dominant dimension and tilting modules we study which algebras have tilting modules that are both generated and cogenerated by projective injective modules crawley boevey and sauter have shown that auslander algebras have such tilting modules and for algebras of global dimension 2 auslander algebras are classified by the existence of such tilting modules in this paper we show that the existence of such a tilting module is equivalent to the algebra having dominant dimension at least 2 independent of its global dimension in general such a tilting module is not necessarily cotilting here we show that the algebras which have a tilting cotilting module generated cogenerated by projective injective modules are precisely 1 minimal auslander gorenstein algebras when considering such a tilting module without the assumption that it is cotilting we study the global dimension of its endomorphism algebra and discuss a connection with the finitistic dimension conjecture furthermore as special cases we show that triangular matrix algebras obtained from auslander algebras and certain injective modules have such a tilting module we also give a description of which nakayama algebras have such a tilting module

the representation dimension of a selfinjective algebra of euclidean type abstract we prove that the representation dimension of a selfinjective algebra of euclidean type is equal to three and give an explicit construction of the auslander generator of its module category

representation dimension and finitely generated cohomology abstract we consider selfinjective artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators for such an algebra we show that the representation dimension is strictly greater than the maximal complexity occurring among its modules this provides a unified approach to computing lower bounds for the representation dimension of group algebras exterior algebras and artin complete intersections we also obtain new examples of classes of algebras with arbitrarily large representation dimension

quantifying the effects of fast acting compression on the envelope of speech fast acting compression has several effects on the envelope of speech signals especially when a target and a background are mixed together three measures of the envelope are described which can be used to quantify these changes 1 within signal modulation correlation or coherence the degree of correlation or coherence of the envelope on a db scale of a single source across different frequency regions which is reduced by fast acting compression 2 fidelity of envelope shape the degree to which the envelope shape of the target speech in different frequency channels is preserved following compression and 3 across signal modulation correlation or coherence asmc the extent to which the target and background acquire a common component of modulation when they are compressed together which becomes greater in absolute value more negative when the target and background are compressed together values of these measures are presented and compared with intelligibility scores obtained using stimuli processed with a noise vocoder so as to preserve mainly envelope cues in a limited number of frequency channels the results suggest that the dominant factor affecting intelligibility is asmc

representation type of hecke algebras of type a in this paper we provide a complete classification of the representation type for the blocks for the hecke algebra of type a stated in terms of combinatorical data the computation of the complexity of young modules is a key component in the proof of this classification result

the radius of convergence of poincare series of loop spaces letr s resp r a be the radius of convergence of the poincare series of a loop space s resp of the betti poincare series of a noetherian connected graded commutative algebraa over a field mathbb k of characteristic zero ifs is a finite 1 connected cw complex the rational homotopy lie algebra ofs is finite dimensional if and only ifr s 1 otherwiser s 1 there is an easily computable upper bound usually less than 1 forr s ifs is formal or coformal on the other handr a if and only ifa is a polynomial algebra andr a 1 if and only ifa is a complete intersection golod and gulliksen conjecture otherwiser a 1 and the sequence dim tor mathbb k mathbb k grows exponentially withp

representation dimension and quasi hereditary algebras we study auslander s representation dimension of artin algebras which is by definition the minimal projective dimension of coherent functors on modules which are both generators and cogenerators we show the following statements 1 if an artin algebra a is stably hereditary then the representation dimension of a is at most 3 2 if two artin algebras are stably equivalent of morita type then they have the same representation dimension particularly if two self injective algebras are derived equivalent then they have the same representation dimension 3 any incidence algebra of a finite partially ordered set over a field has finite representation dimension moreover we use results on quasi hereditary algebras to show that 4 the auslander algebra of a nakayama algebra has finite representation dimension

