mild solutions of non autonomous second order problems with nonlocal initial conditions abstract in this paper we establish the existence of mild solutions for a non autonomous abstract semi linear second order differential equation submitted to nonlocal initial conditions our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the hausdorff measure of non compactness

the drinfeld realization of the elliptic quantum group bq λ a2 2 we construct a realization of the l operator satisfying the rll relation of the face type elliptic quantum group bq a2 2 the construction is based on the elliptic analog of the drinfeld currents of uq a2 2 which forms the elliptic algebra uq p a2 2 we give a realization of the elliptic currents e z f z and k z as a tensor product of the drinfeld currents of uq a2 2 and a heisenberg algebra in the level one representation we also give a free field realization of the elliptic currents applying these results we derive a free field realization of the uq p a2 2 analog of the bq a2 2 intertwining operators the resultant operators coincide with those of the vertex operators in the dilute al model which is known to be a rsos restriction of the a2 2 face model

symmetry detection by generalized complex gc moments a close form solution this paper presents a unified method for detecting both reflection symmetry and rotation symmetry of 2d images based on an identical set of features i e the first three nonzero generalized complex gc moments this method is theoretically guaranteed to detect all the axes of symmetries of every 2d image if more nonzero gc moments are used in the feature set furthermore we establish the relationship between reflectional symmetry and rotational symmetry in an image which can be used to check the correctness of symmetry detection this method has been demonstrated experimentally using more than 200 images

an elliptic algebra and the fusion rsos model we introduce an elliptic algebra with and present its free boson representation at generic level k we show that this algebra governs a structure of the space of states in the k fusion rsos model specified by a pair of positive integers r k or equivalently a q deformation of the coset conformal field theory extending the work by lukyanov and pugai corresponding to the case k 1 we give a full set of screening operators for k 1 the algebra has two interesting degeneration limits p 0 and p 1 the former limit yields the quantum affine algebra whereas the latter yields the algebra the scaling limit of the elliptic algebra using this correspondence we also obtain the highest component of two types of vertex operators which can be regarded as q deformations of the primary fields in the coset conformal field theory

finding imaging patterns of structural covariance via non negative matrix factorization in this paper we investigate the use of non negative matrix factorization nnmf for the analysis of structural neuroimaging data the goal is to identify the brain regions that co vary across individuals in a consistent way hence potentially being part of underlying brain networks or otherwise influenced by underlying common mechanisms such as genetics and pathologies nnmf offers a directly data driven way of extracting relatively localized co varying structural regions thereby transcending limitations of principal component analysis pca independent component analysis ica and other related methods that tend to produce dispersed components of positive and negative loadings in particular leveraging upon the well known ability of nnmf to produce parts based representations of image data we derive decompositions that partition the brain into regions that vary in consistent ways across individuals importantly these decompositions achieve dimensionality reduction via highly interpretable ways and generalize well to new data as shown via split sample experiments we empirically validate nnmf in two data sets i a diffusion tensor dt mouse brain development study and ii a structural magnetic resonance smr study of human brain aging we demonstrate the ability of nnmf to produce sparse parts based representations of the data at various resolutions these representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes moreover we show that these low dimensional representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like pca and ica

spatial normalization of diffusion tensor mri using multiple channels diffusion tensor mri dt mri can provide important in vivo information for the detection of brain abnormalities in diseases characterized by compromised neural connectivity to quantify diffusion tensor abnormalities based on voxel based statistical analysis spatial normalization is required to minimize the anatomical variability between studied brain structures in this article we used a multiple input channel registration algorithm based on a demons algorithm and evaluated the spatial normalization of diffusion tensor image in terms of the input information used for registration registration was performed on 16 dt mri data sets using different combinations of the channels including a channel of t2 weighted intensity a channel of the fractional anisotropy a channel of the difference of the first and second eigenvalues two channels of the fractional anisotropy and the trace of tensor three channels of the eigenvalues of the tensor and the six channel tensor components to evaluate the registration of tensor data we defined two similarity measures i e the endpoint divergence and the mean square error which we applied to the fiber bundles of target images and registered images at the same seed points in white matter segmentation we also evaluated the tensor registration by examining the voxel by voxel alignment of tensors in a sample of 15 normalized dt mris in all evaluations nonlinear warping using six independent tensor components as input channels showed the best performance in effectively normalizing the tract morphology and tensor orientation we also present a nonlinear method for creating a group diffusion tensor atlas using the average tensor field and the average deformation field which we believe is a better approach than a strict linear one for representing both tensor distribution and morphological distribution of the population

new construction of solvable lattice models including an ising model in a field in this letter we report a new construction to obtain restricted solid on solid rsos models out of loop models the method is a generalization of ideas developed by owczarek and baxter and by pasquier in particular we consider a solvable o n model and point out that some of the rsos models thus obtained admit an off critical extension among these models we find a spin 1 ising model which is solvable not only at the critical point but also in a fieldlike deviation away from it we calculate the critical exponent ensuremath delta 15 directly from the relation between the free energy and the field this is the first determination of this exponent without the use of scaling relations

unified framework for anisotropic interpolation and smoothing of diffusion tensor images to enhance the performance of diffusion tensor imaging dti based fiber tractography this study proposes a unified framework for anisotropic interpolation and smoothing of dti data the critical component of this framework is an anisotropic sigmoid interpolation kernel which is adaptively modulated by the local image intensity gradient profile the adaptive modulation of the sigmoid kernel permits image smoothing in homogeneous regions and meanwhile guarantees preservation of structural boundaries the unified scheme thus allows piece wise smooth continuous and boundary preservation interpolation of dti data so that smooth fiber tracts can be tracked in a continuous manner and confined within the boundaries of the targeted structure the new interpolation method is compared with conventional interpolation methods on the basis of fiber tracking from synthetic and in vivo dti data which demonstrates the effectiveness of this unified framework

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

generalized affine invariant image normalization we provide a generalized image normalization technique which basically solves all problems in image normalization the orientation of any image can be uniquely defined by at most three non zero generalized complex moments the correctness of our method is demonstrated theoretically as well as in practice by applying them to a number of degenerate images which have failed other previously reported techniques for image normalization

f timer fast tensor image morphing for elastic registration we propose a novel diffusion tensor imaging dti registration algorithm called fast tensor image morphing for elastic registration f timer f timer leverages multiscale tensor regional distributions and local boundaries for hierarchically driving deformable matching of tensor image volumes registration is achieved by utilizing a set of automatically determined structural landmarks via solving a soft correspondence problem based on the estimated correspondences thin plate splines are employed to generate a smooth topology preserving and dense transformation and to avoid arbitrary mapping of nonlandmark voxels to mitigate the problem of local minima which is common in the estimation of high dimensional transformations we employ a hierarchical strategy where a small subset of voxels with more distinctive attribute vectors are first deployed as landmarks to estimate a relatively robust low degrees of freedom transformation as the registration progresses an increasing number of voxels are permitted to participate in refining the correspondence matching a scheme as such allows less conservative progression of the correspondence matching towards the optimal solution and hence results in a faster matching speed compared with its predecessor timer which has been shown to outperform state of the art algorithms experimental results indicate that f timer is capable of achieving comparable accuracy at only a fraction of the computation cost

regression models for identifying noise sources in magnetic resonance images stochastic noise susceptibility artifacts magnetic field and radiofrequency inhomogeneities and other noise components in magnetic resonance images mris can introduce serious bias into any measurements made with those images we formally introduce three regression models including a rician regression model and two associated normal models to characterize stochastic noise in various magnetic resonance imaging modalities including diffusion weighted imaging dwi and functional mri fmri estimation algorithms are introduced to maximize the likelihood function of the three regression models we also develop a diagnostic procedure for systematically exploring mr images to identify noise components other than simple stochastic noise and to detect discrepancies between the fitted regression models and mri data the diagnostic procedure includes goodness of fit statistics measures of influence and tools for graphical display the goodness of fit statistics can assess the key assumptions of the three r

algebra of screening operators for the deformed wn algebra we construct a family of intertwining operators screening operators between various fock space modules over the deformed wn algebra they are given as integrals involving a product of screening currents and elliptic theta functions we derive a set of quadratic relations among the screening operators and use them to construct a felder type complex in the case of the deformed w3 algebra

margin maximizing feature elimination methods for linear and nonlinear kernel based discriminant functions feature selection for classification in high dimensional spaces can improve generalization reduce classifier complexity and identify important discriminating feature markers for support vector machine svm classification a widely used technique is recursive feature elimination rfe we demonstrate that rfe is not consistent with margin maximization central to the svm learning approach we thus propose explicit margin based feature elimination mfe for svms and demonstrate both improved margin and improved generalization compared with rfe moreover for the case of a nonlinear kernel we show that rfe assumes that the squared weight vector 2 norm is strictly decreasing as features are eliminated we demonstrate this is not true for the gaussian kernel and consequently rfe may give poor results in this case mfe for nonlinear kernels gives better margin and generalization we also present an extension which achieves further margin gains by optimizing only two degrees of freedom the hyperplane s intercept and its squared 2 norm with the weight vector orientation fixed we finally introduce an extension that allows margin slackness we compare against several alternatives including rfe and a linear programming method that embeds feature selection within the classifier design on high dimensional gene microarray data sets university of california at irvine uci repository data sets and alzheimer s disease brain image data mfe methods give promising results

vertex operators for twisted quantum affine algebras we construct explicitly the q vertex operators intertwining operators for the level one modules v i of the classical quantum affine algebras of twisted types using interacting bosons where i 0 1 for a 2 n 1 i 0 for d 3 i 0 n for d 2 1 and i n for a 2 n a perfect crystal graph for d 3 4 is constructed as a by product

discriminative wavelet shape descriptors for recognition of 2 d patterns in this paper we present a set of wavelet moment invariants together with a discriminative feature selection method for the classification of seemingly similar objects with subtle di erences these invariant features are selected automatically based on the discrimination measures defined for the invariant features using a minimum distance classifier our wavelet moment invariants achieved the highest classification rate for all four di erent sets tested compared with zernike s moment invariants and li s moment invariants for a test set consisting of 26 upper cased english letters wavelet moment invariants could obtain 100 classification rate when applied to 26 30 randomly generated noisy and scaled letters whereas zernike s moment invariants and li s moment invariants obtained only 98 7 and 75 3 respectively the theoretical and experimental analyses in this paper prove that the proposed method has the ability to classify many types of image objects and is particularly suitable for classifying seemingly similar objects with subtle di erences 1999 pattern recognition society published by elsevier science ltd all rights reserved

commutation relations of vertex operators for uq sl m n we consider commutation relations and invertibility relations of vertex operators for the quantum affine superalgebra uq sl m n by using bosonization we show that vertex operators give a representation of the graded zamolodchikov faddeev algebra by direct computation invertibility relations of type ii vertex operators for n m are very similar to those of type i for m n we consider commutation relations and invertibility relations of vertex operators for the quantum affine superalgebra uq sl m n by using bosonization we show that vertex operators give a representation of the graded zamolodchikov faddeev algebra by direct computation invertibility relations of type ii vertex operators for n m are very similar to those of type i for m n

hammer hierarchical attribute matching mechanism for elastic registration a new approach is presented for elastic registration of medical images and is applied to magnetic resonance images of the brain experimental results demonstrate very high accuracy in superposition of images from different subjects there are two major novelties in the proposed algorithm first it uses an attribute vector i e a set of geometric moment invariants gmis that are defined on each voxel in an image and are calculated from the tissue maps to reflect the underlying anatomy at different scales the attribute vector if rich enough can distinguish between different parts of an image which helps establish anatomical correspondences in the deformation procedure it also helps reduce local minima by reducing ambiguity in potential matches this is a fundamental deviation of our method referred to as the hierarchical attribute matching mechanism for elastic registration hammer from other volumetric deformation methods which are typically based on maximizing image similarity second in order to avoid being trapped by local minima i e suboptimal poor matches hammer uses a successive approximation of the energy function being optimized by lower dimensional smooth energy functions which are constructed to have significantly fewer local minima this is achieved by hierarchically selecting the driving features that have distinct attribute vectors thus drastically reducing ambiguity in finding correspondence a number of experiments demonstrate that the proposed algorithm results in accurate superposition of image data from individuals with significant anatomical differences

a note on the validity of statistical bootstrapping for estimating the uncertainty of tensor parameters in diffusion tensor images diffusion tensors are estimated from magnetic resonance images mris that are diffusion weighted and those images inherently contain noise therefore noise in the diffusion weighted images produces uncertainty in estimation of the tensors and their derived parameters which include eigenvalues eigenvectors and the trajectories of fiber pathways that are reconstructed from those eigenvalues and eigenvectors although repetition and wild bootstrap methods have been widely used to quantify the uncertainty of diffusion tensors and their derived parameters we currently lack theoretical derivations that would validate the use of these two bootstrap methods for the estimation of statistical parameters of tensors in the presence of noise the aim of this paper is to examine theoretically and numerically the repetition and wild bootstrap methods for approximating uncertainty in estimation of diffusion tensor parameters under two different schemes for acquiring diffusion weighted images whether these bootstrap methods can be used to quantify uncertainty in some diffusion tensor parameters such as fractional anisotropy fa depends critically on the morphology of the diffusion tensor that is being estimated the wild and repetition bootstrap methods in particular cannot quantify uncertainty in the principal direction pd of isotropic or oblate tensor we also examine the use of bootstrap methods in estimating tensors in a voxel containing multiple tensors demonstrating their limitations when quantifying the uncertainty of tensor parameters in those locations simulation studies are also used to understand more thoroughly our theoretical results our findings raise serious concerns about the use of bootstrap methods to quantify the uncertainty of fiber pathways when those pathways pass through voxels that contain either isotropic tensors oblate tensors or multiple tensors

quantum 401 1401 1401 1algebras and macdonald polynomials we derive a quantum deformation of thew n algebra and its quantum miura transformation whose singular vectors realize the macdonald polynomials

theta function solutions of the quantum knizhnik zamolodchikov bernard equation for a face model we consider the quantum knizhnik zamolodchikov bernard equation for a face model with elliptic weights the sos model we provide explicit solutions as theta functions on the so called combinatorial line in which the model is equivalent to the three colour model these solutions are shown to be eigenvectors of the transfer matrix with periodic boundary conditions

measuring size and shape of the hippocampus in mr images using a deformable shape model a method for segmentation and quantification of the shape and size of the hippocampus is proposed based on an automated image analysis algorithm the algorithm uses a deformable shape model to locate the hippocampus in magnetic resonance images and to determine a geometric representation of its boundary the deformable model combines three types of information first it employs information about the geometric properties of the hippocampal boundary from a local and relatively finer scale to a more global and relatively coarser scale second the model includes a statistical characterization of normal shape variation across individuals serving as prior knowledge to the algorithm third the algorithm utilizes a number of manually defined boundary points which can help guide the model deformation to the appropriate boundaries wherever these boundaries are weak or not clearly defined in mr images excellent agreement is demonstrated between the algorithm and manual segmentations by well trained raters with a correlation coefficient equal to 0 97 and algorithm rater differences statistically equivalent to interrater differences for manual definitions

order parameters of the dilute a models the free energy and local height probabilities of the dilute a models with borken 2 symmetry are calculated analytically using inversion and corner transfer matrix methods these models possess four critical branches the first two branches provide new realizations of the unitary minimal series and the other two branches give a direct product of this series with an ising model we identify the integrable perturbations which move the dilute a models away from the critical limit generalized order parameters are defined and their critical exponents extracted the associated conformal weights are found to occur on the diagonal of the relevant kac table in an appropriate regime the dilute a3 model lies in the universality class of the ising model in a magnetic field in this case we obtain the magnetic exponent 15 directly without the use of scaling relations

a geometry driven optical flow warping for spatial normalization of cortical surfaces spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences thereby allowing for group analysis to be carried out the work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold the geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework a multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain creating the desired normalization the partial differential equation that carries out the warping is implemented in a euclidean framework in order to facilitate a multiresolution strategy thereby permitting large deformations between the two surfaces the technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces a quantitative comparison between our proposed surface based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface based spatial normalization performs better in matching homologous cortical anatomies

approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique abstract this paper is concerned with the approximate controllability of the semilinear fractional evolution equations with nonlocal and impulsive conditions our main results are obtained by utilizing the technique of approximate solution and the theory of fixed point in addition the impulsive functions in this paper are supposed to be continuous and the nonlocal item is divided into two cases lipschitz continuous and only continuous which generalizes the previous contributions finally two examples are worked out to illustrate our obtained results

hierarchical unbiased graph shrinkage hugs a novel groupwise registration for large data set normalizing all images in a large data set into a common space is a key step in many clinical and research studies e g for brain development maturation and aging recently groupwise registration has been developed for simultaneous alignment of all images without selecting a particular image as template thus potentially avoiding bias in the registration however most conventional groupwise registration methods do not explore the data distribution during the image registration thus their performance could be affected by large inter subject variations in the data set under registration to solve this potential issue we propose to use a graph to model the distribution of all image data sitting on the image manifold with each node representing an image and each edge representing the geodesic pathway between two nodes or images then the procedure of warping all images to their population center turns to the dynamic shrinking of the graph nodes along their graph edges until all graph nodes become close to each other thus the topology of image distribution on the image manifold is always preserved during the groupwise registration more importantly by modeling the distribution of all images via a graph we can potentially reduce registration error since every time each image is warped only according to its nearby images with similar structures in the graph we have evaluated our proposed groupwise registration method on both infant and adult data sets by also comparing with the conventional group mean based registration and the absorb methods all experimental results show that our proposed method can achieve better performance in terms of registration accuracy and robustness

registration of longitudinal brain image sequences with implicit template and spatial temporal heuristics abstract accurate measurement of longitudinal changes of brain structures and functions is very important but challenging in many clinical studies also across subject comparison of longitudinal changes is critical in identifying disease related changes in this paper we propose a novel method to meet these two requirements by simultaneously registering sets of longitudinal image sequences of different subjects to the common space without assuming any explicit template specifically our goal is to 1 consistently measure the longitudinal changes from a longitudinal image sequence of each subject and 2 jointly align all image sequences of different subjects to a hidden common space to achieve these two goals we first introduce a set of temporal fiber bundles to explore the spatial temporal behavior of anatomical changes in each longitudinal image sequence then a probabilistic model is built upon the temporal fibers to characterize both spatial smoothness and temporal continuity finally the transformation fields that connect each time point image of each subject to the common space are simultaneously estimated by the expectation maximization em approach via the maximum a posterior map estimation of the probabilistic models promising results have been obtained in quantitative measurement of longitudinal brain changes i e hippocampus volume changes showing better performance than those obtained by either the pairwise or the groupwise only registration methods

strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with arbitrary functionals abstract in l byszewski z angew math mech 70 1990 3 202 206 l byszewski j appl math stochastic ann 3 1990 5 65 79 the author studied strong maximum principles for nonlinear parabolic problems with nonlocal inequalities together with particular functionals our purpose here is to extend results in l byszewski z angew math mech 70 1990 3 202 206 l byszewski j appl math stochastic ann 3 1990 5 65 79 to strong maximum principles for nonlinear parabolic problems with nonlocal inequalities together with arbitrary functionals the results obtained in this paper can be applied in the theories of diffusion and heat conduction

boundary finding with prior shape and smoothness models we propose a unified framework for boundary finding where a bayesian formulation based on prior knowledge and the edge information of the input image likelihood is employed the prior knowledge in our framework is based on principal component analysis of four different covariance matrices corresponding to independence smoothness statistical shape and combined models respectively indeed snakes modal analysis fourier descriptors and point distribution models can be derived from or linked to our approaches of different prior models when the true training set does not contain enough variability to express the full range of deformations a mixed covariance matrix uses a combined prior of the smoothness and statistical variation modes it adapts gradually to use more statistical modes of variation as larger data sets are available

a framework for callosal fiber distribution analysis this paper presents a framework for analyzing the spatial distribution of neural fibers in the brain with emphasis on interhemispheric fiber bundles crossing through the corpus callosum the proposed approach combines methodologies for fiber tracking and spatial normalization and is applied on diffusion tensor images and standard magnetic resonance images

adaptive normalization of handwritten characters using global local affine transformation this paper introduces an adaptive or category dependent normalization method that normalizes an input pattern against each reference pattern using global local affine transformation gat lat in a hierarchical manner as a general deformation model also the normalization criterion is clearly defined as minimization of the mean of nearest neighbor interpoint distances between each reference pattern and a normalized input pattern optimal gat lat is determined by iterative application of weighted least squares fitting techniques experiments using input patterns of 3 171 character categories including kanji kana and alphanumerics written by 36 people in the cursive style against square style reference patterns show that the proposed method not only can absorb a fairly large amount of handwriting fluctuation within the same category but the discrimination ability is greatly improved by the suppression of excessive normalization against similarly shaped but different categories furthermore comparative results obtained by the conventional shape normalization method for preprocessing are presented

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

nonrigid image registration with crystal dislocation energy the goal of nonrigid image registration is to find a suitable transformation such that the transformed moving image becomes similar to the reference image the image registration problem can also be treated as an optimization problem which tries to minimize an objective energy function that measures the differences between two involved images in this paper we consider image matching as the process of aligning object boundaries in two different images the registration energy function can be defined based on the total energy associated with the object boundaries the optimal transformation is obtained by finding the equilibrium state when the total energy is minimized which indicates the object boundaries find their correspondences and stop deforming we make an analogy between the above processes with the dislocation system in physics the object boundaries are viewed as dislocations line defects in crystal then the well developed dislocation energy is used to derive the energy assigned to object boundaries in images the newly derived registration energy function takes the global gradient information of the entire image into consideration and produces an orientation dependent and long range interaction between two images to drive the registration process this property of interaction endows the new registration framework with both fast convergence rate and high registration accuracy moreover the new energy function can be adapted to realize symmetric diffeomorphic transformation so as to ensure one to one matching between subjects in this paper the superiority of the new method is theoretically proven experimentally tested and compared with the state of the art syn method experimental results with 3 d magnetic resonance brain images demonstrate that the proposed method outperforms the compared methods in terms of both registration accuracy and computation time

statistical analysis of diffusion tensors in diffusion weighted magnetic resonance imaging data diffusion tensor imaging has been widely used to reconstruct the structure and orientation of fibers in biological tissues particularly in the white matter of the brain because it can track the effective diffusion of water along those fibers the raw diffusion weighted images from which diffusion tensors are estimated however inherently contain noise noise in the images produces uncertainty in the estimation of the tensors which are 3 3 positive definite matrices and of their derived quantities including eigenvalues eigenvectors and the fiber pathways that are reconstructed based on those tensor elements the aim of this article is to provide a comprehensive theoretical framework of statistical inference for quantifying the effects of noise on diffusion tensors on their eigenvalues and eigenvectors and on their morphological classification we propose a semiparametric model to account for noise in diffusion weighted images we then develop a one step weighted least squares estimate of the t

quantum scr w algebras and elliptic algebras we define a quantum open image in new window algebra associated to mathfrak s mathfrak l n as an associative algebra depending on two parameters for special values of the parameters this algebra becomes the ordinary open image in new window algebra of mathfrak s mathfrak l n or theq deformed classical open image in new window algebra algebra of mathfrak s mathfrak l n we construct free field realizations of the quantum open image in new window algebra and the screening currents we also point out some interesting elliptic structures arising in these algebras in particular we show that the screening currents satisfy elliptic analogues of the drinfeld relations in open image in new window

controllability of systems with a general nonlocal condition abstract in this work we are concerned with the controllability of first order distributed systems with a general nonlocal condition specifically by a general nonlocal condition we understand a nonlocal condition modeled in terms of an inclusion in this context assuming that the underlying linear system is approximately controllable we present three types of conditions under which the nonlinear system is also approximately controllable

elliptic algebra drinfeld currents and vertex operators we investigate the structure of the elliptic algebra introduced earlier by one of the authors our construction is based on a new set of generating series in the quantum affine algebra which are elliptic analogs of the drinfeld currents they enable us to identify with the tensor product of and a heisenberg algebra generated by p q with q p 1 in terms of these currents we construct an l operator satisfying the dynamical rll relation in the presence of the central element c the vertex operators of lukyanov and pugai arise as intertwiners of for the level one representation in the sense to be elaborated on in the text we also present vertex operators with higher level spin in the free field representation

3 d moment forms their construction and application to object identification and positioning the 3 d moment method is applied to object identification and positioning a general theory of deriving 3 d moments invariants is proposed the notion of complex moments is introduced complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3 d rotations the application of the 3 d moment method to motion estimation is also discussed using group theoretic techniques various invariant scalars are extracted from compounds of complex moments via clebsch gordon expansion twelve moment invariants consisting of the second order and third order moments are explicitly derived based on a perturbation formula it is shown that the second order moment invariants can be used to predict whether the estimation using noisy data is reliable or not the new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach vectors consisting of the third order moments can be derived in a similar manner

