testing for factor loading structural change under common breaks abstract this paper proposes a new test for factor loading structural change in dynamic factor models we first show that the leading test proposed by breitung and eickmeier 2011 exhibits nonmonotonic power essentially because the breaks are considered as spurious factors with stable factor loadings the proposed test eliminates the effects of the spurious factors by maximizing the test statistic over possible numbers of the original factors monte carlo simulations and an empirical example using u s treasury yield curve data clearly illustrate the usefulness of the proposed test

design sensitivity analysis for nonlinear thermal systems abstract the lagrange multiplier method and convolution theory are used to formulate design sensitivities for nonlinear transient thermal systems variations of a general design functional are expressed in explicit form with respect to variations in structural shape and the conventional design quantities i e material properties applied loads prescribed boundary conditions and initial conditions the design functional depends on these explicit quantities and the implicit repsonse fields temperature temperature gradient heat flux vector and reaction surface flux a finite element implementation of the methodology illustrates the formulation

lie idempotent algebras abstract besides the inner product inherited from each symmetric group algebra ksn on the direct sum ks nksn a second convolution product arises from the hopf algebra structure on ks for any subalgebra a of ks for both the inner and the convolution product it is shown that the lie idempotent algebra l a of a generated by all lie idempotents in a with respect to the convolution product is also closed under inner products its nth homogeneous component l n a is thus a subalgebra of ksn for all n provided that a contains a lie idempotent in ksk for all k n solomon s descent algebra d n is a subalgebra of l n a in this case a number of results on the structure of l n a is derived including a description of its jacobson radical its principal indecomposables and its cartan invariants furthermore solomon s epimorphism from d n onto the ring of class functions clk sn of sn extends to an epimorphism of algebras c n l n a cl k s n additional results are obtained concerning a bialgebra structure of l a in the particular case of a n d n this amounts to a new approach to several well known results on d n

variational approach by means of adjoint systems to structural optimization and sensitivity analysis ii structure shape variation abstract for a linear elastic structure the first variation of an arbitrary stress strain and displacement functionals corresponding to variation of shape of external boundaries or interfaces is derived by using the solutions for primary and adjoint systems the application to optimal design is next presented and the relevant optimally conditions are derived from general expressions the path independent integrals used in fracture mechanics are rederived as a particular case of general expressions

panel data models with interactive fixed effects and multiple structural breaks abstractin this article we consider estimation of common structural breaks in panel data models with unobservable interactive fixed effects we introduce a penalized principal component ppc estimation procedure with an adaptive group fused lasso to detect the multiple structural breaks in the models under some mild conditions we show that with probability approaching one the proposed method can correctly determine the unknown number of breaks and consistently estimate the common break dates furthermore we estimate the regression coefficients through the post lasso method and establish the asymptotic distribution theory for the resulting estimators the developed methodology and theory are applicable to the case of dynamic panel data models simulation results demonstrate that the proposed method works well in finite samples with low false detection probability when there is no structural break and high probability of correctly estimating the break numbers when the structural breaks exist we finall

computations for coxeter arrangements and solomon s descent algebra iii groups of rank seven and eight the authors would like to acknowledge support from the dfg priority program spp1489 algorithmic and experimental methods in algebra geometry and number theory

scale resolution locking and high order finite element modelling of shells abstract we demonstrate both by theory and experiment the benefits of using standard finite elements of relatively high degree in shell problems the difficulty of shell problems lies in their asymptotic diversity at zero thickness and in the multiple scale character of the deformation field when the thickness is small due to these characteristics standard finite elements of low degree often resolve the length scales of practical shell deformation very poorly unless extremely fine meshes are used however with standard finite elements of sufficiently high degree say cubic or quartic at least the quality of numerical scale resolution improves remarkably we show by simple error analysis that this effect is not problem specific but rather robust among the diversity of shell problems as numerical test cases we analyze two challenging problems in cylindrical shell geometry

affine hecke algebras and generalized standard young tableaux abstract this paper introduces calibrated representations for affine hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations the primary technique is to provide indexing sets for controlling the weight space structure of finite dimensional modules for the affine hecke algebra using these indexing sets we show that 1 irreducible calibrated representations are indexed by skew local regions 2 the dimension of an irreducible calibrated representation is the number of chambers in the local region 3 each irreducible calibrated representation is constructed explicitly by formulas which describe the action of the generators of the affine hecke algebra on a specific basis in the representation space the indexing sets for weight spaces are generalizations of standard young tableaux and the construction of the irreducible calibrated affine hecke algebra modules is a generalization of a young s seminormal construction of the irreducible representations of the symmetric group in this sense young s construction has been generalized to arbitrary lie type

