a variational method in image recovery this paper is concerned with a classical denoising and deblurring problem in image recovery our approach is based on a variational method by using the legendre fenchel transform we show how the nonquadratic criterion to be minimized can be split into a sequence of half quadratic problems easier to solve numerically first we prove an existence and uniqueness result and then we describe the algorithm for computing the solution and we give a proof of convergence finally we present some experimental results for synthetic and real images

a class of superrigid group von neumann algebras we prove that for any group g in a fairly large class of generalized wreath product groups the associated von neumann algebra lg completely remembers the group g more precisely if lg is isomorphic to the von neumann algebra l of an arbitrary countable group then must be isomorphic to g this represents the rst superrigidity result pertaining to group von neumann algebras

an optimal control approach to the optical flow problem abstract the optical flow problem is reduced to an optimal control problem governed by a linear parabolic equation having the unknown velocity field the optical flow as drift term this model is derived from a new assumption that is the brightness intensity is conserved on a moving pattern driven by a gaussian stochastic process the optimality conditions are deduced by a passage to the limit technique in an approximating optimal control problem introduced for a regularization purpose finally the controller uniqueness is addressed

image sequence interpolation based on optical flow segmentation and optimal control when using motion fields to interpolate between two consecutive images in an image sequence a major problem is to handle occlusions and disclusions properly however in most cases one of both images contains the information that is either discluded or occluded if the first image contains the information i e the region will be occluded forward interpolation shall be employed while for information that is contained in the second image i e the region will be discluded one should use backward interpolation hence we propose to improve an existing approach for image sequence interpolation by incorporating an automatic segmentation in the process which decides in which region of the image forward or backward interpolation shall be used our approach is a combination of the optimal transport approach to image sequence interpolation and the segmentation by the chan vese approach we propose to solve the resulting optimality condition by a segregation loop combined with a level set approach we provide examples that illustrate the performance both in the interpolation error and in the human perception

w superrigidity for group von neumann algebras of left right wreath products we prove that for many nonamenable groups including all hyperbolic groups and all nontrivial free products the left right wreath product groupg z 2z o is w superrigid this means that the group von neumann algebra lg entirely remembers g more precisely if lg is isomorphic with l for an arbitrary countable group then must be isomorphic withg

some prime factorization results for type ii1 factors we prove several unique prime factorization results for tensor products of type ii1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected lie groups of real rank 1 in particular we show that if mathcal r overline otimes mathcal l mathbb f r 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f r m is isomorphic to a subfactor in mathcal r overline otimes mathcal l mathbb f s 1 overline otimes cdot cdot cdot overline otimes mathcal l mathbb f s n for some 2 ri sj then m n

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

slow decay of concentration variance due to no slip walls in chaotic mixing chaotic mixing in a closed vessel is studied experimentally and numerically in different two dimensional 2d flow configurations for a purely hyperbolic phase space it is well known that concentration fluctuations converge to an eigenmode of the advection diffusion operator and decay exponentially with time we illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern we show for different physical viscous flows that in the case of a fully chaotic poincare section parabolic periodic points at the walls lead to slower algebraic decay a persistent pattern the backbone of which is the unstable manifold of parabolic points can be observed however slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain and hence delays the formation of an eigenmode until it is no longer experimentally observable inspired by the baker s map we introduce a 1d model with a parabolic point that gives a good account of the slow decay observed in experiments we derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no slip wall

a globally convergent version of the polak ribiere conjugate gradient method in this paper we propose a new line search algorithm that ensures global convergence of the polak ribiere conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions in particular we show that with this line search every limit point produced by the polak ribiere iteration is a stationary point of the objective function moreover we define adaptive rules for the choice of the parameters in a way that the first stationary point along a search direction can be eventually accepted when the algorithm is converging to a minimum point with positive definite hessian matrix under strong convexity assumptions the known global convergence results can be reobtained as a special case from a computational point of view we may expect that an algorithm incorporating the step size acceptance rules proposed here will retain the same good features of the polak ribiere method while avoiding pathological situations

a nonlinear conjugate gradient method with a strong global convergence property conjugate gradient methods are widely used for unconstrained optimization especially large scale problems the strong wolfe conditions are usually used in the analyses and implementations of conjugate gradient methods this paper presents a new version of the conjugate gradient method which converges globally provided the line search satisfies the standard wolfe conditions the conditions on the objective function are also weak being similar to those required by the zoutendijk condition

