soliton dynamics in computational anatomy computational anatomy ca has introduced the idea of anatomical structures being transformed by geodesic deformations on groups of diffeomorphisms among these geometric structures landmarks and image outlines in ca are shown to be singular solutions of a partial differential equation that is called the geodesic epdiff equation a recently discovered momentum map for singular solutions of epdiff yields their canonical hamiltonian formulation which in turn provides a complete parameterization of the landmarks by their canonical positions and momenta the momentum map provides an isomorphism between landmarks and outlines for images and singular soliton solutions of the epdiff equation this isomorphism suggests a new dynamical paradigm for ca as well as new data representation

cortical thickness analysis in autism with heat kernel smoothing we present a novel data smoothing and analysis framework for cortical thickness data defined on the brain cortical manifold gaussian kernel smoothing which weights neighboring observations according to their 3d euclidean distance has been widely used in 3d brain images to increase the signal to noise ratio when the observations lie on a convoluted brain surface however it is more natural to assign the weights based on the geodesic distance along the surface we therefore develop a framework for geodesic distance based kernel smoothing and statistical analysis on the cortical manifolds as an illustration we apply our methods in detecting the regions of abnormal cortical thickness in 16 high functioning autistic children via random field based multiple comparison correction that utilizes the new smoothing technique

statistics on diffeomorphisms via tangent space representations in this paper we present a linear setting for statistical analysis of shape and an optimization approach based on a recent derivation of a conservation of momentum law for the geodesics of diffeomorphic flow once a template is fixed the space of initial momentum becomes an appropriate space for studying shape via geodesic flow since the flow at any point along the geodesic is completely determined by the momentum at the origin through geodesic shooting equations the space of initial momentum provides a linear representation of the nonlinear diffeomorphic shape space in which linear statistical analysis can be applied specializing to the landmark matching problem of computational anatomy we derive an algorithm for solving the variational problem with respect to the initial momentum and demonstrate principal component analysis pca in this setting with three dimensional face and hippocampus databases

adjusted exponentially tilted likelihood with applications to brain morphology in this article we develop a nonparametric method called adjusted exponentially tilted et likelihood and apply it to the analysis of morphometric measures the adjusted exponential tilting estimator is shown to have the same first order asymptotic properties as that of the original et likelihood the adjusted et likelihood ratio statistic is applied to test linear hypotheses of unknown parameters such as the associations of brain measures e g cortical and subcortical surfaces with covariates of interest such as age gender and gene simulation studies show that the adjusted exponential tilted likelihood ratio statistic performs as well as the t test when the imaging data are symmetrically distributed while it is superior when the imaging data have skewed distribution we demonstrate the application of our new statistical methods to the detection of statistically significant differences in the morphology of the hippocampus between two schizophrenia groups and healthy subjects

a nonconservative lagrangian framework for statistical fluid registration safira in this paper we used a nonconservative lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3 d brain images this algorithm is named safira acronym for statistically assisted fluid image registration algorithm a nonstatistical version of this algorithm was implemented where the deformation was regularized by penalizing deviations from a zero rate of strain in the terms regularizing the deformation included the covariance of the deformation matrices and the vector fields q here we used a lagrangian framework to reformulate this algorithm showing that the regularizing terms essentially allow nonconservative work to occur during the flow given 3 d brain images from a group of subjects vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated separately or jointly in the nonconservative terms creating four versions of safira we evaluated and compared our algorithms performance on 92 3 d brain scans from healthy monozygotic and dizygotic twins 2 d validations are also shown for corpus callosum shapes delineated at midline in the same subjects after preliminary tests to demonstrate each method we compared their detection power using tensor based morphometry tbm a technique to analyze local volumetric differences in brain structure we compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields all these tests were also run with a traditional fluid method which has been quite widely used in tbm studies the versions incorporating vector based empirical statistics on brain variation were consistently more accurate than their counterparts when used for automated volumetric quantification in new brain images this suggests the advantages of this approach for large scale neuroimaging studies

