complexes de chaines etales et courbes de deligne lusztig abstract in a first part we lift the usual constructions of functors between derived categories of etale sheaves over schemes with a sheaf of algebras to pure derived categories for varieties with finite group actions we recover in a more functorial way rickard s construction we apply this to the case of deligne lusztig varieties and show that broue s conjecture holds for curves the additional ingredient we need is obtained from an easy property of the cohomology of etale covers of the affine line

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

variable selection in semiparametric linear regression with censored data summary we describe two procedures for selecting variables in the semiparametric linear regression model for censored data one procedure penalizes a vector of estimating equations and simultaneously estimates regression coefficients and selects submodels a second proce dure controls systematically the proportion of unimportant variables through forward selection and the addition of pseudorandom variables we explore both rank based statistics and buckley james statistics in the setting proposed and evaluate the performance of all methods through extensive simulation studies and one real data set

on pure derived categories abstract we investigate the properties of pure derived categories of module categories and show that pure derived categories share many nice properties of classical derived categories in particular we show that bounded pure derived categories can be realized as certain homotopy categories we introduce the pure projective resp injective dimension of complexes in pure derived categories and give some criteria for computing these dimensions in terms of the properties of pure projective resp injective resolutions and pure derived functors as a consequence we get some equivalent characterizations for the finiteness of the pure global dimension of rings finally pure projective resp injective resolutions of unbounded complexes are considered

covers envelopes and cotorsion theories in locally presentable abelian categories and contramodule categories we prove general results about completeness of cotorsion theories and existence of covers and envelopes in locally presentable abelian categories extending the well established theory for module categories and grothendieck categories these results are then applied to the categories of contramodules over topological rings which provide examples and counterexamples

large sample theory of a modified buckley james estimator for regression analysis with censored data this approach we introduce herein a slight modification of the buckley james estimator to get around the difficulties caused by the instability at the upper tail of the associated kaplan meier estimate of the underlying error distribution and show that the modified buckleyjames estimator is consistent and asymptotically normal under certain regularity conditions a simple formula for the asymptotic variance of the modified buckley james estimator is also derived and is used to study the asymptotic efficiency of the estimator extensions of these results to the multiple regression model are also given

the derived category of an exact category there is some confusion in the literature regarding the derived category of an exact category 8 thomason gives a satisfactory treatment of the bounded derived category in ct 1 11 6 see also appendix a the result is that provided all weakly split epimorphisms in 8 are admissible the bounded derived category may be defined as usual although thomason does not say it the categories d 6 d d may also be defined in the same way the definition of the unbounded derived category is more difficult and is very poorly treated in the literature for instance in bbd this derived category is only defined provided every morphism in 6 admits a kernel see bbd 1 1 41 this is very unsatisfactory since very few exact categories satisfy the condition in this article we will show that d b may be defined whenever 6 is saturated karoubian in thomason s terminology an exact category is saturated if every idempotent splits i e 6 contains all direct summands of its objects for the purpose of comparing with thomason s result the bounded derived category is defined for more 8 s all that is required to define db is that whenever an idempotent e a a factors as a f ba a with fog lb then e is split thomason calls such idempotents weakly split and we will honor his notation we will show here that these constructions are in some sense best possible remark 1 8 for d 6 remarks 1 9 and 1 10 for d d d b db 6 there are two reasons why i wrote this note one is to correct the misconceptions in the literature but more importantly the proof of the key result lemma 1 2 depends on an important characterization of tpaisse subcategories due to rickard and this article is intended to highlight rickard s criterion a full triangulated subcategory y of a triangulated

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

phantom covering ideals in categories without enough projective morphisms abstract we give sufficient conditions to ensure that the ideal e of e phantom maps in a locally presentable exact category a e is a special pre covering ideal where e is an exact substructure of a e as a byproduct we infer the existence of various covering ideals in categories of sheaves which have a meaningful geometrical motivation in particular we deal with a zariski local notion of phantom maps in categories of sheaves we would like to point out that our approach is necessarily different from 18 as the categories involved in most of the examples we are interested in do not have enough projective morphisms

relative homological algebra in the category of quasi coherent sheaves abstract in this paper we prove the existence of a flat cover and of a cotorsion envelope for any quasi coherent sheaf over a scheme x o x indeed we prove something more general we define what it is understood by the category of quasi coherent r modules where r is a representation by rings of a quiver q and we prove the existence of a flat cover and a cotorsion envelope for quasi coherent r modules then we use the fact that the category of quasi coherent sheaves on x o x is equivalent to the category of quasi coherent r modules for some q and r to get our result

controlling variable selection by the addition of pseudovariables we propose a new approach to variable selection designed to control the false selection rate fsr defined as the proportion of uninformative variables included in selected models the method works by adding a known number of pseudovariables to the real dataset running a variable selection procedure and monitoring the proportion of pseudovariables falsely selected information obtained from bootstrap like replications of this process is used to estimate the proportion of falsely selected real variables and to tune the selection procedure to control the fsr

variable selection for cox s proportional hazards model and frailty model a class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in fan and li 2001a it has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance such a property is called an oracle property the proposed procedures were illustrated in the context of linear regression robust linear regression and generalized linear models in this paper the nonconcave penalized likelihood approach is extended further to the cox proportional hazards model and the cox proportional hazards frailty model two commonly used semi parametric models in survival analysis as a result new variable selection procedures for these two commonly used models are proposed it is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function further with a proper choice of the regularization parameter and the penalty function the proposed estimators possess an oracle property standard error formulae are derived and their accuracies are empirically tested simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection and they reduce model complexity as effectively as the best subset variable selection compared with the lasso which is the penalized likelihood method with the l 1 penalty proposed by tibshirani the newly proposed approaches have better theoretic properties and finite sample performance

limiting shapes of ising droplets ising fingers and ising solitons we examine the evolution of an ising ferromagnet endowed with zero temperature single spin flip dynamics a large droplet of one phase in the sea of the opposite phase eventually disappears an interesting behavior occurs in the intermediate regime when the droplet is still very large compared to the lattice spacing but already very small compared to the initial size in this regime the shape of the droplet is essentially deterministic fluctuations are negligible in comparison with characteristic size in two dimensions the shape is also universal that is independent of the initial shape we analytically determine the limiting shape of the ising droplet on the square lattice when the initial state is a semi infinite stripe of one phase in the sea of the opposite phase it evolves into a finger which translates along its axis we determine the limiting shape and the velocity of the ising finger on the square lattice an analog of the ising finger on the cubic lattice is the translating ising soliton we show that far away from the tip the cross section of the ising soliton coincides with the limiting shape of the two dimensional ising droplet and we determine a relation between the cross section area the distance from the tip and the velocity of the soliton

the lasso method for variable selection in the cox model summary i propose a new method for variable selection and shrinkage in cox s proportional hazards model my proposal minimizes the log partial likelihood subject to the sum of the absolute values of the parameters being bounded by a constant because of the nature of this constraint it shrinks coe cients and produces some coe cients that are exactly zero as a result it reduces the estimation variance while providing an interpretable final model the method is a variation of the lasso proposal of tibshirani designed for the linear regression context simulations indicate that the lasso can be more accurate than stepwise selection in this setting

the low temperature expansion of the wulff crystal in the 3d ising model we compute the expansion of the surface tension of the 3d random cluster model for q 1 in the limit where p goes to 1 we also compute the asymptotic shape of a plane partition of n as n goes to this same shape determines the wulff crystal to order o in the 3d ising model and more generally in the 3d random cluster model for q 1 at temperature

bayesian variable selection method for censored survival data a bayesian variable selection method for censored data is proposed in this paper based on the sufficiency and asymptotic normality of the maximum partial likelihood estimator we approximate the posterior distribution of the parameters in a proportional hazards model we consider a parsimonious model as the full model with some covariates unobserved and replaced by their conditional expected values a loss function based on the posterior expected estimation error of the log risk for the proportional hazards model is used to select a parsimonious model we derive computational expressions for this loss function for both continuous and binary covariates this approach provides an extension of lindley s 1968 journal of the royal statistical society series b 30 31 66 variable selection criterion for the linear case data from a randomized clinical trial of patients with primary biliary cirrhosis of the liver pbc fleming and harrington 1991 counting processes and survival analysis is used to illustrate the proposed method and a simulation study compares it with the backward elimination procedure

the homotopy category of complexes of projective modules abstract the homotopy category of complexes of projective left modules over any reasonably nice ring is proved to be a compactly generated triangulated category and a duality is given between its subcategory of compact objects and the finite derived category of right modules

the covariance inflation criterion for adaptive model selection we propose a new criterion for model selection in prediction problems the covariance inflation criterion adjusts the training error by the average covariance of the predictions and responses when the prediction rule is applied to permuted versions of the data set this criterion can be applied to general prediction problems e g regression or classification and to general prediction rules e g stepwise regression tree based models and neural nets as a by product we obtain a measure of the effective number of parameters used by an adaptive procedure we relate the covariance inflation criterion to other model selection procedures and illustrate its use in some regression and classification problems we also revisit the conditional bootstrap approach to model selection

cartesian modules over representations of small categories we introduce the new concept of cartesian module over a pseudofunctor r from a small category to the category of small preadditive categories already the case when r is a strict functor taking values in the category of commutative rings is sucient

the accelerated gap times model summary this paper develops a new semiparametric model for the effect of covariates on the conditional intensity of a recurrent event counting process the model is a transparent extension of the accelerated failure time model for univariate survival data estimation of the regression parameter is motivated by semiparametric efficiency considerations extending the class of weighted log rank estimating functions originally proposed in prentice 1978 and subsequently studied in detail by tsiatis 1990 and ritov 1990 a novel rank based one step estimator for the regression parameter is proposed an aalen type estimator for the baseline intensity function is obtained asymptotics are handled with empirical process methods and finite sample properties are studied via simulation finally the new model is applied to the bladder tumour data of byar 1980

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

dynamics of an unbounded interface between ordered phases we investigate the evolution of a single unbounded interface between ordered phases in two dimensional ising ferromagnets that are endowed with single spin flip zero temperature glauber dynamics we examine specifically the cases where the interface initially has either one or two corners in both examples the interface evolves to a limiting self similar form we apply the continuum time dependent ginzburg landau equation and a microscopic approach to calculate the interface shape for the single corner system we also discuss a correspondence between the interface and the young diagram that represents the partition of the integers

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

on the relation between k flatness and k projectivity abstract krause 19 has proved that the homotopy category k r pureproj of pure projective modules over an associative ring r is compactly generated and equivalent to the verdier quotient k r t r where t r is the triangulated subcategory of the homotopy category k r consisting of the pure acyclic complexes we provide an alternative proof of this result when restricted to the homotopy category of projective modules this equivalence reduces to that obtained by neeman 26 as an application of this description of k r pureproj we show that the k flat complexes defined by spaltenstein 29 are up to homotopy equivalence the filtered colimits of k projective complexes of pure projective modules

some adjoints in homotopy categories let r be a ring in a previous paper 11 we found a new description for the category k r proj it is equivalent to the verdier quotient k r flat s for some suitable s c k r flat in this article we show that the quotient map from k r flat to k r flat s always has a right adjoint this gives a new fully faithful embedding of k r proj into k r flat its virtue is that it generalizes to nonaffine schemes

approximations and adjoints in homotopy categories we provide a criterion for the existence of right approximations in cocomplete additive categories it is a straightforward generalisation of a result due to el bashir this criterion is used to construct adjoint functors in homotopy categories applications include the study of pure derived categories for instance it is shown that the pure derived category of any module category is compactly generated

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

exactly definable categories op given a skeletally small abelian category c we denote by ex c ab the category of exact additive functors from c op to the category ab of abelian groups we call a category exactly definable provided that it is op equivalent to ex c ab for some skeletally small abelian category c this definition and our interest in this type of categories are motivated by the following example let l be a ring and denote by c l s op fp mod l ab the category of finitely presented functors from the category of finitely presented l modules to the category of abelian groups the c l is skeletally small abelian in fact it is the free abelian category w x over l viewed as a category with a single object 4 and the functor

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

calibration regression of censored lifetime medical cost analysis of lifetime medical cost is challenged by its irregular distribution and by incomplete follow up particularly the latter with limited study duration as is typical in medical research this article proposes the so called calibration regression to address these issues by modeling not only lifetime medical cost but also survival time in a semiparametric fashion it is postulated that both outcomes on possibly transformed scales linearly relate to the covariates however the bivariate model error distribution is completely unspecified whereas this conceptually simple model is a natural multivariate generalization of the accelerated failure time model this article proposes an inference procedure by extending the weighted log rank estimating function to the marked point process framework the resulting estimators are consistent and asymptotically normal in addition robustness and efficiency issues are discussed furthermore a novel sample based variance estimation procedure is proposed for es

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

percolation framework in ising spin relaxation we introduce a framework based on the percolation idea to investigate the relaxation under zero temperature glauber and outflow dynamics on l x l square and triangular lattices this helps us to understand the appearance of a double time regime in the survival probability we show that the first short time regime corresponds to relaxation through droplets and the second long time regime corresponds to relaxation through stripes for both dynamics the probability that the system becomes ordered through droplets which indicates fast relaxation is about 2 3

the homotopy category of flat modules and grothendieck duality let r be a ring we prove that the homotopy category k r proj is always aleph 1 compactly generated and depending on the ring r it may or may not be compactly generated we use this to give a description of k r proj as a quotient of k r flat the remarkable fact is that this new description of k r proj generalizes to non affine schemes this will appear in murfet s thesis

zero temperature freezing in the three dimensional kinetic ising model we investigate the relaxation of the ising glauber model on a periodic cubic lattice after a quench to zero temperature in contrast to the conventional picture from phase ordering kinetics we find the following i domains at long time are highly interpenetrating and topologically complex with average genus growing algebraically with system size ii the long time state is almost never static but rather contains blinker spins that can flip ad infinitum with no energy cost iii the energy relaxation is extremely slow with a characteristic time that grows exponentially with system size

geometric variational problems of statistical mechanics and of combinatorics we present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics together with the wulff construction which predicts the shape of the crystals we discuss the construction which exhibits the shape of a typical young diagram and of a typical skyscraper

more comments on c p we discuss the interpretation of c p plots and show how they can be calibrated in several ways we comment on the practice of using the display as a basis for formal selection of a subset regression model and extend the range of application of the device to encompass arbitrary linear estimates of the regression coefficients for example ridge estimates