recognition of white matter bundles using local and global streamline based registration and clustering virtual dissection of diffusion mri tractograms is cumbersome and needs extensive knowledge of white matter anatomy this virtual dissection often requires several inclusion and exclusion regions of interest that make it a process that is very hard to reproduce across experts having automated tools that can extract white matter bundles for tract based studies of large numbers of people is of great interest for neuroscience and neurosurgical planning the purpose of our proposed method named recobundles is to segment white matter bundles and make virtual dissection easier to perform this can help explore large tractograms from multiple persons directly in their native space recobundles leverages latest state of the art streamline based registration and clustering to recognize and extract bundles using prior bundle models recobundles uses bundle models as shape priors for detecting similar streamlines and bundles in tractograms recobundles is 100 streamline based is efficient to work with millions of streamlines and most importantly is robust and adaptive to incomplete data and bundles with missing components it is also robust to pathological brains with tumors and deformations we evaluated our results using multiple bundles and showed that recobundles is in good agreement with the neuroanatomical experts and generally produced more dense bundles across all the different experiments reported in this paper recobundles was able to identify the core parts of the bundles independently from tractography type deterministic or probabilistic or size thus recobundles can be a valuable method for exploring tractograms and facilitating tractometry studies

closed walks for community detection abstract in this paper we propose a novel measure that integrates both the concept of closed walks and clustering coefficients to replace the edge betweenness in the well known divisive hierarchical clustering algorithm the girvan and newman method gn the edges with the lowest value are removed iteratively until the network is degenerated into isolated nodes the experimental results on computer generated networks and real world networks showed that our method makes a better tradeoff of accuracy and runtime based on the analysis of the results we observe that the nontrivial closed walks of order three and four can be considered as the basic elements in constructing community structures meanwhile we discover that those nontrivial closed walks outperform trivial closed walks in the task of analyzing the structure of networks the double peak structure problem is mentioned in the last part of the article we find that our proposed method is a novel way to solve the double peak structure problem our work can provide us with a new perspective for understanding community structure in complex networks

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

corrected mean field model for random sequential adsorption on random geometric graphs a notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non overlapping congruent spheres in the d dimensional euclidean space with d ge 2 spheres arrive sequentially at uniformly chosen locations in space and are accepted only when there is no overlap with previously deposited spheres due to spatial correlations characterizing the fraction of accepted spheres remains largely intractable we study this fraction by taking a novel approach that compares random sequential adsorption in euclidean space to the nearest neighbor blocking on a sequence of clustered random graphs this random network model can be thought of as a corrected mean field model for the interaction graph between the attempted spheres using functional limit theorems we characterize the fraction of accepted spheres and its fluctuations

belief propagation algorithm and the ising model on networks with arbitrary distributions of motifs we generalize the belief propagation algorithm to sparse random networks with arbitrary distributions of motifs triangles loops etc each vertex in these networks belongs to a given set of motifs generalization of the configuration model these networks can be treated as sparse uncorrelated hypergraphs in which hyperedges represent motifs here a hypergraph is a generalization of a graph where a hyperedge can connect any number of vertices these uncorrelated hypergraphs are treelike hypertrees which crucially simplifies the problem and allows us to apply the belief propagation algorithm to these loopy networks with arbitrary motifs as natural examples we consider motifs in the form of finite loops and cliques we apply the belief propagation algorithm to the ferromagnetic ising model with pairwise interactions on the resulting random networks and obtain an exact solution of this model we find an exact critical temperature of the ferromagnetic phase transition and demonstrate that with increasing the clustering coefficient and the loop size the critical temperature increases compared to ordinary treelike complex networks however weak clustering does not change the critical behavior qualitatively our solution also gives the birth point of the giant connected component in these loopy networks

complete aggregation of the lohe tensor model with the same free flow the lohe tensor model is a first order tensor valued continuous time dynamical system for the aggregation of tensors with the same rank and size it reduces to the well known aggregation models such as the kuramoto model the lohe sphere model and the lohe matrix model as special cases for low rank tensors we present conditions for the solution splitting property asymptotic convergence toward a set of equilibria and analyze two possible asymptotic states completely aggregate state and bi polar state which can emerge from a set of initial data moreover we provide a sufficient framework leading to the aforementioned two asymptotic states in terms of initial data and system parameters

propagation on networks an exact alternative perspective by generating the specifics of a network structure only when needed on the fly we derive a simple stochastic process that exactly models the time evolution of susceptible infectious dynamics on finite size networks the small number of dynamical variables of this birth death markov process greatly simplifies analytical calculations we show how a dual analytical description treating large scale epidemics with a gaussian approximation and small outbreaks with a branching process provides an accurate approximation of the distribution even for rather small networks the approach also offers important computational advantages and generalizes to a vast class of systems

