noncommutative ricci flow in a matrix geometry we study noncommutative ricci flow in a finite dimensional representation of a noncommutative torus it is shown that the flow exists and converges to the flat metric we also consider the evolution of entropy and a definition of scalar curvature in terms of the ricci flow

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

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

godunov type methods for conservation laws with a flux function discontinuous in space scalar conservation laws with a flux function discontinuous in space are approximated using a godunov type method for which a convergence theorem is proved the case where the flux functions at the interface intersect is emphasized a very simple formula is given for the interface flux a numerical comparison between the godunov numerical flux and the upstream mobility flux is presented for two phase flow in porous media a consequence of the convergence theorem is an existence theorem for the solution of the scalar conservation laws under consideration furthermore for regular solutions uniqueness has been shown

convergence of a difference scheme for conservation laws with a discontinuous flux convergence is established for a scalar finite difference scheme based on the godunov or engquist osher eo flux for scalar conservation laws having a flux that is spatially dependent through a possibly discontinuous coefficient other works in this direction have established convergence for methods employing the solution of 2 2 riemann problems the algorithm discussed here uses only scalar riemann solvers satisfaction of a set of kruzkov type entropy inequalities is established for the limit solution from which geometric entropy conditions follow assuming a piecewise constant coefficient it is shown that these conditions imply l1 contractiveness for piecewise c1 solutions thus extending a well known theorem

an engquist osher type scheme for conservation laws with discontinuous flux adapted to flux connections we consider scalar conservation laws with the spatially varying flux h x f u 1 h x g u where h x is the heaviside function and f and g are smooth nonlinear functions adimurthi mishra and veerappa gowda j hyperbolic differ equ 2 2005 pp 783 837 pointed out that such a conservation law admits many l 1 contraction semigroups one for each so called connection a b here we define entropy solutions of type a b involving kruzkov type entropy inequalities that can be adapted to any fixed connection a b it is proved that these entropy inequalities imply the l 1 contraction property for l infty solutions in contrast to the piecewise smooth setting of adimurthi mishra and veerappa gowda for a fixed connection these entropy inequalities include a single adapted entropy of the type used by audusse and perthame proc roy soc edinburgh sect a 135 2005 pp 253 265 we prove convergence of a new difference scheme that approximates entropy solutions of type a b for any connection a b if a few parameters are varied the scheme relies on a modification of the standard engquist osher flux is simple as no 2 times2 riemann solver is involved and is designed such that the steady state solution connecting a to b is preserved in contrast to most analyses of similar problems our convergence proof is not based on the singular mapping or compensated compactness methods but on standard spatial variation estimates away from the flux discontinuity some numerical examples are presented

convergence of upwind finite difference schemes for a scalar conservation law with indefinite discontinuities in the flux function we consider the scalar conservation law with flux function discontinuous in the space variable i e begin eqnarray label eq1 u t h x f u 1 h x g u x 0 quad mbox in r times r nonumber u 0 x u 0 x quad mbox in r label 0 1 end eqnarray where h is the heaviside function and f and g are smooth with the assumptions that either f is convex and g is concave or f is concave and g is convex the existence of a weak solution of ref eq1 is proved by showing that upwind finite difference schemes of godunov and enquist osher type converge to a weak solution uniqueness follows from a kruzkhov type entropy condition we also provide explicit solutions to the riemann problem for ref eq1 at the level of numerics we give easy to implement numerical schemes of godunov and enquist osher type the central feature of this paper is the modification of the singular mapping technique the main analytical tool for these types of equations which allows us to show that the numerical schemes converge equations of type ref eq1 with the above hypothesis on the flux may occur when considering the following scalar conservation law with discontinuous flux begin equation label eq2 begin array email protected l u t k x f u x 0 u 0 x u 0 x end array end equation with f convex and k of indefinite sign

central schemes and systems of conservation laws with discontinuous coefficients modeling gravity separation of polydisperse suspensions in this paper two existing one dimensional mathematical models one for continuous sedimentation of monodisperse suspensions and one for settling of polydisperse suspensions are combined into a model of continuous separation of polydisperse mixtures this model can be written as a first order system of conservation laws for the local concentrations of each particle species with a flux vector that depends discontinuously on the space variable this application motivates the extension of the kurganov tadmor central difference scheme to systems with discontinuous flux the new central schemes are based on discretizing an enlarged system in which the discontinuous coefficients are viewed as additional conservation laws these additional conservation laws can either be discretized and the evolution of the discontinuity parameters is calculated in each time step or solved exactly that is the discontinuity parameters are kept constant with respect to time numerical examples and an l1 error study show that the kurganov tadmor scheme with first order in time discretization produces spurious oscillations whereas its semi discrete version discretized by a second order runge kutta scheme produces good results the scheme with discontinuity parameters kept constant is slightly more accurate than when these are evolved numerical examples illustrate the application to separation of polydisperse suspensions

a difference scheme for conservation laws with a discontinuous flux the nonconvex case in a previous work by the author convergence was established for a simple difference scheme approximating a scalar conservation law where the flux was concave and had a discontinuous spatially varying coefficient j d towers siam j numer anal 38 2000 pp 681 698 the main result of this paper is an extension of that convergence theorem to the situation where the flux may have any finite number of critical points additionally spatially varying source terms are allowed the spatially varying numerical flux is also shown to satisfy maximum and minimum principles and to be total variation decreasing tvd in time

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

from large n matrices to the noncommutative torus we describe how and to what extent the noncommutative two torus can be approximated by a tower of finite dimensional matrix geometries the approximation is carried out for both irrational and rational deformation parameters by embedding the c algebra of the noncommutative torus into an approximately finite algebra the construction is a rigorous derivation of the recent discretizations of noncommutative gauge theories using finite dimensional matrix models and it shows precisely how the continuum limits of these models must be taken we clarify various aspects of morita equivalence using this formalism and describe some applications to noncommutative yang mills theory

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

semidiscrete central upwind scheme for conservation laws with a discontinuous flux function in space abstract in this paper a modified semidiscrete central upwind scheme is derived for the scalar conservation laws with a discontinuous flux function in space the new scheme is based on dealing with the phase transition at the stationary discontinuity where the unknown variable function is not continuous but the flux function is continuous the main advantages of the new scheme are the same as them of the original semidiscrete central upwind scheme numerical results are displayed to illustrate the efficiency of the methods

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

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 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

a conservation law with point source and discontinuous flux function modelling continuous sedimentation continuous sedimentation of solid particles in a liquid takes place in a clarifier thickener unit which has one feed inlet and two outlets the aim of the paper is to formulate and analyse a dynamic model for this process under idealized physical conditions the conservation of mass yields the scalar conservation law frac partial u x t partial t frac partial partial x f u x t x s t delta x where delta is the dirac measure s is a source and f is a flux function which is discontinuous at three points in the one dimensional space coordinate x under certain regularity assumptions a procedure for constructing a solution locally in time is presented the nonlinear phenomena are complicated and so is the general construction of a solution the problem of nonuniqueness due to the discontinuities of f u cdot is handled by a generalized entropy condition an advantage of this approach is that the a priori boundary conditions at the discontinuities

instanton expansion of noncommutative gauge theory in two dimensions we show that noncommutative gauge theory in two dimensions is an exactly solvable model a cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a sum over contributions from classical solutions we derive an explicit formula for the partition function of yang mills theory defined on a projective module for an arbitrary noncommutativity parameter which is manifestly invariant under gauge morita equivalence the energy observables are shown to be smooth functions of the construction of noncommutative instanton contributions to the path integral is described in some detail in general there are infinitely many gauge inequivalent contributions of fixed topological charge along with a finite number of quantum fluctuations about each instanton the associated moduli spaces are combinations of symmetric products of an ordinary two torus whose orbifold singularities are not resolved by noncommutativity in particular the weak coupling limit of the gauge theory is independent of and computes the symplectic volume of the moduli space of constant curvature connections on the noncommutative torus

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