relative tensor triangular chow groups for coherent algebras abstract we apply the machinery of relative tensor triangular chow groups to the action of d qcoh x the derived category of quasi coherent sheaves on a noetherian scheme x on the derived category of quasi coherent a modules d qcoh a where a is a not necessarily commutative coherent o x algebra when a is commutative we recover the tensor triangular chow groups of spec a we also obtain concrete descriptions for integral group algebras and hereditary orders over curves and we investigate the relation of these invariants to the classical ideal class group of an order an important tool for these computations is a new description of relative tensor triangular chow groups as the image of a map in the k theoretic localization sequence associated to a certain verdier localization

application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

the grothendieck duality theorem via bousfield s techniques and brown representability grothendieck proved that if f x y is a proper morphism of nice schemes then rf has a right adjoint which is given as tensor product with the relative canonical bundle the original proof was by patching local data deligne proved the existence of the adjoint by a global argument and verdier showed that this global adjoint may be computed locally in this article we show that the existence of the adjoint is an immediate consequence of brown s representability theorem lit follows almost as imme diately by smashing arguments that the adjoint is given by tensor product with a dualising complex verdier s base change theorem is an easy conse quence department of mathematics university of virginia charlottesville virginia 22903 e mail address an3rqvirginia edu this content downloaded from 157 55 39 27 on wed 07 sep 2016 06 26 19 utc all use subject to http about jstor org terms

line drawing interpretation bilateral symmetry results previously derived by the author are used to investigate the implication of bilateral symmetry in line drawings it is shown that the line drawing of an orthographically protected surface of revolution exhibits bilateral symmetry about the projection of its axis of revolution irrespective of the viewing direction barring one exception a bilaterally symmetric line drawing is necessarily the orthographic projection of a local surface of revolution whenever its symmetry axis continues to be the projection of a fixed line in space under perturbation of viewpoint the axis of revolution is the invariant preimage of the symmetry axis various line drawing causes are detailed which facilitate the deduction of invariant preimages of symmetry axes and consequently of local surfaces of revolution

analyzing skewed symmetries symmetry is pervasive in both man made objects and nature since symmetries project to skew symmetries finding axes of skew symmetry is an important vision task this paper presents a linear time algorithm for finding the axes of skew symmetry where the degree of symmetry is known first we present a review and critique of current methods for finding the axes of skew symmetry next we decompose the problem of finding skew symmetry into the subproblems of solving for the rotational parameter of a shear symmetry and recovering the shear parameter of a reflexive symmetry using this approach the authors derive a direct non heuristic moment based technique for finding the axes of skew symmetry for skew symmetric figures with degree of symmetry less than five we obtain a closed form solution the method does not rely on continuous contours but assumes there is no occlusion and requires knowing the contour s degree of symmetry it is the first algorithm to find the axes of skew symmetry ino n time where n is the number of contour points the method is especially suited to industrial applications where the degree of symmetry is often knowna priori examples of the method are presented for both real and synthetic images and an error analysis of the method is given

chiral coefficient a measure of the amount of structural chirality a new concept of quantitative measurement of chiral structure is introduced and labelled as chiral coefficient chi a distinction is made between geometric and physical chiralities and chi is defined for various physical cases few general geometrical features are discussed and it is shown that for every chiral body there exists a natural z direction depending on the physical property treated possible practical applications of this concept are discussed a few simple examples of the chiral coefficient of mass chi m for chiral molecules are treated

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

coherent sheaves on configuration schemes abstract we introduce and study configuration schemes which are obtained by glueing usual schemes along closed embeddings the category of coherent sheaves on a configuration scheme is investigated smooth configuration schemes provide alternative resolutions of singularities of usual singular schemes we consider in detail the case when the singular scheme is a union of hyperplanes in a projective space

on symmetry detection a straight line is an axis ofsymmetry of a planar figure if the figure is invariant to reflection with respect to that line the purpose of this correspondence is to describe an o n log n time algorithm for enumerating all the axes of symmetry of a planar figure which is made up of possibly intersecting segments circles points etc the solution involves a reduction of the problem to a combinatorial question on words our algorithm is optimal since we can establish an n log n time lower bound for this problem

