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

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

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

a tight upper bound on the second order coding rate of the parallel gaussian channel with feedback this paper investigates the asymptotic expansion for the maximum rate of fixed length codes over a parallel gaussian channel with feedback under the following setting a peak power constraint is imposed on every transmitted codeword and the average error probabilities of decoding the transmitted message are non vanishing as the blocklength increases the main contribution of this paper is a self contained proof of an upper bound on the first and second order asymptotics of the parallel gaussian channel with feedback the proof techniques involve developing an information spectrum bound followed by using curtiss theorem to show that a sum of dependent random variables associated with the information spectrum bound converges in distribution to a sum of independent random variables thus facilitating the use of the usual central limit theorem combined with existing achievability results our result implies that the presence of feedback does not improve the first and second order asymptotics

second order asymptotics for the gaussian mac with degraded message sets this paper studies the second order asymptotics of the gaussian multiple access channel with degraded message sets for a fixed average error probability varepsilon in 0 1 and an arbitrary point on the boundary of the capacity region we characterize the speed of convergence of rate pairs that converge to that boundary point for codes that have asymptotic error probability no larger than varepsilon as a stepping stone to this local notion of the second order asymptotics we study a global notion and establish relationships between the two we provide a numerical example to illustrate how the angle of approach to a boundary point affects the second order coding rate this is the first conclusive characterization of the second order asymptotics of a network information theory problem in which the capacity region is not a polygon

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

a second order achievable rate region for gaussian multi access channels via a central limit theorem for functions motivated by the growing application of multi access networks with stringent delay constraints we investigate the gaussian multiple access channel mac in the finite blocklength regime by applying central limit theorem clt approximations to non asymptotic information spectrum inner bounds we obtain second order achievable rate regions for the gaussian mac with a positive average error probability and per codeword power constraints our achievability results use spherical inputs uniformly distributed on the power shells which lead to summations of dependent information random variables however we conduct the analysis through a convenient yet powerful form of the clt called the clt for functions

te dependent spatial and spectral specificity of functional connectivity abstract previous studies suggest that spontaneous fluctuations in the resting state fmri rs fmri signal may reflect fluctuations in transverse relaxation time t2 rather than spin density s0 however such s0 and t2 features have not been well characterized in this study spatial and spectral characteristics of functional connectivity on sensorimotor default mode dorsal attention and primary visual systems were examined using a multiple gradient echo sequence at 3 t in the spatial domain we found broad local correlations at short echo times te 14 ms due to dominant s0 contribution whereas long range connections mediated by t2 became explicit at tes longer than 22 ms in the frequency domain compared with the flat spectrum of s0 spectral power of the t2 weighted signal elevated significantly with increasing te particularly in the frequency ranges of 0 008 0 023 hz and 0 037 0 043 hz using the s0 spectrum as a reference we propose two indices to measure spectral signal change ssc and spectral contrast to noise ratio scnr respectively for quantifying the rs fmri signal these indices demonstrated te dependency of connectivity related fluctuation strength resembling functional contrasts in activation based fmri these findings further confirm that large scale functional circuit connectivity based on bold contrast may be constrained within specific frequency ranges in every brain network and the spectral features of s0 and t2 could be valuable for interpreting and quantifying rs fmri data

general formulas for capacity of classical quantum channels the capacity of a classical quantum channel or in other words the classical capacity of a quantum channel is considered in the most general setting where no structural assumptions such as the stationary memoryless property are made on a channel a capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of verdu han 1994 which are based on the so called information spectrum method the general results are applied to the stationary memoryless case with or without cost constraint on inputs whereby a deep relation between the channel coding theory and the hypothesis testing for two quantum states is elucidated

optimum power control at finite blocklength this paper investigates the maximal channel coding rate achievable at a given blocklength n and error probability epsilon when the codewords are subjected to a long term i e averaged over all codeword power constraint the second order term in the large n expansion of the maximal channel coding rate is characterized both for additive white gaussian noise awgn channels and for quasi static fading channels with perfect channel state information available at both the transmitter and the receiver it is shown that in both the cases the second order term is proportional to n 1 ln n 1 2 for the quasi static fading case this second order term is achieved by truncated channel inversion namely by concatenating a dispersion optimal code for an awgn channel subject to a short term power constraint with a power controller that inverts the channel whenever the fading gain is above a certain threshold easy to evaluate approximations of the maximal channel coding rate are developed for both the awgn and the quasi static fading case

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

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

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

evaluation of spatio temporal decomposition techniques for group analysis of fmri resting state data sets the existing functional connectivity assessment techniques rely on different mathematical and neuro physiological models they may consequently provide different sets of spatial connectivity maps and associated temporal responses within their significant spatiotemporal sets of components note that the word component is used to generically refer to spatio temporal pairs of maps and associated time courses such differences may confound the application of functional connectivity measurements in neuroscientific and clinical applications using several performance metrics we evaluated six fmri resting state connectivity measurement techniques including three fully exploratory techniques 1 melodic independent component analysis ica 2 agnostic canonical variates analysis acva and 3 generalized canonical correlation analysis gcca and three seed based techniques 1 seed gcca sgcca and 2 3 seed partial least squares spls with a posterior cingulate seed and two different time series normalizations we separately assessed the temporal and spatial domains for 1 technique stability as a function of sample size using rv coefficients and 2 subspace component similarity between pairs of techniques using cca overall gcca was the only technique that displayed high temporal and spatial stabilities together with high spatial and temporal subspace similarities with multiple other techniques ica acva and sgcca tended to be the most stable spatially and produced similar spatial subspaces all techniques produced relatively unstable and dissimilar temporal subspaces except spls that produced relatively high temporal and lower spatial subspace stabilities but with unique power spectral hurst coefficients 1 our results indicate that spatial maps from resting state data sets are much less dependent on the analysis technique used than are the associated time series such temporal variability is coupled with individual spatial component maps which may be quite dissimilar across techniques even with similar spatial subspaces therefore we suggest that consensus estimation approaches i e a 2nd level gcca would have great utility to produce and aid interpretation of stable results from bold fmri resting state data analysis

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

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

optimal feedback communication via posterior matching in this paper we introduce a fundamental principle for optimal communication over general memoryless channels in the presence of noiseless feedback termed posterior matching using this principle we devise a simple sequential generic feedback transmission scheme suitable for a large class of memoryless channels and input distributions achieving any rate below the corresponding mutual information this provides a unified framework for optimal feedback communication in which the horstein scheme bsc and the schalkwijk kailath scheme awgn channel are special cases thus as a corollary we prove that the horstein scheme indeed attains the bsc capacity settling a longstanding conjecture we further provide closed form expressions for the error probability of the scheme over a range of rates and derive the achievable rates in a mismatch setting where the scheme is designed according to the wrong channel model several illustrative examples of the posterior matching scheme for specific channels are given and the corresponding error probability expressions are evaluated the proof techniques employed utilize novel relations between information rates and contraction properties of iterated function systems

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

characterizing the response of pet and fmri data using multivariate linear models this paper presents a new method for characterizing brain responses in both pet and fmri data the aim is to capture the correlations between the scans of an experiment and a set of external predictor variables that are thought to affect the scans such as type intensity or shape of stimulus response its main feature is a canonical variates analysis cva of the estimated effects of the predictors from a multivariate linear model mlm the advantage of this over current methods is that temporal correlations can be incorporated into the model making the mlm method suitable for fmri as well as pet data moreover tests for the presence of any correlation and inference about the number of canonical variates needed to capture that correlation can be based on standard multivariate statistics rather than simulations when applied to an fmri data set previously analyzed by another cva method the mlm method reveals a pattern of responses that is closer to that detected in an earlier non cva analysis

on gaussian channels with feedback under expected power constraints and with non vanishing error probabilities in this paper we consider single and multi user gaussian channels with feedback under expected power constraints and with non vanishing error probabilities in the first of two contributions we study asymptotic expansions for the additive white gaussian noise awgn channel with feedback under the average error probability formalism by drawing ideas from gallager and nakiboglu s work for the direct part and the meta converse for the converse part we establish the varepsilon capacity and show that it depends on varepsilon in general and so the strong converse fails to hold furthermore we provide bounds on the second order term in the asymptotic expansion we show that for any positive integer l the second order term is bounded between a term proportional to ln l n where ln l cdot is the l fold nested logarithm function and a term proportional to n ln n 1 2 where n is the blocklength the lower bound on the second order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available in our second contribution we establish the varepsilon capacity region for the awgn multiple access channel with feedback under the expected power constraint by combining ideas from hypothesis testing information spectrum analysis ozarow s coding scheme and power control

