precovers and orthogonality in the stable module category abstract we show that any module admits a presentation as the quotient of a gorenstein projective module by a submodule which is itself right orthogonal with respect to the standard ext 1 pairing to the class of gorenstein projective modules of type fp for that purpose we use the concept of orthogonality in the stable module category and examine the orthogonal pair which is induced therein by the class of completely finitary gorenstein projective modules

cohen macaulay modules co torsion pairs and virtually gorenstein algebras abstract we use torsion pairs in stable categories and cotorsion pairs in modules categories to study in general infinitely generated cohen macaulay modules and a generalization of modules of finite projective or injective dimension over an artin algebra we concentrate our investigation to the study of virtually gorenstein algebras which provide a common generalization of gorenstein algebras and algebras of finite representation or cohen macaulay type this class of algebras on the one hand has rich homological structure and satisfies several representation torsion theoretic finiteness conditions and on the other hand it is closed under various operations for instance derived equivalences and stable equivalences of morita type in addition virtual gorensteinness provides a useful tool for the study of the gorenstein symmetry conjecture and modified versions of the telescope conjecture for module or stable categories

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

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

the left and right parts of the module category of crossed product group algebras let g be a finite group k be a field with characteristic not dividing the order of g a nd b e at wistedkg module algebra such that g or g for short exists as a crossed product algebra in this paper we study the relationship between the class l g or r g which consists of all finitely generated indecomposable g modules whose predecessors or successors have projective dimension or injective dimension at most one and the class l or r then we study those properties which rely on the left or right part of that are preserved under the extension of crossed product group algebra g

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

tilting categories with applications to stratifying systems abstract in the study of standardly stratified algebras and stratifying systems we find an object which is either a tilting module or one whose properties strongly remind us of a tilting module this tilting module appeared already in dlab and ringel s work on quasi hereditary algebras see v dlab c m ringel the module theoretical approach to quasi hereditary algebras in repr theory and related topics in london math soc lecture note ser 168 1992 200 224 and c m ringel the category of modules with good filtrations over a quasi hereditary algebra has almost split sequences math z 208 1991 209 223 also this tilting module appears on the work on standardly stratified algebras of i agoston d happel e lukacs and l unger and in the paper of m i platzeck and i reiten see i agoston d happel e lukacs l unger standardly stratified algebras and tilting j algebra 226 2000 144 160 and m i platzeck i reiten modules of finite projective dimension for standardly stratified algebras comm algebra 29 3 2001 973 986 inspired by them we introduce the notion of tilting category in order to give a unified approach of these situations for stratifying systems to do so we use the ideas of m auslander o buchweitz and i reiten related to approximation theory see m auslander r o buchweitz the homological theory of maximal cohen macaulay approximations mem soc math fr n s 38 1989 5 37 m auslander i reiten applications of contravariantly finite subcategories adv math 86 1991 111 152

a conservative discrete ordinate method for solving semiclassical boltzmann bgk equation with maxwell type wall boundary condition a robust and efficient numerical method in phase space combining the conservative discrete ordinate method and high order spatial discretization is proposed for the semiclassical boltzmann equation with bhatnagar gross krook bgk relaxation time approximation a general maxwell type partially diffuse and partially specular reflection solid wall boundary condition for modeling the gas surface interactions for semiclassical rarefied gas flows is devised the discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term the high order weighted essentially non oscillatory scheme is then implemented to evolve the solution in physical space and time the conservation property of the bgk collision integral is ensured to be fulfilled at the discrete quadrature level approximation both specular and diffuse reflection boundary conditions are implemented extensive computations of one and two dimensional semiclassical rarefied gas dynamical flows covering wide range of flow regimes for three statistics are presented to illustrate the method and boundary conditions treatment the effect of accommodation coefficient on the rarefied flow field is also examined

syzygy modules for quasi k gorenstein rings abstract let be a right quasi k gorenstein ring for each dth syzygy module m in mod where 0 d k 1 we obtain an exact sequence 0 b m p c 0 in mod with the properties that it is dual exact p is projective c is a d 1 st syzygy module b is a dth syzygy of ext op d 1 tr m and the right projective dimension of b is less than or equal to d 1 we then give some applications of such an exact sequence as follows 1 we obtain a chain of epimorphisms concerning m and by dualizing it we then get the spherical filtration of auslander and bridger for m 2 we get auslander and bridger s approximation theorem for each reflexive module in mod op 3 we show that for any 0 d k 1 each dth syzygy module in mod has an evans griffith presentation as an immediate consequence of 3 we have that if is a commutative noetherian ring with finite self injective dimension then for any non negative integer d each dth syzygy module in mod has an evans griffith presentation which generalizes an evans and griffith s result to much more general setting