emg to force processing iii estimation of model parameters for the human triceps surae muscle and assessment of the accuracy by means of a torque plate the parameters of the active state and the series elastic component of the hill muscle model were estimated for the human calf muscles by means of a torque plate on seven normal subjects together with the results of the calfergometer experiments part ii this yields the complete set of parameters for the emg to force processor based on the hill model part i the accuracy of the processor was assessed by means of a set of severe test contractions in which the subjects tilted on one foot at various velocities slow to as fast as possible the mechanical work m dt and the integrated torque m dt were calculated for these contractions m being the torque calculated by the emg processor and the measured angular velocity these values of the work and the integrated torque were compared to those obtained with the measured torque mm instead of m the relative error for positive work negative work and integrated torque was 6 2 14 means s d data on the peak values of m mm are also given

spectral symmetry analysis we present a spectral approach for detecting and analyzing rotational and reflectional symmetries in n dimensions our main contribution is the derivation of a symmetry detection and analysis scheme for sets of points irn and its extension to image analysis by way of local features each object is represented by a set of points s irn where the symmetry is manifested by the multiple self alignments of s the alignment problem is formulated as a quadratic binary optimization problem with an efficient solution via spectral relaxation for symmetric objects this results in a multiplicity of eigenvalues whose corresponding eigenvectors allow the detection and analysis of both types of symmetry we improve the scheme s robustness by incorporating geometrical constraints into the spectral analysis our approach is experimentally verified by applying it to 2d and 3d synthetic objects as well as real images

derived categories of nodal algebras abstract in this article we classify indecomposable objects of the derived categories of finitely generated modules over certain infinite dimensional algebras the considered class of algebras which we call nodal algebras contains such well known algebras as the complete ring of a double nodal point k x y xy and the completed path algebra of the gelfand quiver as a corollary we obtain a description of the derived category of harish chandra modules over sl 2 r we also give an algorithm which allows to construct projective resolutions of indecomposable complexes in the appendix we prove the krull schmidt theorem for homotopy categories

spherical subcategories in representation theory we introduce a new invariant for triangulated categories the poset of spherical subcategories ordered by inclusion this yields several numerical invariants like the cardinality and the height of the poset we explicitly describe spherical subcategories and their poset structure for derived categories of certain finite dimensional algebras

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

coherent sheaves on rational curves with simple double points and transversal intersections we study the derived categories of coherent sheaves on some singular projective curves and give a complete description of indecomposable objects using the technique of matrix problems

ideal classes of three dimensional sklyanin algebras abstract in this paper we classify graded reflexive ideals up to isomorphism and shift in certain three dimensional artin schelter regular algebras this classification is similar to the classification of right ideals in the first weyl algebra a problem that was completely settled recently the situation we consider is substantially more complicated however

3 d reconstruction using mirror images based on a plane symmetry recovering method three dimensional reconstruction from a perspective 2d image using mirrors is addressed the mirrors are used to form symmetrical relations between the direct image and mirror images by finding correspondences between them the 3d shape can be reconstructed by means of plane symmetry recovering method using the vanishing point two constraints are used in determining the correspondence in the case where only one mirror is used invisible parts both in the direct image and in the mirror image may still remain using multiple mirrors however occluded parts will decrease or disappear and occlusion free object reconstruction becomes possible

tilting on non commutative rational projective curves in this article we introduce a new class of non commutative projective curves and show that in certain cases the derived category of coherent sheaves on them has a tilting complex in particular we prove that the right bounded derived category of coherent sheaves on a reduced rational projective curve with only nodes and cusps as singularities can be fully faithfully embedded into the right bounded derived category of the finite dimensional representations of a certain finite dimensional algebra of global dimension two as an application of our approach we show that the dimension of the bounded derived category of coherent sheaves on a rational projective curve with only nodal or cuspidal singularities is at most two in the case of the kodaira cycles of projective lines the corresponding tilted algebras belong to a well known class of gentle algebras we work out in details the tilting equivalence in the case of the weierstrass nodal curve zy2 x3 x2z

