a spectral approach for sifting process in empirical mode decomposition in this paper we propose an alternative to the algorithmic definition of the sifting process used in the original huang s empirical mode decomposition emd method although it has been proven to be particularly effective in many applications emd method has several drawbacks the major problem with emd is the lack of theoretical framework which leads to difficulties for the characterization and evaluation this approach on top of the mathematical model there are other concerns with mode mixing and transient phenomena such as intermittency or pure tones separation this paper follows a previous published nonlinear diffusion based filtering to solve the mean envelope estimation in sifting process the major improvements made in this present work are a non iterative resolution scheme for the previously proposed partial differential equation pde a new definition of the stopping function used in the pde framework and finally an automatic regularization process based on inverse problem theory to deal with mode mixing or transient detection problem obtained results confirm good properties of the new version of the pde based sifting process and its usefulness for decomposition of various kinds of data the efficiency of the method is illustrated on some examples using informative and pathological signals for which standard emd algorithm fails

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the subsections have to be statistically independent for non stationary and nonlinear processes such an analysis is no longer valid the confidence limit of the method here termed emd hsa for empirical mode decomposition hilbert spectral analysis is introduced by using various adjustable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

convergence of vertex reinforced jump processes to an extension of the supersymmetric hyperbolic nonlinear sigma model in this paper we define an extension of the supersymmetric hyperbolic nonlinear sigma model introduced by zirnbauer we show that it arises as a weak joint limit of a time changed version introduced by sabot and tarres of the vertex reinforced jump process it describes the asymptotics of rescaled crossing numbers rescaled fluctuations of local times asymptotic local times on a logarithmic scale endpoints of paths and last exit trees

viscoplasticity using peridynamics peridynamics is a continuum reformulation of the standard theory of solid mechanics unlike the partial differential equations of the standard theory the basic equations of peridynamics are applicable even when cracks and other singularities appear in the deformation field the assumptions in the original peridynamic theory resulted in severe restrictions on the types of material response that could be modeled including a limitation on the poisson ratio recent theoretical developments have shown promise for overcoming these limitations but have not previously incorporated rate dependence and have not been demonstrated in realistic applications in this paper a new method for implementing a rate dependent plastic material within a peridynamic numerical model is proposed and demonstrated the resulting material model implementation is fitted to rate dependent test data on 6061 t6 aluminum alloy it is shown that with this material model the peridynamic method accurately reproduces the experimental results for taylor impact tests over a wide range of impact velocities the resulting model retains the advantages of the peridynamic formulation regarding discontinuities while allowing greater generality in material response than was previously possible copyright 2009 john wiley sons ltd

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

partial differential equation based approach for empirical mode decomposition application on image analysis the major problem with the empirical mode decomposition emd algorithm is its lack of a theoretical framework so it is difficult to characterize and evaluate this approach in this paper we propose in the 2 d case the use of an alternative implementation to the algorithmic definition of the so called sifting process used in the original huang s emd method this approach especially based on partial differential equations pdes was presented by niang in previous works in 2005 and 2007 and relies on a nonlinear diffusion based filtering process to solve the mean envelope estimation problem in the 1 d case the efficiency of the pde based method compared to the original emd algorithmic version was also illustrated in a recent paper recently several 2 d extensions of the emd method have been proposed despite some effort 2 d versions for emd appear poorly performing and are very time consuming so in this paper an extension to the 2 d space of the pde based approach is extensively described this approach has been applied in cases of both signal and image decomposition the obtained results confirm the usefulness of the new pde based sifting process for the decomposition of various kinds of data some results have been provided in the case of image decomposition the effectiveness of the approach encourages its use in a number of signal and image applications such as denoising detrending or texture analysis

a mesh grading material point method and its parallelization for problems with localized extreme deformation abstract as a kind of meshless method material point method mpm applies an eulerian background grid served as a finite element mesh in each time step and therefore its accuracy and efficiency are mainly dependent on the cell size setting of background grid however the conventional mpm commonly uses a regular background grid with uniform cells which is not apposite for localized extreme deformation problems from the view point of computation efficiency where in fact a local refined background grid is preferable hence a mesh grading material point method mgmpm is proposed here for such problems to supply mpm with the ability for local refinement simulation the edge displacement continuity associated with mesh grading is embedded in the nodal shape functions besides the truss element is incorporated into mgmpm to model the steel reinforcement bars in reinforced concrete impacting problems based on our previous work furthermore the proposed method is parallelized using openmp open multi processing to take advantage of pc power with multi core and hyper threading technologies for large scale engineering problems where both loop level parallelism and code block parallelism are used several numerical examples including stress wave propagation taylor bar impact and penetration problems are studied which show that the efficiency of mgmpm is much higher than that of conventional mpm and with lower memory requirement

a particle method for history dependent materials abstract a broad class of engineering problems including penetration impact and large rotations of solid bodies causes severe numerical problems for these problems the constitutive equations are history dependent so material points must be followed this is difficult to implement in a eulerian scheme on the other hand purely lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables a process which can introduce errors proposed here is an extension of the particle in cell method in which particles are interpreted to be material points that are followed through the complete loading process a fixed eulerian grid provides the means for determining a spatial gradient because the grid can also be interpreted as an updated lagrangian frame the usual convection term in the acceleration associated with eulerian formulations does not appear with the use of maps between material points and the grid the advantages of both eulerian and lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced also it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity

an adaptive finite element material point method and its application in extreme deformation problems abstract taking advantages of both lagrangian and eulerian methods material point method mpm is suitable for modeling problems with extreme deformation however mpm is less accurate and less efficient than finite element method fem for small deformation problems due to particle quadrature and mappings between particles and background grid applied in mpm to take advantages of both fem and mpm an adaptive finite element material point method is developed for modeling the dynamic behavior of material under extreme loading bodies are initially discretized by finite elements and then the elements with large strain are adaptively converted into mpm particles based on their degree of distortion or plastic strain during the solution process the interaction between the remaining finite elements and mpm particles is implemented based on the background grid in mpm framework several numerical examples are presented to validate the efficiency and accuracy of the proposed method and the numerical results are in good agreement with experiments while the efficiency of the method is higher than that of both mpm and fem

vertex reinforced jump processes on trees and finite graphs we study the continuous time process on the vertices of the b ary tree which jumps to each nearest neighbor vertex at the rate of the time already spent at that vertex times plus 1 where is a positive constant we show that for fixed b 1 if is large enough the process is transient and if is close enough to zero it is recurrent related results for some other graphs and trees are also proved

material point method enhanced by modified gradient of shape function a numerical scheme of computing quantities involving gradients of shape functions is introduced for the material point method mpm so that the quantities are continuous as material points move across cell boundaries the noise and instability caused by cell crossing of the material points are then eliminated in this scheme the formulas used to compute these quantities can be expressed in the same forms as in the original material point method but with the gradient of the shape function modified for one dimensional cases the gradient of the shape function used in the generalized interpolation material point gimp method is a special case of the modified gradient if the characteristic function of a material point is introduced the characteristic function of a material point is not otherwise needed in this scheme therefore difficulties in tracking its evolution are avoided although the support of the modified gradient of a shape function is enlarged from the cell containing the material point to also include the immediate neighbor cells all the non local effects of a material point can be accounted for by two consecutive local operations therefore this scheme can be used in calculations with unstructured grids this scheme is proved to satisfy mass and momentum conservations exactly the error in energy conservation is shown to be second order on both spatial and temporal discretizations although the error in energy conservation is the same order as that in the original material point method numerical examples show that this scheme has significantly better energy conservation properties than those of the original material point method

an improved emd method with modified envelope algorithm based on c2 piecewise rational cubic spline interpolation for emi signal decomposition abstract in this paper we propose an improved empirical mode decomposition emd method termed iemd with modified envelope algorithm based on c2 piecewise rational and c2 monotone piecewise rational cubic spline interpolations for the decomposition of nonlinear and non stationary emi signals in the sifting procedure we first construct the upper and lower envelopes employing c2 piecewise rational cubic spline interpolation prcsi technique considering the existence of undershoots we further modify the original envelopes iteratively with c2 monotone piecewise rational cubic spline interpolation mprcsi technique for the elimination of undershoots as accurate as possible experiments on synthetic and real signals compared with three improved versions of emd three for ensemble emd eemd and tl svd demonstrate that the proposed method is more valid and flexible when applied to the decomposition of synthesis harmonic signals and real eeg signals signifying it also can be applied to the decomposition of emi signals which are known to be extremely nonlinear and non stationary

continuous time vertex reinforced jump processes we study the continuous time integer valued process which jumps to each of its two nearest neighbors at the rate of one plus the total time the process has previously spent at that neighbor we show that the proportion of the time before t which this process spends at integers j converges to positive random variables v j which sum to one and whose joint distribution is explicitly described we also show

recurrence of edge reinforced random walk on a two dimensional graph we consider a linearly edge reinforced random walk on a class of two dimensional graphs with constant initial weights the graphs are obtained from 2 by replacing every edge by a sufficiently large but fixed number of edges in series we prove that the linearly edge reinforced random walk on these graphs is recurrent furthermore we derive bounds for the probability that the edge reinforced random walk hits the boundary of a large box before returning to its starting point

transience of edge reinforced random walk we show transience of the edge reinforced random walk errw for small reinforcement in dimension d ge3 this proves the existence of a phase transition between recurrent and transient behavior thus solving an open problem stated by diaconis in 1986 the argument adapts the proof of quasi diffusive behavior of the supersymmetric susy hyperbolic model for fixed conductances by disertori et al commun math phys 300 435 486 2010 using the representation of errw as a mixture of vertex reinforced jump processes vrjp with independent gamma conductances and the interpretation of the limit law of vrjp as a susy hyperbolic sigma model developed by sabot and tarres j eur math soc arxiv 1111 3991 2015

edge and vertex reinforced random walks with super linear reinforcement on infinite graphs in this paper we introduce a new simple but powerful general technique for the study of edge and vertex reinforced processes with super linear reinforcement based on the use of order statistics for the number of edge respectively of vertex traversals the technique relies on upper bound estimates for the number of edge traversals proved in a different context by cotar and limic ann appl probab 2009 for finite graphs with edge reinforcement we apply our new method both to edge and to vertex reinforced random walks with super linear reinforcement on arbitrary infinite connected graphs of bounded degree we stress that unlike all previous results for processes with super linear reinforcement we make no other assumption on the graphs for edge reinforced random walks we complete the results of limic and tarr es ann probab 2007 and we settle a conjecture of sellke technical report 94 26 purdue university 1994 by showing that for any reciprocally summable reinforcement weight function w the walk traverses a random attracting edge at all large times for vertex reinforced random walks we extend results previously obtained on z by volkov ann probab 2001 and by basdevant schapira and singh ann probab 2014 and on complete graphs by benaim raimond and schapira alea 2013 we show that on any infinite connected graph of bounded degree with reinforcement weight function w taken from a general class of reciprocally summable reinforcement weight functions the walk traverses two random neighbouring attracting vertices at all large times

phase transition for the once reinforced random walk on mathbb z d like trees in this short paper we consider the once reinforced random walk with reinforcement parameter a on trees with bounded degree which are transient for the simple random walk on each of these trees we prove that there exists an explicit critical parameter a 0 such that the once reinforced random walk is almost surely recurrent if a a 0 and almost surely transient if a a 0 this provides the first examples of phase transition for the once reinforced random walk

edge reinforced random walk on one dimensional periodic graphs in the present paper linearly edge reinforced random walk is studied on a large class of one dimensional periodic graphs satisfying a certain reflection symmetry it is shown that the edge reinforced random walk is recurrent estimates for the position of the random walker are given the edge reinforced random walk has a unique representation as a random walk in a random environment where the random environment is given by random weights on the edges it is shown that these weights decay exponentially in space the distribution of the random weights equals the distribution of the asymptotic proportion of time spent by the edge reinforced random walker on the edges of the graph the results generalize work of the authors in merkl and rolles ann probab 33 6 2051 2093 2005 35 1 115 140 2007 and rolles probab theory related fields 135 2 216 264 2006 to a large class of graphs and to periodic initial weights with a reflection symmetry

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

limit theorems for reinforced random walks on certain trees consider a linearly edge reinforced random walk defined on the b ary tree b 70 we prove the strong law of large numbers for the distance of this process from the root we give a sufficient condition for this strong law to hold for general edge reinforced random walks and random walks in a random environment we also provide a central limit theorem

phase transition in reinforced random walk and rwre on trees a random walk on an infinite tree is given a particular kind of positive feedback so edges already traversed are more likely to be traversed in the future using exchangeability theory the process is shown to be equivalent to a random walk in a random environment rwre that is to say a mixture of markov chains criteria are given to determine whether a rwre is transient or recurrent these criteria apply to show that the reinforced random walk can vary from transient to recurrent depending on the value of an adjustable parameter measuring the strength of the feedback the value of the parameter at the phase transition is calculated