vertex operators for quantum groups and application to integrable systems starting with any r matrix with spectral parameters and obeying the yang baxter equation and a unitarity condition we construct the corresponding infinite dimensional quantum group r in terms of a deformed oscillator algebra r the realization we present is an infinite series very similar to a vertex operator then considering the integrable hierarchy naturally associated with r we show that r provides its integrals of motion the construction can be applied to any infinite dimensional quantum group e g yangians or elliptic quantum groups taking as an example the r matrix of y n the yangian based on gl n using this construction we recover the nonlinear schrodinger equation and its y n symmetry

free field approach to the dilute al models we construct a free field realization of vertex operators of the dilute al models along with the felder complex for l 3 we also study an e8 structure in terms of the deformed virasoro currents

using a deformable surface model to obtain a shape representation of the cortex this paper examines the problem of obtaining a mathematical representation of the outer cortex of the human brain which is a key problem in several applications including morphological analysis of the brain and spatial normalization and registration of brain images a parameterization of the outer cortex is first obtained using a deformable surface algorithm which motivated by the structure of the cortex is constructed to find the central layer of thick surfaces based on this parameterization a hierarchical representation of the outer cortical structure is proposed through its depth map and its curvature maps at various scales various experiments on magnetic resonance data are presented

approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions in this paper we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable the results are obtained using new properties of symmetric operators which are proved in this paper compact semigroups the schauder fixed point theorem and or the contraction mapping principle

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

gyral folding pattern analysis via surface profiling folding is an essential shape characteristic of the human cerebral cortex descriptors of cortical folding patterns have been studied for decades however many previous studies are either based on local shape descriptors such as curvature or based on global descriptors such as gyrification index or spherical wavelets this paper proposes a gyrus scale folding pattern analysis technique via cortical surface profiling firstly we sample the cortical surface into 2d profiles and model them using a power function this step provides both the flexibility of representing arbitrary shape by profiling and the compactness of representing shape by parametric modeling secondly based on the estimated model parameters we extract affine invariant features on the cortical surface and apply the affinity propagation clustering algorithm to parcellate the cortex into cortical regions with strict hierarchy and smooth transitions among them finally a second round surface profiling is performed on the parcellated cortical surface and the number of hinges is detected to describe the gyral folding pattern we have applied the surface profiling method to two normal brain datasets and a schizophrenia patient dataset the experimental results demonstrate that the proposed method can accurately classify human gyri into 2 hinge 3 hinge and 4 hinge patterns the distribution of these folding patterns on brain lobes and the relationship between fiber density and gyral folding patterns are further investigated results from the schizophrenia dataset are consistent with commonly found abnormality in former studies by others which demonstrates the potential clinical applications of the proposed technique

rism single modal image registration via rank induced similarity measure similarity measure is an important block in image registration most traditional intensity based similarity measures e g sum of squared difference correlation coefficient and mutual information assume a stationary image and pixel by pixel independence these similarity measures ignore the correlation between pixel intensities hence perfect image registration cannot be achieved especially in the presence of spatially varying intensity distortions here we assume that spatially varying intensity distortion such as bias field is a low rank matrix based on this assumption we formulate the image registration problem as a nonlinear and low rank matrix decomposition nllrmd therefore image registration and correction of spatially varying intensity distortion are simultaneously achieved we illustrate the uniqueness of nllrmd and therefore we propose the rank of difference image as a robust similarity in the presence of spatially varying intensity distortion finally by incorporating the gaussian noise we introduce rank induced similarity measure based on the singular values of the difference image this measure produces clinically acceptable registration results on both simulated and real world problems examined in this paper and outperforms other state of the art measures such as the residual complexity approach

adaptive fuzzy segmentation of magnetic resonance images an algorithm is presented for the fuzzy segmentation of two dimensional 2 d and three dimensional 3 d multispectral magnetic resonance mr images that have been corrupted by intensity inhomogeneities also known as shading artifacts the algorithm is an extension of the 2 d adaptive fuzzy c means algorithm 2 d afcm presented in previous work by the authors this algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space it iteratively adapts to the intensity inhomogeneities and is completely automated in this paper the authors fully generalize 2 d afcm to three dimensional 3 d multispectral images because of the potential size of 3 d image data they also describe a new faster multigrid based algorithm for its implementation they show using simulated mr data that 3 d afcm yields lower error rates than both the standard fuzzy c means fcm algorithm and two other competing methods when segmenting corrupted images its efficacy is further demonstrated using real 3 d scalar and multispectral mr brain images

