asymptotics of karhunen loeve eigenvalues and tight constants for probability distributions of passive scalar transport in this paper we study the asymptotics of the probability distribution function for a certain model of freely decaying passive scalar transport in particular we prove rigorous large n or semiclassical asymptotics for the eigenvalues of the covariance of a fractional brownian motion using these asymptotics along with some standard large deviations results we are able to derive tight asymptotics for the rate of decay of the tails of the probability density for a generalization of the majda model of scalar intermittency originally due to vanden eijnden we are also able to derive asymptotically tight estimates for the closely related problem of small l2 ball probabilities for a fractional brownian motion

extensions of exchange rings we define non unital exchange rings and we prove that ifiis an ideal of a ringr thenris an exchange ring if and only ifiandr iare exchange rings and idempotents can be lifted moduloi we also show that we can replace the condition on liftability of idempotents with the condition that the canonical mapk0 r k0 r i be surjective

configuration model for correlation matrices preserving the node strength correlation matrices are a major type of multivariate data to examine properties of a given correlation matrix a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices such as those derived from random matrix theory that partially preserve properties of the original matrix we propose a model to generate such reference correlation and covariance matrices for the given matrix correlation matrices are often analyzed as networks which are heterogeneous across nodes in terms of the total connectivity to other nodes for each node given this background the present algorithm generates random networks that preserve the expectation of total connectivity of each node to other nodes akin to configuration models for conventional networks our algorithm is derived from the maximum entropy principle we will apply the proposed algorithm to measurement of clustering coefficients and community detection both of which require a null model to assess the statistical significance of the obtained results

sharp asymptotics of the functional quantization problem for gaussian processes the sharp asymptotics for the l 2 quantization errors of gaussian measures on a hilbert space and in particular for gaussian processes is derived the condition imposed is regular variation of the eigenvalues

proportional thresholding in resting state fmri functional connectivity networks and consequences for patient control connectome studies issues and recommendations graph theoretical analysis has become an important tool in the examination of brain dysconnectivity in neurological and psychiatric brain disorders a common analysis step in the construction of the functional graph or network involves thresholding of the connectivity matrix selecting the set of edges that together form the graph on which network organization is evaluated to avoid systematic differences in absolute number of edges studies have argued against the use of an absolute threshold in case control studies and have proposed the use of proportional thresholding instead in which a pre defined number of strongest connections are selected as network edges ensuring equal network density across datasets here we systematically studied the effect of proportional thresholding on the construction of functional matrices and subsequent graph analysis in patient control functional connectome studies in a few simple experiments we show that differences in overall strength of functional connectivity fc as often observed between patients and controls can have predictable consequences for between group differences in network organization in individual networks with lower overall fc the proportional thresholding algorithm has to select more edges based on lower correlations which have on average a higher probability of being spurious and thus introduces a higher degree of randomness in the resulting network we show across both empirical and artificial patient control datasets that lower levels of overall fc in either the patient or control group will most often lead to differences in network efficiency and clustering suggesting that differences in fc across subjects will be artificially inflated or translated into differences in network organization based on the presented case control findings we inform about the caveats of proportional thresholding in patient control studies in which groups show a between group difference in overall fc we make recommendations on how to examine report and to take into account overall fc effects in future patient control functional connectome studies

mixed fractional brownian motion a spectral take abstract this paper provides yet another look at the mixed fractional brownian motion fbm this time from the spectral perspective the main result is an asymptotic approximation for the eigenvalues of its covariance operator using this approximation we derive the exact asymptotics of the l 2 small ball probabilities which was previously known only with logarithmic accuracy the obtained expression exhibits an interesting stratification of scales which occurs at certain values of the hurst parameter of the fractional component some of them have been previously encountered in other problems involving such mixtures

weakly clean rings abstract we study the class of weakly clean rings which were introduced in 15 it is known that weakly clean rings are a subclass of exchange rings and that they contain clean rings as a proper subclass in this paper we prove that weakly clean rings also contain some other important examples of exchange rings such as regular rings and c algebras of real rank zero further we prove that many classes of weakly clean rings can be viewed as corners of clean rings this for example implies that every regular ring and every c algebra of real rank zero is a corner of a clean ring lastly we study the question when the ideal extension of weakly clean rings is weakly clean and we give an example of a non weakly clean exchange ring answering the question in 15

