a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

enhancing an algorithm for set covering problems abstract in this note we present enhancements to a previously published algorithm for the optimal solution of set covering problems these enhancements relate to the use of a langrangean heuristic feasible solution exclusion constraints gomory f cuts and an improved branching strategy computational results for problems involving up to 400 rows and 4000 columns indicate that the enhanced algorithm gives better computational results than the original algorithm

almost global existence for quasilinear wave equations in waveguides with neumann boundary conditions in this paper we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with neumann boundary conditions we use a galerkin method to expand the laplacian of the compact base in terms of its eigenfunctions for those terms corresponding to zero modes we obtain decay using analogs of estimates of klainerman and sideris for the nonzero modes estimates for klein gordon equations which provide better decay are available

a fast approximation algorithm for solving the complete set packing problem we study the complete set packing problem cspp where the family of feasible subsets may include all possible combinations of objects this setting arises in applications such as combinatorial auctions for selecting optimal bids and cooperative game theory for finding optimal coalition structures although the set packing problem has been well studied in the literature where exact and approximation algorithms can solve very large instances with up to hundreds of objects and thousands of feasible subsets these methods are not extendable to the cspp since the number of feasible subsets is exponentially large formulating the cspp as an milp and solving it directly using cplex for example is impossible for problems with more than 20 objects we propose a new mathematical formulation for the cspp that directly leads to an efficient algorithm for finding feasible set packings upper bounds we also propose a new formulation for finding tighter lower bounds compared to lp relaxation and develop an efficient method for solving the corresponding large scale milp we test the algorithm with the winner determination problem in spectrum auctions the coalition structure generation problem in coalitional skill games and a number of other simulated problems that appear in the literature

a heuristic method for the set covering problem we present a lagrangian based heuristic for the well known set covering problem scp the algorithm was initially designed for solving very large scale scp instances involving up to 5 000 rows an

new algorithms for 2d and 3d point matching pose estimation and correspondence abstract a fundamental open problem in computer vision determining pose and correspondence between two sets of points in space is solved with a novel fast robust and easily implementable algorithm the technique works on noisy 2d or 3d point sets that may be of unequal sizes and may differ by non rigid transformations using a combination of optimization techniques such as deterministic annealing and the softassign which have recently emerged out of the recurrent neural network statistical physics framework analog objective functions describing the problems are minimized over thirty thousand experiments on randomly generated points sets with varying amounts of noise and missing and spurious points and on hand written character sets demonstrate the robustness of the algorithm

comparing evolutionary algorithms to the 1 1 ea in this paper we study the conditions in which the random hill climbing algorithm 1 1 ea compares favorably to other evolutionary algorithms eas in terms of fitness function distribution at a given iteration and with respect to the average optimization time our approach is applicable when the reproduction operator of an evolutionary algorithm is dominated by the mutation operator of the 1 1 ea in this case one can extend the lower bounds obtained for the expected optimization time of the 1 1 ea to other eas based on the dominated reproduction operator this method is demonstrated on the sorting problem with ham landscape and the exchange mutation operator we consider several simple examples where the 1 1 ea is the best possible search strategy in the class of the eas

a lagrangian based heuristic for large scale set covering problems we present a new lagrangian based heuristic for solving large scale set covering problems arising from crew scheduling at the italian railways ferrovie dello stato our heuristic obtained impressive results when compared to state of the art codes on a test bed provided by the company which includes instances with sizes ranging from 50 000 variables and 500 constraints to 1 000 000 variables and 5000 constraints 1998 the mathematical programming society inc published by elsevier science b v

statistical approaches to feature based object recognition this paper examines statistical approaches to model based object recognition evidence is presented indicating that in some domains normal gaussian distributions are more accurate than uniform distributions for modeling feature fluctuations this motivates the development of new maximum likelihood and map recognition formulations which are based on normal feature models these formulations lead to an expression for the posterior probability of the pose and correspondences given an image several avenues are explored for specifying a recognition hypothesis in the first approach correspondences are included as a part of the hypotheses search for solutions may be ordered as a combinatorial search in correspondence space or as a search over pose space where the same criterion can equivalently be viewed as a robust variant of chamfer matching in the second approach correspondences are not viewed as being a part of the hypotheses this leads to a criterion that is a smooth function of pose that is amenable to local search by continuous optimization methods the criteria is also suitable for optimization via the expectation maximization em algorithm which alternates between pose refinement and re estimation of correspondence probabilities until convergence is obtained recognition experiments are described using the criteria with features derived from video images and from synthetic range images

probe based automatic target recognition in infrared imagery a probe based approach combined with image modeling is used to recognize targets in spatially resolved single frame forward looking infrared flir imagery a probe is a simple mathematical function that operates locally on pixel values and produces an output that is directly usable by an algorithm an empirical probability density function of the probe values is obtained from a local region of the image and used to estimate the probability that a target of known shape is present target shape information is obtained from three dimensional 3 d computer aided design cad models knowledge of the probe values along with probe probability density functions and target shape information allows the likelihood ratio between a target hypothesis and background hypothesis to be written the generalized likelihood ratio test is then used to accept one of the target poses or to choose the background hypothesis we present an image model for infrared images the resulting recognition algorithm and experimental results on three sets of real and synthetic flir imagery

edge covering problem under hybrid uncertain environments edge covering problem ecp is to find an edge cover with the minimum weight in a graph by quantifying costs time or opponent s payoffs as weights on edges ecp is employed to model many real life problems in engineering and management since various types of uncertainty always exist in real world this paper considers ecp under hybrid uncertain environments where randomness and fuzziness coexist we propose three decision models and present a hybrid intelligent algorithm to solve the proposed models where genetic algorithm and random fuzzy simulation are embedded numerical experiments are performed to show the robustness of the proposed algorithm

solving large scale maximum expected covering location problems by genetic algorithms a comparative study abstract this paper compares the performance of genetic algorithms gas on large scale maximum expected coverage problems to other heuristic approaches we focus our attention on a particular formulation with a nonlinear objective function to be optimized over a convex set the solutions obtained by the best genetic algorithm are compared to daskin s heuristic and the optimal or best solutions obtained by solving the corresponding integer linear programming ilp problems we show that at least one of the gas yields optimal or near optimal solutions in a reasonable amount of time

partially occluded object recognition using statistical models in this paper we present a new bayesian framework for partially occluded object recognition based on matching extracted local features on a one to one basis with object features we introduce two different statistical models for occlusion one model assumes that each feature in the model can be occluded independent of whether any other features are occluded whereas the second model uses spatially correlated occlusion to represent the extent of occlusion using these models the object recognition problem reduces to finding the object hypothesis with largest generalized likelihood we develop fast algorithms for finding the optimal one to one correspondence between scene features and object features to compute the generalized likelihoods under both models we conduct experiments illustrating the differences between the two occlusion models using different quantitative metrics we also evaluate the recognition performance of our algorithms using examples extracted from object silhouettes and synthetic aperture radar imagery and illustrate the performance advantages of our approach over alternative algorithms

a genetic algorithm for the set covering problem abstract in this paper we present a genetic algorithm based heuristic for non unicost set covering problems we propose several modifications to the basic genetic procedures including a new fitness based crossover operator fusion a variable mutation rate and a heuristic feasibility operator tailored specifically for the set covering problem the performance of our algorithm was evaluated on a large set of randomly generated problems computational results showed that the genetic algorithm based heuristic is capable of producing high quality solutions

the probabilistic set covering problem in a probabilistic set covering problem the right hand side is a random binary vector and the covering constraint has to be satisfied with some prescribed probability we analyze the structure of the set of probabilistically efficient points of binary random vectors develop methods for their enumeration and propose specialized branch and bound algorithms for probabilistic set covering problems

a population heuristic for constrained two dimensional non guillotine cutting abstract in this paper we present a heuristic algorithm for the constrained two dimensional non guillotine cutting problem this is the problem of cutting a number of rectangular pieces from a single large rectangle so as to maximise the value of the pieces cut in addition the number of pieces of each type that are cut must lie within prescribed limits our heuristic algorithm is a population heuristic where a population of solutions to the problem are progressively evolved this heuristic is based on a new non linear formulation of the problem computational results are presented for a number of standard test problems taken from the literature and for a number of large randomly generated problems

optimal solution of set covering partitioning problems using dual heuristics we present an algorithm for a mixed set covering partitioning model that includes as special cases the well known set covering problem and set partitioning problem the novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm the heuristics are continuous adaptations of the well known greedy and 3 opt methods that have been applied to a variety of combinatorial optimization problems our algorithm has outperformed the current best set covering algorithm of balas and ho 1980 by about a factor of 3 and appears to improve on the best existing set partitioning algorithm by more than an order of magnitude

algorithms for railway crew management crew management is concerned with building the work schedules of crews needed to cover a planned timetable this is a well known problem in operations research and has been historically associated with airlines and mass transit companies more recently railway applications have also come on the scene especially in europe in practice the overall crew management problem is decomposed into two subproblems called crew scheduling and crew rostering in this paper we give an outline of different ways of modeling the two subproblems and possible solution methods two main solution approaches are illustrated for real world applications in particular we discuss in some detail the solution techniques currently adopted at the italian railway company ferrovie dello stato spa for solving crew scheduling and rostering problems

an efficient mean field approach to the set covering problem a mean field feedback artificial neural network ann algorithm is developed and explored for the set covering problem a convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function an approximate energy minimum is obtained by iterating a set of mean field equations in combination with annealing the approach is numerically tested against a set of publicly available test problems with sizes ranging up to 5 103 rows and 106 columns when comparing the performance with exact results for sizes where these are available the approach yields results within a few percent from the optimal solutions comparisons with other approximate methods also come out well in particular given the very low cpu consumption required typically a few seconds arbitrary problems can be processed using the algorithm via a public domain server 2001 elsevier science b v less

partial shape recognition by sub matrix matching for partial matching guided image labeling we propose a new partial shape recognition algorithm by sub matrix matching using a proximity based shape representation given one or more example object templates and a number of candidate object regions in an image points with local maximum curvature along contours of each are chosen as feature points to compute distance matrices for each candidate object region and example template s a sub matrix matching algorithm is then proposed to determine correspondences for evaluation of partial similarity between an example template and a candidate object region the method is translation rotation scale and reflection invariant applications of the proposed partial matching technique include recognition of partially occluded objects in images as well as significant acceleration of recognition matching of full non occluded objects for object based image labeling by learning from examples the speed up in the latter application comes from the fact that we can now search only those combinations of regions in the neighborhood of potential partial matches as soon as they are identified as opposed to all combinations of regions as was done in our prior work xu et al object formation and retrieval using a learning based hierarchical content description proceedings of the icip kobe japan 1999 experimental results are provided to demonstrate both applications

computational experience with approximation algorithms for the set covering problem the set covering problem scp is a well known combinatorial optimization problem which is np hard we conducted a comparative study of eight different approximation algorithms for the scp including several greedy variants fractional relaxations randomized algorithms and a neural network algorithm the algorithms were tested on a set of random generated problems with up to 500 rows and 5000 columns and on two sets of problems originating in combinatorial questions with up to 28160 rows and 11264 columns on the random problems and on one set of combinatorial problems the best algorithm among those we tested was the neural network algorithm with greedy variants very close in second and third place on the other set of combinatorial problems the best algorithm was a greedy variant and the neural network performed quite poorly the other algorithms we tested were always inferior to the ones mentioned above

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

remarks on a paper by j t beale t kato and a majda we prove that the maximum norm of the deformation tensor controls the possible breakdown of smooth solutions for the 3 dimensional euler equations more precisely the loss of regularity in a local smooth solution of the euler equations implies the growth without bound of the deformation tensor as the critical time approaches equivalently if the deformation tensor remains bounded the existence of a smooth solution is guaranteed

a note on a symmetrical set covering problem the lottery problem in a lottery n numbers are drawn from a set of m numbers on a lottery ticket we fill out n numbers consider the following problem what is the minimum number of tickets so that there is at least one ticket with at least p matching numbers we provide a set covering formulation for this problem and characterize its lp solution the existence of many symmetrical alternative solutions makes this a very difficult problem to solve as our computational results indicate

dynamic trees for unsupervised segmentation and matching of image regions we present a probabilistic framework namely multiscale generative models known as dynamic trees dt for unsupervised image segmentation and subsequent matching of segmented regions in a given set of images beyond these novel applications of dts we propose important additions for this modeling paradigm first we introduce a novel dt architecture where multilayered observable data are incorporated at all scales of the model second we derive a novel probabilistic inference algorithm for dts structured variational approximation sva which explicitly accounts for the statistical dependence of node positions and model structure in the approximate posterior distribution thereby relaxing poorly justified independence assumptions in previous work finally we propose a similarity measure for matching dynamic tree models representing segmented image regions across images our results for several data sets show that dts are capable of capturing important component subcomponent relationships among objects and their parts and that dts perform well in segmenting images into plausible pixel clusters we demonstrate the significantly improved properties of the sva algorithm both in terms of substantially faster convergence rates and larger approximate posteriors for the inferred models when compared with competing inference algorithms furthermore results on unsupervised object recognition demonstrate the viability of the proposed similarity measure for matching dynamic structure statistical models

partial shape recognition a landmark based approach a method of recognizing partially occluded objects is presented in which each object is represented by a set of landmarks given a scene consisting of partially occluded objects a model object in the scene is hypothesized by matching the landmarks of the model with those in the scene a measure of similarity between two landmarks is needed to perform this matching a local shape measure sphericity is introduced it is shown that any invariant function under a similarity transformation is a function of the sphericity to match landmarks between the model and the scene a table of compatibility is constructed a technique known as hopping dynamic programming is described to guide the landmark matching through the compatibility table the location of the model in the scene is estimated with a least squares fit among the matched landmarks a heuristic measure is then computed to decide if the model is in the scene

global existence of small amplitude solutions to nonlinear klein gordon equations in four space time dimensions consider the following class of nonlinear wave equations square text u u text text f u u u n k g where t 2 1 2 2 2 3 2 is the d alembertian of the 4 dimensional minkowski space time and f a smooth function of u u t x and its first and second partial derivates vanishing together with its first derivatives at u u u 0 in other words f is at least quadratic in u u u in a neighborhood of the trivial solution u 0 we subject u to the pure initial value problem text u mkern 1mu varepsilon text f x u t varepsilon g x at t 0 i v p with f g c 0 3 and e 0 a small parameter

a 3 flip neighborhood local search for the set covering problem the set covering problem scp calls for a minimum cost family of subsets from n given subsets which together covers the entire ground set in this paper we propose a local search algorithm for scp which has the following three characteristics 1 the use of 3 flip neighborhood which is the set of solutions obtainable from the current solution by exchanging at most three subsets as the size of 3 flip neighborhood is o n3 the neighborhood search becomes expensive if implemented naively to overcome this we propose an efficient implementation that reduces the number of candidates in the neighborhood without sacrificing the solution quality 2 we allow the search to visit the infeasible region and incorporate the strategic oscillation technique realized by adaptive control of penalty weights 3 the size reduction of the problem by using the information from the lagrangian relaxation is incorporated which is indispensable for solving very large instances according to computational comparisons on benchmark instances with other existing heuristic algorithms for scp our algorithm performs quite effectively for various types of problems especially for very large scale instances

hierarchical differential evolution for minimal cut sets identification application to nuclear safety systems in this paper we present a hierarchical differential evolution hde algorithm for minimal cut set mcs identification of coherent and non coherent fault trees fts in realistic application of large size systems problems may be encountered in handling a large number of gates and events in this work to avoid any approximation mcs identification is originally transformed into a hierarchical optimization problem stated as the search for the minimum combination of cut sets that can guarantee the best coverage of all the minterms that make the system fail during the first step of the iterative search a multiple population parallel search policy is used to expedite the convergence of the second step of the exploration algorithm the proposed hierarchical method is applied to the reactor protection system rps of a pressurized water reactor pwr and to the the airlock system as of a canadian deuterium uranium candu reactor results are evaluated with respect to the accuracy and computational demand of the solution found

an algorithm for set covering problem in this paper we present an algorithm for the set covering problem that combines problem reduction tests with dual ascent subgradient optimisation and linear programming computational results are presented for problems involving up to 400 rows and 4000 columns

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

object matching algorithms using robust hausdorff distance measures a hausdorff distance hd is one of commonly used measures for object matching this work analyzes the conventional hd measures and proposes two robust hd measures based on m estimation and least trimmed square lts which are more efficient than the conventional hd measures by computer simulation the matching performance of the conventional and proposed hd measures is compared with synthetic and real images

an electromagnetism metaheuristic for the unicost set covering problem in this paper we propose a new heuristic algorithm to solve the unicost version of the well known set covering problem the method is based on the electromagnetism metaheuristic approach which after generating a pool of solutions to create the initial population applies a fixed number of local search and movement iterations based on the electromagnetism theory in addition to some random aspects used in the construction and local search phases we also apply mutation in order to further escape from local optima the proposed algorithm has been tested over 80 instances of the literature on the classical benchmark instances where the number of columns is larger than the number of rows the algorithm by using a fixed set of parameters always found the best known solution and for 12 instances it was able to improve the current best solution by using different parameter settings the algorithm improved 4 additional best known solutions moreover we proved the effectiveness of the electromagnetism metaheuristic approach for the unicost set covering problem by embedding the procedures of the proposed algorithm in a genetic algorithm scheme the worse results obtained by the genetic algorithm show the impact of the electromagnetism metaheuristic approach in conducting the search of the solution space by applying the movements based on the electromagnetism theory finally we report the results obtained by modifying the proposed electromagnetism metaheuristic algorithm for solving the non unicost set covering problem

an efficient local search heuristic with row weighting for the unicost set covering problem abstract the set covering problem scp is np hard we propose a new row weighting local search rwls algorithm for solving the unicost variant of the scp i e uscps where the costs of all sets are identical rwls is a heuristic algorithm that has three major components united in its local search framework 1 a weighting scheme which updates the weights of uncovered elements to prevent convergence to local optima 2 tabu strategies to avoid possible cycles during the search and 3 a timestamp method to break ties when prioritizing sets rwls has been evaluated on a large number of problem instances from the or library and compared with other approaches it is able to find all the best known solutions bks and improve 14 of them although requiring a higher computational effort on several instances rwls is especially effective on the combinatorial or library instances and can improve the best known solution to the hardest instance cyc11 considerably rwls is conceptually simple and has no instance dependent parameters which makes it a practical and easy to use uscp solver

an effective and simple heuristic for the set covering problem abstract this paper investigates the development of an effective heuristic to solve the set covering problem scp by applying the meta heuristic meta raps meta heuristic for randomized priority search in meta raps a feasible solution is generated by introducing random factors into a construction method then the feasible solutions can be improved by an improvement heuristic in addition to applying the basic meta raps the heuristic developed herein integrates the elements of randomizing the selection of priority rules penalizing the worst columns when the searching space is highly condensed and defining the core problem to speedup the algorithm this heuristic has been tested on 80 scp instances from the or library the sizes of the problems are up to 1000 rows 10 000 columns for non unicost scp and 28 160 rows 11 264 columns for the unicost scp this heuristic is only one of two known scp heuristics to find all optimal best known solutions for those non unicost instances in addition this heuristic is the best for unicost problems among the heuristics in terms of solution quality furthermore evolving from a simple greedy heuristic it is simple and easy to code this heuristic enriches the options of practitioners in the optimization area

minimum weight covering problems in stochastic environments minimum weight covering problems have played an important role in many real applications in this paper two typical minimum weight covering problems namely vertex covering problem and edge covering problem are studied under stochastic environments according to different decision criteria we propose three stochastic programming models the expected minimum weight cover model a minimum weight cover model and the most minimum weight cover model a hybrid intelligent algorithm that integrates stochastic simulation with genetic algorithm is designed to solve the proposed models finally numerical experiments are performed to show the effectiveness and robustness of the proposed algorithm