multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

nonrigid coregistration of diffusion tensor images using a viscous fluid model and mutual information in this paper a nonrigid coregistration algorithm based on a viscous fluid model is proposed that has been optimized for diffusion tensor images dti in which image correspondence is measured by the mutual information criterion several coregistration strategies are introduced and evaluated both on simulated data and on brain intersubject dti data two tensor reorientation methods have been incorporated and quantitatively evaluated simulation as well as experimental results show that the proposed viscous fluid model can provide a high coregistration accuracy although the tensor reorientation was observed to be highly sensitive to the local deformation field nevertheless this coregistration method has demonstrated to significantly improve spatial alignment compared to affine image matching

multiplicity of positive solutions for the kirchhoff type equations with critical exponent in rn abstract in this work we study the existence and multiplicity of solutions to the following kirchhoff type problem with critical nonlinearity in r n a b r n u p d x p u u p 1 f x u x r n u d 1 p r n where n 2 p a b 0 and the nonlinearity f x u satisfies certain subcritical growth conditions by using topological and variational methods infinitely many positive solutions are obtained

ground state of kirchhoff type fractional schrodinger equations with critical growth abstract in this paper we study the critical kirchhoff type fractional schrodinger equation 0 1 1 r 3 r 3 u x u y 2 x y 3 2 s d x d y s u u f u u 2 s 1 in r 3 where s 0 1 and 2 s 6 3 2 s we establish the pohoz ev type identity of 0 1 when s 3 4 1 under some conditions on and f u we obtain some results on the existence of ground state solutions when s 0 3 4 we also prove the non existence result in particular when 0 we obtain an existence result

a multiplicity result for a nonlinear fractional schrodinger equation in rn without the ambrosetti rabinowitz condition abstract in this paper we study the existence and the multiplicity of positive solutions for the following class of fractional schrodinger equations 2 s s u v x u f u in r n where 0 is a parameter s 0 1 n 2 s v r n r is a continuous positive potential and f r r is a c 1 superlinear nonlinearity which does not satisfy the ambrosetti rabinowitz condition the main result is established by using minimax methods and ljusternik schnirelmann theory of critical points

co registration of white matter tractographies by adaptive mean shift and gaussian mixture modeling in this paper we present a robust approach to the registration of white matter tractographies extracted from diffusion tensor magnetic resonance imaging scans the fibers are projected into a high dimensional feature space based on the sequence of their 3 d coordinates adaptive mean shift clustering is applied to extract a compact set of representative fiber modes fm each fm is assigned to a multivariate gaussian distribution according to its population thereby leading to a gaussian mixture model gmm representation for the entire set of fibers the registration between two fiber sets is treated as the alignment of two gmms and is performed by maximizing their correlation ratio a nine parameters affine transform is recovered and eventually refined to a twelve parameters affine transform using an innovative mean shift based registration refinement scheme presented in this paper the validation of the algorithm on synthetic intrasubject data demonstrates its robustness to interrupted and deviating fiber artifacts as well as outliers using real intrasubject data a comparison is conducted to other intensity based and fiber based registration algorithms demonstrating competitive results an option for tracking in time on specific white matter fiber tracts is also demonstrated on the real data

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

ground state sign changing solutions for fractional kirchhoff equations in bounded domains we study the existence of ground state sign changing solutions for the fractional kirchhoff problem under mild assumptions on the nonlinearity by using some new analytical skills and the non nehari manifold method we prove that the fractional kirchhoff problem possesses a ground state sign changing solution ub moreover we show that the energy of ub is strictly larger than twice that of the ground state solutions of nehari type finally we establish the convergence property of ub as the parameter b 0 our results generalize some results obtained by shuai j differ equations 259 1256 2015 and tang and cheng j differ equations 261 2384 2016

on a fractional schrodinger equation with periodic potential abstract in this paper we first consider the spectrum of the fractional schrodinger operator s v x on r n where s 0 1 and v x be continuous periodic in x using a new nonlocal normal derivative we prove that the operator has purely continuous spectrum which is bounded below and consists of closed disjoint intervals then when 0 belongs to a spectral gap of s v x we establish an existence result for the fractional schrodinger equation via a new linking theorem it is worth to mention that the nonlinear term in our problem does not satisfy the periodicity and the existence result is even new for the case s 1

a concave convex elliptic problem involving the fractional laplacian we study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the laplacian operator together with a concave convex term we completely characterize the range of parameters for which solutions of the problem exist and prove a multiplicity result we also prove an associated trace inequality and some liouville type results

controllability of impulsive neutral stochastic functional differential inclusions with infinite delay this paper deals with the controllability of a class of impulsive neutral stochastic functional differential inclusions with infinite delay in an abstract space sufficient conditions for the controllability are derived with the help of the fixed point theorem for discontinuous multi valued operators due to dhage an example is provided to illustrate the obtained theory

iterative learning control of inhomogeneous distributed parameter systems frequency domain design and analysis abstract this paper aims to construct a design and analysis framework for iterative learning control of linear inhomogeneous distributed parameter systems lidpss which may be hyperbolic parabolic or elliptic and include many important physical processes such as diffusion vibration heat conduction and wave propagation as special cases owing to the system model characteristics lidpss are first reformulated into a matrix form in the laplace transform domain then through the determination of a fundamental matrix the transfer function of lidps is precisely evaluated in a closed form the derived transfer function provides the direct input output relationship of the lidps and thus facilitates the consequent ilc design and convergence analysis in the frequency domain the proposed control design scheme is able to deal with parametric and non parametric uncertainties and make full use of the process repetition while avoid any simplification or discretization for the 3d dynamics of lidps in the time space and iteration domains in the end two illustrative processes are addressed to demonstrate the efficacy of the proposed iterative learning control scheme

a survey on iterative learning control for nonlinear systems in this article we review the recent advances in iterative learning control ilc for nonlinear dynamic systems in the research field of ilc two categories of system nonlinearities are considered namely the global lipschitz continuous glc functions and local lipschitz continuous llc functions ilc for glc systems is widely studied and analysed using contraction mapping approach and the focus of recent exploration moves to application problems though a number of theoretical issues remain open ilc for llc systems is currently a hot area and the recent research focuses on ilc design and analysis by means of lyapunov approach the objectives of this article are to introduce recent development and advances in nonlinear ilc schemes highlight their effectiveness and limitations as well as discuss the directions for further exploration of nonlinear ilc

ground state solutions of asymptotically linear fractional schrodinger equations this paper is devoted to a time independent fractional schrodinger equation of the form su v x u f x u inrn where n 2 s 0 1 s stands for the fractional laplacian we apply the variational methods to obtain the existence of ground state solutions when f x u is asymptotically linear with respect to u at infinity

stationary kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity this paper deals with the existence and the asymptotic behavior of non negative solutions for a class of stationary kirchhoff problems driven by a fractional integro differential operator lk and involving a critical nonlinearity in particular we consider the problem m u 2 lku f x u u 2s 2uin u 0in rn where rn is a bounded domain 2s is the critical exponent of the fractional sobolev space hs rn the function f is a subcritical term and is a positive parameter the main feature as well as the main difficulty of the analysis is the fact that the kirchhoff function m could be zero at zero that is the problem is degenerate the adopted techniques are variational and the main theorems extend in several directions previous results recently appeared in the literature

multiplicity results for the non homogeneous fractional p kirchhoff equations with concave convex nonlinearities in this paper we are interested in the multiplicity of solutions for a non homogeneous p kirchhoff type problem driven by a non local integro differential operator as a particular case we deal with the following elliptic problem of kirchhoff type with convex concave nonlinearities a b r 2 n u x u y p x y n s p d x d y 1 p s u 1 x u q 2 u 2 x u r 2 u h x in r n where p s is the fractional p laplace operator a b 0 with a b r 0 0 is a real parameter 0 s 1 p with sp r n under some suitable conditions we obtain the existence of two non trivial entire solutions by applying the mountain pass theorem and ekeland s variational principle a distinguished feature of this paper is that a may be zero which means that the above mentioned problem is degenerate to the best of our knowledge our results are new even in the laplacian case

registration of 4d cardiac ct sequences under trajectory constraints with multichannel diffeomorphic demons we propose a framework for the nonlinear spatiotemporal registration of 4d time series of images based on the diffeomorphic demons dd algorithm in this framework the 4d spatiotemporal registration is decoupled into a 4d temporal registration defined as mapping physiological states and a 4d spatial registration defined as mapping trajectories of physical points our contribution focuses more specifically on the 4d spatial registration that should be consistent over time as opposed to 3d registration that solely aims at mapping homologous points at a given time point first we estimate in each sequence the motion displacement field which is a dense representation of the point trajectories we want to register then we perform simultaneously 3d registrations of corresponding time points with the constraints to map the same physical points over time called the trajectory constraints under these constraints we show that the 4d spatial registration can be formulated as a multichannel registration of 3d images to solve it we propose a novel version of the diffeomorphic demons dd algorithm extended to vector valued 3d images the multichannel diffeomorphic demons mdd for evaluation this framework is applied to the registration of 4d cardiac computed tomography ct sequences and compared to other standard methods with real patient data and synthetic data simulated from a physiologically realistic electromechanical cardiac model results show that the trajectory constraints act as a temporal regularization consistent with motion whereas the multichannel registration acts as a spatial regularization finally using these trajectory constraints with multichannel registration yields the best compromise between registration accuracy temporal and spatial smoothness and computation times a prospective example of application is also presented with the spatiotemporal registration of 4d cardiac ct sequences of the same patient before and after radiofrequency ablation rfa in case of atrial fibrillation af the intersequence spatial transformations over a cardiac cycle allow to analyze and quantify the regression of left ventricular hypertrophy and its impact on the cardiac function

on the ground states and dynamics of space fractional nonlinear schrodinger gross pitaevskii equations with rotation term and nonlocal nonlinear interactions in this paper we propose some efficient and robust numerical methods to compute the ground states and dynamics of fractional schrodinger equation fse with a rotation term and nonlocal nonlinear interactions in particular a newly developed gaussian sum gausum solver is used for the nonlocal interaction evaluation 31 to compute the ground states we integrate the preconditioned krylov subspace pseudo spectral method 4 and the gausum solver for the dynamics simulation using the rotating lagrangian coordinates transform 14 we first reformulate the fse into a new equation without rotation then a time splitting pseudo spectral scheme incorporated with the gausum solver is proposed to simulate the new fse in parallel to the numerical schemes we also prove some existence and nonexistence results for the ground states dynamical laws of some standard quantities including the mass energy angular momentum and the center of mass are stated the ground states properties with respect to the fractional order and or rotating frequencies dynamics involving decoherence and turbulence together with some interesting phenomena are reported

the sign changing solutions for a class of p laplacian kirchhoff type problem in bounded domains abstract in this paper we study the existence of sign changing ground state solutions and properties of such solutions for a class of p laplacian kirchhoff type problem since the appearance of the p laplacian kirchhoff term the problem becomes more complex than kirchhoff type problem for the purpose of overcoming the difficulty we use a quantitative deformation lemma degree theory non nehari manifold method and some mathematical skills to obtain a ground state sign changing solution u b and prove that its energy is strictly larger than twice that of the ground state solutions of nehari type moreover we also obtain the convergence property of u b as the parameter b 0

an alternating direction implicit scheme of a fractional order diffusion tensor image registration model abstract in this paper we propose an alternating direction implicit adi scheme of a fractional order diffusion tensor image dti registration model furthermore compatibility stability and convergence of adi scheme are proved moreover five numerical tests are also performed to show the efficiency of this scheme

existence and symmetry of solutions for critical fractional schrodinger equations with bounded potentials abstract this paper is concerned with the following fractional schrodinger equations involving critical exponents u v x u k x f u u 2 2 u in r n where is the fractional laplacian operator with 0 1 n 2 is a positive real parameter and 2 2 n n 2 is the critical sobolev exponent v x and k x are positive and bounded functions satisfying some extra hypotheses based on the principle of concentration compactness in the fractional sobolev space and the minimax arguments we obtain the existence of a nontrivial radially symmetric weak solution for the above mentioned equations without assuming the ambrosetti rabinowitz condition on the subcritical nonlinearity

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

nonlocal kirchhoff problems extinction and non extinction of solutions abstract in this paper we discuss the extinction and non extinction properties of solutions for the following fractional p kirchhoff problem u t m u s p p p s u u r 2 u u q 2 u x t 0 u 0 x t r n 0 u x 0 u 0 x x where u s p is the gagliardo seminorm of u r n is a bounded domain with lipschitz boundary p s is the fractional p laplacian with 0 s 1 p 2 m 0 0 is a continuous function 1 q 2 r 1 and 0 under suitable assumptions we obtain the extinction of solutions to get more precisely decay estimates of solutions we develop the gagliardo nirenberg inequality moreover the non extinction property of solutions is also investigated

applying the random variable transformation method to solve a class of random linear differential equation with discrete delay abstract we randomize the following class of linear differential equations with delay x t a x t b x t t 0 and initial condition x t g t t 0 by assuming that coefficients a and b are random variables and the initial condition g t is a stochastic process we consider two cases depending on the functional form of the stochastic process g t and then we solve from a probabilistic point of view both random initial value problems by determining explicit expressions to the first probability density function f x t of the corresponding solution stochastic processes afterwards we establish sufficient conditions on the involved random input parameters in order to guarantee that f x t converges as 0 to the first probability density function say f x t of the corresponding associated random linear problem without delay 0 the paper concludes with several numerical experiments illustrating our theoretical findings

on some critical problems for the fractional laplacian operator abstract we study the effect of lower order perturbations in the existence of positive solutions to the following critical elliptic problem involving the fractional laplacian 2 u u q u n n u 0 in u 0 on where r n is a smooth bounded domain n 1 0 0 q n n 0 min n 2 for suitable conditions on depending on q we prove in the case q 1 there exist at least two solutions for every 0 and some 0 at least one if no solution if for q 1 we show existence of at least one solution for 0 1 and nonexistence for 1 when q 1 the existence is shown for every 0 also we prove that the solutions are bounded and regular

symmetric diffeomorphic registration of fibre orientation distributions registration of diffusion weighted images is an important step in comparing white matter fibre bundles across subjects or in the same subject at different time points using diffusion weighted imaging spherical deconvolution enables multiple fibre populations within a voxel to be resolved by computing the fibre orientation distribution fod in this paper we present a novel method that employs fods for the registration of diffusion weighted images registration was performed by optimising a symmetric diffeomorphic non linear transformation model using image metrics based on the mean squared difference and cross correlation of the fod spherical harmonic coefficients the proposed method was validated by recovering known displacement fields using fods represented with maximum harmonic degrees l max of 2 4 and 6 results demonstrate a benefit in using fods at l max 4 compared to l max 2 however a decrease in registration accuracy was observed when l max 6 was used this was likely caused by noise in higher harmonic degrees we compared our proposed method to fractional anisotropy driven registration using an identical code base and parameters fod registration was observed to perform significantly better than fa in all experiments the cross correlation metric performed significantly better than the mean squared difference finally we demonstrated the utility of this method by computing an unbiased group average fod template that was used for probabilistic fibre tractography this work suggests that using crossing fibre information aids in the alignment of white matter and could therefore benefit several methods for investigating population differences in white matter including voxel based analysis tensor based morphometry atlas based segmentation and labelling and group average fibre tractography

brief paper iterative learning control for uncertain systems robust monotonic convergence analysis in this paper we present a novel robust monotonic convergence rmc analysis approach for finite time interval iterative learning control ilc for uncertain systems for that purpose a finite time interval model for uncertain systems is introduced this model is subsequently used in an rmc analysis based on m analysis as a result we can handle additive and multiplicative uncertainty models in the rmc problem formulation analyze rmc of linear time invariant mimo systems controlled by any linear trial invariant ilc controller and formulate additional straightforward rmc conditions for ilc controlled systems to illustrate the derived results we analyze the rmc properties of linear quadratic lq norm optimal ilc

existence of solutions for a bi nonlocal fractional p kirchhoff type problem in this paper we are concerned with the existence of nonnegative solutions for a p kirchhoff type problem driven by a non local integro differential operator with homogeneous dirichlet boundary data as a particular case we study the following problem m x u s p p p s u f x u u s p p in u 0 in r n u s p p r 2 n u x u y p x y n p s d x d y where p s is a fractional p laplace operator is an open bounded subset of r n with lipschitz boundary m r 0 r is a continuous function and f r r 0 r is a continuous function satisfying the ambrosetti rabinowitz type condition the existence of nonnegative solutions is obtained by using the mountain pass theorem and an iterative scheme the main feature of this paper lies in the fact that the kirchhoff function m depends on x and the nonlinearity f depends on the energy of solutions

on the fractional schrodinger kirchhoff equations with electromagnetic fields and critical nonlinearity abstract in this paper we consider the fractional schrodinger kirchhoff equations with electromagnetic fields and critical nonlinearity e 2 s m u s a e 2 a e s u v x u u 2 s 2 u h x u 2 u x r n u x 0 as x where a e s is the fractional magnetic operator with 0 s 1 2 s 2 n n 2 s m r 0 r is a continuous nondecreasing function v r n r 0 and a r n r n are the electric and magnetic potentials respectively by using the fractional version of the concentration compactness principle and variational methods we show that the above problem i has at least one solution provided that e e and ii for any m n has m pairs of solutions if e e m where e and e m are sufficiently small positive numbers moreover these solutions u e 0 as e 0

sign changing solutions for a fractional kirchhoff equation abstract using a minimization argument and a quantitative deformation lemma we establish the existence of least energy sign changing solutions for the following nonlinear kirchhoff problem a b u 2 s u v x u k x f u in r 3 where a b 0 are constants s 0 1 s is the fractional laplacian v k are continuous positive functions allowed for vanishing behavior at infinity and f is a continuous function satisfying suitable growth assumptions moreover when the nonlinearity f is odd we obtain the existence of infinitely many nontrivial weak solutions not necessarily nodals

the brezis nirenberg result for the fractional laplacian the aim of this paper is to deal with the non local fractional counterpart of the laplace equation involving critical non linearities studied in the famous paper of brezis and nirenberg 1983 namely our model is the equation su u u 2 2u in u 0 in rn where s is the fractional laplace operator s 0 1 is an open bounded set of rn n 2s with lipschitz boundary 0 is a real parameter and 2 2n n 2s is a fractional critical sobolev exponent in this paper we first study the problem in a general framework indeed we consider the equation lku u u 2 2u f x u 0 in u 0 in rn where lk is a general non local integrodifferential operator of order s and f is a lower order perturbation of the critical power u 2 2u in this setting we prove an existence result through variational techniques then as a concrete example we derive a brezis nirenberg type result for our model equation that is we show that if 1 s is the first eigenvalue of the non local operator s with homogeneous dirichlet boundary datum then for any 0 1 s there exists a non trivial solution of the above model equation provided n 4s in this sense the present work may be seen as the extension of the classical brezis nirenberg result to the case of non local fractional operators

existence and multiplicity of solutions for fractional schrodinger kirchhoff equations with trudinger moser nonlinearity abstract we study the existence and multiplicity of solutions for a class of fractional schrodinger kirchhoff type equations with the trudinger moser nonlinearity more precisely we consider m u n s n s s u v x u n s 1 u f x u h x u p 2 u in r n u r 2 n u x u y n s x y 2 n d x d y r n v x u n s d x s n where m 0 0 is a continuous function s 0 1 n 2 0 is a parameter 1 p n s s is the fractional n s laplacian v r n 0 is a continuous function f r n r r is a continuous function and h r n 0 is a measurable function first using the mountain pass theorem a nonnegative solution is obtained when f satisfies exponential growth conditions and is large enough and we prove that the solution converges to zero in w v s n s r n as then using the ekeland variational principle a nonnegative nontrivial solution is obtained when is small enough and we show that the solution converges to zero in w v s n s r n as 0 furthermore using the genus theory infinitely many solutions are obtained when m is a special function and is small enough we note that our paper covers a novel feature of kirchhoff problems that is the kirchhoff function m 0 0