standard stratifications of ei categories and alperin s weight conjecture abstract we characterize the finite ei categories whose representations are standardly stratified with respect to the natural preorder on the simple representations the orbit category of a finite group with respect to any set of subgroups is always such a category taking the subgroups to be the p subgroups of the group we reformulate alperin s weight conjecture in terms of the standard and proper costandard representations of the orbit category we do this using the properties of the ringel dual construction and a theorem of dlab which have elsewhere been described for standardly stratified algebras where there is a partial order on the simple modules we indicate that these results hold in the generality of an algebra whose simple modules are preordered rather than partially ordered

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

tilting modules over an algebra by igusa smalo and todorov abstract the finiteness of the little finitistic dimension of an artin algebra r is known to be equivalent to the existence of a tilting r module t such that t p where p is the category of all finitely presented r modules of finite projective dimension moreover t can be taken finitely generated if and only if p is contravariantly finite in this paper we describe explicitly the structure of t for the ist algebra a finite dimensional algebra with p not contravariantly finite we also characterize the indecomposable modules in p and all tilting classes over this algebra

singular equivalence of morita type with level abstract we generalize the notion of stable equivalence of morita type and define what is called singular equivalence of morita type with level such an equivalence induces an equivalence between singular categories we will also prove that a derived equivalence of standard type induces a singular equivalence of morita type with level

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

cotorsion torsion triples and the representation theory of filtered hierarchical clustering abstract we give a full classification of representation types of the subcategories of representations of an m n rectangular grid with monomorphisms dually epimorphisms in one or both directions which appear naturally in the context of clustering as two parameter persistent homology in degree zero we show that these subcategories are equivalent to the category of all representations of a smaller grid modulo a finite number of indecomposables this equivalence is constructed from a certain cotorsion torsion triple which is obtained from a tilting subcategory generated by said indecomposables

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

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

order preserving moves for graph cut based optimization in the last decade graph cut optimization has been popular for a variety of labeling problems typically graph cut methods are used to incorporate smoothness constraints on a labeling encouraging most nearby pixels to have equal or similar labels in addition to smoothness ordering constraints on labels are also useful for example in object segmentation a pixel with a car wheel label may be prohibited above a pixel with a car roof label we observe that the commonly used graph cut alpha expansion move algorithm is more likely to get stuck in a local minimum when ordering constraints are used for a certain model with ordering constraints we develop new graph cut moves which we call order preserving the advantage of order preserving moves is that they act on all labels simultaneously unlike alpha expansion more importantly for most labels alpha the set of alpha expansion moves is strictly smaller than the set of order preserving moves this helps to explain why in practice optimization with order preserving moves performs significantly better than alpha expansion in the presence of ordering constraints we evaluate order preserving moves for the geometric class scene labeling introduced by hoiem et al where the goal is to assign each pixel a label such as sky ground etc so ordering constraints arise naturally in addition we use order preserving moves for certain simple shape priors in graph cut segmentation which is a novel contribution in itself

exact optimization for markov random fields with convex priors we introduce a method to solve exactly a first order markov random field optimization problem in more generality than was previously possible the mrf has a prior term that is convex in terms of a linearly ordered label set the method maps the problem into a minimum cut problem for a directed graph for which a globally optimal solution can be found in polynomial time the convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method

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

singular equivalence and the fg condition abstract we show that singular equivalences of morita type with level between finite dimensional gorenstein algebras over a field preserve the fg condition

dimension estimates for representable equivalences of module categories abstract letrbe a ring pbe a module ands end p inspired by the tilting theory we investigate relations between the global dimensions gl dim rand gl dim s and between the structure of the grothendieck groupsk0 mod r andk0 mod s we prove that gl dim s gl dim r d whered 1 e g forpalmost tilting but the symmetry fails for eachn n ifris right artinian andsright noetherian then there is an isomorphism k 0 mod s k 0 mod r where r r ann r p we also prove that ifrandr are right artinian rings such that there is a torsion theory counter equivalence between mod rand mod r thenk0 mod r k0 mod r