cascades on clique based graphs we present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by gleeson j p gleeson phys rev e 80 036107 2009 a condition for the existence of global cascades is also derived applications of this approach include analyses of percolation and watts s model we show how our techniques can be used to study the effects of in group bias in cascades on social networks

power law relations in random networks with communities most random graph models are locally tree like do not contain short cycles rendering them unfit for modeling networks with a community structure we introduce the hierarchical configuration model hcm a generalization of the configuration model that includes community structures while properties such as the size of the giant component and the size of the giant percolating cluster under bond percolation can still be derived analytically viewing real world networks as realizations of hcm we observe two previously undiscovered power law relations between the number of edges inside a community and the community sizes and between the number of edges going out of a community and the community sizes we also relate the power law exponent of the degree distribution with the power law exponent of the community size distribution in the case of extremely dense communities e g complete graphs this relation takes the simple form 1

diffeomorphic brain registration under exhaustive sulcal constraints the alignment and normalization of individual brain structures is a prerequisite for group level analyses of structural and functional neuroimaging data the techniques currently available are either based on volume and or surface attributes with limited insight regarding the consistent alignment of anatomical landmarks across individuals this article details a global geometric approach that performs the alignment of the exhaustive sulcal imprints cortical folding patterns across individuals this diffeomorphic sulcal based cortical disco technique proceeds to the automatic extraction identification and simplification of sulcal features from t1 weighted magnetic resonance image mri series these features are then used as control measures for fully 3 d diffeomorphic deformations quantitative and qualitative evaluations show that disco correctly aligns the sulcal folds and gray and white matter volumes across individuals the comparison with a recent iconic diffeomorphic approach dartel highlights how the absence of explicit cortical landmarks may lead to the misalignment of cortical sulci we also feature disco in the automatic design of an empirical sulcal template from group data we also demonstrate how disco can efficiently be combined with an image based deformation dartel to further improve the consistency and accuracy of alignment performances finally we illustrate how the optimized alignment of cortical folds across subjects improves sensitivity in the detection of functional activations in a group level analysis of neuroimaging data

emergent behaviors of lohe tensor flocks we present a new aggregation model on the space of rank m tensors with the same size and study emergent dynamics of the proposed model our proposed new aggregation model is general enough to encompass lohe type models such as the kuramoto model the lohe sphere model and the lohe matrix models for the ensemble of real rank 0 rank 1 and rank 2 tensors respectively in this regard we call our proposed model as the lohe tensor model for rank m tensors with the same size for emergent dynamics of the proposed model we employ the ensemble diameter as a lyapunov functional to derive a riccati type differential inequality as a direct application of these differential inequalities we provide two sufficient frameworks leading to the emergent dynamics for homogeneous and heterogeneous ensembles in terms of system parameters and initial data

automatic extraction of sulcal lines on cortical surfaces based on anisotropic geodesic distance analyzing cortical sulci is important for studying cortical morphology and brain functions although sulcal lines on cortical surfaces can be defined in various ways it is critical in a neuroimaging study to define a sulcal line along the valley of a cortical surface with a high curvature within a sulcus to extract the sulcal lines automatically we present a new geometric algorithm based on the computation of anisotropic skeletons of sulcal regions because anisotropic skeletons are highly adaptive to the anisotropic nature of the surface shape the resulting sulcal lines lie accurately on the valleys of the sulcal areas our sulcal lines remain unchanged under local shape variabilities in different human brains through experiments we show that the errors of the sulcal lines for both synthetic data and real cortical surfaces were nearly as constant as the function of random noise by measuring the changes in sulcal shape in alzheimer s disease ad patients we further investigated the effectiveness of the accuracy of our sulcal lines using a large sample of mri data this study involved 70 normal controls n men women 29 41 age mean sd 71 7 4 9 years and 100 ad subjects 37 63 72 3 5 5 we observe significantly lower absolute average mean curvature and shallower sulcal depth in ad subjects where the group difference becomes more significant if we measure the quantities along the sulcal lines rather than over the entire sulcal area the most remarkable difference in the ad patients was the average sulcal depth control 11 70 and ad 11 34

percolation on random networks with arbitrary k core structure the k core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks we now propose its explicit integration in a theoretical model we introduce a hard core random network hrn model that generates maximally random networks with arbitrary degree distribution and arbitrary k core structure we then solve exactly the bond percolation problem on the hrn model and produce fast and precise analytical estimates for the corresponding real networks extensive comparison with real databases reveals that our approach performs better than existing models while requiring less input information

