differential models for b type open closed topological landau ginzburg theories we propose a family of differential models for b type open closed topological landau ginzburg theories defined by a pair x w where x is any non compact calabi yau manifold and w is any holomorphic complex valued function defined on x whose critical set is compact the models are constructed at cochain level using smooth data including the twisted dolbeault algebra of polyvector valued forms and a twisted dolbeault category of holomorphic factorizations of w we give explicit proposals for cochain level versions of the bulk and boundary traces and for the bulk boundary and boundary bulk maps of the landau ginzburg theory we prove that most of the axioms of an open closed tft topological field theory are satisfied on cohomology and conjecture that the remaining two axioms namely non degeneracy of bulk and boundary traces and the topological cardy constraint are also satisfied

canonical q deformations of noncompact lie super algebras the author proposes a procedure for q deformations of the real forms g of complex lie super algebras associated with generalized cartan matrices the procedure gives different q deformations for the nonconjugate cartan subalgebras of g the author gives several illustrations e g q deformed lorentz and conformal super algebras the q deformed conformal algebra contains as a subalgebra a q deformed poincare algebra and as hopf subalgebras two conjugate 11 generator q deformed weyl algebras the q deformed lorentz algebra is a hopf subalgebra of both weyl algebras

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

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

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

fractional gaussian noise functional mri and alzheimer s disease fractional gaussian noise fgn provides a parsimonious model for stationary increments of a self similar process parameterised by the hurst exponent h and variance sigma2 fractional gaussian noise with h 0 5 demonstrates 1 f long memory or persistent behaviour and the special case of fgn with h 0 5 corresponds to classical gaussian white noise we comparatively evaluate four possible estimators of fgn parameters one method implemented in the time domain and three in the wavelet domain we show that a wavelet based maximum likelihood ml estimator yields the most efficient estimates of h and sigma2 in simulated fgn with 0 0 5 tend to be concentrated in cortex whereas voxels with h 0 5 are more frequently located in ventricles and sulcal csf the wavelet ml estimator can be generalised to estimate the parameter vector beta for general linear modelling glm of a physiological response to experimental stimulation and we demonstrate nominal type i error control in multiple testing of beta divided by its standard error in simulated and biological data under the null hypothesis beta 0 we illustrate these methods principally by showing that there are significant differences between patients with early alzheimer s disease ad and age matched comparison subjects in the persistence of fgn in the medial and lateral temporal lobes insula dorsal cingulate medial premotor cortex and left pre and postcentral gyrus patients with ad had greater persistence of resting fmri noise larger h in these regions comparable abnormalities in the ad patients were also identified by a permutation test of local differences in the first order autoregression ar 1 coefficient which was significantly more positive in patients however we found that the hurst exponent provided a more sensitive metric than the ar 1 coefficient to detect these differences perhaps because neurophysiological changes in early ad are naturally better described in terms of abnormal salience of long memory dynamics than a change in the strength of association between immediately consecutive time points we conclude that parsimonious mapping of fmri noise properties in terms of fgn parameters efficiently estimated in the wavelet domain is feasible and can enhance insight into the pathophysiology of alzheimer s disease

chern characters and hirzebruch riemann roch formula for matrix factorizations we study the category of matrix factorizations for an isolated hypersurface singularity we compute the canonical bilinear form on the hochschild homology of this category we find explicit expressions for the chern character and the boundary bulk maps and derive an analogue of the hirzebruch riemann roch formula for the euler characteristic of the hom space between a pair of matrix factorizations we also establish g equivariant versions of these results

quasitriangularity and enveloping algebras for inhomogeneous quantum groups coquasitriangular universal r matrices on quantum lorentz and quantum poincare groups are classified the results are extended under certain assumptions to inhomogeneous quantum groups enveloping algebras on those objects are described

multilevel linear modelling for fmri group analysis using bayesian inference functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and or multiple subjects a hierarchical approach can be taken to modelling such data with a general linear model glm at each level of the hierarchy introducing different random effects variance components inferring on these models is nontrivial with frequentist solutions being unavailable a solution is to use a bayesian framework one important ingredient in this is the choice of prior on the variance components and top level regression parameters due to the typically small numbers of sessions or subjects in neuroimaging the choice of prior is critical to alleviate this problem we introduce to neuroimage modelling the approach of reference priors which drives the choice of prior such that it is noninformative in an information theoretic sense we propose two inference techniques at the top level for multilevel hierarchies a fast approach and a slower more accurate approach we also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them

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

quantum instantons with classical moduli spaces we introduce a quantum minkowski space time based on the quantum group su 2 q extended by a degree operator and formulate a quantum version of the anti self dual yang mills equation we construct solutions of the quantum equations using the classical adhm linear data and conjecture that up to gauge transformations our construction yields all the solutions we also find a deformation of penrose s twistor diagram giving a correspondence between the quantum minkowski space time and the classical projective space p 3

quantum spinors and spin groups from quantum clifford algebras a general construction of multiparametric quantum spinors and corresponding quantum groups associated to pseudo euclidean spaces is presented and their homomorphism to the respective groups is discussed this construction is based on a quantum clifford algebra and is described in detail for involutive pure twists intertwining braids for general braid operators that admit abstract volume elements a procedure is also given for deriving quantum analogues of these groups

