stacs new active contour scheme for cardiac mr image segmentation the paper presents a novel stochastic active contour scheme stacs for automatic image segmentation designed to overcome some of the unique challenges in cardiac mr images such as problems with low contrast papillary muscles and turbulent blood flow stacs minimizes an energy functional that combines stochastic region based and edge based information with shape priors of the heart and local properties of the contour the minimization algorithm solves by the level set method the euler lagrange equation that describes the contour evolution stacs includes an annealing schedule that balances dynamically the weight of the different terms in the energy functional three particularly attractive features of stacs are 1 ability to segment images with low texture contrast by modeling stochastically the image textures 2 robustness to initial contour and noise because of the utilization of both edge and region based information 3 ability to segment the heart from the chest wall and the undesired papillary muscles due to inclusion of heart shape priors application of stacs to a set of 48 real cardiac mr images shows that it can successfully segment the heart from its surroundings such as the chest wall and the heart structures the left and right ventricles and the epicardium we compare stacs automatically generated contours with manually traced contours or the gold standard using both area and edge similarity measures this assessment demonstrates very good and consistent segmentation performance of stacs

on existence and uniqueness for a coupled system modeling immiscible flow through a porous medium we consider a system of nonlinear coupled partial differential equations that models immiscible two phase flow through a porous medium a primary difficulty with this problem is its degenerate nature under reasonable assumptions on the data and for appropriate boundary and initial conditions we prove the existence of a weak solution to the problem in a certain sense using a compactness argument this is accomplished by regularizing the problem and proving that the regularized problem has a unique solution which is bounded independently of the regularization parameter we also establish a priori estimates for uniqueness of a solution

propositional dynamic logic of flowcharts following a suggestion of pratt we consider propositional dynamic logic in which programs are nondeterministic finite automata over atomic programs and tests i e flowcharts rather than regular expressions while the resulting version of pdl call it apdl is clearly equivalent in expressive power to pdl it is also in the worst case exponentially more succinct in particular deciding its validity problem by reducing it to that of pdl leads to a double exponential time procedure although pdl itself is decidable in exponential time we present an elementary combined proof of the completeness of a simple axiom system for apdl and decidability of the validity problem in exponential time the results are thus stronger than those for pdl since pdl can be encoded in apdl with no additional cost and the proofs simpler since induction on the structure of programs is virtually eliminated our axiom system for apdl relates to the pdl system just as floyd s proof method for partial correctness relates to hoare s

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

a review of statistical approaches to level set segmentation integrating color texture motion and shape since their introduction as a means of front propagation and their first application to edge based segmentation in the early 90 s level set methods have become increasingly popular as a general framework for image segmentation in this paper we present a survey of a specific class of region based level set segmentation methods and clarify how they can all be derived from a common statistical framework region based segmentation schemes aim at partitioning the image domain by progressively fitting statistical models to the intensity color texture or motion in each of a set of regions in contrast to edge based schemes such as the classical snakes region based methods tend to be less sensitive to noise for typical images the respective cost functionals tend to have less local minima which makes them particularly well suited for local optimization methods such as the level set method we detail a general statistical formulation for level set segmentation subsequently we clarify how the integration of various low level criteria leads to a set of cost functionals we point out relations between the different segmentation schemes in experimental results we demonstrate how the level set function is driven to partition the image plane into domains of coherent color texture dynamic texture or motion moreover the bayesian formulation allows to introduce prior shape knowledge into the level set method we briefly review a number of advances in this domain

games for the m calculus abstract given a formula of the propositional calculus we construct a tableau of the formula and define an infinite game of two players of which one wants to show that the formula is satisfiable and the other seeks the opposite the strategy for the first player can be further transformed into a model of the formula while the strategy for the second forms what we call a refutation of the formula using martin s determinacy theorem we prove that any formula has either a model or a refutation this completeness result is a starting point for the completeness theorem for the calculus to be presented elsewhere however we argue that refutations have some advantages of their own they are generated by a natural system of sound logical rules and can be presented as regular trees of the size exponential in the size of a refuted formula this last aspect completes the small model theorem for the calculus established by emerson and jutla 1988 thus on a more practical side refutations can be used as small objects testifying incorrectness of a program specification expressed by a formula we illustrate this point by an example