perpendicular categories with applications to representations and sheaves this paper is concerned with the omnipresence of the formation of the subcategories right left perpendicular to a subcategory of objects in an abelian category we encounter these subcategories in various contexts the formation of quotient categories with respect to localizing subcategories cf section 2 the deletion of vertices and shrinking of arrows see 37 in the representation theory of finite dimensional algebras cf section 5 the comparison of the representation theories of different extended dynkin quivers cf section 10 the theory of tilting cf sections 4 and 6 the study of homological epimorphisms of rings cf section 4 the passage from graded modules to coherent sheaves on a possibly weighted projective variety or scheme cf section 7 and 21 the study of maximal cohen macaulay modules over surface singularities cf sections the comparison of weighted projective lines for different weight sequences cf section 9 the formation of affine and local algebras attached to path algebras of extended dynkin quivers canonical algebras and weighted projective lines cf section 11 and 21 and the concept of universal localization in 40 formation of the perpendicular category has many aspects in common with localization and allows one to dispose of localization techniques in situations not accessible to any of the classical concepts of localization this applies in particular to applications in the domain of finite dimensional algebras and their representations several applications of the methods presented in this paper are already in existence partly published or appearing in print in the near future see for instance 40 39 4 45 26 49 46 and have show the versatility of the notion of a perpendicular category it seems that right perpendicular categories first appeared as the subcategories of so called closed objects in the process of the formation of the quotient cateogory of an abelian category with respect to a localizing serre subcategory see 18 47 34 another natural occurrence is encountered in commutative algebra forming the possibly infinitely generated modules of depth 2 cf section 7 the concept and some of the central applications were first presented in a talk given by the first author at the honnef meeting in january 1985 we also note that the perfectly matching nomination perpendicular category was coined by a schofield who discovered independently the usefulness of this concept in dealing with hereditary algebras see 39 cf also section 7 the authors further acknowledge the support of the deutsche forschungsgemeinschaft spp darstellungstheorie von endlichen gruppen und endlichdimensionalen algebren throughout this paper rings are associative with unit and modules are unitary right modules mod r respectively mod r denotes the category of all respectively all finitely presented right r modules

braid group actions on derived categories of coherent sheaves this paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety x the motivation for this is m kontsevich s homological mirror conjecture together with the occurrence of certain braid group actions in symplectic geometry one of the main results is that when dim x geq 2 our braid group actions are always faithful we describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities relations with the mckay correspondence and with exceptional sheaves on fano manifolds are given moreover the case of an elliptic curve is worked out in some detail

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

radial symmetries based decomposition of cell clusters in binary and gray level images the segmentation of structures of complex cytological and histological images is a necessary intermediate step for image analysis that give rise to binary images in many cases these binary images can be rather far away from a subsequent object specific quantification because biological structures digitized by optoelectronic devices may situated close together so that they appear as one fused object in the projective image such fusions of objects may become complex so that large clusters of biological structures emerge to quantify individual objects of a cluster they must be separated the shape size and intensity variation of cells in complex organs like the brain may breed planar configurations that can be splitted only inadequate by common techniques e g watershed separation or basic morphological processing of images considering iteratively object contours suitable features of saliency can be accumulated that give rise to markers of singular objects such significant markers may drive a separation process more effective than common approaches the determination of markers by an iterative method should be scale translation and rotation invariant and robust with regard to noise due to the variability of biological specimen we realize a technique that splits cell clumps consisting of different cell sizes and shapes into meaningful parts the multiscale method applied here is based on the analysis of the contour shape and the object area by iterative voting using oriented kernels these cone shaped kernels vote iteratively for the local center of mass of the components of an aggregation the voting is performed along the gradient of the distance transformation of the binarized image of aggregates iterative voting is initialized by voting along the gradient direction where at each iteration the voting direction and shape of the kernel is refined resp the kernel topography is refined and reoriented iteratively it turned out that the kernel topography is unique because it votes for the most likely set of grid points where the gravity center of an individual cluster component may be located furthermore a new procedure is realized to use the local intensities of aggregations for kernel voting the last voted iteration provides gravitation centers resp centers of mass of the clumped cells these are extracted and used as markers to determine individual cell boundaries by a marker based watershed postprocessing the subject of this paper is to highlight the basic algorithm of iterative kernel voting and expanding it to process intensities within clusters as well as contour information the approach is applied to synthetic images that were modified systematically with regard to object topology natural aggregates of cells at the light microscopic level and cell clusters derived from high resolution flat bed scanning were splitted in addition to these examples images from a benchmark databases were investigated the splittings generated by the iterative voting approach were compared with expected splittings of test persons and with results of the watershed method especially the gray level based iterative voting method provides superior results for cell cluster separation in comparison to the watershed procedure

on the detection of the axes of symmetry of symmetric and almost symmetric planar images a simple algorithm is presented for finding all the axes of symmetry of symmetric and almost symmetric planar images having nonuniform gray level intensity images the technique which can also be used in conjunction with planar curves is based on the identification of the centroids of the given image and other related sets of points followed by a maximization of a specially defined coefficient of symmetry owing to the nature of the required procedures which are strictly based on the computation of mean values the method is not particularly affected by the presence of noise and is especially suited for application in conjunction with digitized figures

motif based defect detection for patterned fabric this paper proposes a generalized motif based method for detecting defects in 16 out of 17 wallpaper groups in 2d patterned texture it assumes that most patterned texture can be decomposed into lattices and their constituents motifs it then utilizes the symmetry property of motifs to calculate the energy of moving subtraction and its variance among different motifs by learning the distribution of these values over a number of defect free patterns boundary conditions for discerning defective and defect free patterns can be determined this paper presents the theoretical foundation of the method and defines the relations between motifs and lattice from which a new concept called energy of moving subtraction is derived using norm metric measurement between a collection of circular shift matrices of motif and itself it has been shown in this paper that the energy of moving subtraction amplifies the defect information of the defective motif together with its variance an energy variance space is further defined where decision boundaries are drawn for classifying defective and defect free motifs as the 16 wallpaper groups of patterned fabric can be transformed into three major groups the proposed method is evaluated over these three major groups from which 160 defect free lattices samples are used for defining the decision boundaries with 140 defect free and 113 defective samples used for testing an overall detection success rate of 93 32 is achieved for the proposed method no other generalized approach can achieve this success rate has been reported before and hence this result outperforms all other previously published approaches

the relative singularity category of a non commutative resolution of singularities abstract in this article we study a triangulated category associated with a non commutative resolution of singularities in particular we give a complete description of this category in the case of a curve with nodal singularities classifying its indecomposable objects and computing its auslander reiten quiver and k group

tame and wild projective curves and classification of vector bundles abstract we propose a new method of classifying vector bundles on projective curves especially singular ones according to their representation type in particular we prove that the classification problem of vector bundles respectively of torsion free sheaves on projective curves is always finite tame or wild we completely classify curves which are of finite respectively tame vector bundle type by their dual graph moreover our methods yield a geometric description of all indecomposable vector bundles and torsion free sheaves on finite and tame curves

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

mapping cones in the bounded derived category of a gentle algebra abstract in this article we describe the triangulated structure of the bounded derived category of a gentle algebra by describing the triangles induced by the morphisms between indecomposable objects in a basis of their hom space

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

classical yang baxter equation and the a constraint abstract we show that elliptic solutions of classical yang baxter equation cybe can be obtained from triple massey products on an elliptic curve we introduce the associative version of this equation which has two spectral parameters and construct its elliptic solutions we also study some degenerations of these solutions

noetherian hereditary abelian categories satisfying serre duality norwegian univ sci technol dept math sci n 7491 trondheim norway limburgs univ ctr dept wni b 3590 diepenbeek belgium reiten i norwegian univ sci technol dept math sci n 7491 trondheim norway

a theory of multiscale curvature based shape representation for planar curves a shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented the method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve three different ways of computing the representation are described they result in three different representations the curvature scale space image the renormalized curvature scale space image and the resampled curvature scale space image the process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve several evolution and arc length evolution properties of planar curves are discussed