global solutions to the two dimensional quasi geostrophic equation with critical or super critical dissipation the two dimensional quasi geostrophic 2d qg equation with critical and super critical dissipation is studied in sobolev space h s 2 for critical case open image in new window existence of global large solutions in h s is proved for s open image in new window when open image in new window is small this generalizes and improves the results of constantin d cordoba and wu 4 for s 1 2 and the result of a cordoba and d cordoba 8 for s open image in new window for s 1 these solutions are also unique the improvement for pushing s down from 1 to open image in new window is somewhat surprising and unexpected for super critical case 0 open image in new window existence and uniqueness of global large solution in h s is proved when the product open image in new window is small for suitable s 2 2 p 1 and 0 1

global regularity for a class of 2d generalized tropical climate models abstract this paper establishes the global existence and regularity of solutions to a two dimensional 2d tropical climate model tcm with fractional dissipation the inviscid counterpart of this model was derived by frierson majda and pauluis 8 as a model for tropical geophysical flows this model reflects the interaction and coupling among the barotropic mode u the first baroclinic mode v of the velocity and the temperature the systems with fractional dissipation studied here may arise in the modeling of geophysical circumstances mathematically these systems allow simultaneous examination of a family of systems with various levels of regularization the aim here is the global regularity with the least dissipation we prove two main results first the global regularity of the system with v and for 1 and 3 2 and second the global regularity of the system with v for 3 2 the proofs of these results are not trivial and the requirements on the fractional indices appear to be optimal the key tools employed here include the maximal regularity for general fractional heat operators the littlewood paley decomposition and besov space techniques lower bounds involving fractional laplacian and simultaneous estimates of several coupled quantities

unsupervised image segmentation using markov random field models abstract we present two unsupervised segmentation algorithms based on hierarchical markov random field models for segmenting both noisy images and textured images each algorithm finds the the most likely number of classes their associated model parameters and generates a corresponding segmentation of the image into these classes this is achieved according to the maximum a posteriori criterion to facilitate this an mcmc algorithm is formulated to allow the direct sampling of all the above parameters from the posterior distribution of the image to allow the number of classes to be sampled a reversible jump is incorporated into the markov chain experimental results are presented showing rapid convergence of the algorithm to accurate solutions

existence of solutions to the convection problem in a pseudomeasure type space we study the well posedness of a convection problem in a pseudomeasure type space pma without assuming that the gravitational field is bounded considering the pma space with right homogeneity th

the well posedness of the surface quasi geostrophic equations in the besov morrey spaces abstract in this paper we develop the boundedness of riesz transform in morrey spaces which generalize the corresponding result in the usual l p spaces as an application of this boundedness we establish the well posedness and blow up criterion for the surface quasi geostrophic equations in the framework of besov morrey spaces

a generalization of chernoff s product formula for time dependent operators in this article we provide a set of sufficient conditions that allow a natural extension of chernoff s product formula to the case of certain one parameter family of functions taking values in the algebra l b of all bounded linear operators defined on a complex banach space b those functions need not be contraction valued and are intimately related to certain evolution operators u t s 0 s t t on b the most direct consequences of our main result are new formulae of the trotter kato type which involve either semigroups with time dependent generators or the resolvent operators associated with these generators in the general case we can apply such formulae to evolution problems of parabolic type as well as to schrodinger evolution equations albeit in some very special cases the formulae we prove may also be relevant to the numerical analysis of non autonomous ordinary and partial differential equations

a region and gradient based active contour model and its application in boundary tracking on anal canal ultrasound images a novel gaussian mixture model gmm based region and gradient active contour model is proposed for general object boundary tracking and the purpose of boundary tracking for anal muscle layers motion information is extracted from adjacent slice and is used to guide the first step of boundary tracking procedure the idea is that gmm is introduced into the statistical feature computation for object region and background region thereby providing an accurate model for regional pixel intensity description expectation maximization algorithm and k means algorithm are used for parameter solutions of gmm based on the available region information gradient information and the self constraints of the contour a unifying active contour model is proposed the proposed active contour models and tracking algorithm were tested on synthetic images and simulated ultrasound images to evaluate some generic features of the model for boundary tracking furthermore it was applied to perform boundary tracking of anal muscle layers the tracking results were evaluated by three experts the results showed that the proposed method has a good performance for boundary tracking on anal wall ultrasound image