cascades on a class of clustered random networks we present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced previously in m e j newman phys rev lett 103 058701 2009 a condition for the existence of global cascades is derived as well as a general criterion that determines whether increasing the level of clustering will increase or decrease the expected cascade size applications examples of which are provided include site percolation bond percolation and watts threshold model in all cases analytical results give excellent agreement with numerical simulations

measuring brain variability by extrapolating sparse tensor fields measured on sulcal lines modeling and understanding the variability of brain structures is a fundamental problem in neurosciences improved mathematical representations of structural brain variation are needed to help detect and understand genetic or disease related sources of abnormality as well as to improve statistical power when integrating functional brain mapping data across subjects in this paper we develop a new mathematical model of normal brain variation based on a large set of cortical sulcal landmarks 72 per brain delineated in each of 98 healthy human subjects scanned with 3d mri age 51 8 6 2 years we propose an original method to compute an average representation of the sulcal curves which constitutes the mean anatomy after affine alignment of the individual data across subjects the second order moment distribution of the sulcal position is modeled as a sparse field of covariance tensors symmetric positive definite matrices to extrapolate this information to the full brain one has to overcome the limitations of the standard euclidean matrix calculus we propose an affine invariant riemannian framework to perform computations with tensors in particular we generalize radial basis function rbf interpolation and harmonic diffusion partial differential equations pdes to tensor fields as a result we obtain a dense 3d variability map that agrees well with prior results on smaller subject samples moreover leave one sulcus out tests show that our model is globally able to recover the missing information on brain variation when there is a consistent neighboring pattern of variability finally we propose an innovative method to analyze the asymmetry of brain variability as expected the greatest asymmetries are found in regions that includes the primary language areas interestingly any such asymmetries in anatomical variance if it remains after anatomical normalization could explain why there may be greater power to detect group activation in one hemisphere versus the other in fmri studies

higher dimensional generalizations of the watanabe strogatz transform for vector models of synchronization we generalize the watanabe strogatz ws transform which acts on the kuramoto model in d 2 dimensions to a higher dimensional vector transform which operates on vector oscillator models of synchronization in any dimension for the case of identical frequency matrices these models have conserved quantities constructed from the cross ratios of inner products of the vector variables which are invariant under the vector transform and have trajectories which lie on the unit sphere s d 1 application of the vector transform leads to a partial integration of the equations of motion leaving independent equations to be solved for any number of nodes n we discuss properties of complete synchronization and use the reduced equations to derive a stability condition for completely synchronized trajectories on s d 1 we further generalize the vector transform to a mapping which acts in and in particular preserves the unit ball and leaves invariant the cross ratios constructed from inner products of vectors in this mapping can be used to partially integrate a system of vector oscillators with trajectories in and for d 2 leads to an extension of the kuramoto system to a system of oscillators with time dependent amplitudes and trajectories in the unit disk we find an inequivalent generalization of the mobius map which also preserves but leaves invariant a different set of cross ratios this time constructed from the vector norms this leads to a different extension of the kuramoto model with trajectories in the complex plane that can be partially integrated by means of fractional linear transformations

random graphs containing arbitrary distributions of subgraphs traditional random graph models of networks generate networks that are locally treelike meaning that all local neighborhoods take the form of trees in this respect such models are highly unrealistic most real networks having strongly nontreelike neighborhoods that contain short loops cliques or other biconnected subgraphs in this paper we propose and analyze a class of random graph models that incorporates general subgraphs allowing for nontreelike neighborhoods while still remaining solvable for many fundamental network properties among other things we give solutions for the size of the giant component the position of the phase transition at which the giant component appears and percolation properties for both site and bond percolation on networks generated by the model

automated 3 d extraction of inner and outer surfaces of cerebral cortex from mri automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging mri is greatly aided by deformable models which are used to extract identify and quantify specific neuroanatomic structures a general method of deforming polyhedra is presented here with two novel features first explicit prevention of self intersecting surface geometries is provided unlike conventional deformable models which use regularization constraints to discourage but not necessarily prevent such behavior second deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using model based constraints such as expected thickness of an anatomic surface these two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human mr images accurately locating the depths of the sulci even where noise and partial volume artifacts in the image obscure the visibility of sulci the extracted surfaces are enforced to be simple two dimensional manifolds having the topology of a sphere even though the data may have topological holes this automatic 3 d cortex segmentation technique has been applied to 150 normal subjects simultaneously extracting both the gray white and gray cerebrospinal fluid interface from each individual the collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter three alternative criteria for defining cortical thickness at each cortical location were developed and compared these results are shown to corroborate published postmortem and in vivo measurements of cortical thickness

network cloning unfolds the effect of clustering on dynamical processes we introduce network l cloning a technique for creating ensembles of random networks from any given real world or artificial network each member of the ensemble is an l cloned network constructed from l copies of the original network the degree distribution of an l cloned network and more importantly the degree degree correlation between and beyond nearest neighbors are identical to those of the original network the density of triangles in an l cloned network and hence its clustering coefficient is reduced by a factor of l compared to those of the original network furthermore the density of loops of any fixed length approaches zero for sufficiently large values of l other variants of l cloning allow us to keep intact the short loops of certain lengths as an application we employ these network cloning methods to investigate the effect of short loops on dynamical processes running on networks and to inspect the accuracy of corresponding tree based theories we demonstrate that dynamics on l cloned networks with sufficiently large l are accurately described by the so called adjacency tree based theories examples of which include the message passing technique some pair approximation methods and the belief propagation algorithm used respectively to study bond percolation si epidemics and the ising model

partition based mass clustering of tractography streamlines we describe a novel scalable clustering framework for streamlines obtained from diffusion tractography clustering is an attractive means of segmenting a large set of streamlines into anatomically relevant bundles for most existing methods however the large datasets produced in high resolution or multiple subject studies are problematical to achieve good scalability our method repeatedly divides the data into subsets which are then partitioned using hierarchical clustering a final partition is obtained by recombining the subsets in addition the recombination scheme provides a consistency measure for cluster assignment of individual streamlines which is used to clean up the final result the clusters have good anatomical plausibility and we show that three clusters corresponding to the three known segments of the arcuate fasciculus show excellent agreement with literature a major advantage of the method is the fact that it can find clusters in datasets of essentially arbitrary size this fact is exploited to find consistent clusters in concatenated tractography data from multiple subjects we expect the identification of bundles across subjects to be an important application of the method

on the schrodinger lohe hierarchy for aggregation and its emergent dynamics the lohe hierarchy is a hierarchy of finite dimensional aggregation models consisting of the kuramoto model the complex lohe sphere model the lohe matrix model and the lohe tensor model in contrast the schrodinger lohe model is the only known infinite dimensional lohe aggregation model in literature in this paper we provide an explicit connection between the schrodinger lohe model and the complex lohe sphere model and then by exploiting this explicit relation we construct infinite dimensional liftings of the lohe matrix and the lohe tensor models in this way we establish the schrodinger lohe hierarchy which corresponds to the infinite dimensional extensions of the lohe hierarchy for the proposed hierarchy we provide sufficient frameworks leading to the complete aggregation in terms of coupling strengths and initial configurations

clique percolation in random graphs as a generation of the classical percolation clique percolation focuses on the connection of cliques in a graph where the connection of two k cliques means that they share at least l 1 makes a step function like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for l 1 more interesting our analysis shows that at the critical point the order parameter c for l 1 is neither 0 nor 1 but a constant depending on k and l all these theoretical findings are in agreement with the simulation results which give theoretical support and clarification for previous simulation studies of clique percolation

tract based morphometry for white matter group analysis we introduce an automatic method that we call tract based morphometry or tbm for measurement and analysis of diffusion mri data along white matter fiber tracts using subject specific tractography bundle segmentations we generate an arc length parameterization of the bundle with point correspondences across all fibers and all subjects allowing tract based measurement and analysis in this paper we present a quantitative comparison of fiber coordinate systems from the literature and we introduce an improved optimal match method that reduces spatial distortion and improves intra and inter subject variability of fa measurements we propose a method for generating arc length correspondences across hemispheres enabling a tbm study of interhemispheric diffusion asymmetries in the arcuate fasciculus af and cingulum bundle cb the results of this study demonstrate that tbm can detect differences that may not be found by measuring means of scalar invariants in entire tracts such as the mean diffusivity md differences found in af we report tbm results of higher fractional anisotropy fa in the left hemisphere in af caused primarily by lower 3 the smallest eigenvalue of the diffusion tensor in the left af and higher left hemisphere fa in cb related to higher 1 the largest eigenvalue of the diffusion tensor in the left cb by mapping the significance levels onto the tractography trajectories for each structure we demonstrate the anatomical locations of the interhemispheric differences the tbm approach brings analysis of dti data into the clinically and neuroanatomically relevant framework of the tract anatomy

changing motif distributions in complex networks by manipulating rich club connections the role of rich club connectivity is significant in the structural property and functional behavior of complex networks in this study we find whether or not a very small portion of rich nodes connected to each other can strongly affect the frequency of occurrence of basic building blocks motifs within a heterogeneous network conversely whether a homogeneous network has a rich club or not generally has no significant effect on its structure these findings open the possibility to optimize and control the structure of complex networks by manipulating rich club connections furthermore based on the subgraph ratio profile we develop a more rigorous approach to judge whether a network has a rich club or not the new method does not calculate how many links there are among rich nodes but depends on how the links among rich nodes can affect the overall structure as well as the function of a given network

