estimation of the false discovery proportion with unknown dependence summary large scale multiple testing with correlated test statistics arises frequently in much scientific research incorporating correlation information in approximating the false discovery proportion fdp has attracted increasing attention in recent years when the covariance matrix of test statistics is known fan and his colleagues provided an accurate approximation of the fdp under arbitrary dependence structure and some sparsity assumption however the covariance matrix is often unknown in many applications and such dependence information must be estimated before approximating the fdp the estimation accuracy can greatly affect the fdp approximation in the current paper we study theoretically the effect of unknown dependence on the testing procedure and establish a general framework such that the fdp can be well approximated the effects of unknown dependence on approximating the fdp are in the following two major aspects through estimating eigenvalues or eigenvectors and through estimating marginal variances to address the challenges in these two aspects we firstly develop general requirements on estimates of eigenvalues and eigenvectors for a good approximation of the fdp we then give conditions on the structures of covariance matrices that satisfy such requirements such dependence structures include banded or sparse covariance matrices and conditional sparse precision matrices within this framework we also consider a special example to illustrate our method where data are sampled from an approximate factor model which encompasses most practical situations we provide a good approximation of the fdp via exploiting this specific dependence structure the results are further generalized to the situation where the multivariate normality assumption is relaxed our results are demonstrated by simulation studies and some real data applications

convergence analysis of compact difference schemes for diffusion equation with nonlocal boundary conditions difference schemes for solving the diffusion equation with nonlocal boundary conditions are considered compact difference is used and the integrals are approximated by the composite simpson scheme convergence of the two compact schemes are derived using the energy method compact difference schemes for solving the diffusion equation with nonlocal boundary conditions are considered in this paper fourth order compact difference is used to approximate the second order spatial derivative and the integrals in the boundary conditions are approximated by the composite simpson quadrature formula the backward euler and crank nicolson schemes are presented as the fully discrete schemes error estimates in the discrete h1 and l norms are given by the energy method showing both schemes are fourth order accurate in space and they have first order and second order accuracy in time respectively numerical results are provided to confirm the theoretical results

changepoint estimation another look at multiple testing problems summary we consider large scale multiple testing for data that have locally clustered signals with this structure we apply techniques from change point analysis and propose a boundary detection algorithm so that the clustering information can be utilised consequently the precision of the multiple testing procedure is substantially improved we study tests with independent as well as dependent p values monte carlo simulations suggest that the methods perform well with realistic sample sizes and show improved detection ability compared with competing methods our procedure is applied to a genome wide association dataset of blood lipids

homotopy perturbation method for quadratic riccati differential equation and comparison with adomian s decomposition method abstract in this paper a homotopy perturbation method is proposed to solve quadratic riccati differential equation comparisons are made between adomian s decomposition method adm and the exact solution and the proposed method the results reveal that the proposed method is very effective and simple

false discovery control in large scale spatial multiple testing summary the paper develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals we consider both pointwise and clusterwise spatial analyses and derive oracle procedures which optimally control the false discovery rate false discovery exceedance and false cluster rate a data driven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain our multiple testing procedures are asymptotically valid and can be effectively implemented using bayesian computational algorithms for analysis of large spatial data sets numerical results show that the procedures proposed lead to more accurate error control and better power performance than conventional methods we demonstrate our methods for analysing the time trends in tropospheric ozone in eastern usa

numerical methods for fourth order elliptic equations with nonlocal boundary conditions this paper is concerned with some numerical methods for a fourth order semilinear elliptic boundary value problem with nonlocal boundary condition the fourth order equation is formulated as a coupled system of two second order equations which are discretized by the finite difference method three monotone iterative schemes are presented for the coupled finite difference system using either an upper solution or a lower solution as the initial iteration these sequences of monotone iterations called maximal sequence and minimal sequence respectively yield not only useful computational algorithms but also the existence of a maximal solution and a minimal solution of the finite difference system also given is a sufficient condition for the uniqueness of the solution this uniqueness property and the monotone convergence of the maximal and minimal sequences lead to a reliable and easy to use error estimate for the computed solution moreover the monotone convergence property of the maximal and minimal sequences is used to show the convergence of the maximal and minimal finite difference solutions to the corresponding maximal and minimal solutions of the original continuous system as the mesh size tends to zero three numerical examples with different types of nonlinear reaction functions are given in each example the true continuous solution is constructed and is used to compare with the computed solution to demonstrate the accuracy and reliability of the monotone iterative schemes