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

noisy texture classification a higher order statistics approach abstract in this paper a novel texture classification scheme using higher order statistics hos functions as discriminating features is proposed it is well known that such statistical parameters are insensitive to additive gaussian noise in particular third order statistical parameters i e third order cumulants and bispectrum are insensitive to any symmetrically distributed noise and also exhibit the capability of better characterizing non gaussian signals by exploiting these hos properties it is possible to devise a robust method for classifying textures affected by noise with different distributions and even with very low signal to noise ratios

object and texture classification using higher order statistics the problem of the detection and classification of deterministic objects and random textures in a noisy scene is discussed an energy detector is developed in the cumulant domain by exploiting the noise insensitivity of higher order statistics an efficient implementation of this detector is described using matched filtering its performance is analyzed using asymptotic distributions in a binary hypothesis testing framework the object and texture discriminant functions are minimum distance classifiers in the cumulant domain and can be efficiently implemented using a bank of matched filters they are immune to additive gaussian noise and insensitive to object shifts important extensions which can handle object rotation and scaling are also discussed an alternative texture classifier is derived from a ml viewpoint and is statistically efficient at the expense of complexity the application of these algorithms to the texture modeling problem is indicated and consistent parameter estimates are obtained

results on the propositional μ calculus abstract in this paper we define and study a propositional calculus l which consists essentially of propositional modal logic with a least fixpoint operator l is syntactically simpler yet strictly more expressive than propositional dynamic logic pdl for a restricted version we give an exponential time decision procedure small model property and complete deductive system theory subsuming the corresponding results for pdl

analysis of fully discrete fem for miscible displacement in porous media with bear scheidegger diffusion tensor fully discrete galerkin finite element methods are studied for the equations of miscible displacement in porous media with the commonly used bear scheidegger diffusion dispersion tensor begin aligned d mathbf u gamma d m i mathbf u bigg alpha t i alpha l alpha t frac mathbf u otimes mathbf u mathbf u 2 bigg end aligned previous works on optimal order l infty 0 t l 2 norm error estimate required the regularity assumption nabla x partial td mathbf u x t in l infty 0 t l infty omega while the bear scheidegger diffusion dispersion tensor is only lipschitz continuous even for a smooth velocity field mathbf u in terms of the maximal l p regularity of fully discrete finite element solutions of parabolic equations optimal error estimate in l p 0 t l q norm and almost optimal error estimate in l infty 0 t l q norm are established under the assumption of d mathbf u being lipschitz continuous with respect to mathbf u

multi reference shape priors for active contours in this paper we present a new way of constraining the evolution of an active contour with respect to a set of fixed reference shapes this approach is based on a description of shapes by the legendre moments computed from their characteristic function this provides a region based representation that can handle arbitrary shape topologies moreover exploiting the properties of moments it is possible to include intrinsic affine invariance in the descriptor which solves the issue of shape alignment without increasing the number of d o f of the initial problem and allows introducing geometric shape variabilities our new shape prior is based on a distance in terms of descriptors between the evolving curve and the reference shapes minimizing the corresponding shape energy leads to a geometric flow that does not rely on any particular representation of the contour and can be implemented with any contour evolution algorithm we introduce our prior into a two class segmentation functional showing its benefits on segmentation results in presence of severe occlusions and clutter examples illustrate the ability of the model to deal with large affine deformation and to take into account a set of reference shapes of different topologies

a logic to reason about likelihood abstract we present a logic ll which uses a modal operator l to help capture the notion of being likely despite the fact that likelihood is not assigned quantitative values through probabilities ll captures many of the properties of likelihood in an intuitively appealing way we give a possible worlds style semantics to ll and using standard techniques of modal logic we give a complete axiomatization for ll and show that satisfiability of ll formulas can be decided in exponential time we discuss how the logic might be used in areas such as medical diagnosis where decision making in the face of uncertainties is crucial we conclude by using ll to give a formal proof of correctness of some aspects of a protocol for exchanging secrets

localizing region based active contours in this paper we propose a natural framework that allows any region based segmentation energy to be re formulated in a local way we consider local rather than global image statistics and evolve a contour based on local information localized contours are capable of segmenting objects with heterogeneous feature profiles that would be difficult to capture correctly using a standard global method the presented technique is versatile enough to be used with any global region based active contour energy and instill in it the benefits of localization we describe this framework and demonstrate the localization of three well known energies in order to illustrate how our framework can be applied to any energy we then compare each localized energy to its global counterpart to show the improvements that can be achieved next an in depth study of the behaviors of these energies in response to the degree of localization is given finally we show results on challenging images to illustrate the robust and accurate segmentations that are possible with this new class of active contour models

on existence and uniqueness results for a coupled system modeling miscible displacement in porous media initial boundary value problems for a nonlinear differential system of two equations are considered in this paper this system of equations one of elliptic form for the pressure and the other of parabolic form for the concentration of one fluid governs the miscible displacement of one incompressible fluid by another in a porous medium under some reasonable assumptions on the data it is proved that the system possesses a weak solution and uniqueness is also established for the semiclassical solution of the system

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

process logic with regular formulas the paper proposes an extension rpl of the process logic pl of harel kozen and parikh 1980 the pl formula operators f and suf are replaced by the operators chop and slice corresponding to kleene s regular operators and thus enabling formulas to express regular sets of paths the main result is that in expressive power pl rpl the hard part being in showing that pl rpl it is argued that this version of pl comes closer to the desired goal of a natural and powerful yet decidable logic for reasoning about the ongoing behavior of programs

looping vs repeating in dynamic logic two extensions of propositional dynamic logic for dealing with infinite computations lpdl and rpdl are compared in expressive power the first is obtained by adding the assertion loop for any program meaning contains an infinite computation and the second by adding repeat meaning can be repeated indefinitely while repeat can be used to encode loop and hence lpdl rpdl it is shown here that the converse fails thus lpdl

local histogram based segmentation using the wasserstein distance we propose and analyze a nonparametric region based active contour model for segmenting cluttered scenes the proposed model is unsupervised and assumes pixel intensity is independently identically distributed our proposed energy functional consists of a geometric regularization term that penalizes the length of the partition boundaries and a region based image term that uses histograms of pixel intensity to distinguish different regions more specifically the region data encourages segmentation so that local histograms within each region are approximately homogeneous an advantage of using local histograms in the data term is that histogram differentiation is not required to solve the energy minimization problem we use wasserstein distance with exponent 1 to determine the dissimilarity between two histograms the wasserstein distance is a metric and is able to faithfully measure the distance between two histograms compared to many pointwise distances moreover it is insensitive to oscillations and therefore our model is robust to noise a fast global minimization method based on chan et al in siam j appl math 66 5 1632 1648 2006 bresson et al in j math imaging vis 28 2 151 167 2007 is employed to solve the proposed model the advantages of using this method are two fold first the computational time is less than that of the method by gradient descent of the associated euler lagrange equation chan et al in proc of ssvm pp 697 708 2007 second it is able to find a global minimizer finally we propose a variant of our model that is able to properly segment a cluttered scene with local illumination changes

the propositional dynamic logic of deterministic well structured programs abstract we consider a restricted propositional dynamic logic strict deterministic propositional dynamic logic sdpdl which is appropriate for reasoning about deterministic well structured programs in contrast to pdl for which the validity problem is known to be complete in deterministic exponential time the validity problem for sdpdl is shown to be polynomial space complete we also show that sdpdl is less expressive than pdl and give a complete axiomatization for it the results rely on structure theorems for models of satisfiable sdpdl formulas and the proofs give insight into the effects of nondeterminism on intractability and expressiveness in program logics

