existence of bounded positive solutions of semilinear elliptic equations abstract in this paper by using fixed point theory under quite general conditions on the nonlinear term we obtain an existence result on bounded positive solutions of certain semilinear elliptic equations in r n n 3

existence of unbounded positive solutions of quasilinear elliptic equations in two dimensional exterior domains in this paper by using the fixed point theory we obtain a new existence result for bounded positive solutions of the quasilinear elliptic equations in two dimensional exterior domains

a new twist two step iterative shrinkage thresholding algorithms for image restoration iterative shrinkage thresholding 1st algorithms have been recently proposed to handle a class of convex unconstrained optimization problems arising in image restoration and other linear inverse problems this class of problems results from combining a linear observation model with a nonquadratic regularizer e g total variation or wavelet based regularization it happens that the convergence rate of these 1st algorithms depends heavily on the linear observation operator becoming very slow when this operator is ill conditioned or ill posed in this paper we introduce two step 1st twist algorithms exhibiting much faster convergence rate than 1st for ill conditioned problems for a vast class of nonquadratic convex regularizers lscrp norms some besov norms and total variation we show that twist converges to a minimizer of the objective function for a given range of values of its parameters for noninvertible observation operators we introduce a monotonic version of twist mtwist although the convergence proof does not apply to this scenario we give experimental evidence that mtwist exhibits similar speed gains over ist the effectiveness of the new methods are experimentally confirmed on problems of image deconvolution and of restoration with missing samples

the globally weak attraction and global semi stability of lienard system this paper obtains some necessary and sufficient conditions for the globally weak attraction and global semi stability of the zero solution for lienard equation x h y f x y g x

blow up phenomena of second order nonlinear differential equations abstract this paper studies the blow up phenomena of the second order nonlinear differential equation x f t x x under appropriate conditions it is shown that some solutions of the equation blow up in finite time

phase unwrapping via graph cuts phase unwrapping is the inference of absolute phase from modulo 2pi phase this paper introduces a new energy minimization framework for phase unwrapping the considered objective functions are first order markov random fields we provide an exact energy minimization algorithm whenever the corresponding clique potentials are convex namely for the phase unwrapping classical lp norm with pges1 its complexity is kt n 3n where k is the length of the absolute phase domain measured in 2pi units and t n m is the complexity of a max flow computation in a graph with n nodes and m edges for nonconvex clique potentials often used owing to their discontinuity preserving ability we face an np hard problem for which we devise an approximate solution both algorithms solve integer optimization problems by computing a sequence of binary optimizations each one solved by graph cut techniques accordingly we name the two algorithms puma for phase unwrapping max flow min cut a set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state of the art phase unwrapping algorithms

the continuation of solutions for certain nonlinear differential equations and its applications we give some sufficient conditions for the continuation of solutions for some nonlinear differential equations as an application we obtain a new criterion for the oscillation of solutions of the lienard equation

graph cut based discrete valued image reconstruction efficient graph cut methods have been used with great success for labeling and denoising problems occurring in computer vision unfortunately the presence of linear image mappings has prevented the use of these techniques in most discrete amplitude image reconstruction problems in this paper we develop a graph cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations we first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator we then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph cut frameworks we use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems we first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter then we focus on nonlocal tomographic examples where we consider limited angle data problems we compare our technique with state of the art discrete and continuous image reconstruction techniques experiments show that the proposed method outperforms state of the art techniques in challenging scenarios involving discrete valued unknowns

roof duality complementation and persistency in quadratic 0 1 optimization the paper is concerned with the primal problem of maximizing a given quadratic pseudo boolean function four equivalent problems are discussed the primal the complementation the discrete rhys lp and the weighted stability problem of a sam graph each of them has a relaxation the roof dual the quadratic complementation the continuous rhys lp and the fractional weighted stability problem of a sam graph the main result is that the four gaps associated with the four relaxations are equal furthermore a solution to any of these problems leads at once to solutions of the other three equivalent ones the four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem the optimal solutions of the roof dual define best linear majorantsp x off having the following persistency property if theith coefficient inp is positive negative thenx i 1 0 in every optimum of the primal problem several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal on the other hand a class of gap free functions properly including the supermodular ones is exhibited