partially dissipative 2d boussinesq equations with navier type boundary conditions abstract this paper concerns itself with two systems of the 2d boussinesq equations with partial dissipation in bounded domains with the navier type boundary conditions we attempt to achieve two main goals first to prove the global existence and uniqueness under minimal regularity assumptions on the initial data and second to provide a direct and transparent approach that explicitly reveals the impacts of the navier boundary conditions the 2d boussinesq equations with partial dissipation have attracted considerable interests in the last few years although most of the results are aimed at sufficiently regular solutions in the whole space or periodic domains larios et al 2013 made serious efforts to minimize the regularity assumptions necessary for the uniqueness of solutions in the spatially periodic setting in contrast to the whole space and the periodic domains the navier boundary conditions generate boundary terms and require compatibility conditions in addition due to the lack of boundary conditions for the pressure we resort to the existence and regularity result on the associated stokes problem with navier boundary conditions the uniqueness relies on the yudovich techniques and the introduction of a lower regularity counterpart of the temperature

multigrid methods for pde optimization research on multigrid methods for optimization problems is reviewed optimization problems considered include shape design parameter optimization and optimal control problems governed by partial differential equations of elliptic parabolic and hyperbolic type

nonlinear parabolic flows with dynamic flux on the boundary a nonlinear divergence parabolic equation with dynamic boundary conditions of wentzell type is studied the existence and uniqueness of a strong solution is obtained as the limit of a finite difference scheme in the time dependent case and via a semigroup approach in the time invariant case

a new conjugate gradient method with guaranteed descent and an efficient line search a new nonlinear conjugate gradient method and an associated implementation based on an inexact line search are proposed and analyzed with exact line search our method reduces to a nonlinear version of the hestenes stiefel conjugate gradient scheme for any inexact line search our scheme satisfies the descent condition bf g k sf t bf d k le frac 7 8 bf g k 2 moreover a global convergence result is established when the line search fulfills the wolfe conditions a new line search scheme is developed that is efficient and highly accurate efficiency is achieved by exploiting properties of linear interpolants in a neighborhood of a local minimizer high accuracy is achieved by using a convergence criterion which we call the approximate wolfe conditions obtained by replacing the sufficient decrease criterion in the wolfe conditions with an approximation that can be evaluated with greater precision in a neighborhood of a local minimum than the usual sufficient decrease criterion numerical comparisons are given with both l bfgs and conjugate gradient methods using the unconstrained optimization problems in the cute library

von neumann algebras of equivalence relations with nontrivial one cohomology abstract using popa s deformation rigidity theory we investigate prime decompositions of von neumann algebras of the form l r for countable probability measure preserving equivalence relations r we show that l r is prime whenever r is nonamenable ergodic and admits an unbounded 1 cocycle into a mixing orthogonal representation weakly contained in the regular representation this is accomplished by constructing the gaussian extension r of r and subsequently an s malleable deformation of the inclusion l r l r we go on to note a general obstruction to unique prime factorization and avoiding it we prove a unique prime factorization result for products of the form l r 1 l r 2 l r k as a corollary we get a unique factorization result in the equivalence relation setting for products of the form r 1 r 2 r k we finish with an application to the measure equivalence of groups

a note about wyl s conjugate gradient method and its applications this paper reviews the development of different versions of nonlinear conjugate gradient methods shortly the special attentions were given to the wyl method which was proposed by zengxin wei et al the convergence properties of some conjugate gradient methods applied mathematics and computation 183 2006 1341 1350 and its applications

the proof of the sufficient descent condition of the wei yao liu conjugate gradient method under the strong wolfe powell line search abstract in z wei et al the convergence properties of some conjugate gradient methods appl math comput 183 2006 1341 1350 wei et al proposed a new conjugate gradient method called wyl method which has good numerical experiments under the sufficient descent condition and wwp line search the given method s convergent results have been established by wei et al so the sufficient descent condition is important for the wyl method in this paper we prove that by restricting the parameter 1 4 under the swp line search condition the wyl method possess the sufficient descent condition which deduces the global convergent results of the wyl method under swp line search

