curve shortening and the rendezvous problem for mobile autonomous robots if a smooth closed and embedded curve is deformed along its normal vector field at a rate proportional to its curvature it shrinks to a circular point this curve evolution is called euclidean curve shortening and the result is known as the gage hamilton grayson theorem motivated by the rendezvous problem for mobile autonomous robots we address the problem of creating a polygon shortening flow a linear scheme is proposed that exhibits several analogues to euclidean curve shortening the polygon shrinks to an elliptical point convex polygons remain convex and the perimeter of the polygon is monotonically decreasing

modified curvature motion for image smoothing and enhancement we formulate a general modified mean curvature based equation for image smoothing and enhancement the key idea is to consider the image as a graph in some r sup 72 and apply a mean curvature type motion to the graph we consider some special cases relevant to grey scale and color images

a stochastic minimum principle and an adaptive pathwise algorithm for stochastic optimal control we present a numerical method for finite horizon stochastic optimal control models we derive a stochastic minimum principle smp and then develop a numerical method based on the direct solution of the smp the method combines monte carlo pathwise simulation and non parametric interpolation methods we present results from a standard linear quadratic control model and a realistic case study that captures the stochastic dynamics of intermittent power generation in the context of optimal economic dispatch models

euler s elastica and curvature based inpainting image inpainting is a special image restoration problem for which image prior models play a crucial role euler s elastica was first introduced to computer vision by mumford algebraic geometry and its applications springer verlag new york 1994 pp 491 506 as a curve prior model by functionalizing the elastica energy masnou and morel proceedings of the 5th ieee international conference image processing 3 1998 pp 259 263 proposed an elastica based variational inpainting model the current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of bertalmio sapiro caselles and ballester siggraph 2000 acm press new york 2000 and chan and shen j visual comm image rep 12 2001 pp 436 449 a computational scheme based on numerical pdes is presented which allows the automatic handling of topologically complex inpainting domains

dynamics of one and two dimensional fronts in a bistable equation with time delayed global feedback propagation failure and control mechanisms we study the evolution of fronts in a bistable equation with time delayed global feedback in the fast reaction and slow diffusion regime this equation generalizes the hodgkin grafstein and allen cahn equations we derive a nonlinear equation governing the motion of fronts which includes a term with delay in the one dimensional case this equation is linear we study the motion of one and two dimensional fronts finding a much richer dynamics than for the previously studied cases without time delayed global feedback we explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a hopf bifurcation as the delay time increases we show that for certain delay times the prevailing phase is different from that corresponding to the system in the absence of global coupling numerical simulations of the partial differential equation are in agreement with the analytical predictions

on stability in fuzzy linear programming problems abstract this study focuses on the problem of stability with respect to changes of centres of fuzzy parameters of the solution in fuzzy linear programming flp problems with symmetrical triangular fuzzy numbers and extended operations and inequalities

level set approach to mean curvature flow in arbitrary codimension we develop a level set theory for the mean curvature evolution of surfaces with arbitrary co dimension thus generalizing the previous work 8 15 on hypersurfaces the main idea is to surround the evolving surface of co dimension k in r by a family of hypersurfaces the level sets of a function evolving with normal velocity equal to the sum of the d k smallest principal curvatures the existence and the uniqueness of a weak level set solution is easily established using mainly the results of 8 and the theory of viscosity solutions for second order nonlinear parabolic equations the level set solutions coincide with the classical solutions whenever the latter exist the proof of this connection uses a careful analysis of the squared distance from the surfaces it is also shown that varifold solutions constructed by brakke 7 are included in the level set solutions the idea of surrounding the evolving surface by a family of hypersurfaces with a certain property is related to the barriers of de giorgi an introduction to the theory of barriers and his connection to the level set solutions is also provided