learning boolean concepts in the presence of many irrelevant features abstract in many domains an appropriate inductive bias is the min features bias which prefers consistent hypotheses definable over as few features as possible this paper defines and studies this bias in boolean domains first it is shown that any learning algorithm implementing the min features bias requires ln l 2 p p ln n e training examples to guarantee pac learning a concept having p relevant features out of n available features this bound is only logarithmic in the number of irrelevant features for implementing the min features bias the paper presents five algorithms that identify a subset of features sufficient to construct a hypothesis consistent with the training examples focus 1 is a straightforward algorithm that returns a minimal and sufficient subset of features in quasi polynomial time focus 2 does the same task as focus 1 but is empirically shown to be substantially faster than focus 1 finally the simple greedy mutual information greedy and weighted greedy algorithms are three greedy heuristics that trade optimality for computational efficiency experimental studies are presented that compare these exact and approximate algorithms to two well known algorithms id3 and fringe in learning situations where many irrelevant features are present these experiments show that contrary to expectations the id3 and fringe algorithms do not implement good approximations of min features the sample complexity and generalization performance of the focus algorithms is substantially better than either id3 or fringe on learning problems where the min features bias is appropriate these experiments also show that among our three heuristics the weighted greedy algorithm provides an excellent approximation to the focus algorithms

on the trace of graded automorphisms abstract leta d 0 adbe a connected algebra with a graded algebra endomorphism the trace of is defined to be tr t d 0 tr ad td we prove that tr t is a rational function ifais either finitely generated commutative or right noetherian with finite global dimension or regular a version of molien s theorem follows in these three cases ifais a regular algebra or a frobenius algebra we prove a reciprocity for the trace we also partially generalize a theorem of watanabe on the gorenstein property to the noncommutative case

on support varieties and tensor products for finite dimensional algebras abstract it has been asked whether there is a version of the tensor product property for support varieties over finite dimensional algebras defined in terms of hochschild cohomology we show that in general no such version can exist in particular we show that for certain quantum complete intersections there are modules and bimodules for which the variety of the tensor product is not even contained in the variety of the one sided module

rigidity of graded regular algebras we prove a graded version of alev polo s rigidity theorem the homogenization of the universal enveloping algebra of a semisimple lie algebra and the rees ring of the weyl algebras a n k cannot be isomorphic to their fixed subring under any finite group action we also show the same result for other classes of graded regular algebras including the sklyanin algebras

cross correlation procedures for measuring noise and distortion in agc hearing aids the magnitude squared coherence function msc has been used to measure noise and distortion in linear and compression hearing aids however the msc will overestimate the distortion in a linear time varying system such as a compression amplifier the reduction in coherence caused by varying the gain in an otherwise linear system can be substantial and can lead to large errors in estimating the distortion present in a compression hearing aid the effects of gain changes in a linear system can be reduced by measuring the normalized system input output cross correlation which emphasizes the variance in the system phase response and deemphasizes the system gain fluctuations estimates of the total noise and distortion produced using the msc phase variance and notched noise measurement techniques are compared for additive noise clipping distortion and compression amplification the msc is found to give the most accurate results for estimating the noise and distortion in a linear time invariant system and the notched noise measurements are the most accurate for a compression system the phase variance is found to give reasonable measurements for a time varying gain as long as the system variations are slow relative to the length of the analysis data segments

random forests with ensemble of feature spaces random forests receive much attention from researchers because of their excellent performance as breiman suggested the performance of random forests depends on the strength of the weak learners in the forests and the diversity among them however in the literature many researchers only considered pre processing of the data or post processing of the random forests models in this paper we propose a new method to increase the diversity of each tree in the forests and thereby improve the overall accuracy during the training process of each individual tree in the forest different rotation spaces are concatenated into a higher space at the root node then the best split is exhaustively searched within this higher space the location where the best split lies decides which rotation method to be used for all subsequent nodes the performance of the proposed method here is evaluated on 42 benchmark data sets from various research fields and compared with the standard random forests the results show that the proposed method improves the performance of the random forests in most cases

representation dimension via tilting theory abstract let be an artin algebra over a commutative artinian ring r and let t be a separating splitting tilting module with endomorphism end t the aim of this paper is to use tilting theory to study the representation dimension of the main result asserts that for an integer n 1 if is n gorenstein of finite cohen macaulay type then r e p d i m n 2 we conclude that if is a n gorenstein artin algebra of finite cohen macaulay type then r e p d i m n 2 this in particular shows that for any artin algebra r e p d i m g l d i m 2