orbit equivalence rigidity and bounded cohomology we establish new results and introduce new methods in the theory of measurable orbit equivalence using bounded cohomology of group representations our rigidity statements hold for a wide uncountable class of groups arising from negative curvature geometry amongst our applications are a measurable mostow type rigidity theorems for products of negatively curved groups b prime factorization results for measure equivalence c superrigidity for orbit equivalence d the first examples of continua of type ii1 equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic

simultaneous identification of the spatio temporal dependent heat transfer coefficient and spatially dependent heat flux using an mcgm in a parabolic system abstract this paper aims to simultaneously identify the spatio temporal dependent heat transfer coefficient x t and the spatially dependent heat flux q x in a parabolic system the simultaneous identification problem is formulated as a constrained minimization problem using the output least squares method with tikhonov regularization the differentiability of the solution and adjoint equations are investigated to obtain the gradient formulae and determine the step lengths respectively to illustrate the efficiency accuracy and robustness of the proposed algorithm numerical results are investigated using the modified conjugate gradient method mcgm

a multiscale measure for mixing abstract we present a multiscale measure for mixing that is based on the concept of weak convergence and averages the mixedness of an advected scalar field at various scales this new measure referred to as the mix norm resolves the inability of the l 2 variance of the scalar density field to capture small scale variations when advected by chaotic maps or flows in addition the mix norm succeeds in capturing the efficiency of a mixing protocol in the context of a particular initial scalar field wherein lyapunov exponent based measures fail to do so we relate the mix norm to the classical ergodic theoretic notion of mixing and present its formulation in terms of the power spectrum of the scalar field we demonstrate the utility of the mix norm by showing how it measures the efficiency of mixing due to various discrete dynamical systems and to diffusion in particular we show that the mix norm can capture known exponential and algebraic mixing properties of certain maps we also analyze numerically the behaviour of scalar fields evolved by the standard map using the mix norm

estimation of parameters in two dimensional transport equations a general approximation framework based on bicubic splines is developed for estimating temporally and spatially varying parameters in two dimensional transport equations the parameter estimation problem is first cast as an abstract infinite dimensional minimization problem then a sequence of approximate finite dimensional minimization problems is defined which yields a sequence of parameter estimates since convergence results relating the approximate problems to the full infinite dimensional problem are presented in 6 and 17 this paper will focus only on the computer implementation of our technique and the results of numerical tests using analytically generated data the technique is also applied to the analysis of actual biological data from an insect dispersal experiment in which the movement of cabbage root flies in the presence of a cabbage crop was studied

noise removal using fourth order partial differential equation with applications to medical magnetic resonance images in space and time we introduce a new method for image smoothing based on a fourth order pde model the method is tested on a broad range of real medical magnetic resonance images both in space and time as well as on nonmedical synthesized test images our algorithm demonstrates good noise suppression without destruction of important anatomical or functional detail even at poor signal to noise ratio we have also compared our method with related pde models

optical flow a curve evolution approach a novel approach for the computation of optical flow based on an l sup 1 type minimization is presented it is shown that the approach has inherent advantages since it does not smooth the flow velocity across the edges and hence preserves edge information a numerical approach based on computation of evolving curves is proposed for computing the optical flow field computations are carried out on a number of real image sequences in order to illustrate the theory as well as the numerical approach

a new version of the liu storey conjugate gradient method in this paper the global convergence of a new version of the liu storey conjugate gradient method is discussed this method combines the liu storey conjugate gradient formula and a new inexact line search we prove that the new method is globally convergent some preliminary numerical results show that the corresponding algorithm is efficient

global convergence properties of conjugate gradient methods for optimization this paper explores the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches the analysis covers two classes of methods that are globally convergent on smooth nonconvex functions some properties of the fletcher reeves method play an important role in the first family whereas the second family shares an important property with the polak ribiere method numerical experiments are presented

fourth order partial differential equations for noise removal a class of fourth order partial differential equations pdes are proposed to optimize the trade off between noise removal and edge preservation the time evolution of these pdes seeks to minimize a cost functional which is an increasing function of the absolute value of the laplacian of the image intensity function since the laplacian of an image at a pixel is zero if the image is planar in its neighborhood these pdes attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image piecewise planar images look more natural than step images which anisotropic diffusion second order pdes uses to approximate an observed image so the proposed pdes are able to avoid the blocky effects widely seen in images processed by anisotropic diffusion while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion although both approaches seem to be comparable in removing speckles in the observed images speckles are more visible in images processed by the proposed pdes because piecewise planar images are less likely to mask speckles than step images and anisotropic diffusion tends to generate multiple false edges speckles can be easily removed by simple algorithms such as the one presented in this paper