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

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

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

enright s completions and injectively copresented modules let 21 be a finite dimensional simple lie algebra over the complex numbers it is shown that a module is complete or relatively complete in the sense of enright if and only if it is injectively copresented by certain injective modules in the bgg category o let a be the finite dimensional algebra associated to a block of o then the corresponding block of the category of complete modules is equivalent to the category of eae modules for a suitable choice of the idempotent e using this equivalence a very easy proof is given for deodhar s theorem also proved by bouaziz that completion functors satisfy braid relations the algebra eae is left properly and standardly stratified it satisfies a double centralizer property similar to soergel s combinatorial description of o its simple objects their characters and their multiplicities in projective or standard objects are determined

derived equivalences induced by big cotilting modules abstract we prove that given a grothendieck category g with a tilting object of finite projective dimension the induced triangle equivalence sends an injective cogenerator of g to a big cotilting module moreover every big cotilting module can be constructed like that in an essentially unique way we also prove that the triangle equivalence is at the base of an equivalence of derivators which in turn is induced by a quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes

partial tilting and cotilting bimodules abstract let r and s be arbitrary associative rings the purpose of this paper is to study the equivalences induced by hom r v v s and their derived functors and the dualities induced by hom r w hom s w and their derived functors with v s r partial tilting bimodule and w s r partial cotilting bimodule without any finiteness condition

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

three results on frobenius categories this paper consists of three results on frobenius categories 1 we give sufficient conditions on when a factor category of a frobenius category is still a frobenius category 2 we show that any frobenius category is equivalent to an extension closed exact subcategory of the frobenius category formed by cohen macaulay modules over some additive category this is an analogue of gabriel quillen s embedding theorem for frobenius categories 3 we show that under certain conditions an exact category with enough projective and enough injective objects allows a natural new exact structure with which the given category becomes a frobenius category several applications of the results are discussed

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

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

turbopixels fast superpixels using geometric flows we describe a geometric flow based algorithm for computing a dense oversegmentation of an image often referred to as superpixels it produces segments that on one hand respect local image boundaries while on the other hand limiting undersegmentation through a compactness constraint it is very fast with complexity that is approximately linear in image size and can be applied to megapixel sized images with high superpixel densities in a matter of minutes we show qualitative demonstrations of high quality results on several complex images the berkeley database is used to quantitatively compare its performance to a number of oversegmentation algorithms showing that it yields less undersegmentation than algorithms that lack a compactness constraint while offering a significant speedup over n cuts which does enforce compactness

from triangulated categories to module categories via localisation we show that the category of finite dimensional modules over the endomorphism algebra of a rigid object in a hom finite triangulated category is equivalent to the gabriel zisman localisation of the category with respect to a certain class of maps this generalises the 2 calabi yau tilting theorem of keller reiten in which the module category is obtained as a factor category to the rigid case

an efficient direct solver for rarefied gas flows with arbitrary statistics a new numerical methodology associated with a unified treatment is presented to solve the boltzmann bgk equation of gas dynamics for the classical and quantum gases described by the bose einstein and fermi dirac statistics utilizing a class of globally stiffly accurate implicit explicit runge kutta scheme for the temporal evolution associated with the discrete ordinate method for the quadratures in the momentum space and the weighted essentially non oscillatory method for the spatial discretization the proposed scheme is asymptotic preserving and imposes no non linear solver or requires the knowledge of fugacity and temperature to capture the flow structures in the hydrodynamic euler limit the proposed treatment overcomes the limitations found in the work by yang and muljadi 2011 33 due to the non linear nature of quantum relations and can be applied in studying the dynamics of a gas with internal degrees of freedom with correct values of the ratio of specific heat for the flow regimes for all knudsen numbers and energy wave lengths the present methodology is numerically validated with the unified treatment by the one dimensional shock tube problem and the two dimensional riemann problems for gases of arbitrary statistics descriptions of ideal quantum gases including rotational degrees of freedom have been successfully achieved under the proposed methodology

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

upwind finite difference solution of boltzmann equation applied to electron transport in semiconductor devices we present a new numerical method for solving the boltzmann poisson system which describes charge transport in semiconductor devices the boltzmann equation is reduced from three dimensions in velocity space to two by taking the electric field parallel to the z axis which implies invariance of the probability density function under rotation around the z axis we develop a finite difference discretization of the boltzmann equation in one spatial dimension and two dimensional velocity space coupled to the poisson equation the system of equations obtained by taking the first five moments of the boltzmann equation coupled to the poisson equation is known as the hydrodynamic model in semiconductor modeling a comparison of the numerical results from our method and the hydrodynamic model is given also a numerical investigation is done with respect to the heat conduction viscosity and momentum relaxation terms in the hydrodynamic model