rings of invariants of finite groups which are hypersurfaces ii let g be a finite subgroup of gl acting naturally on an affine space c of dimension n over the complex number field and denote by v g the quotient variety of c under this action of g an element c of gl is said to be a pseudo reflection if the rank of r 1 is equal to one and g is said to be a reflection group if g is generated by pseudo reflections finite reflection groups were classified by coxeter shephard and todd 8 261 and are characterized by

the representation dimension of a selfinjective algebra of wild tilted type abstract we prove that the representation dimension of a selfinjective algebra of wild tilted type is equal to three and give an explicit construction of an auslander generator of its module category we also show that if a connected selfinjective algebra admits an acyclic generalised standard auslander reiten component then its representation dimension is equal to three

on the representation dimension of tilted and laura algebras abstract we prove that the representation dimension of a tilted or of a strict laura algebra is at most three

finite generation of the cohomology of quotients of pbw algebras abstract in this article we prove finite generation of the cohomology of quotients of a pbw algebra a by relating it to the cohomology of quotients of a quantum symmetric algebra s which is isomorphic to the associated graded algebra of a the proof uses a spectral sequence argument and a finite generation lemma adapted from friedlander and suslin

shape quantization and recognition with randomized trees we explore a new approach to shape recognition based on a virtually infinite family of binary features queries of the image data designed to accommodate prior information about shape invariance and regularity each query corresponds to a spatial arrangement of several local topographic codes or tags which are in themselves too primitive and common to be informative about shape all the discriminating power derives from relative angles and distances among the tags the important attributes of the queries are a natural partial ordering corresponding to increasing structure and complexity semi invariance meaning that most shapes of a given class will answer the same way to two queries that are successive in the ordering and stability since the queries are not based on distinguished points and substructures no classifier based on the full feature set can be evaluated and it is impossible to determine a priori which arrangements are informative our approach is to select informative features and build tree classifiers at the same time by inductive learning in effect each tree provides an approximation to the full posterior where the features chosen depend on the branch that is traversed due to the number and nature of the queries standard decision tree construction based on a fixed length feature vector is not feasible instead we entertain only a small random sample of queries at each node constrain their complexity to increase with tree depth and grow multiple trees the terminal nodes are labeled by estimates of the corresponding posterior distribution over shape classes an image is classified by sending it down every tree and aggregating the resulting distributions the method is applied to classifying handwritten digits and synthetic linear and nonlinear deformations of three hundred l at e x symbols stateof the art error rates are achieved on the national institute of standards and technology database of digits the principal goal of the experiments on l at e x symbols is to analyze invariance generalization error and related issues and a comparison with artificial neural networks methods is presented in this context

tilting modules and representation dimensions in this paper we compare the representation dimensions of two algebras linked by certain tilting modules our main results can be stated as follows suppose t is a tilting module over a and b enda t then 1 if t is separating and splitting then rep dim a rep dim b 2 if t p 1s is an apr tilting module and the injective dimension of s is at most 2 then rep dim b rep dim a 1

separable equivalence complexity and representation type abstract we generalise the notion of separable equivalence originally presented by linckelmann in 13 to an equivalence relation on additive categories we use this generalisation to show that from an initial equivalence between two algebras we may build equivalences between many related categories we also show that separable equivalence preserves the representation type of an algebra this generalises linckelmann s result in 13 where he showed this in the case of symmetric algebras we use these theorems to show that the group algebras of several small cyclic groups cannot be separably equivalent this gives several examples of algebras that have the same complexity but are not separably equivalent

radical embeddings and representation dimension given a representation finite algebra b and a subalgebra a of b such that the jacobson radicals of a and b coincide we prove that the representation dimension of a is at most three by a result of igusa and todorov this implies that the finitistic dimension of a is finite

cohomology of twisted tensor products abstract it is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies we look at twisted tensor products and investigate to which extent this is still true we give an explicit description of the ext algebra of the tensor product of two modules and under certain additional conditions describe an essential part of the hochschild cohomology ring of a twisted tensor product as an application we characterize precisely when the cohomology groups over a quantum complete intersection are finitely generated over the hochschild cohomology ring moreover both for quantum complete intersections and in related cases we obtain a lower bound for the representation dimension of the algebra

modules with reducible complexity abstract for a commutative noetherian local ring we define and study the class of modules having reducible complexity a class containing all modules of finite complete intersection dimension various properties of this class of modules are given together with results on the vanishing of homology and cohomology

on the representation dimension of finite dimensional algebras the importance of the representation finite artin algebras for the whole representation theory of artin algebras is well understood and there is much literature on the subject see 1 6 12 these are artin algebras such that every indecomposable module is finitely generated and every module is a direct sum of indecomposable modules moreover there is a bijective correspondence between the class of representation finite artin algebras and that of artin algebras with global dimension of at most 2 and with dominant dimension of at least 2 this result was established by auslander in 1 motivated by this correspondence auslander introduced the concept of representation dimension for artin algebras to study the connection of arbitrary artin algebras with representation finite artin algebras it is hoped that this notion gives a reasonable way of measuring how far an artin algebra is from being representation finite type 1 p 134 representation dimension is a morita invariant of artin algebras and its definition involves homological dimensions and modules which are both generators and cogenerators unfortunately little seems to be known about representation dimension so there are a lot of essential questions on this invariant dealing with the computation and estimation of the representation dimension of an artin algebra there are a few cases known auslander proved that the representation dimension of an artin algebra is two if and

representation dimensions of triangular matrix algebras abstract let a be a finite dimensional hereditary algebra over an algebraically closed field k t 2 a a 0 a a be the triangular matrix algebra we prove that rep dim t 2 a is at most three if a is dynkin type and rep dim t 2 a is at most four if a is not dynkin type let a 1 a 0 da a be the duplicated algebra of a let t be a tilting a module and t t p be a tilting a 1 module we show that end a 1 t is representation finite if and only if the full subcategory x a y a f x a mod a y a 1 f t a add a of mod t 2 a is of finite type where is the auslander reiten translation and f t a is the torsion free class of mod a associated with t moreover we also prove that rep dim end a 1 t is at most three if a is dynkin type

homology of perfect complexes abstract it is proved that the sum of the loewy lengths of the homology modules of a finite free complex f over a local ring r is bounded below by a number depending only on r this result uncovers in the structure of modules of finite projective dimension obstructions to realizing r as a closed fiber of some flat local homomorphism other applications include as special cases uniform proofs of known results on free actions of elementary abelian groups and of tori on finite cw complexes the arguments use numerical invariants of objects in general triangulated categories introduced here and called levels they allow one to track through changes of triangulated categories homological invariants like projective dimension as well as structural invariants like loewy length an intermediate result sharpens with a new proof the new intersection theorem for commutative algebras over fields under additional hypotheses on the ring r stronger estimates are proved for loewy lengths of modules of finite projective dimension

feature selection with ensembles artificial variables and redundancy elimination predictive models benefit from a compact non redundant subset of features that improves interpretability and generalization modern data sets are wide dirty mixed with both numerical and categorical predictors and may contain interactive effects that require complex models this is a challenge for filters wrappers and embedded feature selection methods we describe details of an algorithm using tree based ensembles to generate a compact subset of non redundant features parallel and serial ensembles of trees are combined into a mixed method that can uncover masking and detect features of secondary effect simulated and actual examples illustrate the effectiveness of the approach

returning arrows for self injective algebras and artin schelter regular algebras abstract we show that when constructing twisted trivial extensions for a graded self injective algebra the returning arrows appear in the quiver and in the meantime the complexity increases by one in koszul cases and the representation dimension also increases by one under certain additional conditions we apply our results to koszul artin schelter regular algebras and obtain a family of extensions of a koszul artin schelter regular algebra among them one is central extension and one is calabi yau

the representation dimension of hecke algebras and symmetric groups abstract we establish a lower bound for the representation dimension of all the classical hecke algebras of types a b and d for all the type a algebras and most of the algebras of types b and d we also establish upper bounds moreover we establish bounds for the representation dimension of group algebras of some symmetric groups

an upper bound for the dimension of bounded derived categories abstract let be an artin algebra we give an upper bound for the dimension of the bounded derived category of the category mod of finitely generated right modules in terms of the projective and injective dimensions of certain class of simple right modules as well as the radical layer length of in addition we give an upper bound for the dimension of the singularity category of mod in terms of the radical layer length of

quality ratings for frequency shaped peak clipped speech peak clipping is a common form of distortion in hearing aids and can reduce the subjective quality of the amplified speech in a typical hearing aid frequency response shaping precedes symmetric peak clipping the effect of peak clipping on speech quality ratings was therefore studied using sentence test materials that were processed using different frequency response contours and then clipped at different clipping thresholds the quality of each processed sentence was rated on a ten point scale by normal hearing subjects the experimental results indicate that the clipping threshold and the interaction of the frequency response shaping with the clipping threshold significantly affect speech quality it is also shown that the distortion effects on speech quality can be modeled by a distortion index computed from the magnitude squared coherence of the speech processing system in response to a shaped noise input signal

additive logistic regression a statistical view of boosting boosting is one of the most important recent developments in classification methodology boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced for many classification algorithms this simple strategy results in dramatic improvements in performance we show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles namely additive modeling and maximum likelihood for the two class problem boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum bernoulli likelihood as a criterion we develop more direct approximations and show that they exhibit nearly identical results to boosting direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations and far superior in some we suggest a minor modification to boosting that can reduce computation often by factors of 10 to 50 finally we apply these insights to produce an alternative formulation of boosting decision trees this approach based on best first truncated tree induction often leads to better performance and can provide interpretable descriptions of the aggregate decision rule it is also much faster computationally making it more suitable to large scale data mining applications

gorenstein derived categories abstract gorenstein derived categories are defined and the relation with the usual derived categories is given the bounded gorenstein derived categories of gorenstein rings and of finite dimensional algebras are explicitly described via the homotopy categories of gorenstein projective modules and some applications are obtained gorenstein derived equivalences between cm finite gorenstein algebras are discussed

n representation infinite algebras abstract from the viewpoint of higher dimensional auslander reiten theory we introduce a new class of finite dimensional algebras of global dimension n which we call n representation infinite they are a certain analog of representation infinite hereditary algebras and we study three important classes of modules n preprojective n preinjective and n regular modules we observe that their homological behaviour is quite interesting for instance they provide first examples of algebras having infinite ext 1 orthogonal families of modules moreover we give general constructions of n representation infinite algebras applying minamoto s theory on fano algebras in non commutative algebraic geometry we describe the category of n regular modules in terms of the corresponding preprojective algebra then we introduce n representation tame algebras and show that the category of n regular modules decomposes into the categories of finite dimensional modules over localizations of the preprojective algebra this generalizes the classical description of regular modules over tame hereditary algebras as an application we show that the representation dimension of an n representation tame algebra is at least n 2

dimensions of triangulated categories via koszul objects lower bounds for the dimension of a triangulated category are provided these bounds are applied to stable derived categories of artin algebras and of commutative complete intersection local rings as a consequence one obtains bounds for the representation dimensions of certain artin algebras

the random subspace method for constructing decision forests much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes the dilemma between overfitting and achieving maximum accuracy is seldom resolved a method to construct a decision tree based classifier is proposed that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity the classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector that is trees constructed in randomly chosen subspaces the subspace method is compared to single tree classifiers and other forest construction methods by experiments on publicly available datasets where the method s superiority is demonstrated we also discuss independence between trees in a forest and relate that to the combined classification accuracy

the representation dimension of k x y x2 yn the representation dimension of an artin algebra was defined by m auslander in 1970 the precise value is not known in general and is very hard to compute even for small examples for group algebras it is known in the case of cyclic sylow subgroups for some group algebras in characteristic 2 of rank at least 3 the precise value of the representation dimension follows from recent work of r rouquier there is a gap for group algebras of rank 2 in this paper we show that for all n 0 and any field k the commutative algebras k x y x2 y2 n have representation dimension 3 for the proof we give an explicit inductive construction of a suitable generator cogenerator as a consequence we obtain that the group algebras in characteristic 2 of the groups c2 c2m have representation dimension 3 note that for m 3 these group algebras have wild representation type