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

nurse scheduling using fuzzy modeling approach nurse scheduling is a complex scheduling problem and involves generating a schedule for each nurse that consists of shift duties and days off within a short term planning period in real world applications multiple sources of uncertainties are needed to be treated in providing higher quality schedules this paper presents a seminal research on the application of fuzzy set theory to the nurse scheduling problem nsp to treat uncertainties in the target values of the hospital management and nurses preferences more specifically a new multi objective integer programming model for the nsp is developed then based on this model three fuzzy goal programming models are developed using different fuzzy solution approaches a real world application is presented to confirm the viability of the proposed models also to provide the decision maker for a more confident solution set for policy decision making a sensitivity analysis is performed additionally to show the efficiency of the proposed model it is applied to several problem instances the paper contributes to the literature by revealing that fuzzy modeling approaches can effectively be used in the nsp in providing schedules which are more personalized and equitable for nurses and more satisfying for hospital management

generalized fuzzy linear programming for decision making under uncertainty feasibility of fuzzy solutions and solving approach in this study a generalized fuzzy linear programming gflp method is developed for dealing with uncertainties expressed as fuzzy sets the feasibility of fuzzy solutions of the gflp problem is investigated a stepwise interactive algorithm sia based on the idea of design of experiment is then advanced to solve the gflp problem this sia method was implemented through i discretizing membership grade of fuzzy parameters into a finite number of a cut levels ii converting the gflp model into an interval linear programming ilp submodel under every a cut level iii solving the ilp submodels through an interactive algorithm and obtaining the associated interval solutions iv acquiring the membership functions of fuzzy solutions through statistical regression methods a simple numerical example is then proposed to illustrate the solution process of the gflp model through sia a comparison between the solutions obtained though sia and monte carlo method is finally conducted to demonstrate the robustness of the sia method the results indicate that the membership functions for decision variables and objective function are reasonable and robust

blow up rates for the general curve shortening flow abstract the blow up rates of derivatives of the curvature function will be presented when the closed curves contract to a point in finite time under the general curve shortening flow in particular this generalizes a theorem of m e gage and r s hamilton about mean curvature flow in r 2

post optimality analysis on the membership functions of a fuzzy linear programming problem models of linear programming problems with fuzzy constraints are very well known in the current literature in almost all cases to solve these problems linear membership functions are used because they have very good properties and are very easy to manipulate in some cases however because of the knowledge that the decision maker has such membership functions could be modeled as nonlinear although the complexity of the problem could increase this paper considers the use of nonlinear membership functions in fuzzy linear programming problems to show that the corresponding solution to be obtained can be derived from a parallel linear model moreover it is easier to solve than the nonlinear model making use of a similar procedure to that of post optimal analysis in classical linear programming the case in which these membership functions are defined by means of piecewise linear approximations is also considered and analyzed

a multilevel algorithm for simultaneously denoising and deblurring images in this paper we develop a fast multilevel algorithm for simultaneously denoising and deblurring images under the total variation regularization although much effort has been devoted to developing fast algorithms for the numerical solution and the denoising problem was satisfactorily solved fast algorithms for the combined denoising and deblurring model remain to be a challenge recently several successful studies of approximating this model and subsequently finding fast algorithms were conducted which have partially solved this problem the aim of this paper is to generalize a fast multilevel denoising method to solving the minimization model for simultaneously denoising and deblurring our new idea is to overcome the complexity issue by a detailed study of the structured matrices that are associated with the blurring operator a fast algorithm can then be obtained for directly solving the variational model supporting numerical experiments on gray scale images are presented

piecewise approximation of contours through scale space selection of dominant points this paper describes a method of approximating a shape contour with a polygon the polygon vertices are extracted from the curvature extremes through a scale space description of the contour via linear diffusion these vertices are located on the contour points where the sharper changes of the contour directions occur using a proper strategy a set of extremes that result in a given approximation level is chosen by adding new vertices the approximation level can be improved and a scalable representation of the contour is identified this method results in an approximation that discriminates local from global geometric features and provides a good visual representation of the original contour this polygonal approximation method is used for scalable encoding of the shape contours in this regard an encoding technique suitable for scalable polygonal approximation has been developed we show that encoding the approximated polygons result in a good relation between the distortion and the bitrate finally we show that in addition to coding this method can be efficiently used for shape comparison and shape retrieval