a sharper bonferroni procedure for multiple tests of significance summary a simple procedure for multiple tests of significance based on individual p values is derived this simple procedure is sharper than holm s 1979 sequentially rejective procedure both procedures contrast the ordered p values with the same set of critical values holm s procedure rejects an hypothesis only if its p value and each of the smaller p values are less than their corresponding critical values the new procedure rejects all hypotheses with smaller or equal p values to that of any one found less than its critical value

stability of the weighted splitting finite difference scheme for a two dimensional parabolic equation with two nonlocal integral conditions nonlocal conditions arise in mathematical models of various physical chemical or biological processes therefore interest in developing computational techniques for the numerical solution of partial differential equations pdes with various types of nonlocal conditions has been growing fast we construct and analyse a weighted splitting finite difference scheme for a two dimensional parabolic equation with nonlocal integral conditions the main attention is paid to the stability of the method we apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite difference scheme we demonstrate that depending on the parameters of the finite difference scheme and nonlocal conditions the proposed method can be stable or unstable the results of numerical experiments with several test problems are also presented and they validate theoretical results

new method based on the hpm and rkhsm for solving forced duffing equations with integral boundary conditions this paper investigates the forced duffing equation with integral boundary conditions its approximate solution is developed by combining the homotopy perturbation method hpm and the reproducing kernel hilbert space method rkhsm hpm is based on the use of the traditional perturbation method and the homotopy technique the hpm can reduce nonlinear problems to some linear problems and generate a rapid convergent series solution in most cases rkhsm is also an analytical technique which can solve powerfully linear boundary value problems therefore the forced duffing equation with integral boundary conditions can be solved using advantages of these two methods two numerical examples are presented to illustrate the strength of the method

innovated higher criticism for detecting sparse signals in correlated noise higher criticism is a method for detecting signals that are both sparse and weak although first proposed in cases where the noise variables are independent higher criticism also has reasonable performance in settings where those variables are correlated in this paper we show that by exploiting the nature of the correlation performance can be improved by using a modified approach which exploits the potential advantages that correlation has to offer indeed it turns out that the case of independent noise is the most difficult of all from a statistical viewpoint and that more accurate signal detection for a given level of signal sparsity and strength can be obtained when correlation is present we characterize the advantages of correlation by showing how to incorporate them into the definition of an optimal detection boundary the boundary has particularly attractive properties when correlation decays at a polynomial rate or the correlation matrix is toeplitz

stability of difference schemes for two dimensional parabolic equations with non local boundary conditions the stability of difference schemes for one dimensional and two dimensional parabolic equations subject to non local bitsadze samarskii type boundary conditions is dealt with to analyze the stability of difference schemes the structure of the spectrum of the matrix that defines the linear system of difference equations for a respective stationary problem is studied depending on the values of parameters in non local conditions this matrix can have one zero one negative or complex eigenvalues the stepwise stability is proved and the domain of stability of difference schemes is found

correlated z values and the accuracy of large scale statistical estimates we consider large scale studies in which there are hundreds or thousands of correlated cases to investigate each represented by its own normal variate typically a z value a familiar example is provided by a microarray experiment comparing healthy with sick subjects expression levels for thousands of genes this paper concerns the accuracy of summary statistics for the collection of normal variates such as their empirical cdf or a false discovery rate statistic it seems like we must estimate an n by n correlation matrix n the number of cases but our main result shows that this is not necessary good accuracy approximations can be based on the root mean square correlation over all n n 1 2 pairs a quantity often easily estimated a second result shows that z values closely follow normal distributions even under nonnull conditions supporting application of the main theorem practical application of the theory is illustrated for a large leukemia microarray study

