rotation vectors and fixed points of area preserving surface diffeomorphisms we consider the homological rotation vectors for area preserving diffeomorphisms of compact surfaces which are homotopic to the identity there are two main results the first is that if 0 is in the interior of the convex hull of the rotation vectors for such a diffeomorphism then f has a fixed point of positive index the second result asserts that if f has a vanishing mean rotation vector then f has a fixed point of positive index there are several applications including a new proof of the arnold conjecture for area preserving diffeomorphisms of compact surfaces in this paper we investigate area preserving diffeomorphisms of compact surfaces we are concerned with rotation vectors defined in terms of homology which can be associated to the points of the surface there are two main results the first is that if f is an area preserving diffeomorphism of a compact surface which is homotopic to the identity and 0 is in the interior of the convex hull of the rotation vectors of f then f has a fixed point of positive index the second result concerns the mean rotation vector of f it asserts that if this vector vanishes then f has a fixed point of positive index a special case of this second result when the surface in question is a surface of genus zero was proved in f5 in 6 we give several applications including a new proof of the arnold conjecture for area preserving diffeomorphisms of compact surfaces

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

bayesian reconstructions from emission tomography data using a modified em algorithm a novel method of reconstruction from single photon emission computerized tomography data is proposed this method builds on the expectation maximization em approach to maximum likelihood reconstruction from emission tomography data but aims instead at maximum posterior probability estimation which takes account of prior belief about smoothness in the isotope concentration a novel modification to the em algorithm yields a practical method the method is illustrated by an application to data from brain scans

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

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

subharmonic solutions of hamiltonian equations on tori let the torus t2n be equipped with the standard symplectic structure and a periodic hamiltonian dt e c3 sx x t2n r we look for periodic orbits of the hamiltonian flow u t j vdt t a subharmonic solution is a periodic orbit with minimal period an integral multiple m of the period of dt with m 1 we prove that if the hamiltonian flow has only finitely many orbits with the same period as dt then there are subharmonic solutions with arbitrarily high minimal period thus there are always infinitely many distinct periodic orbits the results proved here were proved in the nondegenerate case by conley and zehnder and in the case n 1 by le calvez

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

periodic orbits of hamiltonian homeomorphisms of surfaces john franks and michael handel fh2 have recently proved that any nontrivial hamiltonian diffeomorphism of a closed surface of genus at least one has periodic orbits of arbitrarily large period they proved a similar result for a nontrivial area preserving diffeomorphism of a sphere with at least three fixed points we extend these results to the case of the homeomorphisms when the genus is at least one we prove moreover that the periodic orbits may be chosen contractible if the set of contractible fixed points is contained in a disk when the surface is a sphere we extend the result to the case of a nontrivial homeomorphism with no wandering points the proofs make use of an equivariant foliated version of brouwer s plane translation theorem see b proposition 2 1 and some properties of the linking number of fixed points

synthetic magnetic resonance imaging revisited synthetic magnetic resonance mr imaging is an approach suggested in the literature to predict mr images at different design parameter settings from at least three observed mr scans however performance is poor when no regularization is used in the estimation and otherwise computationally impractical to implement for 3 d imaging methods we propose a method which accounts for spatial context in mr images by the imposition of a gaussian markov random field mrf structure on a transformation of the spin lattice relaxation time the spin spin relaxation time and the proton density at each voxel the mrf structure is specified through a matrix normal distribution we also model the observed magnitude images using the more accurate but computationally challenging rice distribution a one step late expectation maximization approach is adopted to make our approach computationally practical we evaluate predictive performance in generating synthetic mr images in a clinical setting our results indicate that our suggested approach is not only computationally feasible to implement but also shows excellent performance

a fast automatic algorithm for image denoising by a regularization method a new fast iterative algorithm is proposed to denoise images affected by gaussian additive noise by solving a constrained optimization problem a family of functionals parameterized by a few hyperparameters already proposed in the literature to solve denoising problems is considered the algorithm estimates jointly the image and the hyperparameters therefore providing an automatic method each member of the family is made up of a coherence with the data term and a term enforcing a roughness penalty and preserving jump discontinuities assuming we know the noise variance an adequacy constraint is also considered the algorithm computes a member of the family and a minimizer of it which satisfies the constraint a convergence proof is provided we then consider a heuristic version of the algorithm which gives restorations of comparable quality whose computational complexity is a linear function of the pixels number experimental results on synthetic and real data are presented moreover numerical comparisons with several fast denoising methods are provided

morse theory for fixed points of symplectic diffeomorphisms on demontre le cas particulier suivant de la conjecture de arnold sur les points fixes d une deformation exacte d une variete symplectique compacte close p si 2 p 0 et tous les points fixes de sont non degeneres alors leur nombre est plus grand ou egal a la somme des nombres de betti de p par rapport aux coefficients z 2