representation theoretic properties of balanced big cohen macaulay modules let r mathfrak m k be a complete cohen macaulay local ring in this paper we assign a numerical invariant for any balanced big cohen macaulay module called underline mathsf h length among other results it is proved that for a given balanced big cohen macaulay r module m with an mathfrak m primary cohomological annihilator if there is a bound on the underline mathsf h length of all modules appearing in mathsf cm support of m then it is fully decomposable i e it is a direct sum of finitely generated modules while the first brauer thrall conjecture fails in general by a counterexample of dieterich dealing with multiplicities to measure the size of maximal cohen macaulay modules our formalism establishes the validity of the conjecture for complete cohen macaulay local rings in addition the pure semisimplicity of a subcategory of balanced big cohen macaulay modules is settled namely it is shown that r is of finite mathsf cm type if and only if r is an isolated singularity and the category of all fully decomposable balanced big cohen macaulay modules is closed under kernels of epimorphisms finally we examine the mentioned results in the context of cohen macaulay artin algebras admitting a dualizing bimodule omega as defined by auslander and reiten it will turn out that omega gorenstein projective modules with bounded mathsf cm support are fully decomposable in particular a cohen macaulay algebra lambda is of finite mathsf cm type if and only if every omega gorenstein projective module is of finite mathsf cm type which generalizes a result of chen for gorenstein algebras our main tool in the proof of results is gabriel roiter co measure an invariant assigned to modules of finite length and defined by gabriel and ringel this in fact provides an application of the gabriel roiter co measure in the category of maximal cohen macaulay modules

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

shortest path constraints for 3d multiobject semiautomatic segmentation via clustering and graph cut we derive shortest path constraints from graph models of structure adjacency relations and introduce them in a joint centroidal voronoi image clustering and graph cut multiobject semiautomatic segmentation framework the vicinity prior model thus defined is a piecewise constant model incurring multiple levels of penalization capturing the spatial configuration of structures in multiobject segmentation qualitative and quantitative analyses and comparison with a potts prior based approach and our previous contribution on synthetic simulated and real medical images show that the vicinity prior allows for the correct segmentation of distinct structures having identical intensity profiles and improves the precision of segmentation boundary placement while being fairly robust to clustering resolution the clustering approach we take to simplify images prior to segmentation strikes a good balance between boundary adaptivity and cluster compactness criteria furthermore allowing to control the trade off compared with a direct application of segmentation on voxels the clustering step improves the overall runtime and memory footprint of the segmentation process up to an order of magnitude without compromising the quality of the result

rarefied flow computations using nonlinear model boltzmann equations high resolution finite difference schemes for solving the nonlinear model boltzmann equations are presented for the computations of rarefied gas flows the discrete ordinate method is first applied to remove the velocity space dependency of the distribution function which renders the model boltzmann equation in phase space to a set of hyperbolic conservation laws with source terms in physical space then a high order essentially nonoscillatory method due to harten et al j comput phys 71 231 1987 is adapted and extended to solve them explicit methods using operator splitting and implicit methods using the lower upper factorization are described to treat multidimensional problems the methods are tested for both steady and unsteady rarefied gas flows to illustrate its potential use the computed results using model boltzmann equations are found to compare well both with those using the direct simulation monte carlo results in the transitional regime flows and those with the continuum navier stokes calculations in near continuum regime flows

reconstruction of path algebras from their posets of tilting modules let a k be the path algebra of a finite quiver without orientedcycles the set of isomorphism classes of multiplicity free tilting modules is in a natural way a partially ordered set we will show here that t a uniquely determines if has no multiple arrows and no isolated vertices

simulation of shock wave diffraction over 90 sharp corner in gases of arbitrary statistics the unsteady shock wave diffraction over a 90 sharp corner in gases of arbitrary particle statistics is simulated using an accurate and direct algorithm for solving the semiclassical boltzmann equation with relaxation time approximation in phase space the numerical method is based on the usage of discrete ordinate method for discretizing the velocity space of the distribution function whereas a second order accurate tvd scheme harten in j comput phys 49 3 357 393 1983 with van leer s limiter j comput phys 32 1 101 136 1979 is used for evolving the solution in physical space and time the specular reflection surface boundary condition is assumed the complete diffraction patterns are recorded using various flow property contours different range of relaxation times approximately corresponding to continuum slip and transitional regimes are considered and the equilibrium euler limit solution is also computed for comparison the effects of gas particles that obey the maxwell boltzmann bose einstein and fermi dirac statistics are examined and depicted

an auslander buchweitz approximation approach to pre silting subcategories in triangulated categories abstract we apply the auslander buchweitz approximation triangles to study pre silting subcategories in a triangulated catego ry t an auslander reiten type correspondence between the class of silting subcategories of t and that of certain covariantly finite subcategories of t is established we introduce a relation on presilting subcategories of t which can be used to obtain another silting subcategory from a given one we also give a bazzoni s characterization for two presilting subcategories satisfying such a relation the results can be used to improve the auslander reiten type correspondence and bazzoni s characterization for small silting complexes established by wei

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

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 galois coverings and tilting modules abstract let a be a basic connected finite dimensional algebra over an algebraically closed field k let t be a basic tilting a module with arbitrary finite projective dimension for a fixed group g we compare the set of isoclasses of connected galois coverings of a with group g and the set of isoclasses of connected galois coverings of end a t with group g using the hasse diagram k a see d happel l unger on a partial order of tilting modules algebr represent theory 8 2 2005 147 156 and c riedtmann a schofield on a simplicial complex associated with tilting modules comment math helv 66 1 1991 70 78 of basic tilting a modules we give sufficient conditions on t under which there is a bijection between these two sets these conditions are always verified when a is of finite representation type then we apply these results to study when the simple connectedness of a implies the one of end a t see i assem e n marcos j a de la pena the simple connectedness of a tame tilted algebra j algebra 237 2 2001 647 656 finally using an argument due to w crawley boevey we prove that the type of any simply connected tilted algebra is a tree and that its first hochschild cohomology group vanishes

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

selforthogonal modules with finite injective dimension ii let be a left and right artin ring and a faithfully balanced selforthogonal bimodule we give a sufficient condition that the injective dimension of is finite implies that of is also finite

persistence based clustering in riemannian manifolds we present a clustering scheme that combines a mode seeking phase with a cluster merging phase in the corresponding density map while mode detection is done by a standard graph based hill climbing scheme the novelty of our approach resides in its use of topological persistence to guide the merging of clusters our algorithm provides additional feedback in the form of a set of points in the plane called a persistence diagram pd which provably reflects the prominences of the modes of the density in practice this feedback enables the user to choose relevant parameter values so that under mild sampling conditions the algorithm will output the correct number of clusters a notion that can be made formally sound within persistence theory in addition the output clusters have the property that their spatial locations are bound to the ones of the basins of attraction of the peaks of the density the algorithm only requires rough estimates of the density at the data points and knowledge of approximate pairwise distances between them it is therefore applicable in any metric space meanwhile its complexity remains practical although the size of the input distance matrix may be up to quadratic in the number of data points a careful implementation only uses a linear amount of memory and takes barely more time to run than to read through the input

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

homological domino effects and the first finitistic dimension conjecture counterexamples to the first finitistic dimension conjecture are constructed in fact for any fieldk and any integerm 2 there exist finite dimensionalk algebras such that the little finitistic dimension of ism while the big finitistic dimension ism 1 our examples are monomial relation algebras within this class of algebras the big and little finitistic dimensions cannot differ by more than 1 the analysis of the examples is based on a sharp picture of arbitrary second syzygies over monomial relation algebras

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

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

a comparative study of energy minimization methods for markov random fields with smoothness based priors among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel labeling tasks such as depth or texture computation it has been known for decades that such problems can be elegantly expressed as markov random fields yet the resulting energy minimization problems have been widely viewed as intractable algorithms such as graph cuts and loopy belief propagation lbp have proven to be very powerful for example such methods form the basis for almost all the top performing stereo methods however the trade offs among different energy minimization algorithms are still not well understood in this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and runtime of several common energy minimization algorithms we investigate three promising methods graph cuts lbp and tree reweighted message passing in addition to the well known older iterated conditional mode icm algorithm our benchmark problems are drawn from published energy functions used for stereo image stitching interactive segmentation and denoising we also provide a general purpose software interface that allows vision researchers to easily switch between optimization methods the benchmarks code images and results are available at http vision middlebury edu mrf

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

gorenstein defect categories of triangular matrix algebras abstract we apply the technique of recollement to study the gorenstein defect categories of triangular matrix algebras first we construct a left recollement of gorenstein defect categories for a triangular matrix algebra under some conditions using it we give a categorical interpretation of the gorenstein properties of the triangular matrix algebras obtained by x w chen b l xiong and p zhang respectively second under some additional conditions a recollement of gorenstein defect categories for a triangular matrix algebra is constructed as an application for a special kind of triangular matrix algebras which are called simple gluing algebras we describe their singularity categories and gorenstein defect categories

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

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