on large toeplitz band matrices with an uncertain block abstract this paper investigates the possible spectra of large finite dimensional toeplitz band matrices with perturbations impurities uncertainties in the upper left m m block the main result shows that the asymptotic spectrum of such a matrix is not affected by these perturbations provided they have sufficiently small norm this follows from analysis of structured pseudospectra structured spectral value sets in contrast for typical non hermitian toeplitz matrices there exist certain rank one perturbations of arbitrarily small norm that move an eigenvalue away from the asymptotic spectrum in the large dimensional limit

on the solutions of a boundary value problem of linear thermoelasticity system with nonlocal conditions abstract this paper studies a boundary value problem with nonlocal conditions for a coupled system of linear thermoelasticity in one dimensional case using an a priori estimate we prove the uniqueness of the solution also some explicit solutions are obtained by using the separation method

on optimality of stepdown and stepup multiple test procedures consider the multiple testing problem of testing k null hypotheses where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption attention is restricted to procedures that control the familywise error rate in the strong sense and which satisfy a monotonicity condition under these assumptions we prove certain maximin optimality results for some well known stepdown and stepup procedures

predicting false discovery proportion under dependence we present a flexible framework for predicting error measures in multiple testing situations under dependence our approach is based on modeling the distribution of the probit transform of the p values by mixtures of multivariate skew normal distributions the model can incorporate dependence among p values and it allows for shape restrictions on the p value density a nonparametric bayesian scheme for estimating the components of the mixture model is outlined and markov chain monte carlo algorithms are developed these lead to the prediction of false discovery proportion and related credible bands an expression for the positive false discovery rate for dependent observations is also derived the power of the mixture model in estimation of key quantities in multiple testing is illustrated by a simulation study a dataset on kidney transplant is also analyzed using the methods developed

eigenvalues of tridiagonal pseudo toeplitz matrices abstract in this article we determine the eigenvalues of sequences of tridiagonal matrices that contain a toeplitz matrix in the upper left block

solving singular two point boundary value problem in reproducing kernel space in this paper we present a new method for solving singular two point boundary value problem for certain ordinary differential equation having singular coefficients its exact solution is represented in the form of series in reproducing kernel space in the mean time the n term approximation u n x to the exact solution u x is obtained and is proved to converge to the exact solution some numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other

on the solvability of a class of nonlinear singular parabolic equation with integral boundary condition abstract in this paper the existence and uniqueness of a weak solution for nonlinear singular parabolic equation with integral boundary conditions is proved first the associated linear problem is solved after writing the linear problem on its operatorial form we establish an a priori bound from which we deduce the uniqueness of the strong solution for the solvability of the associated linear problem we prove that the range of the operator generated by the considered problem is dense on the basis of the obtained results of the linear problem we apply an iterative process to establish the existence and uniqueness of the weak solution of the nonlinear problem

robustness of multiple testing procedures against dependence an important aspect of multiple hypothesis testing is controlling the significance level or the level of type i error when the test statistics are not independent it can be particularly challenging to deal with this problem without resorting to very conservative procedures in this paper we show that in the context of contemporary multiple testing problems where the number of tests is often very large the difficulties caused by dependence are less serious than in classical cases this is particularly true when the null distributions of test statistics are relatively light tailed for example when they can be based on normal or student s t approximations there if the test statistics can fairly be viewed as being generated by a linear process an analysis founded on the incorrect assumption of independence is asymptotically correct as the number of hypotheses diverges in particular the point process representing the null distribution of the indices at which statistically significant test results occur is approximately poisson just as in the case of independence the poisson process also has the same mean as in the independence case and of course exhibits no clustering of false discoveries however this result can fail if the null distributions are particularly heavy tailed there clusters of statistically significant results can occur even when the null hypothesis is correct we give an intuitive explanation for these disparate properties in light and heavy tailed cases and provide rigorous theory underpinning the intuition