a multiscale expectation maximization semisupervised classifier suitable for badly posed image classification this paper deals with the problem of badly posed image classification although underestimated in practice bad posedness is likely to affect many real world image classification tasks where reference samples are difficult to collect e g in remote sensing rs image mapping and or spatial autocorrelation is relevant in an image classification context affected by a lack of reference samples an original inductive learning multiscale image classifier termed multiscale semisupervised expectation maximization msem is proposed the rationale behind msem is to combine useful complementary properties of two alternative data mapping procedures recently published outside of image processing literature namely the multiscale modified pappas adaptive clustering mpac algorithm and the sample based semisupervised expectation maximization sem classifier to demonstrate its potential utility msem is compared against nonstandard classifiers such as mpac sem and the single scale contextual sem csem classifier besides against well known standard classifiers in two rs image classification problems featuring few reference samples and modestly useful texture information these experiments yield weak subjective but numerous quantitative map quality indexes that are consistent with both theoretical considerations and qualitative evaluations by expert photointerpreters according to these quantitative results msem is competitive in terms of overall image mapping performance at the cost of a computational overhead three to six times superior to that of its most interesting rival sem more in general our experiments confirm that even if they rely on heavy class conditional normal distribution assumptions that may not be true in many real world problems e g in highly textured images semisupervised classifiers based on the iterative expectation maximization gaussian mixture model solution can be very powerful in practice when 1 there is a lack of reference samples with respect to the problem model complexity and 2 texture information is considered negligible i e a piecewise constant image model holds

theoretical analysis of multispectral image segmentation criteria markov random field mrf image segmentation algorithms have been extensively studied and have gained wide acceptance however almost all of the work on them has been experimental this provides a good understanding of the performance of existing algorithms but not a unified explanation of the significance of each component to address this issue we present a theoretical analysis of several mrf image segmentation criteria standard methods of signal detection and estimation are used in the theoretical analysis which quantitatively predicts the performance at realistic noise levels the analysis is decoupled into the problems of false alarm rate parameter selection neyman pearson and receiver operating characteristics detection threshold expected a priori boundary roughness and supervision only the performance inherent to a criterion with perfect global optimization is considered the analysis indicates that boundary and region penalties are very useful while distinct mean penalties are of questionable merit region penalties are far more important for multispectral segmentation than for greyscale this observation also holds for gauss markov random fields and for many separable within class pdfs to validate the analysis we present optimization algorithms for several criteria theoretical and experimental results agree fairly well

dissipative quasi geostrophic equation for large initial data in the critical sobolev space the critical and super critical dissipative quasi geostrophic equations are investigated in mathbb r 2 we prove local existence of a unique regular solution for arbitrary initial data in h2 2 which corresponds to the scaling invariant space of the equation we also consider the behavior of the solution near t 0 in the sobolev space

global regularity for the supercritical dissipative quasi geostrophic equation with large dispersive forcing we consider the 2d quasi geostrophic equation with supercritical dis sipation and dispersive forcing in the whole space when the dispersive amplitude parameter is large enough we prove the global well posedness of strong solution to the equation with large initial data we also show the strong convergence result as the amplitude parameter goes to 1 both results rely on the strichartz type estimates for the corresponding linear equation

global well posedness for the critical 2d dissipative quasi geostrophic equation we give an elementary proof of the global well posedness for the critical 2d dissipative quasi geostrophic equation the argument is based on a non local maximum principle involving appropriate moduli of continuity

weighted lp estimates and fujita exponent for a nonlocal equation abstract we investigate a nonlocal equation t u r n j x y u y t d y j l 1 u x t a x t u p in r n where a is unbounded and j belongs to a weighted space crucial weighted l p and interpolation estimates for the green operator are established by a new method based on the sharp young s inequality the asymptotic behavior of a regular varying coefficients exponential series and the properties of auxiliary functions 1 x 2 b 2 that j and b 2 x b b 2 blow up behaviors are investigated by employing test functions r r instead of principal eigenfunctions global well posedness in weighted l p spaces for the cauchy problem is proved when a x the fujita exponent is shown to be 1 2 n our approach generalizes and unifies nonlocal diffusion equations and pseudoparabolic equations

large time asymptotics of a fractional drift diffusion poisson system via the entropy method abstract the self similar asymptotics for solutions to the drift diffusion equation with fractional dissipation coupled to the poisson equation is analyzed in the whole space it is shown that in the subcritical and supercritical cases the solutions converge to the fractional heat kernel with algebraic rate the proof is based on the entropy method and leads to a decay rate in the l 1 r d norm the technique is applied to other semilinear equations with fractional dissipation