meaningful design and contrast estimability in fmri optimising the efficiency of an experimental design is known to be of great importance however existing methods for calculating design rank deficiency and contrast estimability an important aspect of experimental design relate to computational precision rather than image noise and are therefore not very meaningful for example a contrast between two experimental conditions may be mathematically estimable while requiring a huge differential bold response for statistical significance to be reached in this paper we formulate standard efficiency equations in terms of required bold effect and use this to generate measures of rank estimability which are meaningful this takes into account the strength and smoothness of the timeseries noise and is applicable to complex contrasts we show how to re express several regressors and an associated contrast vector as a single equivalent regressor so that we can calculate the contrast s effective peak peak height unambiguously we also present some example results on typical designs and characterise noise results from a range of typical fmri acquisitions in order to allow experimenters to apply efficiency estimation in advance of acquiring data

within subject variation in bold fmri signal changes across repeated measurements quantification and implications for sample size functional magnetic resonance imaging fmri can be used to detect experimental effects on brain activity across measurements the success of such studies depends on the size of the experimental effect the reliability of the measurements and the number of subjects here we report on the stability of fmri measurements and provide sample size estimations needed for repeated measurement studies stability was quantified in terms of the within subject standard deviation w of bold signal changes across measurements in contrast to correlation measures of stability this statistic does not depend on the between subjects variance in the sampled group sample sizes required for repeated measurements of the same subjects were calculated using this w ten healthy subjects performed a motor task on three occasions separated by one week while being scanned in order to exclude training effects on fmri stability all subjects were trained extensively on the task task performance spatial activation pattern and group wise bold signal changes were highly stable over sessions in contrast we found substantial fluctuations up to half the size of the group mean activation level in individual activation levels both in rois and in voxels given this large degree of instability over sessions and the fact that the amount of within subject variation plays a crucial role in determining the success of an fmri study with repeated measurements improving stability is essential in order to guide future studies sample sizes are provided for a range of experimental effects and levels of stability obtaining estimates of these latter two variables is essential for selecting an appropriate number of subjects

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

conservation laws for linear equations on braided linear spaces the properties of linear equations on braided linear spaces are investigated and conservation laws for them are derived the conserved currents are given in the explicit form the procedure is then applied to scalar wave equations on a quantum plane and on q minkowski space

conservation laws for linear equations on quantum minkowski spaces the general linear equations with constant coefficients on quantum minkowski spaces are considered and the explicit formulae for their conserved currents are given the proposed procedure can be simplified for invariant equations the derived method is then applied to klein gordon dirac and wave equations on different classes of minkowski spaces in the examples also symmetry operators for these equations are obtained they include quantum deformations of classical symmetry operators as well as an additional operator connected with deformation of the leibnitz rule in non commutative differential calculus

detecting sparse signals in random fields with an application to brain mapping brain mapping data have been modeled as gaussian random fields and local increases in mean are detected by local maxima of a random field of test statistics derived from these data accurate p values for local maxima are readily available for isotropic data based on the expected euler characteristic of the excursion set of the test statistic random field in this article we give a simple method for dealing with nonisotropic data our approach has connections to the model of sampson and guttorp for nonisotropy in which there exists an unknown mapping of the support of the data to a space in which the random fields are isotropic heuristic justification for our approach comes from the nash embedding theorem formally we show that our method gives consistent unbiased estimators for the true p values based on new results of taylor and adler for random fields on manifolds which replace the euclidean metric by the variogram the results are used to detect gender differences in the cortical thickness of the b

optimal design of multi subject blocked fmri experiments the design of a multi subject fmri experiment needs specification of the number of subjects and scanning time per subject for example for a blocked design with conditions a or b fixed block length and block order abn where n denotes a null block the optimal number of cycles of abn and the optimal number of subjects have to be determined this paper presents a method to determine the optimal number of subjects and optimal number of cycles for a blocked design based on the a optimality criterion and a linear cost function by which the number of cycles and the number of subjects are restricted estimation of individual stimulus effects and estimation of contrasts between stimulus effects are both considered the mixed effects model is applied and analytical results for the a optimal number of subjects and a optimal number of cycles are obtained under the assumption of uncorrelated errors for correlated errors with a first order autoregressive ar1 error structure numerical results are presented our results show how the optimal number of cycles and subjects depend on the within to between subject variance ratio our method is a new approach to determine the optimal scanning time and optimal number of subjects for a multi subject fmri experiment in contrast to previous results based on power analyses the optimal number of cycles and subjects can be described analytically and costs are considered

a bayesian spatiotemporal model for very large data sets functional mri provides a unique perspective of neuronal organization however these data include many complex sources of spatiotemporal variability which require spatial preprocessing and statistical analysis for the latter bayesian models provide a promising alternative to classical inference which uses results from gaussian random field theory to assess the significance of spatially correlated statistic images a bayesian approach generalizes the application of these ideas in that 1 random fields are used to model all spatial parameters not solely observation error 2 their smoothness is optimized and 3 a broader class of models can be compared the main problem however is computational due to the large number of voxels in a brain volume sampling methods are time consuming however approximate inference using variational bayes vb offers a principled and transparent way to specify assumptions necessary for computational tractability penny et al 2005b described such a scheme using a joint spatial prior and approximated the joint posterior density with one that factorized over voxels however a further computational bottleneck is encountered when evaluating the log model evidence used to compare models this has lead to dividing a brain volume into slices and treating each independently this amounts to approximating the spatial prior over a full volume with stacked 2d priors that is smoothness along the z axis is not included in the model here we describe a vb scheme that approximates the zero mean joint spatial prior with a non zero mean empirical prior that factors over voxels thereby overcoming this problem we do this by modifying the original vb algorithm of penny et al using the conditional form of a so called conditional autoregressive car prior to update a marginal prior over voxels we refer to this as a spatially informed voxel wise prior svp and use them to spatially regularise general linear model glm and autoregressive ar coefficients over time to model serial correlations this algorithm scales more favourably with the number of voxels providing a truly 3d spatiotemporal model over volumes containing tens of thousands of voxels we compare the scaling of compute times with the number of voxels and performance with a joint prior applied to synthetic and single subject data

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

kappa minkowski spacetime kappa poincare hopf algebra and realizations we unify minkowki spacetime and lorentz algebra in unique lie algebra introducing commutative momenta a family of deformed heisenberg algebras and deformed poincare algebras are defined they are specified by the matrix depending on momenta we construct all such matrices realizations and star product are defined and analyzed in general and specially their relation to coproduct of momenta is pointed out hopf algebra of the poincare algebra related to the covariant realization is presented in unified covariant form left right dual realizations and dual algebra are introduced and considered the generalized involution and the star inner product are analyzed and their properties are discussed partial integration and deformed trace property are obtained in general the translation invariance of the star product is pointed out finally perturbative approach up to the first order in a is presented in the appendix

quantum 1 1 extended galilei algebras from lie bialgebras to quantum r matrices and integrable systems the lie bialgebras of the 1 1 extended galilei algebra are obtained and classified into four multiparametric families their quantum deformations are obtained together with the corresponding deformed casimir operators for the coboundary cases quantum universal r matrices are also given applications of the quantum extended galilei algebras to classical integrable systems are explicitly developed

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

classification of real three dimensional poisson lie groups all real three dimensional poisson lie pl groups are explicitly constructed and fully classified under group automorphisms by making use of their one to one correspondence with the complete classification of real three dimensional lie bialgebras given in gomez 2000 j math phys 41 4939 many of these 3d pl groups are non coboundary structures whose poisson brackets are given here for the first time casimir functions for all three dimensional pl groups are given and some features of several pl structures are commented

classification of low dimensional lie super bialgebras a thorough analysis of lie super bialgebra structures on lie super algebras osp 1 2 and super e 2 is presented a combined technique of computer algebraic computations and subsequent identification of equivalent structures is applied in all the cases poisson lie brackets on supergroups are found the possibility of quantizing them in order to obtain quantum groups is discussed it turns out to be straightforward for all but one structure for the super e 2 group

estimating the delay of the fmri response we propose a fast efficient general simple valid and robust method of estimating and making inference about the delay of the fmri response modeled as a temporal shift of the hemodynamic response function hrf we estimate the shift unbiasedly using two optimally chosen basis functions for a spectrum of time shifted hrfs this is done at every voxel to create an image of estimated delays and their standard deviations this can be used to compare delays for the same stimulus at different voxels or for different stimuli at the same voxel our method is compared to other alternatives and validated on an fmri data set from an experiment in pain perception

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

estimating the population local wavelet spectrum with application to non stationary functional magnetic resonance imaging time series functional magnetic resonance imaging fmri is a dynamic four dimensional imaging modality however in almost all fmri analyses the time series elements of this data are assumed to be second order stationary in this paper we examine using time series spectral methods whether such stationary assumptions can be made and whether estimates of non stationarity can be used to gain understanding into fmri experiments a non stationary version of replicated stationary time series analysis is proposed that takes into account the replicated time series that are available from nearby voxels in a region of interest roi these are used to investigate non stationarities in both the roi itself and the variations within the roi the proposed techniques are applied to simulated data and to an anxiety inducing fmri experiment

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

revisiting multi subject random effects in fmri advocating prevalence estimation abstract random effect analysis has been introduced into fmri research in order to generalize findings from the study group to the whole population generalizing findings is obviously harder than detecting activation within the study group since in order to be significant an activation has to be larger than the inter subject variability indeed detected regions are smaller when using random effect analysis versus fixed effects the statistical assumptions behind the classic random effect model are that the effect in each location is normally distributed over subjects and activation refers to a non null mean effect we argue that this model is unrealistic compared to the true population variability where due to function anatomy inconsistencies and registration anomalies some of the subjects are active and some are not at each brain location we propose a gaussian mixture random effect that amortizes between subject spatial disagreement and quantifies it using the prevalence of activation at each location we present a formal definition and an estimation procedure of this prevalence the end result of the proposed analysis is a map of the prevalence at locations with significant activation highlighting activation regions that are common over many brains prevalence estimation has several desirable properties a it is more informative than the typical active inactive paradigm b in contrast to the usual display of p values in activated regions which trivially converge to 0 for large sample sizes prevalence estimates converge to the true prevalence

straight to the source detecting aggregate objects in astronomical images with proper error control the next generation of telescopes coming online in the next decade will acquire terabytes of image data each night collectively these large images will contain billions of interesting objects which astronomers call sources one critical task for astronomers is to construct from the image data a detailed source catalog that gives the sky coordinates and other properties of all detected sources the source catalog is the primary data product produced by most telescopes and serves as an important input for studies that build and test new astrophysical theories to construct an accurate catalog the sources must first be detected in the image a variety of effective source detection algorithms exist in the astronomical literature but few if any provide rigorous statistical control of error rates a variety of multiple testing procedures exist in the statistical literature that can provide rigorous error control over pixelwise errors but these do not provide control over errors at the level of sources

constrained linear basis sets for hrf modelling using variational bayes abstract fmri modelling requires flexible haemodynamic response function hrf modelling with the hrf being allowed to vary spatially and between subjects to achieve this flexibility voxelwise parameterised hrfs have been proposed however inference on such models is very slow an alternative approach is to use basis functions allowing inference to proceed in the more manageable general linear model glm framework however a large amount of the subspace spanned by the basis functions produces nonsensical hrf shapes in this work we propose a technique for choosing a basis set and then the means to constrain the subspace spanned by the basis set to only include sensible hrf shapes penny et al neuroimage 2003 showed how variational bayes can be used to infer on the glm for fmri here we extend the work of penny et al to give inference on the glm with constrained hrf basis functions and with spatial markov random fields on the autoregressive noise parameters constraining the subspace spanned by the basis set allows for far superior separation of activating voxels from nonactivating voxels in fmri data we use spatial mixture modelling to produce final probabilities of activation and demonstrate increased sensitivity on an fmri dataset

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

assessing the sensitivity of fmri group maps abstract group maps created from individual functional maps provide useful summaries of patterns of brain activation different methods for combining information have been proposed in the statistical literature and have been recently applied to fmri data since these group maps are statistics it is natural to ask how robust they are that is are they sensitive to the effects of unusual subjects unusual might be in terms of extent location or strength of activation our approach in this paper is to jackknife group maps formed by different combining procedures the jackknife method which involves deleting each observation subject in turn and recalculating the statistic the group map is commonly used for the purpose of assessing sensitivity we examine the theoretical properties of four combining methods in addition via a collection of measures defined on the difference between group maps based on the entire sample and based on the jackknifed samples we evaluate the robustness of these same methods on data from an fmri experiment results indicate that there is a type of tradeoff in the combining techniques we consider between robustness and conservativeness methods that are liberal in that they allow for the discovery of many active voxels tend also to be more sensitive to the influences of individual subjects

conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces the conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived for discrete models the conserved charges are constructed explicitly the applications of the general method include equations on quantum plane supersymmetric equations for chiral and antichiral supermultiplets auxiliary equations of integrable models which means various cases of nonlinear toda lattice equations and anomalous diffusion equation

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

on b type open closed landau ginzburg theories defined on calabi yau stein manifolds we consider the bulk algebra and topological d brane category arising from the differential model of the open closed b type topological landau ginzburg theory defined by a pair x w where x is a non compact calabi yau manifold and w is a complex valued holomorphic function when x is a stein manifold but not restricted to be a domain of holomorphy we extract equivalent descriptions of the bulk algebra and of the category of topological d branes which are constructed using only the analytic space associated to x in particular we show that the d brane category is described by projective factorizations defined over the ring of holomorphic functions of x we also discuss simplifications of the analytic models which arise when x is holomorphically parallelizable and illustrate these in a few classes of examples

quantum deformation of lorentz group a one parameter quantum deformations l 2 ofsl 2 is introduced and investigated an analog of the iwasawa decomposition is proved the compact part of this decomposition coincides withs u 2 whereas the solvable part is identified as a pontryagin dual ofs u 2 it shows thats l 2 is the result of the dual version of drinfeld s double group construction applied tos u 2 the same construction applied to any compact quantum groupgc is discussed in detail in particular the explicit formulae for the haar measures on the pontryagin dualgd ofgc and on the double groupg are given we show that there exists remarkable 1 1 correspondence between representations ofg and bicovariant bimodules tensor bundles overgc the theory of smooth representations ofs l 2 is the same as that ofsl 2 clebsh gordon coefficients are however modified the corresponding tame bicovariant bimodules ons u 2 are classified an application to 4d differential calculus is presented the nonsmooth case is also discussed

multiple testing via fdrl for large scale imaging data the multiple testing procedure plays an important role in detecting the presence of spatial signals for large scale imaging data typically the spatial signals are sparse but clustered this paper provides empirical evidence that for a range of commonly used control levels the conventional fdr procedure can lack the ability to detect statistical significance even if the p values under the true null hypotheses are independent and uniformly distributed more generally ignoring the neighboring information of spatially structured data will tend to diminish the detection effectiveness of the fdr procedure this paper first introduces a scalar quantity to characterize the extent to which the lack of identification phenomenon lip of the fdr procedure occurs second we propose a new multiple comparison procedure called fdrl to accommodate the spatial information of neighboring p values via a local aggregation of p values theoretical properties of the fdrl procedure are investigated under weak dependence of p values it is shown that the fdrl procedure alleviates the lip of the fdr procedure thus substantially facilitating the selection of more stringent control levels simulation evaluations indicate that the fdrl procedure improves the detection sensitivity of the fdr procedure with little loss in detection specificity the computational simplicity and detection effectiveness of the fdrl procedure are illustrated through a real brain fmri dataset

quantum lorentz and braided poincare groups quantum lorentz groups h admitting quantum minkowski space v are selected the natural structure of a quantum space is introduced defining a quantum group structure on g only for triangular h q 1 we show that it defines a braided quantum group structure on g for q 1

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

likelihood based hypothesis tests for brain activation detection from mri data disturbed by colored noise a simulation study functional magnetic resonance imaging fmri data that are corrupted by temporally colored noise are generally preprocessed i e prewhitened or precolored prior to functional activation detection in this paper we propose likelihood based hypothesis tests that account for colored noise directly within the framework of functional activation detection three likelihood based tests are proposed the generalized likelihood ratio glr test the wald test and the rao test the fmri time series is modeled as a linear regression model where one regressor describes the task related hemodynamic response one regressor accounts for a constant baseline and one regressor describes potential drift the temporal correlation structure of the noise is modeled as an autoregressive ar model the order of the ar model is determined from practical null data sets using akaike s information criterion with penalty factor 3 as order selection criterion the tests proposed are based on exact expressions for the likelihood function of the data using monte carlo simulation experiments the performance of the proposed tests is evaluated in terms of detection rate and false alarm rate properties and compared to the current general linear model glm test which estimates the coloring of the noise in a separate step results show that theoretical asymptotic distributions of the glm glr and wald test statistics cannot be reliably used for computing thresholds for activation detection from finite length time series furthermore it is shown that for a fixed false alarm rate the detection rate of the proposed glr test statistic is slightly but statistically significantly improved compared to that of the common glm based tests finally simulations results reveal that all tests considered show seriously inferior performance if the order of the ar model is not chosen sufficiently high to give an adequate description of the correlation structure of the noise whereas the effects of slightly overmodeling are observed to be less harmful

spatial smoothing of autocorrelations to control the degrees of freedom in fmri analysis in the statistical analysis of fmri data the parameter of primary interest is the effect of a contrast of secondary interest is its standard error and of tertiary interest is the standard error of this standard error or equivalently the degrees of freedom df in a reml restricted maximum likelihood analysis we show how spatial smoothing of temporal autocorrelations increases the effective df but not the smoothness of primary or secondary parameter estimates so that the amount of smoothing can be chosen in advance to achieve a target df typically 100 this has already been done at the second level of a hierarchical analysis by smoothing the ratio of random to fixed effects variances worsley k j liao c aston j a d petre v duncan g h morales f evans a c 2002 a general statistical analysis for fmri data neuroimage 15 1 15 we now show how to do it at the first level by smoothing autocorrelation parameters the proposed method is extremely fast and it does not require any image processing it can be used in conjunction with other regularization methods gautama t van hulle m m in press optimal spatial regularisation of autocorrelation estimates in fmri analysis neuroimage to avoid unnecessary smoothing beyond 100 df our results on a typical 6 min tr 3 1 5 t fmri data set show that 8 5 mm smoothing is needed to achieve 100 df and this results in roughly a doubling of detected activations

quantile estimation to derive optimized test thresholds for random field statistics we present a numerical method to estimate the true threshold values in random fields needed to determine the significance of apparent signals observed in noisy images to accomplish this a quantile estimation algorithm is applied to derive the threshold with a predefined confidence interval from a large number of simulated random fields also a computationally efficient method for generating a random field simulation is presented using resampling techniques applying these techniques thresholds have been determined for a large variety of parameter settings smoothness voxel size brain shape type of statistics by means of interpolation techniques thresholds for additional arbitrary settings can be quickly derived without the need to run individual simulations compared to the parametric approach of worsley et al 1996 worsley k j marrett s neelin p vandal a c friston k j evans a c 1996 a unified statistical approach for determining significant signals in images of cerebral activation hum brain mapp 4 58 73 and friston et al 1991 friston k j frith c d liddle p f frackowiak r s 1991 comparing functional pet images the assessment of significant change j cereb blood flow metab 11 4 690 699 and to the bonferroni approach these optimized thresholds lead to higher levels of significance i e lower p values with a specific amount of activation especially with fields of moderate smoothness i e with a relative full width half maximum between 2 and 6 alternatively the threshold for a specified level of significance can be lowered this improved statistical sensitivity is illustrated by the analysis of an actual event related functional magnetic resonance data set and its limitations are tested by determining the false positive rate with experimental mr noise data the grid of estimated threshold values as well as the interpolation algorithm to derive thresholds for arbitrary parameter settings are made available over the internet http neuro2 med uni magdeburg de quantile estimation

wavelets and functional magnetic resonance imaging of the human brain the discrete wavelet transform dwt is widely used for multiresolution analysis and decorrelation or whitening of nonstationary time series and spatial processes wavelets are naturally appropriate for analysis of biological data such as functional magnetic resonance images of the human brain which often demonstrate scale invariant or fractal properties we provide a brief formal introduction to key properties of the dwt and review the growing literature on its application to fmri we focus on three applications in particular i wavelet coefficient resampling or wavestrapping of 1 d time series 2 to 3 d spatial maps and 4 d spatiotemporal processes ii wavelet based estimators for signal and noise parameters of time series regression models assuming the errors are fractional gaussian noise fgn and iii wavelet shrinkage in frequentist and bayesian frameworks to support multiresolution hypothesis testing on spatially extended statistic maps we conclude that the wavelet domain is a rich source of new concepts and techniques to enhance the power of statistical analysis of human fmri data

wavelet variance components in image space for spatiotemporal neuroimaging data neuroimaging studies place great emphasis on not only the estimation but also the standard error estimates of underlying parameters derived from a temporal model this allows inferences to be made about the signal estimates and resulting conclusions to be drawn about the underlying data it can often be advantageous to interrogate temporal models after spatial transformation of the data into the wavelet domain wavelet bases provide a multiresolution decomposition of the spatial data dimension and an ensuing reduction in spatial correlation however widespread acceptance of these wavelet techniques has been hampered by the limited ability to reconstruct both parametric and error estimates into the image domain after analysis of temporal models in the wavelet domain this paper introduces a derivation and a fast implementation of a method for the calculation of the variance of the parametric images obtained from wavelet filters the technique is proposed for a class of estimators that have been shown to be useful in neuroimaging studies the techniques are demonstrated for both functional magnetic resonance imaging fmri and positron emission tomography pet data sets

generalized q exponentials related to orthogonal quantum groups and fourier transformations of noncommutative spaces essential prerequisites for the study of q deformed physics are particle states in position and momentum representation in order to relate x and p space by fourier transformations the appropriate q exponential series related to orthogonal quantum symmetries is constructed it turns out to be a new q special function giving rise to q plane wave solutions that transform with a noncommutative phase under translations

the inhomogeneous quantum groups from differential calculi with classical dimension from the bicovariant first order differential calculus on inhomogeneous hopf algebra b we construct the set of right invariant maurer cartan one forms considered as a right invariant basis of a bicovariant b bimodule over which we develop the woronowicz general theory of differential calculus on quantum groups in this formalism we introduce suitable functionals on b which control the inhomogeneous commutation rules in particular we find that the homogeneous part of commutation rules between the translations and those between the generators of the homogeneous part of b and translations are controlled by different r matrices satisfying characteristic equations

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

q deformed poincare algebra theq differential calculus for theq minkowski space is developed the algebra of theq derivatives with theq lorentz generators is found giving theq deformation of the poincare algebra the reality structure of theq poincare algebra is given the reality structure of theq differentials is also found the real laplacian is constructed finally the comultiplication counit and antipode for theq poincare algebra are obtained making it a hopf algebra

mixed effects and fmri studies abstract this note concerns mixed effect mfx analyses in multisession functional magnetic resonance imaging fmri studies it clarifies the relationship between mixed effect analyses and the two stage summary statistics procedure holmes a p friston k j 1998 generalisability random effects and population inference neuroimage 7 s754 that has been adopted widely for analyses of fmri data at the group level we describe a simple procedure based on restricted maximum likelihood reml estimates of covariance components that enables full mixed effects analyses in the context of statistical parametric mapping using this procedure we compare the results of a full mixed effects analysis with those obtained from the simpler two stage procedure and comment on the situations when the two approaches may give different results

evaluating frequency wise directed connectivity of bold signals applying relative power contribution with the linear multivariate time series models in this article we propose a statistical method to evaluate directed interactions of functional magnetic resonance imaging fmri data the multivariate autoregressive mar model was combined with the relative power contribution rpc in this analysis the mar model was fitted to the data to specify the direction of connections and the rpc quantifies the strength of connections as the rpc is computed in the frequency domain we can evaluate the connectivity for each frequency component from this we can establish whether the specified connections represent low or high frequency connectivity which cannot be examined solely using the estimated mar coefficients we applied this analysis method to fmri data obtained during visual motion tasks confirming previous reports of bottom up connectivity around the frequency corresponding to the block experimental design furthermore we used the mar model with exogenous variables marx to extend our understanding of these data and to show how the input to v1 transfers to higher cortical areas

resampling fmri time series the problem of selecting a threshold for the statistical parameter maps in functional mri fmri is a delicate issue the use of advanced test statistics and or the complex dependence structure of fmri noise may preclude parametric statistical methods for finding appropriate thresholds non parametric statistical methodology has been presented as a feasible alternative in this paper we discuss resampling methods for finding thresholds in single subject fmri analysis it is shown that the presence of a bold response in the time series biases the estimation of the temporal autocorrelation which in turn leads to biased thresholds therefore proposed resampling methods based on fourier and wavelet transforms which employ implicit and weak models of the temporal noise characteristic may produce erroneous thresholds in contrast resampling based on a pre whitening transform which is driven by an explicit noise model is robust to the presence of a bold response the size of the bias is however largely dependent on the complexity of the experimental design while blocked designs can induce large biases event related designs generate significantly smaller biases results supporting these claims are provided

comparing methods of analyzing fmri statistical parametric maps approaches for the analysis of statistical parametric maps spms can be crudely grouped into three main categories in which different philosophies are applied to delineate activated regions these being type i error control thresholding false discovery rate fdr control thresholding and posterior probability thresholding to better understand the properties of these main approaches we carried out a simulation study to compare the approaches as they would be used on real data sets using default settings we find that posterior probability thresholding is the most powerful approach and type i error control thresholding provides the lowest levels of type i error false discovery rate control thresholding performs in between the other approaches for both these criteria although for some parameter settings this approach can approximate the performance of posterior probability thresholding based on these results we discuss the relative merits of the three approaches in an attempt to decide upon an optimal approach we conclude that viewing the problem of delineating areas of activation as a classification problem provides a highly interpretable framework for comparing the methods within this framework we highlight the role of the loss function which explicitly penalizes the types of errors that may occur in a given analysis

false discovery control for random fields this article extends false discovery rates to random fields for which there are uncountably many hypothesis tests we develop a method for finding regions in the field s domain where there is a significant signal while controlling either the proportion of area or the proportion of clusters in which false rejections occur the method produces confidence envelopes for the proportion of false discoveries as a function of the rejection threshold from the confidence envelopes we derive threshold procedures to control either the mean or the specified tail probabilities of the false discovery proportion an essential ingredient of this construnction is a new algorithm to compute a confidence superset for the set of all true null locations we demonstrate our method with applications to scan statistics and functional neuroimaging

anatomically informed basis functions abstract this paper introduces the general framework concepts and procedures of anatomically informed basis functions aibf a new method for the analysis of functional magnetic resonance imaging fmri data in contradistinction to existing voxel based univariate or multivariate methods the approach described here can incorporate various forms of prior anatomical knowledge to specify sophisticated spatiotemporal models for fmri time series in particular we focus on anatomical prior knowledge based on reconstructed gray matter surfaces and assumptions about the location and spatial smoothness of the blood oxygenation level dependent bold effect after reconstruction of the grey matter surface from an individual s high resolution t1 weighted mri we specify a set of anatomically informed basis functions fit the model parameters for a single time point using a regularized solution and finally make inferences about the estimated parameters over time significant effects induced by the experimental paradigm can then be visualized in the native voxel space or on the reconstructed folded inflated or flattened cortical surface as an example we apply the approach to a fmri study finger opposition task and compare the results to those of a voxel based analysis as implemented in the statistical parametric mapping package spm99 additionally we show using simulated data that the approach offers several desirable features particularly in terms of superresolution and localization

advantages and disadvantages of a fast fmri sequence in the context of eeg fmri investigation of epilepsy patients a realistic simulation study abstract eeg fmri is an established technique to allow mapping bold changes in response to interictal discharges recorded in the eeg of epilepsy patients traditional fmri experiments rely on an echo planar imaging epi sequence with a time resolution given by its time to repetition tr of 2 s recently multiple fast fmri sequences have been developed to get around the limited temporal resolution of the epi sequence and achieved a tr in the 100 ms range or lower one such sequence is called magnetic resonance encephalography mreg its high temporal resolution should offer increased detection sensitivity and statistical power in the context of epilepsy studies and in fmri experiments in general the aim of this work was to investigate the advantages and disadvantages offered by mreg this was done by superimposing artificial event related bold responses on epi and mreg background signals from 5 epileptic patients that were free of epileptic discharges spikes on simultaneously recorded eeg these functional datasets simulated different spiking rates and hemodynamic response amplitudes and were analyzed with the commonly used general linear model glm with the canonical hemodynamic response function hrf as a fixed model of the response robustness to violation of the assumptions of the glm was additionally assessed with similar simulations using variable spike to spike response amplitudes and 8 non canonical hrfs consistent with previous work mreg yields higher maximum statistical t values than epi but our simulations showed these statistics to be inflated as the false positive rate at a standard threshold was high at thresholds set to appropriately control specificity epi showed better true positive rate and larger cluster size than mreg however the lack of an appropriate calibration of the amplitude of the responses across the sequences precludes definitive judgment on their relative sensitivity in addition we show that a mismatch between the assumed and actual hrf impairs more mreg detection performance but that epi is more affected by non modeled spike to spike variations of response amplitude filtering out physiological noise which is not aliased at the fast sampling rate of mreg and the modeling of temporal autocorrelation are advantageous in increasing the detection power of mreg this simulation study 1 warrants care when interpreting statistical t values from fast fmri sequences 2 proposes thresholds for valid inferences and processing methods for maximal sensitivities and 3 demonstrates the relative robustness susceptibility of mreg and epi to violation of the glm s assumptions

on crossed product of algebras the concept of a crossed tensor product of algebras is studied from a few points of view some related constructions are considered crossed enveloping algebras and their representations are discussed applications to the noncommutative geometry and particle systems with generalized statistics are indicated

radial asymmetries in population receptive field size and cortical magnification factor in early visual cortex human visual cortex does not represent the whole visual field with the same detail changes in receptive field size population receptive field prf size and cortical magnification factor cmf with eccentricity are well established and associated with changes in visual acuity with eccentricity visual acuity also changes across polar angle however it remains unclear how rf size prf size and cmf change across polar angle here we examine differences in prf size and cmf across polar angle in v1 v2 and v3 using prf modeling of human fmri data in these visual field maps we find smaller prfs and larger cmfs in horizontal left and right than vertical upper and lower visual field quadrants differences increase with eccentricity approximately in proportion to average prf size and cmf similarly we find larger cmfs in the lower than upper quadrant and again differences increase with eccentricity however prf size differences between lower and upper quadrants change direction with eccentricity finally we find slightly smaller prfs in the left than right quadrants of v2 and v3 though this difference is very small and we find no differences in v1 and no differences in cmf moreover differences in prf size and cmf vary gradually with polar angle and are not limited to the meridians or visual field map discontinuities prf size and cmf differences do not consistently follow patterns of cortical curvature despite the link between cortical curvature and polar angle in v1 thus the early human visual cortex has a radially asymmetric representation of the visual field these asymmetries may underlie consistent reports of asymmetries in perceptual abilities

an improved theoretical p value for spms based on discrete local maxima abstract we present a new continuity correction to the p value for local maxima of a statistical parametric map that bridges the gap between small fwhm when the bonferroni correction is accurate and large fwhm when random field theory is accurate the new method based on discrete local maxima is always an upper bound like the bonferroni but lower and hence more accurate for large fwhm without increasing false positives it resulted in p values that were 43 lower than the best of bonferroni or random field theory methods when applied to a typical fmri data set

time series modelling with semiparametric factor dynamics high dimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors the inference on the whole system is then based on the low dimensional time series analysis such high dimensional problems occur frequently in many different fields of science in this article we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods this more flexible modeling approach poses an important question is it justified from an inferential point of view to base statistical inference on the estimated times series factors we show that the difference of the inference based on the estimated time series and true unobserved time series is asymptotically negligible our results justify fitting vector autoregressive processes to the estimated factors which allows one to study the dynamics of the whole high dimensional system with a low dimensional representation we illustrate the theory with a simulati

maximum likelihood computations with repeated measures application of the em algorithm abstract the purpose of this article is to consider the use of the em algorithm dempster laird and rubin 1977 for both maximum likelihood ml and restricted maximum likelihood reml estimation in a general repeated measures setting using a multivariate normal data model with linear mean and covariance structure anderson 1973 several models and methods of analysis have been proposed in recent years for repeated measures data ware 1985 presented an overview because the em algorithm is a general purpose iterative method for computing ml estimates with incomplete data it has often been used in this particular setting dempster et al 1977 andrade and helms 1984 jennrich and schluchter 1985 there are two apparently different approaches to using the em algorithm in this setting in one application each experimental unit is observed under a standard protocol specifying measurements at each of n occasions or under n conditions and incompleteness implies that the number of measurements actua

on the structure of inhomogeneous quantum groups we investigate inhomogeneous quantum groups g built from a quantum group h and translations the corresponding commutation relations contain inhomogeneous terms under certain conditions which are satisfied in our study of quantum poincare groups 12 we prove that our construction has correct size find the r matrices and the analogues of minkowski space for g

solutions of klein gordon and dirac equations on quantum minkowski spaces covariant differential calculi and exterior algebras on quantum homogeneous spaces endowed with the action of inhomogeneous quantum groups are classified in the case of quantum minkowski spaces they have the same dimensions as in the classical case formal solutions of the corresponding klein gordon and dirac equations are found the fock space construction is sketched

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

on the classification of quantum poincare groups using the general theory of 10 quantum poincare groups without dilatations are described and investigated the description contains a set of numerical parameters which satisfy certain polynomial equations for most cases we solve them and give the classification of quantum poincare groups each of them corresponds to exactly one quantum minkowski space the poincare series of these objects are the same as in the classical case we also classify possibler matrices for the fundamental representation of the group

braided momentum in the q poincare group the q poincare group of m schlieker et al z phys c 53 79 1992 is shown to have the structure of a semidirect product and coproduct b soq 1 3 where b is a braided quantum group structure on the q minkowski space of four momentum with braided coproduct p p 1 1 p here the necessary b is not a usual kind of quantum group but one with braid statistics similar braided vectors and covectors v r v r exist for a general r matrix the abstract structure of the q lorentz group is also studied

pic is a contracted functor we show that there is a natural decomposition pic a t t 1 cong pic a oplus npic a oplus npic a oplus h 1 a for any commutative ringa where pic a is the picard group of invertiblea modules andh1 a is the etale cohomology grouph1 spec a a similar decomposition of pic x t t 1 holds for any schemex this makes pic a contracted functor in the sense of bass h1 a is always a torsionfree group and is zero ifa is normal for pseudo geometric rings h1 a is an effectively computable finitely generated free abelian group we also show thath1 a t t 1 h1 a i e nh1 lh1 0 this yields the formula for group rings pic a t 1 t 1 1 t m t m 1 cong pic a oplus coprod limits i 1 m h 1 a oplus coprod limits k 1 m coprod limits i 1 2 k left k m right n k pic a

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

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

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

mixed effect statistics for group analysis in fmri a nonparametric maximum likelihood approach this technical note describes a collection of test statistics accounting for estimation uncertainties at the within subject level that can be used as alternatives to the standard t statistic in one sample random effect analyses i e when testing the mean effect of a population we build such test statistics by estimating the across subject distribution of the effects using maximum likelihood under a nonparametric mixed effect model for inference purposes the statistics are calibrated using permutation tests to achieve exact false positive control under a symmetry assumption regarding the across subject distribution the new tests are implemented in a freely available toolbox for spm called distance

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

local linear discriminant analysis llda for group and region of interest roi based fmri analysis a post processing method for group discriminant analysis of fmri is proposed it assumes that the fmri data have been pre processed and analyzed so that each voxel is given a statistic specifying task related activation s and that individually specific regions of interest rois have been drawn for each subject the method then utilizes local linear discriminant analysis llda to jointly optimize the individually specific and group linear combinations of rois that maximally discriminates between groups or between tasks if using the same subjects llda tries to linearly transform each subject s voxel based activation statistics within rois to a common vector space of roi combinations enabling the relative similarity of different subjects activation to be assessed we applied the method to data recorded from 10 normal subjects during a motor task expected to activate both cortical and subcortical structures the proposed method detected activation in multiple cortical and subcortical structures that were not present when the data were analyzed by warping the data to a common space we suggest that the method be applied to group fmri data when warping to a common space may be ill advised such as examining activation in small subcortical structures susceptible to mis registration or examining older or neurological patient populations

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

matrix factorizations and representations of quivers ii type ade case abstract we study a triangulated category of graded matrix factorizations for a polynomial of type ade we show that it is equivalent to the derived category of finitely generated modules over the path algebra of the corresponding dynkin quiver also we discuss a special stability condition for the triangulated category in the sense of t bridgeland which is naturally defined by the grading