fuzzy pretopological spaces and their representation today it is obvious that topology and uniformity and the many related theories have and will have a fundamental play in applied sciences every representation of real entities in a mathematical language necessarily implies a topological study of its goodness it is a problem of linguistic translation continuity as defined by hammer 71 this translation must preserved some important features of the original the power of actual digital computers enables us to use new ways in automatic pattern recognition but at the same time it shows us the many difficulties we encounter in searching a proper formulation of the topological concepts that everyone has in mind and uses in a naturally and more or less conscientious fashion one of the first axiomatisations of the concept of topological space was done by hausdorff and it is not so old it is only recently that some authors have thought if necessary to generalize these concepts and have obtained practical applications for instance appert 11 hammer 6 71 brissaud 3 mougeot auray duru 2 this has been especially motivated by the necessity of finding new concepts which well apply to finite sets and approx imations as hammer remarks topologists actually had one model in ind the real continuum and its generated euclidean spaces but not approximation and certainly not finite sets we think that the effort of interpretation and application to many fields such as linguistics system theory and education made by hammer is of great importance 7 and its references an important discovery in system theory which has been inforpally stated as a principle by zadeh 111 is as the complexity of a system increases our ability to make precise and yet significant statements about its behaviour diminishes until a threshold is reached beyond which precision and significance become almost mutually exclusive characteristics this principle is very close to limit problems and paradoxes encountered by physicians in particular the similitude with the heisenberg uncertainty prin ciple is clear it is certainly a motivation for the use of fuzzy set theory but these two aspects pretopology or extended topology as named by hammer

influence of complex coefficients on the stability of difference scheme for parabolic equations with non local conditions abstract the stability of a finite difference scheme for schrodinger kuramoto tsuzuki and parabolic equations subject to non local conditions with complex coefficients is dealt with the stability conditions which have to be met by complex coefficients in non local conditions have been determined the main result of this study is that complex coefficients together with non local conditions cause new effects on the stability of difference scheme numerical experiment has revealed additional regularities in the stability conditions

numerical spectral analysis of a difference operator with non local boundary conditions abstract the spectrum of a finite difference operator subject to non local robin type boundary conditions is dealt with we analyse the spectral properties that relate to the stability of finite difference schemes for parabolic equations the impact of functions and parameters defining non local conditions on a spectral structure is examined and theoretical study is supported by numerical experiments also for a difference scheme applied to a parabolic equation with non local conditions a sufficient stability criterion based on spectral properties of the difference operator is discussed numerical evidence suggests that such a criterion is not only sufficient for stability but necessary too

asymptotic optimality of the westfall young permutation procedure for multiple testing under dependence test statistics are often strongly dependent in large scale multiple testing applications most corrections for multiplicity are unduly conservative for correlated test statistics resulting in a loss of power to detect true positives we show that the westfallyoung permutation method has asymptotically optimal power for a broad class of testing problems with a block dependence and sparsity structure among the tests when the number of tests tends to infinity

methods correcting for multiple testing operating characteristics we examine the operating characteristics of 17 methods for correcting p values for multiple testing on synthetic data with known statistical properties these methods are derived p values only and not the raw data with the test cases we systematically varied the number of p values the proportion of false null hypotheses the probability that a false null hypothesis would result in a p value less than 5 per cent and the degree of correlation between p values we examined the effect of each of these factors on family wise and false negative error rates and compared the false negative error rates of methods with an acceptable family wise error only four methods were not bettered in this comparison unfortunately however a uniformly best method of those examined does not exist a suggested strategy for examining corrections uses a succession of methods that are increasingly lax in family wise error a computer program for these corrections is available

similarity of fuzzy sets application to r n as a substratum in this paper we apply to real spaces the concept of similarity relation on fuzzy sets the underlying topological space is said to play the role of an expression substratum these relations can be used to define relative positions of expression of fuzzy sets groups of homeomorphisms of a topological space are important they are representative of the symmetries of the space we give very simple examples to clarify these rather abstract notions

false discovery rate regression an application to neural synchrony detection in primary visual cortex this article introduces false discovery rate regression a method for incorporating covariate information into large scale multiple testing problems fdr regression estimates a relationship between test level covariates and the prior probability that a given observation is a signal it then uses this estimated relationship to inform the outcome of each test in a way that controls the overall false discovery rate at a prespecified level this poses many subtle issues at the interface between inference and computation and we investigate several variations of the overall approach simulation evidence suggests that 1 when covariate effects are present fdr regression improves power for a fixed false discovery rate and 2 when covariate effects are absent the method is robust in the sense that it does not lead to inflated error rates we apply the method to neural recordings from primary visual cortex the goal is to detect pairs of neurons that exhibit fine time scale interactions in the sense that t