screening based on the risk of cancer calculation from bayesian hierarchical changepoint and mixture models of longitudinal markers the standard approach to early detection of disease with a quantitative marker is to set a population based fixed reference level for making further individual screening or referral decisions for many types of disease including prostate and ovarian cancer additional information is contained in the subject specific temporal behavior of the marker which exhibits a characteristic alteration early in the course of the disease in this article we derive a bayesian approach to screening based on calculation of the posterior probability of disease given longitudinal marker levels the method is motivated by a randomized ovarian cancer screening trial in the united kingdom comprising 22 000 women screened over 4 years with an additional 5 years of follow up on average levels of the antigen ca125 were recorded annually in the screened arm ca125 profiles of cases and controls from the u k trial are modeled using hierarchical changepoint and mixture models posterior distributions are calculated using markov

shape design sensitivity analysis via material derivative adjoint variable technique for 3 d and 2 d curved boundary elements a general approach to shape design sensitivity analysis of three and two dimensional elastic solid objects is developed using the material derivative adjoint variable technique and boundary element method the formulation of the problem is general and first order sensitivities in the form of boundary integrals for the effect of boundary shape variations are derived for an arbitrary performance functional second order quadrilateral surface elements for 3 d problems and quadratic boundary elements for 2 d problems are employed in the solution of primary and adjoint systems and discretization of the boundary integral expressions for sensitivities the accuracy of sensitivity information is studied for selected global performance functionals and also for boundary state fields at discrete points numerical results are presented to demonstrate the accuracy and efficiency of this approach

estimating structural changes in regression quantiles this paper considers the estimation of multiple structural changes occurring at unknown dates in one or multiple conditional quantile functions the analysis covers time series models as well as models with repeated cross sections we estimate the break dates and other parameters jointly by minimizing the check function over all permissible break dates the limiting distribution of the estimator is derived and the coverage property of the resulting confidence interval is assessed via simulations a procedure to determine the number of breaks is also discussed empirical applications to the quarterly us real gdp growth rate and the underage drunk driving data suggest that the method can deliver more informative results than the analysis of the conditional mean function alone

a decomposition of the group algebraof a hyperoctahedral group the descent algebra of a finite coxeter group w is a subalgebra of the group algebra defined by solomon descent algebras of symmetric groups have properties that are not shared by other coxeter groups for instance the natural map from the descent algebra of a symmetric group to its character ring is a surjection with kernel equal the jacobson radical thus the descent algebra implicitly encodes information about the representations of the symmetric group and a complete set of primitive idempotents in the character ring leads to a decomposition of the group algebra into a sum of right ideals indexed by partitions stanley asked whether this decomposition of the regular representation of a symmetric group could be realized as a sum of representations induced from linear characters of centralizers this question was answered positively by bergeron bergeron and garsia using a connection with the free lie algebra on n letters and independently by douglass pfeiffer and rohrle who connected the decomposition with the configuration space of n tuples of distinct complex numbers the mantaci reutenauer algebra of a hyperoctahedral group is a subalgebra of the group algebra that contains the descent algebra bonnafe and hohlweg showed that the natural map from the mantaci reutenauer algebra to the character ring is a surjection with kernel equal the jacobson radical in 2008 bonnafe asked whether the analog to stanley s question about the decomposition of the group algebra into a sum of induced linear characters holds in this paper we give a positive answer to bonnafe s question by explicitly constructing the required linear characters

a decomposition of solomon s descent algebra abstract a descent class in the symmetric group sn is the collection of permutations with a given descent set it was shown by l solomon j algebra41 1976 255 264 that the product in the group algebra q sn of two descent classes is a linear combination of descent classes thus descent classes generate a subalgebra of q sn we refer to it here as solomon s descent algebra and denote it by n this algebra is not semisimple but it has a faithul representation in terms of upper triangular matrices the main goal of this paper is a decomposition of its multiplicative structure it develops that n acts in a natural way on the so called lie monomials this action has a purely combinatorial description and is a crucial tool in the construction of a complete set of indecomposable representations of n in particular we obtain a natural basis of irreducible orthogonal idempotents indexed by partitions of n for the quotient n n natural bases of nilpotents and idempotents for the subspaces e ne for two arbitrary partitions and are also constructed and the dimensions of these spaces are given a combinatorial interpretation in terms of the so called decreasing factorization of an arbitary word into a product of lyndon words

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

new distribution theory for the estimation of structural break point in mean abstract based on the girsanov theorem this paper obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model the exact distribution is asymmetric and tri modal indicating that the estimator is biased these two properties are also found in the finite sample distribution of the least squares ls estimator of structural break point in the discrete time model suggesting the classical long span asymptotic theory is inadequate the paper then builds a continuous time approximation to the discrete time model and develops an in fill asymptotic theory for the ls estimator the in fill asymptotic distribution is asymmetric and tri modal and delivers good approximations to the finite sample distribution to reduce the bias in the estimation of both the continuous time and the discrete time models a simulation based method based on the indirect estimation ie approach is proposed monte carlo studies show that ie achieves substantial bias reductions

on the quiver of the descent algebra abstract we study the quiver of the descent algebra of a finite coxeter group w the results include a derivation of the quiver of the descent algebra of types a and b our approach is to study the descent algebra as an algebra constructed from the reflection arrangement associated to w

identification and estimation of a large factor model with structural instability this paper tackles the identification and estimation of a high dimensional factor model with unknown number of latent factors and a single break in the number of factors and or factor loadings occurring at unknown common date first we propose a least squares estimator of the change point based on the second moments of estimated pseudo factors and show that the estimation error of the proposed estimator is op 1 we also show that the proposed estimator has some degree of robustness to misspecification of the number of pseudo factors with the estimated change point plugged in consistency of the estimated number of pre and post break factors and convergence rate of the estimated pre and post break factor space are then established under fairly general assumptions the finite sample performance of our estimators is investigated using monte carlo experiments

a generating set of solomon s descent algebra abstract solomon s descent algebra is generated by sums of descent classes corresponding to certain hook shapes this particularly implies that the ring of class functions of any finite symmetric group s n is generated by the irreducible characters corresponding to certain hook partitions of n as another consequence a second generating set of solomon s descent algebra and of the ring of class functions of s n is obtained related to the major index of permutations

cohomology actions and centralisers in unitary reflection groups in an earlier work the second author proved a general formula for the equivariant poincare polynomial of a linear transformation g which normalises a unitary reflection group g acting on the cohomology of the corresponding hyperplane complement this formula involves a certain function called a z function below on the centraliser cg g which was proved to exist only in certain cases for example when g is a reflection or is g regular or when the centraliser is cyclic in this work we prove the existence of z functions in full generality applications include reduction and product formulae for the equivariant poincare polynomials the method is to study the poset l cg g of subspaces which are fixed points of elements of cg g we show that this poset has euler characteristic 1 which is the key property required for the definition of a z function the fact about the euler characteristic in turn follows from the join atom property of l cg g which asserts that if x1 xk is any set of elements of l cg g which are maximal set theoretically then their setwise intersection bigcap i 1 kx i lies in l cg g 2000 mathematical subject classification primary 14r20 55r80 secondary 20c33 20g40

testing for common breaks in a multiple equations system abstract the issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system our framework is very general and allows integrated regressors and trends as well as stationary regressors the null hypothesis is that breaks in different parameters occur at common locations and are separated by some positive fraction of the sample size unless they occur across different equations under the alternative hypothesis the break dates across parameters are not the same and also need not be separated by a positive fraction of the sample size whether within or across equations the test considered is the quasi likelihood ratio test assuming normal errors though as usual the limit distribution of the test remains valid with non normal errors of independent interest we provide results about the rate of convergence of the estimates when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as some positive fraction of the sample size allowing break dates not separated by a positive fraction of the sample size across equations simulations show that the test has good finite sample properties we also provide an application to issues related to level shifts and persistence for various measures of inflation to illustrate its usefulness

the peak algebra of the symmetric group revisited abstract the linear span p n of the sums of all permutations in the symmetric group sn with a given set of peaks is a sub algebra of the symmetric group algebra due to nyman this peak algebra is a left ideal of the descent algebra d n and the direct sum p of all p n is a hopf sub algebra of the direct sum d of all d n dual to the stembridge algebra of peak functions in our self contained approach peak counterparts of several results on the descent algebra are established including a simple combinatorial characterization of the algebra p n an algebraic characterization of p n based on the action on the poincare birkhoff witt basis of the free associative algebra the display of peak variants of the classical lie idempotents an eulerian type sub algebra of p n a description of the jacobson radical of p n and its nil potency index of the principal indecomposable and irreducible p n modules and of the cartan matrix of p n furthermore it is shown that the primitive lie algebra of p is free and that p is its enveloping algebra

common breaks in means and variances for panel data this paper establishes the consistency of the estimated common break point in panel data consistency is obtainable even when a regime contains a single observation making it possible to quickly identify the onset of a new regime we also propose a new framework for developing the limiting distribution for the estimated break point and show how to construct confidence intervals the least squares method is used for estimating breaks in means and the quasi maximum likelihood qml method is used to estimate breaks in means and in variances qml is shown to be more efficient than the least squares even if there is no change in the variances

