discrete differential geometry the nonplanar quadrilateral mesh we consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes physical models on discrete nonflat spaces are of inherent interest as well as being used in applications such as computation for electromagnetism fluid mechanics and image analysis however the majority of analysis has focused on triangulated meshes we consider two approaches discretizing the tensor calculus and a discrete mesh version of differential forms while these two approaches are equivalent in the continuum we show that this is not true in the discrete case nevertheless we show that it is possible to construct mesh versions of the levi civita connection and hence the tensorial covariant derivative and the associated covariant exterior derivative the torsion and the curvature we show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh rather than only as approximations to the continuum limit we demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models such as fluids

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

model driven parameterization of the cortical surface for localization and inter subject matching in this paper we present a generic and organized model of cortical folding and a way to implement this model on any given cortical surface this results in a model driven parameterization providing an anatomically meaningful coordinate system for cortical localization and implicitly defining inter subject surface matching without any deformation of surfaces we present our cortical folding model and show how it naturally defines a parameterization of the cortex the mapping of the model to any given cortical surface is detailed leading to an anatomically invariant coordinate system the process is evaluated on real data in terms of both anatomical and functional localization and shows improved performance compared to a traditional volume based normalization it is fully automatic and available with the brainvisa software platform

gopakumar vafa invariants via vanishing cycles in this paper we propose an ansatz for defining gopakumar vafa invariants of calabi yau threefolds using perverse sheaves of vanishing cycles our proposal is a modification of a recent approach of kiem li which is itself based on earlier ideas of hosono saito takahashi we conjecture that these invariants are equivalent to other curve counting theories such as gromov witten theory and pandharipande thomas theory our main theorem is that for local surfaces our invariants agree with pt invariants for irreducible one cycles we also give a counter example to the kiem li conjectures where our invariants match the predicted answer finally we give examples where our invariant matches the expected answer in cases where the cycle is non reduced non planar or non primitive

cortical surface based analysis ii inflation flattening and a surface based coordinate system the surface of the human cerebral cortex is a highly folded sheet with the majority of its surface area buried within folds as such it is a difficult domain for computational as well as visualization purposes we have therefore designed a set of procedures for modifying the representation of the cortical surface to i inflate it so that activity buried inside sulci may be visualized ii cut and flatten an entire hemisphere and iii transform a hemisphere into a simple parameterizable surface such as a sphere for the purpose of establishing a surface based coordinate system r 1999 academic press

a comparison of sampford s sampling procedure versus unequal probability sampling with replacement summary the classical result that simple random sampling without replacement is better than simple random sampling with replacement holds in unequal probability sampling for the sampling procedure of sampford

maximum entropy and the lottery abstract the distribution on m tuples of the first m integers is estimated from marginals of the distribution this problem is of interest in determining unpopular numbers in lotto games in canada s lotto 6 49 the proportion of tickets purchased in previous games containing each number is available under certain conditions the limiting distribution subject to the observed marginals is the constrained maximum entropy distribution this distribution is estimated and monte carlo methods are used to estimate the expected return of various lottery strategies tickets consisting of unpopular numbers may have expected return greater than their cost when the weekly sales are large or there are large carryover prizes prizes not won in earlier games the maximum entropy distribution is a rough approximation of the true distribution of tickets purchased certain aspects of the empirical distribution are not consistent with the maximum entropy distribution alternative methods which attempt to model the behavio

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

efficient stream sampling for variance optimal estimation of subset sums from a high volume stream of weighted items we want to maintain a generic sample of a certain limited size k that we can later use to estimate the total weight of arbitrary subsets this is the classic context of on line reservoir sampling thinking of the generic sample as a reservoir we present an efficient reservoir sampling scheme textnormal sc varopt k that dominates all previous schemes in terms of estimation quality textnormal sc varopt k provides variance optimal unbiased estimation of subset sums more precisely if we have seen n items of the stream then for any subset size m our scheme based on k samples minimizes the average variance over all subsets of size m in fact the optimality is against any off line scheme with k samples tailored for the concrete set of items seen in addition to optimal average variance our scheme provides tighter worst case bounds on the variance of particular subsets than previously possible it is efficient handling each new item of the stream in o log k time finally it is particularly well suited for combinations of samples from different streams in a distributed setting

diffeomorphisms groups and pattern matching in image analysis in a previous paper it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group we show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images using lie group ideas we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub optimal gradient pattern matching its links with fluid models are established

large deformation multiresolution diffeomorphic metric mapping for multiresolution cortical surfaces a coarse to fine approach brain surface registration is an important tool for characterizing cortical anatomical variations and understanding their roles in normal cortical development and psychiatric diseases however surface registration remains challenging due to complicated cortical anatomy and its large differences across individuals in this paper we propose a fast coarse to fine algorithm for surface registration by adapting the large diffeomorphic deformation metric mapping lddmm framework for surface mapping and show improvements in speed and accuracy via a multiresolution analysis of surface meshes and the construction of multiresolution diffeomorphic transformations the proposed method constructs a family of multiresolution meshes that are used as natural sparse priors of the cortical morphology at varying resolutions these meshes act as anchor points where the parameterization of multiresolution deformation vector fields can be supported allowing the construction of a bundle of multiresolution deformation fields each originating from a different resolution using a coarse to fine approach we show a potential reduction in computation cost along with improvements in sulcal alignment when compared with lddmm surface mapping