age related changes in modular organization of human brain functional networks graph theory allows us to quantify any complex system e g in social sciences biology or technology that can be abstractly described as a set of nodes and links here we derived human brain functional networks from fmri measurements of endogenous low frequency correlated oscillations in 90 cortical and subcortical regions for two groups of healthy young and older participants we investigated the modular structure of these networks and tested the hypothesis that normal brain aging might be associated with changes in modularity of sparse networks newman s modularity metric was maximised and topological roles were assigned to brain regions depending on their specific contributions to intra and inter modular connectivity both young and older brain networks demonstrated significantly non random modularity the young brain network was decomposed into 3 major modules central and posterior modules which comprised mainly nodes with few inter modular connections and a dorsal fronto cingulo parietal module which comprised mainly nodes with extensive inter modular connections the mean network in the older group also included posterior superior central and dorsal fronto striato thalamic modules but the number of intermodular connections to frontal modular regions was significantly reduced whereas the number of connector nodes in posterior and central modules was increased

towards a statistical test for functional connectivity dynamics abstract sliding window correlation is an emerging method for mapping time resolved resting state functional connectivity to avoid mapping spurious connectivity fluctuations false positives leonardi and van de ville recently recommended choosing a window length exceeding the longest wavelength composing the bold signal usually assumed to be 100 s here we provide further statistical support for this rule of thumb however we demonstrate that non stationary fluctuations in functional connectivity can in theory be detected with much shorter window lengths e g 40 s while maintaining nominal control of false positives we find that statistical power is near maximal for window lengths chosen according to leonardi and van de ville s rule of thumb furthermore we lay some foundations for a parametric test to identify non stationary fluctuations in functional connectivity also noting limitations of the sinusoidal model upon which our work and the work of leonardi and van de ville is based most notably our analytical results pertain to covariances as does our statistical test whereas functional connectivity is more commonly measured using correlations

extracting the multiscale backbone of complex weighted networks a large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength in recent years the study of an increasing number of large scale networks has highlighted the statistical heterogeneity of their interaction pattern with degree and weight distributions that vary over many orders of magnitude these features along with the large number of elements and links make the extraction of the truly relevant connections forming the network s backbone a very challenging problem more specifically coarse graining approaches and filtering techniques come into conflict with the multiscale nature of large scale systems here we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks preserving the edges that represent statistically significant deviations with respect to a null model for the local assignment of weights to edges an important aspect of the method is that it does not belittle small scale interactions and operates at all scales defined by the weight distribution we apply our method to real world network instances and compare the obtained results with alternative backbone extraction techniques

reliability of graph analysis of resting state fmri using test retest dataset from the human connectome project the exploration of brain networks with resting state fmri rs fmri combined with graph theoretical approaches has become popular with the perspective of finding network graph metrics as biomarkers in the context of clinical studies a preliminary requirement for such findings is to assess the reliability of the graph based connectivity metrics in previous test retest trt studies this reliability has been explored using intraclass correlation coefficient icc with heterogeneous results but the issue of sample size has not been addressed using the large trt rs fmri dataset from the human connectome project hcp we computed iccs and their corresponding p values applying permutation and bootstrap techniques and varied the number of subjects from 20 to 100 the scan duration from 400 to 1200 time points the cost and the graph metrics using the anatomic automatic labelling aal parcellation scheme we quantified the reliability of the graph metrics computed both at global and regional level depending at optimal cost on two key parameters the sample size and the number of time points or scan duration in the cost range between 20 to 35 most of the global graph metrics are reliable with 40 subjects or more with long scan duration 14 min 24 s in large samples for instance 100 subjects most global and regional graph metrics are reliable for a minimum scan duration of 7 min 14s finally for 40 subjects and long scan duration 14 min 24 s the reliable regions are located in the main areas of the default mode network dmn the motor and the visual networks