a riemannian framework for tensor computing tensors are nowadays a common source of geometric information in this paper we propose to endow the tensor space with an affine invariant riemannian metric we demonstrate that it leads to strong theoretical properties the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries null eigenvalues are at the infinity the geodesic between two tensors and the mean of a set of tensors are uniquely defined etc we have previously shown that the riemannian metric provides a powerful framework for generalizing statistics to manifolds in this paper we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation filtering diffusion and restoration of missing data for instance most interpolation and gaussian filtering schemes can be tackled efficiently through a weighted mean computation linear and anisotropic diffusion schemes can be adapted to our riemannian framework through partial differential evolution equations provided that the metric of the tensor space is taken into account for that purpose we provide intrinsic numerical schemes to compute the gradient and laplace beltrami operators finally to enforce the fidelity to the data either sparsely distributed tensors or complete tensors fields we propose least squares criteria based on our invariant riemannian distance which are particularly simple and efficient to solve

geodesic estimation for large deformation anatomical shape averaging and interpolation the goal of this research is to promote variational methods for anatomical averaging that operate within the space of the underlying image registration problem this approach is effective when using the large deformation viscous framework where linear averaging is not valid or in the elastic case the theory behind this novel atlas building algorithm is similar to the traditional pairwise registration problem but with single image forces replaced by average forces these group forces drive an average transport ordinary differential equation allowing one to estimate the geodesic that moves an image toward the mean shape configuration this model gives large deformation atlases that are optimal with respect to the shape manifold as defined by the data and the image registration assumptions we use the techniques in the large deformation context here but they also pertain to small deformation atlas construction furthermore a natural inherently inverse consistent image registration is gained for free as is a tool for constant arc length geodesic shape interpolation the geodesic atlas creation algorithm is quantitatively compared to the euclidean anatomical average to elucidate the need for optimized atlases the procedures generate improved average representations of highly variable anatomy from distinct populations

distribution of the sum of two sine waves and gaussian noise the cumulative distribution of the envelope of the sum of two sine waves and narrowband gaussian noise the difference of the phases of the sine waves being uniformly distributed over 0 2 pi is expressed as an integral that is evaluated by numerical quadrature approximation for the distribution valid in the limit of large signal to noise ratio are derived the probability density function of the envelope is similarly treated

high dimensional image registration using symmetric priors this paper is about warping a brain image from one subject the object image so that it matches another the template image a high dimensional model is used whereby a finite element approach is employed to estimate translations at the location of each voxel in the template image bayesian statistics are used to obtain a maximum a posteriori map estimate of the deformation field the validity of any registration method is largely based upon the constraints or in this instance priors incorporated into the model describing the transformations in this approach we assume that the priors should have some form of symmetry in that priors describing the probability distribution of the deformations should be identical to those for the inverses i e warping brain a to brain b should not be different probabilistically from warping b to a the fundamental assumption is that the probability of stretching a voxel by a factor of n is considered to be the same as the probability of shrinking n voxels by a factor of n 1 in the bayesian framework adopted here the priors are assumed to have a gibbs form where the gibbs potential is a penalty function that embodies this symmetry the penalty function of choice is based upon the singular values of the jacobian having a lognormal distribution this enforces a continuous one to one mapping a gradient descent algorithm is presented that incorporates the above priors in order to obtain a map estimate of the deformations we demonstrate this approach for the two dimensional case but the principles can be extended to three dimensions a number of examples are given to demonstrate how the method works

solving second kind fredholm integral equations by periodic wavelet galerkin method in this paper we use the periodized daubechies wavelets based galerkin method pwgm to solve linear nonlinear and singular fredholm integral equations of the second kind a main advantage of the present pwgm over the existing wavelet galerkin methods lies in that the wavelet expansion coefficients are exactly obtained without calculating the wavelet integrations therefore the computational cost is low whereas the accuracy is high after discretization the linear and nonlinear integral equations is converted into a system of linear and nonlinear equations respectively and for the linear case the matrix can be converted into a sparse and symmetrical one by fast wavelet transform fwt numerical experiments show that the pwgm has a good degree of accuracy

characterizing volume and surface deformations in an atlas framework theory applications and implementation given deformations for mapping images or surfaces into an atlas configuration methods are described for characterizing the mean deformation and deviations from this mean jacobian matrices are used to characterize the deformations locally and the method can be applied to any image warping method for which jacobian matrices can be computed the method makes use of the fact that each matrix descriptor of the local deformation required to match an image to the atlas corresponds to a point on a semi riemannian manifold by assuring that the mean matrix lies within this manifold fundamental geometric properties common to all of the images can be preserved local deviations from the mean can be characterized in a euclidean space tangent to the semi riemannian manifold at the mean and can be accumulated globally across multiple sampling locations within the atlas to generate a global multivariate characterization of how each image deviates from the mean

new bounds for the marcum q function new bounds are proposed for the marcum q function which is defined by an integral expression where the 0th order modified bessel function appears the proposed bounds are derived by suitable approximations of the 0th order modified bessel function in the integration region of the marcum q function they prove to be very tight and outperform bounds previously proposed in the literature in particular the proposed bounds are noticeably good for large values of the parameters of the marcum q function where previously introduced bounds fail and where exact computation of the function becomes critical due to numerical problems

computing the generalized marcum q function a modified version of the method of saddlepoint integration is shown to compute the generalized marcum q function accurately over a broad range of parameters bounds on the truncation error incurred by stopping the numerical quadrature at a certain point are presented

computing large deformation metric mappings via geodesic flows of diffeomorphisms this paper examine the euler lagrange equations for the solution of the large deformation diffeomorphic metric mapping problem studied in dupuis et al 1998 and trouve 1995 in which two images i 0 i 1 are given and connected via the diffeomorphic change of coordinates i 0 1 i 1 where 1 is the end point at t 1 of curve t t 0 1 satisfying t v t t t 0 1 with 0 id the variational problem takes the form mathop arg text m in limits upsilon dot phi t upsilon t left dot phi right left int 0 1 left upsilon t right 2 text d t left i 0 circ phi 1 1 i 1 right l 2 2 right where v t v is an appropriate sobolev norm on the velocity field v t and the second term enforces matching of the images with l 2 representing the squared error norm in this paper we derive the euler lagrange equations characterizing the minimizing vector fields v t t 0 1 assuming sufficient smoothness of the norm to guarantee existence of solutions in the space of diffeomorphisms we describe the implementation of the euler equations using semi lagrangian method of computing particle flows and show the solutions for various examples as well we compute the metric distance on several anatomical configurations as measured by 0 1 v t v dt on the geodesic shortest paths

apparent fibre density a novel measure for the analysis of diffusion weighted magnetic resonance images this article proposes a new measure called apparent fibre density afd for the analysis of high angular resolution diffusion weighted images using higher order information provided by fibre orientation distributions fods computed using spherical deconvolution afd has the potential to provide specific information regarding differences between populations by identifying not only the location but also the orientations along which differences exist in this work analytical and numerical monte carlo simulations are used to support the use of the fod amplitude as a quantitative measure i e afd for population and longitudinal analysis to perform robust voxel based analysis of afd we present and evaluate a novel method to modulate the fod to account for changes in fibre bundle cross sectional area that occur during spatial normalisation we then describe a novel approach for statistical analysis of afd that uses cluster based inference of differences extended throughout space and orientation finally we demonstrate the capability of the proposed method by performing voxel based afd comparisons between a group of motor neurone disease patients and healthy control subjects a significant decrease in afd was detected along voxels and orientations corresponding to both the corticospinal tract and corpus callosal fibres that connect the primary motor cortices in addition to corroborating previous findings in mnd this study demonstrates the clear advantage of using this type of analysis by identifying differences along single fibre bundles in regions containing multiple fibre populations

registration of images with varying topology using embedded maps this paper presents registration via embedded maps rem a deformable registration algorithm for images with varying topology the algorithm represents 3 d images as 4 d manifolds in a riemannian space referred to as embedded maps registration is performed as a surface evolution matching one embedded map to another using a diffusion process the approach differs from those existing in that it takes an a priori estimation of image regions where topological changes are present for example lesions and generates a dense vector field representing both the shape and intensity changes necessary to match the images the algorithm outputs both a diffeomorphic deformation field and an intensity displacement which corrects the intensity difference caused by topological changes multiple sets of experiments are conducted on magnetic resonance imaging mri with lesions from oasis and adni datasets these images are registered to either a brain template or images of healthy individuals an exemplar case registering a template to an mri with tumor is also given the resulting deformation fields were compared with those obtained using diffeomorphic demons where topological changes are not modeled these sets of experiments demonstrate the efficacy of our proposed rem method for registration of brain mri with severe topological differences

the detection of local shape changes via the geometry of hotelling s t 2 fields this paper is motivated by the problem of detecting local changes or differences in shape between two samples of objects via the nonlinear deformations required to map each object to an atlas standard local shape changes are then detected by high values of the random field of hotelling s t 2 statistics for detecting a change in mean of the vector deformations at each point in the object to control the null probability of detecting a local shape change we use the recent result of adler that the probability that a random field crosses a high threshold is very accurately approximated by the expected euler characteristic ec of the excursion set of the random field above the threshold we give an exact expression for the expected ec of a hotelling s t 2 field and we study the behavior of the field near local extrema this extends previous results for gaussian random fields by adler and x 2 t and f fields by worsley and cao for illustration these results are applied to the detection of differences in brain shape between a sample of 29 males and 23 females

semiparametric bayesian local functional models for diffusion tensor tract statistics we propose a semiparametric bayesian local functional model bfm for the analysis of multiple diffusion properties e g fractional anisotropy along white matter fiber bundles with a set of covariates of interest such as age and gender bfm accounts for heterogeneity in the shape of the fiber bundle diffusion properties among subjects while allowing the impact of the covariates to vary across subjects a nonparametric bayesian lpp2 prior facilitates global and local borrowings of information among subjects while an infinite factor model flexibly represents low dimensional structure local hypothesis testing and credible bands are developed to identify fiber segments along which multiple diffusion properties are significantly associated with covariates of interest while controlling for multiple comparisons moreover bfm naturally group subjects into more homogeneous clusters posterior computation proceeds via an efficient markov chain monte carlo algorithm a simulation study is performed to evaluate the finite sample performance of bfm we apply bfm to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment in new born infants

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

note on the calculation of the probability of detection and the generalized marcum q function a highly reliable accurate and efficient method of calculating the probability of detection p sub n x y for n incoherently integrated samples where x is the constant received signal to noise ratio of a single pulse and y is the normalized threshold level is presented the useful range of parameters easily exceeds most needs on a vax 11 computer with double precision calculations better than 13 place absolute accuracy is normally achieved there is a gradual loss of accuracy with increasing parameter values for example for n 10 sup 9 and with both nx and y near 10 sup 7 the accuracy can drop to ten places the function p sub n x y can be equated to the generalized marcum q function q sub m alpha beta the corresponding limits on alpha and beta are roughly 4500 for the 13 place accuracy and 60000 for ultimate integer 4 limit

high resolution random mesh algorithms for creating a probabilistic 3d surface atlas of the human brain abstract striking variations exist across individuals in the internal and external geometry of the brain such normal variations in the size orientation topology and geometric complexity of cortical and subcortical structures have complicated the problem of quantifying deviations from normal anatomy and of developing standardized neuroanatomical atlases this paper describes the design implementation and results of a technique for creating a three dimensional 3d probabilistic surface atlas of the human brain we have developed implemented and tested a new 3d statistical method for assessing structural variations in a database of anatomic images the algorithm enables the internal surface anatomy of new subjects to be analyzed at an extremely local level the goal was to quantify subtle and distributed patterns of deviation from normal anatomy by automatically generating detailed probability maps of the anatomy of new subjects connected systems of parametric meshes were used to model the internal course of the following structures in both hemispheres the parieto occipital sulcus the anterior and posterior rami of the calcarine sulcus the cingulate and marginal sulci and the supracallosal sulcus these sulci penetrate sufficiently deeply into the brain to introduce an obvious topological decomposition of its volume architecture a family of surface maps was constructed encoding statistical properties of local anatomical variation within individual sulci a probability space of random transformations based on the theory of gaussian random fields was developed to reflect the observed variability in stereotaxic space of the connected system of anatomic surfaces a complete system of probability density functions was computed yielding confidence limits on surface variation the ultimate goal of brain mapping is to provide a framework for integrating functional and anatomical data across many subjects and modalities this task requires precise quantitative knowledge of the variations in geometry and location of intracerebral structures and critical functional interfaces the surface mapping and probabilistic techniques presented here provide a basis for the generation of anatomical templates and expert diagnostic systems which retain quantitative information on intersubject variations in brain architecture

model based deformable surface finding for medical images describes a new global shape parameterization for smoothly deformable three dimensional 3 d objects such as those found in biomedical images whose diversity and irregularity make them difficult to represent in terms of fixed features or parts this representation is used for geometric surface matching to 3 d medical image data such as from magnetic resonance imaging mri the parameterization decomposes the surface into sinusoidal basis functions four types of surfaces are modeled tori open surfaces closed surfaces and tubes this parameterization allows a wide variety of smooth surfaces to be described with a small number of parameters extrinsic model based information is incorporated by introducing prior probabilities on the parameters surface finding is formulated as an optimization problem results of the method applied to synthetic images and 3 d medical images of the heart and brain are presented

multivariate tensor based morphometry on surfaces application to mapping ventricular abnormalities in hiv aids here we developed a new method called multivariate tensor based surface morphometry tbm and applied it to study lateral ventricular surface differences associated with hiv aids using concepts from differential geometry and the theory of differential forms we created mathematical structures known as holomorphic one forms to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain the new meshing approach also provides a natural way to register anatomical surfaces across subjects and improves on prior methods as it handles surfaces that branch and join at complex 3d junctions to analyze anatomical differences we computed new statistics from the riemannian surface metrics these retain multivariate information on local surface geometry we applied this framework to analyze lateral ventricular surface morphometry in 3d mri data from 11 subjects with hiv aids and 8 healthy controls our method detected a 3d profile of surface abnormalities even in this small sample multivariate statistics on the local tensors gave better effect sizes for detecting group differences relative to other tbm based methods including analysis of the jacobian determinant the largest and smallest eigenvalues of the surface metric and the pair of eigenvalues of the jacobian matrix the resulting analysis pipeline may improve the power of surface based morphometry studies of the brain

generalized tensor based morphometry of hiv aids using multivariate statistics on deformation tensors this paper investigates the performance of a new multivariate method for tensor based morphometry tbm statistics on riemannian manifolds are developed that exploit the full information in deformation tensor fields in tbm multiple brain images are warped to a common neuroanatomical template via 3 d nonlinear registration the resulting deformation fields are analyzed statistically to identify group differences in anatomy rather than study the jacobian determinant volume expansion factor of these deformations as is common we retain the full deformation tensors and apply a manifold version of hotelling s test to them in a log euclidean domain in 2 d and 3 d magnetic resonance imaging mri data from 26 hiv aids patients and 14 matched healthy subjects we compared multivariate tensor analysis versus univariate tests of simpler tensor derived indices the jacobian determinant the trace geodesic anisotropy and eigenvalues of the deformation tensor and the angle of rotation of its eigenvectors we detected consistent but more extensive patterns of structural abnormalities with multivariate tests on the full tensor manifold their improved power was established by analyzing cumulative value plots using false discovery rate fdr methods appropriately controlling for false positives this increased detection sensitivity may empower drug trials and large scale studies of disease that use tensor based morphometry

computational anatomy shape growth and atrophy comparison via diffeomorphisms computational anatomy ca is the mathematical study of anatomy i in i i alpha o g an orbit under groups of diffeomorphisms i e smooth invertible mappings g in g of anatomical exemplars i alpha in i the observable images are the output of medical imaging devices there are three components that ca examines i constructions of the anatomical submanifolds ii comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g in g defining the shape or geometry of the anatomical manifolds and iii generation of probability laws of anatomical variation p on the images i for inference and disease testing within anatomical models this paper reviews recent advances in these three areas applied to shape growth and atrophy

