transformation groups for soliton equations iv a new hierarchy of soliton equations of kp type abstract a new approach to soliton equations based on functions or hirota s dependent variables vertex operators and the clifford algebra of free fermions is applied to study a new hierarchy of kadomtsev petviashvili type equations the bkp hierarchy the infinite dimensional orthogonal group acts on the space of bkp functions the sawada kotera equation is obtained as a reduction of bkp its infinitesimal transformations constitute the euclidean lie algebra a2 2

on the p supports of a holonomic mathcal d d module for a smooth variety y over a perfect field of positive characteristic the sheaf d y of crystalline differential operators on y also called the sheaf of pd differential operators is known to be an azumaya algebra over t y the cotangent space of the frobenius twist y of y thus to a sheaf of modules m over d y one can assign a closed subvariety of t y called the p support namely the support of m seen as a sheaf on t y we study here the family of p supports assigned to the reductions modulo primes p of a holonomic mathcal d module we prove that the azumaya algebra of differential operators splits on the regular locus of the p support and that the p support is a lagrangian subvariety of the cotangent space for p large enough the latter was conjectured by kontsevich our approach also provides a new proof of the involutivity of the singular support of a holonomic mathcal d module by reduction modulo p

a two unit general parallel system with n 2 cold standbys analytic and simulation approach abstract a parallel 2 n 2 system is investigated here where two units start their operation simultaneously and any one of them is replaced instantaneously upon its failure by one of the n 2 cold standbys we assume availability of n non identical non repairable units for replacement or support the system reliability is evaluated by recursive relations with unit lifetimes t i i 1 n that have a general joint distribution function f t on the basis of the derived expression simulation techniques have been developed for the evaluation of the system reliability and the mean time to failure useful when dealing with large systems or correlated unit lifetimes and less mathematically manageable distributions simulation results are presented for various lifetime distributions and comparisons are made with derived analytic results for some special distributions and moderate values of n

kp hierarchy for the cyclic quiver we introduce a generalisation of the kp hierarchy closely related to the cyclic quiver and the cherednik algebra hk zm this hierarchy depends on m parameters one of which can be eliminated with the usual kp hierarchy corresponding to the m 1 case generalising the result of wilson invent math 133 1 1 41 1998 we show that our hierarchy admits solutions parameterised by suitable quiver varieties the pole dynamics for these solutions is shown to be governed by the classical calogero moser system for the wreath product zm sn and its new spin version these results are further extended to the case of the multi component hierarchy

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

reliability analysis of a two unit general parallel system with n 2 warm standbys abstract a parallel 2 n 2 system is investigated here where two units start their operation simultaneously and any one of them is replaced instantaneously upon its failure by one of the n 2 warm standbys we assume availability of n non identical non repairable units the unit lifetimes in full operational mode and in partial operational mode have general distribution functions g i and h i i 1 n respectively the system reliability is evaluated by recursive relations

on the variety of a highest weight module 1 2 let u g be the enveloping algebra of g detailed information on the primitive spectrum prim u g of u g was summarized by conjecture 7 4 of 181 here a main question was to relate prim u g with the springer correspondence parts i ii of this conjecture were established in i ii and a partial solution to iii was given in 21 sufficient e g to treat g of type a meanwhile borho and brylinski 5 have established iii for induced ideals while barbasch and vogan 1 2 have established a version of iii in which gr i i e prim u g is replaced by a certain wavefront set known to be contained in y gr 1 this last work involves some case by case analysis and gives little indication as to why the springer correspondence should arise in the study of prim u g

a class of algebras similar to the enveloping algebra of sl 2 fix f e c x define r c a b h subject to the relations ha ah a hb bh b ab ba f h we study these algebras for different f and in particular show how they are similar to and different from u sl 2 the enveloping algebra of sl 2 c there is a notion of highest weight modules and a category a for such r for each n 0 if f x x 1 n l xn 1 then r has precisely n simple modules in each finite dimension and every finite dimensional r module is semisimple

a general framework for low level vision we introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented we consider intensity images as surfaces in the x i space the image is thereby a two dimensional 2 d surface in three dimensional 3 d space for gray level images and 2 d surfaces in five dimensions for color images the new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast and results in new and efficient schemes extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms

differential operators on homogeneous spaces iii characteristic varieties of harish chandra modules and of primitive ideals letg be a semi simple complex algebraic group with lie algebra and flag varietyx g b for each primitive idealj with trivial central character in the enveloping algebrau we define a characteristic variety in the cotangent bundle ofx which projects under the springer resolution mapt x onto the closure of a nilpotent orbit we prove that this characteristic variety is theg saturation of the characteristic variety of a highest weight module with annihilatorj we conjecture that it is irreducible forg sl n our conjecture would provide a geometrical explanation for the classification of primitive ideals in terms of weyl group representations as achieved by a joseph the presentation of these ideas here is simultaneously used to some extent as an opportunity to continue our more general systematic discussion of differential operators on a complete homogeneous space and to study more generally characteristic varieties of harish chandra modules

characteristic varieties and vanishing cycles on presente une etude systematique des varietes caracteristiques des systemes holonomes a singularites regulieres ce sont des sous varietes lagrangiennes coniques dans le fibre cotangent t x

bispectral algebras of commuting ordinary differential operators we develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank n it combines and unifies the ideas of duistermaat grunbaum and wilson our construction is completely algorithmic and enables us to obtain all previously known classes or individual examples of bispectral operators the method also provides new broad families of bispectral algebras which may help to penetrate deeper into the problem

differential equations in the spectral parameter we determine all the potentialsv x for the schrodinger equation 2 v x k2 such that some family of eigenfunctions satisfies a differential equation in the spectral parameterk of the formb k k o x o for each suchv x we determine the algebra of all possible operatorsb and the corresponding functions x

determinant bundles and virasoro algebras we consider the interplay of infinite dimensional lie algebras of virasoro type and moduli spaces of curves suggested by string theory we will see that the infinitesimal geometry of determinant bundles is governed by virasoro symmetries the mumford forms are just invariants of these symmetries the representations of virasoro algebra define twisted d modules on moduli spaces thesed modules are equations on correlators in conformal field theory

involutive varieties with smooth support abstract we prove a structure theorem for conic involutive varieties of the cotangent bundle of a smooth algebraic varietyxwhose projection onxis smooth the paper includes an example of a conic involutive variety of t xwhich is not the characteristic variety of any d x module

zariski rings and flatness of completion abstract we relate flatness and faithful flatness of the completion to the comparison and zariskian property resp of the filtration some applications have been included

nonholonomic modules over enveloping algebras of semisimple lie algebras abstract we prove that the enveloping algebras of all semisimple lie algebras over the complex numbers which are not of type a 1 admit nonholonomic simple modules

free group algebras in division rings with valuation i abstract let r be an algebra over a commutative ring k suppose that r is endowed with a descending filtration indexed on an ordered group g such that the restriction to k is positive we show that the existence of free algebras on a certain set of generators in the induced graded ring grad r implies the existence of free group algebras in r our best results are obtained for division rings endowed with a valuation

root fernando kac subalgebras of finite type abstract let g be a finite dimensional lie algebra and m be a g module the fernando kac subalgebra of g associated to m is the subset g m g of all elements g g which act locally finitely on m a subalgebra l g for which there exists an irreducible module m with g m l is called a fernando kac subalgebra of g a fernando kac subalgebra of g is of finite type if in addition m can be chosen to have finite jordan holder l multiplicities under the assumption that g is simple i penkov has conjectured an explicit combinatorial criterion describing all fernando kac subalgebras of finite type which contain a cartan subalgebra in the present paper we prove this conjecture for g e 8

mixed hodge complexes on algebraic varieties and t structures abstract the aim of this paper is to provide some complements on the categories of mixed q hodge complexes introduced by m saito in 17 in particular we prove that the category of pure diagrams has a t structure that lifts the perverse t structure and derive some consequences of this fact we also compare the category of mixed hodge complexes defined by m saito with a more naive version these complements are used in 12 to provide a partial generalization to higher dimension of a result of a be linson 1 2 which shows that the derived category of polarizable mixed hodge structures is equivalent to the more flexible triangulated category of polarizable mixed hodge complexes

