removing the effects of task related motion using independent component analysis task related motion is a major source of noise in functional magnetic resonance imaging fmri time series the motion effect usually persists even after perfect spatial realignment is achieved here we propose a new method to remove a certain type of task related motion effect that persists after realignment the procedure consists of the following the decomposition of the realigned time series data into spatially independent components using independent component analysis ica the automatic classification and rejection of the ics of the task related residual motion effects and finally a reconstruction without them to classify the ics we utilized the associated task related changes in signal intensity and variance the effectiveness of the method was verified using an fmri experiment that explicitly included head motion as a main effect the results indicate that our ica based method removed the task related motion effects more effectively than the conventional voxel wise regression based method

empirical analyses of bold fmri statistics ii spatially smoothed data collected under null hypothesis and experimental conditions in the companion to this paper e zarahn g k aguirre and m d esposito 1997 neuroimage 179 197 we describe an implementation of a general linear model for autocorrelated observations in which the voxel wise false positive rates in fmri noise datasets were stabilized and brought close to theoretical values here implementations of the model are tested for use with statistical parametric mapping analysis of spatially smoothed fmri data analyses using varying models of intrinsic temporal autocorrelation and either including or excluding a global signal covariate were conducted upon human subject data collected under null hypothesis as well as under experimental conditions we found that smoothing with an empirically derived impulse response function irf combined with a model of the intrinsic temporal autocorrelation in spatially smoothed fmri data resulted in a map wise false positive rate which did not exceed a 5 level when a nominal alpha 0 05 tabular threshold was applied use of other models of intrinsic temporal autocorrelation resulted in map wise false positive rates that significantly exceeded this level fmri data collected while subjects performed a behavioral task were used to examine a task dependent global signal changes and b the dependence of sensitivity on the temporal smoothing kernel and inclusion exclusion of a global signal covariate the global signal changes within an fmri dataset were shown to be influenced by the performance of a behavioral task however the inclusion of this measure as a covariate did not have an adverse affect upon our measure of sensitivity finally use of an empirically derived estimate of the irf of the system was shown to result in greater map wise sensitivity for signal changes than the use of a broader in time poisson parameter 8 s kernel

single shot compensation of image distortions and bold contrast optimization using multi echo epi for real time fmri abstract functional magnetic resonance imaging fmri is most commonly based on echo planar imaging epi with higher field strengths gradient performance and computational power real time fmri has become feasible that is brain activation can be monitored during the ongoing scan however epi suffers from geometric distortions due to inhomogeneities of the magnetic field especially close to air tissue interfaces thus functional activations might be mislocalized and assigned to the wrong anatomical structures several techniques have been reported which reduce geometric distortions for example mapping of the static magnetic field b0 or the point spread function for all voxels yet these techniques require additional reference scans and in some cases extensive computational time moreover only static field inhomogeneities can be corrected because the correction is based on a static reference scan we present an approach which allows for simultaneous acquisition and distortion correction of a functional image without a reference scan the technique is based on a modified multi echo epi data acquisition scheme using a phase encoding pe gradient with alternating polarity the images exhibit opposite distortions due to the inverted pe gradient after adjusting the contrast of the images acquired at different echo times this information is used for the distortion correction we present the theory implementation and applications of this single shot distortion correction significant reduction in geometric distortion is shown both for phantom images and human fmri data moreover sensitivity to the blood oxygen level dependent bold effect is increased by weighted summation of the undistorted images

bayesian second level analysis of functional magnetic resonance images we propose a new method for the second level analysis of functional mri data based on bayesian statistics our method does not require a computationally costly bayesian model on the first level of analysis rather modeling for single subjects is realized by means of the commonly applied general linear model on the basis of the resulting parameter estimates for single subjects we calculate posterior probability maps and maps of the effect size for effects of interest in groups of subjects a comparison of this method with the conventional analysis based on t statistics shows that the new approach is more robust against outliers moreover our method overcomes some of the severe problems of null hypothesis significance tests such as the need to correct for multiple comparisons and facilitates inferences which are hard to formulate in terms of classical inferences

nirs spm statistical parametric mapping for near infrared spectroscopy near infrared spectroscopy nirs is a non invasive method to measure brain activity via changes in the degree of hemoglobin oxygenation through the intact skull as optically measured hemoglobin signals strongly correlate with bold signals simultaneous measurement using nirs and fmri promises a significant mutual enhancement of temporal and spatial resolutions although there exists a powerful statistical parametric mapping tool in fmri current public domain statistical tools for nirs have several limitations related to the quantitative analysis of simultaneous recording studies with fmri in this paper a new public domain statistical toolbox known as nirs spm is described it enables the quantitative analysis of nirs signal more specifically nirs data are statistically analyzed based on the general linear model glm and sun s tube formula the p values are calculated as the excursion probability of an inhomogeneous random field on a representation manifold that is dependent on the structure of the error covariance matrix and the interpolating kernels nirs spm not only enables the calculation of activation maps of oxy deoxy hemoglobin and total hemoglobin but also allows for the super resolution localization which is not possible using conventional analysis tools extensive experimental results using finger tapping and memory tasks confirm the viability of the proposed method

a new statistical approach to detecting significant activation in functional mri there are many ways to detect activation patterns in a time series of observations at a single voxel in a functional magnetic resonance imaging study the critical problem is to estimate the statistical significance which depends on the estimation of both the magnitude of the response to the stimulus and the serial dependence of the time series and especially on the assumptions made in that estimation we show that for experimental designs with periodic stimuli only a few aspects of the serial dependence are important and these can be estimated reliably via nonparametric estimation of the spectral density of the time series whereas existing techniques are biased by their assumptions the linear model with stationary serially dependent errors can be analyzed entirely in frequency domain and doing so provides many insights in particular we introduce a technique to detect periodic activations and show that it has a distribution theory that enables us to assign significance levels down to 1 in 100 000 levels which are needed when a whole brain image is under consideration nonparametric spectral density estimation is shown to be self calibrating and accurate when compared to several other time domain approaches the technique is especially resistant to high frequency artefacts that we have found in some datasets and we demonstrate that time domain approaches may be sufficiently susceptible to these effects to give misleading results the method is easily generalized to handle event related designs we found it necessary to consider the trends in the time series carefully and use nonlinear filters to remove the trends and robust techniques to remove spikes using this in connection with our techniques allows us to detect activations in clumps of a few even one voxel in periodic designs yet produce essentially no false positive detections at any voxels in null datasets

plurality and resemblance in fmri data analysis abstract we apply nine analytic methods employed currently in imaging neuroscience to simulated and actual bold fmri signals and compare their performances under each signal type starting with baseline time series generated by a resting subject during a null hypothesis study we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple convolved with spatially varying hemodynamic responses and highly spatially interactive we then apply these same nine methods to bold fmri time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study paired comparisons of results across methods include a voxel specific concordance correlation coefficient for reproducibility and a resemblance measure that accommodates spatial autocorrelation of differences in activity surfaces receiver operating characteristic curves show considerable model differences in ranges less than 10 significance level false positives and greater than 80 power true positives concordance and resemblance measures reveal significant differences between activity surfaces in both data sets these measures can assist researchers by identifying groups of models producing similar and dissimilar results and thereby help to validate consolidate and simplify reports of statistical findings a pluralistic strategy for fmri data analysis can uncover invariant and highly interactive relationships between local activity foci and serve as a basis for further discovery of organizational principles of the brain results also suggest that a pluralistic empirical strategy coupled formally with substantive prior knowledge can help to uncover new brain behavior relationships that may remain hidden if only a single method is employed

tests for distributed nonfocal brain activations abstract most approaches to detecting changes in functional brain images assume that activations are focal or very localized however the brain s response to cognitive of sensorimotor challenge may be spatially or anatomically distributed in this paper we consider the use fulness of a test based on the mean sum of squares of statistical parametric maps the performance of this test is evaluated using simulated and real data and is compared to the 2 test a test of the size of the activated region and a focal activation test based on the intensity of local maxima we demonstrate that the mean sum of squares test is more sensitive to nonfocal signals and propose that it could be used to complement approaches that are more sensitive to focal activations

hybrid dirichlet mixture models for functional data summary in functional data analysis curves or surfaces are observed up to measurement error at a finite set of locations for say a sample of n individuals often the curves are homogeneous except perhaps for individual specific regions that provide heterogeneous behaviour e g damaged areas of irregular shape on an otherwise smooth surface motivated by applications with functional data of this nature we propose a bayesian mixture model with the aim of dimension reduction by representing the sample of n curves through a smaller set of canonical curves we propose a novel prior on the space of probability measures for a random curve which extends the popular dirichlet priors by allowing local clustering non homogeneous portions of a curve can be allocated to different clusters and the n individual curves can be represented as recombinations hybrids of a few canonical curves more precisely the prior proposed envisions a conceptual hidden factor with k levels that acts locally on each curve we discuss several models incorporating this prior and illustrate its performance with simulated and real data sets we examine theoretical properties of the proposed finite hybrid dirichlet mixtures specifically their behaviour as the number of the mixture components goes to 1 and their connection with dirichlet process mixtures

general multilevel linear modeling for group analysis in fmri this article discusses general modeling of multisubject and or multisession fmri data in particular we show that a two level mixed effects model where parameters of interest at the group level are estimated from parameter and variance estimates from the single session level can be made equivalent to a single complete mixed effects model where parameters of interest at the group level are estimated directly from all of the original single sessions time series data if the co variance at the second level is set equal to the sum of the co variances in the single level form using the blue with known covariances this result has significant implications for group studies in fmri since it shows that the group analysis requires only values of the parameter estimates and their co variance from the first level generalizing the well established summary statistics approach in fmri the simple and generalized framework allows different prewhitening and different first level regressors to be used for each subject the framework incorporates multiple levels and cases such as repeated measures paired or unpaired t tests and f tests at the group level explicit examples of such models are given in the article using numerical simulations based on typical first level covariance structures from real fmri data we demonstrate that by taking into account lower level covariances and heterogeneity a substantial increase in higher level z score is possible

improved detection of event related functional mri signals using probability functions selecting an optimal event distribution for experimental use in event related fmri studies can require the generation of large numbers of event sequences with characteristics hard to control the use of known probability distributions offers the possibility to control event timing and constrain the search space for finding optimal event sequences we investigated different probability distributions in terms of response estimation estimation efficiency detectability detection power parameter estimation efficiency sensitivity to true positives and false positive activation numerous simulated event sequences were generated selecting interevent intervals iei from the uniform uniform permuted latin square exponential binomial poisson chi 2 geometric and bimodal probability distributions and fixed iei event sequences from the bimodal distribution like block designs had the best performance for detection and the poorest for estimation while high estimation and detectability occurred for the long decay exponential distribution the uniform distribution also yielded high estimation efficiency but probability functions with a long tail toward higher iei such as the geometric and the chi 2 distributions had superior detectability the distributions with the best detection performance also had a relatively high incidence of false positives in contrast to the ordered distributions latin square and uniform permuted the predictions of improved sensitivities for distributions with long tails were confirmed with empirical data moreover the latin square design yielded detection of activated voxels similar to the chi 2 distribution these results indicate that high detection and suitable behavioral designs have compatibility for application of functional mri methods to experiments requiring complex designs

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

testing for a signal with unknown location and scale in a stationary gaussian random field we suppose that our observations can be decomposed into a fixed signal plus random noise where the noise is modelled as a particular stationary gaussian random field in n dimensional euclidean space the signal has the form of a known function centered at an unknown location and multiplied by an unknown amplitude and we are primarily interested in a test to detect such a signal there are many examples where the signal scale or width is assumed known and the test is based on maximising a gaussian random field over all locations in a subset of n dimensional euclidean space the novel feature of this work is that the width of the signal is also unknown and the test is based on maximising a gaussian random field in n 1 dimensions n dimensions for the location plus one dimension for the width two convergent approaches are used to approximate the null distribution one based on the method of knowles and siegmund which uses a version of weyl s tube formula for manifolds with boundaries and the other based on some recent work by worsley which uses the hadwiger characteristic of excursion sets as introduced by adler finally we compare the power of our method with one based on a fixed but perhaps incorrect signal width

analysis of fmri data using improved self organizing mapping and spatio temporal metric hierarchical clustering the self organizing mapping som and hierarchical clustering hc methods are integrated to detect brain functional activation functional magnetic resonance imaging fmri data are first processed by som to obtain a primary merged neural nodes image and then by hc to obtain further brain activation patterns the conventional euclidean distance metric was replaced by the correlation distance metric in som to improve clustering and merging of neural nodes to improve the use of spatial and temporal information in fmri data a new spatial distance node coordinates in the 2 d lattice and temporal correlation correlation degree of each time course in the exemplar matrix are introduced in hc to merge the primary som results two simulation studies and two in vivo fmri data that both contained block design and event related experiments revealed that brain functional activation can be effectively detected and that different response patterns can be distinguished using these methods our results demonstrate that the improved som and hc methods are clearly superior to the statistical parametric mapping spm independent component analysis ica and conventional som methods in the block design especially in the event related experiment as revealed by their performance measured by receiver operating characteristic roc analysis our results also suggest that the proposed new integrated approach could be useful in detecting block design and event related fmri data

optimal spline smoothing of fmri time series by generalized cross validation linear parametric regression models of fmri time series have correlated residuals one approach to address this problem is to condition the autocorrelation structure by temporal smoothing smoothing splines with the degree of smoothing selected by generalized cross validation gcv spline provide a method to find an optimal smoother for an fmri time series the purpose of this study was to determine if gcv spline of fmri time series yields unbiased variance estimates of linear regression model parameters gcv spline was evaluated with a real fmri data set and bias of the variance estimator was computed for simulated time series with autocorrelation structures derived from fmri data this study only considered fmri experimental designs of boxcar type the results from the real data suggest that gcv spline determines appropriate amounts of smoothing the simulations show that the variance estimates are on average unbiased the unbiased variance estimates come at some cost to signal detection efficiency this study demonstrates that gcv spline is an appropriate method for smoothing fmri time series

semiparametric detection of significant activation for brain fmri functional magnetic resonance imaging fmri aims to locate activated regions in human brains when specific tasks are performed the conventional tool for analyzing fmri data applies some variant of the linear model which is restrictive in modeling assumptions to yield more accurate prediction of the time course behavior of neuronal responses the semiparametric inference for the underlying hemodynamic response function is developed to identify significantly activated voxels under mild regularity conditions we demonstrate that a class of the proposed semiparametric test statistics based on the local linear estimation technique follow x 2 distributions under null hypotheses for a number of useful hypotheses furthermore the asymptotic power functions of the constructed tests are derived under the fixed and contiguous alternatives simulation evaluations and real fmri data application suggest that the semiparametric inference procedure provides more efficient detection of activated brain areas than the popular imaging analysis tools afni and fsl

existence uniqueness and attractivity of prime period two solution for a difference equation of exponential form abstract in this paper we study the existence uniqueness and attractivity of prime period two solution of the difference equation x n 1 a bx n 1 e x n where a b are positive constants and the initial values x 1 x 0 are positive numbers

a cluster mass permutation test with contextual enhancement for fmri activation detection gaussian random field grf based methods are commonly used for statistical inference and to control the family wise error rate fwe in neuroimaging they require that the error fields are reasonable lattice approximations to an underlying continuous multivariate gaussian random field and have differentiable and invertible spatial autocorrelation function permutation test estimates the distribution of the test statistic from the data and adjusts automatically for the fwe here we present a new analysis procedure the cluster mass permutation test with contextual enhancement cmpce and compare it to grf in cmpce the data are first pre whitened to remove temporal autocorrelations the fwe rates the cluster detection probability and delineation accuracy of cmpce and grf were compared using measured null data and null data containing simulated activations we also applied both methods to an fmri experiment where tactile somatosensory stimulation into the right hand was used when analyzing the fwe using null data both cmpce and grf gave significantly higher fwes cmpce up to 0 12 grf up to 0 18 than the nominal significance level 0 05 indicating that the pre whitening motion correction or high pass filtering partially failed in the simulated activation data cmpce gave less falsely classified voxels for the same cluster detection probability level than grf the maximal cluster detection probability was on the other hand higher in the grf based method both methods gave qualitatively similar results in the tactile fmri data cmpce seems to be a promising fmri analysis method especially if high delineation accuracy is required

nonparametric inference of the hemodynamic response using multi subject fmri data estimation and inferences for the hemodynamic response functions hrf using multi subject fmri data are considered within the context of the general linear model two new nonparametric estimators for the hrf are proposed the first is a kernel smoothed estimator which is used to construct hypothesis tests on the entire hrf curve in contrast to only summaries of the curve as in most existing tests to cope with the inherent large data variance we introduce a second approach which imposes tikhonov regularization on the kernel smoothed estimator an additional bias correction step which uses multi subject averaged information is introduced to further improve efficiency and reduce the bias in estimation for individual hrfs by utilizing the common properties of brain activity shared across subjects this is the main improvement over the standard methods where each subject s data is usually analyzed independently a fast algorithm is also developed to select the optimal regularization and smoothing parameters the proposed methods are compared with several existing regularization methods through simulations the methods are illustrated by an application to the fmri data collected under a psychology design employing the monetary incentive delay mid task

gravitational wave signal templates pattern recognition and reciprocal eulerian gamma functions the direct detection of gravitational waves gws is one of the most challenging problems in experimental gravitation today it necessitates the use of highly advanced large laser interferometers such as ligo virgo lisa tama 300 geo 600 and aigo the analysis of the data from such instruments requires and combines the expertise from a multitude of scientific disciplines the verification of a detected signal demands an effective way to distinguish the source signal from the background noise such a study is required for an all sky search to determine the f and q angles on the sky of gravitational wave sources and their frequencies in this paper we present analytical solutions and associated numerical approximations for the inner products employed in matched filtering a gw signal using templates an exact closed form expression for the inner products is rigourously derived using the special functions of mathematical physics the inner products involve reciprocal eulerian gamma functions which occur in the study of many diverse phenomena the spectral noise density of the virgo gw detector is shown to be amenable to our analysis spectral noise densities like those for ligo and geo 600 although different and in a slightly more restricted frequency band are likewise amenable we study numerical computation of the inner products estimate the computational time of the solution on serial and parallel computers and show the efficiency of the resulting algorithms the fitting factor that indicates the goodness of fit between a signal and a template is given in closed form and computed numerically the numerical plots display an approximate symmetry in the template f and q domain

study of the asymptotic behavior of the solutions of three systems of difference equations of exponential form in this paper we study the boundedness the persistence and the asymptotic behavior of the positive solutions of the following systems of two difference equations of exponential form xn 1 a be yn c yn 1 y n 1 d e xn f xn 1

the l 2 cohomology of a bounded smooth stein domain is not necessarily hausdorff we give an example of a pseudoconvex domain in a complex manifold whose l 2 dolbeault cohomology is non hausdorff yet the domain is stein the domain is a smoothly bounded levi flat domain in a two complex dimensional compact complex manifold the domain is biholomorphic to a product domain in mathbb c 2 hence stein this implies that for q 0 the usual dolbeault cohomology with respect to smooth forms vanishes in degree p q but the l 2 cauchy riemann operator on the domain does not have closed range on 2 1 forms and consequently its l 2 dolbeault cohomology is not hausdorff

statistical parametric mapping for event related potentials ii a hierarchical temporal model in this paper we describe a temporal model for event related potentials erp in the context of statistical parametric mapping spm in brief we project channel data onto a two dimensional scalp surface or into three dimensional brain space using some appropriate inverse solution we then treat the spatiotemporal data in a mass univariate fashion this implicitly factorises the model into spatial and temporal components the key contribution of this paper is the use of observation models that afford an explicit distinction between observation error and variation in the expression of erps this distinction is created by employing a two level hierarchical model in which the first level models the erp effects within subject and trial type while the second models differences in erp expression among trial types and subjects by bringing the analysis of erp data into a classical hierarchical i e mixed effects framework many apparently disparate approaches e g conventional p300 analyses and time frequency analyses of stimulus locked oscillations can be reconciled within the same estimation and inference procedure inference proceeds in the normal way using t or f statistics to test for effects that are localised in peristimulus time or in some time frequency window the use of f statistics is an important generalisation of classical approaches because it allows one to test for effects that lie in a multidimensional subspace i e of unknown but constrained form we describe the analysis procedures the underlying theory and compare its performance to established techniques

removal of confounding effects of global signal in functional mri analyses local signals obtained from bold fmri are generally confounded by global effects in this paper we make an essential distinction between global effects and the global signal global effects have a similar influence on local signals from a large proportion of cerebral voxels they may reflect diffuse physiological processes or variations in scanner sensitivity and are difficult to measure directly global effects are often estimated from the global signal which is the spatial average of local signals from all cerebral voxels if the global signal is strongly correlated with experimental manipulations meaningfully different results may be obtained whether or not global effects are modeled g k aguirre et al 1998 neuroimage 8 302 306 in particular if local bold signals make a significant contribution to the global signal analyses using ancovaor proportional scaling models may yield artifactual deactivations in this paper we present a modification to the proportional scaling model that accounts for the contribution of local bold signals to the global signal an event related oddball stimulus paradigm and a block design working memory task were used to illustrate the efficacy of our model

estimating efficiency a priori a comparison of blocked and randomized designs this technical note deals with a priori estimation of efficiency of functional magnetic resonance imaging fmri designs the efficiency of an estimator is a measure of how reliable it is and depends on error variance the variance not modeled by explanatory variables in the design matrix and the design variance a function of the explanatory variables and the contrast tested changes in the experimental design can induce changes in the variance of estimated responses this translates into changes in the standard error of the response estimate or equivalently into changes in efficiency one consequence is that statistics testing for the same activation in different contexts i e experimental designs can change substantially even if the activation and error variance are exactly the same we demonstrate this effect using an event related fmri study of single word reading during blocked and randomized trial presentations furthermore we show that the error variance can change with the experimental design this highlights a problem with a priori comparison of efficiency for two or more experimental designs which usually assumes identical error variance

to smooth or not to smooth bias and efficiency in fmri time series analysis this paper concerns temporal filtering in fmri time series analysis whitening serially correlated data is the most efficient approach to parameter estimation however if there is a discrepancy between the assumed and the actual correlations whitening can render the analysis exquisitely sensitive to bias when estimating the standard error of the ensuing parameter estimates this bias although not expressed in terms of the estimated responses has profound effects on any statistic used for inference the special constraints of fmri analysis ensure that there will always be a misspecification of the assumed serial correlations one resolution of this problem is to filter the data to minimize bias while maintaining a reasonable degree of efficiency in this paper we present expressions for efficiency of parameter estimation and bias in estimating standard error in terms of assumed and actual correlation structures in the context of the general linear model we show that i whitening strategies can result in profound bias and are therefore probably precluded in parametric fmri data analyses ii band pass filtering and implicitly smoothing has an important role in protecting against inferential bias

robust smoothness estimation in statistical parametric maps using standardized residuals from the general linear model the assessment of significant activations in functional imaging using voxel based methods often relies on results derived from the theory of gaussian random fields these results solve the multiple comparison problem and assume that the spatial correlation or smoothness of the data is known or can be estimated end results i e p values associated with local maxima clusters or sets of clusters critically depend on this assessment which should be as exact and as reliable as possible in some earlier implementations of statistical parametric mapping spm spm94 spm95 the smoothness was assessed on gaussianized t fields gt f that are not generally free of physiological signal this technique has two limitations first the estimation is not stable the variance of the estimator being far from negligible and second physiological signal in the gt f will bias the estimation in this paper we describe an estimation method that overcomes these drawbacks the new approach involves estimating the smoothness of standardized residual fields which approximates the smoothness of the component fields of the associated t field knowing the smoothness of these component fields is important because it allows one to compute corrected p values for statistical fields other than the t field or the gt f e g the f map and eschews bias due to deviation from the null hypothesis we validate the method on simulated data and demonstrate it using data from a functional mri study

a heuristic for the degrees of freedom of statistics based on multiple variance parameters in neuroimaging data are often modeled using general linear models here we focus on glms with error covariances which are modeled as a linear combination of multiple variance covariance components each of these components is weighted by one variance parameter in many analyses variance parameters are estimated using restricted maximum likelihood reml most classical approaches assume the error covariance matrix can be factorized into a single variance parameter and a nonspherical correlation matrix in this context the f test based on a single variance parameter with a suitable correction to the degrees of freedom is the standard inference tool this correction can also be adapted to models with multiple variance parameters however this extension overlooks the uncertainty about the variance parameter estimates and p values tend to be underestimated here we show how one can overcome this problem to render the f test more exact this issue is important because serial correlations in fmri time series are generally modeled using multiple variance parameters another application is to hierarchical linear models which are used for modeling multisubject data to illustrate our approach we apply it to some typical modeling scenarios in fmri data analysis

multisubject fmri studies and conjunction analyses abstract in this paper we present an approach to making inferences about generic activations in groups of subjects using fmri in particular we suggest that activations common to all subjects reflect aspects of functional anatomy that may be typical of the population from which that group was sampled these commonalities can be identified by a conjunction analysis of the activation effects in which the contrasts testing for an activation are specified separately for each subject a conjunction is the joint refutation of multiple null hypotheses in this instance of no activation in any subject the motivation behind this use of conjunctions is that fixed effect analyses are generally more sensitive than equivalent random effect analyses this is because fixed effect analyses can harness the large degrees of freedom and small scan to scan variability relative to the variability in responses from subject to subject when assessing the significance of an estimated response the price one pays for the apparent sensitivity of fixed effect analyses is that the ensuing inferences pertain to and only to the subjects studied however a conjunction analysis using a fixed effect model allows one to infer i that every subject studied activated and ii that at least a certain proportion of the population would have shown this effect the second inference depends upon a meta analytic formulation in terms of a confidence region for this proportion this approach retains the sensitivity of fixed effect analyses when the inference that only a substantial proportion of the population activates is sufficient

wspm wavelet based statistical parametric mapping recently we have introduced an integrated framework that combines wavelet based processing with statistical testing in the spatial domain in this paper we propose two important enhancements of the framework first we revisit the underlying paradigm i e that the effect of the wavelet processing can be considered as an adaptive denoising step to improve the parameter map followed by a statistical detection procedure that takes into account the non linear processing of the data with an appropriate modification of the framework we show that it is possible to reduce the bias of the method with respect to the best linear estimate providing conservative results that are closer to the original data second we propose an extension of our earlier technique that compensates for the lack of shift invariance of the wavelet transform we demonstrate experimentally that both enhancements have a positive effect on performance in particular we present a reproducibility study for multi session data that compares wspm against spm with different amounts of smoothing the full approach is available as a toolbox named wspm for the spm2 software it takes advantage of multiple options and features of spm such as the general linear model

statistical tests for fmri based on experimental randomization statistical parametric mapping spm analysis of fmri data requires specifying correctly the temporal and spatial noise covariance structure this is a difficult if not impossible task when these assumptions are not satisfied statistical inference can be invalid or inefficient permutation tests are free of strong assumptions on the distribution of signal noise we propose permutation tests of fmri data based on experimental randomization of the stimulus sequences smooth hemodynamic response curves are estimated using quadratic b splines we study fmri data obtained from event related potential erp oddball paradigm tests of two tone and three tone stimulus sequences are conducted to illustrate the application of the proposed method comparisons of the spm and proposed method show that a permutation test is more specific and less susceptible to artifacts

analysis of fmri time series revisited abstract this paper presents a general approach to the analysis of functional mri time series from one or more subjects the approach is predicated on an extension of the general linear model that allows for correlations between error terms due to physiological noise or correlations that ensue after temporal smoothing this extension uses the effective degrees of freedom associated with the error term the effective degrees of freedom are a simple function of the number of scans and the temporal autocorrelation function a specific form for the latter can be assumed if the data are smoothed in time to accentuate hemodynamic responses with a neural basis this assumption leads to an expedient implementation of a flexible statistical framework the importance of this small extension is that in contradistinction to our previous approach any parametric statistical analysis can be implemented we demonstrate this point using a multiple regression analysis that tests for effects of interest activations due to word generation while taking explicit account of some obvious confounds

on bias in the estimation of autocorrelations for fmri voxel time series analysis for fmri time series analysis to be statistically valid it is important to deal correctly with temporal autocorrelation in the noise most of the approaches in the literature adopt a two stage approach in which the autocorrelation structure is estimated using the residuals of an initial model fit this estimate is then used to prewhiten the data and the model before the model is refit to obtain final activation parameter estimates an assumption implicit in this scheme is that the residuals from the initial model fit represent a realization of the true noise process in general this assumption will not be correct as certain components of the noise will be removed by the model fit in this paper we examine i the form of the bias induced by the initial model fit ii methods of correcting for the bias and iii the impact of bias correction on the model parameter estimates we find that while bias correction does result in more accurate estimates of the correlation structure this does not translate into improved estimates of the model parameters in fact estimates of the model parameters and their standard errors are seen to be so accurate that we conclude that bias correction is unnecessary

incorporating prior knowledge into image registration the first step in the spatial normalization of brain images is usually to determine the affine transformation that best maps the image to a template image in a standard space we have developed a rapid and automatic method for performing this registration which uses a bayesian scheme to incorporate prior knowledge of the variability in the shape and size of heads we compared affine registrations with and without incorporating the prior knowledge we found that the affine transformations derived using the bayesian scheme are much more robust and that the rate of convergence is greater

a novel temporal filtering strategy for functional mri using unfold a major challenge for fmri at high spatial resolution is the limited temporal resolution the unfold method increases image acquisition speed and potentially enables high acceleration factors in fmri spatial aliasing artifacts due to interleaved k space sampling are to be removed from the image time series by temporal filtering before statistical mapping in the time domain can be carried out so far low pass filtering and multi band filtering have been proposed particularly at high unfold factors both methods are non optimal low pass filtering severely degrades temporal resolution and multi band filtering leads to temporal autocorrelations affecting statistical modelling of activation in this work we present a novel temporal filtering strategy that significantly reduces temporal autocorrelations compared to multi band filtering two datasets finger tapping and resting state were post processed using the proposed and the multi band filter with varying set ups i e transition bands when the proposed filtering strategy was used a linear regression analysis revealed that the number of false positives was significantly decreased up to 34 whereas the number of activated voxels was not significantly affected for most filter parameters in total this led to an effective increase in the number of activated voxels per false positive for each filter set up at a significance level of 5 the number of activated voxels was increased up to 41 by using the proposed filtering strategy

characterizing the hemodynamic response effects of presentation rate sampling procedure and the possibility of ordering brain activity based on relative timing rapid presentation event related functional mri er fmri allows neuroimaging methods based on hemodynamics to employ behavioral task paradigms typical of cognitive settings however the sluggishness of the hemodynamic response and its variance provide constraints on how er fmri can be applied in a series of two studies estimates of the hemodynamic response in or near the primary visual and motor cortices were compared across various paradigms and sampling procedures to determine the limits of er fmri procedures and more generally to describe the behavior of the hemodynamic response the temporal profile of the hemodynamic response was estimated across overlapping events by solving a set of linear equations within the general linear model no assumptions about the shape were made in solving the equations following estimation of the temporal profile the amplitude and timing were modeled using a gamma function results indicated that 1 within a region for a given subject estimation of the hemodynamic response is extremely stable for both amplitude r 2 0 98 and time to peak r 2 0 95 from one series of measurements to the next and slightly less stable for estimation of time to onset r 2 0 60 2 as the trial presentation rate changed from those spaced 20 s apart to temporally overlapping trials the hemodynamic response amplitude showed a small but significant decrease trial onsets spaced on average 5 s apart showed a 17 25 reduction in amplitude compared to those spaced 20 s apart power analysis indicated that the increased number of trials at fast rates outweighs this decrease in amplitude if statistically reliable response detection is the goal 3 knowledge of the amplitude and timing of the hemodynamic response in one region failed to predict those properties in another region even for within subject comparisons 4 across subjects the amplitude of the response showed no significant correlation with timing of the response for either time to onset or time to peak estimates 5 the within region stability of the response was sufficient to allow offsets in the timing of the response to be detected that were under a second placing event related fmri methods in a position to answer questions about the change in relative timing between regions

nonadditive two way anova for event related fmri data analysis abstract asignificant recent development in functional magnetic resonance imaging fmri is the introduction of event related fmri also known as time resolved fmri because the exact shape of the mr response in an event related fmri experiment is often not known traditional methods developed for block design experiments such as t test and correlation analysis are not well suited for extracting activated pixels from the event related data in this work a statistical technique based on nonadditive two way analysis of variance is developed for use in event related studies theoretical and experimental work were carried out for establishing a statistical threshold to determine pixel activation experimental studies were performed to demonstrate the utility of this approach

separating processes within a trial in event related functional mri many cognitive processes occur on time scales that can significantly affect the shape of the blood oxygenation level dependent bold response in eventrelated functional mri this shape can be estimated from event related designs even if these processes occur in a fixed temporal sequence j m ollinger g l shulman and m corbetta 2001 neuroimage 13 210 217 several important considerations come into play when interpreting these time courses first in single subjects correlations among neighboring time points give the noise a smooth appearance that can be confused with changes in the bold response second the variance and degree of correlation among estimated time courses are strongly influenced by the timing of the experimental design simulations show that optimal results are obtained if the intertrial intervals are as short as possible if they follow an exponential distribution with at least three distinct values and if 40 of the trials are partial trials these results are not particularly sensitive to the fraction of partial trials so accurate estimation of time courses can be obtained with lower percentages of partial trials 20 25 third statistical maps can be formed from f statistics computed with the extra sum of square principle or by t statistics computed from the cross correlation of the time courses with a model for the hemodynamic response the latter method relies on an accurate model for the hemodynamic response the most robust model among those tested was a single gamma function finally the power spectrum of the measured bold signal in rapid event related paradigms is similar to that of the noise nevertheless highpass filtering is desirable if the appropriate model for the hemodynamic response is used 2001 academic press

the impact of temporal regularization on estimates of the bold hemodynamic response function a comparative analysis in fmri data analysis it has been shown that for a wide range of situations the hemodynamic response function hrf can be reasonably characterized as the impulse response function of a linear and time invariant system an accurate and robust extraction of the hrf is essential to infer quantitative information about the relative timing of the neuronal events in different brain regions when no assumptions are made about the hrf shape it is most commonly estimated using time windowed averaging or a least squares estimated general linear model based on either fourier or delta basis functions recently regularization methods have been employed to increase the estimation efficiency of the hrf typically these methods produce more accurate hrf estimates than the least squares approach goutte c nielsen f a hansen l k 2000 modeling the haemodynamic response in fmri using smooth fir filters ieee trans med imag 19 12 1188 1201 here we use simulations to clarify the relative merit of temporal regularization based methods compared to the least squares methods with respect to the accuracy of estimating certain characteristics of the hrf such as time to peak ttp height hr and width w of the response we implemented a bayesian approach proposed by marrelec et al marrelec g benali h ciuciu p pelegrini issac m poline j b 2003 robust estimation of the hemodynamic response function in event related bold fmri using basic physiological information hum brain mapp 19 1 17 marrelec g benali h ciuciu p poline j b bayesian estimation of the hemodynamic of the hemodynamic response function in functional mri in r f editor 2001 melville p 229 247 and its deterministic counterpart based on a combination of tikhonov regularization tikhonov a n arsenin v y 1977 solution of ill posed problems washington dc w h winston and generalized cross validation gcv wahba g 1990 spline models for observational data philadelphia siam for selecting the regularization parameter the performance of both methods is compared with least square estimates as a function of temporal resolution color and strength of the noise and the type of stimulus sequences used in almost all situations under the considered assumptions e g linearity time invariance and smooth hrf the regularization based techniques more accurately characterize the hrf compared to the least squares method our results clarify the effects of temporal resolution noise color and experimental design on the accuracy of hrf estimation

behavior of the bergman projection on the diederich fornaess worm w 1 introduction in this paper we show that the bergman projection operator for certain smooth bounded pseudoconvex domains does not preserve smoothness as measured by sobolev norms let q be a smooth bounded pseudoconvex domain in c and let p t denote the orthogonal projection from l2 f onto the bergman subspace b ff l2 f3 r with respect to the weighted norm i fll j olf z l 2 e t lzll2dv l 2 let wk t denote the sobolev space consisting of functions whose derivatives of order to k g2 on the other hand there is a large collection of results implying that for certain types of domains the unweighted bergman projection p pr preserves w k for all k 0 see fk for the strictly pseudoconvex case for results on weakly pseudoconvex domains the reader may consult ko2 ca si and the recent bstl ch as well as the references cited therein most of these results are focused on the a neumann operator rather than p see bst2 for the connection also except for kol positive results in this area are typically valid for any choice of smooth positive weight function on 0 the question of whether or not p is similarly well behaved for all weakly pseudoconvex domains has remained open for many years in this paper we show that this is not the case in fact when q is the so called worm domain of diederich and forna ss then p does not map w to w k when k zr total amount of winding this latter quantity is explained in section 4 below where the construction of the worm is reviewed and the main result is proved the proof depends on computations for a piecewise levi flat model domain depending in turn on certain one dimensional computations these are treated in sections 3 and 2 respectively section 5 contains additional remarks and questions

condition r and proper holomorphic maps between equidimensional product domains we consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex euclidean space where both source and target can be represented as cartesian products of smoothly bounded domains it is shown that such mappings extend smoothly up to the closures of the domains provided each factor of the source satisfies condition r it also shown that the number of smoothly bounded factors in the source and target must be the same and the proper holomorphic map splits as a product of proper mappings between the factor domains c 2013 elsevier inc all rights reserved

characterization of automorphisms on the barrett and the diederich fornaess worm domains in this paper we show that every automorphism on either the barrett or the diederick fornaess worm domains is given by a rotation in w variable in particular any automorphism on either one of these two domains can be extended smoothly up to the boundary

a comparison of methods for characterizing the event related bold timeseries in rapid fmri abstract information about the shape and temporal duration of the blood oxygenation level dependent bold response can inform both functional neuroanatomy and psychological theory however the bold response evolves over 20 s or more making it difficult to distinguish the unique characteristics of the response evoked by temporally adjacent stimuli fortunately event related bold signals can be extracted given that there is adequate variance in the distribution of inter stimulus intervals isi unfortunately the isi distribution that yields the highest statistical efficiency is not always optimal from a psychological perspective variability in the stimulus timing may complicate the interpretation of neuroimaging data in terms of underlying cognitive operations in the present paper monte carlo simulations are used to evaluate two techniques for estimating the event related bold timeseries event related averaging and deconvolution using the ordinary least squares estimate with respect to maintaining acceptable levels of statistical power and experimental validity while the unbiased deconvolution technique more robustly estimates the shape of the bold response functions both methods succeed in accurately re producing known differences between evoked bold responses when the stimulus ordering is randomized however the deconvolution method is more effective at preserving differences when there are sequential dependencies in the stimulus presentation order and restricted isi distributions are used particularly if the second of two sequentially dependent stimuli is omitted on some portion of the trials importantly the successful re production of the evoked bold response using restricted isi distributions often maximizes the ability to make psychologically valid experimental conclusions

empirical analyses of bold fmri statistics i spatially unsmoothed data collected under null hypothesis conditions temporal autocorrelation spatial coherency and their effects on voxel wise parametric statistics were examined in bold fmri null hypothesis or noise datasets seventeen normal young subjects were scanned using bold fmri while not performing any time locked experimental behavior temporal autocorrelation in these datasets was described well by a 1 frequency relationship voxel wise statistical analysis of these noise datasets which assumed independence i e ignored temporal autocorrelation rejected the null hypothesis at a higher rate than specified by the nominal alpha temporal smoothing in conjunction with the use of a modified general linear model worsley and friston 1995 neuroimage 2 173 182 brought the false positive rate closer to the nominal alpha it was also found that the noise fmri datasets contain spatially coherent time signals this observed spatial coherence could not be fully explained by a continuously differentiable spatial autocovariance function and was much greater for lower temporal frequencies its presence made voxel wise test statistics in a given noise dataset dependent and thus shifted their distributions to the right or left of 0 inclusion of a global signal covariate in the general linear model reduced this dependence and consequently stabilized i e reduced the variance of dataset false positive rates

oscillation and global asymptotic stability in a discrete epidemic model abstract in this paper we study the oscillation global asymptotic stability and other properties of the positive solutions of the difference equation x n 1 1 j 0 k 1 x n j 1 e ax n where a 0 k 2 3 and the initial values x k 1 x k 2 x0 are arbitrary real positive numbers such that j 0k 1x j

on a modification of a discrete epidemic model in this paper under some conditions on the constants a b 0 we study the existence of positive solutions the existence of a unique nonnegative equilibrium and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations x n 1 1 y n y n 1 1 e a y n y n 1 1 x n x n 1 1 e b x n where a b 0 and the initial values x 1 x 0 y 1 y 0 are positive numbers which satisfy the relations x 0 x 1 1 x 0 x 1 1 e b x 0 1 x 0 1 y 0 y 1 1 e a y 0