minimal surfaces based object segmentation a geometric approach for 3d object segmentation and representation is presented the segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3d image the model is based on curvature motion and the computation of surfaces with minimal areas better known as minimal surfaces the space where the surfaces are computed is induced from the 3d image volumetric data in which the objects are to be detected the model links between classical deformable surfaces obtained via energy minimization and intrinsic ones derived from curvature based flows the new approach is stable robust and automatically handles changes in the surface topology during the deformation

convergence past singularities for a fully discrete approximation of curvature drive interfaces consider a closed surface in rn of codimension 1 which propagates in the normal direction with velocity proportional to its mean curvature plus a forcing term this geometric problem is first approximated by a singularly perturbed parabolic double obstacle problem with small parameter eps 0 conforming piecewise linear finite elements over a quasi uniform and strongly acute mesh of size h are further used for space discretization and combined with backward differences for time discretization with uniform time step tau it is shown that the zero level set of the fully discrete solution converges past singularities to the true interface provided tau h 2 approx o eps 3 and no fattening occurs if the more stringent relations tau h 2 approx o eps 4 are enforced then a linear rate of convergence o eps for interfaces is derived in the vicinity of regular points namely those for which the underlying viscosity solution is nondegenerate singularities and their smearing effect are also studied the analysis is based on constructing discrete barriers via a parabolic projection lipschitz dependence of viscosity solutions with respect to perturbations of data and discrete nondegeneracy these issues are proven along with quasi optimality in two dimensions of the parabolic projection in l infty with respect to both order and regularity requirements for functions in w 2 1 p

differential and numerically invariant signature curves applied to object recognition we introduce a new paradigm the differential invariant signature curve or manifold for the invariant recognition of visual objects a general theorem of e cartan implies that two curves are related by a group transformation if and only if their signature curves are identical the important examples of the euclidean and equi affine groups are discussed in detail secondly we show how a new approach to the numerical approximation of differential invariants based on suitable combination of joint invariants of the underlying group action allows one to numerically compute differential invariant signatures in a fully group invariant manner applications to a variety of fundamental issues in vision including detection of symmetries visual tracking and reconstruction of occlusions are discussed

a solution algorithm for fuzzy linear programming with piecewise linear membership functions abstract this paper deals with the fuzzy linear program with continuous piecewise linear membership functions a fuzzy linear program with piecewise linear membership functions has been considered by hannan and nakamura hannan s method can solve the problems only when all membership functions are concave in the range 0 1 and nakamura s method needs to use the linear programming technique repetitionally we propose a technique to solve the problem using a standard linear programming when membership functions are strictly quasiconcave and the minimum operator is adopted for aggregating fuzzy goals the repetitional use of linear programming technique is not required in our method

a general model for fuzzy linear programming abstract in the current literature there are several models of fuzzy linear programming problems the aim of this paper is first to describe the more important problems in fuzzy linear programming and second to give a general model of fuzzy linear programming problems involving all of the above ones finally a resolution method for that general model is proposed

curvature filters efficiently reduce certain variational energies in image processing the rapid approximate solution of variational problems involving generic data fitting terms is often of practical relevance for example in real time applications variational solvers based on diffusion schemes or the euler lagrange equations are too slow and restricted in the types of data fitting terms here we present a filter based approach to reduce variational energies that contain generic data fitting terms but are restricted to specific regularizations our approach is based on reducing the regularization part of the variational energy while guaranteeing non increasing total energy this is applicable to regularization dominated models where the data fitting energy initially increases while the regularization energy initially decreases we present fast discrete filters for regularizers based on gaussian curvature mean curvature and total variation these pixel local filters can be used to rapidly reduce the energy of the full model we prove the convergence of the resulting iterative scheme in a greedy sense and we show several experiments to demonstrate applications in image processing problems involving regularization dominated variational models

three models of fuzzy integer linear programming abstract in this paper we study some models for dealing with fuzzy integer linear programming problems which have a certain lack of precision of a vague nature in their formulation we present methods to solve them with either fuzzy constraints or fuzzy numbers in the objective function or fuzzy numbers defining the set of constraints these methods are based on the representation theorem and on fuzzy number ranking methods

global regularizing flows with topology preservation for active contours and polygons active contour and active polygon models have been used widely for image segmentation in some applications the topology of the object s to be detected from an image is known a priori despite a complex unknown geometry and it is important that the active contour or polygon maintain the desired topology in this work we construct a novel geometric flow that can be added to image based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon we emphasize that unlike other methods for topology preservation the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change the flow also serves as a global regularity term for the evolving contour and has smoothness properties similar to curvature flow these properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes the proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles the evolution of a single point on the contour depends on all other points of the contour which is different from traditional curve evolutions in the computer vision literature

singularly perturbed markov decision processes a multiresolution algorithm singular perturbation techniques allow the derivation of an aggregate model whose solution is asymptotically optimal for markov decision processes with strong and weak interactions we develop an algorithm that takes advantage of the asymptotic optimality of the aggregate model in order to compute the solution of the original model we derive conditions for which the proposed algorithm has better worst case complexity than conventional contraction algorithms based on our complexity analysis we show that the major benefit of aggregation is that the reduced order model is no longer ill conditioned the reduction in the number of states due to aggregation is a secondary benefit this is a surprising result since intuition would suggest that the reduced order model can be solved more efficiently because it has fewer states however we show that this is not necessarily the case our theoretical analysis and numerical experiments show that the proposed algorithm can compute the optimal solution with a redu

stable embedding of ill posted linear equality systems into fuzzified systems abstract in this paper the g p d fuzzification of linear systems is introduced it is shown that this type of fuzzification possesses the feature of regularization i e the maximal height solution of the fuzzified problem is stable for a wide class of problems

fractional order anisotropic diffusion for image denoising this paper introduces a new class of fractional order anisotropic diffusion equations for noise removal these equations are euler lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function so the proposed equations can be seen as generalizations of second order and fourth order anisotropic diffusion equations we use the discrete fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain it is one important aspect of the algorithm that it considers the input image as a periodic image to overcome this problem we use a folded algorithm by extending the image symmetrically about its borders finally we list various numerical results on denoising real images experiments show that the proposed fractional order anisotropic diffusion equations yield good visual effects and better signal to noise ratio

noise removal with gauss curvature driven diffusion in this paper we propose the use of the gauss curvature in a gauss curvature driven diffusion equation for noise removal the proposed scheme uses the gauss curvature as the conductance term and controls the amount of diffusion the main advantage of the scheme is that it preserves important structures such as straight edges curvy edges ramps corners small scaled features etc

generation and propagation of interfaces for reaction diffusion equations abstract this paper is concerned with the asymptotic behavior as e 0 of the solution ue of the reaction diffusion equation in r n r u t 1 2 0 where is the derivative of a bistable potential we show that if the initial data u 0 has values in both domains of attraction of the potential then an interface will develop in a short time o e 2 ln e we also show that if the wells of the potential are of equal depth then this interface will propagate with normal velocity equal to its mean curvature our result is valid as long as the interface remains smooth if the initial interface is compact and n 2 then the interface will disappear in a finite time but not if n 1 in case the depths of the wells are not equal then in order to obtain get reasonable results we must work on the scaled time s t e slower time scale in this scale we show that the interface moves with a constant speed proportional to the difference of the depths of the two wells along the normal towards the domain of the deeper well this result is valid for all s 0 and does not actually depend on the regularity of the interface we also extend the above results to the homogeneous second initial boundary value problem in case the depths of the wells are equal and the initial interface is orthogonal to the boundary we prove that the interface moves with normal velocity equal to its mean curvature provided that there is a family of hypersurfaces which moves according to their mean curvature and intersect the boundary orthogonally

dynamic active contours for visual tracking visual tracking using active contours is usually set in a static framework the active contour tracks the object of interest in a given frame of an image sequence a subsequent prediction step ensures good initial placement for the next frame this approach is unnatural the curve evolution gets decoupled from the actual dynamics of the objects to be tracked true dynamical approaches exist all being marker particle based and thus prone to the shortcomings of such particle based implementations in particular topological changes are not handled naturally in this framework the now classical level set approach is tailored for evolutions of manifolds of codimension one however dynamic curve evolution is at least a codimension two problem we propose an efficient level set based approach for dynamic curve evolution which addresses the artificial separation of segmentation and prediction while retaining all the desirable properties of the level set formulation it is based on a new energy minimization functional which for the first time puts dynamics into the geodesic active contour framework

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

stochastic differential equations and geometric flows in previous years curve evolution applied to a single contour or to the level sets of an image via partial differential equations has emerged as an important tool in image processing and computer vision curve evolution techniques have been utilized in problems such as image smoothing segmentation and shape analysis we give a local stochastic interpretation of the basic curve smoothing equation the so called geometric heat equation and show that this evolution amounts to a tangential diffusion movement of the particles along the contour moreover assuming that a priori information about the shapes of objects in an image is known we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise we also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features in contrast to the original geometric heat flow which tends to circularize any closed curve

dynamics of an unbounded interface between ordered phases we investigate the evolution of a single unbounded interface between ordered phases in two dimensional ising ferromagnets that are endowed with single spin flip zero temperature glauber dynamics we examine specifically the cases where the interface initially has either one or two corners in both examples the interface evolves to a limiting self similar form we apply the continuum time dependent ginzburg landau equation and a microscopic approach to calculate the interface shape for the single corner system we also discuss a correspondence between the interface and the young diagram that represents the partition of the integers

process planning in a fuzzy environment abstract mixed integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted as precise forecasts are difficult to obtain process planning usually involves uncertainty and ambiguity in the data this paper presents an application of fuzzy programming to process planning the forecast parameters are assumed to be fuzzy with a linear or triangular membership function the process planning problem is then formulated in terms of decision making in a fuzzy environment with fuzzy constraints and fuzzy net present value goals the model is transformed to a deterministic mixed integer linear program or mixed integer nonlinear program depending on the type of uncertainty involved in the problem for the nonlinear case a global optimization algorithm is developed for its solution this algorithm is applicable to general possibilistic programs and can be used as an alternative to the commonly used bisection method illustrative examples and computational results for a petrochemical complex with 38 processes and 24 products illustrate the applicability of the developed models and algorithms

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

geometry of total variation regularized l p model in this paper the geometry and scale selection properties of the total variation tv regularized l p model are rigorously analyzed some intrinsic features different from the tv l 1 model are derived and demonstrated numerical algorithms based on recent developed augmented lagrangian methods are implemented and numerical results consistent with the theoretical results are provided

the use of parametric programming in fuzzy linear programming in this paper the possibility of the identification of a complete fuzzy decision not only the maximizing alternative in fuzzy linear programming by use of the parametric programming technique is presented also it is shown that this fact can be useful in the zimmermann approach to multiple objective linear programming the presented remarks are illustrated by some numerical examples

a fully nonlinear flow for two convex hypersurfaces in riemannian manifolds we consider a one parameter family of closed embedded hypersurfaces moving with normal velocity g kappa big sum i j frac 1 lambda i lambda j 2 kappa big 1 where lambda 1 le cdots le lambda n denote the curvature eigenvalues and kappa is a nonnegative constant this defines a fully nonlinear parabolic equation provided that lambda 1 lambda 2 2 kappa in contrast to mean curvature flow this flow preserves the condition lambda 1 lambda 2 2 kappa in a general ambient manifold our main goal in this paper is to extend the surgery algorithm of huisken sinestrari to this fully nonlinear flow this is the first construction of this kind for a fully nonlinear flow as a corollary we show that a compact riemannian manifold satisfying overline r 1313 overline r 2323 ge 2 kappa 2 with non empty boundary satisfying lambda 1 lambda 2 2 kappa is diffeomorphic to a 1 handlebody the main technical advance is the pointwise curvature derivative estimate the proof of this estimate requires a new argument as the existing techniques for mean curvature flow due to huisken sinestrari haslhofer kleiner and brian white cannot be generalized to the fully nonlinear setting to establish this estimate we employ an induction on scales argument this relies on a combination of several ingredients including the almost convexity estimate the inscribed radius estimate as well as a regularity result for radial graphs we expect that this technique will be useful in other situations as well

mean curvature evolution and surface area scaling in image filtering representing the image as a surface an inhomogeneous diffusion algorithm is developed evolving the surface at a speed proportional to its mean curvature reducing noise while preserving image structure an adaptive scaling parameter increases the speed of the diffusion the properties of a discrete algorithm are demonstrated experimentally

some extensions of fuzzy linear programming abstract in the formulation of fuzzy linear programming proposed by zimmermann it is assumed that fuzzy goals and fuzzy constraints are explicitly given as fuzzy sets on appropriate real lines respectively and are actually characterized by membership functions in linear form for relaxing those assumptions two kinds of extensions are derived in this paper in the first extension it is shown that fuzzy goals and fuzzy constraints expressed as fuzzy relations with fuzzy parameters can be treated as fuzzy sets on different real lines under some assumptions in the second extension it is shown that optimization in the case where the membership functions of the fuzzy goals and the fuzzy constraints are given in piecewise linear form can be achieved by using a standard linear programming technique repetitionally

the hele shaw problem and area preserving curve shortening motions we prove existence locally in time of a solution of the following hele shaw problem given a simply connected curve contained in a smooth bounded domain find the motion of the curve such that its normal velocity equals the jump of the normal derivatives of a function which is harmonic in the complement of the curve in and whose boundary value on the curve equals its curvature we show that this motion is a curve shortening motion which does not change the area of the region enclosed by the curve in case is the whole plane 2 we also show that if the initial curve is close to an equilibrium curve i e to a circle then there exists a global solution and the global solution tends to some circle exponentially fast as time tends to infinity

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

the variational problem for a certain space time functional defined on planar closed curves abstract we consider a variational problem for a certain space time functional defined on planar closed curves the functional is related to the functional appeared in bellettini and mugnai 2008 4 the variational problem is stated as follows let 0 and 1 denote planar closed curves and t be a positive constant minimize the space time functional over family of planar closed curves which change from 0 at time t 0 into 1 at time t t concerning the variational problem we prove the existence of minimizer in a radially symmetric class and determine all the minimizers for each initial final data moreover we show that there exists a unique non radially symmetric critical point in a neighborhood of a certain radially symmetric minimizer

hydroelectric reservoir optimization in a pool market for a price taking generator operating a hydro electric reservoir in a pool electricity market the optimal stack to offer in each trading period over a planning horizon can be computed using dynamic programming however the market trading period usually 1 hour or less may be much shorter than the inherent time scale of the reservoir often many months we devise a dynamic programming model for such situations in which each stage represents many trading periods in this model the decision made at the beginning of each stage consists of a target mean and variance of the water release in the coming stage this decomposes the problem into inter stage and intra stage subproblems

on the planar dual minkowski problem abstract in this paper we resolve the planar dual minkowski problem proposed by huang et al 2016 31 for all positive indices without any symmetry assumption more precisely given any q 0 and function f on s 1 bounded by two positive constants we show that there exists a convex body in the plane containing the origin in its interior whose dual curvature measure c q has density f in particular if f is smooth then is also smooth

homogeneity similarity based image denoising this paper presents a homogeneity similarity based method which is a new patch based image denoising method in traditional patch based methods such as the nl means method block matching mainly depends on structure similarity the homogeneity similarity is defined in adaptive weighted neighborhoods which can find more similar points than the structure similarity and so it is more effective especially for points with less repetitive patterns such as corner and end points comparative results on synthetic and real image denoising indicate that our method can effectively remove noise and preserve effective information such as edges and contrast while avoiding artifacts the application on medical image denoising also demonstrates that our method is practical

a singular perturbation approach to modeling and control of markov chains finite state continuous time markov processes with weak interactions are modeled as singularly perturbed systems aggregate states are obtained using a grouping algorithm two time scale expansions simplify cost equations and lead to decentralized optimization algorithms

a multilevel proximal gradient algorithm for a class of composite optimization problems composite optimization models consist of the minimization of the sum of a smooth not necessarily convex function and a nonsmooth convex function such models arise in many applications where in addition to the composite nature of the objective function a hierarchy of models is readily available it is common to take advantage of this hierarchy of models by first solving a low fidelity model and then using the solution as a starting point to a high fidelity model we adopt an optimization point of view and show how to take advantage of the availability of a hierarchy of models in a consistent manner we do not use the low fidelity model just for the computation of promising starting points but also for the computation of search directions we establish the convergence and convergence rate of the proposed algorithm our numerical experiments on large scale image restoration problems and the transition path problem suggest that for certain classes of problems the proposed algorithm is significantly fas