one cohomology and the uniqueness of the group measure space decomposition of a ii1 factor we provide a unified and self contained treatment of several of the recent uniqueness theorems for the group measure space decomposition of a ii1 factor we single out a large class of groups characterized by a one cohomology property and prove that for every free ergodic probability measure preserving action of the associated ii1 factor has a unique group measure space cartan subalgebra up to unitary conjugacy our methods follow closely a recent article of chifan peterson but we replace the usage of peterson s unbounded derivations by thomas sinclair s dilation into a malleable deformation by a one parameter group of automorphisms

l 2 rigidity in von neumann algebras we introduce the notion of l2 rigidity for von neumann algebras a generalization of property t which can be viewed as an analogue for the vanishing of 1 cohomology into the left regular representation of a group we show that l2 rigidity passes to normalizers and is satisfied by nonamenable ii1 factors which are non prime have property or are weakly rigid as a consequence we obtain that if m is a free product of diffuse von neumann algebras or if m l where is a finitely generated group with 1 2 0 then any nonamenable regular subfactor of m is prime and does not have properties or t in particular this gives a new approach for showing solidity for a free group factor thus recovering a well known recent result of n ozawa

the convergence properties of some new conjugate gradient methods abstract in this paper a new conjugate gradient formula k is given to compute the search directions for unconstrained optimization problems general convergence results for the proposed formula with some line searches such as the exact line search the wolfe powell line search and the grippo lucidi line search are discussed under the above line searches and some assumptions the global convergence properties of the given methods are discussed the given formula k 0 and has the similar form with k prp preliminary numerical results show that the proposed methods are efficient

higher degree total variation hdtv regularization for image recovery we introduce novel image regularization penalties to overcome the practical problems associated with the classical total variation tv scheme motivated by novel reinterpretations of the classical tv regularizer we derive two families of functionals involving higher degree partial image derivatives we term these families as isotropic and anisotropic higher degree tv hdtv penalties respectively the isotropic penalty is the mixed norm of the directional image derivatives while the anisotropic penalty is the separable norm of directional derivatives these functionals inherit the desirable properties of standard tv schemes such as invariance to rotations and translations preservation of discontinuities and convexity the use of mixed norms in isotropic penalties encourages the joint sparsity of the directional derivatives at each pixel thus encouraging isotropic smoothing in contrast the fully separable norm in the anisotropic penalty ensures the preservation of discontinuities while continuing to smooth along the line like features this scheme thus enhances the linenlike image characteristics analogous to standard tv we also introduce efficient majorize minimize algorithms to solve the resulting optimization problems the numerical comparison of the proposed scheme with classical tv penalty current second degree methods and wavelet algorithms clearly demonstrate the performance improvement specifically the proposed algorithms minimize the staircase and ringing artifacts that are common with tv and wavelet schemes while better preserving the singularities we also observe that anisotropic hdtv penalty provides consistently improved reconstructions compared with the isotropic hdtv penalty

global convergence of a modified fletcher reeves conjugate gradient method with armijo type line search in this paper we are concerned with the conjugate gradient methods for solving unconstrained optimization problems it is well known that the direction generated by a conjugate gradient method may not be a descent direction of the objective function in this paper we take a little modification to the fletcher reeves fr method such that the direction generated by the modified method provides a descent direction for the objective function this property depends neither on the line search used nor on the convexity of the objective function moreover the modified method reduces to the standard fr method if line search is exact under mild conditions we prove that the modified method with armijo type line search is globally convergent even if the objective function is nonconvex we also present some numerical results to show the efficiency of the proposed method

the estimation of l diffusion coefficients in the parabolic equations abstract the estimation of diffusion coefficients having only l bounds in parabolic equations is considered existence is obtained within a more general class of parabolic operators by means of g convergence the corresponding semi discrete problems are related to the original problem

