network clustering coefficient without degree correlation biases the clustering coefficient quantifies how well connected are the neighbors of a vertex in a graph in real networks it decreases with the vertex degree which has been taken as a signature of the network hierarchical structure here we show that this signature of hierarchical structure is a consequence of degree correlation biases in the clustering coefficient definition we introduce a definition in which the degree correlation biases are filtered out and provide evidence that in real networks the clustering coefficient is constant or decays logarithmically with vertex degree

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

a numerical method for one dimensional diffusion problem using fourier transform and the b spline galerkin method this paper deals with the diffusion transport equation in one dimensional space the b spline galerkin approximation method together with the fourier transform and gauss hermite quadrature are proposed to compute approximate solution we give some theoretical results such as existence and uniqueness of the solution and an upper error bound estimates we also give some numerical examples to illustrate the effectiveness of a such method

a simple resampling method by perturbing the minimand suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a u process structure the covariance matrix of the estimator is generally a function of the underlying density function which may be difficult to estimate well by conventional methods in this paper we present a simple resampling method by perturbing the objective function repeatedly inferences of the parameters can then be made based on a large collection of the resulting optimisers we illustrate our proposal by three examples with a heteroscedastic regression model

validation of structural brain connectivity networks the impact of scanning parameters evaluation of the structural connectivity sc of the brain based on tractography has mainly focused on the choice of diffusion model tractography algorithm and their respective parameter settings here we systematically validate sc derived from a post mortem monkey brain while varying key acquisition parameters such as the b value gradient angular resolution and image resolution as gold standard we use the connectivity matrix obtained invasively with histological tracers by markov et al 2014 as performance metric we use cross entropy as a measure that enables comparison of the relative tracer labeled neuron counts to the streamline counts from tractography we find that high angular resolution and high signal to noise ratio are important to estimate sc and that sc derived from low image resolution 1 03 mm3 are in better agreement with the tracer network than those derived from high image resolution 0 53 mm3 or at an even lower image resolution 2 03 mm3 in contradiction sensitivity and specificity analyses suggest that if the angular resolution is sufficient the balanced compromise in which sensitivity and specificity are identical remains 60 64 regardless of the other scanning parameters interestingly the tracer graph is assumed to be the gold standard but by thresholding the balanced compromise increases to 70 75 hence by using performance metrics based on binarized tracer graphs one risks losing important information changing the performance of sc graphs derived by tractography and their dependence of different scanning parameters

a fast multilevel algorithm for the solution of nonlinear systems of conductive radiative heat transfer equations in this paper we describe and analyze a fast multilevel algorithm for the solution of a system of nonlinear integro differential equations that model steady state combined conductive radiative heat transfer this system of equations for radiative intensity and temperature can be formulated as a compact fixed point problem in temperature alone with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation we obtain an efficient evaluation of the fixed point map by coupling a finite element diffusion solver with a fast transport solver developed by the second author as a solver we apply a modification of the atkinson brakhage method with newton gmres as the coarse mesh solver to the full nonlinear system we compare our discretization solver pair with newton gmres and the classical atkinson brakhage algorithm

a unified approach to semiparametric transformation models under general biased sampling schemes we propose a unified estimation method for semiparametric linear transformation models under general biased sampling schemes the new estimator is obtained from a set of counting process based unbiased estimating equations developed through introducing a general weighting scheme that offsets the sampling bias the usual asymptotic properties including consistency and asymptotic normality are established under suitable regularity conditions a closed form formula is derived for the limiting variance and the plug in estimator is shown to be consistent we demonstrate the unified approach through the special cases of left truncation length bias the case cohort design and variants thereof simulation studies and applications to real datasets are presented

studying the human brain anatomical network via diffusion weighted mri and graph theory our goal is to study the human brain anatomical network for this the anatomical connection probabilities acp between 90 cortical and subcortical brain gray matter areas are estimated from diffusion weighted magnetic resonance imaging dw mri techniques the acp between any two areas gives the probability that those areas are connected at least by a single nervous fiber then the brain is modeled as a non directed weighted graph with continuous arc weights given by the acp matrix based on this approach complex networks properties such as small world attributes efficiency degree distribution vulnerability betweenness centrality and motifs composition are studied the analysis was carried out for 20 right handed healthy subjects mean age 31 10 s d 7 43 according to the results all networks have small world and broad scale characteristics additionally human brain anatomical networks present bigger local efficiency and smaller global efficiency than the corresponding random networks in a vulnerability and betweenness centrality analysis the most indispensable and critical anatomical areas were identified putamens precuneus insulas superior parietals and superior frontals interestingly some areas have a negative vulnerability e g superior temporal poles pallidums supramarginals and hechls which suggest that even at the cost of losing in global anatomical efficiency these structures were maintained through the evolutionary processes due to their important functions finally symmetrical characteristic building blocks motifs of size 3 and 4 were calculated obtaining that motifs of size 4 are the expanded version of motif of size 3 these results are in agreement with previous anatomical studies in the cat and macaque cerebral cortex

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

identifying the brain s most globally connected regions recent advances in brain connectivity methods have made it possible to identify hubs the brain s most globally connected regions such regions are essential for coordinating brain functions due to their connectivity with numerous regions with a variety of specializations current structural and functional connectivity methods generally agree that default mode network dmn regions have among the highest global brain connectivity gbc we developed two novel statistical approaches using resting state functional connectivity mri weighted and unweighted gbc wgbc and ugbc to test the hypothesis that the highest global connectivity also occurs in the cognitive control network ccn a network anti correlated with the dmn across a variety of tasks high global connectivity was found in both ccn and dmn the newly developed wgbc approach improves upon existing methods by quantifying inter subject consistency quantifying the highest gbc values by percentage and avoiding arbitrarily connection strength thresholding the ugbc approach is based on graph theory and includes many of these improvements but still requires an arbitrary connection threshold we found high gbc in several subcortical regions e g hippocampus basal ganglia only with wgbc despite the regions extensive anatomical connectivity these results demonstrate the complementary utility of wgbc and ugbc analyses for the characterization of the most highly connected and thus most functionally important regions of the brain additionally the high connectivity of both the ccn and the dmn demonstrates that brain regions outside primary sensory motor networks are highly involved in coordinating information throughout the brain

comparing connectomes across subjects and populations at different scales brain connectivity can be represented by a network that enables the comparison of the different patterns of structural and functional connectivity among individuals in the literature two levels of statistical analysis have been considered in comparing brain connectivity across groups and subjects 1 the global comparison where a single measure that summarizes the information of each brain is used in a statistical test 2 the local analysis where a single test is performed either for each node connection which implies a multiplicity correction or for each group of nodes connections where each subset is summarized by one single test in order to reduce the number of tests to avoid a penalizing multiplicity correction we comment on the different levels of analysis and present some methods that have been proposed at each scale we highlight as well the possible factors that could influence the statistical results and the questions that have to be addressed in such an analysis

transformed dynamic quantile regression on censored data we propose a class of power transformed linear quantile regression models for time to event observations subject to censoring by introducing a process of power transformation with different transf