the multiscale character of evoked cortical activity abstract both the architecture and the dynamics of the brain have characteristic features at different spatial scales however the existence nature and function of dynamical interdependencies between such scales have not been investigated we studied the multiscale properties of functional magnetic resonance imaging fmri data acquired while human subjects viewed a visual image traditional region of interest analysis of this data set revealed evoked activity in primary and extrastriate visual cortex wavelet transform in the spatial domain provides a multiscale representation of this evoked brain activity studying the correlation structure of this representation revealed strong and novel interdependencies in these data within and between different spatial scales we found that such correlations are stronger than those evident in the original data and comparable in magnitude to those obtained after gaussian smoothing however analysis of the data in the wavelet domain revealed additional structure such as positive correlations strong anti correlations and phase lagged interdependencies statistical significance of these effects was inferred through nonparametric bootstrap techniques we conclude that the spatial analysis of functional neuroimaging data in the wavelet domain provides novel information which may reflect complex spatiotemporal neuronal activity and information encoding it also affords a quantitative means of testing hierarchical and multiscale models of cortical activity

effective degrees of freedom of the pearson s correlation coefficient under autocorrelation abstract the dependence between pairs of time series is commonly quantified by pearson s correlation however if the time series are themselves dependent i e exhibit temporal autocorrelation the effective degrees of freedom edf are reduced the standard error of the sample correlation coefficient is biased and fisher s transformation fails to stabilise the variance since fmri time series are notoriously autocorrelated the issue of biased standard errors before or after fisher s transformation becomes vital in individual level analysis of resting state functional connectivity rsfc and must be addressed anytime a standardised z score is computed we find that the severity of autocorrelation is highly dependent on spatial characteristics of brain regions such as the size of regions of interest and the spatial location of those regions we further show that the available edf estimators make restrictive assumptions that are not supported by the data resulting in biased rsfc inferences that lead to distorted topological descriptions of the connectome on the individual level we propose a practical xdf method that accounts not only for distinct autocorrelation in each time series but instantaneous and lagged cross correlation we find the xdf correction varies substantially over node pairs indicating the limitations of global edf corrections used previously in addition to extensive synthetic and real data validations we investigate the impact of this correction on rsfc measures in data from the young adult human connectome project showing that accounting for autocorrelation dramatically changes fundamental graph theoretical measures relative to no correction

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

clean general rings an associative ring with unity is called clean respectively uniquely clean if every element is uniquely the sum of an idempotent and a unit in this paper we define clean general rings with or without a unity and extend many of the basic results to the wider class in particular a clean general ring is an exchange ring in the sense of ara we then study the general analogue of the uniquely clean rings and their relationship to the boolean rings finally we introduce semiboolean rings as a natural generalization of boolean rings 2005 elsevier inc all rights reserved

changes in dynamic functional connections with aging despite numerous studies on age related changes in static functional connections fcs the available literature on the changes in dynamic fcs with aging is lacking this study investigated the changes in dynamic fcs with aging based on resting state fmri data of 61 healthy adults aged 30 85 years the time resolved fcs among 160 pre defined regions of interest rois were first estimated using sliding window correlation based on the dynamic fc matrices we then analyzed the dynamic switches between different fc states using k means clustering and correlated age with the dwell time of each fc state across subjects the elderly were observed to spend more time in an fc state characterized by weak interactions throughout the brain and less time in an fc state characterized by strong interactions within the sensory motor network and the cognitive control network these results may reflect an overall weakening of connections in the elderly which support less efficient information transfer in them based on the dynamic fc matrices we also evaluated the variability and amplitude of fc time series which measure the relative to mean and absolute strength of fc fluctuations respectively and correlated age with the two measures across subjects relatively weak age vs variability correlations were observed but we did observe significant negative age vs amplitude correlations at both the global and regional level these results indicate that amplitude may be another effective metric for assessing fc fluctuations in addition to the widely used variability metric moreover the observed declines in the amplitude of fc fluctuations in the elderly may support the assumption that it should be the weakening of absolute interactions between brain regions rather than toggling between positive and negative correlations that causes the repeatedly reported widespread static fc decreases with aging overall the present results not only reflect an overall weakening of connections in the elderly but indicate the potential of dynamic fc analyses in studies of age related psychiatric and neurological disorders

