deformed preprojective algebras of generalized dynkin type we introduce the class of deformed preprojective algebras of generalized dynkin graphs an n 1 d n n 4 eg e 7 eg and l n n 1 and prove that it coincides with the class of all basic connected finite dimensional self injective algebras for which the inverse nakayama shift v 1 s of every non projective simple module s is isomorphic to its third syzygy 3 s

deformed preprojective algebras of type l kulshammer spaces and derived equivalences abstract bialkowski erdmann and skowronski classified those indecomposable selfinjective algebras for which the nakayama shift of every non projective simple module is isomorphic to its third syzygy it turned out that these are precisely the deformations in a suitable sense of preprojective algebras associated to the simply laced ade dynkin diagrams and of another graph l n which also occurs in the happel preiser ringel classification of subadditive but not additive functions in this paper we study these deformed preprojective algebras of type l n via their kulshammer spaces for which we give precise formulae for their dimensions these are known to be invariants of the derived module category and even invariants under stable equivalences of morita type as main application of our study of kulshammer spaces we can distinguish many but not all deformations of the preprojective algebra of type l n up to stable equivalence of morita type and hence also up to derived equivalence

periodicity of self injective algebras of polynomial growth abstract let a be an indecomposable representation infinite tame finite dimensional algebra of polynomial growth over an algebraically closed field we prove that a is a periodic algebra with respect to action of the bimodule syzygy operator if and only if a is morita equivalent to a socle deformation of an orbit algebra b g where b is the repetitive category of a tubular algebra b and g is an admissible infinite cyclic automorphism group of b the main contribution in the paper is to prove the sufficiency part of this equivalence it is known that every orbit algebra b g of a tubular algebra b admits a presentation as an orbit algebra t b r h of an r fold trivial extension algebra t b r of b with respect to free action of a finite cyclic automorphism group h of t b r a significant part of the paper is devoted to explicit descriptions of the minimal projective bimodule resolutions of properly chosen ten exceptional self injective algebras of polynomial growth and showing that all of them are periodic algebras then we deduce the periodicity of all algebras socle equivalent to the orbit algebras b g t b r h of tubular algebras b from the periodicity of these ten exceptional algebras using invariance of periodicity for finite galois coverings and derived equivalences of algebras

on nonparametric confidence intervals an inequality is given for the expected length of a confidence interval given that a particular distribution generated the data and assuming that the confidence interval has a given coverage probability over a family of distributions as a corollary attempts to adapt to the regularity of the true density within derivative smoothness classes cannot improve the rate of convergence of the length of the confidence interval over minimax fixed length intervals and still maintain uniform coverage probability however adaptive confidence intervals can attain improved rates of convergence in some other classes of densities such as those satisfying a shape restriction

testing continuity of a density via g order statistics in the regression discontinuity design abstract in the regression discontinuity design rdd it is common practice to assess the credibility of the design by testing the continuity of the density of the running variable at the cut off e g mccrary 2008 in this paper we propose an approximate sign test for continuity of a density at a point based on the so called g order statistics and study its properties under two complementary asymptotic frameworks in the first asymptotic framework the number q of observations local to the cut off is fixed as the sample size n diverges to infinity while in the second framework q diverges to infinity slowly as n diverges to infinity under both of these frameworks we show that the test we propose is asymptotically valid in the sense that it has limiting rejection probability under the null hypothesis not exceeding the nominal level more importantly the test is easy to implement asymptotically valid under weaker conditions than those used by competing methods and exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity in a simulation study we find that the approximate sign test provides good control of the rejection probability under the null hypothesis while remaining competitive under the alternative hypothesis we finally apply our test to the design in lee 2008 a well known application of the rdd to study incumbency advantage

a bayesian analysis of kriging this article is concerned with predicting for gaussian random fields in a way that appropriately deals with uncertainty in the covariance function to this end we analyze the best linear unbiased prediction procedure within a bayesian framework particular attention is paid to the treatment of parameters in the covariance structure and their effect on the quality both real and perceived of the prediction these ideas are implemented using topographical data from davis

large sample properties of simulations using latin hypercube sampling latin hypercube sampling mckay conover and beckman 1979 is a method of sampling that can be used to produce input values for estimation of expectations of functions of output variables the asymptotic variance of such an estimate is obtained the estimate is also shown to be asymptotically normal asymptotically the variance is less than that obtained using simple random sampling with the degree of variance reduction depending on the degree of additivity in the function being integrated a method for producing latin hypercube samples when the components of the input variables are statistically dependent is also described these techniques are applied to a simulation of the performance of a printer actuator

inference for deterministic simulation models the bayesian melding approach abstract deterministic simulation models are used in many areas of science engineering and policy making typically these are complex models that attempt to capture underlying mechanisms in considerable detail and they have many user specified inputs the inputs are often specified by some form of trial and error approach in which plausible values are postulated the corresponding outputs inspected and the inputs modified until plausible outputs are obtained here we address the issue of more formal inference for such models a probabilistic approach called bayesian synthesis was shown to suffer from the borel paradox according to which the results can depend on the parameterization of the model we propose a modified approach called bayesian melding which takes into full account information and uncertainty about both inputs and outputs to the model while avoiding the borel paradox this is done by recognizing the existence of two priors one implicit and one explicit on each input and output

deformed preprojective algebras of generalized dynkin type ln classification and symmetricity abstract we give a complete classification of the isomorphism classes of the deformed preprojective algebras of generalized dynkin type l n and show that all these algebras are symmetric moreover we show that the deformed preprojective algebras of type l n are isomorphic to the stable auslander algebras of simple plane curve singularities of dynkin type a 2 n

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

factorial sampling plans for preliminary computational experiments a computational model is a representation of some physical or other system of interest first expressed mathematically and then implemented in the form of a computer program it may be viewed as a function of inputs that when evaluated produces outputs motivation for this article comes from computational models that are deterministic complicated enough to make classical mathematical analysis impractical and that have a moderate to large number of inputs the problem of designing computational experiments to determine which inputs have important effects on an output is considered the proposed experimental plans are composed of individually randomized one factor at a time designs and data analysis is based on the resulting random sample of observed elementary effects those changes in an output due solely to changes in a particular input advantages of this approach include a lack of reliance on assumptions of relative sparsity of important inputs monotonicity of outputs with respect to inputs or ad

randomization tests under an approximate symmetry assumption this paper develops a theory of randomization tests under an approximate symmetry assumption randomization tests provide a general means of constructing tests that control size in nite samples whenever the distribution of the observed data exhibits symmetry under the null hypothesis here by exhibits symmetry we mean that the distribution remains invariant under a group of transformations in this paper we provide conditions under which the same construction can be used to construct tests that asymptotically control the probability of a false rejection whenever the distribution of the observed data exhibits approximate symmetry in the sense that the limiting distribution of a function of the data exhibits symmetry under the null hypothesis an important application of this idea is in settings where the data may be grouped into a xed number of clusters with a large number of observations within each cluster in such settings we show that the distribution of the observed data satises our approximate symmetry requirement under weak assumptions in particular our results allow for the clusters to be heterogeneous and also have dependence not only within each cluster but also across clusters this approach enjoys several advantages over other approaches in these settings among other things it leads to a test that is asymptotically similar which as shown in a simulation study translates into improved power at many alternatives finally we use our results to revisit the analysis of angrist and lavy 2009 who examine the impact of a cash award on exam performance for low achievement students in israel

on hochschild cohomology of preprojective algebras i abstract we study the hochschild cohomology of a finite dimensional preprojective algebra this is periodic by a result of a schofield we determine the ring structure of the hochschild cohomology ring given by the yoneda product as a result we obtain an explicit presentation by generators and relations

experimental design and observation for large systems large systems require new methods of experimental designs suitable for the highly adaptive models which are employed to cope with complex non linear responses and high dimensionality of input spaces the area of computer experiments has started to provide such designs especially latin hypercube and lattice designs system decomposition prevalent in several branches of engineering can be employed to decrease complexity a combination of system decomposition using a sparse matrix method experimental design and modelling is applied to one example of an electrical circuit simulator producing a usable emulator of the circuit for use in optimization and sensitivity analysis

predicting the output from a complex computer code when fast approximations are available s we consider prediction and uncertainty analysis for complex computer codes which can be run at different levels of sophistication in particular we wish to improve efficiency by combining expensive runs of the most complex versions of the code with relatively cheap runs from one or more simpler approximations a bayesian approach is described in which prior beliefs about the codes are represented in terms of gaussian processes an example is presented using two versions of an oil reservoir simulator 1 c complex mathematical models implemented in large computer codes have been used to study real systems in many areas of scientific research sacks et al 1989 usually because physical experimentation is too costly and sometimes impossible as in the case of large environmental systems a computer experiment involves running the code with various input values for the purpose of learning something about the real system often a simulator can be run at different levels of complexity with versions ranging from the most sophisticated high level code to the most basic for example in 4 we consider two codes which simulate oil pressure at a well of a hydrocarbon reservoir both codes use finite element analysis in which the rocks comprising the reservoir are represented by small interacting grid blocks the flow of oil within the reservoir can be simulated by considering the interaction between the blocks the two codes differ in the resolution of the grid so that we have a very accurate slow version using many small blocks and a crude approximation using large blocks which runs much faster alternatively a mathematical model could be expanded to include more of the scientific laws underlying the physical processes simple fast versions of the code may well include the most important features and are useful for preliminary investigations in real time applications the number of runs from a high level simulator may be limited by expense then there is a need to trade off the complexity of the expensive code with the availability of the simpler approximations the purpose of the current paper is to explore ways in which runs from several levels of a code can be used to make inference about the output from the most complex code we may also have uncertainty about values for the input parameters which apply in any given application uncertainty analysis of computer codes describes how this uncertainty on the inputs affects our uncertainty about the output

simple local polynomial density estimators this article introduces an intuitive and easy to implement nonparametric density estimator based on local polynomial techniques the estimator is fully boundary adaptive and automatic but does not

optimal inference in a class of regression models we consider the problem of constructing confidence intervals cis for a linear functional of a regression function such as its value at a point the regression discontinuity parameter or a regression coefficient in a linear or partly linear regression our main assumption is that the regression function is known to lie in a convex function class which covers most smoothness and or shape assumptions used in econometrics we derive finite sample optimal cis and sharp efficiency bounds under normal errors with known variance we show that these results translate to uniform over the function class asymptotic results when the error distribution is not known when the function class is centrosymmetric these efficiency bounds imply thatminimax cis are close to efficient at smooth regression functions this implies in particular that it is impossible to form cis that are tighter using data dependent tuning parameters and maintain coverage over the whole function class we specialize our results to inference in a linear regression and inference on the regression discontinuity parameter and illustrate them in an empirical application

bayesian design and analysis of computer experiments use of derivatives in surface prediction this article is concerned with the problem of predicting a deterministic response function yo over a multidimensional domain t given values of yo and all of its first derivatives at a set of design sites points in t the intended application is to computer experiments in which yo is an output from a computer model of a physical system and each point in t represents a particular configuration of the input parameters it is assumed that the first derivatives are already available e g from a sensitivity analysis or can be produced by the code that implements the model a bayesian approach in which the random function that represents prior uncertainty about yo is taken to be a stationary gaussian stochastic process is used the calculations needed to update the prior given observations of yo and its first derivatives at the design sites are given and are illustrated in a small example the issue of experimental design is also discussed in particular the criterion of maximizing the reduction in entropy

identification and estimation of treatment effects with a regression discontinuity design the regression discontinuity rd data design is a quasi experimental design with the defining characteristic that the probability of receiving treatment changes discontinuously as a function of one or more underlying variables this data design arises frequently in economic and other applications but is only infrequently exploited as a source of identifying information in evaluating effects of a treatment in the first application and discussion of the rd method thistlethwaite and campbell 1960 study the effect of student scholarships on career aspirations using the fact that awards are only made if a test score exceeds a threshold more recently van der klaauw 1997 estimates the effect of financial aid offers on students decisions to attend a particular college taking into account administrative rules that set the aid amount partly on the basis of a discontinuous function of the students grade point average and sat score angrist and lavy 1999 estimate the effect of class size on student test scores taking advantage of a rule stipulating that another classroom be added when the average class size exceeds a threshold level finally black 1999 uses an rd approach to estimate parents willingness to pay for higher quality schools by comparing housing prices near geographic school attendance boundaries regression discontinuity methods have potentially broad applicability in economic research because geographic boundaries or rules governing programs often create discontinuities in the treatment assignment mechanism that can be exploited under the method although there have been several discussions and applications of rd methods in the literature important questions still remain concerning sources of identification and ways of estimating treatment effects under minimal parametric restrictions here we show that identifying conditions invoked in previous applications of rd methods are often overly strong and that treatment effects can be nonparametrically identified under an rd design by a weak functional form restriction the restriction is unusual in that it requires imposing continuity assumptions in order to take advantage of the known discontinuity in the treatment assignment mechanism we also propose a way of nonparametrically estimating treatment effects and offer an interpretation of the wald estimator as an rd estimator

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise