the effect of two stage sampling on ordinary least squares methods abstract we look at the effect of intracluster correlation on standard procedures in linear regression the ordinary least squares estimator of the coefficient vector performs well in most cases but the usual estimator of cov and procedures based on this such as confidence intervals and hypothesis tests can be seriously misleading the size of the effect however tends to be smaller than the corresponding effect on the variance of an estimated mean in two stage sampling provided that the cluster sample sizes are approximately equal

a two stage estimator for probit models with structural group effects this paper outlines a two stage technique for estimation and inference in probit models with structural group effects the structural group specification belongs to a broader class of random components models in particular individuals in a given group share a common component in the specification of the conditional mean of a latent variable for a number of computational reasons existing random effects models are impractical for estimation and inference in this type of problem our two stage estimator provides an easily estimable alternative to the random effects specification in addition we conduct a monte carlo simulation comparing the performance of alternative es timators and find that the two stage estimator is superior both in terms of estimation and inference to traditional estimators

on the hull of two dimensional percolation clusters a recently proven equivalence between certain random walks with memory and the hull of percolation clusters in two dimensions is used to estimate the fractal dimension of the latter by means of monte carlo simulations the authors calculate the value dh 1 750 or 0 002 in agreement with a recent conjecture that dh 7 4 exactly

on the exact separation of mixed integer knapsack cuts during the last decades much research has been conducted on deriving classes of valid inequalities for mixed integer knapsack sets which we call knapsack cuts bixby et al the sharpest cut the impact of manfred padberg and his work mps siam series on optimization pp 309 326 2004 empirically observe that within the context of branch and cut algorithms to solve mixed integer programming problems the most important inequalities are knapsack cuts derived by the mixed integer rounding mir procedure in this work we analyze this empirical observation by developing an algorithm to separate over the convex hull of a mixed integer knapsack set the main feature of this algorithm is a specialized subroutine for optimizing over a mixed integer knapsack set which exploits dominance relationships the exact separation of knapsack cuts allows us to establish natural benchmarks by which to evaluate specific classes of them using these benchmarks on miplib 3 0 and miplib 2003 instances we analyze the performance of mir inequalities our computations which are performed in exact arithmetic are surprising in the vast majority of the instances in which knapsack cuts yield bound improvements mir cuts alone achieve over 87 of the observed gain

aggregation and mixed integer rounding to solve mips in this paper we discuss the use of mixed integer rounding mir inequalities to solve mixed integer programs mir inequalities are essentially gomory mixed integer cuts however as we wish to use problem structure we insist that mir inequalities be generated from constraints or simple aggregations of constraints of the original problem this idea is motivated by the observation that several strong valid inequalities based on specific problem structure can be derived as mir inequalities here we present and test a separation routine for such mir inequalities that includes a heuristic row aggregation procedure to generate a single knapsack plus continuous variables constraint complementation of variables and finally the generation of an mir inequality inserted in a branch and cut system the results suggest that such a routine is a useful additional tool for tackling a variety of mixed integer programming problems

structure and perimeters of percolation clusters site percolation clusters are simulated at the percolation threshold on the square lattice an algorithm for walks around each cluster is used to obtain information on its fractal geometry the fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it if the vacant perimeter sites have only nearest neighbour connectivity then the perimeter has dimension de 1 37 or 0 03 instead of that of the hull dh 1 75 the authors also measured the mass of internal dangling sites surrounded by the backbone s blobs singly and doubly connected sites the number of blobs and the average linear distance between entry into the exit from a blob

cross section regression with common shocks this paper considers regression models for cross section data that exhibit cross section dependence due to common shocks such as macroeconomic shocks the paper analyzes the properties of least squares ls estimators in this context the results of the paper allow for any form of cross section dependence and heterogeneity across population units the probability limits of the ls estimators are determined and necessary and sufficient conditions are given for consistency the asymptotic distributions of the estimators are found to be mixed normal after recentering and scaling the t wald and f statistics are found to have asymptotic standard normal x 2 and scaled x 2 distributions respectively under the null hypothesis when the conditions required for consistency of the parameter under test hold however the absolute values of t wald and f statistics are found to diverge to infinity under the null hypothesis when these conditions fail confidence intervals exhibit similarly dichotomous behavior hence common shocks are found to be innocuous in some circumstances but quite problematic in others models with factor structures for errors and regressors are considered using the general results conditions are determined under which consistency of the ls estimators holds and fails in models with factor structures the results are extended to cover heterogeneous and functional factor structures in which common factors have different impacts on different population units

efficient estimation and inference in linear pseudo panel data models we consider pseudo panel data models constructed from repeated cross sections in which the number of individuals per group is large relative to the number of groups and time periods first we show that when time invariant group fixed effects are neglected the ols estimator does not converge in probability to a constant but rather to a random variable second we show that while the fixed effects fe estimator is consistent the usual t statistic is not asymptotically normally distributed and we propose a new robust t statistic whose asymptotic distribution is standard normal third we propose efficient gmm estimators using the orthogonality conditions implied by grouping and we provide t tests that are valid even in the presence of time invariant group effects our monte carlo results show that the proposed gmm estimator is more precise than the fe estimator and that our new t test has good size and is powerful

on the 0 1 knapsack polytope this paper deals with the 0 1 knapsack polytope in particular we introduce the class ofweight inequalities this class of inequalities is needed to describe the knapsack polyhedron when the weights of the items lie in certain intervals a generalization of weight inequalities yields the so called weight reduction principle and the class of extended weight inequalities the latter class of inequalities includes minimal cover and l k configuration inequalities the properties of lifted minimal cover inequalities are extended to this general class of inequalities

eden growth on multifractal lattices a modified eden model has been investigated in which the growth probabilities are determined by a fractal measure on the underlying lattice both the spatial distribution and probability distribution of surface sites on the growing clusters have been investigated for the case where the multifractal substrate is constructed using a 2 2 multiplicative generator with the probabilities p1 1 p2 r p3 r3 and p4 r3 the spatial distribution of surface sites and the sites comprising the inner and outer hulls have a fractal geometry which can be described by dimensionalities which depend on r for the total surface this dimensionality converges to a value of about 1 76 or 0 01 as r to 0 for the inner and outer hulls the fractal dimensionality approaches a value of about 1 48 or 0 02

monte carlo series analysis of irreversible self avoiding walks i the indefinitely growing self avoiding walk igsaw high precision monte carlo data are used to estimate the exponents which govern the asymptotic behaviour of the recently introduced indefinitely growing self avoiding walk in two dimensions for this walk the exponent gamma is by definition equal to one applying the same methods which are used to extract the exponents from exact series enumeration the authors give an estimate for the exponent nu of 0 567 or 0 003 the leading corrections to this asymptotic behaviour are also calculated

binary extended formulations of polyhedral mixed integer sets we analyze different ways of constructing binary extended formulations of polyhedral mixed integer sets with bounded integer variables and compare their relative strength with respect to split cuts we show that among all binary extended formulations where each bounded integer variable is represented by a distinct collection of binary variables what we call unimodular extended formulations are the strongest we also compare the strength of some binary extended formulations from the literature finally we study the behavior of branch and bound on such extended formulations and show that branching on the new binary variables leads to significantly smaller enumeration trees in some cases

anti red bonds distribution law in 3d percolation abstract combining two independent approaches the power law structure of the anti red bonds distribution in d 3 percolation can be derived this result is important to understand the dynamical behaviour of fluctuating fronts during diffusion and invasion processes but also in problems of fragmentation aggregation of percolation clusters in d 2 it allows to calculate the fractal dimension of the hull d h 1 1 a known result not easy to prove in d 2 dimensions it gives an anti red bonds equal to d anti red 2d 1 d

on scaling relations in growth models for percolating clusters and diffusion fronts employing analogies between the growth of the incipient percolating cluster and the growth of a diffusion front the authors develop a scaling theory for this latter model their scaling assumptions support the sapoval rosso gouyet conjecture dh 1 1 nu which relates in two dimensions the fractal dimension dh of the hull of the incipient percolating cluster to the correlation length exponent nu in percolation and yield relations between the static and dynamic exponents of the growth of a diffusion front

theoretical challenges towards cutting plane selection while many classes of cutting planes are at the disposal of integer programming solvers our scientific understanding is far from complete with regards to cutting plane selection i e the task of selecting a portfolio of cutting planes to be added to the lp relaxation at a given node of the branch and bound tree in this paper we review the different classes of cutting planes available known theoretical results about their relative strength important issues pertaining to cut selection and discuss some possible new directions to be pursued in order to accomplish cutting plane selection in a more principled manner finally we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection

random group effects and the precision of regression estimates abstract when explanatory variable data in a regression model are drawn from a population with grouped structure the regression errors are often correlated within groups error component and random coefficient regression models are considered as models of the intraclass correlation this paper analyzes several empirical examples to investigate the applicability of random effects models and the consequences of inappropriately using ordinary least squares ols estimation in the presence of random group effects the principal findings are that the assumption of independent errors is usually incorrect and the unadjusted ols standard errors often have a substantial downward bias suggesting a considerable danger of spurious regression

the fractal dimension of percolation cluster hulls large simulations of 2d site percolation on a square lattice provide several estimates of the fractal dimension dh of the hull or outer boundary of percolation clusters close to criticality statistical estimates based on an ensemble of more than 106 clusters with varying sizes yield dh 1 74 or 0 02 geometrical measurements of the hull two point correlation for individual clusters with more than 105 sites give dh 1 76 or 0 01 the observed scaling behaviour is the same both slightly above and below pc

continuous knapsack sets with divisible capacities we study two continuous knapsack sets mathcal y ge y and mathcal y le y with n n integer one unbounded continuous and m m bounded continuous variables in either ge or le form when the coefficients of the integer variables are integer and divisible we show in both cases that the convex hull is the intersection of the bound constraints and 2 m 2m polyhedra arising as the convex hulls of continuous knapsack sets with a single unbounded continuous variable the latter convex hulls are completely described by an exponential family of partition inequalities and a polynomial size extended formulation is known in the ge case we also provide an extended formulation for the le case it follows that given a specific objective function optimization over both mathcal y ge y and mathcal y le y can be carried out by solving m m polynomial size linear programs a further consequence of these results is that the coefficients of the continuous variables all take the values 0 or 1 after scaling in any non trivial facet defining inequality of the convex hull of such sets

easily computable facets of the knapsack polytope it is known that facets and valid inequalities for the knapsack polytope p can be obtained by lifting a simple inequality derived from each minimal cover we study the computational complexity of such lifting in particular we show that the task of computing a lifted facet can be accomplished in o ns where s n is the cardinality of the minimal cover also for a lifted inequality with integer coefficients we show that the dual tasks of recognizing whether the inequality is valid for p or is a facet of p can be done within the same time bound

the 0 1 knapsack problem with a single continuous variable constraints arising in practice often contain many 0 1 variables and one or a small number of continuous variables existing knapsack separation routines cannot be used on such constraints here we study such constraint sets and derive valid inequalities that can be used as cats for such sets as well for more general mixed 0 1 constraints specifically we investigate the polyhedral structure of the knapsack problem with a single continuous variable called the mixed 0 1 knapsack problem first different classes of facet defining inequalities are derived based on restriction and lifting the order of lifting particularly of the continuous variable plays an important role secondly we show that the flow cover inequalities derived for the single node flow set consisting of are flows into and out of a single node with binary variable lower and upper bounds on each are can be obtained from valid inequalities for the mixed 0 1 knapsack problem thus the separation heuristic we derive for mixed knapsack sets can also be used to derive cuts for more general mixed 0 1 constraints initial computational results on a variety of problems are presented

a recursive procedure to generate all cuts for 0 1 mixed integer programs we study several ways of obtaining valid inequalities for mixed integer programs we show how inequalities obtained from a disjunctive argument can be represented by superadditive functions and we show how the superadditive inequalities relate to gomory s mixed integer cuts we also show how all valid inequalities for mixed 0 1 programs can be generated recursively from a simple subclass of the disjunctive inequalities

on splittable and unsplittable flow capacitated network design arc set polyhedra we study the polyhedra of splittable and unsplittable single arc set relaxations of multicommodity flow capacitated network design problems we investigate the optimization problems over these sets and the separation and lifting problems of valid inequalities for them in particular we give a linear time separation algorithm for the residual capacity inequalities 19 and show that the separation problem of c strong in equalities 7 is np hard but can be solved over the subspace of fractional variables only we introduce two classes of inequalities for the unsplittable flow problems we present a summary of computational experiments with a branch and cut algorithm for multicommodity flow capacitated network design problems to test the effectiveness of the results presented here empirically

pseudo gaussian and rank based optimal tests for random individual effects in large n small t panels we consider the problem of detecting unobserved heterogeneity that is the problem of testing the absence of random individual effects in an n t panel we establish a local asymptotic normality property with respect to intercept regression coefficient the scale parameter of the error and the scale parameter u of individual effects which is the parameter of interest for given scaled density f 1 of the error terms when n tends to infinity and t is fixed this result allows via the hk representation theorem for developing asymptotically optimal rank based tests for the null hypothesis u 0 absence of individual effects these tests are locally asymptotically optimal at correctly specified innovation densities f 1 but remain valid irrespective of the actual underlying density the limiting distribution of our test statistics is obtained both under the null and under sequences of contiguous alternatives a local asymptotic linearity property is established in order to control for the effect of substituting estimators for nuisance parameters the asymptotic relative efficiencies of the proposed procedures with respect to the corresponding pseudo gaussian parametric tests are derived in particular the van der waerden version of our rank based tests uniformly dominates from the point of view of pitman efficiency the classical honda test small sample performances are investigated via a monte carlo study and confirm theoretical findings

valid inequalities based on simple mixed integer sets in this paper we use facets of simple mixed integer sets with three variables to derive a parametric family of valid inequalities for general mixed integer sets we call these inequalities two step mir inequalities as they can be derived by applying the simple mixed integer rounding mir principle of wolsey 1998 twice the two step mir inequalities define facets of the master cyclic group polyhedron of gomory 1969 in addition they dominate the strong fractional cuts of letchford and lodi 2002

distance weighted city growth urban agglomerations exhibit complex emergent features of which zipf s law i e a power law size distribution and fractality may be regarded as the most prominent ones we propose a simplistic model for the generation of citylike structures which is solely based on the assumption that growth is more likely to take place close to inhabited space the model involves one parameter which is an exponent determining how strongly the attraction decays with the distance in addition the model is run iteratively so that existing clusters can grow together and new ones can emerge the model is capable of reproducing the size distribution and the fractality of the boundary of the largest cluster although the power law distribution depends on both the imposed exponent and the iteration the fractality seems to be independent of the former and only depends on the latter analyzing land cover data we estimate the parameter value ensuremath gamma ensuremath approx 2 5 for paris and its surroundings

percolation and self avoiding random loops presents simulations supporting the conjecture that properly defined exterior perimeters of 2d critical percolation clusters have the same fractal dimension d 4 3 as self avoiding random walks in addition the authors discuss possible generalizations

scaling behaviour of cluster hulls in spiral site percolation the scaling behaviour of the percolation hull rotationally constrained site percolation on the square and triangular lattices is studied the single cluster growth method has been used to determine the values of some critical exponents evidence is obtained for a scaling form of the hull size distribution function

properties of ordinary least squares estimators in regression models with nonspherical disturbances abstract a general discussion is presented of the properties of the ols estimator in regression models where the disturbances do not have a scalar identity covariance matrix several new and interesting characterizations are provided together with a synthesis of existing results a distinguishing feature of the paper is the unified treatment of the issues of efficiency and inference the theoretical material is illustrated by examples covering a wide range of models of interest to applied econometricians

on the problem of measuring fractal dimensions of random interfaces various authors have shown that the experimentally observed fractal dimension of a random interface may depend drastically on the size of the probe used for the measurements the authors propose a general explanation for such dependence that they can explicitly calculate for a simple model

sequence independent lifting for mixed integer programming we show that superadditive lifting functions lead to sequence independent lifting of inequalities for general mixed integer programming as an application we note that mixed integer rounding mir may be viewed as sequence independent lifting consequently we obtain facet conditions for mir inequalities for mixed integer knapsacks

on capacitated network design cut set polyhedra this paper provides an analysis of capacitated network design cut set polyhedra we give a complete linear description of the cut set polyhedron of the single commodity single facility capacitated network design problem then we extend the analysis to single commodity multifacility and multicommodity multifacility capacitated network design problems valid inequalities described here are applicable to directed network design problems with any number of facility types and any level of capacities we report results from a computational study done for testing the effectiveness of the new inequalities

on the facets of the mixed integer knapsack polyhedron we study the mixed integer knapsack polyhedron that is the convex hull of the mixed integer set defined by an arbitrary linear inequality and the bounds on the variables we describe facet defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities containing a single integer variable these inequalities strengthen and or generalize known inequalities for several special cases we report computational results on using the inequalities as cutting planes for mixed integer programming

multiple intersection exponents for planar brownian motion let p 2 n1 np be positive integers and b 1 1 ldots b n 1 1 ldots b 1 p ldots b n p p be independent planar brownian motions started uniformly on the boundary of the unit circle we define a p fold intersection exponent p n1 np as the exponential rate of decay of the probability that the packets bigcup j 1 n i b j i 0 t 2 i 1 p have no joint intersection the case p 2 is well known and following two decades of numerical and mathematical activity lawler et al acta math 187 275 308 2001 rigorously identified precise values for these exponents the exponents have not been investigated so far for p 2 we present an extensive mathematical and numerical study leading to an exact formula in the case n1 1 n2 2 and several interesting conjectures for other cases

alternative tests of the error components model the error components regression model is now widely applied in econometics and statistics given the potentially high costs of incorrectly excluding the component from the model an error components test should have high power in addition if a test is to gain acceptance from practitioners the test should be computed easily to obtain improved critical value approximations we introduce a standardized lagrange multiplier slm test statistic which is centered and scaled to have a zero mean and unit variance under the null hypothesis we also examine the f test which is easily computed and has a well known exact distribution under the null hypothesis if the regression errors are normally distributed

on the strength of gomory mixed integer cuts as group cuts gomory mixed integer gmi cuts generated from optimal simplex tableaus are known to be useful in solving mixed integer programs further it is well known that gmi cuts can be derived from facets of gomory s master cyclic group polyhedron and its mixed integer extension studied by gomory and johnson in this paper we examine why cutting planes derived from other facets of master cyclic group polyhedra group cuts do not seem to be as useful when used in conjunction with gmi cuts for many practical problem instances we numerically show that once gmi cuts from different rows of the optimal simplex tableau are added to the formulation all other group cuts from the same tableau rows are satisfied

clustering spatial correlations and randomization inference it is a standard practice in regression analyses to allow for clustering in the error covariance matrix if the explanatory variable of interest varies at a more aggregate level e g the state level than the units of observation e g individuals often however the structure of the error covariance matrix is more complex with correlations not vanishing for units in different clusters here we explore the implications of such correlations for the actual and estimated precision of least squares estimators our main theoretical result is that with equal sized clusters if the covariate of interest is randomly assigned at the cluster level only accounting for nonzero covariances at the cluster level and ignoring correlations between clusters as well as differences in within cluster correlations leads to valid confidence intervals however in the absence of random assignment of the covariates ignoring general correlation structures may lead to biases in standard errors we illustrate our findings

n step mingling inequalities new facets for the mixed integer knapsack set the n step mixed integer rounding mir inequalities of kianfar and fathi math program 120 2 313 346 2009 are valid inequalities for the mixed integer knapsack set that are derived by using periodic n step mir functions and define facets for group problems the mingling and 2 step mingling inequalities of atamturk and gunluk math program 123 2 315 338 2010 are also derived based on mir and they incorporate upper bounds on the integer variables it has been shown that these inequalities are facet defining for the mixed integer knapsack set under certain conditions and generalize several well known valid inequalities in this paper we introduce new classes of valid inequalities for the mixed integer knapsack set with bounded integer variables which we call n step mingling inequalities for positive integer n these inequalities incorporate upper bounds on integer variables into n step mir and therefore unify the concepts of n step mir and mingling in a single class of inequalities furthermore we show that for each n the n step mingling inequality defines a facet for the mixed integer knapsack set under certain conditions for n 2 we extend the results of atamturk and gunluk on facet defining properties of 2 step mingling inequalities for n 3 we present new facets for the mixed integer knapsack set as a special case we also derive conditions under which the n step mir inequalities define facets for the mixed integer knapsack set in addition we show that n step mingling can be used to generate new valid inequalities and facets based on covers and packs defined for mixed integer knapsack sets

invasion percolation and invading eden growth on multifractal lattices eden growth and invasion percolation models have been explored on square lattices with a multifractal distribution of growth probabilities these models generate structures with a mass fractal dimensionality of 2 and surfaces which can be described in terms of self similar fractal geometry with a fractal dimensionality larger than 1 and smaller than 2 for the eden growth models the fractal dimensions of the total perimeter internal hull and external hull depend on the probabilities associated with the generator of the multifractal measure for the invasion percolation model the three fractal dimensionalities are relatively insensitive to the structure of the generator and may be universal the distribution of growth probabilities associated with the eden models can also be described as a fractal measure and the spectrum of singularities f alpha associated with this measure has been estimated for some of these models for the eden growth models the fractal dimensionalities describing the structure of total perimeter internal hull and external hull are given by d d xi where xi is the variance of the logarithms of the probabilities used in the multiplicative generators for the multifractal growth probability measure

lifting for conic mixed integer programming lifting is a procedure for deriving valid inequalities for mixed integer sets from valid inequalities for suitable restrictions of those sets lifting has been shown to be very effective in developing strong valid inequalities for linear integer programming and it has been successfully used to solve such problems with branch and cut algorithms here we generalize the theory of lifting to conic integer programming i e integer programs with conic constraints we show how to derive conic valid inequalities for a conic integer program from conic inequalities valid for its lower dimensional restrictions in order to simplify the computations we also discuss sequence independent lifting for conic integer programs when the cones are restricted to nonnegative orthants conic lifting reduces to the lifting for linear integer programming as one may expect

generating facets for finite master cyclic group polyhedra using n step mixed integer rounding functions the n step mixed integer rounding mir functions generate n step mir inequalities for mip problems and are facets for the infinite group problems we show that the n step mir functions also directly generate facets for the finite master cyclic group polyhedra especially in many cases where the breakpoints of the n step mir function are not necessarily at the elements of the group hence the linear interpolation of the facet coefficients obtained has more than two slopes

probability density of the 2d percolation cluster perimeter the authors study the form of the probability density p r t of the end to end distance r of a segment of length t of the perimeter of the 2d percolation cluster at criticality they find that p r t behaves as p r t varies as t 2dh exp r t1dh delta where delta 1 1 1 dh the exponent dh 7 4 is the fractal dimension of the hull the external perimeter of a percolation cluster this result fits very well with recent numerical data

percolation in a symmetric random potential abstract we study percolation in a two dimensional random gaussian potential and calculate p c the critical exponents the fractal dimension of the percolating equipotential lines and the amplitude ratio c c of the perlocation susceptibility these quantities including the amplitude ratio match the known results of the two dimensional lattice percolation models

cluster hull algorithms for large systems with small memory requirement improved hull walking algorithms for two dimensional percolation are proposed in these algorithms a walker explores the external perimeter of percolation clusters with our modifications very large systems sizel can be studied with finite and small memory requirement and in computation time l7 4 applications in determining spanning probabilities continuum percolation and percolation with nonuniform occupation probability are pointed out

asymptotic inference from multi stage samples i develop a gmm based framework for asymptotic inference to analyze data from surveys whose designs involve stratification and clustering i set up the estimation problem derive the appropriate asymptotic distribution theory as the number of clusters per stratum tends to infinity and compute asymptotic standard errors that are robust to sample design effects the analysis is then extended to nonparametric regression and to semiparametric estimation based on u processes empirical illustrations are provided using consumption expenditure data from the complexly designed indian national household survey

generalized least squares inference in panel and multilevel models with serial correlation and fixed effects in this paper i consider generalized least squares gls estimation in fixed effects panel and multilevel models with autocorrelation the presence of fixed effects complicates implementation of gls as estimating the fixed effects will typically render standard estimators of the covariance parameters necessary for obtaining feasible gls estimates inconsistent i focus on the case where the disturbances follow an ar p process and offer a simple to implement bias correction for the ar coefficients the usefulness of gls and the derived bias correction for the parameters of the autoregressive process is illustrated through a simulation study which uses data from the current population survey

generalized mixed integer rounding inequalities facets for infinite group polyhedra we present a generalization of the mixed integer rounding mir approach for generating valid inequalities for mixed integer programming mip problems for any positive integer n we develop n facets for a certain n 1 dimensional single constraint polyhedron in a sequential manner we then show that for any n the last of these facets which we call the n step mir facet can be used to generate a family of valid inequalities for the feasible set of a general mixed ip constraint which we refer to as the n step mir inequalities the gomory mixed integer cut and the 2 step mir inequality of dash and gunluk math program 105 1 29 53 2006 are the first two families corresponding to n 1 2 respectively the n step mir inequalities are easily produced using periodic functions which we refer to as the n step mir functions none of these functions dominates the other on its whole period finally we prove that the n step mir inequalities generate two slope facets for the infinite group polyhedra and hence are potentially strong

possibly exact fractal dimensions from conformal invariance based on an equivalence between the q state potts model and conformally invariant field theories the author speculates that all fractal dimensionalities of two dimensional percolation are given by the formula d 100 x2 48 where x is an integer the same formula should also apply to self avoiding walks and lattice animals this approach is extended to cluster weighted percolation his conjecture seems to agree with previous exact and numerical results except for the backbone exponent and possibly for lattice animals

difference in difference meets generalized least squares higher order properties of hypotheses tests we investigate the estimation and inference in difference in difference econometric models used in the analysis of treatment effects when the innovations in such models display serial correlation commonly used ordinary least squares ols procedures are inefficient and may lead to tests with incorrect size implementation of feasible generalized least squares fgls procedures is often hindered by too few observations in the cross section to allow for unrestricted estimation of the weight matrix without leading to tests with similar size distortions as conventional ols based procedures we analyze the small sample properties of fgls based tests with a formal higher order edgeworth expansion that allows us to construct a size corrected version of the test we also address the question of optimal temporal aggregation as a method to reduce the dimension of the weight matrix we apply our procedure to data on regulation of mobile telephone service prices we find that a size corrected fgls based test outperforms tests based on ols

interdiffusion fractal structures scaling size effect interdiffusion that proceeds via the vacancy mechanism with formation of an ideal substitutional solid solution is investigated by monte carlo simulation on a square lattice the produced stochastic structures studied are the percolation diffusion front and the total boundary of the clusters it is shown that they have a fractal geometry and that their evolution is characterized by a number of critical exponents a conclusion is made that the fractal nature of the diffusion front leads to diffusion size effect in thin films the approach used permits description of propagation of superconducting conducting magnetic and other phases during interdiffusion

accessible external perimeters of percolation clusters the authors introduce a new definition of a cluster s accessible external perimeter which is different from the usual definition of the hull this external perimeter can be measured by probing adsorbent particles coming from the cluster s exterior the size of these particles determines which perimeter sites are accessible from the outside and hence one can define different external or accessible perimeters according to this size using a monte carlo simulation they measured the fractal dimensions of these accessible perimeters de for percolation clusters at the threshold on the square and the triangular lattices the fractal dimension of the accessible perimeter is found to depend on the size of the probing particles for several sizes which are larger than some lattice dependent threshold they find de approximately 4 3 which is significantly smaller than the hull dimension dh 7 4 found with smaller probing particles

equivariant perturbation in gomory and johnson s infinite group problem i the one dimensional case we give an algorithm for testing the extremality of minimal valid functions for gomory and johnson s infinite group problem that are piecewise linear possibly discontinuous with rational breakpoints this is the first set of necessary and sufficient conditions that can be tested algorithmically for deciding extremality in this important class of minimal valid functions we also present an extreme function that is a piecewise linear function with some irrational breakpoints whose extremality follows from a new principle

illumination a new method for studying 3d percolation fronts in a concentration gradient a new method of studying percolation fronts is introduced in situations where the concentration is not constant gradient percolation approach it consists in an efficient way of determining subsets of the percolation cluster which are exactly at the percolation threshold the method is applied to both lattice and continuum percolation in order to determine the percolation threshold in 3d more accurately two variations of this method illumination and projection seem to give a similar scaling behaviour at low gradients for the cubic lattice case leading to a new estimate for the percolation threshold pc 0 31173 or 0 00007 for continuum percolation of overlapping spheres the new estimate for the critical volume fraction is 0 291 or 0 002 and the value of the critical exponent alpha sigma for the width of the front scaled with the concentration gradient is very close to the one for the lattice case

using cuts for mixed integer knapsack sets to generate cuts for mixed integer polyhedral conic sets based on a bijective mapping between two mixed integer sets we introduce a new perspective on developing cuts for the mixed integer polyhedral conic mipc set by establishing a one to one correspondence between the cuts for this set and those for a related mixed integer knapsack mik set the face facet defining properties of the corresponding cuts are identical for their respective sets we further show that the cut generation approach for the mipc set resulting from this new perspective always produces cuts that dominate those generated based on any of the two individual mik constraints corresponding to the mipc constraint our computational results show this dominance can be quite significant as a special case of this new perspective the conic mir inequality of atamturk and narayanan for the mipc set and its properties can be directly derived from the mir inequality for the mik set and its properties we also generalize these cuts to the n step conic mir inequalities which are directly derived form the n step mir inequalities for the mik set

cutting planes for integer programs with general integer variables we investigate the use of cutting planes for integer programs with general integer variables we show how cutting planes arising from knapsack inequalities can be generated and lifted as in the case of 0 1 variables we also explore the use of gomory s mixed integer cuts we address both theoretical and computational issues and show how to embed these cutting planes in a branch and bound framework we compare results obtained by using our cut generation routines in two existing systems with a commercially available branch and bound code on a range of test problems arising from practical applications 1998 the mathematical programming society inc published by elsevier science b v

kinetic growth walks and trails on oriented square lattices hull percolation and percolation hulls the authors have studied kinetic growth walks on the manhattan lattice and kinetic growth trails on the l lattice they find that the directional properties of these lattices prevent the kinetic growth walks from being trapped except at the origin as a consequence kgws are found to be in the skw universality class for these lattices extensive numerical calculations support this fact moreover it has been shown that the recently introduced hull percolation is equivalent to the kinetic growth walks on the manhattan lattice and the bond percolation hull on the square lattice at the percolation threshold is equivalent to the kinetic growth trails on the l lattice their numerical estimates agree nicely with the original estimates and thus support the equivalence

concentration gradient approach to continuum percolation in two dimensions the author has investigated percolation properties of a system of overlapping discs randomly distributed with a gradient of concentration fractal properties and critical exponents of this system appear to be identical to their counterparts on a lattice this is in agreement with the universality of critical exponents of percolation the concentration gradient approach permits a precise calculation of the percolation threshold corresponding to a critical area fraction of 0 6766 or 0 0005 he has investigated the part of the external perimeter of the percolation cluster which is accessible to discs of various sizes the fractal dimension of this accessible perimeter is found to decrease abruptly as a function of the radius of invading discs from 1 75 or 0 02 to 1 35 or 0 02

asymptotic theory and wild bootstrap inference with clustered errors abstract we study inference based on cluster robust variance estimators for regression models with clustered errors focusing on the wild cluster bootstrap we state conditions under which asymptotic and bootstrap tests and confidence intervals are asymptotically valid these conditions put limits on the rates at which the cluster sizes can increase as the number of clusters tends to infinity we also derive edgeworth expansions for the asymptotic and bootstrap test statistics simulation experiments illustrate the theoretical results and suggest that alternative variants of the wild cluster bootstrap may perform quite differently the edgeworth expansions explain the overrejection of asymptotic tests and shed light on the choice of auxiliary distribution and whether to use restricted or unrestricted estimates in the bootstrap data generating process

n n step cycle inequalities facets for continuous multi mixing set and strong cuts for multi module capacitated lot sizing problem in this paper we introduce a generalization of the continuous mixing set which we refer to as the continuous multi mixing set this set is closely related to the feasible set of the multi module capacitated lot sizing mml problem with out backlogging we present a family of valid inequalities for the continuous multi mixing set and identify conditions under which they are facet defining the cycle inequalities n n step mir inequalities and mixed n n step mir inequalities are special cases of these inequalities we also present an exact separation algorithm for our inequalities we then use these inequalities to generate valid inequalities for mml with out backlogging our computational results show that our cuts are very effective in solving the mml instances resulting in substantial reduction in the integrality gap number of nodes and total solution time

lifted inequalities for 0 mathord 1 mixed integer bilinear covering sets in this paper we study 0 mathord 1 mixed integer bilinear covering sets we derive several families of facet defining inequalities via sequence independent lifting techniques we then show that these sets have a polyhedral structure that is similar to that of a certain fixed charge single node flow set as a result we also obtain new facet defining inequalities for the single node flow set that generalize well known lifted flow cover inequalities from the integer programming literature

fractality in complex networks critical and supercritical skeletons fractal scaling char22 a power law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box char22 is studied we introduce a box covering algorithm that is a modified version of the original algorithm introduced by song et al nature london 433 392 2005 this algorithm enables easy implementation fractal networks are viewed as comprising a skeleton and shortcuts the skeleton embedded underneath the original network is a special type of spanning tree based on the edge betweenness centrality it provides a scaffold for the fractality of the network when the skeleton is regarded as a branching tree it exhibits a plateau in the mean branching number as a function of the distance from a root for nonfractal networks on the other hand the mean branching number decays to zero without forming a plateau based on these observations we construct a fractal network model by combining a random branching tree and local shortcuts the scaffold branching tree can be either critical or supercritical depending on the small worldness of a given network for the network constructed from the critical supercritical branching tree the average number of vertices within a given box grows with the lateral size of the box according to a power law an exponential form in the cluster growing method the critical and supercritical skeletons are observed in protein interaction networks and the world wide web respectively the distribution of box masses i e the number of vertices within each box follows a power law p m m ensuremath sim m ensuremath ensuremath eta the exponent ensuremath eta depends on the box lateral size ensuremath ell b for small values of ensuremath ell b ensuremath eta is equal to the degree exponent ensuremath gamma of a given scale free network whereas ensuremath eta approaches the exponent ensuremath tau ensuremath gamma ensuremath gamma ensuremath 1 as ensuremath ell b increases which is the exponent of the cluster size distribution of the random branching tree finally we study the perimeter h ensuremath alpha of a given box ensuremath alpha i e the number of edges connected to different boxes from a given box ensuremath alpha as a function of the box mass m b ensuremath alpha it is obtained that the average perimeter over the boxes with box mass m b is likely to scale as h m b ensuremath sim m b irrespective of the box size ensuremath ell b

mingling mixed integer rounding with bounds mixed integer rounding mir is a simple yet powerful procedure for generating valid inequalities for mixed integer programs when used as cutting planes mir inequalities are very effective for mixed integer programming problems with unbounded integer variables for problems with bounded integer variables however cutting planes based on lifting techniques appear to be more effective this is not surprising as lifting techniques make explicit use of the bounds on variables whereas the mir procedure does not in this paper we describe a simple procedure which we call mingling for incorporating variable bound information into mir by explicitly using the variable bounds the mingling procedure leads to strong inequalities for mixed integer sets with bounded variables we show that facets of mixed integer knapsack sets derived earlier by superadditive lifting techniques can be obtained by the mingling procedure in particular the mingling inequalities developed in this paper subsume the continuous cover and reverse continuous cover inequalities of marchand and wolsey math program 85 15 33 1999 as well as the continuous integer knapsack cover and pack inequalities of atamturk math program 98 145 175 2003 ann oper res 139 21 38 2005 in addition mingling inequalities give a generalization of the two step mir inequalities of dash and gunluk math program 105 29 53 2006 under some conditions

external surface of site percolation clusters in three dimensions the authors study the external surface of site percolation clusters in three dimensions by monte carlo simulations on a simple cubic lattice at p pc 0 3117 their results show that for all cluster sizes s more than 99 8 of the occupied sites are on the external surface the number of unoccupied boundary sites t is found to obey t s 1 pc pc as psi with psi 0 54 1 sigma in agreement with the prediction of a scaling argument the same argument also predicts psi 0 60 in two dimensions and it is confirmed the relevance of these results to dynamical percolation growth models is discussed

the convex hull of two core capacitated network design problems the network loading problem nlp is a specialized capacitated network design problem in which prescribed point to point demand between various pairs of nodes of a network must be met by installing loading a capacitated facility we can load any number of units of the facility on each of the arcs at a specified arc dependent cost the problem is to determine the number of facilities to be loaded on the arcs that will satisfy the given demand at minimum cost

hypothesis testing in linear models when the error covariance matrix is nonscalar a well developed exact statistical theory exists for hypothesis testing in the normal linear regression model when the errors are independent and homoscedastic in the more general case where the error covariance matrix is nonscalar and depends on a set of unknown parameters exact analysis is difficult and reliance is usually placed on asymptotic approximations for large sample size n in this paper higher order asymptotic expansions are developed for comparing the size and power of some common procedures for testing linear hypotheses on the regression coefficients in a class of generalized normal linear models the class investigated is essentially the same as in breusch 4 and magnus 6 and includes many of the examples of heteroscedasticity and autocorrelation discussed in the literature we assume simply that the regressors are nonrandom and that the error covariance matrix is a smooth function of a few parameters that can be efficiently estimated by maximum likelihood tests based on the wald likelihood ratio and lagrange multiplier principles are considered these principles lead to three tests which though distinct in finite samples are locally asymptotically equivalent and share certain asymptotic optimality properties of course there are infinitely many other tests that are asymptotically equivalent to the ones examined here although the techniques of this paper can be applied to any of them our results concern only the tests arising from the three traditional principles we show that to a second order of approximation under local alternatives the likelihood ratio test statistic is a simple average of the wald statistic and the lagrange multiplier statistic when the null hypothesis is one dimensional the three tests are to second order equally powerful that is after the critical regions are adjusted so that the tests have to order n i the same size the local power functions differ by terms of smaller order than n when the null hypothesis contains more than one

the unbalanced nested error component regression model abstract this paper considers a nested error component model with unbalanced data and proposes simple analysis of variance anova maximum likelihood mle and minimum norm quadratic unbiased estimators minque type estimators of the variance components these are natural extensions from the biometrics statistics and econometrics literature the performance of these estimators is investigated by means of monte carlo experiments while the mle and minque methods perform the best in estimating the variance components and the standard errors of the regression coefficients the simple anova methods perform just as well in estimating the regression coefficients these estimation methods are also used to investigate the productivity of public capital in private production

lifted flow cover inequalities for mixed 0 1 integer programs we investigate strong inequalities for mixed 0 1 integer programs derived from flow cover inequalities flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities however because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting coefficients lifting of flow cover inequalities is computationally very demanding we present a computationally efficient way to lift flow cover inequalities based on sequence independent lifting techniques and give computational results that show the effectiveness of our lifting procedures

gradient stabilized and destabilized invasion percolation abstract the effects of gravity stabilization and destabilization on the slow displacement of a wetting fluid by a non wetting fluid in two dimensional and three dimensional porous media have been investigated experimentally the characteristic features of the resulting displacement patterns can be reproduced quite well by invasion percolation models with a spatial gradient added to the usual random threshold distribution in the case of destabilized displacement the patterns can be described in terms of a string of blobs of size that form a directed walk the internal structure of the blobs is like that of an invasion percolation cluster with trapping in the two dimensional case in the stabilized case the structure is like that of a fractal invasion percolation cluster on short length scales lengths and is uniform on longer lengths the correlation length also describes the maximum hole diameter the invasion front is a self similar fractal on length scales shorter than and flat on longer length scales in both the experiments and the simulations the correlation length is related to the bond number b0 the ratio between buoyancy and capillary forces by b0 1 where is the ordinary percolation correlation length exponent in accord with the theoretical arguments of wilkinson phys rev a 30 1984 520 34 1986 1380

lifting inequalities a framework for generating strong cuts for nonlinear programs in this paper we introduce the first generic lifting techniques for deriving strong globally valid cuts for nonlinear programs the theory is geometric and provides insights into lifting based cut generation procedures yielding short proofs of earlier results in mixed integer programming using convex extensions we obtain conditions that allow for sequence independent lifting in nonlinear settings paving a way for efficient cut generation procedures for nonlinear programs this sequence independent lifting framework also subsumes the superadditive lifting theory that has been used to generate many general purpose strong cuts for integer programs we specialize our lifting results to derive facet defining inequalities for mixed integer bilinear knapsack sets finally we demonstrate the strength of nonlinear lifting by showing that these inequalities cannot be obtained using a single round of traditional integer programming cut generation techniques applied on a tight reformulation of the problem

the sequential knapsack polytope in this paper we describe the convex hull of all solutions of the integer bounded knapsack problem in the special case when the weights of the items are divisible the corresponding inequalities are defined via an inductive scheme that can also be used in a more general setting

lifting two integer knapsack inequalities in this paper we discuss the derivation of strong valid inequalities for mixed integer knapsack sets based on lifting of valid inequalities for basic knapsack sets with two integer variables and one continuous variable the basic polyhedra can be described in polynomial time we use superadditive valid lifting functions in order to obtain sequence independent lifting most of these superadditive functions and valid inequalities are not obtained in polynomial time

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

incomplete panels a comparative study of alternative estimators for the unbalanced one way error component regression model abstract this paper considers a one way error component regression model with unbalanced data and investigates by means of monte carlo experiments the performance of anova mle and mivque type estimators of the variance components some of the basic findings are the following 1 for the regression coefficients the computationally simple anova methods perform reasonably well when compared with the computationally involved mle and mivque methods 2 mle and mivque perform better than the anova methods in the estimation of the individual variance component especially for severely unbalanced patterns and large variance component ratio however for the remainder variance component there is nothing much to choose among these methods 3 better estimates of the variance components do not necessarily imply better estimates of the regression coefficients 4 making the data balanced by dropping observations worsens the performance of these estimators when compared to those from the entire unbalanced data

valid inequalities for the single item capacitated lot sizing problem with step wise costs this paper presents a new class of valid inequalities for the single item capacitated lot sizing problem with step wise production costs ls sw we first provide a survey of different optimization methods proposed to solve ls sw then flow cover and flow cover inequalities derived from the single node flow set are described in order to generate the new class of valid inequalities the single node flow set can be seen as a generalization of some valid relaxations of ls sw a new class of valid inequalities we call mixed flow cover is derived from the integer flow cover inequalities by a lifting procedure the lifting coefficients are sequence independent when the batch sizes v and the production capacities p are constant and if v divides p when the restriction of the divisibility is removed the lifting coefficients are shown to be sequence independent we identify some cases where the mixed flow cover inequalities are facet defining a cutting plane algorithm is proposed for these three classes of valid inequalities the exact separation algorithm proposed for the constant capacitated case runs in polynomial time finally some computational results are given to compare the performance of the different optimization methods including the new class of valid inequalities

asymptotic theory for clustered samples abstract we provide a complete asymptotic distribution theory for clustered data with a large number of independent groups generalizing the classic laws of large numbers uniform laws central limit theory and clustered covariance matrix estimation our theory allows for clustered observations with heterogeneous and unbounded cluster sizes our conditions cleanly nest the classical results for i n i d observations in the sense that our conditions specialize to the classical conditions under independent sampling we use this theory to develop a full asymptotic distribution theory for estimation based on linear least squares 2sls nonlinear mle and nonlinear gmm