orlov spectra bounds and gaps the orlov spectrum is a new invariant of a triangulated category it was introduced by d orlov building on work of a bondal m van den bergh and r rouquier the supremum of the orlov spectrum of a triangulated category is called the ultimate dimension in this work we study orlov spectra of triangulated categories arising in mirror symmetry we introduce the notion of gaps and outline their geometric significance we provide the first large class of examples where the ultimate dimension is finite categories of singularities associated to isolated hypersurface singularities similarly given any nonzero object in the bounded derived category of coherent sheaves on a smooth calabi yau hypersurface we produce a generator by closing the object under a certain monodromy action and uniformly bound this generator s generation time in addition we provide new upper bounds on the generation times of exceptional collections and connect generation time to braid group actions to provide a lower bound on the ultimate dimension of the derived fukaya category of a symplectic surface of genus greater than one

invariant properties of representations under excellent extensions abstract in this paper we introduce the notion of weak excellent extensions of rings as a generalization of that of excellent extensions of rings let be a weak excellent extension of an artinian algebra we prove that if is of finite representation type resp cm finite cm free then so is furthermore if is an excellent extension of then the converse also holds true we also study when the representation dimension of an artinian algebra is invariant under excellent extensions

coherence and the speech intelligibility index the speech intelligibility index sii ansi s3 5 1997 provides a means for estimating speech intelligibility under conditions of additive stationary noise or bandwidth reduction the sii concept for estimating intelligibility is extended in this paper to include broadband peak clipping and center clipping distortion with the coherence between the input and output signals used to estimate the noise and distortion effects the speech intelligibility predictions using the new procedure are compared with intelligibility scores obtained from normal hearing and hearing impaired subjects for conditions of additive noise and peak clipping and center clipping distortion the most effective procedure divides the speech signal into low mid and high level regions computes the coherence sii separately for the signal segments in each region and then estimates intelligibility from a weighted combination of the three coherence sii values

cohomological symmetry in triangulated categories abstract we give a criterion for cohomological symmetry in a triangulated category as an application we show that such cohomological symmetry holds for all pairs of modules over any exterior algebra

noncommutative complete intersections abstract several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded k algebra these notions are justified by examples from noncommutative invariant theory

the avrunin scott theorem for quantum complete intersections abstract we prove the avrunin scott theorem for quantum complete intersections relating the rank variety of a module to its support variety

ideals in triangulated categories phantoms ghosts and skeleta we begin by showing that in a triangulated category specifying a projective class is equivalent to specifying an ideal i of morphisms with certain properties and that if i has these properties then so does each of its powers we show how a projective class leads to an adams spectral sequence and give some results on the convergence and collapsing of this spectral sequence we use this to study various ideals in the stable homotopy category we examine phantom maps skeletal phantom maps superphantom maps and ghosts a ghost is a map which induces the zero map of homotopy groups we show that ghosts lead to a stable analogue of the lusternik schnirelmann category of a space and we calculate this stable analogue for low dimensional real projective spaces we also give a relation between ghosts and the hopf and kervaire invariant problems in the case ofa modules over ana ring spectrum the ghost spectral sequence is a universal coefficient spectral sequence from the phantom projective class we derive a generalized milnor sequence for filtered diagrams of finite spectra and from this it follows that the group of phantom maps fromxtoycan always be described as alim 1group the last two sections focus on algebraic examples in the derived category of an abelian category we study the ideal of maps inducing the zero map of homology groups and find a natural setting for a result of kelly on the vanishing of composites of such maps we also explain how pure exact sequences relate to phantom maps in the derived category of a ring and give an example showing that phantoms can compose non trivially