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

determining the geometry of boundaries of objects from medial data we consider a region in r2 or r3 with generic smooth boundary b and blum medial axis m on which is defined a multivalued radial vector field u from points x on m to the points of tangency of the sphere at x with b we introduce a radial shape operator srad and an edge shape operator se which measure how u bends along m these are not traditional differential geometric shape operators nonetheless we derive all local differential geometric invariants of b from these operators this allows us to define from m u a geometric medial map on m which corresponds via a radial map from m to b to the differential geometric properties of b the geometric medial map also includes a description of the relative geometry of b this is defined using the relative critical set of the radius function r on m this set consists of a network of curves on m which describe where b is thickest and thinnest it is computed using the covariant derivative of the tangential component of the unit radial vector field we further determine how these invariants are related to the differential geometric invariants of m and how these invariants change under deforming diffeomorphisms of m

systems of matrix riccati equations linear fractional transformations partial integrability and synchronization we partially integrate a system of rectangular matrix riccati equations which describe the synchronization behavior of a nonlinear complex system of n globally connected oscillators the equations take a restricted form in which the time dependent matrix coefficients are independent of the node we use linear fractional transformations to perform the partial integration resulting in a system of reduced size which is independent of n generalizing the well known watanabe strogatz reduction for the kuramoto model for square matrices the resulting constants of motion are related to the eigenvalues of matrix cross ratios which we show satisfy various properties such as symmetry relations for square matrices the variables can be regarded as elements of a classical lie group not necessarily compact satisfying the matrix riccati equations trajectories lie either within or on the boundary of a classical domain and we show by numerical example that complete synchronization can occur even for the mixed case provided that certain unitarity conditions are satisfied we extend the definition of cross ratios to rectangular matrix systems and show that again the eigenvalues are conserved special cases are models with real vector unknowns for which trajectories lie on the unit sphere in higher dimensions with well known synchronization behavior and models with complex vector wavefunctions that describe synchronization in quantum systems possibly infinite dimensional we partially integrate a system of rectangular matrix riccati equations which describe the synchronization behavior of a nonlinear complex system of n globally connected oscillators the equations take a restricted form in which the time dependent matrix coefficients are independent of the node we use linear fractional transformations to perform the partial integration resulting in a system of reduced size which is independent of n generalizing the well known watanabe strogatz reduction for the kuramoto model for square matrices the resulting constants of motion are related to the eigenvalues of matrix cross ratios which we show satisfy various properties such as symmetry relations for square matrices the variables can be regarded as elements of a classical lie group not necessarily compact satisfying the matrix riccati equations trajectories lie either within or on the boundary of a classical domain and we show by numerical example that complete synchronization can occur even for the mixed ca

a novel quantitative cross validation of different cortical surface reconstruction algorithms using mri phantom cortical surface reconstruction is important for functional brain mapping and morphometric analysis of the brain cortex several methods have been developed for the faithful reconstruction of surface models which represent the true cortical surface in both geometry and topology however there has been no explicit comparison study among those methods because each method has its own procedures file formats coordinate systems and use of the reconstructed surface there has also been no explicit evaluation method except visual inspection to validate the whole cortical surface models quantitatively in this study we presented a novel phantom based validation method of the cortical surface reconstruction algorithm and quantitatively cross validated the three most prominent cortical surface reconstruction algorithms which are used in freesurfer brainvisa and clasp respectively the validation included geometrical accuracy and mesh characteristics such as euler number fractal dimension fd total surface area and local density of points clasp showed the best geometric topologic accuracy and mesh characteristics such as fd and total surface area compared to freesurfer and brainvisa in the validation of local density of points freesurfer and brainvisa showed more even distribution of points on the cortical surface compared to clasp