global convergence of the polak ribiere polyak conjugate gradient method with an armijo type inexact line search for nonconvex unconstrained optimization problems we propose two algorithms for nonconvex unconstrained optimization problems that employ polak ribiere polyak conjugate gradient formula and new inexact line search techniques we show that the new algorithms converge globally if the function to be minimized has lipschitz continuous gradients preliminary numerical results show that the proposed methods for particularly chosen line search conditions are very promising

w superrigidity for arbitrary actions of central quotients of braid groups for any n geqslant 4 let tilde b n b n z b n be the quotient of the braid group b n through its center we prove that any free ergodic probability measure preserving pmp action tilde b n curvearrowright x mu is virtually hbox w superrigid in the following sense if l infty x rtimes tilde b n cong l infty y rtimes lambda for an arbitrary free ergodic pmp action lambda curvearrowright y nu then the actions tilde b n curvearrowright x lambda curvearrowright y are virtually conjugate moreover we prove that the same holds if tilde b n is replaced with a finite index subgroup of the direct product tilde b n 1 times cdots times tilde b n k for some n 1 ldots n k geqslant 4 the proof uses the dichotomy theorem for normalizers inside crossed products by free groups from popa and vaes 212 141 198 2014 in combination with the oe superrigidity theorem for actions of mapping class groups from kida 131 99 109 2008 similar techniques allow us to prove that if a group gamma is hyperbolic relative to a finite family of proper finitely generated residually finite infinite subgroups then the hbox ii 1 factor l infty x rtimes gamma has a unique cartan subalgebra up to unitary conjugacy for any free ergodic pmp action gamma curvearrowright x mu

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

unique cartan decomposition for ii1 factors arising from arbitrary actions of free groups we prove that for any free ergodic probability measure preserving action mathbb f n curvearrowright x mu of a free group on n generators mathbb f n 2 leq n leq infty the associated group measure space ii1 factor l infty x rtimes mathbb f n has l x as its unique cartan subalgebra up to unitary conjugacy we deduce that group measure space ii1 factors arising from actions of free groups with different number of generators are never isomorphic we actually prove unique cartan decomposition results for ii1 factors arising from arbitrary actions of a much larger family of groups including all free products of amenable groups and their direct products

new properties of a nonlinear conjugate gradient method this paper provides several new properties of the nonlinear conjugate gradient method in 5 firstly the method is proved to have a certain self adjusting property that is independent of the line search and the function convexity secondly under mild assumptions on the objective function the method is shown to be globally convergent with a variety of line searches thirdly we find that instead of the negative gradient direction the search direction defined by the nonlinear conjugate gradient method in 5 can be used to restart any optimization method while guaranteeing the global convergence of the method some numerical results are also presented

over parameterized variational optical flow a novel optical flow estimation process based on a spatio temporal model with varying coefficients multiplying a set of basis functions at each pixel is introduced previous optical flow estimation methodologies did not use such an over parameterized representation of the flow field as the problem is ill posed even without introducing any additional parameters neighborhood based methods of the lucas kanade type determine the flow at each pixel by constraining the flow to be described by a few parameters in small neighborhoods modern variational methods represent the optic flow directly via the flow field components at each pixel the benefit of over parametrization becomes evident in the smoothness term which instead of directly penalizing for changes in the optic flow accumulates a cost of deviating from the assumed optic flow model our proposed method is very general and the classical variational optical flow techniques are special cases of it when used in conjunction with constant basis functions experimental results with the novel flow estimation process yield significant improvements with respect to the best results published so far

an approximating approach for boundary control of optimal mixing via navier stokes flows abstract the present work focuses on an approximating control design for optimal mixing of a non dissipative scalar via navier stokes flows in an open bounded and connected domain r 2 the objective is to achieve optimal mixing at a given final time t 0 via the active control of the flow velocity through the navier slip boundary control where sobolev norm for the dual space h 1 of h 1 is adopted for quantifying mixing both passive and active scalars governed by the transport equation will be investigated our current approach will lead to a more transparent optimality system for characterizing the optimal solution compared to our previous work 12 this is achieved by first introducing a small diffusivity to the transport equation and then establishing a rigorous analysis of convergence of the approximating control problem to the original one as the diffusivity converges to zero moreover uniqueness of the optimal solution is obtained