weight conserving characterization of complex functional brain networks complex functional brain networks are large networks of brain regions and functional brain connections statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures important functional network measures include measures of modularity measures of the goodness with which a network is optimally partitioned into functional subgroups and measures of centrality measures of the functional influence of individual brain regions characterizations of functional networks are increasing in popularity but are associated with several important methodological problems these problems include the inability to characterize densely connected and weighted functional networks the neglect of degenerate topologically distinct high modularity partitions of these networks and the absence of a network null model for testing hypotheses of association between observed nontrivial network properties and simple weighted connectivity properties in this study we describe a set of methods to overcome these problems specifically we generalize measures of modularity and centrality to fully connected and weighted complex networks describe the detection of degenerate high modularity partitions of these networks and introduce a weighted connectivity null model of these networks we illustrate our methods by demonstrating degenerate high modularity partitions and strong correlations between two complementary measures of centrality in resting state functional magnetic resonance imaging mri networks from the 1000 functional connectomes project an open access repository of resting state functional mri datasets our methods may allow more sound and reliable characterizations and comparisons of functional brain networks across conditions and subjects

exact l2 small ball behavior of integrated gaussian processes and spectral asymptotics of boundary value problems we find the exact small deviation asymptotics for the l 2 norm of various m times integrated gaussian processes closely connected with the wiener process and the ornstein uhlenbeck process using a general approach from the spectral theory of linear differential operators we obtain the two term spectral asymptotics of eigenvalues in corresponding boundary value problems this enables us to improve the recent results from 15 on the small ball asymptotics for a class of m times integrated wiener processes moreover the exact small ball asymptotics for the m times integrated brownian bridge the m times integrated ornstein uhlenbeck process and similar processes appear as relatively simple examples illustrating the developed general theory

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

stereotypical modulations in dynamic functional connectivity explained by changes in bold variance abstract spontaneous activity measured in human subject under the absence of any task exhibits complex patterns of correlation that largely correspond to large scale functional topographies obtained with a wide variety of cognitive and perceptual tasks these resting state networks rsns fluctuate over time forming and dissolving on the scale of seconds to minutes while these fluctuations most prominently those of the default mode network have been linked to cognitive function it remains unclear whether they result from random noise or whether they index a nonstationary process which could be described as state switching in this study we use a sliding windows approach to relate temporal dynamics of rsns to global modulations in correlation and bold variance we compare empirical data phase randomized surrogate data and data simulated with a stationary model we find that rsn time courses exhibit a large amount of coactivation in all three cases and that the modulations in their activity are closely linked to global dynamics of the underlying bold signal we find that many properties of the observed fluctuations in fc and bold including their ranges and their correlations amongst each other are explained by fluctuations around the average fc structure however we also report some interesting characteristics that clearly support nonstationary features in the data in particular we find that the brain spends more time in the troughs of modulations than can be expected from stationary dynamics

test retest reliability of dynamic functional connectivity in resting state fmri abstract while static functional connectivity sfc of resting state fmri rfmri measures the average functional connectivity fc over the entire rfmri scan dynamic fc dfc captures the temporal variations of fc at shorter time windows although numerous studies have implemented dfc analyses only a few studies have investigated the reliability of dfc and this limits the biological interpretation of dfc here we used a large cohort n 820 of subjects and four rfmri scans from the human connectome project to systematically explore the relationship between sfc dfc and their test retest reliabilities through intra class correlation icc dfc icc was explored through the sliding window approach with three dfc statistics standard deviation alff and excursion excursion demonstrated the highest dfc icc and the highest age prediction accuracy dfc icc was generally higher at window sizes less than 40 s sfc and dfc were negatively correlated compared to sfc dfc was less reliable while sfc and sfc icc were positively correlated dfc and dfc icc were negatively correlated indicating that fc that was more dynamic was less reliable intra network fcs in the frontal parietal default mode sensorimotor and visual networks demonstrated high sfc and low dfc moreover iccs of both sfc and dfc in these regions were higher the above results were consistent across two brain atlases and independent component analysis based networks multiple window sizes and all three dfc statistics in summary dfc is less reliable than sfc and additional experiments are required to better understand the neurophysiological relevance of dfc