small world and scale free organization of voxel based resting state functional connectivity in the human brain the brain is a complex dynamic system of functionally connected regions graph theory has been successfully used to describe the organization of such dynamic systems recent resting state fmri studies have suggested that inter regional functional connectivity shows a small world topology indicating an organization of the brain in highly clustered sub networks combined with a high level of global connectivity in addition a few studies have investigated a possible scale free topology of the human brain but the results of these studies have been inconclusive these studies have mainly focused on inter regional connectivity representing the brain as a network of brain regions requiring an arbitrary definition of such regions however using a voxel wise approach allows for the model free examination of both inter regional as well as intra regional connectivity and might reveal new information on network organization especially a voxel based study could give information about a possible scale free organization of functional connectivity in the human brain resting state 3 tesla fmri recordings of 28 healthy subjects were acquired and individual connectivity graphs were formed out of all cortical and sub cortical voxels with connections reflecting inter voxel functional connectivity graph characteristics from these connectivity networks were computed the clustering coefficient of these networks turned out to be much higher than the clustering coefficient of comparable random graphs together with a short average path length indicating a small world organization furthermore the connectivity distribution of the number of inter voxel connections followed a power law scaling with an exponent close to 2 suggesting a scale free network topology our findings suggest a combined small world and scale free organization of the functionally connected human brain the results are interpreted as evidence for a highly efficient organization of the functionally connected brain in which voxels are mostly connected with their direct neighbors forming clustered sub networks which are held together by a small number of highly connected hub voxels that ensure a high level of overall connectivity

power transformation toward a linear regression quantile in this article we consider the linear quantile regression model with a power transformation on the dependent variable like the classical box cox transformation approach it extends the applicability of linear models without resorting to nonparametric smoothing but transformations on the quantile models are more natural due to the equivariance property of the quantiles under monotone transformations we propose an estimation procedure and establish its consistency and asymptotic normality under some regularity conditions the objective function employed in the estimation can also be used to check inadequacy of a power transformed linear quantile regression model and to obtain inference on the transformation parameter the proposed approach is shown to be valuable through illustrative examples

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

an a posteriori error estimate for the generalized finite element method for transient heat diffusion problems summary we propose the study of a posteriori error estimates for time dependent generalized finite element simulations of heat transfer problems a residual estimate is shown to provide reliable and practically useful upper bounds for the numerical errors independent of the heuristically chosen enrichment functions two sets of numerical experiments are presented first the error estimate is shown to capture the decrease in the error as the number of enrichment functions is increased or the time discretization refined second the estimate is used to predict the behaviour of the error where no exact solution is available it also reflects the errors incurred in the poorly conditioned systems typically encountered in generalised finite element methods finally we study local error indicators in individual time steps and elements of the mesh this creates a basis towards the adaptive selection and refinement of the enrichment functions this article is protected by copyright all rights reserved

time independent hybrid enrichment for finite element solution of transient conduction radiation in diffusive grey media we investigate the effectiveness of the partition of unity finite element method for transient conduction radiation problems in diffusive grey media the governing equations consist of a semi linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media the coupled equations are integrated in time using a semi implicit method in the finite element framework we show that for the considered problems a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method it is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls the performance of the proposed partition of unity method is analyzed on several test examples for transient conduction radiation problems in two space dimensions

scale free brain functional networks functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites analysis of the resulting networks in different tasks shows that a the distribution of functional connections and the probability of finding a link versus distance are both scale free b the characteristic path length is small and comparable with those of equivalent random networks and c the clustering coefficient is orders of magnitude larger than those of equivalent random networks all these properties typical of scale free small world networks reflect important functional information about brain states

model reduction techniques for frequency averaging in radiative heat transfer we study model reduction techniques for frequency averaging in radiative heat transfer especially we employ proper orthogonal decomposition in combination with the method of snapshots to devise an automated a posteriori algorithm which helps to reduce significantly the dimensionality for further simulations the reliability of the surrogate models is tested and we compare the results with two other reduced models which are given by the approximation using the weighted sum of gray gases and by an frequency averaged version of the so called mathrm sp n model we present several numerical results underlining the feasibility of our approach

estimation and inference of quantile regression for survival data under biased sampling abstractbiased sampling occurs frequently in economics epidemiology and medical studies either by design or due to data collecting mechanism failing to take into account the sampling bias usually leads to incorrect inference we propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for quantile regression with survival data under general biased sampling schemes including but not limited to the length biased sampling the case cohort design and variants thereof we establish the uniform consistency and weak convergence of the proposed estimator as a process of the quantile level we also investigate more efficient estimation using the generalized method of moments and derive the asymptotic normality we further propose a new resampling method for inference which differs from alternative procedures in that it does not require to repeatedly solve estimating equations it is proved that the resampling method consistently estimates the asymptoti