unique prime factorization and bicentralizer problem for a class of type iii factors abstract we show that whenever m 1 and m 1 m m are nonamenable factors in a large class of von neumann algebras that we call c ao and which contains all free araki woods factors the tensor product factor m 1 m m retains the integer m and each factor m i up to stable isomorphism after permutation of the indices our approach unifies the unique prime factorization upf results from 33 25 and moreover provides new upf results in the case when m 1 m m are free araki woods factors in order to obtain the aforementioned upf results we show that connes s bicentralizer problem has a positive solution for all type i i i 1 factors in the class c ao

approximate periodic solutions of a nonlinear parabolic system and an identification problem this work continues our study in l lei identification of parameters through the approximate periodic solutions of a linear parabolic system preprint 2005 on the identification problem for the coefficients for the lower order terms in a parabolic system through its approximate periodic solutions different from the work in l lei identification of parameters through the approximate periodic solutions of a linear parabolic system preprint 2005 our system now is nonlinear and the coefficients to be detected are from the first order term from the application point of view we now try to determine the diffusion coefficients for the system by the observation over a subregion of the physical domain the existence and uniqueness problem of the approximate periodic solutions is studied in the first part of the paper

asymptotic properties of receding horizon optimal control problems the asymptotic behavior of receding horizon optimal control problems with terminal cost chosen as a control liapunov function is analyzed for regulator as well as disturbance attenuation problems both the continuous as well as the discrete time cases are treated further the approximation of the continuous time optimal control problem by the discrete time receding horizon problems is studied

variational optical flow computation in real time this paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations although these numerical schemes are among the fastest methods for solving equation systems they are rarely applied in the field of computer vision we demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real time performance on standard pcs as a representative for variational optic flow methods we consider the recently introduced combined local global method it can be considered as a noise robust generalization of the horn and schunck technique we present a decoupled as well as a coupled version of the classical gau spl szlig seidel solver and we develop several multigrid implementations based on a discretization coarse grid approximation in contrast with standard bidirectional multigrid algorithms we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies as a consequence no restrictions concerning the image size or the number of traversed levels have to be imposed in the experimental section we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multigrid methods and nonhierachical solvers for the well known 316 spl times 252 yosemite sequence we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3 06 ghz pentium4 pc this corresponds to a frame rate of 18 flow fields per second which outperforms the widely used gau spl szlig seidel method by almost three orders of magnitude

image denoising by a nonlinear control technique abstractwe propose a technique for image denoising by solving a nonconvex optimal control problem with the state and controller connected on a manifold described by a nonlinear elliptic equation the existence of a control able to denoise an initial blurred image is proved and the optimality conditions are determined by a passing to the limit technique in an appropriate approximating problem involving the legendre fenchel relations an algorithm constructed on the basis of the theoretical results is developed and numerical simulations are provided

measure equivalence rigidity and bi exactness of groups we get three types of results on measurable group theory direct product groups of ozawa s class s groups wreath product groups and amalgamated free products we prove measure equivalence factorization results on direct product groups of ozawa s class s groups as consequences monod shalom type orbit equivalence rigidity theorems follow we prove that if two wreath product groups a g b of non amenable exact direct product groups g with amenable bases a b are measure equivalent then g and are measure equivalent we get bass serre rigidity results on amalgamated free products of non amenable exact direct product groups

some global convergence properties of the wei yao liu conjugate gradient method with inexact line search abstract in z wei s yao l liu the convergence properties of some new conjugate gradient methods applied mathematics and computation 183 2006 1341 1350 wei et al proposed a new conjugate gradient method called wyl method which has good numerical experiments and some excellent properties such as k wyl 0 in this paper we prove that while t k 1 c 2 l g k 2 d k 2 the sufficient descent condition can be satisfied at each iteration of the wyl method based on this the global convergence of the wyl method with the standard armijo line search and the generalized wolfe powell line search is established