sensitivity of the stationary distribution vector for an ergodic markov chain stationary distribution vectors p sup infinity for markov chains with associated transition matrices t are important in the analysis of many models in the mathematical sciences such as queuing networks input output economic models and compartmental tracer analysis models the purpose of this paper is to provide insight into the sensitivity of p sup infinity to perturbations in the transition probabilities of t and to understand some of the difficulties in computing an accurate p sup infinity the group inverse a sup number of i t is shown to be of fundamental importance in understanding sensitivity or conditioning of p sup infinity the main result shows that if there is a state that is accessible from every other state and the corresponding column of t has no small off diagonal elements then p sup infinity cannot be sensitive to small perturbations in t ecological examples are given a new stable algorithm for calculating a sup number is described

on the perturbation of markov chains with nearly transient states leta be an irreducible stochastic matrix of the form a left begin array 20 c a 11 e 12 a 21 a 22 end array right ife 12 were zero the states corresponding toa 22 would be transient in the sense that if the steady state vectory t is partitioned conformally in the form y 1 t y 2 t theny 2 t 0 ife 12 is small theny 2 t will be small and the states are said to be nearly transient in this paper it is shown that small relative perturbations ina 11 a 21 anda 22 though potentially larger thany 2 t induce only small relative perturbations iny 2 t

global well posedness for the 2d inviscid benard system with fractional diffusivity and yudovichʼs type data abstract in this paper we consider the cauchy problem of the two dimensional inviscid benard system with fractional diffusivity we show that there is a global unique solution to this system with yudovich s type data

global well posedness in the super critical dissipative quasi geostrophic equations we consider the quasi geostrophic equation with the dissipation term in the case constantin cordoba wu 6 proved the global existence of strong solution in h 1 and h 2 under the assumption of small l norm of initial data in this paper we prove the global existence in the scale invariant besov space b 2 2 2 1 for initial data small in the b 2 2 2 1 norm we also prove a global stability result in b 1 2 1

algebraic l 2 decay for weak solutions of a viscous boussinesq system in exterior domains abstract the algebraic decay rates for the total kinetic energy of weak solutions of the n dimensional viscous boussinesq system in exterior domains are established by means of the spectral decomposition method of fractional powers of the laplacian and stokes operators the results reveal that l 2 decay of the velocity field with zero divergence becomes slower than that of the temperature

iterative aggregation disaggregation techniques for nearly uncoupled markov chains iterative aggregation disaggregation methods provide an efficient approach for computing the stationary probability vector of nearly uncoupled also known as nearly completely decomposable markov chains three such methods that have appeared in the literature recently are considered and their similarities and differences are outlined specifically it is shown that the method of takahashi corresponds to a modified block gauss seidel step and aggregation whereas that of vantilborgh corresponds to a modified block jacobi step and aggregation the third method that of koury et al is equivalent to a standard block gauss seidel step and iteration for each of these methods a lemma is established which shows that the unique fixed point of the iterative scheme is the left eigenvector corresponding to the dominant unit eigenvalue of the stochastic transition probability matrix in addition conditions are established for the convergence of the first two of these methods convergence conditions for the third having already been established by stewart et al all three methods are shown to have the same asymptotic rate of convergence

operator splitting for non autonomous evolution equations abstract we establish general product formulas for the solutions of non autonomous abstract cauchy problems the main technical tools are evolution semigroups allowing the direct application of existing results on autonomous problems the results obtained are illustrated by the example of an autonomous diffusion equation perturbed with time dependent potential we also prove convergence rates for the sequential splitting applied to this problem

a maximum principle for the muskat problem for fluids with different densities we study the fluid interface problem given by two incompressible fluids with different densities evolving by darcy s law this scenario is known as the muskat problem for fluids with the same viscosities being in two dimensions mathematically analogous to the two phase hele shaw cell we prove in the stable case the denser fluid is below a maximum principle for the l norm of the free boundary

stochastic relaxation on partitions with connected components and its application to image segmentation we present a new method of segmentation in which images are segmented in partitions with connected components we give computationally inexpensive algorithms for probability simulation and simulated annealing on the space of partitions with connected components of a general graph in particular hastings algorithms 1970 and generalized metropolis algorithms are defined to avoid heavy computation to achieve segmentation we propose a hierarchical approach which at each step minimizes a cost function on the space of partitions with connected components of a graph the algorithm is applied to segment gray level color and textured images

entrywise perturbation theory and error analysis for markov chains grassmann taksar and heyman introduced a variant of gaussian climination for computing the steady state vector of a markov chain in this paper we prove that their algorithm is stable and that the problem itself is well conditioned in the sense of entrywise relative error thus the algorithm computes each entry of the steady state vector with low relative error even the small steady state probabilities are computed accurately the key to our analysis is to focus on entrywise relative error in both the data and the computed solution rather than making the standard assessments of error based on norms our conclusions do not depend on any condition numbers for the problem

perturbation results for nearly uncoupled markov chains with applications to iterative methods the standard perturbation theory for linear equations states that nearly uncoupled markov chains numcs are very sensitive to small changes in the elements indeed some algorithms such as standard gaussian elimination will obtain poor results for such problems a structured perturbation theory is given that shows that numcs usually lead to well conditioned problems it is shown that with appropriate stopping criteria iterative aggregation disaggregation algorithms will achieve these structured error bounds a variant of gaussian elimination due to grassman taksar and heyman was recently shown by o cinneide to achieve such bounds

regenerative analysis and steady state distributions for markov chains we apply regenerative theory to derive certain relations between steady state probabilities of a markov chain these relations are then used to develop a numerical algorithm to find these probabilities the algorithm is a modification of the gauss jordan method in which all elements used in numerical computations are nonnegative as a consequence the algorithm is numerically stable

determining modes for the surface quasi geostrophic equation abstract we introduce a determining wavenumber for the surface quasi geostrophic sqg equation defined for each individual trajectory and then study its dependence on the force while in the subcritical and critical cases this wavenumber has a uniform upper bound it may blow up when the equation is supercritical a bound on the determining wavenumber provides determining modes and measures the number of degrees of freedom of the flow or resolution needed to describe a solution to the sqg equation

bayesian clustering for unsupervised estimation of surface and texture models a method of calculating the maximum likelihood clustering for the unsupervised estimation of polynomial models for the data in images of smooth surfaces or for range data for such surfaces is presented an image or a depth map of a region of smooth 3 d surface is modeled as a polynomial plus white noise a region of physically meaningful textured image such as the image of foliage grass or road in outdoor scenes or conductor or lintburn on a thick film substrate is modeled as a colored gaussian markov random field mrf with a polynomial mean value function unsupervised model parameter estimation is accomplished by determining the segmentation and model parameter values that maximize the likelihood of the data or a more general bayesian performance functional agglomerative clustering is used for this purpose

boundary detection by constrained optimization a statistical framework is used for finding boundaries and for partitioning scenes into homogeneous regions the model is a joint probability distribution for the array of pixel gray levels and an array of labels in boundary finding the labels are binary zero or one representing the absence or presence of boundary elements in partitioning the label values are generic two labels are the same when the corresponding scene locations are considered to belong to the same region the distribution incorporates a measure of disparity between certain spatial features of block pairs of pixel gray levels using the kolmogorov smirnov nonparametric measures of difference between the distributions of these features the number of model parameters is minimized by forbidding label configurations which are assigned probability zero the maximum a posteriori estimator of boundary placements and partitionings is examined the forbidden states introduce constraints into the calculation of these configurations stochastic relaxation methods are extended to accommodate constrained optimization

a region level motion based graph representation and labeling for tracking a spatial image partition abstract this paper addresses two image sequence analysis issues under a common framework these tasks are first motion based segmentation and second updating and tracking over time of a spatial partition of an image by spatial partition we mean that constituent regions display an intensity color or texture based homogeneity criterion several issues in dynamic scene analysis or in image sequence coding can motivate this kind of development a general purpose methodology involving a region level motion based graph representation of the partition is presented this graph is built from the topology of the spatial segmentation map a statistical motion based labeling of its nodes is carried out and formalized within a markovian approach groups of spatial regions with consistent motion are identified using this labeling framework leading to a motion based segmentation that is both useful in itself and for propagating the spatial partition over time results on synthetic and real world image sequences are shown and provide a validation of the proposed approach

on a rayleigh ritz refinement technique for nearly uncoupled stochastic matrices abstract an analysis is presented for the convergence of an iterative technique for computing the dominant left eigenvector of a nearly uncoupled nearly completely decomposable stochastic matrix the technique combines the power method and rayleigh ritz refinement to force rapid convergence to the stationary probability vector of the associated markov chain

pointwise estimates for solutions of fractal burgers equation abstract in this paper we provide two sided estimates and uniform asymptotics for the solution of d dimensional critical fractal burgers equation u t 2 u b u u q 0 1 2 b r d for q 1 d and u 0 l 1 r d we consider also q 1 d under additional condition u 0 l r d in both cases we assume u 0 0 which implies that the solution is non negative the estimates are given in the terms of the function p t u 0 where p t denotes the semigroup for the operator t 2

formation of singularities for a transport equation with nonlocal velocity we study a 1d transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data by adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time

identification of almost invariant aggregates in reversible nearly uncoupled markov chains the topic of the present paper has been motivated by a recent computational approach to identify metastable chemical conformations and patterns of conformational changes within molecular systems after proper discretization such conformations show up as almost invariant aggregates in reversible nearly uncoupled markov chains numcs most of the former work on this subject treated the direct problem given the aggregates analyze the loose coupling in connection with the computation of the stationary distribution aggregation disaggregation techniques in contrast to that the present paper focuses on the inverse problem given the system as a whole identify the almost invariant aggregates together with the small probabilities of transitions between them a robust algorithm is worked out on the basis of some detailed perturbation analysis and illustrated at a simple molecular system

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

blockwise perturbation theory for block p cyclic stochastic matrices summary let p be a block p cyclic stochastic matrix with stationary distribution bf pi rm t which is partitioned conformally in the form bf pi 1 rm t ldots bf pi p rm t this paper establishes the relative error bound for bf pi i rm t when each block of p gets a small relative perturbation

remarks on global regularity of 2d generalized mhd equations abstract in this paper we investigate the global regularity of 2d generalized mhd equations in which the dissipation term and magnetic diffusion term are u and b respectively let u 0 b 0 h s with s 2 it is showed that the smooth solution u x t b x t is globally regular for the case 0 1 2 3 2

on the well posedness of various one dimensional model equations for fluid motion abstract we consider 1d equations with nonlocal velocity of the form w t u w x u x w w where the nonlocal velocity u is given by 1 u 1 x x w 0 or 2 u h w h is the hilbert transform in this paper we address several local well posedness results with blow up criteria for smooth initial data we then establish the global well posedness by using the blow up criteria

on the global well posedness of 2 d boussinesq system with variable viscosity abstract in this paper we investigate the global well posedness of 2 d boussinesq system which has variable kinematic viscosity and with thermal conductivity of d with general initial data provided that the viscosity coefficient is sufficiently close to some positive constant in l norm

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

nonexistence of simple hyperbolic blow up for the quasi geostrophic equation the problem we are concerned with is whether singularities form in finite time in incompressible fluid flows it is well known that the answer is no in the case of euler and navier stokes equations in dimension two in dimension three it is still an open problem for these equations in this paper we focus on a two dimensional active scalar model for the 3d euler vorticity equation constantin majda and tabak 7 suggested by studying rigorous theorems and detailed numerical experiments a general principle if the level set topology in the temperature field for the 2d quasi geostrophic active scalar in the region of strong scalar gradients does not contain a hyperbolic saddle then no finite time singularity is possible numerical simulations showed evidence of singular behavior when the geometry of the level sets of the active scalar contain a hyperbolic saddle there is a naturally associated notion of simple hyperbolic saddle breakdown the main theorem we present in this paper shows that such breakdown cannot occur in finite time we also show that the angle of the saddle cannot close in finite time and it cannot be faster than a double exponential in time using the same techniques we see that analogous results hold for incompressible 2d and 3d euler these results were announced in 9 but with a slight difference in the definition of a simple hyperbolic saddle the definition given in section 4 generalizes the one given in the announcement see also constantin 4 discussed in section 7 remark 5 below the whole work described in this paper is basically part of the author s thesis i am particularly grateful to my thesis advisor charles fefferman for his attention support guidance and advice i am indebted to d christodoulou and p constantin for helpful corrections and suggestions i wish to thank a majda for suggesting the subject and e tabak for discussions and com

a voting based computational framework for visual motion analysis and interpretation most approaches for motion analysis and interpretation rely on restrictive parametric models and involve iterative methods which depend heavily on initial conditions and are subject to instability further difficulties are encountered in image regions where motion is not smooth typically around motion boundaries this work addresses the problem of visual motion analysis and interpretation by formulating it as an inference of motion layers from a noisy and possibly sparse point set in a 4d space the core of the method is based on a layered 4d representation of data and a voting scheme for affinity propagation the inherent problem caused by the ambiguity of 2d to 3d interpretation is usually handled by adding additional constraints such as rigidity however enforcing such a global constraint has been problematic in the combined presence of noise and multiple independent motions by decoupling the processes of matching outlier rejection segmentation and interpretation we extract accurate motion layers based on the smoothness of image motion and then locally enforce rigidity for each layer in order to infer its 3d structure and motion the proposed framework is noniterative and consistently handles both smooth moving regions and motion discontinuities without using any prior knowledge of the motion model

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

aggregation disaggregation methods for computing the stationary distribution of a markov chain we implement and analyse aggregation disaggregation procedures constructed to accelerate the convergence of successive approximation methods suitable for computing the stationary distribution of a finite markov chain we define six of these methods and analyse them in detail in particular we show that some existing procedures lie in the aggregation disaggregation framework we set and hence can be considered as special cases also for all described methods we identify cases where they are promising numerical examples for the applications of some of the methods for nearly completely decomposable stochastic matrices are given as well

commutator estimate and its application to regularity criteria of the dissipative quasi geostrophic equation abstract a new commutator estimate with respect to a nonlinear convection upper bounded by a single partial derivative component in hilbert spaces is obtained as an application regularity criteria on the supercritical quasi geostrophic equation are obtained provided that solution growth conditions are assumed to involve a single partial derivative component

on the two dimensional muskat problem with monotone large initial data we consider the evolution of two incompressible immiscible fluids with different densities in porous media known as the muskat problem 21 which in two dimensions is analogous to the hele shaw cell 24 we establish for a class of large and monotone initial data the global existence of weak solutions the proof is based on a local well posedness result for the initial data with certain specific asymptotics at spatial infinity and a new maximum principle for the first derivative of the graph function 2016 wiley periodicals inc

viewpoint invariant texture description using fractal analysis image texture provides a rich visual description of the surfaces in the scene many texture signatures based on various statistical descriptions and various local measurements have been developed existing signatures in general are not invariant to 3d geometric transformations which is a serious limitation for many applications in this paper we introduce a new texture signature called the multifractal spectrum mfs the mfs is invariant under the bi lipschitz map which includes view point changes and non rigid deformations of the texture surface as well as local affine illumination changes it provides an efficient framework combining global spatial invariance and local robust measurements intuitively the mfs could be viewed as a better histogram with greater robustness to various environmental changes and the advantage of capturing some geometrical distribution information encoded in the texture experiments demonstrate that the mfs codes the essential structure of textures with very low dimension and thus represents an useful tool for texture classification

global regularity of the two dimensional incompressible generalized magnetohydrodynamics system abstract in this paper we consider the global regularity of the two dimensional generalized incompressible magnetohydrodynamics system with velocity dissipation exponent 1 4 and magnetic diffusion exponent 1 based on the improved integrability in terms of vorticity this result is a further improvement of very recent works jiu and zhao 2014 and yamazaki 2013 which require 1 3 and 1 therefore our result is more closer to the resolution of the well known global regularity issue on the 2d magnetohydrodynamics system 0 1

dynamics of a fractional hydrodynamical equation for the heisenberg paramagnet in the present work we study the global solvability and large time dynamics for a fractional generalization of the hydrodynamical equation modeling the soft micromagnetic materials introducing a cancellation property we prove the existence of weak solutions and establish a uniqueness criterion a maximal principle is obtained and the global existence and uniqueness of smooth solutions are proved by some a priori estimates finally we analyze the asymptotic behavior of the solutions within the theory of infinite dimensional dissipative dynamical systems we prove that the problem generates a strongly continuous semigroup on a suitable phase space and show the existence of a maximal global attractor a in this phase space moreover in absence of external force global attractor a converges exponentially to a single equilibrium

stationary distributions and mean first passage times of perturbed markov chains stationary distributions of perturbed finite irreducible discrete time markov chains are intimately connected with the behaviour of associated mean first passage times this interconnection is explored through the use of generalized matrix inverses some interesting qualitative results regarding the nature of the relative and absolute changes to the stationary probabilities are obtained together with some improved bounds ams classification 15a51 60j10 60j20 65f20 65f35

construction of solutions of the critical sqg equation in bounded domains abstract we consider the critical dissipative sqg equation in bounded domains with the square root of the dirichlet laplacian dissipation we construct global bounded interior lipschitz solutions from arbitrary large bounded interior lipschitz initial data

growth of solutions for qg and 2d euler equations the work of constantin majda tabak 1 developed an analogy between the quasi geostrophic and 3d euler equations constantin majda and tabak proposed a candidate for a singularity for the quasi geostrophic equation their numerics showed evidence of a blow up for a particular initial data where the level sets of the temperature contain a hyperbolic saddle the arms of the saddle tend to close in finite time producing a sharp front numerics studies done later by ohkitani yamada 8 and constantin nie schorghofer 2 with the same initial data suggested that instead of a singularity the derivatives of the temperature were increasing as double exponential in time the study of collapse on a curve was first studied in 1 for the quasi geostrophic equation where they considered a simplified ansatz for classical frontogenesis with trivial topology at the time of collapse the scalar is discontinuous across the curve x2 f x1 with different limiting values for the temperature on each side of the front they show that under this topology the directional field remains smooth up to the collapse which contradicts the following theorem proven in 1

on a 1d nonlocal transport equation with nonlocal velocity and subcritical or supercritical diffusion abstract we study a 1d transport equation with nonlocal velocity with subcritical or supercritical dissipation for all data in the weighted sobolev space h k w l where k max 0 3 2 and w is a given family of muckenhoupt weights we prove a global existence result in the subcritical case 1 2 we also prove a local existence theorem for large data in h 2 w l in the supercritical case 0 1 the proofs are based on the use of the weighted littlewood paley theory interpolation along with some new commutator estimates

analytical behavior of two dimensional incompressible flow in porous media in this paper we study the analytic structure of a two dimensional mass balance equation of an incompressible fluid in a porous medium given by darcy s law we obtain local existence and uniqueness by the particle trajectory method and we present different global existence criterions these analytical results with numerical simulations are used to indicate nonformation of singularities moreover blow up results are shown in a class of solutions with infinite energy

blockwise perturbation theory for nearly uncoupled markov chains and its application abstract let p be the transition matrix of a nearly uncoupled markov chain the states can be grouped into aggregates such that p has the block form p p ij i j 1 k where p ii is square and p ij is small for i j let t be the stationary distribution partitioned conformally as t 1 t k t in this paper we bound the relative error in each aggregate distribution i t caused by small relative perturbations in p ij the error bounds demonstrate that nearly uncoupled markov chains usually lead to well conditioned problems in the sense of blockwise relative error as an application we show that with appropriate stopping criteria iterative aggregation disaggregation algorithms will achieve such structured backward errors and compute each aggregate distribution with high relative accuracy

l2 stability for solutions of subcritical quasi geostrophic equation with large perturbations abstract this paper concerns with the asymptotic stability for the weak solution of the two dimensional dissipative subcritical quasi geostrophic equation in the class l p 0 t l q r 2 for p 2 q 2 q 1 2 it is proved that although the initial data and external force perturbations from are large every perturbed weak solution converges asymptotically to in l 2 r 2 as t as a byproduct we also obtain the weak strong uniqueness criterion of subcritical quasi geostrophic equation which improves the earlier results

finite time singularities in a 1d model of the quasi geostrophic equation in this paper we study 1d equations with nonlocal flux these models have resemblance of the 2d quasi geostrophic equation we show the existence of singularities in finite time and construct explicit solutions to the equations where the singularities formed are shocks for the critical viscosity case we show formation of singularities and global existence of solutions for small initial data

on the global evolution of vortex filaments blobs and small loops in 3d ideal flows we consider a wide class of approximate models of evolution of singular distributions of vorticity in three dimensional incompressible fluids and we show that they have global smooth solutions the proof exploits the existence of suitable hamiltonian functions the approximate models we analyze essentially discrete and continuous vortex filaments and vortex loops are related to some problem of classical physics concerning turbulence and also to the numerical approximation of flows with very high reynolds number finally we apply our strategy to discrete models for filaments used in numerical methods

a pointwise estimate for fractionary derivatives with applications to partial differential equations this article emphasizes the role played by a remarkable pointwise inequality satisfied by fractionary derivatives in order to obtain maximum principles and lp decay of solutions of several interesting partial differential equations in particular there are applications to quasigeostrophic flows in two space variables with critical viscosity that model the eckman pumping see baroud ch n plapp b b she z s swinney h l 2002 phys rev lett 88 114501 and constantin p 2002 phys rev lett 89 184501

a frequency localized maximum principle applied to the 2d quasi geostrophic equation in this paper we prove a maximum principle for a frequency localized transport diffusion equation as an application we prove the local well posedness of the supercritical quasi geostrophic equation in the critical besov spaces mathring b 1 alpha infty q and global well posedness of the critical quasi geostrophic equation in mathring b 0 infty q for all 1 q here mathring b s infty q is the closure of the schwartz functions in the norm of b s infty q

operator splitting for two dimensional incompressible fluid equations we analyze splitting algorithms for a class of two dimensional fluid equations which includes the incompressible navier stokes equations and the surface quasi geostrophic equation our main result is that the godunov and strang splitting methods converge with the expected rates provided the initial data are sufficiently regular