a critical nonlinear fractional elliptic equation with saddle like potential in ℝn in this paper we study the existence of positive solution for the following class of fractional elliptic equation 2s su v z u uq 2u u2s 2uinrn where 0 are positive parameters q 2 2s 2s 2nn 2s n 2s s 0 1 su is the fractional laplacian and v is a saddle like potential the result is proved by using minimizing method constrained to the nehari manifold a special minimax level is obtained by using an argument made by benci and cerami

unified bundling and registration of brain white matter fibers magnetic resonance diffusion tensor imaging is being widely used to reconstruct brain white matter fiber tracts to characterize structural properties of the tracts reconstructed fibers are often grouped into bundles that correspond to coherent anatomic structures for further group analysis of fiber bundles it is desirable that corresponding bundles from different studies are coregistered to address these needs simultaneously a unified fiber bundling and registration ufibre framework is proposed in this work the framework is based on maximizing a posteriori bayesian probabilities using an expectation maximization algorithm given a set of segmented template bundles and a whole brain target fiber set the ufibre algorithm optimally bundles the target fibers and registers them with the template the bundling component in the ufibre algorithm simplifies fiber based registration into bundle to bundle registration and the registration component in turn guides the bundling process to find bundles consistent with the template experiments with in vivo data demonstrate that the estimated bundles have an 80 consistency with ground truth and the root mean square error between their bundle medial axes is less than one voxel the proposed algorithm is highly efficient offering potential routine use for group analysis of white matter fibers

approximate solution of the backward problem for kirchhoff s model of parabolic type with discrete random noise abstract in this paper we consider the final boundary value problem for non local kirchhoff s model of parabolic type with discrete random noise we first discuss the instability of solutions then we present the regularized solution by the trigonometric method in non parametric regression associated with the truncated expansion method in addition under a prior assumption on the exact solution the convergence rate is obtained in the last section the effectiveness and suitability of our results are justified via numerical experiments

spatial normalization and averaging of diffusion tensor mri data sets diffusion tensor magnetic resonance imaging dt mri is unique in providing information about both the structural integrity and the orientation of white matter fibers in vivo and through tractography revealing the trajectories of white matter tracts dt mri is therefore a promising technique for detecting differences in white matter architecture between different subject populations however while studies involving analyses of group averages of scalar quantities derived from dt mri data have been performed as yet there have been no similar studies involving the whole tensor here we present the first step towards realizing such a study i e the spatial normalization of whole tensor data sets the approach is illustrated by spatial normalization of 10 dt mri data sets to a standard anatomical template both qualitative and quantitative approaches are described for assessing the results of spatial normalization techniques are then described for combining the spatially normalized data sets according to three definitions of average i e the mean median and mode of a distribution of tensors the current absence of and hence need for appropriate statistical tests for comparison of results derived from group averaged dt mri data sets is then discussed finally the feasibility of performing tractography on the group averaged dt mri data set is investigated and the possibility and implications of generating a generic map of brain connectivity from a group of subjects is considered

existence and concentration result for the kirchhoff type equations with general nonlinearities in this paper we study the existence and concentration behaviors of positive solutions to the kirchhoff type equations varepsilon 2 m left varepsilon 2 n int mathbf r n nabla u 2 mathrm d x right delta u v x u f u quad rm in mathbf r n quad u in h 1 mathbf r n n geqq 1 where m and v are continuous functions under suitable conditions on m and general conditions on f we construct a family of positive solutions u varepsilon varepsilon in 0 tilde varepsilon which concentrates at a local minimum of v after extracting a subsequence ek

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

controllability of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in this work the controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in a banach space has been established by using the theory of fractional calculus fixed point technique and also we introduced a new concept called a u resolvent family as an application that illustrates the abstract results an example is given

eigenvalue problems with unbalanced growth nonlinear patterns and standing wave solutions abstract we consider two classes of nonlinear eigenvalue problems with double phase energy and lack of compactness we establish existence and non existence results and related properties of solutions our analysis combines variational methods with the generalized pucci serrin maximum principle

on fractional schrodinger equation in rn with critical growth in this paper we study the following nonlinear fractional schrodinger equation with critical exponent h2 u v x u u 2 2u u q 2u x rn where h is a small positive parameter 0 2 0 is a parameter the potential v rn r is a positive continuous function satisfying some natural assumptions by using variational methods we obtain the existence of solutions in the following case if 2 0 such that for all 0 we show that it has one nontrivial solution and there exist at least cat nontrivial solutions if max 2 4 n 2 0

existence and multiplicity of solutions for critical kirchhoff type p laplacian problems abstract in this paper we deal with the existence multiplicity and asymptotic behavior of solutions for the following stationary kirchhoff problems involving the p laplacian m u p d x p u f x u u p 2 u in u 0 on where is a bounded smooth domain of r n m r 0 r 0 is a continuous function satisfying some extra assumptions by using the mountain pass theorem the existence of solutions is obtained by applying an abstract critical point theorem based on the cohomological index we prove the existence of multiple solutions for the above problem when parameter belongs to some left neighborhood of the eigenvalue of the nonlinear operator u 1 p p where p n p p we also investigate the asymptotic behavior of solutions when converges to infinity the main feature as well as the main difficulty of our problem is the fact that the kirchhoff term m could be zero at zero i e the problem is degenerate

existence of a positive solution for a kirchhoff problem type with critical growth via truncation argument abstract in this paper we shall show an existence result of a positive solution for a kirchhoff problem type in a bounded domain of r n that is for the problem m u 2 d x u f x u u 2 2 u in u 0 on we shall study the asymptotic behavior of this solution when converges to infinity our approach is based on the variational method an appropriated truncated argument and a priori estimates to obtain the solution

critical fractional p kirchhoff type problem with a generalized choquard nonlinearity in this article based on the concentration compactness principle and the mountain pass theorem we establish the existence of positive solutions to the fractional p kirchhoff type problem with a generalized choquard nonlinearity and a critical hardy sobolev term

fractional schrodinger equation some properties of the fractional schrodinger equation are studied we prove the hermiticity of the fractional hamilton operator and establish the parity conservation law for fractional quantum mechanics as physical applications of the fractional schrodinger equation we find the energy spectra of a hydrogenlike atom fractional bohr atom and of a fractional oscillator in the semiclassical approximation an equation for the fractional probability current density is developed and discussed we also discuss the relationships between the fractional and standard schrodinger equations

critical fractional p laplacian problems with possibly vanishing potentials abstract we obtain nontrivial solutions of a critical fractional p laplacian equation in the whole space and with possibly vanishing potentials in addition to the usual difficulty of the lack of compactness associated with problems involving critical sobolev exponents the problem is further complicated by the absence of a direct sum decomposition suitable for applying classical linking arguments we overcome this difficulty using a generalized linking construction based on the z 2 cohomological index

a class of boundary value problems for first order impulsive integro differential equations with deviating arguments this paper is concerned with a class of boundary value problems for nonlinear mixed impulsive integro differential equations with deviating arguments we establish a new comparison principle and use the method of upper and lower solutions together with the monotone iterative technique under suitable conditions we obtain the existence results of extremal solutions for the problems an example is also given to illustrate our results

existence of ground state solutions for the nonlinear fractional schrodinger poisson system with critical sobolev exponent abstract in this paper we study the existence of ground state solutions for the nonlinear fractional schrodinger poisson system with critical sobolev exponent s u v x u u u q 1 u u 2 s 2 u in r 3 t u 2 in r 3 where r is a parameter 1 q 2 s 1 3 2 s 3 2 s s t 0 1 and 2 s 2 t 3 under certain assumptions on v x using the method of pohozaev nehari manifold and the arguments of brezis nirenberg the monotonic trick and global compactness lemma we prove the existence of a nontrivial ground state solution

global nonexistence for nonlinear kirchhoff systems in this paper we consider the problem of non continuation of solutions of dissipative nonlinear kirchhoff systems involving the p x laplacian operator and governed by nonlinear driving forces f f t x u as well as nonlinear external damping terms q q t x u u t both of which could significantly dependent on the time t the theorems are obtained through the study of the natural energy eu associated to the solutions u of the systems thanks to a new approach of the classical potential well and concavity methods we show the nonexistence of global solutions when the initial energy is controlled above by a critical value that is when the initial data belong to a specific region in the phase plane several consequences interesting in applications are given in particular subcases the results are original also for the scalar standard wave equation when p 2 and even for problems linearly damped

global nonexistence for abstract evolution equations with positive initial energy abstract in this paper we consider the problem of noncontinuation of solutions of the initial value problem for abstract evolution equations of the form pu tt q t u t a t u f t u t j 0 wherepandqare linear self adjoint operators anda t u andf t u are respectively a linear operator inu typically of differential type and a nonlinear driving force our principal concern is the noncontinuation or blow up of solutions when the initial energy is positive but appropriately bounded

iterative learning control with initial state learning for fractional order nonlinear systems this paper presents a p type iterative learning control ilc scheme with initial state learning for a class of a 0 a 1 fractional order nonlinear systems by introducing the l norm and using a generalized gronwall inequality the sufficient condition for the robust convergence of the tracking errors with respect to initial positioning errors under p type ilc is obtained based on this convergence condition the learning gain of the initial learning and input learning updating law can be determined unlike the existing methods the ilc scheme will not fix the initial value on the expected condition at the beginning of each iteration finally the validity of the methods are verified by a numerical example

on a critical kirchhoff type problem abstract in the present paper we study a kirchhoff type problem involving the critical sobolev exponent we give sufficient conditions for the sequentially weakly lower semicontinuity and the palais smale property of the energy functional associated to the problem

on the boundary strichartz estimates for wave and schrodinger equations abstract we consider the l t 2 l x r estimates for the solutions to the wave and schrodinger equations in high dimensions for the homogeneous estimates we show l t 2 l x estimates fail at the critical regularity in high dimensions by using stable levy process in r d moreover we show that some spherically averaged l t 2 l x estimate holds at the critical regularity as a by product we obtain strichartz estimates with angular smoothing effect for the inhomogeneous estimates we prove double l t 2 type estimates

best constants for sobolev inequalities for higher order fractional derivatives we obtain sharp constants for sobolev inequalities for higher order fractional derivatives as an application we give a new proof of a theorem of w beckner concerning conformally invariant higher order differential operators on the sphere

an iterative learning control approach for linear systems with randomly varying trial lengths this technical note addresses an iterative learning control ilc design problem for discrete time linear systems where the trial lengths could be randomly varying in the iteration domain an ilc scheme with an iteration average operator is introduced for tracking tasks with non uniform trial lengths which thus mitigates the requirement on classic ilc that all trial lengths must be identical in addition the identical initialization condition can be absolutely removed the learning convergence condition of ilc in mathematical expectation is derived through rigorous analysis as a result the proposed ilc scheme is applicable to more practical systems in the end two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ilc scheme for both time invariant and time varying linear systems

an average operator based pd type iterative learning control for variable initial state error this note studies the effect of variable initial state error in iterative learning control ilc systems and proposes a new ilc algorithm based on an average operator then it is shown that when the proposed algorithm is applied to linear time invariant lti systems the effect of the initial state error can be exactly estimated under a specific condition while the existing algorithms guarantee only the boundness of the error or the convergence from stochastic point of view to show the validity of the proposed algorithm a numerical example is given

a critical kirchhoff type problem involving a nonlocal operator abstract in this paper we show the existence of non negative solutions for a kirchhoff type problem driven by a nonlocal integrodifferential operator that is m u z 2 l k u f x u u 2 2 u in u 0 in r n where l k is an integrodifferential operator with kernel k is a bounded subset of r n m and f are continuous functions z is a functional norm and 2 is a fractional sobolev exponent

higher nonlocal problems with bounded potential abstract the aim of this paper is to study a class of nonlocal fractional laplacian equations depending on two real parameters more precisely by using an appropriate analytical context on fractional sobolev spaces due to servadei and valdinoci we establish the existence of three weak solutions for nonlocal fractional problems exploiting an abstract critical point result for smooth functionals we emphasize that the dependence of the underlying equation from one of the real parameters is not necessarily of affine type

multiple solutions for a fractional p kirchhoff problem with hardy nonlinearity abstract this paper is devoted to study the existence of multiple solutions for the following fractional p kirchhoff problem 0 1 m r 2 n u x u y p x y n p s d x d y p s u u q 2 u u r 2 u x in u 0 in r n where p s denotes the fractional p laplace operator is a smooth bounded set in r n containing 0 with lipschitz boundary m t a b t 1 with a 0 b 0 1 0 1 q p p r p p n p n p s is the fractional critical hardy sobolev exponent for 0 p s n by using fibering maps and nehari manifold we obtain that the existence of multiple solutions to problem 0 1 for both hardy sobolev subcritical and critical cases in particular the concentration compactness principle will be used to overcome the lack of compactness for the critical case

a large deformation diffeomorphic metric mapping solution for diffusion spectrum imaging datasets spatial transformation for diffusion spectrum imaging dsi is an important step for group analyses of dsi datasets in this study we developed a transformation method for dsi datasets under the framework of large deformation diffeomorphic metric mapping lddmm which is termed lddmm dsi the proposed method made use of the fact that a dsi dataset is 6d and generalized the original 2d 3d lddmm algorithm to the 6d case with some modifications made for the dsi datasets in this manner the conventional reorientation problem that arises from transforming diffusion weighted datasets was avoided by making the dsi datasets capable of being freely deformed in the q space the algorithm treated the data matching task as a variational problem under the lddmm framework and sought optimal velocity fields from which the generated transformations were diffeomorphic and the transformation curve was a geodesic the mathematical materials and numerical implementation are detailed in the paper and experiments were performed to analyze the proposed method on real brain dsi datasets the results showed that the method was capable of registering different dsi datasets in both global structural shapes and local diffusion profiles in conclusion the proposed method can facilitate group analyses of dsi datasets and the generation of a dsi template

multiplicity results for stationary kirchhoff problems involving fractional elliptic operator and critical nonlinearity in rn in this paper we study a class of stationary kirchhoff problems involving a fractional elliptic operator and critical nonlinearity in rn g u s2 su k x u q 2u u 2s 2u by using a fractional version of lions second concentration compactness principle and concentration compactness principle at infinity to prove that the ps c condition holds locally and by minimax methods and krasnoselskii genus theory we establish the multiplicity of solutions for suitable positive parameters

positive solutions of nonlinear problems involving the square root of the laplacian abstract we consider nonlinear elliptic problems involving a nonlocal operator the square root of the laplacian in a bounded domain with zero dirichlet boundary conditions for positive solutions to problems with power nonlinearities we establish existence and regularity results as well as a priori estimates of gidas spruck type in addition among other results we prove a symmetry theorem of gidas ni nirenberg type

exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations this paper is concerned with exponential stability of a class of linear impulsive delay differential equations iddes exponential stability of this kind of equations is studied by the properties of delay differential equations ddes without impulsive perturbations when different delay differential equations ddes without impulsive perturbations are chosen different sufficient conditions for exponential stability of the linear impulsive delay differential equations iddes are provided numerical methods for this kind of equations are constructed the convergence and exponential stability of the numerical solutions are studied and some experiments are given

multiplicity of solutions for p x polyharmonic elliptic kirchhoff equations abstract in this paper we establish the existence of an unbounded sequence of solutions for a class of quasilinear elliptic p x polyharmonic kirchhoff equations including the new delicate degenerate case not yet covered in the literature the main tool is the symmetric mountain pass theorem of ambrosetti and rabinowitz

existence and multiplicity of solutions for superlinear fractional schrodinger equations in ℝn in this paper we are concerned with superlinear fractional schrodinger equation su v x u f x u x n where f is continuous when v and f are asymptotically periodic in x we show the existence of ground states when v and f are periodic in x we obtain infinitely many geometrically distinct solutions the method used here is based on the method of nehari manifold and lusternik schnirelmann category theory

multiple and nodal solutions for parametric neumann problems with nonhomogeneous differential operator and critical growth abstract we consider a parametric neumann problem with nonhomogeneous differential operator and critical growth combining variational methods based on critical point theory with suitable truncation techniques and flow invariance arguments we show that for all large the problem has at least three nontrivial smooth solutions two of constant sign one positive the other negative and the third nodal we also study the asymptotic behavior of all solutions obtained when converges to infinity the interesting point is that we do not impose any restrictions to the behavior of the nonlinear term f at infinity our work unifies and sharply improves several recent papers

bound state for the fractional schrodinger equation with unbounded potential this paper considers the fractional schrodinger equation with unbounded potential we prove the existence of ground state by lagrange multiplier method the standing wave with prescribed frequency is also obtained by nehari s manifold approach in the last part we obtain that the standing wave is bound state

on the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths abstract in this paper a new class of stochastic impulsive differential equations involving bernoulli distribution is introduced for tracking the random discontinuous trajectory a modified tracking error associated with a piecewise continuous variable by zero order holder is defined in the sequel a new random ilc scheme by adopting global and local iteration average operators is designed too sufficient conditions to guarantee the convergence of modified tracking error are obtained by using the tools of mathematical analysis via an impulsive gronwall inequality finally two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ilc scheme to track the random discontinuous trajectory

a local fast marching based diffusion tensor image registration algorithm by simultaneously considering spatial deformation and tensor orientation it is a key step to spatially align diffusion tensor images dti to quantitatively compare neural images obtained from different subjects or the same subject at different timepoints different from traditional scalar or multi channel image registration methods tensor orientation should be considered in dti registration recently several dti registration methods have been proposed in the literature but deformation fields are purely dependent on the tensor features not the whole tensor information other methods such as the piece wise affine transformation and the diffeomorphic non linear registration algorithms use analytical gradients of the registration objective functions by simultaneously considering the reorientation and deformation of tensors during the registration however only relatively local tensor information such as voxel wise tensor similarity is utilized this paper proposes a new dti image registration algorithm called local fast marching fm based simultaneous registration the algorithm not only considers the orientation of tensors during registration but also utilizes the neighborhood tensor information of each voxel to drive the deformation and such neighborhood tensor information is extracted from a local fast marching algorithm around the voxels of interest these local fast marching based tensor features efficiently reflect the diffusion patterns around each voxel within a spherical neighborhood and can capture relatively distinctive features of the anatomical structures using simulated and real dti human brain data the experimental results show that the proposed algorithm is more accurate compared with the fa based registration and is more efficient than its counterpart the neighborhood tensor similarity based registration

infinitely many radial and non radial solutions for a fractional schrodinger equation in this paper we study the following fractional schrodinger equation s u v x u f x u x r n where s s 0 1 denotes the fractional laplacian by variational methods we obtain the existence of a sequence of radial solutions for n 2 a sequence of non radial solutions for n 4 or n 6 and a non radial solution for n 5

existence and multiplicity of solutions for a superlinear kirchhoff type equations with critical sobolev exponent in r n abstract in this article we consider a class of superlinear kirchhoff type equations with critical growth a b r n u 2 d x u u 2 1 k x u q 1 x r n u d 1 2 r n where 0 n 4 2 q 2 2 2 n n 2 a b 0 and a b 0 k satisfies some conditions by using the variational method the multiplicity of positive solutions and infinitely many pairs of solutions are obtained

variational methods for multimodal image matching matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations handling complex nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years the thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities e g ssd can be extended to the multimodal case where more complex intensity similarity measures are necessary to this end we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures and use the results to generalize a recently proposed and very effective optical flow algorithm l alvarez j weickert and j sanchez 2000 technical report and ijcv 39 1 41 56 to the case of multimodal image registration our method readily extends to the case of locally computed similarity measures thus providing the flexibility to cope with spatial non stationarities in the way the intensities in the two images are related the well posedness of the resulting equations is proved in a complementary work o d faugeras and g hermosillo 2001 technical report 4235 inria using well established techniques in functional analysis we briefly describe our numerical implementation of these equations and show results on real and synthetic data