comments on exact solutions of electromagnetic fields in both near and far zones radiated by thin circular loop antennas a general representation with reply this paper presents an alternative vector analysis of the electromagnetic em fields radiated from thin circular loop antennas of arbitrary radius a this method which employs the dyadic green s function in the derivation of the em radiated fields makes the analysis more general compact and straightforward than those two methods published recently by werner 1996 and overfelt 1996 both near and far zones are considered so that the em radiated fields are expressed in terms of the vector wave eigenfunctions not only the exact solution of the em fields in the near and far zones outside the region where r a is derived by the use of the spherical hankel function of the first kind but also the closed series form of the em fields radiated in the near zone inside the region 0 spl les r a is obtained in series of the spherical bessel functions of the first kind as an example a fourier cosine series is used to expand an arbitrary current distribution along the loop and the exact representations of the em radiated fields due to the loop everywhere are obtained in closed form the closed form reduces to those for the sinusoidal current loop and further for the uniform current loop validity of the approximate formulas is discussed and clarified error analysis based on numerical computations of the radiated fields is also given to show the accuracy of the limiting cases

the expressive power of valued constraints hierarchies and collapses in this paper we investigate the ways in which a fixed collection of valued constraints can be combined to express other valued constraints we show that in some cases a large class of valued constraints of all possible arities can be expressed by using valued constraints over the same domain of a fixed finite arity we also show that some simple classes of valued constraints including the set of all monotonic valued constraints with finite cost values cannot be expressed by a subset of any fixed finite arity and hence form an infinite hierarchy

some applications of covariance identities and inequalities to functions of multivariate normal variables abstract we apply general covariance identities and inequalities to some functions of multivariate normal variables we recover in particular a recent covariance identity due to siegel and provide simple estimates on the variance of order statistics we also present some computations

domain permutation reduction for constraint satisfaction problems this paper is concerned with the constraint satisfaction problem csp it is well known that the general csp is np hard however there has been significant success in discovering subproblems which are tractable polynomial time solvable one of the most effective ways to obtain a tractable subproblem has been to force all of the constraint relations to lie in some tractable language in this paper we define a new way of identifying tractable subproblems of the csp let p be an arbitrary csp instance and c be any tractable language suppose there exists for each variable of p a permutation of the domain such the resultant permuted constraint relations of p all lie in c the domain permuted instance is then an instance of a tractable class and can be solved by the polynomial time algorithm for c solutions to p can be obtained by inverting the domain permutations the question for a given class of instances and language c whether such a set of domain permutations can be found efficiently is the key to this method s tractability one of the important contributions made in this paper is the notion of a lifted constraint instance which is a powerful tool to study this question we consider the open problem of discovering domain permutations which make instances max closed we show that for bounded arity instances over a boolean domain this problem is tractable while for domain size three it is intractable even for binary instances we give a simple proof verifying the tractability of discovering domain permutations which make instances row convex we refute a published result by giving a simple proof of the intractability of discovering domain permutations which make instances even with domain size four connected row convex we demonstrate that triangulated and stable marriage instances are reducible via domain permutations to max closed instances this provides a simple explanation for arc consistency deciding these instances we verify with a simple direct proof the tractability of identification of renamable horn instances and the intractability of finding the largest renamable horn subset of clauses of an instance of sat we describe natural tractable classes which properly extend the maximal relational classes arising from tractable constraint languages we believe that domain permutation reductions have a significant chance of being useful in practical applications

constraint relaxation may be perfect abstract networks of constraints are a simple knowledge representation method useful for describing those problems whose solution is required to satisfy several simultaneous constraints the problem of solving a network of constraints with finite domains is np complete the standard solution technique for such networks of constraints is the backtrack search but many relaxation algorithms to be applied before backtracking have been developed they transform a network in an equivalent but more explicit one the idea is to make the backtrack search have a better average time complexity in fact if the network elaborated by the backtrack algorithm is more explicit the algorithm backtracks less in this paper we describe relaxation algorithms as sequences of applications of relaxation rules moreover we define perfect relaxation algorithms as relaxation algorithms which not only return a more explicit network but also exactly solve the given network of constraints by applying every relaxation rule only once finally we characterize a family of classes of networks on which certain perfect relaxation algorithms are very efficient the exact solution of each network in a class is found in linear time

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

learnability of quantified formulas we consider the following classes of quantified formulas fix a set of basic relations called a basis take conjunctions of these basic relations applied to variables and constants in arbitrary ways finally quantify existentially or universally some of the variables we introduce some conditions on the basis that guarantee efficient learnability furthermore we show that with certain restrictions on the basis the classification is complete we introduce as an intermediate tool a link between this class of quantified formulas and some well studied structures in universal algebra called clones more precisely we prove that the computational complexity of the learnability of these formulas is completely determined by a simple algebraic property of the basis of relations their clone of polymorphisms finally we use this technique to give a simpler proof of the already known dichotomy theorem over boolean domains

generalizing constraint satisfaction on trees hybrid tractability and variable elimination the constraint satisfaction problem csp is a central generic problem in artificial intelligence considerable progress has been made in identifying properties which ensure tractability in such problems such as the property of being tree structured in this paper we introduce the broken triangle property which allows us to define a novel tractable class for this problem which significantly generalizes the class of problems with tree structure we show that the broken triangle property is conservative i e it is preserved under domain reduction and hence under arc consistency operations and that there is a polynomial time algorithm to determine an ordering of the variables for which the broken triangle property holds or to determine that no such ordering exists we also present a non conservative extension of the broken triangle property which is also sufficient to ensure tractability and can also be detected in polynomial time we show that both the broken triangle property and its extension can be used to eliminate variables and that both of these properties provide the basis for preprocessing procedures that yield unique closures orthogonal to value elimination by enforcement of consistency finally we also discuss the possibility of using the broken triangle property in variable ordering heuristics

exact field expressions for circular loop antennas using spherical functions expansion a new technique is introduced for evaluating the vector potential of circular loop antennas clas with arbitrary current distribution and dimensions which can be used to obtain the exact electromagnetic fields in near and far regions of the antenna the technique is based on the spherical bessel functions sbfs and associated legendre polynomials alps expansion this expansion is used to decouple the azimuth variables of the integrand of the vector potential integrals from the other variables in a separate functions that depend exponentially on azimuth variables this technique reduces greatly the mathematical operations for evaluation of the vector potential to only one simple integration the technique is used to obtain exact electromagnetic fields expressions for a thin wire cla of arbitrary current distribution and dimension which is valid everywhere except on the loop the well known far fields for the cla of arbitrary current distribution as well as near and far fields for uniform current loop and small loop are obtained from the general field expressions presented in this paper as an special cases

analysis and regularization of the thin wire integral equation with reduced kernel for the straight wire modeled as a hollow tube we establish a conditional equivalence relation between the integral equations with exact and reduced kernel this relation allows us to examine the existence and uniqueness conditions for the integral equation with reduced kernel based on a local argument further we characterize the ill posedness of integral equation with reduced kernel and we propose a regularization and filtering procedure to extend the range of this integral equation

on the minimality and global consistency of row convex constraint networks constraint networks have been shown to be useful in formulating such diverse problems as scene labeling natural language parsing and temporal reasoning given a constraint network we often wish to i find a solution that satisfies the constraints and ii find the corresponding minimal network where the constraints are as explicit as possible both tasks are known to be np complete in the general case task 1 is usually solved using a backtracking algorithm and task ii is often solved only approximately by enforcing various levels of local consistency in this paper we identify a property of binary constraint called row convexity and show its usefulness in deciding when a form of local consistency called path consistency is sufficient to guarantee that a network is both minimal and globally consistent globally consistent networks have the property that a solution can be found without backtracking we show that one can test for the row convexity property efficiently and we show by examining applications of constraint networks discussed in the literature that our results are useful in practice thus we identify a class of binary constraint networks for which we can solve both tasks i and ii efficiently finally we generalize the results for binary constraint networks to networks with nonbinary constraints

combinatorial problems raised from 2 semilattices abstract the constraint satisfaction problem csp provides a general framework for many combinatorial problems in a a bulatov a a krokhin p g jeavons classifying the complexity of constraints using finite algebras siam j comput 34 3 2005 720 742 p g jeavons on the algebraic structure of combinatorial problems theoret comput sci 200 1998 185 204 and then in a a bulatov p g jeavons algebraic structures in combinatorial problems technical report math al 4 2001 technische universitat dresden dresden germany 2001 a new approach to the study of the csp has been developed which uses properties of universal algebras assigned to certain subclasses of the csp such that the time complexity and other properties of subclasses can be derived from the properties of the assigned algebras in this paper we briefly survey this approach and then prove that problem classes corresponding to finite 2 semilattices that is groupoids satisfying the identities x x x x y y x x x y x x y can be solved in polynomial time making use of this result we classify finite conservative groupoids and 4 element algebras with minimal clone of term operations with respect to the complexity of the corresponding csp class

new exact solution procedure for the near fields of the general thin circular loop antenna an analytical method is presented which gives the various fields including the scalar potential of a general circular loop antenna in cylindrical coordinates in terms of six separate series three of the series are elementary and the other three involve legendre functions of the second kind and half integral order the results obtained are compared with direct numerical integration and with two far field formulae the standard textbook expression and what appears to be a new formula which gives more accurate results the series solution is more robust than numerical integration for the higher fourier terms of the general solution close to the loop the solution has also been compared with the solution of werner and it agrees exactly the solution presented here gives better convergence close to the loop whereas werner s solution is better far from the loop sample calculations are given for the axisymmetric case

network based heuristics for constraint satisfaction problems abstract many ai tasks can be formulated as constraint satisfaction problems csp i e the assignment of values to variables subject to a set of constraints while some csps are hard those that are easy can often be mapped into sparse networks of constraints which in the extreme case are trees this paper identifies classes of problems that lend themselves to easy solutions and develops algorithms that solve these problems optimally the paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree structured csps the advice is generated by simplifying the pending subproblems into trees counting the number of consistent solutions in each simplified subproblem and comparing these counts to decide among the choices pending in the original problem

classifying the complexity of constraints using finite algebras many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra hence we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra we introduce a notion of tractable algebra and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it including its subalgebras and homomorphic images this allows us to reduce significantly the types of algebras which need to be classified using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently then so can the corresponding search problem we then classify all finite strictly simple surjective algebras with respect to tractability obtaining a dichotomy theorem which generalizes schaefer s dichotomy for the generalized satisfiability problem finally we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem

feasibility checking in horn constraint systems through a reduction based approach abstract in this paper we detail a new algorithm for the problem of checking linear and integer feasibility in a system of horn constraints for certain special cases the proposed algorithm is faster than the lifting algorithm for horn constraint feasibility described in 2 moreover the new approach is based on different ideas and in fact exploits several properties of horn constraint systems hcs which were heretofore unknown to the best of our knowledge in the case of constraints of bounded width corresponding to loosely coupled systems our algorithm can be modified to run in o n 3 m n m n 2 log max m n time where n and m represent the number of variables and the number of constraints respectively in the input hcs our main result establishes that checking the feasibility of an hcs can be reduced to three subproblems negative cost cycle detection in networks nccd matrix vector multiplication mv and the conversion of an hcs to a non redundant set of difference constraints h2d the mv problem and the nccd problem have both been studied extensively as per the literature and there exist specialized fast algorithms for the cases that are relevant to feasibility checking in horn constraint systems we have identified a new problem viz h2d which warrants future research since improved algorithms for the h2d problem could be implemented in our algorithm to decrease its running time even further

characterising tractable constraints abstract finding solutions to a binary constraint satisfaction problem is known to be an np complete problem in general but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted this paper considers restricted sets of constraints which are closed under permutation of the labels we identify a set of constraints which gives rise to a class of tractable problems and give polynomial time algorithms for solving such problems and for finding the equivalent minimal network we also prove that the class of problems generated by any set of constraints not contained in this restricted set is np complete

a generic arc consistency algorithm and its specializations consistency techniques have been studied extensively in the past as a way of tackling constraint satisfaction problems csp in particular various arc consistency algorithms have been proposed originating from waltz s filtering algorithm and culminating in the optimal algorithm ac 4 of mohr and henderson ac 4 runs in o ed 2 in the worst case where e is the number of arcs or constraints and d is the size of the largest domain being applicable to the whole class of binary csp these algorithms do not take into account the semantics of constraints in this paper we present a new generic arc consistency algorithm ac 5 the algorithm is parameterized on two specified procedures and can be instantiated to reduce to ac 3 and ac 4 more important ac 5 can be instantiated to produce an o ed 2 algorithm for a number of important classes of constraints functional anti functional monotonic and their generalization to functional anti functional and monotonic piecewise constraints we also show that ac 5 has an important application in constraint logic programming over finite domains the kernel of the constraint solver for such a programming language is an arc consistency algorithm for a set of basic constraints we prove that ac 5 in conjuction with node consistency provides a decision procedure for these constraints running in time o ed

tractable constraints on ordered domains abstract finding solutions to a constraint satisfaction problem is known to be an np complete problem in general but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted in this paper we identify a restricted set of contraints which gives rise to a class of tractable problems this class generalizes the notion of a horn formula in propositional logic to larger domain sizes we give a polynomial time algorithm for solving such problems and prove that the class of problems generated by any larger set of constraints is np complete

linear time algorithms for testing the realisability of line drawings of curved objects this paper shows that the semantic labelling of line drawings of curved objects with piecewise c 3 surfaces is solvable in linear time this result is robust to changes in the assumptions on object shape when all vanishing points are known a different linear time algorithm exists to solve the labelling problem furthermore in both cases all legally labelled line drawings of curved objects are shown to be physically realisable however when some but not all of the vanishing points are known when the drawing is an orthographic projection of a scene containing parallel lines or when we wish to minimise the number of phantom junctions the labelling problem becomes np hard the introduction of collinearity constraints also renders the labelling problem np complete except in the case when all vanishing points are known 1999 elsevier science b v all rights reserved

generalising submodularity and horn clauses tractable optimization problems defined by tournament pair multimorphisms the submodular function minimization problem sfm is a fundamental problem in combinatorial optimization and several fully combinatorial polynomial time algorithms have recently been discovered to solve this problem the most general versions of these algorithms are able to minimize any submodular function whose domain is a set of tuples over any totally ordered finite set and whose range includes both finite and infinite values in this paper we demonstrate that this general form of sfm is just one example of a much larger class of tractable discrete optimization problems defined by valued constraints these tractable problems are characterized by the fact that their valued constraints have an algebraic property which we call a tournament pair multimorphism this larger tractable class also includes the problem of satisfying a set of horn clauses horn sat as well as various extensions of this problem to larger finite domains

an exact formulation for the vector potential of a cylindrical antenna with uniformly distributed current and arbitrary radius an exact formulation is given for the vector potential and corresponding electric fields associated with a uniform current cylindrical dipole antenna of arbitrary radius the exact expressions converge rapidly in the induction and near field regions of the antenna they are completely general and independent of the usual restrictions involving the wavelength field point distance dipole radius and length the properties of these expressions allow them to be readily used for the efficient as well as accurate computational modeling of cylindrical wire antennas an exact expression for the cylindrical wire kernel which is analytically as well as numerically convenient to work with is presented it is demonstrated that the integral of the kernel can be expressed in terms of a series which involves a generalized exponential integral and higher order associated integrals several methods for evaluating the generalized exponential integral are discussed including some useful asymptotic expansions a numerically stable forward recurrence relation for the higher order associated integrals is also presented

a recursive algorithm for the inversion of matrices with circulant blocks we investigate the recursive inversion of matrices with circulant blocks matrices of this type appear in several applications of computational electromagnetics and in the numerical solution of integral equations with the boundary element method the inversion is based on the diagonalization of each circulant block by means of the discrete fourier transform and the application of a recursive algorithm for the inversion of the matrix with diagonal blocks determined by the eigenvalues of each block the efficiency of the recursive inversion is exhibited by determining its computational complexity an implementation of the algorithm in matlab is given and numerical results are presented to demonstrate the efficiency in terms of cpu time of our approach

correlation analysis of extreme observations from a multivariate normal distribution abstract in measuring visual acuity the extremes of a set of normally distributed measures are of concern together with one or more covariates this leads to a model in which x y 1 y 2 are jointly normally distributed with y 1 y 2 exchangeable and x y i having a common correlation inferential procedures are developed for correlations and linear regressions among x and the ordered y values this requires determination of the covariance matrix of x y 1 min y 1 y 2 and y 2 max y 1 y 2 the inadequacy of certain estimates that ignore the nonnormality of x y 1 y 2 is also discussed although the bivariate case is emphasized because of the context of the visual acuity model many results are given for the more general multivariate case

a sufficient condition for backtrack bounded search backtrack search is often used to solve constraint satisfaction problems a relationship involving the structure of the constraints is described that provides a bound on the backtracking required to advance deeper into the backtrack tree this analysis leads to upper bounds on the effort required for solution of a class of constraint satisfaction problems the solutions involve a combination of relaxation preprocessing and backtrack search the bounds are expressed in terms of the structure of the constraint connections specifically the effort is shown to have a bound exponential in the size of the largest biconnected component of the constraint graph as opposed to the size of the graph as a whole

decomposing constraint satisfaction problems using database techniques abstract there is a very close relationship between constraint satisfaction problems and the satisfaction of join dependencies in a relational database which is due to a common underlying structure namely a hypergraph by making that relationship explicit we are able to adapt techniques previously developed for the study of relational databases to obtain new results for constraint satisfaction problems in particular we prove that a constraint satisfaction problem may be decomposed into a number of subproblems precisely when the corresponding hypergraph satisfies a simple condition we show that combining this decomposition approach with existing algorithms can lead to a significant improvement in efficiency

near fields of the constant current thin circular loop antenna of arbitrary radius assuming a known constant current distribution on the thin circular loop antenna of arbitrary radius in free space an exact integration of the vector potential is performed without recourse to approximations the only restrictions on the solution variables are that the observation point distance must be greater than the loop radius and that the polar angle must run between 0 and spl pi the resulting vector potential infinite series solution possesses a real part composed of linear combinations of complete elliptic integrals of the first and second kind and an imaginary part composed of elementary functions thus it is possible to obtain an exact solution which is valid everywhere that r a and 0 spl les spl theta spl les spl pi the electromagnetic field components of the constant current circular loop antenna are then determined by direct series differentiation these solutions are valid in the near and induction fields converging rapidly there and are also valid in the far field although many terms of the series are needed for convergence

an exact integration procedure for vector potentials of thin circular loop antennas a direct integration procedure for far zone vector potentials of thin circular loop antennas has been known for many years this method is general in the sense that it leads to simple integrals which have closed form solutions for most commonly assumed loop current distributions however a comparable integration technique has not been available for evaluating the more complicated near zone vector potentials this paper introduces a systematic approach for the exact integration of general near zone vector potentials associated with current carrying circular loop antennas a particular example is considered where this new integration technique is used to find exact solutions to the vector potential and electromagnetic field integrals for loops with a fourier cosine series expansion of the current the observation is made that degenerate forms of these exact representations lead to simplified expressions for the important special cases of a uniform and cosinusoidal current loop two equivalent forms of exact series expansions are derived for the uniform current vector potential and field integrals it is shown that the familiar small loop approximations as well as the classical far field expressions may be obtained as limiting cases of the more general exact series representations for the uniform current loop obtained in this paper convenient asymptotic far field expansions are derived for the loop with a cosinusoidal current distribution finally the far field analysis for the cosinusoidal loop is generalized to loops having an arbitrary current represented by a fourier cosine series

the exact analytical solution for large circular loops radiating around a dielectric coated conducting sphere in this paper the electromagnetic field of electrically large circular loop antennas with different radii and different nonuniform current values around a dielectric coated conducting sphere is considered one or more loop antennas are located on the outer surface of a spherical dielectric shell covering a conducting sphere eigenfunction series solutions for the field are assumed in two regions the current distribution on the wire loop driven by a voltage source is determined by fourier series expansion and all necessary harmonics are taken into account exact analytical field expressions in closed forms are derived and field patterns are plotted the antenna model and formulation presented in this paper offer exact analytical solutions to several loop antenna problems

edge effects in axial arrays of circular rings a boundary value problem is solved for the current induced by any source in particular for an incident plane wave on any number of identical rings that are arranged to form an axisymmetric linear array the net aperture distribution along the finite array is approximated by a combination of three physically identifiable components a term from the related infinite array plus contributions from two independent edge effect waves that originate from each of the two ends however if individually resonant loops are closer than a critical spacing the entire structure exhibits a wild resonance and the simple approximation becomes invalid

entire domain mom analysis of an array of arbitrarily oriented circular loop antennas a general formulation this paper presents a general formulation for the entire domain method of moments analysis of an n element array of arbitrarily oriented coupled circular loop antennas the orientations of the loops with respect to each other are defined through the use of eulerian angles the positions of the loops in space are defined by translation vectors from the center of a loop to another by making use of coordinate transformations and vector algebra a concise set of linear equations for solving the currents on the loops is obtained the formulation is sufficiently general to be used for all the previously reported coupled loop orientations it is also ideal for the study of skewed circular loops which may be oriented in innumerable ways and in turn demand a general formulation for their analysis the use of the general formulation is illustrated by analyzing the coupling currents between collocated skewed loops the formulation is also applied to study the effects on the transfer impedance between a pair of noncollocated skewed loops as one of the loops is rotated about various axes

the complexity of soft constraint satisfaction over the past few years there has been considerable progress in methods to systematically analyse the complexity of constraint satisfaction problems with specified constraint types one very powerful theoretical development in this area links the complexity of a set of constraints to a corresponding set of algebraic operations known as polymorphisms in this paper we extend the analysis of complexity to the more general framework of combinatorial optimisation problems expressed using various forms of soft constraints we launch a systematic investigation of the complexity of these problems by extending the notion of a polymorphism to a more general algebraic operation which we call a multimorphism we show that many tractable sets of soft constraints both established and novel can be characterised by the presence of particular multimorphisms we also show that a simple set of np hard constraints has very restricted multimorphisms finally we use the notion of multimorphism to give a complete classification of complexity for the boolean case which extends several earlier classification results for particular special cases

a surprising covariance involving the minimum of multivariate normal variables aformula is provided for the covariance of x 1 with the minimum of the multivariate normal vector x1 x2 xn the resulting expression has an intuitive interpretation as the weighted average of then covariances of x1 with x1 x2 xn where the ith weight equals the probability that x1 is the minimum the formula is surprising for several reasons first results involving extrema of order statistics in the presence of correlation are usually much more complex second anattempt at adirect proof runs into difficulties involving the nontrivial distinction between a conditional expectation and an ordinary covariance finally although these difficulties are genuine on a term by term basis they cancel out when weighted and combined the geometric interpretation in n dimensional space is that although the vector of covariances of x1 with x1 x2 xn is in general different from the vector of appropriate conditional expectations these vectors always have the same projection on to the vector of prob

fast simple and accurate computation of the currents on an arbitrarily large circular loop antenna this paper is presenting a very efficient method for computing the currents on a circular loop antenna with arbitrarily large size pocklington s integral equation is formulated for the circular loop geometry and the method of moments with point matching is applied to cast the equation s discrete counterpart the basis functions are chosen in such a way that the relevant square matrix is circulant and therefore amenable to exact eigenvalue analysis subsequently the matrix is diagonalized and inverted analytically yielding simple analytical expressions for the weights of the basis functions and hence the current and the input admittance of the antenna the algorithm utilizes mainly elementary mathematical functions as opposed to already known expressions in the literature and yields results in the form of a rapidly convergent single series applicable to extremely large loops

building tractable disjunctive constraints many combinatorial search problems can be expressed as constraint satisfaction problems this class of problems is known to be np hard in general but a number of restricted constraint classes have been identified which ensure tractability this paper presents the first general results on combining tractable constraint classes to obtain larger more general tractable classes we give examples to show that many known examples of tractable constraint classes from a wide variety of different contexts can be constructed from simpler tractable classes using a general method we also construct several new tractable classes that have not previously been identified

closure properties of constraints many combinatorial search problems can be expressed as constraint satisfaction problems and this class of problems is known to be np complete in general in this paper we investigate the subclasses that arise from restricting the possible constraint types we first show that any set of constraints that does not give rise to an np complete class of problems must satisfy a certain type of algebraic closure condition we then investigate all the different possible forms of this algebraic closure property and establish which of these are sufficient to ensure tractability as examples we show that all known classes of tractable constraints over finite domains can be characterized by such an algebraic closure property finally we describe a simple computational procedure that can be used to determine the closure properties of a given set of constraints this procedure involves solving a particular constraint satisfaction problem which we call an indicator problem

on the use of nonsingular kernels in certain integral equations for thin wire circular loop antennas fundamental properties of certain popular integral equations for thin wire circular loop antennas with nonsingular kernels are studied the cornerstone of our study is a large asymptotic formula for the n th fourier coefficient of the nonsingular kernel four different methods of driving the circular loop are considered namely the delta function generator the finite gap generator a certain type of frill generator and the case of plane wave incidence the excitation model is crucial to our discussions since it determines the behavior of the solution convergence also discussed are associated difficulties that may arise when moment methods are applied to the aforementioned equations as well as a simple improvement to the fourier series method for determining the current in the case of the frill generator the main results herein closely parallel recent results for the case of the straight antenna and similarities and differences between the straight and circular cases are discussed

synthesis of wire antennas using the multipole expansion method a rigorous mathematical solution to the problem of synthesizing wire antennas using the multipole expansion method mem is presented the input current and required size of the antenna are estimated using the knowledge of the required field pattern this solution is based on three steps first obtaining the expansion s weighting coefficients that carry both the signature of the current and size of the antenna in essence the analysis of the direct modeling needs to be addressed first in order to define these coefficients second extracting the coefficients from the required field pattern using the natural orthogonality property of the spherical harmonic functions finally performing a numerical search for the argument of the spherical bessel functions to satisfy the ratio between two successive moments once the size of the antenna is found a recursive expression is used to obtain the input current for the current distributions assumed herein the odd order coefficients of the mem are shown to be the only necessary coefficients to construct the radiation far field also it is found that the estimated model parameters are in excellent agreement with the analytical ones

the complexity of temporal constraint satisfaction problems a temporal constraint language is a set of relations that has a first order definition in q an extended abstract of this article appeared in the proceedings of stoc 08

fast parallel constraint satisfaction a constraint satisfaction problem csp involves searching for an assignment of values to a given set of variables so that the values assigned satisfy a given set of constraints the general csp is np complete to confront the intractability of the general csp relaxation procedures have been devised instead of searching for a globally consistent assignment of values to the variables try to restrict the domain of values of each variable in a way that ensures local consistency only the relaxation procedures are efficient but have been proved to be inherently sequential in this paper we define a class of csps for which a global solution can be found by a fast parallel algorithm no relaxation preprocessing is needed for the parallel algorithm to work the result is motivated from the problem of labelling a 2 d line drawing of a 3 d object by the clowes huffman malik labelling scheme an important application of csp in computer vision for such a labelling csp the constraint graph can be general but the constraint relations are usually of the type we call implicational it is shown here that a csp with this type of constraint relations and no restrictions on its graph can be solved by an efficient i e with polynomial time complexity sequential algorithm also it is shown that it can be solved by a fast parallel algorithm that executes in time o log3n with o m n3 log n processors on a exlusive read exclusive write parallel random access machine n is the number of variables and m is the number of constrain relations the constraint relations may have arity more than two

structure identification in relational data this paper presents several investigations into the prospects for identifying meaningful structures in empirical data namely structures permitting effective organization of the data to meet requirements of future queries we propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability using this framework we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a cnf theory with desirable topology and if the answer is positive identifying the desired decomposition finally we address the problem of expressing a given relation as a horn theory and if this is impossible finding the best k horn approximation to the given relation we show that both problems can be solved in time polynomial in the length of the data

max ones generalized to larger domains we study a family of problems called maximum solution where the objective is to maximize a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints when the domain is boolean i e restricted to 0 1 the maximum solution problem is identical to the well studied max ones problem and the approximability is completely understood for all restrictions on the underlying constraints s khanna m sudan l trevisan and d p williamson siam j comput 30 2001 pp 1863 1920 we continue this line of research by considering domains containing more than two elements we present two main results a complete classification for the approximability of all maximal constraint languages over domains of cardinality at most 4 and a complete classification of the approximability of the problem when the set of allowed constraints contains all permutation constraints under the assumption that a conjecture due to szczepara minimal clones generated by groupoids ph d thesis universite de montreal montreal qc 1996 holds we give a complete classification for all maximal constraint languages these classes of languages are well studied in universal algebra and computer science they have for instance been considered in connection with machine learning and constraint satisfaction our results are proved by using algebraic results from clone theory and the results indicate that this approach is very powerful for classifying the approximability of certain optimization problems

constraints consistency and closure although the constraint satisfaction problem is np complete in general a number of constraint classes have been identified for which some fixed level of local consistency is sufficient to ensure global consistency in this paper we describe a simple algebraic property which characterises all possible constraint types for which strong k consistency is sufficient to ensure global consistency for each k 2 we give a number of examples to illustrate the application of this result

a proof of the csp dichotomy conjecture many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability the standard way to parameterize interesting subclasses of the constraint satisfaction problem is via finite constraint languages the main problem is to classify those subclasses that are solvable in polynomial time and those that are np complete it was conjectured that if a constraint language has a weak near unanimity polymorphism then the corresponding constraint satisfaction problem is tractable otherwise it is np complete in the article we present an algorithm that solves constraint satisfaction problem in polynomial time for constraint languages having a weak near unanimity polymorphism which proves the remaining part of the conjecture 1

disjunctions independence refinements an important question in constraint satisfaction is how to restrict the problem to ensure tractability since the general problem is np hard the use of disjunctions has proven to be a useful method for constructing tractable constraint classes from existing classes the well known max closed and ord horn constraints are examples of tractable classes that can be constructed this way three sufficient conditions the guaranteed satisfaction property 1 independence and 2 independence that each ensure the tractability of constraints combined by disjunctions have been proposed in the literature we show that these conditions are both necessary and sufficient for tractability in three different natural classes of disjunctive constraints this suggests that deciding this kind of property is a very important task when dealing with disjunctive constraints we provide a simple automatic method for checking the 1 independence property this method is applicable whenever the consistency of the constraints under consideration can be decided by path consistency our method builds on a connection between independence and refinements which is a way of reducing one constraint satisfaction problem to another

comments on exact field expressions for circular loop antennas using spherical functions expansion the author would like to thank the commentators dr zheng and dr li for reviewing and commenting on the work reported in 1 the author disagrees with their conclusion that the author in 1 is criticizing the merits of their published papers the author is merely explaining the differences between the author s work in 1 and the commentators work reported in 2 this should not detract from the contribution they made in 2 as indicated in their comments

soft arc consistency revisited the valued constraint satisfaction problem vcsp is a generic optimization problem defined by a network of local cost functions defined over discrete variables it has applications in artificial intelligence operations research bioinformatics and has been used to tackle optimization problems in other graphical models including discrete markov random fields and bayesian networks the incremental lower bounds produced by local consistency filtering are used for pruning inside branch and bound search in this paper we extend the notion of arc consistency by allowing fractional weights and by allowing several arc consistency operations to be applied simultaneously over the rationals and allowing simultaneous operations we show that an optimal arc consistency closure can theoretically be determined in polynomial time by reduction to linear programming this defines optimal soft arc consistency osac to reach a more practical algorithm we show that the existence of a sequence of arc consistency operations which increases the lower bound can be detected by establishing arc consistency in a classical constraint satisfaction problem csp derived from the original cost function network this leads to a new soft arc consistency method called virtual arc consistency which produces improved lower bounds compared with previous techniques and which can solve submodular cost functions these algorithms have been implemented and evaluated on a variety of problems including two difficult frequency assignment problems which are solved to optimality for the first time our implementation is available in the open source toulbar2 platform

the exact kernel for cylindrical antenna in the numerical calculation for a cylindrical antenna the thin wire kernel is widely used as a convenient approximation to the exact kernel of the electric field equation however this thin wire approximation is valid only if the radius of wire is much less than its length and the wavelength furthermore arbitrarily using this approximation may not obtain the convergent outcomes the expression of the exact kernel for the cylindrical antenna which would be useful in the numerical work is presented

on a new cylindrical harmonic representation for spherical waves an exact series representation is presented for integrals whose integrands are products of cosine and spherical wave functions where the argument of the cosine term can be any integral multiple n of the azimuth angle spl phi this series expansion is shown to have the following form i n e sup jkr0 r sub 0 spl delta sub no jk spl sigma sub m 1 sup spl infin c m n k sup 2 spl rho spl rho 0 m h sub m sup 2 kr sub 0 kr sub 0 sup m it is demonstrated that in the special cases n 0 and n 1 this series representation corresponds to existing expressions for the cylindrical wire kernel and the uniform current circular loop vector potential respectively a new series representation for spherical waves in terms of cylindrical harmonics is then derived using this general series representation finally a closed form far field approximation is developed and is shown to reduce to existing expressions for the cylindrical wire kernel and the uniform current loop vector potential as special cases

from local to global consistency abstract in reasoning tasks involving the maintenance of consistent databases so called qqconstraint networks q q it is customary to enforce local consistency conditions in order to simplify the subsequent construction of a globally coherent model of the data in this paper we present a relationship between the sizes of the variables domains the constraints arity and the level of local consistency sufficient to ensure global consistency based on these parameters a new tractability classification of constraint networks is presented we also show based on this relationship that any relation on bi valued variables which is not representable by a network of binary constraints cannot be represented by networks with any number of hidden variables

efficient modeling of radiation and scattering for a large array of loops a computationally efficient technique based on the method of moments mom formulation is invoked in the characterization of radiation and scattering properties of an array of coaxial circular non identical loops a set of pocklington type integral equations for the loop currents is formulated and subsequently discretized by a standard procedure thanks to a suitable choice of the basis functions the resulting matrix corresponding to the pertinent linear system is forced to consist of circulant blocks this type of system is solvable by an innovative recursive algorithm featuring several important advantages such as lower memory and execution time consumption over standard purely numerical inversion the overall procedure is simpler in implementation than already existing methods based on fourier analysis the procedure invokes almost exclusively elementary functions and is applicable to large arrays with respect to diameter or number of loops data for such configurations are presented for the first time in literature

and or search spaces for graphical models the paper introduces an and or search space perspective for graphical models that include probabilistic networks directed or undirected and constraint networks in contrast to the traditional or search space view the and or search tree displays some of the independencies present in the graphical model explicitly and may sometimes reduce the search space exponentially indeed most algorithmic advances in search based constraint processing and probabilistic inference can be viewed as searching an and or search tree or graph familiar parameters such as the depth of a spanning tree treewidth and pathwidth are shown to play a key role in characterizing the effect of and or search graphs vs the traditional or search graphs we compare memory intensive and or graph search with inference methods and place various existing algorithms within the and or search space

efficient algorithms for description problems over finite totally ordered domains given a finite set of vectors over a finite totally ordered domain we study the problem of computing a constraint in conjunctive normal form such that the set of solutions for the produced constraint is identical to the original set we develop an efficient polynomial time algorithm for the general case followed by specific polynomial time algorithms producing horn dual horn and bijunctive formulas for sets of vectors closed under the operations of conjunction disjunction and median respectively our results generalize the work of dechter and pearl on relational data as well as the papers by hebrard and zanuttini they complement the results of hahnle et al on multivalued logics and jeavons et al on the algebraic approach to constraints

response to comments on exact field expressions for circular loop antennas using spherical functions expansion the author would like to thank the commentators dr zheng and dr li for reviewing and commenting on the work reported in the author disagrees with their conclusion that the author in is criticizing the merits of their published papers the author is merely explaining the differences between the author s work in and the commentators work reported in this should not detract from the contribution they made in as indicated in their comments