fuzzification of the miscible displacement model in heterogeneous porous media abstract typical realistic models for multiphase flow in heterogeneous formations are complex and random and must incorporate the uncertainties inherent to the mixture process these uncertainties can be modeled using differential equations coefficients such as hydrodynamic dispersivity in this work the mathematical model is expressed in terms of a nonlinear coupled system of stochastic partial differential equations a second order elliptic equation for the pressure and a hyperbolic dominated transport diffusion equation for the solvent concentration in the mixture besides the longitudinal dispersion coefficient is a fuzzy number new perspective on the quantification of uncertainty for parameter estimation problems by means of numerical simulations and membership functions is the purpose of this research in this way a fuzzification of the semiclassical solution numerical approximation is built in this regard it is proved the continuity of the function that assigns the 3 tuple comprised by longitudinal dispersion transverse dispersion and molecular diffusion to the corresponding value of the semiclassical solution at a fixed point of the domain the continuity result along with zadeh s extension principle is applied to obtain the fuzzification the relevance of this study resides in the novelty of the methodology that considers a model parameter as a fuzzy number meanwhile it is usually taken as a constant in literature other unprecedented result lays in the discovery of the link between theoretical concepts and numerical approximations to obtain a fuzzification

a guide to completeness and complexity for modal logics of knowledge and belief abstract we review and re examine possible worlds semantics for propositional logics of knowledge and belief with three particular points of emphasis 1 we show how general techniques for finding decision procedures and complete axiomatizations apply to models for knowledge and belief 2 we show how sensitive the difficulty of the decision procedure is to such issues as the choice of modal operators and the axiom system and 3 we discuss how notions of common knowledge and distributed knowledge among a group of agents fit into the possible worlds framework as far as complexity is concerned we show among other results that while the problem of deciding satisfiability of an s5 formula with one agent is np complete the problem for many agents is pspace complete adding a distributed knowledge operator does not change the complexity but once a common knowledge operator is added to the language the problem becomes complete for exponential time

discontinuous galerkin finite element convergence for incompressible miscible displacement problems of low regularity in this article we analyze the numerical approximation of incompressible miscible displacement problems with a combined mixed finite element and discontinuous galerkin method under minimal regularity assumptions the main result is that sequences of discrete solutions weakly accumulate at weak solutions of the continuous problem in order to deal with the nonconformity of the method and to avoid overpenalization of jumps across interelement boundaries the careful construction of a reflexive subspace of the space of bounded variation which compactly embeds into l 2 omega and of a lifting operator which is compatible with the nonlinear diffusion coefficient are required an equivalent skew symmetric formulation of the convection and reaction terms of the nonlinear partial differential equation allows us to avoid flux limitation and nonetheless leads to an unconditionally stable and convergent numerical method numerical experiments underline the robustness of the proposed algorithm

the complementation problem for bu chi automata with applications to temporal logic the problem of complementing buchi automata arises when developing procedures for temporal logics of programs unfortunately previously known constructions for complementing buchi automata involve a doubly exponential blow up in the size of the automaton we present a construction that involves only an exponential blow up we use this construction to prove a polynomial space upper bound for the propositional temporal logic of regular events and to prove a complexity hierarchy result for quantified propositional temporal logic

subject oriented spatial logic abstract we present a modal logic for subject oriented representation and reasoning about a two dimensional space which we call sosl the space is represented with the polar coordinate system where the subject occupies the central point and modal operators are interpreted by relations defined relatively to the position and orientation of the subject namely outwards inwards clockwise counter clockwise and the transitive closures of the first two such logic enables to express operators for the intrinsic relations in front behind to the left and to the right of the subject for the relative relations behind an object between the subject and an object to the left of an object and to the right of an object and hybrid or distance operators we prove that the satisfiability problem in sosl is pspace complete the same complexity holds over the classes of finite or infinite models however for models of fixed size the problem becomes np complete

dream 2 s deformable regions driven by an eulerian accurate minimization method for image and video segmentation this paper deals with image and video segmentation using active contours we propose a general form for the energy functional related to region based active contours we compute the associated evolution equation using shape derivation tools and accounting for the evolving region based terms then we apply this general framework to compute the evolution equation from functionals that include various statistical measures of homogeneity for the region to be segmented experimental results show that the determinant of the covariance matrix appears to be a very relevant tool for segmentation of homogeneous color regions as an example it has been successfully applied to face segmentation in real video sequences