probabilistic thresholding of functional connectomes application to schizophrenia abstract functional connectomes are commonly analysed as sparse graphs constructed by thresholding cross correlations between regional neurophysiological signals thresholding generally retains the strongest edges correlations either by retaining edges surpassing a given absolute weight or by constraining the edge density the latter more widely used method risks inclusion of false positive edges at high edge densities and exclusion of true positive edges at low edge densities here we apply new wavelet based methods which enable construction of probabilistically thresholded graphs controlled for type i error to a dataset of resting state fmri scans of 56 patients with schizophrenia and 71 healthy controls by thresholding connectomes to fixed edge specific p value we found that functional connectomes of patients with schizophrenia were more dysconnected than those of healthy controls exhibiting a lower edge density and a higher number of dis connected components furthermore many participants connectomes could not be built up to the fixed edge densities commonly studied in the literature 5 30 while controlling for type i error additionally we showed that the topological randomisation previously reported in the schizophrenia literature is likely attributable to non significant edges added when thresholding connectomes to fixed density based on correlation finally by explicitly comparing connectomes thresholded by increasing p value and decreasing correlation we showed that probabilistically thresholded connectomes show decreased randomness and increased consistency across participants our results have implications for future analysis of functional connectivity using graph theory especially within datasets exhibiting heterogenous distributions of edge weights correlations between groups or across participants

continuous modules are clean ar ingr is said to be clean if every element of r is a sum of an idempotent and a unit the class of clean rings is quite large and includes for instance semiperfect rings and thus finite rings and rings of linear transformations of vector spaces we prove that the endomorphism ring of every continuous or discrete module is clean

on rings whose projective modules have the exchange property it is well known that all projective modules over a perfect ring have the exchange property this was shown by yamagata 32 and independently by harada and ishii lo provided that the identity of the ring can be expressed as a sum of orthogonal primitive idempotents the converse is also true 32 that it fails in general was demonstrated by kutami and oshiro ls who constructed a nonartinian boolean ring whose projective modules nevertheless have the exchange property as it turned out this outsider example is representative of an extensive class of rings in fact both perfect and regular rings are subsumed in the hypotheses of the following

functional connectivity and structural covariance between regions of interest can be measured more accurately using multivariate distance correlation studies of brain wide functional connectivity or structural covariance typically use measures like the pearson correlation coefficient applied to data that have been averaged across voxels within regions of interest rois however averaging across voxels may result in biased connectivity estimates when there is inhomogeneity within those rois e g sub regions that exhibit different patterns of functional connectivity or structural covariance here we propose a new measure based on distance correlation a test of multivariate dependence of high dimensional vectors which allows for both linear and non linear dependencies we used simulations to show how distance correlation out performs pearson correlation in the face of inhomogeneous rois to evaluate this new measure on real data we use resting state fmri scans and t1 structural scans from 2 sessions on each of 214 participants from the cambridge centre for ageing neuroscience cam can project pearson correlation and distance correlation showed similar average connectivity patterns for both functional connectivity and structural covariance nevertheless distance correlation was shown to be 1 more reliable across sessions 2 more similar across participants and 3 more robust to different sets of rois moreover we found that the similarity between functional connectivity and structural covariance estimates was higher for distance correlation compared to pearson correlation we also explored the relative effects of different preprocessing options and motion artefacts on functional connectivity because distance correlation is easy to implement and fast to compute it is a promising alternative to pearson correlations for investigating roi based brain wide connectivity patterns for functional as well as structural data

dem a variational treatment of dynamic systems this paper presents a variational treatment of dynamic models that furnishes time dependent conditional densities on the path or trajectory of a system s states and the time independent densities of its parameters these are obtained by maximising a variational action with respect to conditional densities under a fixed form assumption about their form the action or path integral of free energy represents a lower bound on the model s log evidence or marginal likelihood required for model selection and averaging this approach rests on formulating the optimisation dynamically in generalised coordinates of motion the resulting scheme can be used for online bayesian inversion of nonlinear dynamic causal models and is shown to outperform existing approaches such as kalman and particle filtering furthermore it provides for dual and triple inferences on a system s states parameters and hyperparameters using exactly the same principles we refer to this approach as dynamic expectation maximisation dem

the in stability of functional brain network measures across thresholds the large scale organization of the brain has features of complex networks that can be quantified using network measures from graph theory however many network measures were designed to be calculated on binary graphs whereas functional brain organization is typically inferred from a continuous measure of correlations in temporal signal between brain regions thresholding is a necessary step to use binary graphs derived from functional connectivity data however there is no current consensus on what threshold to use and network measures and group contrasts may be unstable across thresholds nevertheless whole brain network analyses are being applied widely with findings typically reported at an arbitrary threshold or range of thresholds this study sought to evaluate the stability of network measures across thresholds in a large resting state functional connectivity dataset network measures were evaluated across absolute correlation based and proportional sparsity based thresholds and compared between sex and age groups overall network measures were found to be unstable across absolute thresholds for example the direction of group differences in a given network measure may change depending on the threshold network measures were found to be more stable across proportional thresholds these results demonstrate that caution should be used when applying thresholds to functional connectivity data and when interpreting results from binary graph models

negative edges and soft thresholding in complex network analysis of resting state functional connectivity data complex network analyses of functional connectivity have consistently revealed non random modular small world scale free like behavior of hard thresholded networks constructed from the right tail of the similarity histogram in the present study we determined network properties resulting from edges constrained to specific ranges across the full correlation histogram in particular the left negative most tail and their dependence on the confound signal removal strategy employed in the absence of global signal correction left tail networks comprised predominantly long range connections associated with weak correlations and were characterized by substantially reduced modularity and clustering negative assortativity and 1 deconvolution of specific confound signals white matter csf and motion resulted in the most robust within subject reproducibility of global network parameters iccs 0 5 global signal removal altered the network topology in the left tail with the clustering coefficient and assortativity converging to zero networks constructed from the absolute value of the correlation coefficient were thus compromised following global signal removal since the different right tail and left tail topologies were mixed these findings informed the construction of soft thresholded networks replacing the hard thresholding or binarization operation with a continuous mapping of all correlation values to edge weights suppressing rather than removing weaker connections and avoiding issues related to network fragmentation a power law adjacency function with 12 yielded modular networks whose parameters agreed well with corresponding hard thresholded values that were reproducible in repeated sessions across many months and evidenced small world like and scale free like properties

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

consistency based thresholding of the human connectome densely seeded probabilistic tractography yields weighted networks that are nearly fully connected hence containing many spurious fibers it is thus necessary to prune spurious connections from probabilistically derived networks to obtain a more reliable overall estimate of the connectivity a standard method is to threshold by weight keeping only the strongest edges here by measuring the consistency of edge weights across subjects we propose a new thresholding method that aims to reduce the rate of false positives in group averaged connectivity matrices close inspection of the relationship between consistency weight and distance suggests that the most consistent edges are in fact those that are strong for their length rather than simply strong overall hence retaining the most consistent edges preserves more long distance connections than traditional weight based thresholding which penalizes long connections for being weak regardless of anatomy by comparing our thresholded networks to mouse and macaque tracer data we also show that consistency based thresholding exhibits the species invariant exponential decay of connection weights with distance while weight based thresholding does not we also show that consistency based thresholding can be used to identify highly consistent and highly inconsistent subnetworks across subjects enabling more nuanced analyses of group level connectivity than just the mean connectivity

mixed gaussian processes a filtering approach this paper presents a new approach to the analysis of mixed processes xt bt gt t 0 t xt bt gt t 0 t where btbt is a brownian motion and gtgt is an independent centered gaussian process we obtain a new canonical innovation representation of xx using linear filtering theory when the kernel k s t 2 s tegtgs s t k s t 2 s tegtgs s t has a weak singularity on the diagonal our results generalize the classical innovation formulas beyond the square integrable setting for kernels with stronger singularity our approach is applicable to processes with additional fractional structure including the mixed fractional brownian motion from mathematical finance we show how previously known measure equivalence relations and semimartingale properties follow from our canonical representation in a unified way and complement them with new formulas for radon nikodym densities

variational bayesian identification and prediction of stochastic nonlinear dynamic causal models in this paper we describe a general variational bayesian approach for approximate inference on nonlinear stochastic dynamic models this scheme extends established approximate inference on hidden states to cover i nonlinear evolution and observation functions ii unknown parameters and precision hyperparameters and iii model comparison and prediction under uncertainty model identification or inversion entails the estimation of the marginal likelihood or evidence of a model this difficult integration problem can be finessed by optimising a free energy bound on the evidence using results from variational calculus this yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables we derive such a variational bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models for both model identification and time series prediction the computational complexity of the scheme is comparable to that of an extended kalman filter which is critical when inverting high dimensional models or long time series using monte carlo simulations we assess the estimation efficiency of this variational bayesian approach using three stochastic variants of chaotic dynamic systems we also demonstrate the model comparison capabilities of the method its self consistency and its predictive power