on the superrigidity of malleable actions with spectral gap some of the most interesting aspects of the dynamics of measure preserving actions of countable groups on probability spaces v rx x are revealed by the study of group measure space von neumann algebras l x x t mvnl and the classification of actions up to orbit equivalence oe i e up to isomorphism of probability spaces carrying the orbits of actions onto each other although one is in von neumann algebras and the other in ergodic theory the two problems are closely related as an oe of actions v rx x a rxy has been shown to implement an algebra isomorphism l x x t l y x a taking l x onto l y and vice versa si dy fm in particular the isomorphism class of l x xi t only depends on the equivalence relation 7 r t gt 1t x g t thus von neumann equivalence vne of group actions requiring isomorphism of their group measure space algebras is weaker than oe since there are exam ples of non oe actions whose associated von neumann algebras are all isomorphic cj1 it is in general strictly weaker on the other hand oe is manifestly weaker than classical conjugacy which for free actions r rx x a rx y requires isomor phism of probability spaces a x p y v satisfying ar a 1 a so in particular r a how much weaker vne and oe can be with respect to conju gacy is best seen in the amenable case where by a celebrated theorem of connes all free ergodic actions of all infinite amenable groups give rise to the same hi factor cl and by dy ow cfw they are undistinguishable under oe as well also any embedding of algebras l x xi t c l y x a with a amenable forces t to be amenable but the non amenable case is extremely complex and for many years progress has been slow mvn2 dy me c2 cw sc even after the discovery of the first rigidity phenomena by connes in von neumann algebras c3 c4 and by zimmer in oe ergodic theory zi z2 this changed dramatically over the last 7 8 years with the advent of a variety of striking rigidity results ful gl g2 mosh h hk p1 p8 see p9 for a survey also sh for a survey on oe rigidity our aim in this paper is to investigate the most extreme such phenomena called strong rigidity which show that for certain classes of source group actions

a modified wei yao liu conjugate gradient method for unconstrained optimization in this paper we give a modified wei yao liu conjugate gradient method wei et al 2006 18 which will reduce to the original wei yao liu method and possess the sufficient descent property without any line search furthermore we prove that the presented method is globally convergent for nonconvex functions with the weak wolfe powell line search in a similar way we also extend these results to the modified liu storey method preliminary numerical results show that the proposed methods are effective for the given test problems

optimal control formulation for determining optical flow an optimal control formulation for determining optical flow is presented the new framework differs from preceding approaches in that it does not require differentiation of the data and does combine optical flow with image reconstruction it can be considered as a control in the coefficients problem with a cost functional of tracking type a numerical algorithm that solves the optimality system consisting of hyperbolic and elliptic partial differential equations is presented numerical experiments demonstrate the effectiveness of the optimal control approach

on the regularity for the boussinesq equations in a bounded domain we address the regularity for the 2d boussinesq equations with zero diffusivity and positive viscosity on an open bounded smooth domain in particular we prove that for the initial velocity in h2 and the initial density in h1 there exists a global in time solution for which the velocity and the density are locally in time bounded functions in h2 and h1 respectively

new nonlinear conjugate gradient formulas for large scale unconstrained optimization problems abstract we propose new conjugate gradient formulas for computing the search directions for unconstrained optimization problems the new formulas turn out to be the conjugate descent formula if exact line searches are made some formulas possess the sufficient descent property without any line searches general convergence results for the proposed formulas with the weak wolfe powell conditions are studied we prove that some of the formulas with the steplength technique which ensures the zoutendijk condition to be held are globally convergent in addition the global convergence results for some other formulas with the standard armijo line search are also given preliminary numerical results show that the proposed methods are very promising

a method for determination of optimal gaits with application to a snake like serial link structure in this paper we present a method of determining optimal gaits for shape actuated locomotion systems this method is the synthesis of techniques for computing reduced equations for robotic locomotion systems and a numerical optimal control strategy symmetry reduction processes induce a form of locomotion system dynamics that reveals a cyclic like coupling between group shape and momenta coordinates this form allows one to focus on designing gaits abandoning concern over shape dynamics using this vantage point we indicate how a numerical optimal control method based on gaussian quadrature may be acclimatized to periodicity thus providing optimal gaits the method is demonstrated by means of its application to a snake like serial link structure or snake robot this application provides scientific merit to hypotheses concerning observed locomotion phenomena amongst animals employing undulatory propulsive mechanisms

a multigrid platform for real time motion computation with discontinuity preserving variational methods variational methods are among the most accurate techniques for estimating the optic flow they yield dense flow fields and can be designed such that they preserve discontinuities estimate large displacements correctly and perform well under noise and varying illumination however such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution consequently variational methods are considered to be too slow for real time performance in our paper we address this problem in two ways i we present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions thereby our work focuses particularly on regularisation strategies that preserve discontinuities ii we show by the examples of five classical and two recent variational techniques that real time performance is possible in all cases even for very complex optic flow models that offer high accuracy experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 120 can be achieved on a standard pc compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude

an improved wei yao liu nonlinear conjugate gradient method for optimization computation in this paper we take a little modification to the wei yao liu nonlinear conjugate gradient method proposed by wei et al z wei s yao l liu the convergence properties of some new conjugate gradient methods appl math comput 183 2006 1341 1350 such that the modified method possesses better convergence properties in fact we prove that the modified method satisfies sufficient descent condition with greater parameter email protected 0 12 in the strong wolfe line search and converges globally for nonconvex minimization we also extend these results to the hestenes stiefel method and prove that the modified hs method is globally convergent for nonconvex functions with the standard wolfe conditions numerical results are reported by using some test problems in the cute library

a class of one parameter conjugate gradient methods this paper proposes a class of one parameter conjugate gradient methods which can be regarded as some kinds of convex combinations of some modified form of prp and hs methods the scalar k has the form of k k 1 k the convergence of the given methods is analyzed by some unified tools which show the global convergence of the proposed methods numerical experiments with the cute collections show that the proposed methods are promising

completely bounded multipliers of the fourier algebra of a simple lie group of real rank one the fourier algebra a g of a locally compact group g is the space of matrix coefficients of the regular representation and is the predual of the yon neumann algebra vn g generated by the regular representation of g on l 2 g a multiplier m of a g is a bounded operator on a g given by pointwise multiplication by a function on g also denoted m we say m is a completely bounded multiplier ofa g if the transposed operator on vn g is completely bounded definition below it may be possible to find a net ofa g functions m i ie i say such that mi tends to

parameter identification for a class of abstract nonlinear parabolic distributed parameter systems this paper studies the parameter identification problem of nonlinear abstract parabolic distributed parameter systems via variational method 1 based on the fundamental optimal control theory and the transposition method studied in 2 the existence of optimal parameter is proved and the necessary condition for the optimal parameter is established

an augmented lagrangian method for parameter identifications in parabolic systems the identification of parameters in parabolic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method the minimization problem is then proved to be equivalent to the saddle point problem of an augmented lagrangian

on solid ergodicity for gaussian actions we investigate gaussian actions through the study of their crossed product von neumann algebra the motivational result is chifan and ioana s ergodic decomposition theorem for bernoulli actions chifan and ioana 2010 4 that we generalize to gaussian actions theorem a we also give general structural results theorems 3 4 and 3 8 that allow us to get a more accurate result at the level of von neumann algebras more precisely for a large class of gaussian actions x we show that any subfactor n of l x containing l x is either hyperfinite or is non gamma and prime at the end of the article we show a similar result for bogoliubov actions

the parameter estimation problem for parabolic equations and discontinuous observation operators parameter estimation problems are studied for a class of linear autonomous parabolic partial differential equations with various fit to data criteria which may be discontinuous with respect to the state variable we analyze the convergence of galerkin schemes approximating the optimization problems and generalize results to higher dimensional problems an example is then presented for the case of point observation fit to data criteria in higher dimensions finally discretization of coefficients is discussed for identification problems with variable coefficients

a new family of conjugate gradient methods in this paper we develop a new class of conjugate gradient methods for unconstrained optimization problems a new nonmonotone line search technique is proposed to guarantee the global convergence of these conjugate gradient methods under some mild conditions in particular polak ribiere polyak and liu storey conjugate gradient methods are special cases of the new class of conjugate gradient methods by estimating the local lipschitz constant of the derivative of objective functions we can find an adequate step size and substantially decrease the function evaluations at each iteration numerical results show that these new conjugate gradient methods are effective in minimizing large scale non convex non quadratic functions

orbit equivalence rigidity consider a countable group acting ergodically by measure p reserving transformations on a probability space x and let r be the corresponding orbit equivalence relation on x the following rigidity phenomenon is shown there exist group actions such that the equivalence relation r on x determines the group and the action x uniquely up to finite groups the natural action of sln z on the n torus r n z n for n 2 is one of such examples the interpretation of these results in the context of von neumann algebras provides some support to the conjecture of connes on rigidity of group algebras for groups with property t our rigidity results also give examples of countable equivalence relations of type ii1 which cannot be generated mod 0 by a free action of any group this gives a negative answer to a long standing problem of feldman and moore