local adaptivity to variable smoothness for exemplar based image regularization and representation a novel adaptive and exemplar based approach is proposed for image restoration denoising and representation the method is based on a pointwise selection of similar image patches of fixed size in the variable neighborhood of each pixel the main idea is to associate with each pixel the weighted sum of data points within an adaptive neighborhood we use small image patches e g 7 7 or 9 9 patches to compute these weights since they are able to capture local geometric patterns and texels seen in images in this paper we mainly focus on the problem of adaptive neighborhood selection in a manner that balances the accuracy of approximation and the stochastic error at each spatial position the proposed pointwise estimator is then iterative and automatically adapts to the degree of underlying smoothness with minimal a priori assumptions on the function to be recovered the method is applied to artificially corrupted real images and the performance is very close and in some cases even surpasses to that of the already published denoising methods the proposed algorithm is demonstrated on real images corrupted by non gaussian noise and is used for applications in bio imaging

solutions of the 2d quasi geostrophic equation in holder spaces abstract the 2d quasi geostrophic equation t u 0 u r is a two dimensional model of the 3d hydrodynamics equations when 1 2 the issue of existence and uniqueness concerning this equation becomes difficult it is shown here that this equation with either 0 or 0 and 0 1 2 has a unique local in time solution corresponding to any initial datum in the space c r l q for r 1 and q 1

stochastic complementation uncoupling markov chains and the theory of nearly reducible systems a concept called stochastic complementation is an idea which occurs naturally although not always explicitly in the theory and application of finite markov chains this paper brings this idea to the forefront with an explicit definition and a development of some of its properties applications of stochastic complementation are explored with respect to problems involving uncoupling procedures in the theory of markov chains furthermore the role of stochastic complementation in the development of the classical simon ando theory of nearly reducible system is presented

existence and decay of solutions to the dissipative quasi geostrophic equation with delays abstract we consider the dissipative quasi geostrophic equation with forcing and advective terms containing delays we prove the existence of weak solutions and algebraic decay of the energy provided the initial data 0 is in l p l 2 1 p 2 and the forcing term satisfies some mild conditions on its long time behavior

layered 4d representation and voting for grouping from motion we address the problem of perceptual grouping from motion cues by formulating it as a motion layers inference from a sparse and noisy point set in a 4d space our approach is based on a layered 4d representation of data and a voting scheme for token communication within a tensor voting computational framework given two sparse sets of point tokens the image position and potential velocity of each token are encoded into a 4d tensor by enforcing the smoothness of motion through a voting process the correct velocity is selected for each input point as the most salient token an additional dense voting step allows for the inference of a dense representation in terms of pixel velocities motion regions and boundaries using a 4d space for this tensor voting approach is essential since it allows for a spatial separation of the points according to both their velocities and image coordinates unlike most other methods that optimize certain objective functions our approach is noniterative and therefore does not suffer from local optima or poor convergence problems we demonstrate our method with synthetic and real images by analyzing several difficult cases opaque and transparent motion rigid and nonrigid motion curves and surfaces in motion

asymptotic expansion of solutions to the drift diffusion equation with fractional dissipation abstract the initial value problem for the drift diffusion equation arising from the model of semiconductor device simulations is studied the dissipation on this equation is given by the fractional laplacian 2 large time behavior of solutions to the drift diffusion equation with 0 1 is discussed when 1 large time behavior of solutions is known however when 0 1 the perturbation methods used in the preceding works would not work in this paper the asymptotic expansion of solutions with high order is derived

unsupervised texture segmentation using markov random field models the problem of unsupervised segmentation of textured images is considered the only explicit assumption made is that the intensity data can be modeled by a gauss markov random field gmrf the image is divided into a number of nonoverlapping regions and the gmrf parameters are computed from each of these regions a simple clustering method is used to merge these regions the parameters of the model estimated from the clustered segments are then used in two different schemes one being all approximation to the maximum a posterior estimate of the labels and the other minimizing the percentage misclassification error the proposed approach is contrasted with the algorithm of s lakshamanan and h derin 1989 which uses a simultaneous parameter estimation and segmentation scheme the results of the adaptive segmentation algorithm of lakshamanan and derin are compared with a simple nearest neighbor classification scheme to show that if enough information is available simple techniques could be used as alternatives to computationally expensive schemes

a markov random field model based approach to unsupervised texture segmentation using local and global spatial statistics many studies have proven that statistical model based texture segmentation algorithms yield good results provided that the model parameters and the number of regions be known a priori in this correspondence we present an unsupervised texture segmentation method that does not require knowledge about the different texture regions their parameters or the number of available texture classes the proposed algorithm relies on the analysis of local and global second and higher order spatial statistics of the original images the segmentation map is modeled using an augmented state markov random field including an outlier class that enables dynamic creation of new regions during the optimization process a bayesian estimate of this map is computed using a deterministic relaxation algorithm results on real world textured images are presented