periodic solutions of forced lienard type equations using mawhin s coincidence degree theory and brosuk s theorem some new sufficient conditions of the existence of periodic solutions for the well known forced lienard type equations email protected f 1 x email protected f 2 x email protected 2 g x e t are given these new conditions are natural extension and generalization of the corresponding results already obtained results in the literature

an efficient algorithm for image segmentation markov random fields and related problems problems of statistical inference involve the adjustment of sample observations so they fit some a priori rank requirements or order constraints in such problems the objective is to minimize the deviation cost function that depends on the distance between the observed value and the modify value in markov random field problems there is also a pairwise relationship between the objects the objective in markov random field problem is to minimize the sum of the deviation cost function and a penalty function that grows with the distance between the values of related pairs separation function we discuss markov random fields problems in the context of a representative application the image segmentation problem in this problem the goal is to modify color shades assigned to pixels of an image so that the penalty function consisting of one term due to the deviation from the initial color shade and a second term that penalizes differences in assigned values to neighboring pixels is minimized we present here an algorithm that solves the problem in polynomial time when the deviation function is convex and separation function is linear and in strongly polynomial time when the deviation cost function is linear quadratic or piecewise linear convex with few pieces where few means a number exponential in a polynomial function of the number of variables and constraints the complexity of the algorithm for a problem on n pixels or variables m adjacency relations or constraints and range of variable values colors u is o t n m n log u where t n m is the complexity of solving the minimum s t cut problem on a graph with n nodes and m arcs furthermore other algorithms are shown to solve the problem with convex deviation and convex separation in running time o mn log n log nu and the problem with nonconvex deviation and convex separation in running time o t nu mu the nonconvex separation problem is np hard even for fixed value of u for the family of problems with convex deviation functions and linear separation function the algorithm described here runs in polynomial time which is demonstrated to be fastest possible

minimizing nonsubmodular functions with graph cuts a review optimization techniques based on graph cuts have become a standard tool for many vision applications these techniques allow to minimize efficiently certain energy functions corresponding to pairwise markov random fields mrfs currently there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of mrf energies e g submodular functions in this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions in particular nonsubmodular functions while these results are well known in the optimization community to our knowledge they were not used in the context of computer vision and mrf optimization we demonstrate the relevance of these results to vision on the problem of binary texture restoration

exact optimization for markov random fields with convex priors we introduce a method to solve exactly a first order markov random field optimization problem in more generality than was previously possible the mrf has a prior term that is convex in terms of a linearly ordered label set the method maps the problem into a minimum cut problem for a directed graph for which a globally optimal solution can be found in polynomial time the convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method

a geometric approach to periodically forced dynamical systems in presence of a separatrix we consider the periodic boundary value problem for the non autonomous scalar second order equation x f x x e t with e a continuous and t periodic forcing term using a continuation theorem adapted from capietto et al trans amer math soc 329 1992 41 72 we propose some new conditions for the existence of t periodic solutions to the forced equation in terms of the dynamical properties of the trajectories of the associated autonomous equation x f x x 0 special emphasis will be addressed to the study of the case in which the presence of an unbounded separatrix for the autonomous system in the phase plane allows to obtain a priori bounds for the t periodic solutions of the homotopic equation x f x x e t

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

boundedness and convergence of solutions of a second order nonlinear differential system abstract consider the second order nonlinear differential system x 1 a x h y f x y a x g x e t where a is a positive and continuous function on r h f and g are continuous functions on r and e t is a continuous function on i 0 we obtain sufficient and necessary conditions for all solutions to be bounded and to converge to zero our results can be applied to the well known equation x f 1 x x f 2 x x 2 g x e t which substantially extends and improves important results in the literature

a characterization of p i algebras with bounded multiplicities of the cocharacters abstract we characterize varieties of p i algebras with bounded multiplicities of the cocharacters a variety is such if and only if it does not contain the upper triangular 2 2 matrices this also yields a characterization of the varieties with bounded colength

a unifying approach to isotropic and anisotropic total variation denoising models total variation minimisation is a well established method for digital image restoration its implicit preservation of edges permits the derivation of anisotropic models for a qualitative improvement at corners this paper is a synopsis of anisotropic models with state of the art insights into the numerics of isotropic models we generalise two representative models from both branches of research this formulation leads to a general convergent algorithm and a general highly efficient algorithm which apply for both cases a transfer of the discretisation from the anisotropic model to the isotropic setting results in an improvement of rotational invariance

on minimal varieties of quadratic growth abstract in this paper we investigate the polynomial identities of an important subalgebra of the pi algebra ut 3 of 3 3 upper triangular matrices in characteristic zero moreover we prove that the five algebras which were used in giambruno and la mattina a giambruno d la mattina pi algebras with slow codimension growth j algebra 284 2005 371 391 to classify up to pi equivalence the algebras whose sequence of codimensions is bounded by a linear function generate the only five minimal varieties of quadratic growth

qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method abstract the phase portrait of the second order differential equation x l 0 n f l x x l 0 is studied some results concerning existence non existence and uniqueness of limit cycles are presented in particular a generalization of the classical massera uniqueness result is proved

intersection with the vertical isocline in the generalized lienard equations abstract we consider the generalized lienard system d x d t 1 a x h y f x d y d t a x g x where a f g and h are continuous functions on r and a x 0 for x r under the assumptions that the origin is a unique equilibrium we study the problem whether all trajectories of this system intersect the vertical isocline h y f x which is very important in the global asymptotic stability of the origin oscillation theory and existence of periodic solutions under quite general assumptions we obtain sufficient and necessary conditions which are very sharp our results extend the results of villari and zanolin and hara and sugie for this system with h y y and a x 1 and improve the results presented by sugie et al and gyllenberg and ping

majorization minimization algorithms for wavelet based image restoration standard formulations of image signal deconvolution under wavelet based priors regularizers lead to very high dimensional optimization problems involving the following difficulties the non gaussian heavy tailed wavelet priors lead to objective functions which are nonquadratic usually nondifferentiable and sometimes even nonconvex the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet based denoising this paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems placing them in a common majorization minimization mm framework one of the classes of algorithms considered when using quadratic bounds on nondifferentiable log priors shares the infamous singularity issue si of iteratively re weighted least squares irls algorithms the possibility of having to handle infinite weights which may cause both numerical and convergence issues in this paper we prove several new results which strongly support the claim that the si does not compromise the usefulness of this class of algorithms exploiting the unified mm perspective we introduce a new algorithm resulting from using bounds for nonconvex regularizers the experiments confirm the superior performance of this method when compared to the one based on quadratic majorization finally an experimental comparison of the several algorithms reveals their relative merits for different standard types of scenarios

air tools a matlab package of algebraic iterative reconstruction methods we present a matlab package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems these so called row action methods rely on semi convergence for achieving the necessary regularization of the problem two classes of methods are implemented algebraic reconstruction techniques art and simultaneous iterative reconstruction techniques sirt in addition we provide a few simplified test problems from medical and seismic tomography for each iterative method a number of strategies are available for choosing the relaxation parameter and the stopping rule the relaxation parameter can be fixed or chosen adaptively in each iteration in the former case we provide a new training algorithm that finds the optimal parameter for a given test problem the stopping rules provided are the discrepancy principle the monotone error rule and the ncp criterion for the first two methods training can be used to find the optimal discrepancy parameter

global asymptotic stability of nonautonomous systems of lienard type this paper deals with nonautonomous lienard type systems sufficient conditions are given for the zero solution of the systems to be globally asymptotically stable the main result is proved by means of phase plane analysis with a liapunov function examples are included to contrast our theorem with results which were presented by hatvani and cantarelli some global phase portraits are also attached

on global asymptotic stability of systems of lienard type we give new necessary and sufficient conditions under which the zero solution of lienard type systems is globally asymptotically stable to this end we examine i whether all trajectories intersect the vertical isocline or not and ii whether all trajectories tend to the origin or not we also apply our results to a pseudolinear system

explicit conditions for asymptotic stability of stochastic lienard type equations with markovian switching this paper deals with the boundedness in probability and convergence for solutions of stochastic lienard type equations some explicit conditions to ensure that all solution is bounded in probability and convergent to some fixed sets are obtained we also show that white noise can affect the boundedness of corresponding deterministic lienard equations

pi algebras with slow codimension growth let cn a n 1 2 be the sequence of codimensions of an algebra a over a field f of characteristic zero we classify the algebras a up to pi equivalence in case this sequence is bounded by a linear function we also show that this property is closely related to the following if ln a n 1 2 denotes the sequence of colengths of a counting the number of sn irreducibles appearing in the nth cocharacter of a then limn ln a exists and is bounded by 2