variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

trajectory generation for the n trailer problem using goursat normal form develops the machinery of exterior differential forms more particularly the goursat normal form for a pfaffian system for solving nonholonomic motion planning problems i e motion planning for systems with nonintegrable velocity constraints the authors use this technique to solve the problem of steering a mobile robot with n trailers the authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the goursat canonical form two of these transformations are studied in detail the goursat normal form for exterior differential systems is dual to the so called chained form for vector fields that has been studied previously consequently the authors are able to give the state feedback law and change of coordinates to convert the n trailer system into chained form three methods for planning trajectories for chained form systems using sinusoids piecewise constants and polynomials as inputs are presented the motion planning strategy is therefore to first convert the n trailer system into goursat form use this to find the chained form coordinates plan a path for the corresponding chained form system and then transform the resulting trajectory back into the original coordinates simulations and frames of movie animations of the n trailer system for parallel parking and backing into a loading dock using this strategy are included

direct estimation of the fiber orientation density function from diffusion weighted mri data using spherical deconvolution diffusion weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers the diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel however this model has been shown to fail in regions containing several fiber populations with distinct orientations a number of alternative models have been suggested such as multiple tensor fitting q space and q ball imaging however each of these has inherent limitations in this study we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion weighted mr data without the need for prior assumptions regarding the number of fiber populations present we assume that all white matter fiber bundles in the brain share identical diffusion characteristics thus implicitly assigning any differences in diffusion anisotropy to partial volume effects the diffusion weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function the diffusion weighted attenuation profile for a typical fiber bundle with the fiber orientation density function odf the fiber odf the distribution of fiber orientations within the voxel can therefore be obtained using spherical deconvolution the properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1 5 t clinical scanner the technique can recover the fiber odf in regions of multiple fiber crossing and holds promise for applications such as tractography

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

prolongational limit sets of control systems abstract this article introduces the notions of prolongations and prolongational limit sets of control systems it is shown how the prolongational limit sets play in studying recursive and dispersive concepts of control systems

approximate solutions for boundary value problems of time fractional wave equation in this article we implement relatively a new analytical technique the adomian decomposition method for solving the boundary value problems of time fractional wave equation the fractional derivative is described in the caputo sense the decomposition method is used to construct analytical approximate solutions of time fractional wave equation subject to specified boundary conditions the solutions are calculated in the form of a convergent series with easily computable components some examples are given the results reveal that the adomian method is very effective and convenient

probabilistic diffusion tractography with multiple fibre orientations what can we gain we present a direct extension of probabilistic diffusion tractography to the case of multiple fibre orientations using automatic relevance determination we are able to perform online selection of the number of fibre orientations supported by the data at each voxel simplifying the problem of tracking in a multi orientation field we then apply the identical probabilistic algorithm to tractography in the multi and single fibre cases in a number of example systems which have previously been tracked successfully or unsuccessfully with single fibre tractography we show that multi fibre tractography offers significant advantages in sensitivity when tracking non dominant fibre populations but does not dramatically change tractography results for the dominant pathways

variational iteration method new development and applications variational iteration method has been favourably applied to various kinds of nonlinear problems the main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper recent trends and developments in the use of the method are reviewed major applications to nonlinear wave equation nonlinear fractional differential equations nonlinear oscillations and nonlinear problems arising in various engineering applications are surveyed the confluence of modern mathematics and symbol computation has posed a challenge to developing technologies capable of handling strongly nonlinear equations which cannot be successfully dealt with by classical methods variational iteration method is uniquely qualified to address this challenge the flexibility and adaptation provided by the method have made the method a strong candidate for approximate analytical solutions this paper outlines the basic conceptual framework of variational iteration technique with application to nonlinear problems both achievements and limitations are discussed with direct reference to approximate solutions for nonlinear equations a new iteration formulation is suggested to overcome the shortcoming a very useful formulation for determining approximately the period of a nonlinear oscillator is suggested examples are given to illustrate the solution procedure

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

an efficient method for solving systems of fractional integro differential equations in this study a decomposition method for approximating the solution of systems of fractional integro differential equations is implemented the fractional derivative is considered in the caputo sense the approximate solutions are calculated in the form of a convergent series with easily computable components numerical results show that this approach is easy to implement and accurate when applied to integro differential equations

analytical solution of a time fractional navier stokes equation by adomian decomposition method abstract the aim of the present analysis is to apply adomian decomposition method for the solution of a time fractional navier stokes equation in a tube by using an initial value the explicit solution of the equation has been presented in the closed form and then its numerical solution has been represented graphically the present method performs extremely well in terms of efficiency and simplicity

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

unified bundling and registration of brain white matter fibers magnetic resonance diffusion tensor imaging is being widely used to reconstruct brain white matter fiber tracts to characterize structural properties of the tracts reconstructed fibers are often grouped into bundles that correspond to coherent anatomic structures for further group analysis of fiber bundles it is desirable that corresponding bundles from different studies are coregistered to address these needs simultaneously a unified fiber bundling and registration ufibre framework is proposed in this work the framework is based on maximizing a posteriori bayesian probabilities using an expectation maximization algorithm given a set of segmented template bundles and a whole brain target fiber set the ufibre algorithm optimally bundles the target fibers and registers them with the template the bundling component in the ufibre algorithm simplifies fiber based registration into bundle to bundle registration and the registration component in turn guides the bundling process to find bundles consistent with the template experiments with in vivo data demonstrate that the estimated bundles have an 80 consistency with ground truth and the root mean square error between their bundle medial axes is less than one voxel the proposed algorithm is highly efficient offering potential routine use for group analysis of white matter fibers

a new modification of the adomian decomposition method for linear and nonlinear operators in this paper we present an efficient modification of the adomian decomposition method that will facilitate the calculations we then conduct a comparative study between the new modification and the modified decomposition method the study is conducted through illustrative examples the new modification introduces a promising tool for many linear and nonlinear models

variational iteration method for solving nonlinear boundary value problems abstract in this paper he s variational iteration method is implemented to give approximate and analytical solutions for a class of boundary value problems the variational iteration method which produces the solutions in terms of convergent series requiring no linearization or small perturbation numerical examples are given and comparisons are made with the adomian decomposition method the fact that this method solves nonlinear equations without using adomian polynomials can be considered as an advantage of this method over adomian decomposition method

tract based morphometry for white matter group analysis we introduce an automatic method that we call tract based morphometry or tbm for measurement and analysis of diffusion mri data along white matter fiber tracts using subject specific tractography bundle segmentations we generate an arc length parameterization of the bundle with point correspondences across all fibers and all subjects allowing tract based measurement and analysis in this paper we present a quantitative comparison of fiber coordinate systems from the literature and we introduce an improved optimal match method that reduces spatial distortion and improves intra and inter subject variability of fa measurements we propose a method for generating arc length correspondences across hemispheres enabling a tbm study of interhemispheric diffusion asymmetries in the arcuate fasciculus af and cingulum bundle cb the results of this study demonstrate that tbm can detect differences that may not be found by measuring means of scalar invariants in entire tracts such as the mean diffusivity md differences found in af we report tbm results of higher fractional anisotropy fa in the left hemisphere in af caused primarily by lower 3 the smallest eigenvalue of the diffusion tensor in the left af and higher left hemisphere fa in cb related to higher 1 the largest eigenvalue of the diffusion tensor in the left cb by mapping the significance levels onto the tractography trajectories for each structure we demonstrate the anatomical locations of the interhemispheric differences the tbm approach brings analysis of dti data into the clinically and neuroanatomically relevant framework of the tract anatomy

the variational iteration method for solving linear and nonlinear systems of pdes in this work the variational iteration method vim is used for analytic treatment of the linear and nonlinear systems of partial differential equations the method reduces the calculation size and overcomes the difficulty of handling nonlinear terms numerical examples are examined to highlight the significant features of the vim method the method shows improvements over existing numerical techniques

analytical approximate solutions for nonlinear fractional differential equations we consider a class of nonlinear fractional differential equations fdes based on the caputo fractional derivative and by extending the application of the adomian decomposition method we derive an analytical solution in the form of a series with easily computable terms for linear equations the method gives exact solution and for non linear equations it provides an approximate solution with good accuracy several examples are discussed

numerical solution of non linear klein gordon equations by variational iteration method in this paper numerical solution of non linear klein gordon equations with power law non linearities are obtained by the new application of he s variational iteration method numerical illustrations that include non linear klein gordon equations and non linear partial differential equations are investigated to show the pertinent features of the technique copyright 2006 john wiley sons ltd

sufficient conditions for dispersiveness of invariant control affine systems on the heisenberg group abstract the notion of dispersiveness in control systems is characterized by the absence of recursive properties it implies uncontrollability and poisson instability the present manuscript exhibits sufficient conditions for an invariant control affine system on the heisenberg group to be dispersive for a control affine system with pairwise commutative matrices the condition for dispersiveness is the drift not depend linearly on the controlled matrices for a general control affine system with bounded control range the condition is the drift not be an affine transformation of the controlled matrices these results consequently yield necessary conditions for controllability

numerical approach to differential equations of fractional order in this paper the variational iteration method and the adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order the two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations in these schemes the solution takes the form of a convergent series with easily computable components this paper presents a numerical comparison between the two methods for solving systems of fractional differential equations numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order