frats functional regression analysis of dti tract statistics diffusion tensor imaging dti provides important information on the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo this paper presents a functional regression framework called frats for the analysis of multiple diffusion properties along fiber bundle as functions in an infinite dimensional space and their association with a set of covariates of interest such as age diagnostic status and gender in real applications the functional regression framework consists of four integrated components the local polynomial kernel method for smoothing multiple diffusion properties along individual fiber bundles a functional linear model for characterizing the association between fiber bundle diffusion properties and a set of covariates a global test statistic for testing hypotheses of interest and a resampling method for approximating the p value of the global test statistic the proposed methodology is applied to characterizing the development of five diffusion properties including fractional anisotropy mean diffusivity and the three eigenvalues of diffusion tensor along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment significant age and gestational age effects on the five diffusion properties were found in both tracts the resulting analysis pipeline can be used for understanding normal brain development the neural bases of neuropsychiatric disorders and the joint effects of environmental and genetic factors on white matter fiber bundles

morphometric tools for landmark data geometry and biology 1 introduction 2 preliminaries 3 landmarks 4 distance measures 5 shape coordinates 6 principal axes of shape change for triangles 7 features of shape comparison 8 retrospect and prospect

probability convexity and harmonic maps with small image i uniqueness and fine existence this paper uses probability theory to provide an approach to the dirichlet problem for harmonic maps the probabilistic tools used are those of manifold valued brownian motion and martingales probabilistic proofs are given of uniqueness continuous dependence on data and existence of generalized solutions finely harmonic maps for target domains which have convex geometry this class of domain includes all regular geodesic balls links are made with new results in other fields the martingale dirichlet problem riemannian centres of mass

new bounds for the generalized marcum q function in this paper we study the generalized marcum q function q nu a b where a nu 0 and b ges 0 our aim is to extend the results of corazza and ferrari ieee trans inf theory vol 48 pp 3003 3008 2002 to the generalized marcum q function in order to deduce some new tight lower and upper bounds the key tools in our proofs are some monotonicity properties of certain functions involving the modified bessel function of the first kind and some classical inequalities i e the cauchy buniakowski schwarz and chebyshev integral inequalities these bounds are shown to be very tight for large b i e the relative errors of our bounds converge to zero as b increases both theoretical analysis and numerical results are provided to show the tightness of our bounds

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

surface fluid registration of conformal representation application to detect disease burden and genetic influence on hippocampus in this paper we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1 forms inverse consistent surface fluid registration and multivariate tensor based morphometry mtbm first we conformally map a surface onto a planar rectangle space with holomorphic 1 forms second we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface third we align the feature image with a chosen template image via the fluid image registration algorithm which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization the inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images this alignment induces a corresponding deformation on the surface we tested the system on alzheimer s disease neuroimaging initiative adni baseline dataset to study ad symptoms on hippocampus in our system by modeling a hippocampus as a 3d parametric surface we nonlinearly registered each surface with a selected template surface then we used mtbm to analyze the morphometry difference between diagnostic groups experimental results show that the new system has better performance than two publicly available subcortical surface registration tools first and spharm we also analyzed the genetic influence of the apolipoprotein e 4 allele apoe4 which is considered as the most prevalent risk factor for ad our work successfully detected statistically significant difference between apoe4 carriers and non carriers in both patients of mild cognitive impairment mci and healthy control subjects the results show evidence that the apoe genotype may be associated with accelerated brain atrophy so that our work provides a new mri analysis tool that may help presymptomatic ad research

