proper resolutions and gorenstein categories abstract let a be an abelian category and c an additive full subcategory of a we provide a method to construct a proper c resolution resp coproper c coresolution of one term in a short exact sequence in a from that of the other two terms by using these constructions we answer affirmatively an open question on the stability of the gorenstein category g c posed by sather wagstaff sharif and white and also prove that g c is closed under direct summands in addition we obtain some criteria for computing the c dimension and the g c dimension of an object in a

classifying thick subcategories of the stable category of cohen macaulay modules abstract various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics in this paper as a higher dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p group due to benson carlson and rickard we consider classifying thick subcategories of the stable category of cohen macaulay modules over a gorenstein local ring the main result of this paper yields a complete classification of the thick subcategories of the stable category of cohen macaulay modules over a local hypersurface in terms of specialization closed subsets of the prime ideal spectrum of the ring which are contained in its singular locus

a categorification of biclosed sets of strings abstract we consider a closure space known as biclosed sets of strings of a gentle algebra of finite representation type palu pilaud and plamondon proved that the collection of all biclosed sets of strings forms a lattice and moreover that this lattice is congruence uniform many interesting examples of finite congruence uniform lattices may be represented as the lattice of torsion classes of an associative algebra we introduce a generalization the lattice of torsion shadows and we prove that the lattice of biclosed sets of strings is isomorphic to a lattice of torsion shadows when every indecomposable module over the gentle algebra is a brick finite congruence uniform lattices admit an alternate partial order known as the core label order in many cases the core label order of a congruence uniform lattice is isomorphic to a lattice of wide subcategories of an associative algebra analogous to torsion shadows we introduce wide shadows and prove that the core label order of the lattice of biclosed sets is isomorphic to a lattice of wide shadows

extending stochastic resonance for neuron models to general levy noise a recent paper by patel and kosko 2008 demonstrated stochastic resonance sr for general feedback continuous and spiking neuron models using additive levy noise constrained to have finite second moments in this brief we drop this constraint and show that their result extends to general levy noise models we achieve this by showing that large jump discontinuities in the noise can be controlled so as to allow the stochastic model to tend to a deterministic one as the noise dissipates to zero sr then follows by a forbidden intervals theorem as in patel and kosko s paper

tilting modules and auslander s gorenstein property abstract the notion of generalized tilting modules is introduced over arbitrary rings it is shown that many results on tilting modules over artin algebras are naturally generalized the auslander s gorenstein property for tilting modules is considered over noetherian rings

g dimension complete intersection dimension complexity and relative homological algebra abstract it is shown that the g dimension and the complete intersection dimension are relative projective dimensions relative auslander buchsbaum formulas are discussed new cohomology theories called complexity cohomology are constructed the new theories play the same role in identifying rings and modules with prescribed complexity as tate vogel cohomology does in identifying modules of finite projective dimension

standardly stratified algebras and tilting abstract the concept of the characteristic tilting module and of the ringel dual for quasi hereditary algebras is generalized for the setting of standardly stratified algebras

an rbf based compression method for image based relighting in image based relighting a pixel is associated with a number of sampled radiance values this paper presents a two level compression method in the first level the plenoptic property of a pixel is approximated by a spherical radial basis function srbf network that means that the spherical plenoptic function of each pixel is represented by a number of srbf weights in the second level we apply a wavelet based method to compress these srbf weights to reduce the visual artifact due to quantization noise we develop a constrained method for estimating the srbf weights our proposed approach is superior to jpeg jpeg2000 and mpeg compared with the spherical harmonics approach our approach has a lower complexity while the visual quality is comparable the real time rendering method for our srbf representation is also discussed

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

algebras with irreducible module varieties i abstract we call a finite dimensional k algebra a geometrically irreducible if for all d 0 all connected components of the affine scheme of d dimensional a modules are irreducible we show that the geometrically irreducible algebras without loops this includes all algebras of finite global dimension are the hereditary algebras we also show that truncated polynomial rings are the only geometrically irreducible local algebras finally we formulate a conjectural classification of all geometrically irreducible algebras

almost split sequences in subcategories let r be a commutative artin ring and let i be an r algebra which is a finitely generated r module in 5 auslander and reiten introduced the notion of an almost split sequence in mod a the category of finitely generated modules over a and the existence and uniqueness of such short exact sequences were established there the theory of almost split sequences developed further and similar results for certain subcategories of mod i were proved by bautista and martinez 8 and roggenkamp 9 the main purpose of this paper is to develop a more general theory for subcategories of mod i having almost split sequences which has the previous examples as special cases notions closely related to that of almost split sequences are those of minimal left and right almost split morphisms these notions were introduced in 61 for mod i and further developed in 7 for subcategories of mod ii this paper is based upon 7 and we therefore use the same notations and conventions as used there we now give some definitions and then proceed to describe the content of the paper section by section let c be a subcategory of mod ii then a morphism g b c in c is said to be a right almost split morphism in c if i g is not a splittable epimorphism and ii whenever there is a nonsplittable epimorphism h c c in c there exists an h c b such that gh h dually a morphismfi a f b in c is said to be left almost split if i f is not a splittable monomorphism and ii whenever there is a nonsplittable monomorphism h a a there exists an h b a such that h f h we say that c has right almost split morphisms if for all indecomposable objects

predicting the future advantages of semilocal units in investigating gaussian radial basis function rbf networks for their ability to model nonlinear time series we have found that while rbf networks are much faster than standard sigmoid unit backpropagation for low dimensional problems their advantages diminish in high dimensional input spaces this is particularly troublesome if the input space contains irrelevant variables we suggest that this limitation is due to the localized nature of rbfs to gain the advantages of the highly nonlocal sigmoids and the speed advantages of rbfs we propose a particular class of semilocal activation functions that is a natural interpolation between these two families we present evidence that networks using these gaussian bar units avoid the slow learning problem of sigmoid unit networks and very importantly are more accurate than rbf networks in the presence of irrelevant inputs on the mackey glass and coupled lattice map problems the speedup over sigmoid networks is so dramatic that the difference in training time between rbf and gaussian bar networks is minor gaussian bar architectures that superpose composed gaussians gaussians of gaussians to approximate the unknown function have the best performance we postulate that an interesing behavior displayed by gaussian bar functions under gradient descent dynamics which we call automatic connection pruning is an important factor in the success of this representation

endomorphism algebras of tilting modules over m replicated algebras abstract let a be a finite dimensional hereditary algebra over an algebraically closed field k and let a m be the m replicated algebra of a in this paper we investigate the structure properties of the endomorphism algebras of tilting modules of a m and prove that all the endomorphism algebras of tilting modules of a m can be realized as the iterated endomorphism algebras of bb tilting modules that is for each pair of basic tilting a m modules t 1 and t 2 there exists a series of finite dimensional algebras 0 1 s which are the endomorphism algebras of some basic tilting a m modules and for each i there is a bb tilting i module m i such that 0 end a m t 1 i end i 1 m i 1 for 1 i s and end a m t 2 end s m s

on arkhipov s and enright s functors we give a description of arkhipov s and joseph s and deodhar mathieu s versions of enright s endofunctors on the category open image in new window associated with a fixed triangular decomposition of a complex finite dimensional semi simple lie algebra in terms of co approximation functors with respect to suitably chosen injective resp projective modules we establish some new connections between these functors for example we show that arkhipov s and joseph s functors are adjoint to each other we also give several proofs of braid relations for arkhipov s and enright s functors

gorenstein projective modules and symmetric recollements we introduce compatible bimodules if m is a compatible a b bimodule then the gorenstein projective modules over algebra am0b are explicitly described and if is gorenstein then this description implies that m is compatible as an application if m is compatible then there is a left recollement of the stable category gp and if is gorenstein and ma is projective then there is a symmetric recollement of the singularity category dsgb

the transpose of modules relative to subcategories abstract let r be a left noetherian ring and s a right noetherian ring and let x be a subcategory of finitely generated left r modules and b s r a finite r s bimodule as a generalization of the auslander transpose replacing a projective presentation by an x presentation and the functor hom r r by the functor hom r b we introduce the x b transpose of an r module m admitting an x presentation for a suitable subcategory x some useful properties of x b transposes are obtained it is shown that the x b transpose shares many nice properties with the auslander transpose some known results are obtained as corollaries

maximal rigid subcategories and cluster tilting subcategories in 2 cy categories abstract let c be a connected hom finite 2 cy triangulated category we prove that if t is a functorially finite maximal rigid subcategory of c without loops in its quiver then t is cluster tilting in particular this gives a positive answer to a conjecture proposed in 5

double centralizer properties dominant dimension and tilting modules double centralizer properties play a central role in many parts of algebraic lie theory soergel s double centralizer theorem relates the principal block of the bernstein gelfand gelfand category o of a semisimple complex lie algebra with the coinvariant algebra i e the cohomology algebra of the corresponding flag manifold schur weyl duality relates the representation theories of general linear and symmetric groups in defining characteristic or via the quantized version in nondefining characteristic in this paper we exhibit algebraic structures behind these double centralizer properties we show that the finite dimensional algebras relevant in this context have dominant dimension at least two with respect to some projective injective or tilting modules general arguments which combine methods from ring theory qf 3 rings and dominant dimension with tools from representation theory approximations tilting modules then imply the validity of these double centralizer properties as well as new ones in contrast to the traditional proofs e g by the fundamental theorems of invariant theory no computations are necessary

the homological theory of quasi resolving subcategories abstract as a generalization of a resolving subcategory which was introduced by auslander and bridger in 2 the notion of a quasi resolving subcategory of an abelian category is introduced the homological theory on quasi resolving subcategories is studied it is shown that many results in 1 2 4 5 6 8 13 14 17 18 22 25 26 27 are unified and naturally generated

absolute relative and tate cohomology of modules of finite gorenstein dimension we study finitely generated modules m over a ring r noetherian on both sides if m has finite gorenstein dimension mbox g dim rm in the sense of auslander and bridger then it determines two other cohomology theories besides the one given by the absolute cohomology functors rm ext n r m relative cohomology functors rm ext n mathcal g m are defined for all non negative integers n they treat the modules of gorenstein dimension 0 as projectives and vanish for n mbox g dim rm tate cohomology functors widehat rm ext n r m are defined for all integers n all groups widehat rm ext n r m n vanish if m or n has finite projective dimension comparison morphisms varepsilon mathcal g n colon rm ext n mathcal g m to rm ext n r m and varepsilon r n colon rm ext n r m to widehat rm ext n r m link these functors we give a self contained treatment of modules of finite g dimension establish basic properties of relative and tate cohomology and embed the comparison morphisms into a canonical long exact sequence 0 to rm ext 1 mathcal g m to cdots to rm ext n mathcal g m to rm ext n r m to widehat rm ext n r m to rm ext n 1 mathcal g m to cdots we show that these results provide efficient tools for computing old and new numerical invariants of modules over commutative local rings 2000 mathematical subject classification 16e05 13h10 18g25

tilting modules of finite projective dimension tilting modules are well known and are useful in the representation theory of artinian algebras 2 4 6 11 the purpose of this paper is to define tilting modules of finite projective dimension and prove some fundamental results a unital left a module a t over a ring a is said to be a tilting module of projective dimension 0 is an integer if it satisfies the following three conditions 1 a t has a projective resolution

a spherical basis function neural network for modeling auditory space this paper describes a neural network for approximation problems on the sphere the von mises basis function is introduced whose activation depends on polar rather than cartesian input coordinates the architecture of the von mises basis function vmbf neural network is presented along with the corresponding gradient descent learning rules the vmbf neural network is used to solve a particular spherical problem of approximating acoustic parameters used to model perceptual auditory space this model ultimately serves as a signal processing engine to synthesize a virtual auditory environment under headphone listening conditions advantages of the vmbf over standard planar radial basis functions rbfs are discussed

the structure of preenvelopes with respect to maximal cohen macaulay modules abstract this paper studies the structure of special preenvelopes and envelopes with respect to maximal cohen macaulay modules we investigate the structure of them in terms of their kernels and cokernels moreover using this result we also study the structure of special proper coresolutions with respect to maximal cohen macaulay modules over a henselian cohen macaulay local ring

a size insensitive integrity based fuzzy c means method for data clustering fuzzy c means fcm is one of the most popular techniques for data clustering since fcm tends to balance the number of data points in each cluster centers of smaller clusters are forced to drift to larger adjacent clusters for datasets with unbalanced clusters the partition results of fcm are usually unsatisfactory cluster size insensitive fcm csifcm dealt with cluster size sensitivity problem by dynamically adjusting the condition value for the membership of each data point based on cluster size after the defuzzification step in each iterative cycle however the performance of csifcm is sensitive to both the initial positions of cluster centers and the distance between adjacent clusters in this paper we present a cluster size insensitive integrity based fcm method called siibfcm to improve the deficiency of csifcm the siibfcm method can determine the membership contribution of every data point to each individual cluster by considering cluster s integrity which is a combination of compactness and purity compactness represents the distribution of data points within a cluster while purity represents how far a cluster is away from its adjacent cluster we tested our siibfcm method and compared with the traditional fcm and csifcm methods extensively by using artificially generated datasets with different shapes and data distributions synthetic images real images and escherichia coli dataset experimental results showed that the performance of siibfcm is superior to both traditional fcm and csifcm in terms of the tolerance for distance between adjacent clusters and the flexibility of selecting initial cluster centers when dealing with datasets with unbalanced clusters

generalized tilting modules with finite injective dimension let r be a left noetherian ring s be a right noetherian ring and r be a generalized tilting module with s end r we mainly consider the conditions such that l id r 1 in this paper and obtain some characterizations for this inequality further when l id r and r id s are finite we provide the conditions such that r and s are injective as a direct application we get some necessary and sufficient conditions for a gorenstein ring to be a qf ring

feature based fuzzy classification for interpretation of mammograms abstract methods in fuzzy logic have been applied to serve as secondary classifier for a hierarchical classification model the use of this model in interpretation of mammograms is discussed also is discussed the inevitability of using a fuzzy approach in the problem finally the two different fuzzy approaches for secondary classification are compared on basis of their performance as far as clustering is concerned the idea of using a fuzzy covariance matrix 5 6 in the distance metric of the classical c means algorithm 1 3 has also been tried

a note on abelian quotient categories abstract let c be a triangulated category with a serre functor s and x a non zero contravariantly finite rigid subcategory of c then x is cluster tilting if and only if the quotient category c x is abelian and s x x 2 as an application this result generalizes the work by beligiannis

on modules with trivial self extensions throughout this note all rings will be self basic connected artin algebras over a fixed commutative local artin ring k and all modules will be finitely generated homomorphisms will be written on the opposite side of the scalars by mod a resp a mod we denote the category of all right resp left a modules for an artin algebra a the ordinary duality functor is denoted by d mod a 2 a mod i e d hom f with the minimal injective cogenerator i over k we are interested in the bimodules bta with the following properties

approximations and the little finitistic dimension of artinian rings let r be a ring and let simp r be a representative set of all simple right r modules denote by p the class of all modules which are finitely generated and have finite projective dimension the little finitistic dimension of r is defined by fdim r sup proj dim m m p let a b be the complete cotorsion theory cogenerated by p for each s simp r let fs xs s be a special a precover of s we prove that fdim r max proj dim xs s simp r provided that r is right artinian as a corollary we extend to right artinian rings the well known auslander reiten sufficient condition for finiteness of the little finitistic dimension

efficient relighting of rbf based illumination adjustable images an illumination adjustable image iai contains a large number of prerecorded images under various light directions relighting a scene under complicated lighting conditions can be achieved from the iai using the radial basis function rbf approach to represent an iai is proven to be more efficient than using the spherical harmonic approach however to represent high frequency lighting effects we need to use many rbfs hence the relighting speed could be very slow this brief investigates a partial reconstruction scheme for relighting an iai based on the locality of rbfs compared with the conventional rbf and spherical harmonics sh approaches the proposed scheme has a much faster relighting speed under the similar distortion performance

totally reflexive extensions and modules abstract we introduce the notion of totally reflexive extension of rings it unifies gorenstein orders and frobenius extensions we prove that for a totally reflexive extension a module over the extension ring is totally reflexive if and only if its underlying module over the base ring is totally reflexive

wakamatsu tilting modules abstract we study a generalization of tilting modules to modules of possibly infinite projective dimension introduced by wakamatsu in j algebra 114 1988 106 114 in particular we characterize these modules in terms of suitable subcategories of finitely generated modules and in terms of cotorsion theories

a model of head related transfer functions based on principal components analysis and minimum phase reconstruction free field to eardrum transfer functions hrtfs were measured from both ears of 10 subjects with sound sources at 265 different positions a principal components analysis of the resulting 5300 hrtf magnitude functions revealed that the hrtfs can be modeled as a linear combination of five basic spectral shapes basis functions and that this representation accounts for approximately 90 of the variance in the original hrtf magnitude functions hrtf phase was modeled by assuming that hrtfs are minimum phase functions and that interaural phase differences can be approximated by a simple time delay subjects judgments of the apparent directions of headphone presented sounds that had been synthesized from the modeled hrtfs were nearly identical to their judgments of sounds synthesized from measured hrtfs with fewer than five basis functions used in the model a less faithful reconstruction of the hrtf was produced and the frequency of large localization errors increased dramatically

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

on algebras of finite cohen macaulay type abstract we study artin algebras and commutative noetherian complete local rings r in connection with the following decomposition property of gorenstein projective modules any gorenstein projective module is a direct sum of finitely generated modules we show that the class of algebras enjoying coincides with the class of virtually gorenstein algebras of finite cohen macaulay type introduced in beligiannis and reiten 2007 27 beligiannis 2005 24 thus we solve the problem stated in chen 2008 33 this is proved by characterizing when a resolving subcategory is of finite representation type in terms of decomposition properties of its closure under filtered colimits thus generalizing a classical result of auslander 1976 9 and ringel and tachikawa 1974 63 in the commutative case if r admits a non free finitely generated gorenstein projective module then we show that r is of finite cohen macaulay type iff r is gorenstein and satisfies we also generalize a result of yoshino 2005 68 by characterizing when finitely generated modules without extensions with the ring are gorenstein projective finally we study the stable relative auslander algebra of a virtually gorenstein algebra of finite cohen macaulay type and under the presence of a cluster tilting object we give descriptions of the stable category of gorenstein projective modules in terms of the cluster category associated to the quiver of the stable relative auslander algebra in this setting we show that the cluster category is invariant under derived equivalences