morita theory and singularity categories abstract we propose an analogue of the bounded derived category for an augmented ring spectrum defined in terms of a notion of noether normalization in many cases we show this category is independent of the chosen normalization based on this we define the singularity and cosingularity categories measuring the failure of regularity and coregularity and prove they are koszul dual in the style of the bgg correspondence examples of interest include koszul algebras and ginzburg dg algebras c b g for finite groups or for compact lie groups with orientable adjoint representation cochains in rational homotopy theory and various examples from chromatic homotopy theory

a robust method for detecting interdependences application to intracranially recorded eeg we present a measure for characterizing statistical relationships between two time sequences in contrast to commonly used measures like cross correlations coherence and mutual information the proposed measure is non symmetric and provides information about the direction of interdependence it is closely related to recent attempts to detect generalized synchronization however we do not assume a strict functional relationship between the two time sequences and try to define the measure so as to be robust against noise and to detect also weak interdependences we apply our measure to intracranially recorded electroencephalograms of patients suffering from severe epilepsies

comparison of nonlinear granger causality extensions for low dimensional systems the identification of hidden interdependences among the parts of a complex system is a fundamental issue typically the objective is given only a sequence of scalar measurements to infer as much as possible about the internal dynamics of the system and about the interactions between its subsystems in general such interactions are not only nonlinear but also asymmetric constraints on the estimation of hidden relationships are further posed by noise and by the length of signals sampled from real world systems the focus of this paper is causal dependences between bivariate time series we especially focus on the nonlinear extension of granger causality with polynomial terms of the conventional embedding vector in this paper we study the performance of this measure in comparison with three alternative methods proposed recently in low dimensional and low order nonlinearity systems those methods are tested with three different artificial chaotic maps with several noise contamination setups as a result we find that the polynomial embedding technique successfully detects asymmetric causal dependences between bivariate time series in many low dimensional cases

tree structured classification via generalized discriminant analysis abstract the problem of constructing classification rules that can be represented as decision trees is considered each object to be classified has an associated x vector containing possibly incomplete covariate information tree construction is based on the information provided in a learning sample of objects with known class identities the x vectors in the learning sample may have missing values as well procedures are proposed for each of the components of classifier construction such as split selection tree size determination treatment of missing values and ranking of variables the main idea is recursive application of linear discriminant analysis with the variables at each stage being appropriately chosen according to the data and the type of splits desired standard statistical techniques used as basic building blocks include analysis of variance linear and canonical discriminant analysis and principal component analysis a new method of tree structured classification is obtained by assem

redundant variables and granger causality we discuss the use of multivariate granger causality in presence of redundant variables the application of the standard analysis in this case leads to under estimation of causalities using the un normalized version of the causality index we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches to group redundant variables i for a given target the remaining variables are grouped so as to maximize the total causality and ii the whole set of variables is partitioned to maximize the sum of the causalities between subsets we show the application to a real neurological experiment aiming to a deeper understanding of the physiological basis of abnormal neuronal oscillations in the migraine brain the outcome by our approach reveals the change in the informational pattern due to repetitive transcranial magnetic stimulations

the algebraic chromatic splitting conjecture for noetherian ring spectra we formulate a version of hopkins chromatic splitting conjecture for an arbitrary structured ring spectrum r and prove it whenever pi r is noetherian as an application these results provide a new local to global principle in the modular representation theory of finite groups

on formal local cohomology and connectedness let a denote an ideal of a local ring r m let m be a finitely generated r module there is a systematic study of the formal cohomology modules lim hmi m anm i z we analyze their r module structure the upper and lower vanishing and non vanishing in terms of intrinsic data of m and its functorial behavior these cohomology modules occur in relation to the formal completion of the punctured spectrum specr v m as a new cohomological data there is a description on the formal grade fgrade a m defined as the minimal non vanishing of the formal cohomology modules there are various exact sequences concerning the formal cohomology modules among them a mayer vietoris sequence for two ideals it applies to new connectedness results there are also relations to local cohomological dimensions

injective dg modules over non positive dg rings abstract let a be an associative non positive differential graded ring in this paper we make a detailed study of a category inj a of left dg modules over a which generalizes the category of injective modules over a ring we give many characterizations of this category generalizing the theory of injective modules and prove a derived version of the bass papp theorem the category inj a is closed in the derived category d a under arbitrary direct sums if and only if the ring h 0 a is left noetherian and for every i 0 the left h 0 a module h i a is finitely generated specializing further to the case of commutative noetherian dg rings we generalize the matlis structure theory of injectives to this context as an application we obtain a concrete version of grothendieck s local duality theorem over commutative noetherian local dg rings

additive risk models for survival data with high dimensional covariates as a useful alternative to cox s proportional hazard model the additive risk model assumes that the hazard function is the sum of the baseline hazard function and the regression function of covariates this article is concerned with estimation and prediction for the additive risk models with right censored survival data especially when the dimension of the covariates is comparable to or larger than the sample size principal component regression is proposed to give unique and numerically stable estimators asymptotic properties of the proposed estimators component selection based on the weighted bootstrap and model evaluation techniques are discussed this approach is illustrated with analysis of the primary biliary cirrhosis clinical data and the diffuse large b cell lymphoma genomic data it is shown that this methodology is numerically stable and effective in dimension reduction while still being able to provide satisfactory prediction and classification results

completion of g spectra and stable maps between classifying spaces abstract we prove structural theorems for computing the completion of a g spectrum at the augmentation ideal of the burnside ring of a finite group g first we show that a g spectrum can be replaced by a spectrum obtained by allowing only isotropy groups of prime power order without changing the homotopy type of the completion we then show that this completion can be computed as a homotopy colimit of completions of spectra obtained by further restricting isotropy to one prime at a time and that these completions can be computed in terms of completion at a prime as an application we show that the spectrum of stable maps from bg to the classifying space of a compact lie group k splits non equivariantly as a wedge sum of p completed suspension spectra of classifying spaces of certain subquotients of g k in particular this describes the dual of bg

a local homology theory for linearly compact modules abstract we introduce a local homology theory for linearly compact modules which is in some sense dual to the local cohomology theory of a grothendieck a grothendieck local cohomology lecture notes in math vol 20 springer verlag berlin tokyo new york 1967 10 some basic properties such as the noetherianness the vanishing and non vanishing of local homology modules of linearly compact modules are proved a duality theory between local homology and local cohomology modules of linearly compact modules is developed by using matlis duality and macdonald duality as consequences of the duality theorem we obtain some generalizations of well known results in the theory of local cohomology for semi discrete linearly compact modules

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

high dimensional variable selection for survival data the minimal depth of a maximal subtree is a dimensionless order statistic measuring the predictiveness of a variable in a survival tree we derive the distribution of the minimal depth and use it f

l1 regularization path algorithm for generalized linear models summary we introduce a path following algorithm for l1 regularized generalized linear models the l1 regularization procedure is useful especially because it in effect selects variables according to the amount of penalization on the l1 norm of the coefficients in a manner that is less greedy than forward selection backward deletion the generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor corrector method of convex optimization selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths we suggest intuitive and flexible strategies for choosing appropriate values we demonstrate the implementation with several simulated and real data sets

weak proregularity weak stability and the noncommutative mgm equivalence abstract let a be a commutative ring and let a be a finitely generated ideal in it it is known that a necessary and sufficient condition for the derived a torsion and a adic completion functors to be nicely behaved is the weak proregularity of a in particular the mgm equivalence holds because weak proregularity is defined in terms of elements of the ring it involves limits of koszul complexes it is not suitable for noncommutative ring theory in this paper we introduce a new condition on a torsion class t in a module category weak stability our first main theorem says that in the commutative case the ideal a is weakly proregular if and only if the corresponding torsion class t is weakly stable we then study weak stability of torsion classes in module categories over noncommutative rings there are three main theorems in this context for a torsion class t that is weakly stable quasi compact and finite dimensional the right derived torsion functor is isomorphic to a left derived tensor functor the noncommutative mgm equivalence that holds under the same assumptions on t a theorem about symmetric derived torsion for complexes of bimodules this last theorem is a generalization of a result of van den bergh from 1997 and corrects an error in a paper of yekutieli zhang from 2003

cosupports and minimal pure injective resolutions of affine rings abstract we prove that any affine ring r over a field k has full cosupport i e the cosupport of r is equal to spec r using this fact we give a complete description of all terms in a minimal pure injective resolution of r provided that k 1 and dim r 2 or k 1 and dim r 2 as a corollary we obtain a partial answer to a conjecture by gruson

regularized estimation in the accelerated failure time model with high dimensional covariates we consider two regularization approaches the lasso and the threshold gradient directed regularization for estimation and variable selection in the accelerated failure time model with multiple covariates based on stute s weighted least squares method the stute estimator uses kaplan meier weights to account for censoring in the least squares criterion the weighted least squares objective function makes the adaptation of this approach to multiple covariate settings computationally feasible we use v fold cross validation and a modified akaike s information criterion for tuning parameter selection and a bootstrap approach for variance estimation the proposed method is evaluated using simulations and demonstrated on a real data example

variable selection in a log linear birnbaum saunders regression model for high dimensional survival data via the elastic net and stochastic em the birnbaum saunders bs distribution is broadly used to model failure times in reliability and survival analysis in this article we propose a simultaneous parameter estimation and variable selection procedure in a log linear bs regression model for high dimensional survival data to deal with censored survival data we iteratively run a combination of the stochastic em algorithm sem and variable selection procedure to generate pseudo complete data and select variables until convergence treating pseudo complete data as uncensored data via sem makes it possible to incorporate iterative penalized least squares and simplify computation we demonstrate the efficacy of our method using simulated and real datasets

recursively imputed survival trees we propose recursively imputed survival tree rist regression for right censored data this new nonparametric regression procedure uses a novel recursive imputation approach combined with extremely randomized trees that allows significantly better use of censored data than previous tree based methods yielding improved model fit and reduced prediction error the proposed method can also be viewed as a type of monte carlo em algorithm which generates extra diversity in the tree based fitting process simulation studies and data analyses demonstrate the superior performance of rist compared with previous methods

complete modules and torsion modules suppose that r is a ring and that a is a chain complex over r inside the derived category of differential graded a modules there are naturally defined subcategories of a torsion objects and of a complete objects under a finiteness condition on a we develop a morita theory for these subcat egories find conceptual interpretations for some associated algebraic functors and in appropriate commutative situations identify the associated functors as local homology or local cohomology some of the results are suprising even in the case r z and a z p 1 introduction let r be a ring and r mod the derived category of chain complexes of left modules see section 1 2 we choose a fixed complex a which is perfect in other words isomorphic in mod to a complex of finite length in which the entries are finitely generated projective modules we de clare another complex n to be a trivial if hom a a0 0 where hom denotes the chain complex of morphisms in r mod going further we say that x is a torsion if hom x at 0 for all a trivial n9 and that x is a complete if homr n9x 0 for all a trivial n we then study the category ators of a torsion complexes and the category acomp of a complete complexes both of these are triangulated full subcategories of r mod it turns out that these categories are equivalent to one another and also equivalent to the derived category of dif ferential graded modules over the endomorphism complex of a we construct approximation functors celu r mod at0rs and a r mod acomp for an object m of r mod9 the complex celu m is a kind of a cellular approxi mation to m in the sense that it is the best approximation to m which can be cobbled together from a and its suspensions the complex ma is the bousfield localization of m with respect to a homology theory on r mod derived from a we provide algebraic formulas for the functors and find that the functors are related in interesting ways one of which involves an arithmetic square we also show that if cciia r has certain finite dimensionality properties then an object m of r mod is a torsion or a complete if and only if the homology groups 77 m individually satisfy appropriate torsion or completeness conditions suppose now that r is a commutative ring that 7 c r is a finitely generated ideal that a r i9 and that k is the associated koszul complex the complex a