the exact solution of system of linear operator equations in reproducing kernel spaces abstract in this paper we discuss the problem of how to solve the system of linear operator equations in hilbert spaces and applied the result to reproducing kernel spaces under the assumption that the operator equations has a unique solution its formal solution is given as a result when h h 1 are both reproducing kernel spaces the formal solution turned into analytic solution truncating the series where formal solution and the analytic solution are denoted by a series the approximate solution of the operator equations is obtained when increasing the number of the nodes the error of the approximate solution is monotone decreasing in the sense of the norm of the hilbert space the final numerical experiment shows the efficiency of our method

robustness and accuracy of methods for high dimensional data analysis based on student s t statistic summary student s t statistic is finding applications today that were never envisaged when it was introduced more than a century ago many of these applications rely on properties e g robustness against heavy tailed sampling distributions that were not explicitly considered until relatively recently we explore these features of the t statistic in the context of its application to very high dimensional problems including feature selection and ranking the simultaneous testing of many different hypotheses and sparse high dimensional signal detection robustness properties of the t ratio are highlighted and it is established that those properties are preserved under applications of the bootstrap in particular bootstrap methods correct for skewness and therefore lead to second order accuracy even in the extreme tails indeed it is shown that the bootstrap and also the more popular but less accurate t distribution and normal approximations are more effective in the tails than towards the middle of the distribution these properties motivate new methods e g bootstrap based techniques for signal detection that confine attention to the significant tail of a statistic

smooth topological spaces abstract in 1986 badard introduced the concept of a smooth topological space in this paper we give some links between smooth topological spaces and the corresponding results in chang s fuzzy topological spaces the concepts of subspace continuity and compactness are studied

the control of the false discovery rate in multiple testing under dependency benjamini and hochberg suggest that the false discovery rate may be the appropriate error rate to control in many applied multiple testing problems a simple procedure was given there as an fdr controlling procedure for independent test statistics and was shown to be much more powerful than comparable procedures which control the traditional familywise error rate we prove that this same procedure also controls the false discovery rate when the test statistics have positive regression dependency on each of the test statistics corresponding to the true null hypotheses this condition for positive dependency is general enough to cover many problems of practical interest including the comparisons of many treatments with a single control multivariate normal test statistics with positive correlation matrix and multivariate t furthermore the test statistics may be discrete and the tested hypotheses composite without posing special difficulties for all other forms of dependency a simple conservative modification of the procedure controls the false discovery rate thus the range of problems for which a procedure with proven fdr control can be offered is greatly increased 1 1 simultaneous hypotheses testing the control of the increased type i error when testing simultaneously a family of hypotheses is a central issue in the area of multiple comparisons rarely are we interested only in whether all hypotheses are jointly true or not which is the test of the intersection null hypothesis in most applications we infer about the individual hypotheses realizing that some of the tested hypotheses are usually true we hope not all and some are not we wish to decide which ones are not true indicating statistical discoveries an important such problem is that of multiple endpoints in a clinical trial a new treatment is compared with an existing one in terms of a large number of potential benefits endpoints

stepwise stability for the heat equation with a nonlocal constraint the authors prove the stepwise stability for a finite difference scheme for the heat equation with an integral constraint the resulting matrix is nonsymmetric and does not have the usual band structure the proof is based on the method of matrix analysis the eigenvalues of several matrices are found explicitly or their location described precisely this method relies upon the relationship of the characteristic polynomials of these matrices with orthogonal polynomials

false discovery and false nondiscovery rates in single step multiple testing procedures results on the false discovery rate fdr and the false nondiscovery rate fnr are developed for single step multiple testing procedures in addition to verifying desirable properties of fdr and fnr as measures of error rates these results extend previously known results providing further insights particularly under dependence into the notions of fdr and fnr and related measures first considering fixed configurations of true and false null hypotheses inequalities are obtained to explain how an fdr or fnr controlling single step procedure such as a bonferroni or sidak procedure can potentially be improved two families of procedures are then constructed one that modifies the fdr controlling and the other that modifies the fnr controlling sidak procedure these are proved to control fdr or fnr under independence less conservatively than the corresponding families that modify the fdr or fnr controlling bonferroni procedure results of numerical investigations of the performance of the modified sidak fdr procedure over its competitors are presented second considering a mixture model where different configurations of true and false null hypotheses are assumed to have certain probabilities results are also derived that extend some of storey s work to the dependence case

a galerkin method for two dimensional hyperbolic integro differential equation with purely integral conditions the present paper is devoted to the solution for two dimensional hyperbolic integro differential equations subject to purely integral conditions first it is demonstrated the existence and uniqueness of the solution under certain conditions for the numerical approach a galerkin method based on least squares is proposed the numerical examples illustrate the technique and show the efficiency of the proposed method

expressions on a fuzzy pretopological substratum in this paper we define similarity relations on fuzzy sets of a pretopological space the underlying pretopological space will be said to play the role of an expression substratum we compare these relations with pretopological homeomorphisms these relations can be used to define relative positions of expression of fuzzy sets groups of homeomorphisms of a pretopological space are key concepts they are representative of some symmetries of the space we give very simple examples to clarify these rather abstract notions

confounder adjustment in multiple hypothesis testing we consider large scale studies in which thousands of significance tests are performed simultaneously in some of these studies the multiple testing procedure can be severely biased by latent confounding factors such as batch effects and unmeasured covariates that correlate with both primary variable s of interest e g treatment variable phenotype and the outcome over the past decade many statistical methods have been proposed to adjust for the confounders in hypothesis testing we unify these methods in the same framework generalize them to include multiple primary variables and multiple nuisance variables and analyze their statistical properties in particular we provide theoretical guarantees for ruv 4 gagnon bartsch jacob and speed 2013 and leapp ann appl stat 6 2012 1664 1688 which correspond to two different identification conditions in the framework the first requires a set of negative controls that are known a priori to follow the null distribution the second requires the true nonnulls to be sparse two different estimators which are based on ruv 4 and leapp are then applied to these two scenarios we show that if the confounding factors are strong the resulting estimators can be asymptotically as powerful as the oracle estimator which observes the latent confounding factors for hypothesis testing we show the asymptotic z tests based on the estimators can control the type i error numerical experiments show that the false discovery rate is also controlled by the benjamini hochberg procedure when the sample size is reasonably large

a sequentially rejective test procedure based on a modified bonferroni inequality summary a sharper bonferroni procedure for multiple tests of significance is derived this procedure is an improvement of hochberg s 1988 procedure which contrasts the individual p values with corresponding critical points it is shown that hochberg s original procedure is conservative and can be made more powerful by enlarging the rejection region so that the type one error is exactly at the nominal level it is also shown that the modified procedure retains all the desired properties of the original procedure

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

adaptive absorbing boundary conditions for schrodinger type equations application to nonlinear and multi dimensional problems we propose an adaptive approach in picking the wave number parameter of absorbing boundary conditions for schrodinger type equations based on the gabor transform which captures local frequency information in the vicinity of artificial boundaries the parameter is determined by an energy weighted method and yields a quasi optimal absorbing boundary conditions it is shown that this approach can minimize reflected waves even when the wave function is composed of waves with different group velocities we also extend the split local absorbing boundary slab method z xu h han phys rev e 74 2006 037704 to problems in multi dimensional nonlinear cases by coupling the adaptive approach numerical examples of nonlinear schrodinger equations in one and two dimensions are presented to demonstrate the properties of the discussed absorbing boundary conditions

adomian method for a class of hyperbolic equations with an integral condition abstract in this paper adomian decomposition method adm is applied to the solvability of a boundary problem with a nonlocal condition for a class of hyperbolic equations and illustrated with a few simple examples

solving nonlocal initial boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations by the adomian decomposition method in this paper we present a new approach to solve nonlocal initial boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations subject to initial and nonlocal boundary conditions of integral type we first transform the given nonlocal initial boundary value problems of integral type for the linear and nonlinear parabolic and hyperbolic partial differential equations into local dirichlet initial boundary value problems and then use a relatively new modified adomian decomposition method adm furthermore we investigate the fourier adomian method which also does not require any a priori assumptions on the solution for the solution of nonlocal initial boundary value problems combined with our new approach several examples are presented to demonstrate the efficiency of the adm