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

quantile regression methods for reference growth charts estimation of reference growth curves for children s height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population age specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods non parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions we compare estimated reference curves for height using the penalized likelihood approach of cole and green statistics in medicine 1992 11 1305 1319 with quantile regression curves based on data used for modern finnish reference charts an advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated copyright 2005 john wiley sons ltd

threshold free cluster enhancement addressing problems of smoothing threshold dependence and localisation in cluster inference many image enhancement and thresholding techniques make use of spatial neighbourhood information to boost belief in extended areas of signal the most common such approach in neuroimaging is cluster based thresholding which is often more sensitive than voxel wise thresholding however a limitation is the need to define the initial cluster forming threshold this threshold is arbitrary and yet its exact choice can have a large impact on the results particularly at the lower e g t z 4 cluster forming thresholds frequently used furthermore the amount of spatial pre smoothing is also arbitrary given that the expected signal extent is very rarely known in advance of the analysis in the light of such problems we propose a new method which attempts to keep the sensitivity benefits of cluster based thresholding and indeed the general concept of clusters of signal while avoiding or at least minimising these problems the method takes a raw statistic image and produces an output image in which the voxel wise values represent the amount of cluster like local spatial support the method is thus referred to as threshold free cluster enhancement tfce we present the tfce approach and discuss in detail roc based optimisation and comparisons with cluster based and voxel based thresholding we find that tfce gives generally better sensitivity than other methods over a wide range of test signal shapes and snr values we also show an example on a real imaging dataset suggesting that tfce does indeed provide not just improved sensitivity but richer and more interpretable output than cluster based thresholding

survival analysis with quantile regression models quantile regression offers great flexibility in assessing covariate effects on event times thereby attracting considerable interests in its applications in survival analysis but currently available methods often require stringent assumptions or complex algorithms in this article we develop a new quantile regression approach for survival data subject to conditionally independent censoring the proposed martingale based estimating equations naturally lead to a simple algorithm that involves minimizations only of l1 type convex functions we establish uniform consistency and weak convergence of the resultant estimators we develop inferences accordingly including hypothesis testing second stage inference and model diagnostics we evaluate the finite sample performance of the proposed methods through extensive simulation studies an analysis of a recent dialysis study illustrates the practical utility of our proposals

a dti derived measure of cortico cortical connectivity we arm researchers with a simple method to chart a macroscopic cortico cortical connectivity network in living human subjects the researcher provides a diffusion magnetic resonance imaging mri data set and n cortical regions of interest in return we provide an n times n structural adjacency matrix sam quantifying the relative connectivity between all cortical region pairs we also return a connectivity map for each pair to enable visualization of interconnecting fiber bundles the measure of connectivity we devise is 1 free of length bias 2 proportional to fiber bundle cross sectional area and 3 invariant to an exchange of seed and target we construct a 3 d lattice scaffolding graph for white matter by drawing a link between each pair of voxels in a 26 voxel neighborhood for which their two respective principal eigenvectors form a sufficiently small angle the connectivity between a cortical region pair is then measured as the maximum number of link disjoint paths that can be established between them in the white matter graph we devise an efficient edmonds karp like algorithm to compute a conservative bound on the maximum number of link disjoint paths using both simulated and authentic diffusion tensor imaging data we demonstrate that the number of link disjoint paths as a measure of connectivity satisfies properties 1 3 unlike the fraction of intersecting streamlines the measure intrinsic to most existing probabilistic tracking algorithms finally we present connectivity maps of some notoriously difficult to track longitudinal and contralateral fasciculi