complete axiomatizations for reasoning about knowledge and time sound and complete axiomatizations are provided for a number of different logics involving modalities for knowledge and time these logics arise from different choices for various parameters regarding the interaction of knowledge with time and regarding the language used all the logics considered involve the discrete time linear temporal logic operators next and until and an operator for the knowledge of each of a number of agents both the single agent and multiple agent cases are studied in some instances of the latter there is also an operator for the common knowledge of the group of all agents four different semantic properties of agents are considered whether they i have a unique initial state ii operate synchronously iii have perfect recall and iv learn the property of no learning is essentially dual to perfect recall not all settings of these parameters lead to recursively axiomatizable logics but sound and complete axiomatizations are presented for all the ones that do

image segmentation using active contours calculus of variations or shape gradients we consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals we show that one can go from one class to the otherby solving poisson s orhelmholtz s equation with well chosen boundar y conditions using this equivalence we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding euler lagrange equations we revisit this problem using the notion of a shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals we also define a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding gateaux derivatives and euler lagrange equations finally we apply this new functional to the problem of regions segmentation in sequences of color images we briefly describe our numerical scheme and show some experimental results

accepting conditions for automata on ω languages abstract in this paper we study the languages accepted by finite automata under a new type of accepting conditions which are based on whether the automaton enters all of its accepting states infinitely many times or not we investigate the classes of languages defined thereby in relation to other well known subclasses of the class of regular languages

on a fully coupled nonlinear parabolic problem modelling miscible compressible displacement in porous media we study a model describing a compressible and miscible displacement in a porous medium it consists of a coupled system of nonlinear parabolic partial differential equations using nonclassical estimates and renormalization tools we prove the existence of relevant weak solutions for the problem this is the first existence result obtained for a transport model containing both the coupling due to the compressibility assumption and the coupling due to the concentration dependent viscosity

active contours driven by the salient edge energy model in this brief we present a new indicator i e salient edge energy for guiding a given contour robustly and precisely toward the object boundary specifically we define the salient edge energy by exploiting the higher order statistics on the diffusion space and incorporate it into a variational level set formulation with the local region based segmentation energy for solving the problem of curve evolution in contrast to most previous methods the proposed salient edge energy allows the curve to find only significant local minima relevant to the object boundary even in the noisy and cluttered background moreover the segmentation performance derived from our new energy is less sensitive to the size of local windows compared with other recently developed methods owing to the ability of our energy function to suppress diverse clutters the proposed method has been tested on various images and experimental results show that the salient edge energy effectively drives the active contour both qualitatively and quantitatively compared to various state of the art methods

finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials in this paper we study heat and moisture transport through porous textile materials with phase change described by a degenerate nonlinear and strongly coupled parabolic system an uncoupled finite difference method with semi implicit euler scheme in time direction is proposed for the system we prove the existence and uniqueness of the solution of the finite difference system the optimal error estimates in both discrete l 2 and h 1 norms are obtained under the condition that the mesh sizes and h are smaller than a positive constant which depends solely upon physical parameters involved numerical results are presented to confirm our theoretical analysis and compared with experimental data

convergence analysis of a mixed finite volume scheme for an elliptic parabolic system modeling miscible fluid flows in porous media we study a finite volume discretization of a strongly coupled elliptic parabolic pde system describing miscible displacement in a porous medium we discretize each equation by a finite volume scheme which allows a wide variety of unstructured grids in any space dimension and gives strong enough convergence for handling the nonlinear coupling of the equations we prove the convergence of the scheme as the time and space steps go to 0 finally we provide numerical results to demonstrate the efficiency of the proposed numerical scheme