a hybrid system with filter approach and multiple population genetic algorithm for feature selection in credit scoring abstract with the financial crisis happened in 2007 massive credit risks are exposed to the banking sectors so credit scoring has attracted more and more attention bank owns a lot of customer data by using those data credit scoring model can judge the applicants credit risk accurately but those data are often high dimensional and have some irrelevant features those irrelevant features will affect classifiers accuracy therefore feature selection is an important topic this paper proposes a two phase hybrid approach based on filter approach and multiple population genetic algorithm hmpga in phase 1 it introduces the idea of wrapper approach into three filter approaches to acquire some important prior information for initial populations setting of mpga in phase 2 it takes advantage of mpga s characteristics of global optimization and quick convergence to find optimal feature subset this paper uses two real credit scoring datasets of uci databases to compare hmpga mpga and ga it verifies that the accuracies of feature subsets acquired from hmpga mpga and ga are superior to three filter approaches meanwhile nonparametric wilcoxon signed rank test is held to confirm that hmpga is better than mpga and ga hmpga not only can be applied to feature selection of credit scoring but also can be applied to more fields of data mining

powers of the phantom ideal the mono epi me exact structure on the morphisms of an exact category a e is introduced and used to prove ideal versions of salce s lemma christensen s ghost lemma and wakamatsu s lemma for an exact category salce s lemma establishes a bijective correspondence i i between the class of special precovering ideals of a e and that of its special preenveloping ideals me extensions of morphisms are used to define an extension i j of ideals christensen s lemma asserts that the class of special precovering respectively special preenveloping ideals is closed under products and extensions and that the bijective correspondence of salce s lemma satisfies ij j i and i j j i wakamatsu s lemma asserts that if a covering ideal i is closed under me extensions then it is a special precovering ideal as an application it is proved that if g is a finite group and is the ideal of phantom morphisms in the category k g mod then n 1 is the object ideal generated by projective modules where n is the nilpotency index of the jacobson radical j if r is a semiprimary ring with jn 0 then n is generated by projective modules for a right coherent ring r over which every cotorsion left r module has a coresolution of length n by pure injective modules n 1 is generated by flat modules

lower bounds for auslander s representation dimension the notion of representation dimension of a finite dimensional algebra has been introduced by auslander he has shown that an algebra is of finite representation type if and only if its representation dimension is at most two he has expected that the representation dimension of a representation infinite algebra should measure how far this algebra is from being representation finite in many cases and thanks to iyama also in general upper bounds for the representation dimension are known however there are non trivial lower bounds only for two similarly constructed series of algebras in this thesis new lower bounds for auslander s representation dimension are constructed and more general methods are developed first we consider group algebras of elementary abelian groups we show that their representation dimension is greater than the rank of the group this leads to a proof of a conjecture of benson concerning the loewy length of blocks of group algebras then a notion of dimension of a module category is introduced this notion enables us to find better lower bounds for the representation dimension in particular it allows us for the first time to determine the value of the representation dimension of non self injective algebras of representation dimension greater than three finally we give a general criterion for finding lower bounds for auslander s representation dimension suppose there is a family of modules such that sufficiently many members of the family have certain d extensions then the representation dimension of the algebra is at least d 2 we illustrate how this criterion is applied on some interesting families of algebras it turns out that the lower bound is often the precise value of the representation dimension

greedy function approximation a gradient boosting machine function estimation approximation is viewed from the perspective of numerical optimization in function space rather than parameter space a connection is made between stagewise additive expansions and steepest descent minimization a general gradient descent boosting paradigm is developed for additive expansions based on any fitting criterion specific algorithms are presented for least squares least absolute deviation and huber m loss functions for regression and multiclass logistic likelihood for classification special enhancements are derived for the particular case where the individual additive components are regression trees and tools for interpreting such treeboost models are presented gradient boosting of regression trees produces competitive highly robust interpretable procedures for both regression and classification especially appropriate for mining less than clean data connections between this approach and the boosting methods of freund and shapire and friedman hastie and tibshirani are discussed

model selection beyond the bayesian frequentist divide the principle of parsimony also known as ockham s razor has inspired many theories of model selection yet such theories all making arguments in favor of parsimony are based on very different premises and have developed distinct methodologies to derive algorithms we have organized challenges and edited a special issue of jmlr and several conference proceedings around the theme of model selection in this editorial we revisit the problem of avoiding overfitting in light of the latest results we note the remarkable convergence of theories as different as bayesian theory minimum description length bias variance tradeoff structural risk minimization and regularization in some approaches we also present new and interesting examples of the complementarity of theories leading to hybrid algorithms neither frequentist nor bayesian or perhaps both frequentist and bayesian

ranking a random feature for variable and feature selection we describe a feature selection method that can be applied directly to models that are linear with respect to their parameters and indirectly to others it is independent of the target machine it is closely related to classical statistical hypothesis tests but it is more intuitive hence more suitable for use by engineers who are not statistics experts furthermore some assumptions of classical tests are relaxed the method has been used successfully in a number of applications that are briefly described

auslander type conditions and cotorsion pairs we study the properties of rings satisfying auslander type conditions if an artin algebra satisfies the auslander condition that is is an gorenstein artin algebra then we construct two kinds of subcategories which form functorially finite cotorsion pairs

the green correspondence for the representations of hecke algebras of type ᵣ we first prove the conjecture mentioned by leonard k jones in his thesis by applying this conjecture we obtain that the vertex of an indecomposable xf module is an i parabolic subgroup finally we establish the green correspondence for the representations of hecke algebras of type ar

gene selection with guided regularized random forest the regularized random forest rrf was recently proposed for feature selection by building only one ensemble in rrf the features are evaluated on a part of the training data at each tree node we derive an upper bound for the number of distinct gini information gain values in a node and show that many features can share the same information gain at a node with a small number of instances and a large number of features therefore in a node with a small number of instances rrf is likely to select a feature not strongly relevant here an enhanced rrf referred to as the guided rrf grrf is proposed in grrf the importance scores from an ordinary random forest rf are used to guide the feature selection process in rrf experiments on 10 gene data sets show that the accuracy performance of grrf is in general more robust than rrf when their parameters change grrf is computationally efficient can select compact feature subsets and has competitive accuracy performance compared to rrf varselrf and lasso logistic regression with evaluations from an rf classifier also rf applied to the features selected by rrf with the minimal regularization outperforms rf applied to all the features for most of the data sets considered here therefore if accuracy is considered more important than the size of the feature subset rrf with the minimal regularization may be considered we use the accuracy performance of rf a strong classifier to evaluate feature selection methods and illustrate that weak classifiers are less capable of capturing the information contained in a feature subset both rrf and grrf were implemented in the rrf r package available at cran the official r package archive

dimensions of triangulated categories with respect to subcategories abstract this paper introduces a concept of dimension of a triangulated category with respect to a fixed full subcategory for the bounded derived category of an abelian category upper bounds of the dimension with respect to a contravariantly finite subcategory and a resolving subcategory are given our methods not only recover some known results on the dimensions of derived categories in the sense of rouquier but also apply to various commutative and non commutative noetherian rings

generalizing the notion of koszul algebra we introduce a generalization of the notion of a koszul algebra which includes graded algebras with relations in different degrees and we establish some of the basic properties of these algebras this class is closed under twists twisted tensor products regular central extensions and ore extensions we explore the monomial algebras in this class and we include some well known examples of algebras that fall into this class

representation dimension of exterior algebras we determine the representation dimension of exterior algebras this provides the first known examples of representation dimension 3 we deduce that the loewy length of the group algebra over f2 of a finite group is strictly bounded below by the 2 rank of the group a conjecture of benson a key tool is the use of the concept of dimension of a triangulated category

on the finitistic dimension conjecture of artin algebras abstract let a be an artin algebra and e be an idempotent element of a we prove that if a has representation dimension at most three then the finitistic dimension of eae is finite and deduce that if quasi hereditary algebras have representation dimensions at most three then the finitistic dimension conjecture holds

on subcategories closed under predecessors and the representation dimension abstract let be an artin algebra a and c be full subcategories of the category of finitely generated modules consisting of indecomposable modules and closed under predecessors and successors respectively in this paper we relate under various hypotheses the representation dimension of to those of the left support algebra of a and the right support algebra of c our results are then applied to the classes of laura algebras ada algebras and nakayama oriented pullbacks

on the structure and cohomology ring of connected hopf algebras abstract let p be a prime and k be a field of characteristic p we investigate the algebra structure and the structure of the cohomology ring for the connected hopf algebras of dimension p 3 which appear in the classification obtained in 20 the list consists of 23 algebras together with two infinite families we identify the morita type of the algebra and in almost all cases this is sufficient to clarify the structure of the cohomology ring