simplified p n approximations to the equations of radiative heat transfer and applications simplified pn spn approximations to the equations of radiative heat transfer are derived for optically thick diffusive systems and appropriate boundary conditions are formulated the spn equations are derived by an asymptotic analysis while the boundary conditions are obtained from a variational analysis numerical comparisons of the spn equilibrium diffusion and full transport equations are presented to demonstrate the accuracy and efficiency of the spn approximations

cure rate quantile regression for censored data with a survival fraction censored quantile regression offers a valuable complement to the traditional cox proportional hazards model for survival analysis survival times tend to be right skewed particularly when there exists a substantial fraction of long term survivors who are either cured or immune to the event of interest for survival data with a cure possibility we propose cure rate quantile regression under the common censoring scheme that survival times and censoring times are conditionally independent given the covariates in a mixture formulation we apply censored quantile regression to model the survival times of susceptible subjects and logistic regression to model the indicators of whether patients are susceptible we develop two estimation methods using martingale based equations one approach fully uses all regression quantiles by iterating estimation between the cure rate and quantile regression parameters and the other separates the two via a nonparametric kernel smoothing estimator we establish the uniform

efficient numerical methods for radiation in gas turbines numerical methods for radiative heat transfer equations coupled to a temperature equation are considered efficient solution methods and approximate equations for this system are investigated and a comparative numerical study of the different approximations is given the approximate equations considered in this paper include moment methods and diffusive approximations fast iterative solvers for the problem like multilevel methods with suitable preconditioning are considered in detail numerical experiments and comparisons in different space dimensions and for various physical situations are presented

network based statistic identifying differences in brain networks large scale functional or structural brain connectivity can be modeled as a network or graph this paper presents a statistical approach to identify connections in such a graph that may be associated with a diagnostic status in case control studies changing psychological contexts in task based studies or correlations with various cognitive and behavioral measures the new approach called the network based statistic nbs is a method to control the family wise error rate in the weak sense when mass univariate testing is performed at every connection comprising the graph to potentially offer a substantial gain in power the nbs exploits the extent to which the connections comprising the contrast or effect of interest are interconnected the nbs is based on the principles underpinning traditional cluster based thresholding of statistical parametric maps the purpose of this paper is to i introduce the nbs for the first time ii evaluate its power with the use of receiver operating characteristic roc curves and iii demonstrate its utility with application to a real case control study involving a group of people with schizophrenia for which resting state functional mri data were acquired the nbs identified a expansive dysconnected subnetwork in the group with schizophrenia primarily comprising fronto temporal and occipito temporal dysconnections whereas a mass univariate analysis controlled with the false discovery rate failed to identify a subnetwork

quantile calculus and censored regression quantile regression has been advocated in survival analysis to assess evolving covariate effects however challenges arise when the censoring time is not always observed and may be covariate dependent particularly in the presence of continuously distributed covariates in spite of several recent advances existing methods either involve algorithmic complications or impose a probability grid the former leads to difficulties in the implementation and asymptotics whereas the latter introduces undesirable grid dependence to resolve these issues we develop fundamental and general quantile calculus on cumulative probability scale in this article upon recognizing that probability and time scales do not always have a one to one mapping given a survival distribution these results give rise to a novel estimation procedure for censored quantile regression based on estimating integral equations a numerically reliable and efficient progressive localized minimization plmin algorithm is proposed for the computation this procedure reduces exactly to the kaplan meier method in the k sample problem and to standard uncensored quantile regression in the absence of censoring under regularity conditions the proposed quantile coefficient estimator is uniformly consistent and converges weakly to a gaussian process simulations show good statistical and algorithmic performance the proposal is illustrated in the application to a clinical study

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

a partition of unity fem for time dependent diffusion problems using multiple enrichment functions an enriched partition of unity fem is developed to solve time dependent diffusion problems in the present formulation multiple exponential functions describing the spatial and temporal diffusion decay are embedded in the finite element approximation space the resulting enrichment is in the form of a local asymptotic expansion unlike previous works in this area where the enrichment must be updated at each time step here the temporal decay in the solution is embedded in the asymptotic expansion thus the system matrix that is evaluated at the first time step may be decomposed and retained for every next time step by just updating the right hand side of the linear system of equations the advantage is a significant saving in the computational effort where previously the linear system must be reevaluated and resolved at every time step in comparison with the traditional finite element analysis with p version refinements the present approach is much simpler more efficient and yields more accurate solutions for a prescribed number of dofs numerical results are presented for a transient diffusion equation with known analytical solution the performance of the method is analyzed on two applications the transient heat equation with a single source and the transient heat equation with multiple sources the aim of such a method compared with the classical fem is to solve time dependent diffusion applications efficiently and with an appropriate level of accuracy

power transformed linear quantile regression with censored data we propose a class of power transformed linear quantile regression models for survival data subject to random censoring the estimation procedure follows two sequential steps first for a given transformation parameter we can easily obtain the estimates for the regression coefficients by minimizing a well defined convex objective function second we can estimate the transformation parameter based on a model discrepancy measure by constructing cumulative sum processes we show that both the regression and transformation parameter estimates are strongly consistent and asymptotically normal the variance covariance matrix depends on the unknown density function of the error term so we estimate the variance by the usual bootstrap approach we examine the performance of the proposed method for finite sample sizes through simulation studies and illustrate it with a real data example

statistical parametric network analysis of functional connectivity dynamics during a working memory task abstract network analysis has become a tool of choice for the study of functional and structural magnetic resonance imaging mri data little research however has investigated connectivity dynamics in relation to varying cognitive load in fmri correlations among slow

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

an enriched finite element model with q refinement for radiative boundary layers in glass cooling radiative cooling in glass manufacturing is simulated using the partition of unity finite element method the governing equations consist of a semi linear transient heat equation for the temperature field and a stationary simplified p 1 approximation for the radiation in non grey semitransparent media to integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework a class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls using an industrial electromagnetic spectrum the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h version finite element method furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries the time integration choice is essential to implement a q refinement procedure introduced in the current study the enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment the performance of the proposed method is analysed for glass annealing in two enclosures where the simplified p 1 approximation solution with the partition of unity method the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical rosseland model

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

locally weighted censored quantile regression censored quantile regression offers a valuable supplement to cox proportional hazards model for survival analysis existing work in the literature often requires stringent assumptions such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile levels moreover some of the work uses recursive algorithms making it challenging to derive asymptotic normality to overcome these drawbacks we propose a new locally weighted censored quantile regression approach that adopts the redistribution of mass idea and employs a local reweighting scheme its validity only requires conditional independence of the survival time and the censoring variable given the covariates and linearity at the particular quantile level of interest our method leads to a simple algorithm that can be conveniently implemented with r software applying recent theory of m estimation with infinite dimensional parameters we establish the consistency and asymptotic normality of the pr

non parametric bayesian graph models reveal community structure in resting state fmri modeling of resting state functional magnetic resonance imaging rs fmri data using network models is of increasing interest it is often desirable to group nodes into clusters to interpret the communication patterns between nodes in this study we consider three dierent nonparametric bayesian

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

persistent brain network homology from the perspective of dendrogram the brain network is usually constructed by estimating the connectivity matrix and thresholding it at an arbitrary level the problem with this standard method is that we do not have any generally accepted criteria for determining a proper threshold thus we propose a novel multiscale framework that models all brain networks generated over every possible threshold our approach is based on persistent homology and its various representations such as the rips filtration barcodes and dendrograms this new persistent homological framework enables us to quantify various persistent topological features at different scales in a coherent manner the barcode is used to quantify and visualize the evolutionary changes of topological features such as the betti numbers over different scales by incorporating additional geometric information to the barcode we obtain a single linkage dendrogram that shows the overall evolution of the network the difference between the two networks is then measured by the gromov hausdorff distance over the dendrograms as an illustration we modeled and differentiated the fdg pet based functional brain networks of 24 attention deficit hyperactivity disorder children 26 autism spectrum disorder children and 11 pediatric control subjects