estimating a common deterministic time trend break in large panels with cross sectional dependence abstract this paper develops an estimation procedure for a common deterministic time trend break in large panels the dependent variable in each equation consists of a deterministic trend and an error term the deterministic trend is subject to a change in the intercept slope or both and the break date is common for all equations the estimation method is simply minimizing the sum of squared residuals for all possible break dates both serial and cross sectional correlations are important factors that decide the rate of convergence and the limiting distribution of the break date estimate the rate of convergence is faster when the errors are stationary than when they have a unit root when there is no cross sectional dependence among the errors the rate of convergence depends on the number of equations and thus is faster than the univariate case when the errors have a common factor structure with factor loadings correlated with the intercept and slope change parameters the rate of convergence does not depend on the number of equations and thus reduces to the univariate case the limiting distribution of the break date estimate is also provided some monte carlo experiments are performed to assess the adequacy of the asymptotic results a brief empirical example using the us gdp price index is offered

shrinkage estimation of common breaks in panel data models via adaptive group fused lasso abstract in this paper we consider estimation and inference of common breaks in panel data models via adaptive group fused lasso we consider two approaches penalized least squares pls for first differenced models without endogenous regressors and penalized gmm pgmm for first differenced models with endogeneity we show that with probability tending to one both methods can correctly determine the unknown number of breaks and estimate the common break dates consistently we establish the asymptotic distributions of the lasso estimators of the regression coefficients and their post lasso versions we also propose and validate a data driven method to determine the tuning parameter used in the lasso procedure monte carlo simulations demonstrate that both the pls and pgmm estimation methods work well in finite samples we apply our pgmm method to study the effect of foreign direct investment fdi on economic growth using a panel of 88 countries and regions from 1973 to 2012 and find multiple breaks in the model

cohomology of coxeter arrangements and solomon s descent algebra the authors would like to acknowledge support from the dfg priority programme spp1489 algorithmic and experimental methods in algebra geometry and number theory part of the research for this paper was carried out while the authors were staying at the mathematical research institute oberwolfach supported by the research in pairs programme the second author wishes to acknowledge support from science foundation ireland

estimation and inference of change points in high dimensional factor models abstract in this paper we consider the estimation of break points in high dimensional factor models where the unobserved factors are estimated by principal component analysis pca the factor loading matrix is assumed to have a structural break at an unknown time we establish the conditions under which the least squares ls estimator is consistent for the break date our consistency result holds for both large and small breaks we also find the ls estimator s asymptotic distribution simulation results confirm that the break date can be accurately estimated by the ls even if the magnitudes of breaks are small in two empirical applications we implement the method to estimate break points in the u s stock market and u s macroeconomy respectively

optimal design of nonlinear parabolic systems part ii variable spatial domain with applications to casting optimization abstract in part i design sensitivity expressions for nonlinear parabolic systems were derived and then specialized for the analysis for thermal systems which govern many processing operations however that presentation did not account for shape variations here we present the shape sensitivity analysis for the thermal system the sensitivities are derived via the domain parameterization method and computed with the finite element method various means for parameterizing the shape are also discussed finally the sensitivity analysis is coupled with nonlinear programming to optimize the design of a sand casting

sensitivity and optimization for shape and non linear boundary conditions in thermal boundary elements this paper is concerned with the minimization of functionals of the form b f h t b h d b where variation of the vector b modifies the shape of the domain on which the potential problem 2t 0 is defined the vector h is dependent on non linear boundary conditions that are defined on the boundary the method proposed is founded on the material derivative adjoint variable method traditionally used for shape optimization attention is restricted to problems where the shape of is described by a boundary element mesh where nodal co ordinates are used in the definition of b propositions are presented to show how design sensitivities for the modified functional b f h t b h d b b b h 2t b h d b can be derived more readily with knowledge of the form of the adjoint function determined via non shape variations the methods developed in the paper are applied to a problem in pressure die casting where the objective is the determination of cooling channel shapes for optimum cooling the results of the method are shown to be highly convergent copyright 2002 john wiley sons ltd

a non physical enthalpy method for the numerical solution of isothermal solidification in this paper a new formulation for the solution of the discontinuous isothermal solidification problem is presented the formulation has similarities with the now classical capacitance and source methods traditionally used in commercial software however the new approach focuses on the solution of the governing enthalpy transport equation rather than the governing parabolic partial differential heat equation the advantage is that discontinuous physics can be accounted for without approximation and the arbitrariness common to classic approaches is avoided also introduced is the concept of non physical enthalpy which unlike physical enthalpy has numerical values that are not moving frame invariant understanding the behaviour of the non physical enthalpy is central to the successful treatment of discontinuities a particular drawback is that non physical enthalpy is non intuitive and new mathematical constructs are required to describe its behaviour this involves the introduction of transport equations which provide the new concept of relative moving frame invariance for the non physical enthalpy the principal advantage however is that a unified methodology is established for the treatment of discontinuities this is shown to establish real rigour and in many respects the formulation highlights the erroneous choices made with established classical approaches and casts in a totally new light a somewhat traditional problem the new methodology is applied to a range of simple problems not only to provide an in depth treatment and for ease of understanding but also to best describe the behaviour of the non intuitive non physical enthalpy demonstrated in the paper is the methods remarkable accuracy and stability