estimation of the intrinsic dimensionality of fmri data a new method based on an autoregressive noise model of order 1 is introduced to the problem of detecting the number of components in fmri data unlike current information theoretic criteria like aic mdl and related ppca which do not incorporate autocorrelations in the noise the new method leads to more consistent estimates of the model order as illustrated in simulated and real fmri resting state 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

variations on a theme by schalkwijk and kailath schalkwijk and kailath 1966 developed a class of block codes for gaussian channels with ideal feedback for which the probability of decoding error decreases as a second order exponent in block length for rates below capacity this well known but surprising result is explained and simply derived here in terms of a result by elias 1956 concerning the minimum mean square distortion achievable in transmitting a single gaussian random variable over multiple uses of the same gaussian channel a simple modification of the schalkwijk kailath scheme is then shown to have an error probability that decreases with an exponential order which is linearly increasing with block length in the infinite bandwidth limit this scheme produces zero error probability using bounded expected energy at all rates below capacity a lower bound on error probability for the finite bandwidth case is then derived in which the error probability decreases with an exponential order which is linearly increasing in block length at the same rate as the upper bound

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

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

variable precision registration via wavelets optimal spatial scales for inter subject registration of functional mri abstract the detection of significantly activated brain regions in multi subject functional magnetic resonance imaging fmri studies almost invariably entails the coregistration of individual subjects data in a standard space here we investigate how sensitivity to detect loci of generic activation in such studies may be conditioned by the precision of anatomical registration we describe a novel algorithm implemented in the wavelet domain for inhomogeneous deformation of individual images to match a template the algorithm matches anatomical features in a coarse to fine fashion first minimising a cost function in terms of relatively coarse spatial features and then proceeding iteratively to match the images in terms of progressively more detailed anatomical features applying the method to data acquired from two groups of 12 healthy volunteers with mean age 27 and 70 years respectively during performance of a paired associate learning task we show that geometrical overlap between template and individual images is monotonically improved compared to an affine transform by additional inhomogeneous deformations informed by more detailed features likewise sensitivity to detect activated voxels can be substantially improved by a factor of 4 or more if wavelet mediated deformations informed by medium sized anatomical features are applied in addition to a preliminary affine transform however sensitivity to detect activated voxels was reduced by over registering data or matching anatomical features at the finest scales of the wavelet transform the benefits of variable precision registration are particularly salient for data acquired in older subjects which showed evidence of greater inter subject anatomic variability and generally required more extensive local deformation to achieve a satisfactory match to the template image we conclude that major benefits in sensitivity to detect functional activation in multi subject fmri studies can be attained with an inhomogeneous deformation applied over appropriate spatial scales

feedback does not increase the capacity of discrete channels with additive noise we consider discrete time finite alphabet channels with additive random noise we show that output feedback does not increase the capacity of such channels this result holds in the most general case i e for arbitrary additive noise processes

new bounds for variable sized online bin packing in the variable sized online bin packing problem one has to assign items to bins one by one the bins are drawn from some fixed set of sizes and the goal is to minimize the sum of the sizes of the bins used we present new algorithms for this problem and show upper bounds for them which improve on the best previous upper bounds we also show the first general lower bounds for this problem the case in which bins of two sizes 1 and alpha in 0 1 are used is studied in detail this investigation leads us to the discovery of several interesting fractal like curves

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

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

resampling methods for improved wavelet based multiple hypothesis testing of parametric maps in functional mri abstract two or three dimensional wavelet transforms have been considered as a basis for multiple hypothesis testing of parametric maps derived from functional magnetic resonance imaging fmri experiments most of the previous approaches have assumed that the noise variance is equally distributed across levels of the transform here we show that this assumption is unrealistic fmri parameter maps typically have more similarity to a 1 f type spatial covariance with greater variance in 2d wavelet coefficients representing lower spatial frequencies or coarser spatial features in the maps to address this issue we resample the fmri time series data in the wavelet domain using a 1d discrete wavelet transform dwt to produce a set of permuted parametric maps that are decomposed using a 2d dwt to estimate level specific variances of the 2d wavelet coefficients under the null hypothesis these resampling based estimates of the wavelet variance spectrum are substituted in a bayesian bivariate shrinkage operator to denoise the observed 2d wavelet coefficients which are then inverted to reconstitute the observed denoised map in the spatial domain multiple hypothesis testing controlling the false discovery rate in the observed denoised maps then proceeds in the spatial domain using thresholds derived from an independent set of permuted denoised maps we show empirically that this more realistic resampling based algorithm for wavelet based denoising and multiple hypothesis testing has good type i error control and can detect experimentally engendered signals in data acquired during auditory linguistic processing

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

an information spectrum approach to capacity theorems for the general multiple access channel the paper deals with the capacity problems for the general multiple access channel where the channel transition probabilities are arbitrary for every blocklength n the approach used here which is called the information spectrum approach is quite different from the standard typical sequence and or aep techniques the general formula for the capacity region for the general multiple access channel is thus established in order to examine the potentiality we apply it to the mixed channel to obtain the formula for its capacity region the case where input cost constraints are imposed is also considered

second order rate region of constant composition codes for the multiple access channel this paper studies the second order asymptotics of coding rates for the discrete memoryless multiple access channel mac with a fixed target error probability using constant composition random coding coded time sharing and a variant of hoeffding s combinatorial central limit theorem an inner bound on the set of locally achievable second order coding rates is given for each point on the boundary of the capacity region it is shown that the inner bound for constant composition random coding includes that recovered by independent identically distributed random coding and that the inclusion may be strict the inner bound is extended to the gaussian mac via an increasingly fine quantization of the inputs

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

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

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

wavelet based multifractal analysis of fmri time series functional magnetic resonance imaging fmri time series are investigated with a multifractal method based on the wavelet modulus maxima wtmm method to extract local singularity fractal exponents the spectrum of singularity exponents of each fmri time series is quantified by spectral characteristics including its maximum and the corresponding dimension we found that the range of holder exponents in voxels with activation is close to 1 whereas exponents are close to 0 5 in white matter voxels without activation the maximum dimension decreases going from white matter to gray matter and is lower still for activated time series the full width at half maximum of the spectra is higher in activated areas the proposed method becomes particularly effective when combining these spectral characteristics into a single parameter using these multifractal parameters it is possible to identify activated areas in the human brain in both hybrid and in vivo fmri data sets without knowledge of the stimulation paradigm applied

on gaussian macs with variable length feedback and non vanishing error probabilities we characterize the fundamental limits of transmission of information over a gaussian multiple access channel mac with the use of variable length feedback codes and under a non vanishing error probability formalism we develop new achievability and converse techniques to handle the continuous nature of the channel and the presence of expected power constraints we establish the varepsilon capacity regions and bounds on the second order asymptotics of the gaussian mac with variable length feedback with termination codes and stop feedback codes we show that the former outperforms the latter significantly due to the multi terminal nature of the channel model we leverage tools from renewal theory developed by lai and siegmund to bound the asymptotic behavior of the maximum of a finite number of stopping times

feedback in the non asymptotic regime without feedback the backoff from capacity due to non asymptotic blocklength can be quite substantial for blocklengths and error probabilities of interest in many practical applications in this paper novel achievability bounds are used to demonstrate that in the non asymptotic regime the maximal achievable rate improves dramatically thanks to variable length coding and feedback for example for the binary symmetric channel with capacity 1 2 the blocklength required to achieve 90 of the capacity is smaller than 200 compared to at least 3100 for the best fixed blocklength code even with noiseless feedback virtually all the advantages of noiseless feedback are shown to be achievable even if the feedback link is used only to send a single signal informing the encoder to terminate the transmission stop feedback it is demonstrated that the non asymptotic behavior of the fundamental limit depends crucially on the particular model chosen for the end of packet control signal fixed blocklength codes and related questions concerning communicating with a guaranteed delay are discussed in which situation feedback is demonstrated to be almost useless even non asymptotically

achievable rates for gaussian degraded relay channels with non vanishing error probabilities this paper revisits the gaussian degraded relay channel where the link that carries information from the source to the destination is a physically degraded version of the link that carries information from the source to the relay the source and the relay are subject to expected power constraints the varepsilon capacity of the channel is characterized and it is strictly larger than the capacity for any varepsilon 0 which implies that the channel does not possess the strong converse property the proof of the achievability part is based on several key ideas block markov coding which is used in the classical decode forward strategy power control for gaussian channels under expected power constraints and a careful scaling between the block size and the total number of block uses the converse part is proved by first establishing two non asymptotic lower bounds on the error probability which are derived from the type ii errors of some binary hypothesis tests subsequently each lower bound is simplified by conditioning on an event related to the power of some linear combination of the codewords transmitted by the source and the relay lower and upper bounds on the second order term of the optimal coding rate are also obtained