efficient algorithm for level set method preserving distance function the level set method is a popular technique for tracking moving interfaces in several disciplines including computer vision and fluid dynamics however despite its high flexibility the original level set method is limited by two important numerical issues first the level set method does not implicitly preserve the level set function as a distance function which is necessary to estimate accurately geometric features s a the curvature or the contour normal second the level set algorithm is slow because the time step is limited by the standard courant friedrichs lewy cfl condition which is also essential to the numerical stability of the iterative scheme recent advances with graph cut methods and continuous convex relaxation methods provide powerful alternatives to the level set method for image processing problems because they are fast accurate and guaranteed to find the global minimizer independently to the initialization these recent techniques use binary functions to represent the contour rather than distance functions which are usually considered for the level set method however the binary function cannot provide the distance information which can be essential for some applications s a the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging in this paper we propose a fast algorithm to preserve distance functions in level set methods our algorithm is inspired by recent efficient l1 optimization techniques which will provide an efficient and easy to implement algorithm it is interesting to note that our algorithm is not limited by the cfl condition and it naturally preserves the level set function as a distance function during the evolution which avoids the classical re distancing problem in level set methods we apply the proposed algorithm to carry out image segmentation where our methods prove to be 5 6 times faster than standard distance preserving level set techniques we also present two applications where preserving a distance function is essential nonetheless our method stays generic and can be applied to any level set methods that require the distance information

an elementary proof of the completeness of pdl abstract we give an elementary proof of the completeness of the segerberg axions for propositional dynamic logic

unconditional convergence and optimal error estimates of a galerkin mixed fem for incompressible miscible flow in porous media in this paper we study the unconditional convergence and error estimates of a galerkin mixed fem with the linearized semi implicit euler scheme for the equations of incompressible miscible flow in porous media we prove that the optimal l 2 error estimates hold without any time step convergence conditions while all previous works require certain time step restrictions our theoretical results provide a new understanding on commonly used linearized schemes the proof is based on a splitting of the error into two parts the error from the time discretization of the pdes and the error from the finite element discretization of corresponding time discrete pdes the approach used in this paper can be applied to more general nonlinear parabolic systems and many other linearized semi implicit time discretizations

integrated active contours for texture segmentation we address the issue of textured image segmentation in the context of the gabor feature space of images gabor filters tuned to a set of orientations scales and frequencies are applied to the images to create the gabor feature space a two dimensional riemannian manifold of local features is extracted via the beltrami framework the metric of this surface provides a good indicator of texture changes and is used therefore in a beltrami based diffusion mechanism and in a geodesic active contours algorithm for texture segmentation the performance of the proposed algorithm is compared with that of the edgeless active contours algorithm applied for texture segmentation moreover an integrated approach extending the geodesic and edgeless active contours approaches to texture segmentation is presented we show that combining boundary and region information yields more robust and accurate texture segmentation results

error estimates of splitting galerkin methods for heat and sweat transport in textile materials this paper is concerned with a single component model of heat and vapor sweat transport through three dimensional porous textile materials with phase change which is described by a nonlinear degenerate and strongly coupled parabolic system an uncoupled splitting galerkin method with semi implicit euler scheme in time direction is proposed for the system in this method a linearized scheme is applied for the approximation to darcy s velocity simultaneously in the mass and energy equations which leads to physical conservation of the method in the flow convection the existence and uniqueness of solution of the finite element system is proved and the optimal error estimate in an energy norm is obtained numerical results are presented to confirm our theoretical analysis and are compared with experimental data

nonlinear darcy fluid flow with deposition in this article we consider a model of a filtration process the process is modeled using the nonlinear darcy fluid flow equations with a varying permeability coupled with a deposition equation existence and uniqueness of the solution to the modeling equations is established a numerical approximation scheme is proposed and analyzed with an a priori error estimate derived numerical experiments are presented which support the obtained theoretical results

concurrent program schemes and their logics abstract we define and investigate several classes of concurrent program schemes including goto schemes and two versions of structured schemes based on extensions of the regular expressions to trees the schemes are studied on the first order boolean variable and propositional levels we also define and study the dynamic logics based on these classes of schemes including issues of decidability and axiomatization

propositional dynamic logic of looping and converse is elementarily decidable propositional dynamic logic is a formal system for reasoning about the before after behavior of regular program schemes an extension of propositional dynamic logic which includes both an infinite looping construct and a converse or backtracking construct is considered and it is proved that the satisfiability problem for this logic is elementarily decidable in order to establish this result deterministic two way automata on infinite trees are defined and it is shown how they can be simulated by nondeterministic one way automata the satisfiability problem for propositional dynamic logic of looping and converse is then reduced to the emptiness problem for these two way automata