fuzzy programming with nonlinear membership functions piecewise linear approximation one promising approach that has been proposed for dealing with multicriteria i e multiple objective programming models has been fuzzy linear programming flp in essence the flp approach involves the replacement of the multiple objectives with goals by means of assigning an aspiration level to each objective fuzzy membership functions are then introduced to represent the measure of the achievement of the actual solution for each goal relative to its aspired level it has been shown that if the flp problem is linear and if linear membership functions are employed to reflect goal achievement then the flp problem may be transformed into a conventional i e single objective linear programming model as such one may use any conventional linear programming algorithm to solve the transformed model however in the more general case of nonlinear membership functions the transformation process becomes considerably more involved and has in the past typically led to less desirable formulations in this paper we present what we believe to be a straightforward and computationally efficient procedure for dealing with the flp problem with any general class of nonlinear membership functions conversion of such a flp will result in either a regular linear programming model or a linear integer programming model depending upon the specific characteristics of the membership function in either case existing commercial software is readily available to solve such models

deforming convex curves with fixed elastic energy abstract this paper presents a curve flow which preserves the elastic energy of the evolving curve if the initial curve is a planar simple and smooth curve with positive curvature then the local and global existence of the flow is proved under this flow the evolving curve will converge to a finite circle in the c metric as time goes to infinity

linear programming with multiple fuzzy goals abstract this paper describes the use of fuzzy set theory in goal programming gp problems in particular it is demonstrated how fuzzy or imprecise aspirations of the decision maker dm can be quantified through the use of piecewise linear and continuous functions models are then presented for the use of fuzzy goal programming with preemptive priorities with archimedean weights and with the maximization of the membership function corresponding to the minimum goal examples are also provided

a stochastic multiscale model for electricity generation capacity expansion abstract long term planning for electric power systems or capacity expansion has traditionally been modeled using simplified models or heuristics to approximate the short term dynamics however current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics we present an efficient method for coupling multiple temporal scales using the framework of singular perturbation theory for the control of markov processes in continuous time we show that the uncertainties that exist in many energy planning problems in particular load demand uncertainty and uncertainties in generation availability can be captured with a multiscale model we then use a dimensionality reduction technique which is valid if the scale separation present in the model is large enough to derive a computationally tractable model we show that both wind data and electricity demand data do exhibit sufficient scale separation a numerical example using real data and a finite difference approximation of the hamilton jacobi bellman equation is used to illustrate the proposed method we compare the results of our approximate model with those of the exact model we also show that the proposed approximation outperforms a commonly used heuristic used in capacity expansion models

multiscale tikhonov total variation image restoration using spatially varying edge coherence exponent edge preserving regularization using partial differential equation pde based methods although extensively studied and widely used for image restoration still have limitations in adapting to local structures we propose a spatially adaptive multiscale variable exponent based anisotropic variational pde method that overcomes current shortcomings such as over smoothing and staircasing artifacts while still retaining and enhancing edge structures across scale our innovative model automatically balances between tikhonov and total variation tv regularization effects using scene content information by incorporating a spatially varying edge coherence exponent map constructed using the eigenvalues of the filtered structure tensor the multiscale exponent model we develop leads to a novel restoration method that preserves edges better and provides selective denoising without generating artifacts for both additive and multiplicative noise models mathematical analysis of our proposed method in variable exponent space establishes the existence of a minimizer and its properties the discretization method we use satisfies the maximum minimum principle which guarantees that artificial edge regions are not created extensive experimental results using synthetic and natural images indicate that the proposed multiscale tikhonov tv mttv and dynamical mttv methods perform better than many contemporary denoising algorithms in terms of several metrics including signal to noise ratio improvement and structure preservation promising extensions to handle multiplicative noise models and multichannel imagery are also discussed