spectral based automatic labeling and refining of human cortical sulcal curves using expert provided examples we present a spectral based method for automatically labeling and refining major sulcal curves of a human cerebral cortex given a set of input unlabeled sulcal curves automatically extracted from a cortical surface and a collection of expert provided examples labeled sulcal curves our objective is to identify the input major sulcal curves and assign their neuroanatomical labels and then refines these curves based on the expert provided example data without employing any atlas based registration scheme as preprocessing in order to construct the example data neuroanatomists manually labeled a set of 24 major sulcal curves 12 each for the left and right hemispheres for each individual subject according to a precise protocol we collected 30 sets of such curves from 30 subjects given the raw input sulcal curve set of a subject we choose the most similar example curve to each input curve in the set to label and refine the latter according to the former we adapt a spectral matching algorithm to choose the example curve by exploiting the sulcal curve features and their relationship the high dimensionality of sulcal curve data in spectral matching is addressed by using their multi resolution representations which greatly reduces time and space complexities our method provides consistent labeling and refining results even under high variability of cortical sulci across the subjects through experiments we show that the results are comparable in accuracy to those done manually most output curves exhibited accuracy values higher than 80 and the mean accuracy values of the curves in the left and the right hemispheres were 84 69 and 84 58 respectively

deterministic and probabilistic tractography based on complex fibre orientation distributions we propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function odf estimated from high angular resolution diffusion imaging hardi we show that in order to perform accurate probabilistic tractography one needs to use a fibre odf estimation and not the diffusion odf we use a new fibre odf estimation obtained from a sharpening deconvolution transform sdt of the diffusion odf reconstructed from q ball imaging qbi this sdt provides new insight into the relationship between the hardi signal the diffusion odf and the fibre odf we demonstrate that the sdt agrees with classical spherical deconvolution and improves the angular resolution of qbi another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre odf an extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions finally as an application of our new probabilistic tracking we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects most current diffusion tensor imaging dti based methods neglect these fibres which might lead to incorrect interpretations of brain functions

an intrinsic approach to formation control of regular polyhedra for reduced attitudes this paper addresses formation control of reduced attitudes in which a continuous control protocol is proposed for achieving and stabilizing all regular polyhedra also known as platonic solids un

hybrid evolving clique networks and their communicability aiming to understand real world hierarchical networks whose degree distributions are neither power law nor exponential we construct a hybrid clique network that includes both homogeneous and inhomogeneous parts and introduce an inhomogeneity parameter to tune the ratio between the homogeneous part and the inhomogeneous one we perform monte carlo simulations to study various properties of such a network including the degree distribution the average shortest path length the clustering coefficient the clustering spectrum and the communicability c 2014 published by elsevier b v

almost global consensus on the n sphere this paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multiagent systems that evolve in continuous time on the n dimensional unit sphere or n sphere for any connected undirected graph and all n in mathbb n backslash lbrace 1 rbrace each protocol in said class is shown to yield almost global consensus the feedback laws are negative gradients of lyapunov functions and one instance generates the canonical intrinsic gradient descent protocol this convergence result sheds new light on the general problem of consensus on riemannian manifolds the n sphere for n in mathbb n backslash lbrace 1 rbrace differs from the circle and mathsf so 3 where the corresponding protocols fail to generate almost global consensus moreover we derive a novel consensus protocol on mathsf so 3 by combining two almost globally convergent protocols on the n sphere for n in lbrace 1 2 rbrace theoretical and simulation results suggest that the combined protocol yields almost global consensus on mathsf so 3

tractography segmentation using a hierarchical dirichlet processes mixture model in this paper we propose a new nonparametric bayesian framework to cluster white matter fiber tracts into bundles using a hierarchical dirichlet processes mixture hdpm model the number of clusters is automatically learned driven by data with a dirichlet process dp prior instead of being manually specified after the models of bundles have been learned from training data without supervision they can be used as priors to cluster classify fibers of new subjects for comparison across subjects when clustering fibers of new subjects new clusters can be created for structures not observed in the training data our approach does not require computing pairwise distances between fibers and can cluster a huge set of fibers across multiple subjects we present results on several data sets the largest of which has more than 120 000 fibers

fiberprint a subject fingerprint based on sparse code pooling for white matter fiber analysis white matter characterization studies use the information provided by diffusion magnetic resonance imaging dmri to draw cross population inferences however the structure function and white matter geometry vary across individuals here we propose a subject fingerprint called fiberprint to quantify the individual uniqueness in white matter geometry using fiber trajectories we learn a sparse coding representation for fiber trajectories by mapping them to a common space defined by a dictionary a subject fingerprint is then generated by applying a pooling function for each bundle thus providing a vector of bundle wise features describing a particular subject s white matter geometry these features encode unique properties of fiber trajectories such as their density along prominent bundles an analysis of data from 861 human connectome project subjects reveals that a fingerprint based on approximately 3000 fiber trajectories can uniquely identify exemplars from the same individual we also use fingerprints for twin sibling identification our observations consistent with the twin data studies of white matter integrity our results demonstrate that the proposed fiberprint can effectively capture the variability in white matter fiber geometry across individuals using a compact feature vector dimension of 50 making this framework particularly attractive for handling large datasets

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

reproducibility of superficial white matter tracts using diffusion weighted imaging tractography human brain connection map is far from being complete in particular the study of the superficial white matter swm is an unachieved task its description is essential for the understanding of human brain function and the study of pathogenesis triggered by abnormal connectivity in this work we automatically created a multi subject atlas of swm diffusion based bundles of the whole brain for each subject the complete cortico cortical tractogram is first split into sub tractograms connecting pairs of gyri then intra subject shape based fiber clustering performs compression of each sub tractogram into a set of bundles proceeding further with shape based clustering provides a match of the bundles across subjects bundles found in most of the subjects are instantiated in the atlas to increase robustness this procedure was performed with two independent groups of subjects in order to discard bundles without match across the two independent atlases finally the resulting intersection atlas was projected on a third independent group of subjects in order to filter out bundles without reproducible and reliable projection the final multi subject diffusion based u fiber atlas is composed of 100 bundles in total 50 per hemisphere from which 35 are common to both hemispheres

control of a driftless bilinear vector field on n sphere in this paper we consider a multi input driftless bilinear system evolving on the n dimensional sphere s n we first provide examples drawn from rigid body mechanics that provide the motivation for the control of bilinear systems on s n for the general framework we establish the global controllability on s n and propose two linear control laws on s n that achieve asymptotic stabilization of an equilibrium point with an almost global domain of attraction further the asymptotically stable closed loop system trajectories are shown to be arcs on the geodesics of s n for a particular choice of the equilibrium point next we propose two linear time varying control laws to achieve trajectory tracking on s n and show the asymptotic stability of the tracking error a distributed control is designed for the consensus of multiagent bilinear systems on s n with an undirected tree as the communication graph the consensus manifold is shown to have an almost global domain of attraction

anatomicuts hierarchical clustering of tractography streamlines based on anatomical similarity diffusion mri tractography produces massive sets of streamlines that contain a wealth of information on brain connections the size of these datasets creates a need for automated clustering methods to group the streamlines into meaningful bundles conventional clustering techniques group streamlines based on their spatial coordinates neuroanatomists however define white matter bundles based on the anatomical structures that they go through or next to rather than their spatial coordinates thus we propose a similarity measure for clustering streamlines based on their position relative to cortical and subcortical brain regions we incorporate this measure into a hierarchical clustering algorithm and compare it to a measure that relies on euclidean distance using data from the human connectome project we show that the anatomical similarity measure leads to a 20 improvement in the overlap of clusters with manually labeled tracts importantly this is achieved without introducing any prior information from a tract atlas into the clustering algorithm therefore without imposing the existence of any named tracts

exponential synchronization of the high dimensional kuramoto model with identical oscillators under digraphs abstract for the kuramoto model and its variations it is difficult to analyze the exponential synchronization under the general digraphs due to the lack of symmetry in this paper for the high dimensional kuramoto model of identical oscillators a matrix riccati differential equation mrde is proposed to describe the error dynamics based on the mrde the exponential synchronization is proved by constructing a total error function for the case of digraphs admitting directed spanning trees

general and exact approach to percolation on random graphs we present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs our contribution can be summarized in three main points i we introduce a set of iterative equations that solve the exact distribution of the size and composition of components in finite size quenched or random multitype graphs ii we define a very general random graph ensemble that encompasses most of the models published to this day and also makes it possible to model structural properties not yet included in a theoretical framework site and bond percolation on this ensemble is solved exactly in the infinite size limit using probability generating functions i e the percolation threshold the size and the composition of the giant extensive and small components several examples and applications are also provided iii our approach can be adapted to model interdependent graphs whose most striking feature is the emergence of an extensive component via a discontinuous phase transition in an equally general fashion we show how a graph can successively undergo a continuous then a discontinuous phase transition and preliminary results suggest that clustering increases the amplitude of the discontinuity at the transition

clustering determines the dynamics of complex contagions in multiplex networks we present the mathematical analysis of generalized complex contagions in a class of clustered multiplex networks the model is intended to understand spread of influence or any other spreading process implying a threshold dynamics in setups of interconnected networks with significant clustering the contagion is assumed to be general enough to account for a content dependent linear threshold model where each link type has a different weight for spreading influence that may depend on the content e g product rumor political view that is being spread using the generating functions formalism we determine the conditions probability and expected size of the emergent global cascades this analysis provides a generalization of previous approaches and is especially useful in problems related to spreading and percolation the results present nontrivial dependencies between the clustering coefficient of the networks and its average degree in particular several phase transitions are shown to occur depending on these descriptors generally speaking our findings reveal that increasing clustering decreases the probability of having global cascades and their size however this tendency changes with the average degree there exists a certain average degree from which on clustering favors the probability and size of the contagion by comparing the dynamics of complex contagions over multiplex networks and their monoplex projections we demonstrate that ignoring link types and aggregating network layers may lead to inaccurate conclusions about contagion dynamics particularly when the correlation of degrees between layers is high

high dimensional kuramoto models on stiefel manifolds synchronize complex networks almost globally abstract the kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature some applications e g quantum synchronization and rigid body attitude synchronization involve high dimensional kuramoto models where each oscillator lives on the n sphere or so n these manifolds are special cases of the compact real stiefel manifold st p n using tools from optimization and control theory we prove that the generalized kuramoto model on st p n converges to a synchronized state for any connected graph and from almost all initial conditions provided p n satisfies p 2 3 n 1 and all oscillator frequencies are equal this result could not have been predicted based on knowledge of the kuramoto model in complex networks over the circle in that case almost global synchronization is graph dependent it applies if the network is acyclic or sufficiently dense this paper hence identifies a property that distinguishes many high dimensional generalizations of the kuramoto models from the original model

multi contrast large deformation diffeomorphic metric mapping for diffusion tensor imaging diffusion tensor imaging dti can reveal detailed white matter anatomy and has the potential to detect abnormalities in specific white matter structures such detection and quantification are however not straightforward the voxel based analysis after image normalization is one of the most widely used methods for quantitative image analyses to apply this approach to dti it is important to examine if structures in the white matter are well registered among subjects which would be highly dependent on employed algorithms for normalization in this paper we evaluate the accuracy of normalization of dti data using a highly elastic transformation algorithm called large deformation diffeomorphic metric mapping after simulation based validation of the algorithm dti data from normal subjects were used to measure the registration accuracy to examine the impact of morphological abnormalities on the accuracy the algorithm was also tested using data from alzheimer s disease ad patients with severe brain atrophy the accuracy level was measured by using manual landmark based white matter matching and surface based brain and ventricle matching as gold standard to improve the accuracy level cascading and multi contrast approaches were developed the accuracy level for the white matter was 1 88 0 55 and 2 19 0 84 mm for the measured locations in the controls and patients respectively

analysis of percolation behaviors of clustered networks with partial support dependence relations we carry out a study of percolation behaviors of clustered networks with partial support dependence relations by adopting two different attacking strategies attacking only one network and both networks which help to further understand real coupled networks for two different attacking strategies we find that the system changes from a second order phase transition to a first order phase transition as coupling strengthq increases we also notice that the first order region becomes smaller and the secondorder region becomes larger as average degree or clustering coefficient increases and as the average supported degree approaches infinity coupled clustered networks become independent and only the second order transition is observed which is similar toq 0 furthermore we find that clustering coefficient has a significant impact on robustness of the system for strong coupling strength but for weak coupling strength it has little influence especially for attacking both networks the study implies that we can obtain a more robust network by reducing clustering coefficient and increasing average degree for strong coupling strength however for weak coupling strength a more robust network is obtained only by increasing average degree for the same support average degree

automatic fiber bundle segmentation in massive tractography datasets using a multi subject bundle atlas this paper presents a method for automatic segmentation of white matter fiber bundles from massive dmri tractography datasets the method is based on a multi subject bundle atlas derived from a two level intra subject and inter subject clustering strategy this atlas is a model of the brain white matter organization computed for a group of subjects made up of a set of generic fiber bundles that can be detected in most of the population each atlas bundle corresponds to several inter subject clusters manually labeled to account for subdivisions of the underlying pathways often presenting large variability across subjects an atlas bundle is represented by the multi subject list of the centroids of all intra subject clusters in order to get a good sampling of the shape and localization variability the atlas composed of 36 known deep white matter bundles and 47 superficial white matter bundles in each hemisphere was inferred from a first database of 12 brains it was successfully used to segment the deep white matter bundles in a second database of 20 brains and most of the superficial white matter bundles in 10 subjects of the same database

tweaking synchronization by connectivity modifications acknowledgments the authors wish to thank the nesin foundation for an amazing working group activity in nesin math village and we wish to thank tiago pereira for fruitful discussions p s and j k acknowledge gratefully the support of bmbf condynet fk 03sf0472a t p acknowledges fapesp no 2012 22160 7 and no 2015 02486 3 and irtg 1740 d e acknowledge support by the leibniz association wgl under grant no saw 2013 izw 2542