seminonparametric bayesian estimation of the asymptotically ideal production model abstract recently it has been shown that seminonparametric methods can be used to produced high quality approximations to a firm s technology unlike the local approximations provided by the conventional class of flexible functional forms seminonparametric methods generate global spans within large classes of functions however that approach usually spans a much larger space than the neoclassical function space relevant to most production modeling an exception is the asymptotically ideal model aim generated from the muntz szatz series expansion since every basis function in that expansion is within the neoclassical function space a straightforward method exists for imposing neoclassical regularity when all factors are substitutes since the relevant constraints are inequality restrictions we implement the approach using bayesian methods to avoid the problems of sampling distribution truncation that would occur from sampling theoretic methods we further discuss the relevant extensions that would permit complementary factors nonconstant returns to scale and technological change

the treatment of lubrication forces in boundary integral equations despite their many advantages over other numerical methods boundary integral formulations still fail to provide accurate predictions of mesoscale motion in dense suspensions of rigid particles because the nearly singular flow between surfaces in close proximity cannot be resolved accurately a procedure for incorporating analytical solutions for the lubrication flow within a large scale boundary integral equation method is shown although the method is applied to the case of spherical particles in conjunction with the completed double layer boundary integral equation it can be developed further to treat more complex geometries and can be adapted to other numerical techniques in contrast to other apparently similar approaches the present method does not resort to effective medium approximations and in principle retains all the advantages typical of boundary integral approaches the framework also allows for forces other than those due to hydrodynamic lubrication between particles provided that they are a linear function of the relative velocity or at least can be linearized for example forces due to sub continuum fluid behaviour or forces resulting from surface chemistry it is shown using several benchmarks that the relative motion between two particles in various flows is captured accurately both statically and dynamically in situations where uncorrected simulations fail moreover the computational effort is reduced substantially by the application of the method

perfect ideal and balanced matrices abstract in this paper we survey results and open problems on perfect ideal and balanced matrices these matrices arise in connection with the set packing and set covering problems two integer programming models with a wide range of applications we concentrate on some of the beautiful polyhedral results that have been obtained in this area in the last 30 years this survey first appeared in ricerca operativa

generalized quadratic revenue functions abstract in this paper we focus on the specification of revenue functions in their dual price space we consider two distance functions the shephard output distance function and the directional output distance function and define both in price space the former is multiplicative in nature and satisfies homogeneity whereas the latter is additive and satisfies the translation property functional equation methods yield the translog specification in the case of the shephard distance function and a quadratic specification in the case of the directional distance function monte carlo evidence suggests that the quadratic specification outperforms the translog in large samples and in true models with plenty of curvature

the global properties of the minflex laurent generalized leontief and translog flexible functional forms caves and christensen 16 have provided a procedure for displaying the regular regions of a flexible functional form in the 2 good homothetic and nonhomothetic cases and in the 3 good homothetic case we extend the procedure to the nonhomothetic 3 good case and we apply the extended procedure to the translog generalized leontief and minflex laurent flexible functional forms in addition we acquire the regular regions for the minflex laurent model in the 2 good nonhomothetic case and superimpose the resulting regions on those already found by caves and christensen for the translog and generalized leontief models we find that the new minflex laurent model generally has the largest regular regions of the three fiexible functional forms in addition the regular region of the minflex laurent model is found to expand as real income increases as a result that model is particularly well suited for use with time series data which typically is characterized by positive long term growth trends in real income in such applications all recent data and future forecasts can be expected to lie within the regular region of the minflex laurent model although it is possible for some of the earliest data to fall outside that regular region the model s regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets the regular region of each of three models moves when the model s parameters are changed with the generalized leontief or translog model the regular region s shape location and size are unpredictable without prior knowledge of the model s parameters with either of those two models the intersection of the model s regular regions as the parameters are changed is contained within a very small neighborhood of the one point at which we require the model to be regular with the minflex laurent model the primary properties of the regular regions are invariant to the values of the parameters and the intersection of the displayed regular regions is a very large unbounded set the width of that intersection increases without limit as real income increases

a characterization of oriented hypergraphic balance via signed weak walks abstract an oriented hypergraph is a hypergraph where each vertex edge incidence is given a label of 1 or 1 and each adjacency is signed the negative of the product of the incidences an oriented hypergraph is balanced if the product of the adjacencies in each circle is positive we provide a combinatorial interpretation for entries of k th power of the oriented hypergraphic laplacian via the number of signed weak walks of length k using closed weak walks we prove a new characterization of balance for oriented hypergraphs and matrices that generalizes harary s theorem for signed graphs

balance 0 1 matrices bicoloring and total dual integrality a 0 1 matrixa is balanced if in every submatrix with two nonzero entries per row and column the sum of the entries is a multiple of four this definition was introduced by truemper 1978 and generalizes the notion of a balanced 0 1 matrix introduced by berge 1970 in this paper we extend a bicoloring theorem of berge 1970 and total dual integrality results of fulkerson hoffman and oppenheim 1974 to balanced 0 1 matrices

transitive packing a unifying concept in combinatorial optimization this paper attempts to provide a better understanding of the facial structure of polyhedra previously investigated separately it introduces the notion of transitive packing and the transitive packing polytope polytopes that turn out to be special cases of the transitive packing polytope include the node packing acyclic subdigraph bipartite subgraph planar subgraph clique partitioning partition transitive acyclic subdigraph interval order and relatively transitive subgraph polytopes we give cutting plane proofs for several rich classes of valid inequalities of the transitive packing polytope thereby introducing generalized cycle generalized clique generalized antihole generalized antiweb and odd partition inequalities on the one hand these classes subsume several known classes of valid inequalities for several special cases on the other hand they yield many new inequalities for several other special cases for some of the classes we also prove a lower bound on their gomory chvatal rank finally we relate the concept of transitive packing to generalized set packing and covering as well as to balanced and ideal matrices

numerical p version refinement studies for the regularized stress bem in the development of the boundary element method bem and the finite element method fem researchers have typically selected similar basis functions that is both methods typically employ low order interpolations such as piece wise linear or piece wise quadratic and rely on h version refinement to increase accuracy as required in the case of the fem the decision to use low order elements is made for computational efficiency as an attractive compromise between local modeling accuracy and sparseness of the resulting linear system however in many bem formulations low order elements may be the only practical choice given the complexity of using analytic integration formulae in conjunction with special integral interpretations unlike their efficient use in the fem fine meshes of low order elements in the bem are highly inefficient from a computational standpoint given the dense nature of bem systems moreover owing to singularities in the kernel functions the bem should be expected to benefit more so than the fem from very high levels of local accuracy through the use of regularized algorithms which only require numerical integration p version refinement in the bem is easily extended to include any set of basis functions with no significant increase in programming complexity numerical results show that by using interpolations as high as 12th and 16th order one can expect reductions in error by as many as five orders of magnitude over comparable algorithms based on similar system size for two dimensional problems it is also shown that for a given level of error one can expect reductions in system size by an order of magnitude thus leading to a reduction in computational expense for conventional algorithms by three orders of magnitude copyright 2003 john wiley sons ltd

imposing curvature restrictions on flexible functional forms abstract a general computational method for estimating the parameters of a flexible functional form subject to convexity quasi convexity concavity or quasi concavity at a point at several points or over a region is set forth and illustrated with an example

short cuts to dynamic factor demand modelling abstract by means of so called virtual or shadow prices short run factor demands short run marginal costs etc can be derived from any long run cost function the traditional approach short run restricted conditional variable cost functions is criticized and it is also shown that technological change scale effects etc can be added to any cost function by means of disembodied factor augmenting efficiency indexes easing the interpretations of the effects but without loss of flexibility it is shown that the trend and scale parameters of the long run translog cost function can be directly translated into trend and scale parameters of such efficiency indexes the techniques are illustrated on the well known berndt wood data set using a diewert long run generalized leontief gl cost function and assuming that capital and labour are quasi fixed

integral equation methods for stokes flow and isotropic elasticity in the plane we present a class of integral equation methods for the solution of biharmonic boundary value problems with applications to two dimensional stokes flow and isotropic elasticity the domains may be multiply connected and finite infinite or semi infinite in extent our analytic formulation is based on complex variables and our fast multipole based iterative solution procedure requireso n operations wherenis the number of nodes in the discretization of the boundary the performance of the methods is illustrated with several large scale numerical examples

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

on the bias in flexible functional forms and an essentially unbiased form the fourier flexible form abstract the fourier flexible form and its derived expenditure system are introduced subject to smoothness conditions on the consumer s true indirect utility function the consumer s true expenditure system must be of the fourier form over the region of interest in an empirical investigation arbitrarily accurate finite parameter approximations of the consumer s true expenditure system are obtained by dropping all high order terms of the fourier expenditure system past an appropriate truncation point the resulting finite parametersystem is tractable in empirical studies the reader who is primarily interested in applications need only read the second and fifth sections the remainder of the article is concerned with the verification of these claims and an investigation of some aspects of the bias in translog specifications

on a high dimensional model representation method based on copulas abstract this article provides an alternative to high dimensional model representation using a copula approximation of an unknown functional form we apply our methodology in the context of an extensive monte carlo study and to a sample of large us commercial banks in the monte carlo experiment the approximations errors of the copula approach are small and behave randomly in our empirical application we find that the copula approximation performs much better in terms of bayes factors for model comparison compared to high dimensional model representation which in turn provides better results when compared with standard flexible functional forms like the translog the minflex laurent and the generalized leontief or a multilayer perceptron moreover the choice of approximation has significant implications for productivity and its components returns to scale technical inefficiency technical change and efficiency change

perfect and ideal 0 1 matrices a 0 1 matrix a is said to be perfect resp ideal if the corresponding generalized packing resp covering polytope is integral given a 0 1 matrix a we construct a 0 1 matrix that is perfect if and only if a is perfect a similar result is obtained for the generalized covering problem we also extend some known results on perfect 0 1 matrices to the 0 1 case

estimating demand with distance functions parameterization in the primal and dual abstract our purpose is to investigate the ability of different parametric forms to correctly estimate consumer demands based on distance functions using monte carlo methods our approach combines economic theory econometrics and quadratic approximation we begin by deriving parameterizations for transformed quadratic functions which are linear in parameters and characterized by either homogeneity or which satisfy the translation property homogeneity is typical of shephard distance functions and expenditure functions whereas translation is characteristic of benefit shortage or directional distance functions the functional forms which satisfy these conditions and include both first and second order terms are the translog and quadratic forms respectively we then derive a primal characterization which is homogeneous and parameterized as translog and a dual model which satisfies the translation property and is specified as quadratic we assess functional form performance by focusing on empirical violations of the regularity conditions our analysis corroborates results from earlier monte carlo studies on the production side suggesting that the quadratic form more closely approximates the true technology or in our context consumer preferences than the translog

perfect 0 pl matrices and perfect bidirected graphs abstract perfect 0 1 matrices and perfect bidirected graphs are independently defined but are closely related in this paper we discuss these relations and give several characterizations of perfectness the generalized stable set problem associated with bidirected graphs is a generalization of the maximum weighted stable set problem we also give a brief proof that if a given bidirected graph is perfect then the problem can be solved in polynomial time

the fast solution of poisson s and the biharmonic equations on irregular regions we present fast methods for solving laplace s and the biharmonic equations on irregular regions with smooth boundaries the methods used for solving both equations make use of fast poisson solvers on a rectangular region in which the irregular region is embedded they also both use an integral equation formulation of the problem where the integral equations are fredholm integral equations of the second kind the main idea is to use the integral equation formulation to define a discontinuous extension of the solution to the rest of the rectangular region fast solvers are then used to compute the extended solution aside from solving the equations we have also been able to compute derivatives of the solutions with little loss of accuracy when the data was sufficiently smooth

introduction to internally consistent modeling aggregation inference and policy abstract this special issue of the journal of econometrics honors william a barnett s exceptional contributions to unifying economic theory with rigorous statistical inference to interpret economic data and inform public policy it is devoted to papers that advance microeconometrics macroeconometrics and financial econometrics to build models to interpret evidence

a multi level boundary element method for stokes flows in irregular two dimensional domains recently we have developed multi level boundary element methods mlbem for the solution of the laplace and helmholtz equations that involve asymptotically decaying non oscillatory and oscillatory singular kernels respectively the accuracy and efficiency of the fast boundary element methods for steady state heat diffusion and acoustics problems have been investigated for square domains the current work extends the mlbem methodology to the solution of stokes equation in more complex two dimensional domains the performance of the fast boundary element method for the stokes flows is first investigated for a model problem in a unit square then we consider an example problem possessing an analytical solution in a rectangular domain with 5 1 aspect ratio and finally we study the performance of the mlbem algorithm in a c shaped domain

stokes flow around cylinders in a bounded two dimensional domain using multipole accelerated boundary element methods the multipole technique has recently received attention in the field of boundary element analysis as a means of reducing the order of data storage and calculation time requirements from o n2 iterative solvers or o n3 gaussian elimination to o n log n or o n where n is the number of nodes in the discretized system such a reduction in the growth of the calculation time and data storage is crucial in applications where n is large such as when modelling the macroscopic behaviour of suspensions of particles in such cases a minimum of 1000 particles is needed to obtain statistically meaningful results leading to systems with n of the order of 10 000 for the smallest problems when only boundary velocities are known the indirect boundary element formulation for stokes flow results in fredholm equations of the second kind which generally produce a well posed set of equations when discretized a necessary requirement for iterative solution methods the direct boundary element formulation on the other hand results in fredholm equations of the first kind which upon discretization produce ill conditioned systems of equations the model system here is a two dimensional wide gap couette viscometer where particles are suspended in the fluid between the cylinders this is a typical system that is efficiently modelled using boundary element method simulations the multipolar technique is applied to both direct and indirect formulations it is found that the indirect approach is sufficiently well conditioned to allow the use of fast multipole methods the direct approach results in severe ill conditioning to a point where application of the multipole method leads to non convergence of the solution iteration copyright 1999 john wiley sons ltd

a comparison of domain integral evaluation techniques for boundary element methods in many cases boundary integral equations contain a domain integral this can be evaluated by discretization of the domain into domain elements historically this was seen as going against the spirit of boundary element methods and several methods were developed to avoid this discretization notably dual and multiple reciprocity methods and particular solution methods these involved the representation of the interior function with a set of basis functions generally of the radial type in this study meshless methods dual reciprocity and particular solution are compared to the direct domain integration methods the domain integrals are evaluated using traditional methods and also with multipole acceleration it is found that the direct integration always results in better accuracy as well as smaller computation times in addition the multipole method further improves on the computation times in particular where multiple evaluations of the integral are required as when iterative solvers are used the additional error produced by the multipole acceleration is negligible copyright 2001 john wiley sons ltd

fractional demand systems abstract this paper provides a complete characterization of fractional demand systems which are utility derived demand equations having quantities or budget shares proportional to af bg where f and g depend on income and a and b vary across goods and depend on prices it is proved that all such demand systems reduce to seven basic forms only four of which homothetic pigl piglog and translog have been previously described in the literature uses and virtues of fractional demand systems in terms of estimation aggregation possible global properties and uses for testing the adequacy of other common functional forms are described an empirical example comparing the general fractional form of the translog system to its more usual piglog form is provided

smoothing bias in the measurement of marginal effects abstract this paper examines the tendency of kernel regression estimators to underestimate marginal effects or derivatives by developing the connection between smoothing and errors in variables structure we explain how smoothing itself leads to attenuation bias in derivatives or bias toward zero when the true model is linear and the regressors normal the attenuation bias is uniform and can be accurately explained by standard errors in variables bias formulae these formulations also indicate the seriousness of the attenuation bias with different numbers of regressors and different sample sizes for the situation where the true model is nonlinear we examine the related errors in variables structure and indicate what features affect the size of attenuation bias in derivatives finally we explain the connections between our analysis and the standard bias expansion for kernel regression estimators including brief consideration of technical devices such as higher order kernels

berge acyclic multilinear 0 1 optimization problems abstract the problem of optimizing a multilinear polynomial f in 0 1 variables arises in applications from many different areas we are interested in resolution methods based on reformulating the polynomial problem into an equivalent linear one an approach that attempts to draw benefit from the extensive literature in integer linear programming more precisely we characterize instances for which the classical standard linearization procedure guarantees integer optimal solutions we show that the standard linearization polytope ph is integer if and only if the hypergraph h defined by the higher degree monomials of f is berge acyclic or equivalently when the matrix defining ph is balanced this characterization follows from more general conditions that guarantee integral optimal vertices for a relaxed formulation depending on the sign pattern of the monomials of f

a parallel multipolar indirect boundary element method for the neumann interior stokes flow problem a multipolar expansion technique is applied to the indirect formulation of the boundary element method in order to solve the two dimensional internal stokes flow second kind boundary value problems the algorithm is based on a multipolar expansion for the far field and numerical evaluation for the near field due to the nature of the algorithm it is necessary to resort to the use of an iterative solver for the resulting algebraic linear system of equations a parallel implementation is designed to take advantage of the natural domain decomposition of fast multipolar techniques and bring further improvements copyright 2000 john wiley sons ltd

fast multipole boundary element method for the laplace equation in a locally perturbed half plane with a robin boundary condition a fast multipole boundary element method fm bem for solving large scale potential problems ruled by the laplace equation in a locally perturbed 2 d half plane with a robin boundary condition is developed in this paper these problems arise in a wide gamut of applications being the most relevant one the scattering of water waves by floating and submerged bodies in water of infinite depth the method is based on a multipole expansion of an explicit representation of the associated green s function which depends on a combination of complex valued exponential integrals and elementary functions the resulting method exhibits a computational performance and memory requirements similar to the classic fm bem for full plane potential problems numerical examples demonstrate the accuracy and efficiency of the method

the global properties of the two minflex laurent flexible functional forms abstract the minflex laurent flexible functional form is a special case of a second order laurent series expansion the minflex laurent when constructed in square roots is called the minflex laurent ml generalized leontief the minflex laurent ml translog model is the minflex laurent in logarithms we find that the regular region of the ml translog is most often even larger than that of the ml generalized leontief model except when substitutability is very low we previously have shown that the regular region of the ml generalized leontief is substantially larger than that of the usual translog and generalized leontief models

mip reformulations of the probabilistic set covering problem in this paper we address the following probabilistic version psc of the set covering problem min cx mathbb p ax ge xi ge p x in 0 1 n where a is a 0 1 matrix xi is a random 0 1 vector and p in 0 1 is the threshold probability level we introduce the concepts of p inefficiency and polarity cuts while the former is aimed at deriving an equivalent mip reformulation of psc the latter is used as a strengthening device to obtain a stronger formulation simplifications of the mip model which result when one of the following conditions hold are briefly discussed a is a balanced matrix a has the circular ones property the components of xi are pairwise independent the distribution function of xi is a stationary distribution or has the disjunctive shattering property we corroborate our theoretical findings by an extensive computational experiment on a test bed consisting of almost 10 000 probabilistic instances this test bed was created using deterministic instances from the literature and consists of probabilistic variants of the set covering model and capacitated versions of facility location warehouse location and k median models our computational results show that our procedure is orders of magnitude faster than any of the existing approaches to solve psc and in many cases can reduce hours of computing time to a fraction of a second

the three dimensional global properties of the minflex laurent generalized leontief and translog flexible functional forms abstract we use the caves and christensen procedure to produce the regular regions of three flexible functional forms generalized leontief translog and barnett s new minflexlaurent model we display the regular regions in six cases with three goods using both three dimensional color graphics and two dimensional sections we find that minflex laurent generally has the largest regular region in addition the regular regions of that model are the most stable in shape across the six cases and always expand as real income increases consequently that model is especially well suited for use with income trended time series data

recognizing balanceable matrices a 0 1 matrix is balanced if it does not contain a square submatrix with exactly two nonzero entries per row and per column in which the sum of all entries is 2 modulo 4 a 0 1 matrix is balanceable if its nonzero entries can be signed 1 so that the resulting matrix is balanced a signing algorithm due to camion shows that the problems of recognizing balanced 0 1 matrices and balanceable 0 1 matrices are equivalent conforti cornuejols kapoor and vuskovic gave an algorithm to test if a 0 1 matrix is balanced truemper has characterized balanceable 0 1 matrices in terms of forbidden submatrices in this paper we give an algorithm that explicitly finds one of these forbidden submatrices or shows that none exists

the minflex laurent translog flexible functional form abstract barnett s minflex laurent generalized leontief model was produced from a special case of a second order laurent series expansion in the square roots in this paper we produce a minflex laurent translog flexible functional form by the analogous expansion in the logarithms we prove that the model s regular region always grows monotonically as real income increases as a result the model is especially well suited for use with income trended time series data we also prove that the model satisfies diewert s definition of a flexible functional form and is no more deeply parameterized than is necessary to satisfy the flexibility criterion

perfect 0 1 matrices abstract perfect graphs and perfect 0 1 matrices are well studied in the literature here we introduce perfect 0 1 matrices our main result is a characterization of these matrices in terms of a family of perfect 0 1 matrices

0 1 ideal matrices a 0 1 matrixa is said to be ideal if all the vertices of the polytopeq a x ax 1 0 x 1 are integral the issue of finding a satisfactory characterization of those matrices which are minimally non ideal is a well known open problem an outstanding result toward the solution of this problem due to alfred lehman is the description of crucial properties of minimally non ideal matrices in this paper we consider the extension of the notion of ideality to 0 1 matrices by means of a standard transformation we associate with any 0 1 matrixa a suitable 0 1 matrixd a then we introduce the concept of disjoint completiona of a 0 1 matrixa and we show thata is ideal if and only ifd a is ideal moreover we introduce a suitable concept of a minimally non ideal 0 1 matrix and we prove a lehman type characterization of minimally non ideal 0 1 matrices 1998 the mathematical programming society inc published by elsevier science b v