homotopy techniques for tensor decomposition and perfect identifiability let t be a general complex tensor of format n1 nd when the fraction i ni 1 i ni 1 is an integer and a natural inequality called balancedness is satisfied it is expected that t has finitely many minimal decomposition as a sum of decomposable tensors we show how homotopy techniques allow us to find all the decompositions of t starting from a given one in particular this gives a guess true with high probability about the total number of these decompositions this guess matches exactly with all cases previously known and predicts several unknown cases some surprising experiments yielded two new cases of generic identifiability formats 3 4 5 and 2 2 2 3 which have a unique decomposition as the sum of 6 and 4 decomposable tensors respectively we conjecture that these two cases together with the classically known matrix pencils are the only cases where generic identifiability holds i e the only identifiable cases building on the computational experiments we also use basic tools from algebraic geometry to prove these two new cases are indeed generically identifiable

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

classical and bayesian inference in neuroimaging theory this paper reviews hierarchical observation models used in functional neuroimaging in a bayesian light it emphasizes the common ground shared by classical and bayesian methods to show that conventional analyses of neuroimaging data can be usefully extended within an empirical bayesian framework in particular we formulate the procedures used in conventional data analysis in terms of hierarchical linear models and establish a connection between classical inference and parametric empirical bayes peb through covariance component estimation this estimation is based on an expectation maximization or em algorithm the key point is that hierarchical models not only provide for appropriate inference at the highest level but that one can revisit lower levels suitably equipped to make bayesian inferences bayesian inferences eschew many of the difficulties encountered with classical inference and characterize brain responses in a way that is more directly predicated on what one is interested in the motivation for bayesian approaches is reviewed and the theoretical background is presented in a way that relates to conventional methods in particular restricted maximum likelihood reml this paper is a technical and theoretical prelude to subsequent papers that deal with applications of the theory to a range of important issues in neuroimaging these issues include i estimating nonsphericity or variance components in fmri time series that can arise from serial correlations within subject or are induced by multisubject i e hierarchical studies ii spatiotemporal bayesian models for imaging data in which voxels specific effects are constrained by responses in other voxels iii bayesian estimation of nonlinear models of hemodynamic responses and iv principled ways of mixing structural and functional priors in eeg source reconstruction although diverse all these estimation problems are accommodated by the peb framework described in this paper

detection power estimation efficiency and predictability in event related fmri experimental designs for event related functional magnetic resonance imaging can be characterized by both their detection power a measure of the ability to detect an activation and their estimation efficiency a measure of the ability to estimate the shape of the hemodynamic response randomized designs offer maximum estimation efficiency but poor detection power while block designs offer good detection power at the cost of minimum estimation efficiency periodic single trial designs are poor by both criteria we present here a theoretical model of the relation between estimation efficiency and detection power and show that the observed trade off between efficiency and power is fundamental using the model we explore the properties of semirandom designs that offer intermediate trade offs between efficiency and power these designs can simultaneously achieve the estimation efficiency of randomized designs and the detection power of block designs at the cost of increasing the length of an experiment by less than a factor of 2 experimental designs can also be characterized by their predictability a measure of the ability to circumvent confounds such as habituation and anticipation we examine the relation between detection power estimation efficiency and predictability and show that small increases in predictability can offer significant gains in detection power with only a minor decrease in estimation efficiency

spherical blow ups of grassmannians and mori dream spaces abstract in this paper we classify weak fano varieties that can be obtained by blowing up general points in prime fano varieties we also classify spherical blow ups of grassmannians in general points and we compute their effective cone these blow ups are in particular mori dream spaces furthermore we compute the stable base locus decomposition of the blow up of a grassmannian in one point and we show how it is determined by linear systems of hyperplanes containing the osculating spaces of the grassmannian at the blown up point and by the rational normal curves in the grassmannian passing through the blown up point

computation of second order accurate unsteady aerodynamic generalized forces a classical variational statement is used to derive special properties of a weighted residual method it is shown that some weighted integral of the sought solution can be obtained to second order accuracy in the solution to the original and adjoint problems for aerodynamic problems it is assumed that the reverse flow problem is adjoint to the original problem examples on airfoils and wings demonstrate the fast convergence of generalized aerodynamic forces the singular behavior of aerodynamic problems is shown to be the factor that makes the application of these techniques so attractive in aerodynamics

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

the possible dimensions of the higher secant varieties let x c p be an irreducible closed subvariety of projective space the kth higher secant variety of x denoted x is the closure of the union of all linear spaces spanned by k points of x let a ix dim x dim x l it is known that the sequence ty x is nonincreasing and that there may be at most one 1 in such a sequence we prove that these two conditions are also sufficient conditions for an arbitrary sequence a of nonnegative integers to be the fl x s for an irreducible variety x to this end we exhibit the ideals of the higher secant varities of rational normal scrolls as determinantal ideals this allows us to compute their dimensions showing that there is in fact always a rational normal scroll x such that ak x a for any sequence a satisfying the two conditions above adlandsvik al a2 and flenner and vogel f v much of this work has centered on the behavior of the differences ak x dimx dimx 1 of the dimensions of consecutive higher secant varieties it is well known that this sequence is nonincreasing and that there is at most one 1 in the sequence palatini claimed moreover that once ak x 1 were counterexamples a2 we answer here the question of what sequences actually appear as the ai x s of some variety x some of the guiding examples of varieties with degenerate higher secant varieties come from rational normal scrolls explicit equations for the scrolls themselves have been known for some time cf acgh we give a determi nantal presentation of the ideals of their higher secant varieties generalizing a result for rational normal scrolls in w this presentation enables us to compute the dimensions of all the higher secant varieties of a rational normal scroll and gives examples of varieties x with a prescribed nonincreasing ak x with at most one 1

positivity of divisors on blown up projective spaces ii we construct log resolutions of pairs on the blow up of the projective space in an arbitrary number of general points and we discuss the semi ampleness of the strict transforms as an application we give an explicit proof that the abundance conjecture holds for an infinite family of such pairs for n 2 points these strict transforms are f nef divisors on the moduli space m0 n 3 in a kapranov s model we show that all of them are nef

singularities of linear systems and the waring problem the waring problem for homogeneous forms asks for additive decomposition of a form f into powers of linear forms a classical problem is to determine when such a decomposition is unique in this paper we answer this question when the degree of f is greater than the number of variables to do this we translate the algebraic statement into a geometric one concerning the singularities of linear systems of p with assigned singularities

decomposition of homogeneous polynomials with low rank let f be a homogeneous polynomial of degree d in m 1 variables defined over an algebraically closed field of characteristic 0 and suppose that f belongs to the s th secant variety of the d uple veronese embedding of mathbb p m into mathbb p tiny left begin array c rm m d rm d end array right 1 but that its minimal decomposition as a sum of d th powers of linear forms m1 mr is f m 1 d cdots m r d with r s we show that if s r 2d 1 then such a decomposition of f can be split in two parts one of them is made by linear forms that can be written using only two variables the other part is uniquely determined once one has fixed the first part we also obtain a uniqueness theorem for the minimal decomposition of f if r is at most d and a mild condition is satisfied

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

on the branch curve of a general projection of a surface to a plane in this paper we prove that the branch curve of a general projection of a surface to the plane is irreducible with only nodes and cusps this is a basic result in surface theory extremely useful in various applications however its proof in this general setting was so far lacking our approach substantially uses a powerful tool from projective differential geometry i e the concept of focal schemes

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

varieties with minimal secant degree and linear systems of maximal dimension on surfaces abstract in this paper we prove using a refinement of terracini s lemma a sharp lower bound for the degree of higher secant varieties to a given projective variety which extends the well known lower bound for the degree of a variety in terms of its dimension and codimension in projective space moreover we study varieties for which the bound is attained proving some general properties related to tangential projections e g these varieties are rational in particular we completely classify surfaces and curves for which the bound is attained it turns out that these surfaces enjoy some maximality properties for their embedding dimension in terms of their degree or sectional genus this is related to classical beautiful results of castelnuovo and enriques that we revise here in terms of adjunction theory

postulation of general quintuple fat point schemes in p 3 we study the postulation of a general union y of double triple quartuple and quintuple points of p 3 in characteristic 0 we prove that y has good postulation in degree d 11 the proof is based on the combination of the horace differential lemma with a computer assisted proof we also classify the exceptions in degree 9 and 10

vanishing theorems for linearly obstructed divisors we study divisors on the blow up of pn at points in general position that are non special with respect to the notion of linear speciality introduced in 6 we describe the cohomology groups of their strict transforms via the blow up of the space along their linear base locus we extend the result to non effective divisors that sit in a small region outside the effective cone as an application we describe linear systems of divisors in pn blown up at points in star configuration and their strict transforms via the blow up of the linear base locus

signal processing applications of oblique projection operators oblique projection operators are used to project measurements onto a low rank subspace along a direction that is oblique to the subspace they may be used to enhance signals while nulling interferences in the paper the authors give several basic results for oblique projections including formulas for constructing oblique projections with desired range and null space they analyze the algebra and geometry of oblique projections in order to understand their properties they then show how oblique projections can be used to separate signals from structured noise such as impulse noise damped or undamped interfering sinusoids such as power line interference and narrow band noise in some of the problems addressed the oblique projection provides an alternative way to implement an already known solution expressing these solutions as oblique projections brings geometrical insight to the study of the solution the geometry of oblique projections enables one to compute performance in terms of angles between signal and noise subspaces as a special case of removing impulse noise the authors can use oblique projections to interpolate missing data samples in array processing oblique projections can be used to simultaneously steer beams and nulls in communications oblique projections can be used to remove intersymbol interference

voxelwise encoding models with non spherical multivariate normal priors predictive models for neural or fmri data are often fit using regression methods that employ priors on the model parameters one widely used method is ridge regression which employs a spherical multivariate normal prior that assumes equal and independent variance for all parameters however a spherical prior is not always optimal or appropriate there are many cases where expert knowledge or hypotheses about the structure of the model parameters could be used to construct a better prior in these cases non spherical multivariate normal priors can be employed using a generalized form of ridge known as tikhonov regression yet tikhonov regression is only rarely used in neuroscience in this paper we discuss the theoretical basis for tikhonov regression demonstrate a computationally efficient method for its application and show several examples of how tikhonov regression can improve predictive models for fmri data we also show that many earlier studies have implicitly used tikhonov regression by linearly transforming the regressors before performing ridge regression

on generic identifiability of symmetric tensors of subgeneric rank we prove that the general symmetric tensor in sdcn 1 of rank r is identifiable provided that r is smaller than the generic rank that is its waring decomposition as a sum of r powers of linear forms is unique only three exceptional cases arise all of which were known in the literature our original contribution regards the case of cubics d 3 while for d 4 we rely on known results on weak defectivity by ballico ciliberto chiantini and mella

group level impacts of within and between subject hemodynamic variability in fmri inter subject fmri analyses have specific issues regarding the reliability of the results concerning both the detection of brain activation patterns and the estimation of the underlying dynamics among these issues lies the variability of the hemodynamic response function hrf that is usually accounted for using functional basis sets in the general linear model context here we use the joint detection estimation approach jde makni et al 2008 vincent et al 2010 which combines regional nonparametric hrf inference with spatially adaptive regularization of activation clusters to avoid global smoothing of fmri images we show that the jde based inference brings a significant improvement in statistical sensitivity for detecting evoked activity in parietal regions in contrast the canonical hrf associated with spatially adaptive regularization is more sensitive in other regions such as motor cortex this different regional behavior is shown to reflect a larger discrepancy of hrf with the canonical model by varying parallel imaging acceleration factor snr specific region based hemodynamic parameters activation delay and duration were extracted from the jde inference complementary analyses highlighted their significant departure from the canonical parameters and the strongest between subject variability that occurs in the parietal region irrespective of the snr value finally statistical evidence that the fluctuation of the hrf shape is responsible for the significant change in activation detection performance is demonstrated using paired t tests between hemodynamic parameters inferred by glm and jde

ranks of tensors secant varieties of segre varieties and fat points abstract a classical unsolved problem of projective geometry is that of finding the dimensions of all the higher secant varieties of the segre embeddings of an arbitrary product of projective spaces an important subsidiary problem is that of finding the smallest integer t for which the secant variety of projective t spaces fills the ambient projective space in this paper we give a new approach to these problems the crux of our method is the translation of a well known lemma of terracini into a question concerning the hilbert function of fat points in a multiprojective space our approach gives much new information on the classical problem even in the case of three factors a case also studied in the area of algebraic complexity theory

using voxel specific hemodynamic response function in eeg fmri data analysis most existing analytical techniques for eeg fmri data need specific assumptions about the hemodynamic response function hrf these assumptions may not be appropriate when the hrf varies from subject to subject or from region to region in this article we introduce a deconvolution method for eeg fmri activation detection which can be implemented with voxel specific hrfs a comparison of performance is made between three fixed hrfs and the deconvolution method under the framework of the general linear model the main results are as follows 1 the volume of detected regions from the deconvolved hrfs is larger 2 in some subjects the deconvolution technique can find areas of activation that have not been detected with the three fixed hrfs at our threshold of significance 3 deconvolution obtained higher adjusted coefficients of multiple determination compared to those obtained with the three fixed hrfs the results suggest that the fixed hrf methods may not be the most appropriate for the analysis of epileptic activity with eeg fmri and the deconvolution method may be a better choice

a general statistical analysis for fmri data we propose a method for the statistical analysis of fmri data that seeks a compromise between efficiency generality validity simplicity and execution speed the main differences between this analysis and previous ones are a simple bias reduction and regularization for voxel wise autoregressive model parameters the combination of effects and their estimated standard deviations across different runs sessions subjects via a hierarchical random effects analysis using the em algorithm overcoming the problem of a small number of runs session subjects using a regularized variance ratio to increase the degrees of freedom

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

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

birational aspects of the geometry of varieties of sums of powers abstract varieties of sums of powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms the study of these varieties dates back to sylvester and hilbert but only few of them for special degrees and number of variables are concretely identified in this paper we aim to understand a general birational behavior of vsp to do this we birationally embed these varieties into grassmannians and prove the rational connectedness of many vsp in arbitrary degrees and number of variables

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

weakly defective varieties a projective variety x is k weakly defective when its intersection with a general k 1 tangent hyperplane has no isolated singularities at the k 1 points of tangency if x is k defective i e if the k secant variety of x has dimension smaller than expected then x is also k weakly defective the converse does not hold in general a classification of weakly defective varieties seems to be a basic step in the study of defective varieties of higher dimension we start this classification here describing all weakly defective irreducible surfaces our method also provides a new proof of the classical terracini s classification of k defective surfaces

secant varieties of segre veronese embeddings of p 1 r we use a double degeneration technique to calculate the dimension of the secant variety of any segre veronese embedding of mathbb p 1 r

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

characterizing the functional mri response using tikhonov regularization summary the problem of evaluating an averaged functional magnetic resonance imaging fmri response for repeated block design experiments was considered within a semiparametric regression model with autocorrelated residuals we applied functional data analysis fda techniques that use a least squares fitting of b spline expansions with tikhonov regularization to deal with the noise autocorrelation we proposed a regularization parameter selection method based on the idea of combining temporal smoothing with residual whitening a criterion based on a generalized 2 test of the residuals for white noise was compared with a generalized cross validation scheme we evaluated and compared the performance of the two criteria based on their effect on the quality of the fmri response we found that the regularization parameter can be tuned to improve the noise autocorrelation structure but the whitening criterion provides too much smoothing when compared with the cross validation criterion the ultimate goal of the proposed smoothing techniques is to facilitate the extraction of temporal features in the hemodynamic response for further analysis in particular these fda methods allow us to compute derivatives and integrals of the fmri signal so that fmri data may be correlated with behavioral and physiological models for example positive and negative hemodynamic responses may be easily and robustly identified on the basis of the first derivative at an early time point in the response ultimately these methods allow us to verify previously reported correlations between the hemodynamic response and the behavioral measures of accuracy and reaction time showing the potential to recover new information from fmri data copyright q 2007 john wiley sons ltd