orthogonal moment features for use with parametric and non parametric classifiers this research examines a variety of approaches for using two dimensional orthogonal polynomials for the recognition of handwritten arabic numerals it also makes use of parametric and non parametric statistical and neural network classifiers polynomials including legendre zernike and pseudo zernike are used to generate moment based features which are invariant to location size and optionally rotation an efficient method for computing the moments via geometric moments is presented a side effect of this method also yields scale invariance a new approach to location invariance using a minimum bounding circle is presented and a detailed analysis of the rotational properties of the moments is given data partitioning tests are performed to evaluate the various feature types and classifiers for rotational invariant character recognition the highest percentage of correctly classified characters was 91 7 and for non rotational invariant recognition it was 97 6 this compares with a previous effort using the same data and test conditions of 94 8 the techniques developed here should also be applicable to other areas of shape recognition

intermediate templates guided groupwise registration of diffusion tensor images registration of a population of diffusion tensor images dtis is one of the key steps in medical image analysis and it plays an important role in the statistical analysis of white matter related neurological diseases however pairwise registration with respect to a pre selected template may not give precise results if the selected template deviates significantly from the distribution of images to cater for more accurate and consistent registration a novel framework is proposed for groupwise registration with the guidance from one or more intermediate templates determined from the population of images specifically we first use a euclidean distance defined as a combinative measure based on the fa map and adc map for gauging the similarity of each pair of dtis a fully connected graph is then built with each node denoting an image and each edge denoting the distance between a pair of images the root template image is determined automatically as the image with the overall shortest path length to all other images on the minimum spanning tree mst of the graph finally a sequence of registration steps is applied to progressively warping each image towards the root template image with the help of intermediate templates distributed along its path to the root node on the mst extensive experimental results using diffusion tensor images of real subjects indicate that registration accuracy and fiber tract alignment are significantly improved compared with the direct registration from each image to the root template image

existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions abstract in this work we establish several results about the existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions we assume that the linear part generates a strongly continuous semigroup on a general banach space

vertex operators in solvable lattice models the basic properties of q vertex operators are formulated in the context of the andrews baxter forrester abf series as an example of face interaction models the q difference equations satisfied by their correlation functions are derived and their connection with representation theory established the q difference equations of the kashiwara miwa km series are discussed as an example of edge interaction models next the ising model the simplest special case of both abf and km series is studied in more detail using the jordan wigner fermions in particular all matrix elements of vertex operators are calculated

the elliptic algebra and the deformation of wn algebra after reviewing the recent results on the drinfeld realization of the face type elliptic quantum group b q sl n by the elliptic algebra u q p sl n we investigate a fusion of the vertex operators of u q p sl n the basic generating functions j z 1 j n 1 of the deformed w n algebra are derived explicitly

morphological appearance manifolds in computational anatomy groupwise registration and morphological analysis abstract existing approaches to computational anatomy assume that a perfectly conforming diffeomorphism applied to an anatomy of interest captures its morphological characteristics relative to a template however the amount of biological variability in a groupwise analysis renders this task practically impossible due to the nonexistence of a single template that matches all anatomies in an ensemble even if such a template is constructed by group averaging procedures consequently anatomical characteristics not captured by the transformation and which are left out in the residual image are lost permanently from subsequent analysis if only properties of the transformation are examined this paper extends our recent work makrogiannis s verma r davatzikos c 2007 anatomical equivalence class a computational anatomy framework using a lossless shape descriptor ieee trans biomed imag 26 4 619 631 on characterizing subtle morphological variations via a lossless morphological descriptor that takes the residual into account along with the transformation since there are infinitely many transformation residual pairs that reconstruct a given anatomy we treat them as members of an anatomical equivalence class aec thereby forming a manifold embedded in the space spanned by transformation residual this paper develops a unique and optimal representation of each anatomy that is estimated from the corresponding aecs by solving a global optimization problem this effectively determines the optimal template and transformation parameters for each individual anatomy and eliminates respective confounding variation in the data it therefore constitutes the second novelty in that it represents a group wise optimal registration strategy that individually adjusts the template and the smoothness of the transformation according to each anatomy experimental results support the superiority of our morphological analysis framework over conventional analysis and demonstrate better diagnostic accuracy