morava e theory of filtered colimits morava e theory e v n is a much studied theory in algebraic topology but it is not a homology theory in the usual sense because it fails to preserve coproducts resp filtered homotopy colimits the object of this paper is to construct a spectral sequence to compute the morava e theory of a coproduct resp filtered homotopy colimit the e 2 term of this spectral sequence involves the derived functors of direct sum resp filtered colimit in an appropriate abelian category we show that there are at most n 1 resp n of these derived functors when n 1 we recover the known result that homotopy commutes with an appropriate version of direct sum in the k 1 local stable homotopy category

a systematic approach to the analysis of complex interaction patterns in two level factorial designs analysis of data from two level full factorial designs often ends up with a final prediction equation that gives only the significant main effect and interaction terms when the number of interactions is small simple and useful interpretation of the equation can then be drawn immediately this article addresses a different situation in which the number of significant interactions may be large so that additional efforts are needed to sort out the pattern and the relationship between them in particular we bring out a class of models in which most interactions can be attributed to just one or two or very few factors and conditional on these factors the models become essentially linear we offer a strategy for uncovering this structure by linear domain splitting whereby a complicated global model is replaced by a series of local domain specific linear models we present a recommended methodology phd principal hessian direction for systematically proceeding from the global equation to local split dom

adaptive lasso for cox s proportional hazards model summary we investigate the variable selection problem for cox s proportional hazards model and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience the new method is based on a penalized log partial likelihood with the adaptively weighted l1 penalty on regression coefficients providing what we call the adaptive lasso estimator the method incorporates different penalties for different coefficients unimportant variables receive larger penalties than important ones so that important variables tend to be retained in the selection process whereas unimportant variables are more likely to be dropped theoretical properties such as consistency and rate of convergence of the estimator are studied we also show that with proper choice of regularization parameters the proposed estimator has the oracle properties the convex optimization nature of the method leads to an efficient algorithm both simulated and real examples show that the method performs competitively

vanishing of local homology we study the vanishing properties of local homology of complexes of modules without assuming that its homology is artinian using vanishing results for local homology and cohomology we prove new vanishing results for ext and tor modules

local duality in algebra and topology abstract the first goal of this paper is to provide an abstract framework in which to formulate and study local duality in various algebraic and topological contexts for any stable category c together with a collection of compact objects k c we construct local cohomology and local homology functors satisfying an abstract version of local duality when specialized to the derived category of a commutative ring a and a suitable ideal in a we recover the classical local duality due to grothendieck as well as generalizations by greenlees and may more generally applying our result to the derived category of quasi coherent sheaves on a quasi compact and separated scheme x implies the local duality theorem of alonso tarrio jeremias lopez and lipman as a second objective we establish local duality for quasi coherent sheaves over many algebraic stacks in particular those arising naturally in stable homotopy theory after constructing an appropriate model of the derived category in terms of comodules over a hopf algebroid we show that in familiar cases the resulting local cohomology and local homology theories coincide with functors previously studied by hovey and strickland furthermore our framework applies to global and local stable homotopy theory in a way which is compatible with the algebraic avatars of these theories in order to aid computability we provide spectral sequences relating the algebraic and topological local duality contexts

radial basis function approach to nonlinear granger causality of time series we consider an extension of granger causality to nonlinear bivariate time series in this frame if the prediction error of the first time series is reduced by including measurements from the second time series then the second time series is said to have a causal influence on the first one not all the nonlinear prediction schemes are suitable to evaluate causality indeed not all of them allow one to quantify how much knowledge of the other time series counts to improve prediction error we present an approach with bivariate time series modeled by a generalization of radial basis functions and show its application to a pair of unidirectionally coupled chaotic maps and to physiological examples

nonparametric variable selection the earth algorithm we consider regression experiments involving a response variable y and a large number of predictor variables x1 xd many of which may be irrelevant for the prediction of y and thus must be removed before y can be predicted from the x s we consider two procedures that select variables by using importance scores that measure the strength of the relationship between predictor variables and a response and keep those variables whose importance scores exceed a threshold in the first of these procedures scores are obtained by randomly drawing subregions tubes of the predictor space that constrain all but one predictor and in each subregion computing a signal to noise ratio efficacy based on a nonparametric univariate regression of y on the unconstrained variable the subregions are adapted to boost weak variables iteratively by searching hunting for the subregions in which the efficacy is maximized the efficacy can be viewed as an approximation to a one to one function of the probability of identif

on gorenstein projective injective and flat dimensions a functorial description with applications gorenstein homological dimensions are refinements of the classical homological dimensions and finiteness singles out modules with amenable properties reflecting those of modules over gorenstein rings as opposed to their classical counterparts these dimensions do not immediately come with practical and robust criteria for finiteness not even over commutative noetherian local rings in this paper we enlarge the class of rings known to admit good criteria for finiteness of gorenstein dimensions

bousfield localization on formal schemes let x ox be a noetherian formal scheme and consider dqct x its derived category of sheaves with quasi coherent torsion homology we show that there is a bijection between the set of rigid i e ideals localizing subcategories of dqct x and subsets in x generalizing previous work by neeman if moreover x is separated the associated localization and acyclization functors are described in certain cases when z x is a stable for specialization subset its associated acyclization is r z when x is a scheme the corresponding localizing subcategories are generated by perfect complexes and we recover thomason s classification of thick subcategories on the other hand if y x is generically stable we show that the associated localization functor is hom x r x yo x g

adelic models of tensor triangulated categories abstract we show that a well behaved noetherian finite dimensional stable monoidal model category has a model built from categories of modules over completed rings in an adelic fashion special cases include abelian groups the hasse square chromatic homotopy theory a module theoretic chromatic fracture square and rational torus equivariant homotopy theory first step to the model of 30

binomial d modules fil dickenstein alicia marcela universidad de buenos aires facultad de ciencias exactas y naturales departamento de matematica argentina consejo nacional de investigaciones cientificas y tecnicas oficina de coordinacion administrativa ciudad universitaria instituto de investigaciones matematicas luis a santalo argentina

localization and completion theorems for mu module spectra let g be a finite extension of a torus working with highly structured ring and module spectra let m be any module over mu examples include all of the standard homotopical mu modules such as the brown peterson and morava k theory spectra we shall prove localization and completion theorems for the computation of m bg and m bg the g spectrum mug that represents stabilized equivariant complex cobordism is an algebra over the equivariant sphere spectrum sg and there is an mug module mg whose underlying mu module is m this allows the use of topological analogues of constructions in commutative algebra the computation ofm bg andm bg is expressed in terms of spectral sequences whose respective e2 terms are computable in terms of local cohomology and local homology groups that are constructed from the coefficient ring mu and its module m the central feature of the proof is a new norm map in equivariant stable homotopy theory the construction of which involves the new concept of a global i functor with smash product

on principal hessian directions for data visualization and dimension reduction another application of stein s lemma abstract modern graphical tools have enhanced our ability to learn many things from data directly with much user friendly graphical software available we are encouraged to plot a lot more often than before the benefits from direct interaction with graphics have been enormous but trailing behind these high tech advances is the issue of appropriate guidance on what to plot there are too many directions to project a high dimensional data set and unguided plotting can be time consuming and fruitless in a recent article li set up a statistical framework for study on this issue based on a notion of effective dimension reduction edr directions they are the directions to project a high dimensional input variable for the purpose of effectively viewing and studying its relationship with an output variable a methodology sliced inverse regression was introduced and shown to be useful in finding edr directions this article introduces another method for finding edr directions it begins with the observat

discriminant analysis when all variables are ordered determination of the equation that relates an ordered dependent variable to ordered independent variables is sought one solution non parametric discriminant analysis npd involves obtaining the best monotonic step function by means of a computer search procedure although one can use alternative selection criteria in obtaining the equation the illustrative examples use absolute distance this paper compares the prediction procedures obtained from npd with those from linear discriminant analysis linear regression with and without transformed variables and logistic regression we show that npd is analogous to regression tree analysis with incorporation of ordered variables and monotonicity we use various prediction functions to predict the example data the data using the leave one out technique and a verification set consistently non parametric discriminant analysis performs as good as or better than the tested alternatives