the x 0 and x limits are further confirmed our work demonstrates that the geometric structure of high dimensional percolation clusters cannot be fully accounted for by their complete graph counterparts

a critical exponent for shortest path scaling in continuum percolation we carry out monte carlo experiments to study the scaling behavior of shortest path lengths in continuum percolation these studies suggest that the critical exponent governing this scaling is the same for both continuum and lattice percolation we use splitting a technique that has not yet been fully exploited in the physics literature to increase the speed of our simulations this technique can also be applied to other models where clusters are grown sequentially

the fourier pseudospectral method with a restrain operator for the korteweg de vries equation abstract in this paper we develop a fourier pseudospectral method with a restrain operator for the korteweg de vries equation we prove the generalized stability of the schemes and give convergence estimations depending on the smoothness of the solution of the p d e

red bond exponents of the critical and the tricritical ising model in three dimensions using the wolff and geometric cluster algorithms and finite size scaling analysis we investigate the critical ising and the tricritical blume capel models with nearest neighbor interactions on the simple cubic lattice the sampling procedure involves the decomposition of the ising configuration into geometric clusters each of which consists of a set of nearest neighboring spins of the same sign connected with bond probability p these clusters include the well known kasteleyn fortuin clusters as a special case for p 1 exp 2k where k is the ising spin spin coupling along the critical line k kc the size distribution of geometric clusters is investigated as a function of p we observe that unlike in the case of two dimensional tricriticality the percolation threshold in both models lies at pc 1 exp 2kc further we determine the corresponding red bond exponents as yr 0 757 2 and 0 501 5 for the critical ising and the tricritical blume capel models respectively on this basis we conjecture yr 1 2 for the latter model

optimal error estimates of the legendre petrov galerkin method for the korteweg de vries equation in this paper the legendre petrov galerkin method for the korteweg de vries equation with nonperiodic boundary conditions is analyzed the nonlinear term is computed with the legendre spectral method and some pseudospectral methods respectively optimal error estimates in l2 norm are obtained for both semidiscrete and fully discrete schemes the method is also applicable to some 2m 1 th order differential equations

a small time solutions for the korteweg de vries equation in this paper a heat balance integral hbi method is applied to the one dimensional non linear korteweg de vries kdv equation prescribed by appropriate homogenous boundary conditions and a set of initial conditions to obtain its approximate analytical solutions at small times it is shown that the hbi solutions obtained by the method may be used effectively at small times when the exact solution of the kdv equation is not known

improving quality of sample entropy estimation for continuous distribution probability functions abstract entropy is a one of the key parameters characterizing state of system in statistical physics although the entropy is defined for systems described by discrete and continuous probability distribution function pdf in numerous applications the sample entropy is estimated by a histogram which in fact denotes that the continuous pdf is represented by a set of probabilities such a procedure may lead to ambiguities and even misinterpretation of the results within this paper two possible general algorithms based on continuous pdf estimation are discussed in the application to the shannon and tsallis entropies it is shown that the proposed algorithms may improve entropy estimation particularly in the case of small data sets

a hybrid numerical method for the kdv equation by finite difference and sinc collocation method abstract in this paper we propose a hybrid numerical method for the kdv equation more precisely we discretize the temporal derivative of kdv equation by a weighted scheme and treat the implicitly nonlinear term with the combination of finite difference and sinc collocation method the stability analysis is presented and numerical experiments illustrate the efficiency and stability of the proposed hybrid method the motions and the interactions of solitary waves relying on particular initial boundary conditions are also simulated

phase diagram of inhomogeneous percolation with a defect plane let mathbb l be the d dimensional hypercubic lattice and let mathbb l 0 be an s dimensional sublattice with 2 le s p c d and a surface supercritical regime for p sigma p we show that sigma p is a strictly decreasing function for p in 0 p c d with a jump discontinuity at p c d we extend the aizenman barsky differential inequalities for homogeneous percolation to the inhomogeneous model and use them to prove that the susceptibility is finite inside the subcritical phase we prove that the cluster size distribution decays exponentially in the subcritical phase and sub exponentially in the supercritical phases for a model of lattice animals with a defect plane the free energy is related to functions of the inhomogeneous percolation model and we show how the percolation transition implies a non analyticity in the free energy of the animal model finally we present simulation estimates of the critical curve sigma p

solution of nonlinear initial boundary value problems by sinc collocation interpolation methods abstract this paper deals with the solution of initial boundary value problems for nonlinear evolution equations in one and two space dimensions the solution technique is based on collocation interpolation methods which use sinc functions the application refers to some direct and inverse type problems

globalization entropy unification through the theil index abstract a time series is remapped onto an entropy concept based on the theil index the manhattan distance between these surrogate series is calculated and contrasted to the usual correlation distance measure the idea is applied to several gross domestic product relative increments of rich countries such distances are calculated for various time window sizes the role of time averaging in such finite size windows is discussed we construct the locally minimum spanning tree lmst corresponding to the distance matrix another hierarchical network structure unidirectional minimal length path is compared with the lmst for confirming that the mean distance between the most developed countries on different networks actually decreases in time which we consider as a proof of economy globalization it is stressed that this entropy distance measure seems more suitable in detecting some phase transition in time series like a globalization process than the usual correlation based measure

numerical methods for the solution of the third and fifth order dispersive korteweg de vries equations abstract two numerical methods are proposed for the solution of the third and fifth order korteweg de vries equations the first method is derived using central differences to replace the space derivatives with a predictor corrector time stepping and the second method by linearizing the implicit corrector scheme in which the solution is then found by solving a linear algebraic system at each time step rather than a nonlinear algebraic system which is more usual an important advantage to be gained from the use of the linearized implicit method over the predictor corrector method which is optimally stable is the ability to vary the mesh length the methods are analysed with respect to stability criteria and numerical dispersion numerical results portraying a single soliton solution and the interaction of more than one soliton are reported for the third order korteweg de vries equation numerical results for the fifth order korteweg de vries equation using the linearized implicit method are also reported

the chebyshev legendre method implementing legendre methods on chebyshev points a new collocation method for the numerical solution of partial differential equations is presented this method uses the chebyshev collocation points but because of the way the boundary conditions are implemented it has all the advantages of the legendre methods in particular l 2 estimates can be easily obtained for hyperbolic and parabolic problems

sinc collocation interpolation method for the simulation of nonlinear waves abstract numerical simulation is of great importance in the study of nonlinear waves where several delicate aspects must be dealt with the presence of spatial and time gradients of complex nonlinearities and high order derivatives in fact generates various complex problems this paper develops a collocation interpolation method based on interpolation by the sine functions after a description of the method several examples are shown these show the good results that can be obtained the efficency and stability of the method and the low computing time

spanning forests and osp n 2m invariant σ models the present paper is part of our ongoing work on osp n 2m supersymmetric models their relation with the potts model at q 0 and spanning forests and the rigorous analytic continuation of the partition function as an entire function of n 2m a feature first predicted by parisi and sourlas in the 1970s here we accomplish two main steps first we analyze in detail the role of the ising variables that arise when the constraint in the osp 1 2 model is solved and we point out two situations in which the ising and forest variables decouple second we establish the analytic continuation for the osp n 2m model in some special cases when the underlying graph is a forest and for the nienhuis action on a cubic graph we also make progress in understanding the series parallel graphs

benford s law first significant digit and distribution distances for testing the reliability of financial reports in developing countries abstract we discuss a common suspicion about reported financial data in 10 industrial sectors of the 6 so called main developing countries over the time interval 2000 2014 these data are examined through benford s law first significant digit and through distribution distances tests it is shown that several visually anomalous data have to be a priori removed thereafter the distributions much better follow the first digit significant law indicating the usefulness of a benford s law test from the research starting line the same holds true for distance tests a few outliers are pointed out

an analytical numerical method for solving the korteweg de vries equation in this paper an analytical numerical method is applied to the one dimensional korteweg de vries equation with a variant of boundary and initial conditions to obtain its numerical solutions at small times two test problem with known exact solutions are studied to demonstrate the accuracy of the present method the obtained results are compared with the exact solution of each problem and are found to be in good agreement with each other the numerical scheme is also compared with earlier work and shown to be accurate and efficient

implicit explicit methods for time dependent partial differential equations implicit explicit imex schemes have been widely used especially in conjunction with spectral methods for the time integration of spatially discretized partial differential equations pdes of diffusion convection type typically an implicit scheme is used for the diffusion term and an explicit scheme is used for the convection term reaction diffusion problems can also be approximated in this manner in this work we systematically analyze the performance of such schemes propose improved new schemes and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods for the prototype linear advection diffusion equation a stability analysis for first second third and fourth order multistep imex schemes is performed stable schemes permitting large time steps for a wide variety of problems and yielding appropriate decay of high frequency error modes are identified numerical experiments demonstrate that weak decay

a legendre petrov galerkin and chebyshev collocation method for third order differential equations a legendre petrov galerkin lpg method for the third order differential equation is developed by choosing appropriate base functions the method can be implemented efficiently also this new approach enables us to derive an optimal rate of convergence in l2 norm the method is applied to some nonlinear problems such as the korteweg de vries kdv equation with the chebyshev collocation treatment for the nonlinear term it is a legendre petrov galerkin and chebyshev collocation lpg cc method numerical experiments are given to confirm the theoretical result

surface critical phenomena in three dimensional percolation using monte carlo methods and finite size scaling we investigate surface critical phenomena in the bondpercolation model on the simple cubic lattice with two open surfaces in one direction we decompose the whole lattice into percolation clusters and sample the surface and bulk dimensionless ratios q1 and qb defined on the basis of the moments of the cluster size distribution these ratios are used to determine critical points at the bulk percolation threshold pbc we determine the surface bond occupation probability at the special transition as p 1c ssd 0 418 17s2d and further obtain the corresponding surface thermal and magnetic exponents as y t1 ssd 0 5387s2d and y h1 ssd 1 8014s6d respectively next from the pair correlation function on the surfaces we determine y h1 sod 1 0246s4d and y h1 sed 1 25s6d for the ordinary and the extraordinary transition respectively of which the former is consistent with the existing result y h1 sod 1 024s4d we also numerically derive the line of surface phase transitions occurring at pb pbc and determine the pertinent asymptotic values of the universal ratios q1 and qb

scaling of cluster mass between two lines in 3d percolation abstract we consider the cluster mass distribution between two lines of arbitrary orientations and lengths in porous media in three dimensions and model the porous media by bond percolation at the percolation threshold p c we observe that for many geometrical configurations the mass probability distribution presents power law behavior we determine how the characteristic mass of the distribution scales with such geometrical parameters as the line length w the minimal distance between lines r and the angle between the lines the fractal dimensions of the cluster mass are independent of w r and the slope of the power law regime of the cluster mass is unaffected by changes in these three variables however the characteristic mass of the cluster depends upon we propose new scaling functions that reproduce the dependence of the characteristic mass found in the simulations

scaling of cluster heterogeneity in percolation transitions we investigate a critical scaling law for the cluster heterogeneity h in site and bond percolations in d dimensional lattices with d 2 6 the cluster heterogeneity is defined as the number of distinct cluster sizes as an occupation probability p increases the cluster size distribution evolves from a monodisperse distribution to a polydisperse one in the subcritical phase and back to a monodisperse one in the supercritical phase we show analytically that h diverges algebraically approaching the percolation critical point p c as h p p c 1 with the critical exponent associated with the characteristic cluster size interestingly its finite size scaling behavior is governed by a new exponent h 1 d f d where d f is the fractal dimension of the critical percolating cluster and is the correlation length exponent the corresponding scaling variable defines a singular path to the critical point all results are confirmed by numerical simulations

exponential finite difference method applied to korteweg de vries equation for small times the korteweg de vries equation is numerically solved by using the exponential finite difference technique the accuracy of computed solutions is examined by comparison with other numerical and analytical solutions using two examples the close results agreement between the current results and the exact solutions confirms that the proposed finite difference procedure is an effective technique for the solution of the korteweg de vries equation at the small times

a new dual petrov galerkin method for third and higher odd order differential equations application to the kdv equation a new dual petrov galerkin method is proposed analyzed and implemented for third and higher odd order equations using a spectral discretization the key idea is to use trial functions satisfying the underlying boundary conditions of the differential equations and test functions satisfying the dual boundary conditions the method leads to linear systems which are sparse for problems with constant coefficients and well conditioned for problems with variable coefficients our theoretical analysis and numerical results indicate that the proposed method is extremely accurate and efficient and most suitable for the study of complex dynamics of higher odd order equations

high temperature series expansions for the q state potts model on a hypercubic lattice and critical properties of percolation we present results for the high temperature series expansions of the susceptibility and free energy of the q state potts model on a d dimensional hypercubic lattice zd for arbitrary values of q the series are up to order 20 for dimension d 1 limit of these series we estimate the percolation threshold pc and critical exponent gamma for bond percolation in different dimensions we also extend the 1 d expansion of the critical coupling for arbitrary values of q up to order d 9

energy conserving hamiltonian boundary value methods for the numerical solution of the korteweg de vries equation abstract in this paper we study the efficient solution of the well known korteweg de vries equation equipped with periodic boundary conditions a fourier galerkin space semi discretization at first provides a large size hamiltonian ode problem whose solution in time is then carried out by means of energy conserving methods in the hbvm class hamiltonian boundary value methods the efficient implementation of the methods for the resulting problem is also considered and several numerical examples are reported

fourier methods with extended stability intervals for the korteweg de vries equation a full leap frog fourier method for integrating the korteweg de vries kdv equation u t uu x varepsilon u xxx 0 results in an o n 3 stability constraint on the time step where n is the number of fourier modes used this stability limit is much more restrictive than the accuracy limit for many applications in this paper we propose a method for which the stability limit is extended by treating the linear dispersive u xxx term implicitly thus timesteps can be taken up to an accuracy limit larger than the explicit stability limit the implicit method is implemented without solving linear systems by integrating in time in the fourier space and discretizing the nonlinear uu x term by leap frog a second method we propose uses basis functions which solve the linear part of the kdv equation and leap frog for time integration a linearized stability analysis of the proposed schemes proves that a version of the first scheme possesses a certain kind of unconditional stability and that

integration preconditioning of pseudospectral operators i basic linear operators this paper develops a family of preconditioners for pseudospectral approximations of pth order linear differential operators subject to various types of boundary conditions the approximations are based on ultraspherical polynomials with special attention being paid to legendre and chebyshev polynomial methods based on gauss lobatto quadrature points the eigenvalue spectrum of the preconditioned operators are obtained in closed analytic form and the weakly enforced boundary conditions are shown to result in a rank 2p perturbation of the identity operator i e the majority of the preconditioned eigenvalues are unity the spectrum of the preconditioned advective operator is shown to be bounded independent of the order of the approximation n however the preconditioned diffusive operator is in general indefinite with four real eigenvalues for dirichlet boundary conditions the spectral radius grows as sqrt n while it scales as n for the case of neumann boundary conditions these results are shown to be asymptotically optimal within the present framework generalizations to higher order differential operators general boundary conditions and arbitrary polynomial basis and quadrature nodes are discussed

percolation threshold fisher exponent and shortest path exponent for four and five dimensions we develop a method of constructing percolation clusters that allows us to build very large clusters using very little computer memory by limiting the maximum number of sites for which we maintain state information to a number of the order of the number of sites in the largest chemical shell of the cluster being created the memory required to grow a cluster of mass s is of the order of s ensuremath theta bytes where ensuremath theta ranges from 0 4 for two dimensional 2d lattices to 0 5 for six or higher dimensional lattices we use this method to estimate d mathrm min the exponent relating the minimum path mathcal l to the euclidean distance r for 4d and 5d hypercubic lattices analyzing both site and bond percolation we find d mathrm min 1 607 ifmmode pm else textpm fi 0 005 4d and d mathrm min 1 812 ifmmode pm else textpm fi 0 006 5d in order to determine d mathrm min to high precision and without bias it was necessary to first find precise values for the percolation threshold p c p c 0 196889 ifmmode pm else textpm fi 0 000003 4d and p c 0 14081 ifmmode pm else textpm fi 0 00001 5d for site and p c 0 160130 ifmmode pm else textpm fi 0 000003 4d and p c 0 118174 ifmmode pm else textpm fi 0 000004 5d for bond percolation we also calculate the fisher exponent ensuremath tau determined in the course of calculating the values of p c ensuremath tau 2 313 ifmmode pm else textpm fi 0 003 4d and ensuremath tau 2 412 ifmmode pm else textpm fi 0 004 5d

numerical solution of korteweg de vries equation by galerkin b spline finite element method a finite element solution of the kdv equation is presented to demonstrate the efficiency of the method two test problems are considered the numerical solutions of the kdv equation are compared with both the exact solutions and other numerical solutions in the literature the numerical solutions are found to be in good agreement with the exact solutions

efficient spectral galerkin method i direct solvers of second and fourth order equations using legendre polynomials this paper presents some efficient algorithms based on the legendre galerkin approximations for the direct solution of the second and fourth order elliptic equations the key to the efficiency of these algorithms is to construct appropriate base functions which lead to systems with sparse matrices for the discrete variational formulations the complexities of the algorithms are a small multiple of n d 1 operations for a d dimensional domain with n 1 d unknowns while the convergence rates of the algorithms are exponential for problems with smooth solutions in addition the algorithms can be effectively parallelized since the bottlenecks of the algorithms are matrix matrix multiplications

the transmission of fluctuation among price indices based on granger causality network abstract in this paper we provide a method of statistical physics to analyze the fluctuation of transmission by constructing granger causality network among price indices pigcn from a systematical perspective using complex network theory combined with granger causality method in economic system there are numerous price indices of which the relationships are extreme complicated thus time series data of 6 types of price indices of china including 113 kinds of sub price indices are selected as example of empirical study through the analysis of the structure of pigcn we identify important price indices with high transmission range high intermediation capacity high cohesion and the fluctuation transmission path of price indices respectively furthermore dynamic relationships among price indices are revealed based on these results we provide several policy implications for monitoring the diffusion of risk of price fluctuation our method can also be used to study the price indices of other countries which is generally applicable

entropy correlation distance method the euro introduction effect on the consumer price index the idea of entropy was introduced in thermodynamics but it can be used in time series analysis there are various ways to define and measure the entropy of a system here the so called theil index which is often used in economy and finance is applied as it were an entropy measure in this study the time series are remapped through the theil index then the linear correlation coefficient between the remapped time series is evaluated as a function of time and time window size and the corresponding statistical distance is defined the results are compared with the the usual correlation distance measure for the time series themselves as an example this entropy correlation distance method ecdm is applied to several series as those of the consumer price index cpi in order to test some so called globalisation processes distance matrices are calculated in order to construct two network structures which are next analysed the role of two different time scales introduced by the theil index and a correlation coefficient is also discussed the evolution of the mean distance between the most developed countries is presented and the globalisation periods of the prices discussed it is finally shown that the evolution of mean distance between the most developed countries on several networks follows the process of introducing the european currency the euro it is contrasted to the gdp based analysis it is stressed that the entropy correlation distance measure is more suitable in detecting significant changes like a globalisation process than the usual statistical correlation based measure