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

a bayesian approach to synthetic magnetic resonance imaging summary synthetic magnetic resonance imaging involves the estimation based on a set of measured images with noise of three basic physical quantities that are nonlinearly related to the observations the methods currently available for this ill conditoned inverse problem either do not provide sufficiently accurate estimates or require time consuming data collection we formulate this nonlinear problem in a bayesian framework taking into account knowledge about the physics of the magnetic resonance imaging experiment statistical properties of the experimental noise and prior information about the underlying physical quantities modelled by a suitable markov random field a new multilayer markov random field is proposed inference is drawn by means of markov chain monte carlo methods or iterated conditional modes some examples are included to demonstrate how synthetic magnetic resonance imaging by this approach can be performed in an accurate and reliable way

morse type index theory for flows and periodic solutions for hamiltonian equations an index theory for flows is presented which extends the classical morse theory for gradient flows on compact manifolds the theory is used to prove a morse type existence statement for periodic solutions of a time dependent periodic in time and asymptotically linear hamiltonian equation

factorial property of a ring of automorphic forms a ring of automorphic forms is shown to be factorial under some conditions on the domain and on the picard group as an application we show that any divisor on the moduli space 2jf k of curves of genus g 3 is defined by a single element and that the satake compactification of u is is written as a projective spectrum of a factorial graded ring we find a single element which defines the closure of w4 in 5w4 where 3tf 4 is the moduli of curves of genus four whose canonical curves are exhibited as complete intersections of quadric cones and of cubics in p3 introduction let x be a normal quasi projective variety over c such that i x has a normal projective compactification x with codim a a 2 and ii x is a quotient space 2 t of a connected domain 2 with pic 0 by a discontinu ous group t of holomorphic automorphisms then the canonically determined homogeneous coordinate ring of x is factorial under some conditions on t or essentially on the picard group pic t in our notation theorem 1 when 2 is the siegel space and t is the modular group freitag 9 10 has shown that the homogeneous coordinate ring of x or more precisely the graded ring of siegel modular forms is factorial provided that the degree is greater than two our theorem is applicable to the case when x is the moduli space wlg of curves of genus g we need to know the first or second betti number of 3rg or of the teichmuller modular group tg which will almost determine the picard group in mumford 19 the first betti number ex 2rg of 3 would be one harer 12 proved it for g 5 and in this paper we show it for g 3 4 which seems more or less well known as for the case of 2 being a bounded symmetric domain the determination of the betti numbers is covered by the calculation of the stable real cohomology due to borel 2 for a fairly large class of 2 as an application of our method we show that the closure in 9ji4 of the moduli w4 of nonhyperelliptic curves of genus four exhibited as complete intersections of quadric cones and of cubics in ip3 is a subvariety defined by a principal ideal and gives the generator of the principal ideal this work was done while the author was staying at harvard university he

a c 0 counterexample to the arnold conjecture the arnold conjecture states that a hamiltonian diffeomorphism of a closed and connected symplectic manifold m omega must have at least as many fixed points as the minimal number of critical points of a smooth function on m it is well known that the arnold conjecture holds for hamiltonian homeomorphisms of closed symplectic surfaces the goal of this paper is to provide a counterexample to the arnold conjecture for hamiltonian homeomorphisms in dimensions four and higher more precisely we prove that every closed and connected symplectic manifold of dimension at least four admits a hamiltonian homeomorphism with a single fixed point

noise estimation in magnitude mr datasets estimating the noise parameter in magnitude magnetic resonance mr images is important in a wide range of applications we propose an automatic noise estimation method that does not rely on a substantial proportion of voxels being from the background specifically we model the magnitude of the observed signal as a mixture of rice distributions with common noise parameter the expectation maximization em algorithm is used to estimate all parameters including the common noise parameter the algorithm needs initializing values for which we provide some strategies that work well the number of components in the mixture model also needs to be estimated en route to noise estimation and we provide a novel approach to doing so our methodology performs very well on a range of simulation experiments and physical phantom data finally the methodology is demonstrated on four clinical datasets