analytic expressions and bounds for special functions and applications in communication theory this paper is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory these functions are the well known nuttall q function incomplete toronto function rice ie function and incomplete lipschitz hankel integrals capitalizing on the offered results useful identities are additionally derived between the above functions and humbert phi 1 function as well as for specific cases of the kampede feriet function these functions can be considered as useful mathematical tools that can be employed in applications relating to the analytic performance evaluation of modern wireless communication systems such as cognitive radio cooperative and free space optical communications as well as radar diversity and multiantenna systems as an example new closed form expressions are derived for the outage probability over nonlinear generalized fading channels namely alpha eta mu alpha lambda mu and alpha kappa mu as well as for specific cases of the eta mu and lambda mu fading channels furthermore simple expressions are presented for the channel capacity for the truncated channel inversion with fixed rate and corresponding optimum cutoff signal to noise ratio for single antenna and multiantenna communication systems over rician fading channels the accuracy and validity of the derived expressions is justified through extensive comparisons with respective numerical results

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

tight bounds for the generalized marcum q function abstract in this paper we study the generalized marcum q function of order 0 real defined by q a b 1 a 1 b t e t 2 a 2 2 i 1 a t dt where a 0 b 0 and i stands for the modified bessel function of the first kind our aim is to improve and extend some recent results of wang to the generalized marcum q function in order to deduce some sharp lower and upper bounds in both cases b a and b a we give the best possible upper bound for q a b the key tools in our proofs are some monotonicity properties of certain functions involving the modified bessel function of the first kind these monotonicity properties are deduced from some results on modified bessel functions which have been used in wave mechanics and finite elasticity

computing and bounding the first order marcum q function a geometric approach a geometric interpretation of the first order marcum q function q a b is introduced as the probability that a complex gaussian random variable with real mean a takes on values outside of a disk co b of radius b centered at the origin o this interpretation engenders a fruitful approach for deriving new representations and tight upper and lower bounds on q a b the new representations obtained involve finite range integrals with pure exponential integrands they are shown to be simpler and more robust than their counterparts in the literature the new bounds obtained include the generic exponential bounds which involve an arbitrarily large number of exponential functions and the simple erfc bounds which involve just a few erfc functions together with exponential functions in some cases the new generic exponential bounds approach the exact value of q a b as the number of exponential terms involved increases these generic exponential bounds evaluated with only two terms and the new simple erfc bounds are much tighter than the existing exponential bounds in most cases especially when the arguments a and b are large thus in many applications requiring further analytical manipulations of q a b these new bounds can lead to some closed form results which are better than the results available so far

algorithm for calculating the noncentral chi square distribution this article presents a new algorithm for evaluating the noncentral chi square distribution based on parl s 1980 method of neumann series expansion it is applicable to both even and odd degrees of freedom unlike most prior work which has been directed at the even cases convergence tests and procedures for detection of loss of precision are given the overall method is extremely simple to program accurate to many decimal places where applicable and efficient over a wide range of parameters the method is reliable provided the proper expansion is chosen based on the parameters

fadtts functional analysis of diffusion tensor tract statistics the aim of this paper is to present a functional analysis of a diffusion tensor tract statistics fadtts pipeline for delineating the association between multiple diffusion properties along major white matter fiber bundles with a set of covariates of interest such as age diagnostic status and gender and the structure of the variability of these white matter tract properties in various diffusion tensor imaging studies the fadtts integrates five statistical tools i a multivariate varying coefficient model for allowing the varying coefficient functions in terms of arc length to characterize the varying associations between fiber bundle diffusion properties and a set of covariates ii a weighted least squares estimation of the varying coefficient functions iii a functional principal component analysis to delineate the structure of the variability in fiber bundle diffusion properties iv a global test statistic to test hypotheses of interest and v a simultaneous confidence band to quantify the uncertainty in the estimated coefficient functions simulated data are used to evaluate the finite sample performance of fadtts we apply fadtts to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment fadtts can be used to facilitate the understanding of normal brain development the neural bases of neuropsychiatric disorders and the joint effects of environmental and genetic factors on white matter fiber bundles the advantages of fadtts compared with the other existing approaches are that they are capable of modeling the structured inter subject variability testing the joint effects and constructing their simultaneous confidence bands however fadtts is not crucial for estimation and reduces to the functional analysis method for the single measure