convergence analysis of a family of ellam schemes for a fully coupled model of miscible displacement in porous media we analyse the convergence of numerical schemes in the gdm ellam gradient discretisation method eulerian lagrangian localised adjoint method framework for a strongly coupled elliptic parabolic pde which models miscible displacement in porous media these schemes include but are not limited to mixed finite element ellam and hybrid mimetic mixed ellam schemes a complete convergence analysis is presented on the coupled model using only weak regularity assumptions on the solution which are satisfied in practical applications and not relying on l infty bounds which are impossible to ensure at the discrete level given the anisotropic diffusion tensors and the general grids used in applications

the complexity of propositional linear temporal logics the complexity of satisfiability and determination of truth in a particular finite structure are considered for different propositional linear temporal logics it is shown that these problems are np complete for the logic with f and are pspace complete for the logics with f x with u with u s x operators and for the extended logic with regular operators given by wolper

a deposition model coupling stokes and darcy s equations with nonlinear deposition abstract in this work we investigate a filtration process whereby particulate is deposited in the flow domain causing the porosity of the region to decrease the fluid flow is modeled as a coupled stokes darcy flow problem and the deposition in the darcy domain is modeled using a nonlinear equation for the porosity existence and uniqueness of a solution to the governing equations is established additionally the nonnegativity and boundedness of the porosity is shown a finite element approximation scheme that preserves the nonnegativity and boundedness of the porosity is investigated accompanying numerical experiments support the analytical findings

minimization of region scalable fitting energy for image segmentation intensity inhomogeneities often occur in real world images and may cause considerable difficulties in image segmentation in order to overcome the difficulties caused by intensity inhomogeneities we propose a region based active contour model that draws upon intensity information in local regions at a controllable scale a data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour this energy is then incorporated into a variational level set formulation with a level set regularization term from which a curve evolution equation is derived for energy minimization due to a kernel function in the data fitting term intensity information in local regions is extracted to guide the motion of the contour which thereby enables our model to cope with intensity inhomogeneity in addition the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function experimental results for synthetic and real images show desirable performances of our method

distance regularized level set evolution and its application to image segmentation level set methods have been widely used in image processing and computer vision in conventional level set formulations the level set function typically develops irregularities during its evolution which may cause numerical errors and eventually destroy the stability of the evolution therefore a numerical remedy called reinitialization is typically applied to periodically replace the degraded level set function with a signed distance function however the practice of reinitialization not only raises serious problems as when and how it should be performed but also affects numerical accuracy in an undesirable way this paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution the level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations the distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward and backward fab diffusion effect which is able to maintain a desired shape of the level set function particularly a signed distance profile near the zero level set this yields a new type of level set evolution called distance regularized level set evolution drlse the distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors in contrast to complicated implementations of conventional level set formulations a simpler and more efficient finite difference scheme can be used to implement the drlse formulation drlse also allows the use of more general and efficient initialization of the level set function in its numerical implementation relatively large time steps can be used in the finite difference scheme to reduce the number of iterations while ensuring sufficient numerical accuracy to demonstrate the effectiveness of the drlse formulation we apply it to an edge based active contour model for image segmentation and provide a simple narrowband implementation to greatly reduce computational cost

global existence of weak solution to the heat and moisture transport system in fibrous porous media abstract this paper is concerned with theoretical analysis of a heat and moisture transfer model arising from textile industries which is described by a degenerate and strongly coupled parabolic system we prove the global in time existence of weak solution by constructing an approximate solution with some standard smoothing the proof is based on the physical nature of gas convection in which the heat energy flux in convection is determined by the mass vapor flux in convection

reasoning about infinite computations we investigate extensions of temporal logic by connectives defined by finite automata on infinite words we consider three different logics corresponding to three different types of acceptance conditions finite looping and repeating for the automata it turns out however that these logics all have the same expressive power and that their decision problems are all pspace complete we also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem