the relative performance of bivariate causality tests in small samples causality tests have been applied to establish directional effects and to reduce the set of potential predictors for the latter type of application only bivariate tests can be used in this study we compare bivariate causality tests although the problem addressed is general and could benefit researchers from different fields most attention is given to marketing applications even though there are many alternative tests applications in marketing have almost exclusively been based on the i laugh pierce test we compare five bivariate tests in a specific marketing application the empirical results indicate that conclusions about causality may depend strongly on the test used to provide generalizable insights about the relative performances of alternative tests we conduct a simulation study with data characteristics that cover the range of conditions encountered by researchers who have applied causality tests in marketing we find that the granger wald test has the highest power but also the greatest upward bias in alpha the probability of a type i error if causality testing is done for the purpose of selecting a good subset of the available predictors this combination of high power and high alpha may be attractive for researchers desiring a simple test with a substantial amount of power and little upward bias in alpha we recommend the granger sargent teal interestingly neither of these granger tests has been used in marketing c 1997 a elsevier science b v

rational points on k3 surfaces a new canonical height a fundamental tenet of diophantine geometry is that the geometric properties of an algebraic variety should determine its basic arithmetic properties this is certainly true for curves where the sign of the euler characteristic of c determines whether the set of rational points on c is finite x c 0 for higher dimensional varieties there are some precise conjectures due to bombieri lang and vojta 15 which predict when the rational points on a variety should be finite or degenerate i e not zariski dense and some conjectures of manin et al 2 5 on the distribution of rational points in those cases when they are zariski dense but except for abelian varieties their subvarieties and some fano varieties varieties for which the anticanonical bundle is ample there are very few general theorems in this paper we will study the rational points on a certain class of k 3 surfaces defined over a number field k the moduli space of marked algebraic k3 surfaces is a countable union of 19 dimensional quasi projective varieties we are going to look at the 18 dimensional family studied by wehler 1 17 wehler s family consists of k3 surfaces s whose automorphism group aut s contains a subgroup d isomorphic to the free product 7 2 2 of two cyclic groups of order 2 we will use the geometric information provided by this infinite automorphism group to study the k rat ional points on s for any point pes we can look at the orbit of p under the action of d

on the stable dynamical spectrum of complex surfaces we characterize salem numbers which have some power arising as dynamical degree of an automorphism on a complex projective 2 torus k3 or enriques surface

assignment problems a golden anniversary survey abstract having reached the 50th golden anniversary of the publication of kuhn s seminal article on the solution of the classic assignment problem it seems useful to take a look at the variety of models to which it has given birth this paper is a limited survey of what appear to be the most useful of the variations of the assignment problem that have appeared in the literature over the past 50 years the intention here is not to identify every such paper of which there have been hundreds nor to identify the best solution procedure for each variation rather the intention is to identify what these variations are and what they are called so as to make it easier for a researcher trying to develop some variation of the assignment problem for a particular application to find the relevant literature

reflection groups in algebraic geometry after a brief exposition of the theory of discrete reflection groups in spherical euclidean and hyperbolic geometry as well as their analogs in complex spaces we present a survey of appearances of these groups in various areas of algebraic geometry

a comparison of tests of the independence of two covariance stationary time series abstract the approximate slopes of several tests of the independence of two covariance stationary time series are derived and compared it is shown that the approximate slopes of regression tests are at least as great as those based on the residuals of univariate arima models and that there are cases in which the former are arbitrarily great while the latter are arbitrarily small these analytical findings are supported by a monte carlo study that shows that in samples of size 100 and 250 the asymptotic distribution theory under the null hypothesis is adequate for all tests but under alternatives to the null hypothesis the rate of type ii error for the test based on arima model residuals is often more than double that of the regression tests

a heuristic procedure for the crew rostering problem abstract this paper deals with the problem of planning work schedules in a given time horizon so as to evenly distribute the workload among the drivers in a mass transit system an integer programming formulation of this problem is given an iterative heuristic algorithm is described which makes use of a lower bound derived from the mathematical formulation furthermore the algorithm at each iteration solves a multilevel bottleneck assignment problem for which a new procedure that gives asymptotically optimal solutions is proposed computational results for both the rostering problem and the multilevel bottleneck assignment problem are given

minimum positive entropy of complex enriques surface automorphisms we determine the minimum positive entropy of complex enriques surface automorphisms this together with mcmullen s work completes the determination of the minimum positive entropy of complex surface automorphisms in each class of the enriques kodaira classification of complex surfaces

automorphisms of even unimodular lattices and unramified salem numbers abstract in this paper we study the characteristic polynomials s x det xi f iip q of automorphisms of even unimodular lattices with signature p q in particular we show that any salem polynomial of degree 2n satisfying s 1 s 1 1 n arises from an automorphism of an indefinite lattice a result with applications to k3 surfaces

measurement of linear dependence and feedback between multiple time series abstract measures of linear dependence and feedback for multiple time series are defined the measure of linear dependence is the sum of the measure of linear feedback from the first series to the second linear feedback from the second to the first and instantaneous linear feedback the measures are nonnegative and zero only when feedback causality of the relevant type is absent the measures of linear feedback from one series to another can be additively decomposed by frequency a readily usable theory of inference for all of these measures and their decompositions is described the computations involved are modest

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

the approximate slopes of econometric tests in this paper the concept of approximate slope introduced by r r bahadur is used to make asymptotic global power comparisons of econometric tests the approximate slope of a test is the rate at which the logarithm of the asymptotic marginal significance level of the test decreases as sample size increases under a given alternative a test with greater approximate slope may therefore be expected to reject the null hypothesis more frequently under that alternative than one with smaller approximate slope two theorems which facilitate the computation and interpretation of the approximate slopes of most econometric tests are established these results are used to undertake some illustrative comparisons sampling experiments and an empirical illustration suggest that the comparison of approximate slopes may provide an adequate basis for evaluating the actual performance of alternative tests of the same hypothesis

the classification of purely non symplectic automorphisms of high order on k3 surfaces abstract an automorphism of order n of a k3 surface is called purely non symplectic if it multiplies the holomorphic symplectic form by a primitive n th root of unity we give the classification of purely non symplectic automorphisms with n 12 where denotes the euler totient function

comparing alternative tests of causality in temporal systems abstract this paper discusses eight alternative tests of the absence of casual ordering all of which are asymptotically valid under the null hypothesis in the sense that their limiting size is known their behavior under alternatives is compared analytically using the concept of approximate slope and these results are supported by the outcomes of monte carlo experiments the implications of these comparisons for applied work are unambiguous wald variants of a test attributed to granger and a lagged dependent variable version of sim s test introduced in this paper are equivalent in all relevant respects and are preferred to the other tests discussed

testing causality using efficiently parametrized vector arma models we outline a practical methodology for fitting to data vector autoregressive moving average models and employ these models to test for granger causality the procedures are applied to data on employment and hourly wages in manufacturing in the united states

causality tests and observationally equivalent representations of econometric models abstract this article deals with the problem of observational equivalence of alternative econometric equation systems on the same data as a practical obstacle to econometricians success in applying definitions of causality by simon 1953 strotz and wold 1960 and granger 1969 to economic time series

random assignment problems abstract analysis of random instances of optimization problems provides valuable insights into the behavior and properties of problem s solutions feasible region and optimal values especially in large scale cases a class of problems that have been studied extensively in the literature using the methods of probabilistic analysis is represented by the assignment problems and many important problems in operations research and computer science can be formulated as assignment problems this paper presents an overview of the recent results and developments in the area of probabilistic assignment problems including the linear and multidimensional assignment problems quadratic assignment problem etc

testing causality between two vectors in multivariate autoregressive moving average models abstract in the analysis of economic time series a question often raised is whether a vector of variables causes another one in the sense of granger most of the literature on this topic is concerned with bivariate relationships or uses finite order autoregressive specifications the purpose of this article is to develop a causality analysis in the sense of granger for general vector autoregressive moving average arma models we give a definition of granger noncausality between vectors which is a natural and simple extension of the notion of granger noncausality between two variables in our context this definition is shown to be equivalent to a more complex definition proposed by tjostheim for the class of linear invertible processes we derive a necessary and sufficient condition for noncausality between two vectors of variables when the latter do not necessarily include all the variables considered in the analysis this result is then specialized to the class of stationary invertible arma process

dynamics on k3 surfaces salem numbers and siegel disks this paper presents the first examples of k3 surface automorphisms f x rightarrow x with siegel disks domains on which f acts by an irrational rotation the set of such examples is countable and the surface x must be non projective to carry a siegel disk these automorphisms are synthesized from salem numbers of degree 22 and trace 1 which play the role of the leading eigenvalue for f h 2 x the construction uses the torelli theorem the atiyah bott fixed point theorem and results from transcendence theory

modeling and solving the crew rostering problem the crew rostering problem crp aims at determining an optimal sequencing of a given set of duties into rosters satisfying operational constraints deriving from union contract and company regulations previous work on crp addresses mainly urban mass transit systems in which the minimum number of crews to perform the duties can easily be determined and the objective is to evenly distribute the workload among the crews in typical railway applications however the roster construction has to take into account more involved sequencing rules and the main objective is the minimization of the number of crews needed to perform the duties in this paper we propose a basic model for crp and describe a lagrangian lower bound based on the solution of an assignment problem on a suitably defined graph the information obtained through the lower bound computation is used to drive an effective algorithm for finding a tight approximate solution to the problem computational results for real world instances from railway applications involving up to 1 000 duties are presented showing that the proposed approach yields within short computing time lower and upper bound values that are typically very close the code based on the approach we propose won the faro competition organized by the italian railway company ferrovie dello stato spa in 1995

non liftability of automorphism groups of a k3 surface in positive characteristic we show that a characteristic 0 model x r rightarrow mathrm spec r with picard number 1 over a geometric generic point of a k3 surface in characteristic p ge 3 essentially kills all automorphisms theorem 5 1 we show that there is an explicitely constructed automorphism on a supersingular k3 surface in characteristic 3 which has positive entropy the logarithm of a salem number of degree 22 theorem 6 4 in particular it does not lift to characteristic 0 in addition we show that in any large characteristic there is an automorphism of a supersingular k3 which has positive entropy and does not lift to characteristic 0 theorem 7 5

a multi level bottleneck assignment approach to the bus drivers rostering problem abstract the problem of finding a work assignment for drivers in a given time horizon in such a way as to have an even distribution of the workload is considered this problem is formulated as a multi level bottleneck assignment problem mba the mba problem is studied it is shown that it is np complete and an asymptotically optimal algorithm is presented some computational results are illustrated which prove the efficiency of the algorithm