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

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

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

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

1 f noise in diffuse optical imaging and wavelet based response estimation in diffuse optical imaging doi data analysis the functional response is contaminated with physiological noise as in functional magnetic resonance imaging fmri in this work we extend a previously proposed method for fmri to estimate the parameters of a linear model of doi time series the regression is performed in the wavelet domain to infer drift coefficients at different scales and to estimate the strength of the hemodynamic response function hrf this multiresolution approach benefits from the whitening property of the discrete wavelet transform dwt which approximately decorrelates long memory noise processes we also show that a more accurate estimation is obtained by removing some regressors correlating with the protocol moreover we observe that this improvement is related to a quantitative measure of 1 f noise the performances of the method are first evaluated against a standard spline cosine drift approach with simulated hrf and real background physiology lastly the technique is applied to experimental event related data acquired by near infrared spectroscopy nirs

upper bounds of error probabilities for stationary gaussian channels with feedback in this paper we discuss the coding schemes and error probabilities in information transmission over additive gaussian noise channels with feedback where the gaussian noise processes are stationary but not necessarily white in the case of the white gaussian channel it is known that the minimum error probability under the average power constraint decreases faster than the exponential of any order recently gallager and nakiboglu 2010 proposed a coding scheme for the white gaussian channel and successfully showed the multiple exponential decay of the error probability for all rates below capacity this paper aims to prove that without any special assumptions on the noise of the stationary gaussian channel the minimum error probability decreases multiple exponentially fast in general no explicit formulas are known for the capacity of the stationary gaussian channel in this paper we introduce a lower bound c on the capacity c then we prove that the minimum error probability decreases multiple exponentially fast for all rates below c but not for all rates below c in the process of proving the scheme proposed by gallager and nakiboglu proves itself to be quite useful even though the gaussian channel is not white

variable sized bin packing in the classical bin packing problem one seeks to pack a list of pieces in the minimum space using unit capacity bins this paper addresses the more general problem in which a fixed collection of bin sizes is allowed three efficient approximation algorithms are described and analyzed they guarantee asymptotic worst case performance bounds of 2 3 2 and 4 3

an aptas for generalized cost variable sized bin packing bin packing is a well known problem which has a large number of applications classical bin packing is a simple model in which all bins are identical in the bin packing problem with variable sized bins we are given a supply of a variety of sizes this latter model assumes however that the cost of a bin is always defined to be its exact size in this paper we study the more general problem where an available bin size is associated with a fixed cost which may be smaller or larger than its size the costs of different bin sizes are unrelated this generalized problem has various applications in storage and scheduling in order to generalize previous work we design new rounding and allocation methods our main result is an asymptotic polynomial time approximation scheme for the generalized problem

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

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

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

new lower bounds for certain classes of bin packing algorithms on line algorithms have been extensively studied for the one dimensional bin packing problem in this paper we investigate two classes of one dimensional bin packing algorithms and we give better lower bounds for their asymptotic worst case behavior for on line algorithms so far the best lower bound was given by van vliet in 1992 12 he proved that there is no on line bin packing algorithm with better asymptotic performance ratio than 1 54014 in this paper we give an improvement on this bound to 248161 1 54037 and we investigate the parametric case as well for those lists where the elements are preprocessed according to their sizes in non increasing order csirik et al 1983 1 proved that no on line algorithm can have an asymptotic performance ratio smaller than 87 we improve this result to 5447

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

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

strong converse theorems for classes of multimessage multicast networks a renyi divergence approach this paper establishes that the strong converse holds for some classes of discrete memoryless multimessage multicast networks dm mmns whose corresponding cut set bounds are tight i e coincide with the corresponding sets of achievable rate tuples our strong converse result implies that for any dm mmn of these classes the average error probabilities of any sequence of codes operated at a rate tuple belonging to the exterior of the cut set bound must tend to one and are not simply bounded away from zero as the block length grows examples in the classes of dm mmns include wireless erasure networks dm mmns consisting of independent discrete memoryless channels dmcs as well as single destination dm mmns consisting of independent dmcs with destination feedback our elementary proof technique leverages properties of the renyi divergence

bin packing with controllable item sizes we consider a natural resource allocation problem in which we are given a set of items where each item has a list of pairs associated with it each pair is a configuration of an allowed size for this item together with a nonnegative penalty and an item can be packed using any configuration in its list the goal is to select a configuration for each item so that the number of unit bins needed to pack the sizes plus the sum of penalties is minimized this problem has applications in operating systems bandwidth allocation and discrete time cost tradeoff planning problems for the offline version of the problem we design an augmented asymptotic ptas that is an asymptotic approximation scheme that uses bins of size slightly larger than 1 we further consider the online bounded space variant where only a constant number of bins can be open simultaneously we design a sequence of algorithms where the sequence of their competitive ratios tends to the best possible asymptotic competitive ratio finally we study the bin covering problem in which a bin is covered if the sum of sizes allocated to it is at least 1 in this setting penalties are interpreted as profits and the goal is to maximize the sum of profits plus the number of covered bins we design an algorithm of best possible competitive ratio which is 2 we generalize our results for online algorithms and unit sized bins to the case of variable sized bins where there may be several distinct sizes of bins available for packing or covering and get that the competitive ratios are again the same as for the more standard online problems

the third order term in the normal approximation for the awgn channel this paper shows that under the average error probability formalism the third order term in the normal approximation for the additive white gaussian noise channel with a maximal or equal power constraint is at least 1 2 log n o 1 this improves on the lower bound by polyanskiys poor verdu 2010 and matches the upper bound proved by the same authors

a simple on line bin packing algorithm the one dimensional on line bin packing problem is considered a simple o 1 space and o n time algorithm called harmonic m is presented it is shown that this algorithm can achieve a worst case performance ratio of less than 1 692 which is better than that of the o n space and o n log n time algorithm first fit also shown is that 1 691 is a lower bound for all 0 1 space on line bin packing algorithms finally a revised version of harmonic m an o n space and o n time algorithm is presented and is shown to have a worst case performance ratio of less than 1 636 d

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

information spectrum approach to second order coding rate in channel coding in this paper second order coding rate of channel coding is discussed for general sequence of channels the optimum second order transmission rate with a constant error constraint epsiv is obtained by using the information spectrum method we apply this result to the discrete memoryless case the discrete memoryless case with a cost constraint the additive markovian case and the gaussian channel case with an energy constraint we also clarify that the gallager bound does not give the optimum evaluation in the second order coding rate

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

a proof of the strong converse theorem for gaussian multiple access channels we prove the strong converse for the n source gaussian multiple access channel in particular we show that any rate tuple that can be supported by a sequence of codes with asymptotic average error probability 1 must lie in the cover wyner capacity region our proof consists of the following first we perform an expurgation step to convert any given sequence of codes with asymptotic average error probability 1 to codes with asymptotic maximal error probability 1 second we quantize the input alphabets with an appropriately chosen resolution upon quantization we apply the wringing technique by ahlswede on the quantized inputs to obtain further subcodes from the subcodes obtained in the expurgation step so that the resultant correlations among the symbols transmitted by the different sources vanish as the blocklength grows finally we derive upper bounds on achievable sum rates of the subcodes in terms of the type ii error of a binary hypothesis test these upper bounds are then simplified through judicious choices of auxiliary output distributions our strong converse result carries over to the gaussian interference channel under strong interference as long as the sum of the two asymptotic average error probabilities 1

polyharmonic smoothing splines and the multidimensional wiener filtering of fractal like signals motivated by the fractal like behavior of natural images we develop a smoothing technique that uses a regularization functional which is a fractional iterate of the laplacian this type of functional was initially introduced by duchon for the approximation of nonuniformily sampled multidimensional data he proved that the general solution is a smoothing spline that is represented by a linear combination of radial basis functions rbfs unfortunately this is tedious to implement for images because of the poor conditioning of rbfs and their lack of decay here we present a much more efficient method for the special case of a uniform grid the key idea is to express duchon s solution in a fractional polyharmonic b spline basis that spans the same space as the rbfs this allows us to derive an algorithm where the smoothing is performed by filtering in the fourier domain next we prove that the above smoothing spline can be optimally tuned to provide the mmse estimation of a fractional brownian field corrupted by white noise this is a strong result that not only yields the best linear filter wiener solution but also the optimal interpolation space which is not bandlimited it also suggests a way of using the noisy data to identify the optimal parameters order of the spline and smoothing strength which yields a fully automatic smoothing procedure we evaluate the performance of our algorithm by comparing it against an oracle wiener filter which requires the knowledge of the true noiseless power spectrum of the signal we find that our approach performs almost as well as the oracle solution over a wide range of conditions