fibertract segmentation in position orientation space from high angular resolution diffusion mri in diffusion mri standard approaches for fibertract identification are based on algorithms that generate lines of coherent diffusion currently known as tractography a tract is then identified as a set of such lines selected on some criteria in the present study we investigate whether fibertract identification can be formulated as a segmentation task that recognizes a fibertract as a region where diffusion is intense and coherent indeed we show that it is possible to segment efficiently well known fibertracts with classical image processing methods provided that the problem is formulated in a five dimensional space of position and orientation as an example we choose to adapt to this newly defined high dimensional non euclidean space called position orientation space an algorithm based on the hidden markov random field framework structures such as the cerebellar peduncles corticospinal tract association bundles can be identified and represented in three dimensions by a back projection technique similar to maximum intensity projection potential advantages and drawbacks as compared to classical tractography are discussed for example it appears that our formulation handles naturally crossing tracts and is not biased by human intervention

variational iteration method for elastodynamic green s functions abstract in this study a new application of the variational iteration method is presented we use this method to obtain approximations to 3d green s function for the dynamic system of anisotropic elasticity the numerical results obtained from convolution of green s function and data of the cauchy problem are compared with the exact solution for cubic media

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

an iterative method for solving nonlinear functional equations an iterative method for solving nonlinear functional equations viz nonlinear volterra integral equations algebraic equations and systems of ordinary differential equation nonlinear algebraic equations and fractional differential equations has been discussed

atlas based fiber bundle segmentation using principal diffusion directions and spherical harmonic coefficients abstract purpose to develop an automatic atlas based method for segmentation of fiber bundles using high angular resolution diffusion imaging hardi data hypothesis quantitative evaluation of diffusion characteristics inside specific fiber bundles provides new insights into disease developments evolutions therapy effects and surgical interventions background most of previous segmentation methods use similarity measures and strategies that do not lead to accurate segmentation results they also suffer from subjectivity of initial seeds and regions of interest roi defined by operator materials and methods we propose a novel method that uses spherical harmonic coefficients shc of hardi diffusion signals to compute orientation distribution function odf and to extract principal diffusion directions pdds the proposed method selects most collinear pdd of neighbors of each voxel then based on shc and selected pdd a similarity measure is proposed and used as a speed function in the level set framework that segments fiber bundles to automate the process an atlas based method is used to select initial seeds for fiber bundles to generate data for evaluation of the proposed method an artificial pattern consisting of three crossing bundles intersected by a circular bundle is created also two normal controls are imaged by two different hardi protocols results segmentation results for different fiber bundles in simulated data and normal control data are presented influence of threshold selection on the proposed segmentation method is evaluated using dice coefficient also effect of increasing the number of gradient directions on accuracy of extracted pdds is evaluated conclusion the proposed segmentation method has advantages over previous methods especially those that use similarity measures based on diffusion tensor imaging dti data these advantages are achieved by proper propagation of a hyper surface in fiber crossing areas without making assumptions about diffusivity profile and selection of initial seeds or roi

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

clustering method for estimating principal diffusion directions diffusion tensor magnetic resonance imaging dtmri is a non invasive tool for the investigation of white matter structure within the brain however the traditional tensor model is unable to characterize anisotropies of orders higher than two in heterogeneous areas containing more than one fiber population to resolve this issue high angular resolution diffusion imaging hardi with a large number of diffusion encoding gradients is used along with reconstruction methods such as q ball using hardi data the fiber orientation distribution function odf on the unit sphere is calculated and used to extract the principal diffusion directions pdds fast and accurate estimation of pdds is a prerequisite for tracking algorithms that deal with fiber crossings in this paper the pdds are defined as the directions around which the odf data is concentrated estimates of the pdds based on this definition are less sensitive to noise in comparison with the previous approaches a clustering approach to estimate the pdds is proposed which is an extension of fuzzy c means clustering developed for orientation of points on a sphere mdl minimum description length principle is proposed to estimate the number of pdds using both simulated and real diffusion data the proposed method has been evaluated and compared with some previous protocols experimental results show that the proposed clustering algorithm is more accurate more resistant to noise and faster than some of techniques currently being utilized

dti segmentation by statistical surface evolution we address the problem of the segmentation of cerebral white matter structures from diffusion tensor images dti a dti produces from a set of diffusion weighted mr images tensor valued images where each voxel is assigned with a 3 times 3 symmetric positive definite matrix this second order tensor is simply the covariance matrix of a local gaussian process with zero mean modeling the average motion of water molecules as we will show in this paper the definition of a dissimilarity measure and statistics between such quantities is a nontrivial task which must be tackled carefully we claim and demonstrate that by using the theoretically well founded differential geometrical properties of the manifold of multivariate normal distributions it is possible to improve the quality of the segmentation results obtained with other dissimilarity measures such as the euclidean distance or the kullback leibler divergence the main goal of this paper is to prove that the choice of the probability metric i e the dissimilarity measure has a deep impact on the tensor statistics and hence on the achieved results we introduce a variational formulation in the level set framework to estimate the optimal segmentation of a dti according to the following hypothesis diffusion tensors exhibit a gaussian distribution in the different partitions we must also respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the dti we show how to express all the statistical quantities for the different probability metrics we validate and compare the results obtained on various synthetic data sets a biological rat spinal cord phantom and human brain dtis

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation