some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

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

some isometric embedding and rigidity results for riemannian manifolds in this note we announce some new results concerning rigidity and isometric embeddings of riemannian manifolds a special case of the main result states that a general mn unk rn r r n 1 n 2 2 is uniquely determined up to finitely many constants by its induced ds2

investigating the impact of autocorrelation on time varying connectivity in recent years a number of studies have reported on the existence of time varying functional connectivity tvc in resting state functional magnetic resonance imaging rs fmri data the sliding window technique is currently one of the most commonly used methods to estimate tvc although previous studies have shown that autocorrelation can negatively impact estimates of static functional connectivity its impact on tvc estimates is not well known at this time in this paper we show both theoretically and empirically that the existence of autocorrelation within a time series can inflate the sampling variability of tvc estimated using the sliding window technique this can in turn increase the risk of misinterpreting noise as true tvc and negatively impact subsequent estimation of whole brain time varying fc profiles or brain states the latter holds as more variable input measures lead to more variable output measures in the state estimation procedure finally we demonstrate that prewhitening the data prior to analysis can lower the variance of the estimated tvc and improve brain state estimation these results suggest that careful consideration is required when making inferences on tvc

the linearized system for isometric embeddings and its characteristic variety abstract in this paper we prove a conjecture of bryant griffiths and yang concerning the characteristic variety for the determined isometric embedding system in particular we show that the characteristic variety is not smooth for any dimension greater than 4 this is accomplished by introducing a smaller yet equivalent linearized system in an appropriate way which facilitates analysis of the characteristic variety

temporal autocorrelation in univariate linear modeling of fmri data in functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them shaping or coloring attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering removing the autocorrelation or prewhitening gives the best linear unbiased estimator assuming that the autocorrelation is accurately known for single event designs the efficiency of the estimator is considerably higher for prewhitening compared with coloring however it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias to overcome this we consider different ways to estimate the autocorrelation for use in prewhitening after high pass filtering is performed a tukey taper set to smooth the spectral density more than would normally be used in spectral density estimation performs best importantly estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation but only within tissue type using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 x 10 5

residuation of linear series and the effective cone of cd we obtain new information about divisors on the dth symmetric power cd of a general curve c of genus g 4 this includes a complete description of the effective cone of cg 1 and a partial computation of the volume function on one of its non nef subcones as well as new bounds for the effective and movable cones of cd in the range g 1 d g 2 we also obtain for each g 5 a divisor on cg 1 with non equidimensional stable base locus for a general hyperelliptic curve c of genus g we obtain a complete description of the effective cone of cd for 2 d g and an integral divisor on cg 1 which has non integral volume whenever g is not a power of 2 1 introduction let c be a smooth complex projective algebraic curve and let d 1 be an integer the dth symmetric power cd c d sd is a smooth d dimensional complex projective variety which is a fine moduli space parametriz ing effective divisors of degree d on c in this paper we study the cone of effective divisors on cd and its refinements there are two natural divisor classes on cd for each p c the image of the embedding

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

the local isometric embedding in r3 of two dimensional riemannian manifolds with gaussian curvature changing sign cleanly on etudie le plongement isometrique local de surfaces a 2 dimensions dans r 3 on suppose que la premiere forme fondamentale edu 2 2fdudv gdv 2 on cherche trois fonctions c 2 x u v y u v z u v telles que dx 2 dy 2 dz 2 edu 2 2fdudv gdv 2 dans un voisinage de p

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

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

existence of elastic deformations with prescribed principal strains and triply orthogonal systems on montre la possibilite de prescrire les deformations principales de la deformation finie d un milieu elastique on prouve l existence de coordonnees orthogonales locales sur des varietes riemaniennes tridimensionnelles

a global estimator unbiased by local changes the global activity is an important confound when analyzing pet data in that its inclusion in the statistical model can substantially reduce error variance and increase sensitivity however by defining global activity as the average over all voxels one introduces a bias that is collinear with experimental factors this leads to an underestimation of true activations and the introduction of artefactual deactivations we propose a novel estimator for the global activity based on the notion of finding a maximally nonlocal mode in a multivariate characterization of the data while maximizing the locality of the remaining modes the approach uses singular value decomposition svd to find a provisional set of modes which are subsequently rotated such that a metric based on the above heuristic is maximized this metric is a version of the stochastic sign change ssc criterion that has been used previously for normalizing medical images with focal defects the estimator was evaluated on simulated and real functional imaging pet data the simulations show that the bias of the global mean introduced by focal activations is reduced by 80 90 with the new estimator comparison with a previous unbiased estimator using the empirical data yielded similar results the advantage of the new estimator is that it is not informed of experimental design and relies only on general assumptions regarding the nature of the signal

experimental design and the relative sensitivity of bold and perfusion fmri this paper compares the statistical power of bold and arterial spin labeling perfusion fmri for a variety of experimental designs within and across subjects based on theory and simulations we predict that perfusion data are composed of independent observations in time under the null hypothesis in contrast to bold data which possess marked autocorrelation we also present a method sinc subtraction of generating perfusion data from its raw source signal that minimizes the presence of oxygen sensitive signal changes and can be used with any experimental design empirically we demonstrate the absence of autocorrelation in perfusion noise examine the shape of the hemodynamic response function for bold and perfusion and obtain a measure of signal to noise for each method this information is then used to generate a model of relative sensitivity of the bold and perfusion methods for within subject experimental designs of varying temporal frequency it is determined that perfusion fmri provides superior sensitivity for within subject experimental designs that concentrate their power at or below approximately 0 009 hz corresponding to a blocked experimental design of 60 s epochs additionally evidence is presented that across subject hypothesis tests may be more sensitive when conducted using perfusion imaging despite the better within subject signal to noise obtained in some cases with bold

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

bv weak solutions to gauss codazzi system for isometric immersions abstract the isometric immersion problem for surfaces embedded into r 3 is studied via the fluid dynamic framework introduced in chen et al 2010 6 as a system of balance laws of mixed type the techniques developed in the theory of weak solutions of bounded variation in continuum physics are employed to deal with the isometric immersions in the setting of differential geometry the so called bv framework is formed that establishes convergence of approximate solutions of bounded variation to the gauss codazzi system and yields the c 1 1 isometric realization of two dimensional surfaces into r 3 local and global existence results are established for weak solutions of small bounded variation to the gauss codazzi system for negatively curved surfaces that admit equilibrium configurations as an application the case of catenoidal shell of revolution is provided

optimal spatial regularisation of autocorrelation estimates in fmri analysis in the general linear model glm framework for the statistical analysis of fmri data the problem of temporal autocorrelations in the residual signal after regression has been frequently addressed in the open literature there exist various methods for correcting the ensuing bias in the statistical testing among which the prewhitening strategy which uses a prewhitening matrix for rendering the residual signal white i e without temporal autocorrelations this correction is only exact when the autocorrelation structure of the noise generating process is accurately known and the estimates derived from the fmri data are too noisy to be used for correction recently worsley and co workers proposed to spatially smooth the noisy autocorrelation estimates effectively reducing their variance and allowing for a better correction in this article a systematic study into the effect of the smoothing kernel width is performed and a method is introduced for choosing this bandwidth in an optimal manner several aspects of the prewhitening strategy are investigated namely the choice of the autocorrelation estimate biased or unbiased the accuracy of the estimates the degree of spatial regularisation and the order of the autoregressive model used for characterising the noise the proposed method is extensively evaluated on both synthetic and real fmri data

a spatio temporal regression model for the analysis of functional mri data the standard method for analyzing functional magnetic resonance imaging fmri data applies the general linear model to the time series of each voxel separately such a voxelwise approach however does not consider the spatial autocorrelation between neighboring voxels in its model formulation and parameter estimation we propose a spatio temporal regression analysis for detecting activation in fmri data its main features are that 1 each voxel has a regression model that involves the time series of the neighboring voxels together with its own 2 the regression coefficient assigned to the center voxel is estimated so that the time series of these multiple voxels will best fit the model 3 a generalized least squares gls method was employed instead of the ordinary least squares ols to put intrinsic autocorrelation structures into the model and 4 the underlying spatial and temporal correlation structures are modeled using a separable model which expresses the combined correlation structures as a product of the two we evaluated the statistical power of our model in comparison with voxelwise ols gls models and a multivoxel ols model our model s power to detect clustered activation was higher than that of the two voxelwise models and comparable to that of the multivoxel ols we examined the usefulness and goodness of fit of our model using real experimental data our model successfully detected neural activity in expected brain regions and realized better fit than the other models these results suggest that our spatio temporal regression model can serve as a reliable analysis suited for the nature of fmri data

existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in eulerian and lagrangian coordinates we prove the existence and compactness stability of entropy solutions for the hyperbolic systems of conservation laws corresponding to the isentropic gas dynamics where the pressure and density are related by a law for any 1 our results considerably extend and simplify the program initiated by diperna and provide a complete existence proof our methods are based on the compensated compactness and the kinetic formulation of systems of conservation laws 1996 john wiley sons inc

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

a semi parametric approach to estimate the family wise error rate in fmri using resting state data one of the most important considerations in any hypothesis based fmri data analysis is to choose the appropriate threshold to construct the activation maps which is usually based on p values however in fmri data there are three factors which necessitate severe corrections in the process of estimating the p values first the fmri time series at an individual voxel has strong temporal autocorrelation which needs to be estimated to obtain the corrected parametric p value the second factor is the multiple comparisons problem arising from simultaneously testing tens of thousands of voxels for activation a common way in the statistical literature to account for multiple testing is to consider the family wise error rate fwe which is related to the distribution of the maximum observed value over all voxels the third problem which is not mentioned frequently in the context of adjusting the p value is the effect of inherent low frequency processes present even in resting state data that may introduce a large number of false positives without proper adjustment in this article a novel and efficient semi parametric method using resampling of normalized spacings of order statistics is introduced to address all the three problems mentioned above the new method makes very few assumptions and demands minimal computational effort unlike other existing resampling methods in fmri furthermore it will be demonstrated that the correction for temporal autocorrelation is not critical in implementing the proposed method results using the proposed method are compared with spm2

algebraic structure of classical field theory i kinematics and linearized dynamics for real scalar fields we describe the elements of a novel structural approach to classical field theory inspired by recent developments in perturbative algebraic quantum field theory this approach is local and focuses mainly on the observables over field configurations given by certain spaces of functionals which are studied here in depth the analysis of such functionals is characterized by a combination of geometric analytic and algebraic elements which 1 make our approach closer to quantum field theory 2 allow for a rigorous analytic refinement of many computational formulae from the functional formulation of classical field theory and 3 provide a new pathway towards understanding dynamics particular attention will be paid to aspects related to nonlinear hyperbolic partial differential equations and their linearizations

morphology based hypothesis testing in discrete random fields a non parametric method to address the multiple comparison problem in neuroimaging a new method for detecting activations in random fields which may be useful for addressing the issue of multiple comparisons in neuroimaging is presented this method is based on some constructs of mathematical morphology specifically morphological erosions and dilations that enable the detection of active regions in random fields possessing moderate activation levels and relatively large spatial extension which may not be detected by the standard methods that control the family wise error rate the method presented here permits an appropriate control of the false positive errors without having to adjust any threshold values other than the significance level the method is easily adapted to permutation based procedures with the usual restrictions and therefore does not require strong assumptions about the distribution and spatio temporal correlation structure of the data some examples of applications to synthetic data including realistic fmri simulations as well as to real fmri and electroencephalographic data are presented illustrating the power of the presented technique comparisons with other methods that combine voxel intensity and cluster size as well as some extensions of the method presented here based on their basic ideas are presented as well

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

identification of physiological response functions to correct for fluctuations in resting state fmri related to heart rate and respiration abstract functional magnetic resonance imaging fmri is widely viewed as the gold standard for studying brain function due to its high spatial resolution and non invasive nature however it is well established that changes in breathing patterns and heart rate strongly influence the blood oxygen level dependent bold fmri signal and this in turn can have considerable effects on fmri studies particularly resting state studies the dynamic effects of physiological processes are often quantified by using convolution models along with simultaneously recorded physiological data in this context physiological response function p r f curves cardiac and respiratory response functions which are convolved with the corresponding physiological fluctuations are commonly employed while it has often been suggested that the p r f curves may be region or subject specific it is still an open question whether this is the case in the present study we propose a novel framework for the robust estimation of p r f curves and use this framework to rigorously examine the implications of using population subject session and scan specific p r f curves the proposed framework was tested on resting state fmri and physiological data from the human connectome project our results suggest that p r f curves vary significantly across subjects and to a lesser extent across sessions from the same subject these differences can be partly attributed to physiological variables such as the mean and variance of the heart rate during the scan the proposed methodological framework can be used to obtain robust scan specific p r f curves from data records with duration longer than 5 min exhibiting significantly improved performance compared to previously defined canonical cardiac and respiration response functions besides removing physiological confounds from the bold signal accurate modeling of subject or session scan specific p r f curves is of importance in studies that involve populations with altered vascular responses such as aging subjects

isometric immersions and compensated compactness a fundamental problem in differential geometry is to characterize intrinsic metrics on a two dimensional riemannian manifold mathcal m 2 which can be realized as isometric immersions into mathbb r 3 this problem can be formulated as initial and or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic hyperbolic type whose mathematical theory is largely incomplete in this paper we develop a general approach which combines a fluid dynamic formulation of balance laws for the gauss codazzi system with a compensated compactness framework to deal with the initial and or boundary value problems for isometric immersions in mathbb r 3 the compensated compactness framework formed here is a natural formulation to ensure the weak continuity of the gauss codazzi system for approximate solutions which yields the isometric realization of two dimensional surfaces in mathbb r 3

application of bayesian inference to fmri data analysis the methods of bayesian statistics are applied to the analysis of fmri data three specific models are examined the first is the familiar linear model with white gaussian noise in this section the jeffreys rule for noninformative prior distributions is stated and it is shown how the posterior distribution may be used to infer activation in individual pixels next linear time invariant lti systems are introduced as an example of statistical models with nonlinear parameters it is shown that the bayesian approach can lead to quite complex bimodal distributions of the parameters when the specific case of a delta function response with a spatially varying delay is analyzed finally a linear model with auto regressive noise is discussed as an alternative to that with uncorrelated white gaussian noise the analysis isolates those pixels that have significant temporal correlation under the model it is shown that the number of pixels that have a significantly large auto regression parameter is dependent on the terms used to account for confounding effects

hyperelliptic jacobians and isogenies abstract in this note we mainly consider abelian varieties isogenous to hyperelliptic jacobians in the first part we prove that a very general hyperelliptic jacobian of genus g 4 is not isogenous to a non hyperelliptic jacobian as a consequence we obtain that the intermediate jacobian of a very general cubic threefold is not isogenous to a jacobian another corollary tells that the jacobian of a very general d gonal curve of genus g 4 is not isogenous to a different jacobian in the second part we consider a closed subvariety y a g of the moduli space of principally polarized varieties of dimension g 3 we show that if a very general element of y is dominated by the jacobian of a curve c and dim y 2 g then c is not hyperelliptic in particular if the general element in y is simple its kummer variety does not contain rational curves finally we show that a closed subvariety y m g of dimension 2 g 1 such that the jacobian of a very general element of y is dominated by a hyperelliptic jacobian is contained either in the hyperelliptic or in the trigonal locus

network connectivity modulates power spectrum scale invariance measures of complexity are sensitive in detecting disease which has made them attractive candidates for diagnostic biomarkers one complexity measure that has shown promise in fmri is power spectrum scale invariance pssi even if scale free features of neuroimaging turn out to be diagnostically useful however their underlying neurobiological basis is poorly understood using modeling and simulations of a schematic prefrontal limbic meso circuit with excitatory and inhibitory networks of nodes we present here a framework for how network density within a control system can affect the complexity of signal outputs our model demonstrates that scale free behavior similar to that observed in fmri pssi data can be obtained for sufficiently large networks in a context as simple as a linear stochastic system of differential equations although the scale free range improves when introducing more realistic nonlinear behavior in the system pssi values reflective of complexity vary as a function of both input type excitatory inhibitory and input density mean number of long range connections or strength independent of their node specific geometric distribution signals show pink noise 1 f behavior when excitatory and inhibitory influences are balanced as excitatory inputs are increased and decreased signals shift towards white and brown noise respectively as inhibitory inputs are increased and decreased signals shift towards brown and white noise respectively the results hold qualitatively at the hemodynamic scale which we modeled by introducing a neurovascular component comparing hemodynamic simulation results to fmri pssi results from 96 individuals across a wide spectrum of anxiety levels we show how our model can generate concrete and testable hypotheses for understanding how connectivity affects regulation of meso circuits in the brain

probabilistic independent component analysis for functional magnetic resonance imaging we present an integrated approach to probabilistic independent component analysis ica for functional mri fmri data that allows for nonsquare mixing in the presence of gaussian noise in order to avoid overfitting we employ objective estimation of the amount of gaussian noise through bayesian analysis of the true dimensionality of the data i e the number of activation and non gaussian noise sources this enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data it reduces problems of interpretation as each final independent component is now much more likely to be due to only one physical or physiological process we also describe other improvements to standard ica such as temporal prewhitening and variance normalization of timeseries the latter being particularly useful in the context of dimensionality reduction when weak activation is present we discuss the use of prior information about the spatiotemporal nature of the source processes and an alternative hypothesis testing approach for inference using gaussian mixture models the performance of our approach is illustrated and evaluated on real and artificial fmri data and compared to the spatio temporal accuracy of results obtained from classical ica and glm analyses

contextual clustering for analysis of functional mri data presents a contextual clustering procedure for statistical parametric maps spm calculated from time varying three dimensional images the algorithm can be used for the detection of neural activations from functional magnetic resonance images fmri an important characteristic of spm is that the intensity distribution of background nonactive area is known whereas the distributions of activation areas are not the developed contextual clustering algorithm divides an spm into background and activation areas so that the probability of detecting false activations by chance is controlled i e hypothesis testing is performed unlike the much used voxel by voxel testing neighborhood information is utilized an important difference this is achieved by using a markov random field prior and iterated conditional modes icm algorithm however unlike in the conventional use of icm algorithm the classification is based only on the distribution of background the results from the authors simulations and human fmri experiments using visual stimulation demonstrate that a better sensitivity is achieved with a given specificity in comparison to the voxel by voxel thresholding technique the algorithm is computationally efficient and can be used to detect and delineate objects from a noisy background in other applications

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

a high performance 3d cluster based test of unsmoothed fmri data cluster size tests cst based on random field theory have been widely adopted in fmri data analysis to detect brain activation however most existing approaches can be used appropriately only when the image is highly smoothed in the spatial domain unfortunately spatial smoothing degrades spatial specificity recently a threshold free cluster enhancement technique was proposed which does not require spatial smoothing but this method can be used only for group level analysis advances in imaging technology now yield high quality high spatial resolution imaging data in single subjects and an inference approach that retains the benefits of greater spatial resolution is called for in this work we present a new cst with a correction for voxelation to address this problem the theoretical formulation of the new approach based on gaussian random fields is developed to estimate statistical significance using 3d statistical parametric maps without assuming spatial smoothness simulated phantom and resting state fmri experimental data are then used to compare the voxelation corrected procedure to the widely used standard random field theory unlike standard random field theory approaches which require heavy spatial smoothing the new approach has a higher sensitivity for localizing activation regions without the requirement of spatial smoothness

combining spatial extent and peak intensity to test for activations in functional imaging within the framework of statistical mapping there are up to now only two tests used to assess the regional significance in functional images one is based on the magnitude of the foci and tends to detect high intensity signals while the second is based on the spatial extent of regions defined by a simple thresholding of the statistical map a test that is more sensitive to extended signals the aim of this paper is to combine the two tests into a single test that is more sensitive to a wider range of signals this combined test is based on an analytical approximation of the distribution of these two parameters size and height and is applied in the context of statistical maps the risk of error in noise only 2d or 3d volumes is assessed under a wide range of experimental conditions obtained by varying both the resolution of the map and the threshold at which clusters are defined in addition we have investigated this new test on simulated signals and applied it to an experimental pet dataset the experimental risk of error is close to the predicted one and the overall sensitivity increases when analyzing a volume containing different types of signals

detection of consistently task related activations in fmri data with hybrid independent component analysis fmri data are commonly analyzed by testing the time course from each voxel against specific hypothesized waveforms despite the fact that many components of fmri signals are difficult to specify explicitly in contrast purely data driven techniques by focusing on the intrinsic structure of the data lack a direct means to test hypotheses of interest to the examiner between these two extremes there is a role for hybrid methods that use powerful data driven techniques to fully characterize the data but also use some a priori hypotheses to guide the analysis here we describe such a hybrid technique hybica which uses the initial characterization of the fmri data from independent component analysis and allows the experimenter to sequentially combine assumed task related components so that one can gracefully navigate from a fully data derived approach to a fully hypothesis driven approach we describe the results of testing the method with two artificial and two real data sets a metric based on the diagnostic predicted sum of squares statistic was used to select the best number of spatially independent components to combine and utilize in a standard regressional framework the proposed metric provided an objective method to determine whether a more data driven or a more hypothesis driven approach was appropriate depending on the degree of mismatch between the hypothesized reference function and the features in the data hybica provides a robust way to combine the data derived independent components into a data derived activation waveform and suitable confounds so that standard statistical analysis can be performed

ellipsoidal support vector clustering for functional mri analysis as an exploratory approach the clustering of fmri time series has proved its effectiveness in analyzing the functional mri especially in the detection of activated regions due to the arbitrary distribution of fmri time series in the temporal domain imposing simple assumption on the data structure usually could be misleading and limit the detector s performance therefore a true data driven clustering algorithm that adapts to the data structure is preferred and only high level control over the clustering procedure is desired support vector clustering svc is a suitable one in some extent because of its advantages such as no cluster shape restriction no need to explicitly specify the number of clusters and the mechanism in outlier elimination in this work we propose an extension of the svc to step further toward a data sensitive detector this approach is named as ellipsoidal support vector clustering esvc to be robust to noise the clustering is performed on features extracted from the fmri time series via fourier transform experimental results on simulated and real data sets demonstrate the effectiveness of incorporating data structure in clustering fmri time series

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

monte carlo sure a black box optimization of regularization parameters for general denoising algorithms we consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white gaussian noise to achieve this we propose to minimize stein s unbiased risk estimate sure which provides a means of assessing the true mean squared error mse purely from the measured data without need for any knowledge about the noise free signal specifically we present a novel monte carlo technique which enables the user to calculate sure for an arbitrary denoising algorithm characterized by some specific parameter setting our method is a black box approach which solely uses the response of the denoising operator to additional input noise and does not ask for any information about its functional form this therefore permits the use of sure for optimization of a wide variety of denoising algorithms we justify our claims by presenting experimental results for sure based optimization of a series of popular image denoising algorithms such as total variation denoising wavelet soft thresholding and wiener filtering smoothing splines in the process we also compare the performance of these methods we demonstrate numerically that sure computed using the new approach accurately predicts the true mse for all the considered algorithms we also show that sure uncovers the optimal values of the parameters in all cases

group analysis in functional neuroimaging selecting subjects using similarity measures standard group analyses of fmri data rely on spatial and temporal averaging of individuals this averaging operation is only sensible when the mean is a good representation of the group this is not the case if subjects are not homogeneous and it is therefore a major concern in fmri studies to assess this group homogeneity we present a method that provides relevant distances or similarity measures between temporal series of brain functional images belonging to different subjects the method allows a multivariate comparison between data sets of several subjects in the time or in the space domain these analyses assess the global intersubject variability before averaging subjects and drawing conclusions across subjects at the population level we adapt the rv coefficient to measure meaningful spatial or temporal similarities and use multidimensional scaling to give a visual representation of each subject s position with respect to other subjects in the group we also provide a measure for detecting subjects that may be outliers results show that the method is a powerful tool to detect subjects with specific temporal or spatial patterns and that despite the apparent loss of information restricting the analysis to a homogeneous subgroup of subjects does not reduce the statistical sensitivity of standard group fmri analyses

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

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

characteristics and existence of isometric embeddings soit m ds 2 une variete de riemann c a 3 dimensions et x 0 m un point tel que le tenseur d einstein 7b g x 0 n est pas l 2 ou l t x0 m alors il existe un plongement isometrique local c d un voisinage de x 0 dans e 6

measuring interregional functional connectivity using coherence and partial coherence analyses of fmri data understanding functional connectivity within the brain is crucial to understanding neural function even the simplest cognitive operations are supported by highly distributed neural circuits we developed a novel method to measure task related functional interactions between neural regions by applying coherence and partial coherence analyses to functional magnetic resonance imaging fmri data coherence and partial coherence are spectral measures that estimate the linear time invariant lti relationship between time series they can be used to generate maps of task specific connectivity associated with seed regions of interest rois these maps may then be compared across tasks revealing nodes with task related changes of connectivity to the seed roi to validate the method we applied it to an event related fmri data set acquired while subjects performed two sequence tapping tasks one of which required more bimanual coordination areas showing increased functional connectivity with both tasks were the same as those showing increased activity furthermore though there were no significant differences in mean activity between the two tasks significant increases in interhemispheric coherence were found between the primary motor m1 and premotor pm regions for the task requiring more bimanual coordination this increase in interhemispheric connectivity is supported by other brain imaging techniques as well as patient studies

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

local likelihood density estimation local likelihood was introduced by tibshirani and hastie as a method of smoothing by local polynomials in non gaussian regression models in this paper an extension of these methods to density estimation is discussed and comparison with other methods of density estimation presented the local likelihood method has particularly strong advantages over kernel methods when estimating tails of densities and in multivariate settings suppose constraints are incorporated in a simple manner asymptotic properties of the estimate are discussed a method for computing the estimate is outlined c code to implement the estimation procedure described in this paper together with s interfaces for graphical display of results are available at http cm bell labs com stat project locfit index html

a priori bounds for co dimension one isometric embeddings let x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i be a c 4 isometric embedding of a c4 metric g of nonnegative sectional curvature on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i into the euclidean space inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i we prove a priori bounds for the trace of the second fundamental form h in terms of the scalar curvature r of g and the diameter d of the space inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 05i g these estimates give a bound on the extrinsic geometry in terms of intrinsic quantities they generalize estimates originally obtained by weyl for the case n 2 and positive curvature and then by p guan and the first author for nonnegative curvature and n 2 using c 2 interior estimates of evans and krylov for concave fully nonlinear elliptic partial differential equations these bounds allow us to obtain the following convergence theorem for any 0 the set of metrics of nonnegative sectional curvature and scalar curvature bounded below by which are isometrically embedable in euclidean space inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 06i is closed in the holder space c 4 0 suppose that g is a smooth metric of nonnegative sectional curvature and positive scalar curvature on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 07i which admits locally convex isometric embedding into inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 08i does inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 09i g then admit a smooth global isometric embedding x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 10i g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 11i

global voxel and cluster tests by theory and permutation for a difference between two groups of structural mr images of the brain the authors describe almost entirely automated procedures for estimation of global voxel and cluster level statistics to test the null hypothesis of zero neuroanatomical difference between two groups of structural magnetic resonance imaging mri data theoretical distributions under the null hypothesis are available for 1 global tissue class volumes 2 standardized linear model analysis of variance anova and ancova coefficients estimated at each voxel and 3 an area of spatially connected clusters generated by applying an arbitrary threshold to a two dimensional 2 d map of normal statistics at voxel level the authors describe novel methods for economically ascertaining probability distributions under the null hypothesis with fewer assumptions by permutation of the observed data nominal type i error control by permutation testing is generally excellent whereas theoretical distributions may be over conservative permutation has the additional advantage that it can be used to test any statistic of interest such as the sum of suprathreshold voxel statistics in a cluster or cluster mass regardless of its theoretical tractability under the null hypothesis these issues are illustrated by application to mri data acquired from 18 adolescents with hyperkinetic disorder and 16 control subjects matched for age and gender

a study of analysis parameters that influence the sensitivity of event related fmri analyses to assess the effect of various analysis parameters on the sensitivity of event related fmri analyses 36 analyses were performed on a single fmri data set varying parameters along four axes 1 resampled voxel size 2 spatial smoothing 3 temporal smoothing and 4 the set of basis functions used to model event related responses sensitivity i e the probability of detecting an activation given it exists was assessed in terms of z scores and by a metric for corrected p values the negative log of the expected euler characteristic sixteen brain regions distributed across cortical and subcortical areas were included in the meta analysis main effects on sensitivity were found for resampled voxel size spatial smoothing temporal smoothing and the set of basis functions chosen the analysis parameters that generally produced the most sensitive analyses were a 2 mm 3 resampled voxel size 10 mm spatial smoothing 4 s temporal smoothing and a basis set comprising a hemodynamic response function and its temporal derivative r 2000 academic press

a wavelet based estimator of the degrees of freedom in denoised fmri time series for probabilistic testing of functional connectivity and brain graphs connectome mapping using techniques such as functional magnetic resonance imaging fmri has become a focus of systems neuroscience there remain many statistical challenges in analysis of functional connectivity and network architecture from bold fmri multivariate time series one key statistic for any time series is its effective degrees of freedom df which will generally be less than the number of time points or nominal degrees of freedom n if we know the df then probabilistic inference on other fmri statistics such as the correlation between two voxel or regional time series is feasible however we currently lack good estimators of df in fmri time series especially after the degrees of freedom of the raw data have been modified substantially by denoising algorithms for head movement here we used a wavelet based method both to denoise fmri data and to estimate the effective df of the denoised process we show that seed voxel correlations corrected for locally variable df could be tested for false positive connectivity with better control over type i error and greater specificity of anatomical mapping than probabilistic connectivity maps using the nominal degrees of freedom we also show that wavelet despiked statistics can be used to estimate all pairwise correlations between a set of regional nodes assign a p value to each edge and then iteratively add edges to the graph in order of increasing p these probabilistically thresholded graphs are likely more robust to regional variation in head movement effects than comparable graphs constructed by thresholding correlations finally we show that time windowed estimates of df can be used for probabilistic connectivity testing or dynamic network analysis so that apparent changes in the functional connectome are appropriately corrected for the effects of transient noise bursts wavelet despiking is both an algorithm for fmri time series denoising and an estimator of the effective df of denoised fmri time series accurate estimation of df offers many potential advantages for probabilistically thresholding functional connectivity and network statistics tested in the context of spatially variant and non stationary noise code for wavelet despiking seed correlational testing and probabilistic graph construction is freely available to download as part of the brainwavelet toolbox at www brainwavelet org

filtering induces correlation in fmri resting state data abstract correlation based functional mri connectivity methods typically impose a temporal sample independence assumption on the data however the conventional use of temporal filtering to address the high noise content of fmri data may introduce sample dependence violation of the independence assumption has ramifications for the distribution of sample correlation which if unaccounted for may invalidate connectivity results to enable the use of temporal filtering for noise suppression while maintaining the integrity of connectivity results we derive the distribution of sample correlation between filtered timeseries as a function of the filter frequency response corrected distributions are also derived for statistical inference tests of sample correlation between filtered timeseries including fisher s z transformation and the student s t test crucially the proposed corrections are valid for any unknown true correlation and arbitrary filter specifications empirical simulations demonstrate the potential for temporal filtering to artificially induce connectivity by introducing sample dependence and verify the utility of the proposed corrections in mitigating this effect the importance of our corrections is exemplified in a resting state fmri connectivity analysis seed voxel correlation maps generated from filtered data using uncorrected test variates yield an unfeasible number of connections to the left primary motor cortex suggesting artificially induced connectivity while maps acquired from filtered data using corrected test variates exhibit bilateral connectivity in the primary motor cortex in conformance with expected results as seen in the literature

wavelet based estimation of a semiparametric generalized linear model of fmri time series addresses the problem of detecting significant changes in fmri time series that are correlated to a stimulus time course this paper provides a new approach to estimate the parameters of a semiparametric generalized linear model of the fmri time series the fmri signal is described as the sum of two effects a smooth trend and the response to the stimulus the trend belongs to a subspace spanned by large scale wavelets the wavelet transform provides an approximation to the karhunen loeve transform for the long memory noise and we have developed a scale space regression that permits one to carry out the regression in the wavelet domain while omitting the scales that are contaminated by the trend in order to demonstrate that our approach outperforms the state of the art detrending technique we evaluated our method against a smoothing spline approach experiments with simulated data and experimental fmri data demonstrate that our approach can infer and remove drifts that cannot be adequately represented with splines

on the existence of c 1 1 isometric immersions of several classes of negatively curved surfaces into mathbb r 3 we prove the existence of c 1 1 isometric immersions of several classes of negatively curved riemannian surfaces mathcal m g into the 3 dimensional euclidean space mathbb r 3 including the standard hyperbolic plane the generalised helicoid type metrics and the generalised enneper metrics our proof is based on the theory of compensated compactness and the method of invariant regions in hyperbolic conservation laws together with several new observations on relevant geometric quantities gauss curvature metric components etc for negatively curved surfaces

spatiotemporal wavelet analysis for functional mri characterizing the spatiotemporal behavior of the bold signal in functional magnetic resonance imaging fmri is a central issue in understanding brain function while the nature of functional activation clusters is fundamentally heterogeneous many current analysis approaches use spatially invariant models that can degrade anatomic boundaries and distort the underlying spatiotemporal signal furthermore few analysis approaches use true spatiotemporal continuity in their statistical formulations to address these issues we present a novel spatiotemporal wavelet procedure that uses a stimulus convolved hemodynamic signal plus correlated noise model the wavelet fits computed by spatially constrained maximum likelihood estimation provide efficient multiscale representations of heterogeneous brain structures and give well identified parsimonious spatial activation estimates that are modulated by the temporal fmri dynamics in a study of both simulated data and actual fmri memory task experiments our new method gave lower mean squared error and seemed to result in more localized fmri activation maps compared to models using standard wavelet or smoothing techniques our spatiotemporal wavelet framework suggests a useful tool for the analysis of fmri studies

local smooth isometric embeddings of low dimensional riemannian manifolds into euclidean spaces on demontre l existence d un plongement isometrique lisse locale d une 3 variete de riemann lisse a courbure qui ne s annule pas dans un 6 espace euclidien

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics

detecting and adjusting for artifacts in fmri time series data we present a new method to detect and adjust for noise and artifacts in functional mri time series data we note that the assumption of stationary variance which is central to the theoretical treatment of fmri time series data is often violated in practice sporadic events such as eye mouth or arm movements can increase noise in a spatially global pattern throughout an image leading to a non stationary noise process we derive a restricted maximum likelihood reml algorithm that estimates the variance of the noise for each image in the time series these variance parameters are then used to obtain a weighted least squares estimate of the regression parameters of a linear model we apply this approach to a typical fmri experiment with a block design and show that the noise estimates strongly vary across different images and that our method detects and appropriately weights images that are affected by artifacts furthermore we show that the noise process has a global spatial distribution and that the variance increase is multiplicative rather than additive the new algorithm results in significantly increased sensitivity in the ability to detect regions of activation the new method may be particularly useful for studies that involve special populations e g children or elderly where sporadic artifact generating events are more likely

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

generalized least squares method applied to fmri time series with empirically determined correlation matrix functional magnetic resonance imaging fmri time series analysis and statistical inferences about the effect of a cognitive task on the regional cerebral blood flow rcbf are largely based on the linear model however this method requires that the error vector is a gaussian variable with an identity correlation matrix when this assumption cannot be accepted statistical inferences can be made using generalized least squares in this case knowledge of the covariance matrix of the error vector is needed in the present report we propose a method that needs stationarity of the autocorrelation function but is more flexible than autoregressive model of order p ar p models because it is not necessary to predefine a relation between coefficients of the correlation matrix we tested this method on sets of simulated data with presence of an effect of interest or not representing a time series with a monotonically decreasing autocorrelation function this time series mimicked an experiment using a random event related design that does not create correlation between scans the autocorrelation function is empirically determined and used to reconstitute the correlation matrix as the toeplitz matrix built from the autocorrelation function when applied to simulated time series with no effect of interest this method allows the determination of f values corresponding to the accurate false positive level moreover when applied to time series with an effect of interest this method gives a density function of f values which allows the rejection of the null hypothesis this method provides a flexible but interpretable time domain noise model