applying tensor based morphometry to parametric surfaces can improve mri based disease diagnosis many methods have been proposed for computer assisted diagnostic classification full tensor information and machine learning with 3d maps derived from brain images may help detect subtle differences or classify subjects into different groups here we develop a new approach to apply tensor based morphometry to parametric surface models for diagnostic classification we use this approach to identify cortical surface features for use in diagnostic classifiers first with holomorphic 1 forms we compute an efficient and accurate conformal mapping from a multiply connected mesh to the so called slit domain next the surface parameterization approach provides a natural way to register anatomical surfaces across subjects using a constrained harmonic map to analyze anatomical differences we then analyze the full riemannian surface metric tensors which retain multivariate information on local surface geometry as the number of voxels in a 3d image is large sparse learning is a promising method to select a subset of imaging features and to improve classification accuracy focusing on vertices with greatest effect sizes we train a diagnostic classifier using the surface features selected by an l1 norm based sparse learning method stability selection is applied to validate the selected feature sets we tested the algorithm on mri derived cortical surfaces from 42 subjects with genetically confirmed williams syndrome and 40 age matched controls multivariate statistics on the local tensors gave greater effect sizes for detecting group differences relative to other tbm based statistics including analysis of the jacobian determinant and the largest eigenvalue of the surface metric our method also gave reasonable classification results relative to the jacobian determinant the pair of eigenvalues of the jacobian matrix and volume features this analysis pipeline may boost the power of morphometry studies and may assist with image based classification

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

multi contrast multi scale surface registration for improved alignment of cortical areas the position of cortical areas can be approximately predicted from cortical surface folding patterns however there is extensive inter subject variability in cortical folding patterns prohibiting a one to one mapping of cortical folds in certain areas in addition the relationship between cortical area boundaries and the shape of the cortex is variable and weaker for higher order cortical areas current surface registration techniques align cortical folding patterns using sulcal landmarks or cortical curvature for instance the alignment of cortical areas by these techniques is thus inherently limited by the sole use of geometric similarity metrics magnetic resonance imaging t1 maps show intra cortical contrast that reflects myelin content and thus can be used to improve the alignment of cortical areas in this article we present a new symmetric diffeomorphic multi contrast multi scale surface registration mmsr technique that works with partially inflated surfaces in the level set framework mmsr generates a more precise alignment of cortical surface curvature in comparison to two widely recognized surface registration algorithms the resulting overlap in gyrus labels is comparable to freesurfer most importantly mmsr improves the alignment of cortical areas further by including t1 maps as a first application we present a group average t1 map at a uniquely high resolution and multiple cortical depths which reflects the myeloarchitecture of the cortex mmsr can also be applied to other mr contrasts such as functional and connectivity data

on removing interpolation and resampling artifacts in rigid image registration we show that image registration using conventional interpolation and summation approximations of continuous integrals can generally fail because of resampling artifacts these artifacts negatively affect the accuracy of registration by producing local optima altering the gradient shifting the global optimum and making rigid registration asymmetric in this paper after an extensive literature review we demonstrate the causes of the artifacts by comparing inclusion and avoidance of resampling analytically we show the sum of squared differences cost function formulated as an integral to be more accurate compared with its traditional sum form in a simple case of image registration we then discuss aliasing that occurs in rotation which is due to the fact that an image represented in the cartesian grid is sampled with different rates in different directions and propose the use of oscillatory isotropic interpolation kernels which allow better recovery of true global optima by overcoming this type of aliasing through our experiments on brain fingerprint and white noise images we illustrate the superior performance of the integral registration cost function in both the cartesian and spherical coordinates and also validate the introduced radial interpolation kernel by demonstrating the improvement in registration

dt refind diffusion tensor registration with exact finite strain differential in this paper we propose the dt refind algorithm for the diffeomorphic nonlinear registration of diffusion tensor images unlike scalar images deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently these methods often approximate the gradient of the objective function in the case of the finite strain fs reorientation strategy we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function by utilizing the closed form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms the resulting registration algorithm is diffeomorphic and fast we contrast the algorithm with a traditional fs alternative that ignores the reorientation in the gradient computation we show that the exact gradient leads to significantly better registration at the cost of computation time independently of the choice of euclidean or log euclidean interpolation and sum of squared differences dissimilarity measure the exact gradient achieves better alignment over an entire spectrum of deformation penalties alignment quality is assessed with a battery of metrics including tensor overlap fractional anisotropy inverse consistency and closeness to synthetic warps the improvements persist even when a different reorientation scheme preservation of principal directions is used to apply the final deformations

bayesian models for multiple local sequence alignment and gibbs sampling strategies abstract a wealth of data concerning life s basic molecules proteins and nucleic acids has emerged from the biotechnology revolution the human genome project has accelerated the growth of these data multiple observations of homologous protein or nucleic acid sequences from different organisms are often available but because mutations and sequence errors misalign these data multiple sequence alignment has become an essential and valuable tool for understanding structures and functions of these molecules a recently developed gibbs sampling algorithm has been applied with substantial advantage in this setting in this article we develop a full bayesian foundation for this algorithm and present extensions that permit relaxation of two important restrictions we also present a rank test for the assessment of the significance of multiple sequence alignment as an example we study the set of dinucleotide binding proteins and predict binding segments for dozens of its members

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

the construction of pi ps sampling designs through a method of emptying boxes we present a simple but universal technique for the construction of iips sampling designs a tool that is used in the construction consists of playing a game in which objects are removed from n boxes n at a time and at most one from each box at a time it is shown that every iips design can be derived from such a game sampling designs with additional properties are obtained through additional restrictions on emptying the boxes the emphasis is on controlling sample selection probabilities and inequalities for the first and second order inclusion probabilities

fast geodesic active fields for image registration based on splitting and augmented lagrangian approaches in this paper we present an efficient numerical scheme for the recently introduced geodesic active fields gaf framework for geometric image registration this framework considers the registration task as a weighted minimal surface problem hence the data term and the regularization term are combined through multiplication in a single parametrization invariant and geometric cost functional the multiplicative coupling provides an intrinsic spatially varying and data dependent tuning of the regularization strength and the parametrization invariance allows working with images of nonflat geometry generally defined on any smoothly parametrizable manifold the resulting energy minimizing flow however has poor numerical properties here we provide an efficient numerical scheme that uses a splitting approach data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented lagrangian approach our approach is more flexible than standard gaussian regularization since one can interpolate freely between isotropic gaussian and anisotropic tv like smoothing in this paper we compare the geodesic active fields method with the popular demons method and three more recent state of the art algorithms nl optical flow mrf image registration and landmark enhanced large displacement optical flow thus we can show the advantages of the proposed fastgaf method it compares favorably against demons both in terms of registration speed and quality over the range of example applications it also consistently produces results not far from more dedicated state of the art methods illustrating the flexibility of the proposed framework

weighted finite population sampling to maximize entropy summary attention is drawn to a method of sampling a finite population of n units with unequal probabilities and without replacement the method was originally proposed by stern cover 1989 as a model for lotteries the method can be characterized as maximizing entropy given coverage probabilities 7ci or equivalently as having the probability of a selected sample proportional to the product of a set of weights wi we show the essential uniqueness of the wi given the 7i and describe practical geometrically convergent algorithms for computing the wi from the 7i we present two methods for stepwise selection of sampling units and corresponding schemes for removal of units that can be used in connection with sample rotation inclusion probabilities of any order can be written explicitly in closed form second order inclusion probabilities 7rij satisfy the condition 0 ij 7ic 7j which guarantees yates grundy s variance estimator to be unbiased definable for all samples and always nonnegative for any sample size

improved inference for respondent driven sampling data with application to hiv prevalence estimation respondent driven sampling is a form of link tracing network sampling which is widely used to study hard to reach populations often to estimate population proportions previous treatments of this process have used a with replacement approximation which we show induces bias in estimates for large sample fractions and differential network connectedness by characteristic of interest we present a treatment of respondent driven sampling as a successive sampling process unlike existing representations our approach respects the essential without replacement feature of the process while converging to an existing with replacement representation for small sample fractions and to the sample mean for a full population sample we present a successive sampling based estimator for population means based on respondent driven sampling data and demonstrate its superior performance when the size of the hidden population is known we present sensitivity analyses for unknown population sizes in addition we note tha

towards a coherent statistical framework for dense deformable template estimation summary the problem of estimating probabilistic deformable template models in the field of computer vision or of probabilistic atlases in the field of computational anatomy has not yet received a coherent statistical formulation and remains a challenge we provide a careful definition and analysis of a well defined statistical model based on dense deformable templates for grey level images of deformable objects we propose a rigorous bayesian framework for which we prove asymptotic consistency of the maximum a posteriori estimate and which leads to an effective iterative estimation algorithm of the geometric and photometric parameters in the small sample setting the model is extended to mixtures of finite numbers of such components leading to a fine description of the photometric and geometric variations of an object class we illustrate some of the ideas with images of handwritten digits and apply the estimated models to classification through maximum likelihood

sampling for conditional inference on network data random graphs with given vertex degrees have been widely used as a model for many real world complex networks however both statistical inference and analytic study of such networks present great challenges in this article we propose a new sequential importance sampling method for sampling networks with a given degree sequence these samples can be used to approximate closely the null distributions of a number of test statistics involved in such networks and provide an accurate estimate of the total number of networks with given vertex degrees we study the asymptotic behavior of the proposed algorithm and prove that the importance weight remains bounded as the size of the graph grows this property guarantees that the proposed sampling algorithm can still work efficiently even for large sparse graphs we apply our method to a range of examples to demonstrate its efficiency in real problems

multidirectional and topography based dynamic scale varifold representations with application to matching developing cortical surfaces the human cerebral cortex is marked by great complexity as well as substantial dynamic changes during early postnatal development to obtain a fairly comprehensive picture of its age induced and or disorder related cortical changes one needs to match cortical surfaces to one another while maximizing their anatomical alignment methods that geodesically shoot surfaces into one another as currents a distribution of oriented normals and varifolds a distribution of non oriented normals provide an elegant riemannian framework for generic surface matching and reliable statistical analysis however both conventional current and varifold matching methods have two key limitations first they only use the normals of the surface to measure its geometry and guide the warping process which overlooks the importance of the orientations of the inherently convoluted cortical sulcal and gyral folds second the conversion of a surface into a current or a varifold operates at a fixed scale under which geometric surface details will be neglected which ignores the dynamic scales of cortical foldings to overcome these limitations and improve varifold based cortical surface registration we propose two different strategies the first strategy decomposes each cortical surface into its normal and tangent varifold representations by integrating principal curvature direction field into the varifold matching framework thus providing rich information of the orientation of cortical folding and better characterization of the complex cortical geometry the second strategy explores the informative cortical geometric features to perform a dynamic scale measurement of the cortical surface that depends on the local surface topography e g principal curvature thereby we introduce the concept of a topography based dynamic scale varifold we tested the proposed varifold variants for registering 12 pairs of dynamically developing cortical surfaces from 0 to 6 months of age both variants improved the matching accuracy in terms of closeness to the target surface and the goodness of alignment with regional anatomical boundaries when compared with three state of the art methods 1 diffeomorphic spectral matching 2 conventional current based surface matching and 3 conventional varifold based surface matching

exact tests for the rasch model via sequential importance sampling rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability this paper furthers rasch s approach by 1 providing an efficient monte carlo methodology for accurately approximating the required probability and 2 illustrating the usefulness of rasch s approach for several important testing problems through simulation studies our monte carlo methodology is shown to compare favorably to other monte carlo methods proposed for this problem in two respects it is considerably faster and it provides more reliable estimates of the monte carlo standard error

quantitative evaluation of lddmm freesurfer and caret for cortical surface mapping cortical surface mapping has been widely used to compensate for individual variability of cortical shape and topology in anatomical and functional studies while many surface mapping methods were proposed based on landmarks curves spherical or native cortical coordinates few studies have extensively and quantitatively evaluated surface mapping methods across different methodologies in this study we compared five cortical surface mapping algorithms including large deformation diffeomorphic metric mapping lddmm for curves lddmm curve for surfaces lddmm surface multi manifold lddmm mm lddmm freesurfer and caret using 40 mri scans and 10 simulated datasets we computed curve variation errors and surface alignment consistency for assessing the mapping accuracy of local cortical features e g gyral sulcal curves and sulcal regions and the curvature correlation for measuring the mapping accuracy in terms of overall cortical shape in addition the simulated datasets facilitated the investigation of mapping error distribution over the cortical surface when the mm lddmm freesurfer and caret mapping algorithms were applied our results revealed that the lddmm curve mm lddmm and caret approaches best aligned the local curve features with their own curves the mm lddmm approach was also found to be the best in aligning the local regions and cortical folding patterns e g curvature as compared to the other mapping approaches the simulation experiment showed that the mm lddmm mapping yielded less local and global deformation errors than the caret and freesurfer mappings

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

observer independent method for microstructural parcellation of cerebral cortex a quantitative approach to cytoarchitectonics we describe a new observer independent procedure for identifying boundaries between cortical areas the method is useful for images obtained from sections which provide microstructural information on the cortical laminar pattern e g nissl myelin or immunohistochemically stained sections or receptor autoradiographs the laminar pattern is represented by profile curves extending from the cortical surface to the white matter boundary these profiles are constructed from digitized images digitization is based on the grey level index nissl or densitometry myelin immunohistochemistry receptor autoradiography the shapes of neighboring profiles are compared by calculating their distances according to feature vectors extracted from the profiles profiles derived from a homogeneous area can be expected to be similar in shape and hence show low distance values between each other maximum distances can be found between profiles which lie on opposite sides of a structural boundary the mahalanobis distance was found to be more sensitive and to yield greater spatial resolution than other distance measures such as the euclidean distance cell stained sections of the human neocortex were analyzed the method not only verified boundaries which had been defined by visual inspection it also revealed new ones which had not been detected visually the procedure offers an important supplement to the traditional methods based on visual inspection which for the first time is based on quantitative data and therefore offers a new level of reproducibility and observer independence anatomical atlases based on this procedure thus provide a new tool for the interpretation of structural data obtained from functional imaging techniques

spectral log demons diffeomorphic image registration with very large deformations this paper presents a new framework for capturing large and complex deformations in image registration and atlas construction this challenging and recurrent problem in computer vision and medical imaging currently relies on iterative and local approaches which are prone to local minima and therefore limit present methods to relatively small deformations our general framework introduces to this effect a new direct feature matching technique that finds global correspondences between images via simple nearest neighbor searches more specifically very large image deformations are captured in spectral forces which are derived from an improved graph spectral representation we illustrate the benefits of our framework through a new enhanced version of the popular log demons algorithm named the spectral log demons as well as through a groupwise extension named the groupwise spectral log demons which is relevant for atlas construction the evaluations of these extended versions demonstrate substantial improvements in accuracy and robustness to large deformations over the conventional demons approaches

functional density and edge maps characterizing functional architecture in individuals and improving cross subject registration population level inferences and individual level analyses are two important aspects in functional magnetic resonance imaging fmri studies extracting reliable and informative features from fmri data that capture biologically meaningful inter subject variation is critical for aligning and comparing functional networks across subjects and connecting the properties of functional brain organization with variations in behavior cognition and genetics in this study we derive two new measures which we term functional density map and edge map and demonstrate their usefulness in characterizing the function of individual brains specifically using data from the human connectome project hcp we show that 1 both functional maps capture intrinsic properties of the functional connectivity pattern in individuals while exhibiting large variation across subjects 2 functional maps derived from either resting state or task evoked fmri can be used to accurately identify subjects from a population and 3 cross subject alignment using these functional maps considerably reduces functional variation and improves functional correspondence across subjects over state of the art multimodal registration algorithms our results suggest that the proposed functional density and edge maps are promising features in characterizing the functional architecture in individuals and provide an alternative way to explore the functional variation across subjects

brain surface conformal parameterization with the ricci flow in brain mapping research parameterized 3 d surface models are of great interest for statistical comparisons of anatomy surface based registration and signal processing here we introduce the theories of continuous and discrete surface ricci flow which can create riemannian metrics on surfaces with arbitrary topologies with user defined gaussian curvatures the resulting conformal parameterizations have no singularities and they are intrinsic and stable first we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves secondly we conformally parameterize each cortical surface to a parameter domain with a user designed gaussian curvature arrangement in the parameter domain a shape index based on conformal invariants is computed and inter subject cortical surface matching is performed by solving a constrained harmonic map we illustrate various target curvature arrangements and demonstrate the stability of the method using longitudinal data to map statistical differences in cortical morphometry we studied brain asymmetry in 14 healthy control subjects we used a manifold version of hotelling s t2 test applied to the jacobian matrices of the surface parameterizations a permutation test along with the cumulative distribution of p values were used to estimate the overall statistical significance of differences the results show our algorithm s power to detect subtle group differences in cortical surfaces

three dimensional flops and noncommutative rings limburgs univ ctr dept math b 3590 diepenbeek belgium van den bergh m limburgs univ ctr dept math univ campus b 3590 diepenbeek belgium vdbergh luc ac be

diffeomorphic sulcal shape analysis on the cortex we present a diffeomorphic approach for constructing intrinsic shape atlases of sulci on the human cortex sulci are represented as square root velocity functions of continuous open curves in r 3 and their shapes are studied as functional representations of an infinite dimensional sphere this spherical manifold has some advantageous properties it is equipped with a riemannian l 2 metric on the tangent space and facilitates computational analyses and correspondences between sulcal shapes sulcal shape mapping is achieved by computing geodesics in the quotient space of shapes modulo scales translations rigid rotations and reparameterizations the resulting sulcal shape atlas preserves important local geometry inherently present in the sample population the sulcal shape atlas is integrated in a cortical registration framework and exhibits better geometric matching compared to the conventional euclidean method we demonstrate experimental results for sulcal shape mapping cortical surface registration and sulcal classification for two different surface extraction protocols for separate subject populations

sequential monte carlo methods for statistical analysis of tables we describe a sequential importance sampling sis procedure for analyzing two way zero one or contingency tables with fixed marginal sums an essential feature of the new method is that it samples the columns of the table progressively according to certain special distributions our method produces monte carlo samples that are remarkably close to the uniform distribution enabling one to approximate closely the null distributions of various test statistics about these tables our method compares favorably with other existing monte carlo based algorithms and sometimes is a few orders of magnitude more efficient in particular compared with markov chain monte carlo mcmc based approaches our importance sampling method not only is more efficient in terms of absolute running time and frees one from pondering over the mixing issue but also provides an easy and accurate estimate of the total number of tables with fixed marginal sums which is far more difficult for an mcmc method to achieve

a multi resolution scheme for distortion minimizing mapping between human subcortical structures based on geodesic construction on riemannian manifolds in this paper we deal with a subcortical surface registration problem subcortical structures including hippocampi and caudates have a small number of salient features such as heads and tails unlike cortical surfaces therefore it is hard if not impossible to perform subcortical surface registration with only such features it is also non trivial for neuroanatomical experts to select landmarks consistently for subcortical surfaces of different subjects we therefore present a landmark free approach for subcortical surface registration by measuring the amount of mesh distortion between subcortical surfaces assuming that the surfaces are represented by meshes the input meshes can be constructed using any surface modeling tool available in the public domain since our registration method is independent of a surface modeling process given the source and target surfaces together with their representing meshes the vertex positions of the source mesh are iteratively displaced while preserving the underlying surface shape in order to minimize the distortion to the target mesh by representing each surface mesh as a point on a high dimensional riemannian manifold we define a distance metric on the manifold that measures the amount of distortion from a given source mesh to the target mesh based on the notion of isometry while penalizing triangle flipping under this metric we reduce the distortion minimization problem to the problem of constructing a geodesic curve from the moving source point to the fixed target point on the manifold while satisfying the shape preserving constraint we adopt a multi resolution framework to solve the problem for distortion minimizing mapping between the source and target meshes we validate our registration scheme through several experiments distance metric comparison visual validation using real data robustness test to mesh variations feature alignment using anatomic landmarks consistency with previous clinical findings and comparison with a surface based registration method lddmm surface

model driven harmonic parameterization of the cortical surface hip hop in the context of inter subject brain surface matching we present a parameterization of the cortical surface constrained by a model of cortical organization the parameterization is defined via an harmonic mapping of each hemisphere surface to a rectangular planar domain that integrates a representation of the model as opposed to previous landmark based registration methods we do not match folds between individuals but instead optimize the fit between cortical sulci and specific iso coordinate axis in the model this strategy overcomes some limitation to sulcus based registration techniques such as topological variability in sulcal landmarks across subjects experiments on 62 subjects with manually traced sulci are presented and compared with the result of the freesurfer software the evaluation involves a measure of dispersion of sulci with both angular and area distortions we show that the model based strategy can lead to a natural efficient and very fast less than 5 min per hemisphere method for defining inter subjects correspondences we discuss how this approach also reduces the problems inherent to anatomically defined landmarks and open the way to the investigation of cortical organization through the notion of orientation and alignment of structures across the cortex

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

spherical demons fast diffeomorphic landmark free surface registration we present the spherical demons algorithm for registering two spherical images by exploiting spherical vector spline interpolation theory we show that a large class of regularizors for the modified demons objective function can be efficiently approximated on the sphere using iterative smoothing based on one parameter subgroups of diffeomorphisms the resulting registration is diffeomorphic and fast the spherical demons algorithm can also be modified to register a given spherical image to a probabilistic atlas we demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject registration of a cortical surface mesh to an atlas mesh both with more than 160 k nodes requires less than 5 min when warping the atlas and less than 3 min when warping the subject on a xeon 3 2 ghz single processor machine this is comparable to the fastest nondiffeomorphic landmark free surface registration algorithms furthermore the accuracy of our method compares favorably to the popular freesurfer registration algorithm we validate the technique in two different applications that use registration to transfer segmentation labels onto a new image 1 parcellation of in vivo cortical surfaces and 2 brodmann area localization in ex vivo cortical surfaces

biometrika centenary sample surveys summary despite karl pearson s stated aim that the evolutionist has to become in the widest sense of the words a registrar general for all forms of life the papers published in biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s there has been little work on sampling in the life sciences with the exception of capture recapture methods the major areas have been in variable probability designs the foundations of inference for finite populations analytic surveys and the role of selection mechanisms in inference in recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory with interesting consequences for both areas

a jackknife variance estimator for unistage stratified samples with unequal probabilities summary existing jackknife variance estimators used with sample surveys can seriously overestimate the true variance under unistage stratified sampling without replacement with unequal probabilities a novel jackknife variance estimator is proposed which is as numerically simple as existing jackknife variance estimators under certain regularity conditions the proposed variance estimator is consistent under stratified sampling without replacement with unequal probabilities the high entropy regularity condition necessary for consistency is shown to hold for the rao sampford design an empirical study of three unequal probability sampling designs supports our findings

applying the horvitz thompson criterion in complex designs a computer intensive perspective for estimating inclusion probabilities a modification of the horvitz thompson estimator is proposed for complex sampling designs the inclusion probabilities are estimated by means of independent replications of the sampling scheme the properties of the resulting estimator are derived guidelines for choosing the appropriate number of replications are given and some applications are considered

a general purpose unequal probability sampling plan summary we present a general purpose unequal probability without replacement sampling plan with fixed sample size in contrast to existing such plans our scheme keeps the sample size fixed and lets the population units enter the sample one at a time through a carefully designed random mechanism consequently all high order inclusion probabilities can be easily computed

a prediction based test for multiple endpoints this article introduces a global hypothesis test intended for studies with multiple endpoints our test makes use of a priori predictions about the direction of the result of each endpoint and we weight these predictions using the sample correlation matrix the global alternative hypothesis concerns a parameter defined as the researcher s ability to correctly predict the direction of each measure essentially a binomial parameter this allows for the test to include expected effects that are all positive all negative or both while still using the cumulative information across those endpoints a rejection of the null hypothesis h0 0 provides evidence that the researcher s underlying theory about the natural process provides a better prediction of the observed results relative to the null hypothesized predictive ability thus indicating the theory is worthy of further study we compare our test to o brien s ordinary least squares ols test and show that for small samples and situations where the effect is not in the same direction across all endpoints our approach has better power while if the effect is equidirectional across all endpoints the ols test can have greater power

the orbifold topological vertex abstract we develop a topological vertex formalism for computing the donaldson thomas invariants of calabi yau orbifolds the basic combinatorial object is the orbifold vertex v g a generating function for the number of 3d partitions asymptotic to 2d partitions and colored by representations of a finite abelian group g acting on c 3 in the case where g z n acting on c 3 with transverse a n 1 quotient singularities we give an explicit formula for v g in terms of schur functions we discuss applications of our formalism to the donaldson thomas crepant resolution conjecture and to the orbifold donaldson thomas gromov witten correspondence we also explicitly compute the donaldson thomas partition function for some simple orbifold geometries the local football p a b 1 and the local b z 2 gerbe

metric optimization for surface analysis in the laplace beltrami embedding space in this paper we present a novel approach for the intrinsic mapping of anatomical surfaces and its application in brain mapping research using the laplace beltrami eigen system we represent each surface with an isometry invariant embedding in a high dimensional space the key idea in our system is that we realize surface deformation in the embedding space via the iterative optimization of a conformal metric without explicitly perturbing the surface or its embedding by minimizing a distance measure in the embedding space with metric optimization our method generates a conformal map directly between surfaces with highly uniform metric distortion and the ability of aligning salient geometric features besides pairwise surface maps we also extend the metric optimization approach for group wise atlas construction and multi atlas cortical label fusion in experimental results we demonstrate the robustness and generality of our method by applying it to map both cortical and hippocampal surfaces in population studies for cortical labeling our method achieves excellent performance in a cross validation experiment with 40 manually labeled surfaces and successfully models localized brain development in a pediatric study of 80 subjects for hippocampal mapping our method produces much more significant results than two popular tools on a multiple sclerosis study of 109 subjects

unequal probability sampling without replacement through a splitting method summary a very general class of sampling methods without replacement and with unequal probabilities is proposed it consists of splitting the inclusion probability vector into several new inclusion probability vectors one of these vectors is chosen randomly thus the initial problem is reduced to another sampling problem with unequal probabilities this splitting is then repeated on these new vectors of inclusion probabilities at each step the sampling problem is reduced to a simpler problem the simplicity of this technique allows one to generate easily new sampling procedures with unequal probabilities the splitting method also generalises well known methods such as the midzuno method the elimination procedure and the chao procedure next a sufficient condition is given in order that a splitting method satisfies the sen yates grundy condition finally it is shown that the elimination procedure satisfies the gabler sufficient condition

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

design based asymptotics for two phase sampling strategies in environmental surveys summary we analyse design based properties of two phase strategies for estimating totals and nonlinear functions of totals for environmental populations when the sampling schemes are uniquely determined by points placed in the study region in the first phase points are located using tessellation stratified sampling whereas in the second phase a finite population sampling scheme is adopted we give sufficient conditions on second phase designs that ensure consistency and we investigate the variance convergence rate for some familiar schemes

automatic alignment of genus zero surfaces a new algorithm is presented that provides a constructive way to conformally warp a triangular mesh of genus zero to a destination surface with minimal metric deformation as well as a means to compute automatically a measure of the geometric difference between two surfaces of genus zero the algorithm takes as input a pair of surfaces that are topological 2 spheres each surface given by a distinct triangulation the algorithm then constructs a map f between the two surfaces first each of the two triangular meshes is mapped to the unit sphere using a discrete conformal mapping algorithm the two mappings are then composed with a mobius transformation to generate the function f the mobius transformation is chosen by minimizing an energy that measures the distance of f from an isometry we illustrate our approach using several real life data sets we show first that the algorithm allows for accurate automatic and landmark free nonrigid registration of brain surfaces we then validate our approach by comparing shapes of proteins we provide numerical experiments to demonstrate that the distances computed with our algorithm between low resolution surface based representations of proteins are highly correlated with the corresponding distances computed between high resolution atomistic models for the same proteins

an elimination procedure for unequal probability sampling without replacement summary an exact without replacement sampling procedure with fixed sample size and unequal inclusion probabilities is presented the proposed method eliminates a unit of the population at each of the n n steps of the algorithm in order finally to retain n units a simple expression is given for the joint inclusion probabilities

automated sulcal segmentation using watersheds on the cortical surface the human cortical surface is a highly complex folded structure sulci the spaces between the folds define location on the cortex and provide a parcellation into anatomically distinct areas a topic that has recently received increased attention is the segmentation of these sulci from magnetic resonance images with most work focusing on extracting either the sulcal spaces between the folds or curve representations of sulci unlike these methods we propose a technique that extracts actual regions of the cortical surface that surround sulci which we call sulcal regions the method is based on a watershed algorithm applied to a geodesic depth measure on the cortical surface a well known problem with the watershed algorithm is a tendency toward oversegmentation meaning that a single region is segmented as several pieces to address this problem we propose a postprocessing algorithm that merges appropriate segments from the watershed algorithm the sulcal regions are then manually labeled by simply selecting the appropriate regions with a mouse click and a preliminary study of sulcal depth is reported finally a scheme is presented for computing a complete parcellation of the cortical surface

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

construction of a fetal spatio temporal cortical surface atlas from in utero mri application of spectral surface matching abstract in this study we construct a spatio temporal surface atlas of the developing cerebral cortex which is an important tool for analysing and understanding normal and abnormal cortical development in utero magnetic resonance imaging mri of 80 healthy fetuses was performed with a gestational age range of 21 7 to 38 9 weeks topologically correct cortical surface models were extracted from reconstructed 3d mri volumes accurate correspondences were obtained by applying a joint spectral analysis to cortices for sets of subjects close to a specific age sulcal alignment was found to be accurate in comparison to spherical demons a state of the art registration technique for aligning 2d cortical representations average frechet distance 0 4 mm at 30 weeks we construct consistent unbiased average cortical surface templates for each week of gestation from age matched groups of surfaces by applying kernel regression in the spectral domain these were found to accurately capture the average cortical shape of individuals within the cohort suggesting a good alignment of cortical geometry each spectral embedding and its corresponding cortical surface template provide a dual reference space where cortical geometry is aligned and a vertex wise morphometric analysis can be undertaken

general type token distribution the problem of estimating the number of unique types or dis tinct species in a group occurs in many fields but is not a straightforward one given an arbitrary probabilistic distribution of entries to be sam pled this study shows in exact and approximated forms the conditional probabilistic distribution of unique entries sampled independently given the number of samples the numerical evaluation validates the proposed ap proximation finally we discuss a theory that unifies the related approaches regarding estimation of the number of classes ams 2000 subject classifications primary 60c05 62p99 secondary 62f10

diffeomorphic functional brain surface alignment functional demons aligning brain structures across individuals is a central prerequisite for comparative neuroimaging studies typically registration approaches assume a strong association between the features used for alignment such as macro anatomy and the variable observed such as functional activation or connectivity here we propose to use the structure of intrinsic resting state fmri signal correlation patterns as a basis for alignment of the cortex in functional studies rather than assuming the spatial correspondence of functional structures between subjects we have identified locations with similar connectivity profiles across subjects we mapped functional connectivity relationships within the brain into an embedding space and aligned the resulting maps of multiple subjects we then performed a diffeomorphic alignment of the cortical surfaces driven by the corresponding features in the joint embedding space results show that functional alignment based on resting state fmri identifies functionally homologous regions across individuals with higher accuracy than alignment based on the spatial correspondence of anatomy further functional alignment enables measurement of the strength of the anatomo functional link across the cortex and reveals the uneven distribution of this link stronger anatomo functional dissociation was found in higher association areas compared to primary sensory and motor areas functional alignment based on resting state features improves group analysis of task based functional mri data increasing statistical power and improving the delineation of task specific core regions finally a comparison of the anatomo functional dissociation between cohorts is demonstrated with a group of left and right handed subjects

a fast diffeomorphic image registration algorithm abstract this paper describes dartel which is an algorithm for diffeomorphic image registration it is implemented for both 2d and 3d image registration and has been formulated to include an option for estimating inverse consistent deformations nonlinear registration is considered as a local optimisation problem which is solved using a levenberg marquardt strategy the necessary matrix solutions are obtained in reasonable time using a multigrid method a constant eulerian velocity framework is used which allows a rapid scaling and squaring method to be used in the computations dartel has been applied to intersubject registration of 471 whole brain images and the resulting deformations were evaluated in terms of how well they encode the shape information necessary to separate male and female subjects and to predict the ages of the subjects

optical flow and advection on 2 riemannian manifolds a common framework dynamic pattern analysis and motion extraction can be efficiently addressed using optical flow techniques this paper presents a generalization of these questions to nonflat surfaces where optical flow is tackled through the problem of evolution processes on non euclidean domains the classical equations of optical flow in the euclidean case are transposed to the theoretical framework of differential geometry we adopt this formulation for the regularized optical flow problem prove its mathematical well posedness and combine it with the advection equation the optical flow and advection problems are dual a motion field may be retrieved from some scalar evolution using optical flow conversely a scalar field may be deduced from a velocity field using advection these principles are illustrated with qualitative and quantitative evaluations from numerical simulations bridging both approaches the proof of concept is further demonstrated with preliminary results from time resolved functional brain imaging data where organized propagations of cortical activation patterns are evidenced using our approach

simple design efficient calibration estimators for rejective and high entropy sampling summary for survey calibration consider the situation where the population totals of auxiliary variables are known or where auxiliary variables are measured for all population units for each situation wedevelopdesign efficientcalibrationestimatorsunderrejectiveorhigh entropysampling a general approach is to extend efficient estimators for missing data problems with independent and identically distributed data to the survey setting we show that this approach effectively resolves two long standing issues in existing approaches how to achieve design efficiency regardless of a linear superpopulation model in generalized regression and calibration estimation and how to find a simple approximation in optimal regression estimation moreover the proposed approach sheds light on several issues that seem not to be well studied in the literature examples include use of the weighted kullback leibler distance in calibration estimation and efficient estimation allowing for misspecification of a nonlinear superpopulation model