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

network algorithmics and the emergence of information integration in cortical models an information theoretic framework known as integrated information theory iit has been introduced recently for the study of the emergence of consciousness in the brain d balduzzi and g tononi plos comput biol 4 e1000091 2008 iit purports that this phenomenon is to be equated with the generation of information by the brain surpassing the information that the brain s constituents already generate independently of one another iit is not fully plausible in its modeling assumptions nor is it testable due to severe combinatorial growth embedded in its key definitions here we introduce an alternative to iit which while inspired in similar information theoretic principles seeks to address some of iit s shortcomings to some extent our alternative framework uses the same network algorithmic cortical model we introduced earlier a nathan and v c barbosa phys rev e 81 021916 2010 and to allow for somewhat improved testability relative to iit adopts the well known notions of information gain and total correlation applied to a set of variables representing the reachability of neurons by messages in the model s dynamics we argue that these two quantities relate to each other in such a way that can be used to quantify the system s efficiency in generating information beyond that which does not depend on integration we give computational results on our cortical model and on variants thereof that are either structurally random in the sense of an erd s renyi random directed graph or structurally deterministic we have found that our cortical model stands out with respect to the others in the sense that many of its instances are capable of integrating information more efficiently than most of those others instances

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

conditional growth charts growth charts are often more informative when they are customized per subject taking into account prior measurements and possibly other covariates of the subject we study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions the model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers and it is also flexible for including covariate information we propose a rank score test for large sample inference on covariates and develop a new model assessment tool for longitudinal growth data our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis

non parametric model selection for subject specific topological organization of resting state functional connectivity abstract in recent years graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain most of these networks have shown small world topological characteristics high efficiency in long distance communication between nodes combined with highly interconnected local clusters of nodes moreover functional studies performed at high resolutions have presented convincing evidence that resting state functional connectivity networks exhibits exponentially truncated scale free behavior such evidence however was mostly presented qualitatively in terms of linear regressions of the degree distributions on log log plots even when quantitative measures were given these were usually limited to the r 2 correlation coefficient however the r 2 statistic is not an optimal estimator of explained variance when dealing with truncated power law models recent developments in statistics have introduced new non parametric approaches based on the kolmogorov smirnov test for the problem of model selection in this work we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest the analysis performed at voxel level and in a subject specific fashion confirmed the superiority of a truncated power law model showing high consistency across subjects moreover the most highly connected voxels were found to be consistently part of the default mode network our results provide statistically sound support to the evidence previously presented in literature for a truncated power law model of resting state functional connectivity

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

censored regression quantiles using quantile regression to analyze survival times offers an valuable complement to traditional cox proportional hazards modelling unfortunately this approach has been hampered by the lack of a conditional quantile estimator for censored data that is directly analogous to the kaplan meier estimator and applies under standard assumptions for censored regression models here a recursively reweighted estimator of the regression quantile process is developed as a direct generalization of the kaplan meier estimator specifically the asymptotic behavior is directly analogous to that of the kaplan meier estimator and computation is essentially equivalent to current simplex methods for the quantile process in the uncensored case some preliminary examples suggest the strong potential of these methods as a complement to the use of cox models

multigrid newton krylov method for radiation in diffusive semitransparent media we present a fast multigrid solver for simplified p n sp n approximations to the diffusive radiation in non grey semitransparent media the method consists on reformulating the equations as a nonlinear fixed point problem in the temperature only given a mesh hierarchy time and space discretizations are performed using second order implicit and finite differencing methods respectively at each mesh level a newton krylov algorithm is applied to the discrete equations as a smoother on the coarse meshes we propose the atkinson brakhage operator numerical results are shown for glass cooling process using different geometry enclosures the sp n approximations capture the correct asymptotic behavior of the numerical solution with a computational cost lower than using the full radiative transfer equations