microlocal properties of filtered rings the process of microlocalization appeared first in a strongly analytic frame in relation to systems of linear differential equations with holomorphic coefficients see e g 13 from the strictly algebraic point of view the process of microlocalization gives an answer to the following universal problem if r is a filtered ring and s c r is a multiplicatively closed subset does there exist a complete filtered ring denoted by q r with a filtered ring homomorphism 9 r q r such that the two conditions below are satisfied

a lie algebra variation on a theorem of wedderburn theorem let a be a finite dimensional associative algebra over a field f suppose that a has a basis over f consisting of nilpotent elements then a itself must be nilpotent given a finite dimensional lie algebra l which is a lie subalgebra of an associative algebra a possibly infinite dimensional we can ask what results from supposing that l has a basis over f consisting of elements that are nilpotent in the associative algebra we cannot conclude that l is nilpotent and finite dimensional in fact this is rarely the case for example

a new algebraic approach to microlocalization of filtered rings using the construction of the rees ring associated to a filtered ring we provide a description of the microlocalization of the filtered ring by using only purely algebraic techniques the method yields an easy approach towards the study of exactness properties of the microlocalization functor every microlocalization at a regular multiplicative ore set in the associated graded ring can be obtained as the completion of a localization at an ore set of the filtered ring

automorphisms and ideals of the weyl algebra let a 1 be the first weyl algebra and let g be its automorphism group we study the natural action of g on the space of isomorphism classes of right ideals of a 1 equivalently of finitely generated rank 1 torsion free right a 1 modules we show that this space breaks up into a countable number of orbits each of which is a finite dimensional algebraic variety our results are strikingly similar to those for the commutative algebra of polynomials in two variables however we do not know of any general principle that would allow us to predict this in advance as a key step in the proof we obtain a new description of the bispectral involution of w1 we also make some comments on the group g from the viewpoint of shafarevich s theory of infinite dimensional algebraic groups

existence theorems for dualizing complexes over non commutative graded and filtered rings abstract in this note we prove existence theorems for dualizing complexes over graded and filtered rings thereby generalizing some results by zhang yekutieli and jorgensen

anisotropic diffusion of multivalued images with applications to color filtering a general framework for anisotropic diffusion of multivalued images is presented we propose an evolution equation where at each point in time the directions and magnitudes of the maximal and minimal rate of change in the vector image are first evaluated these are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric then the image diffuses via a system of coupled differential equations in the direction of minimal change the diffusion strength is controlled by a function that measures the degree of dissimilarity between the eigenvalues we apply the proposed framework to the filtering of color images represented in cie l a b space

lie stacks and their enveloping algebras abstract a lie stack is an algebra morphisms a a bwhereaandbare finite dimensional c algebras withbbeing augmented local we construct the enveloping algebrau s of a lie stack and show that it is an irreducible hopf algebra domain with a poincare birkhoff witt basis we recover the enveloping algebrasu g of lie algebras as special instances we give conditions such thatu s is neither commutative nor cocommutative and we give such examples forbbeing any non commutative augmented local algebra and for beingathe path algebra of a suitable bipartite quiver by studying orbit closes in the variety of lie stacks of fixed dimension one obtains in this way deformations of enveloping algebras of lie algebras

a deteriorating cold standby repairable system with priority in use abstract in this paper a cold standby repairable system consisting of two dissimilar components and one repairman is studied in this system it is assumed that the working time distributions and the repair time distributions of the two components are both exponential and component 1 is given priority in use after repair component 2 is as good as new while component 1 follows a geometric process repair under these assumptions using the geometric process and a supplementary variable technique some important reliability indices such as the system availability reliability mean time to first failure mttff rate of occurrence of failure rocof and the idle probability of the repairman are derived a numerical example for the system reliability r t is given and it is considered that a repair replacement policy based on the working age t of component 1 under which the system is replaced when the working age of component 1 reaches t our problem is to determine an optimal policy t such that the long run average cost per unit time of the system is minimized the explicit expression for the long run average cost per unit time of the system is evaluated and the corresponding optimal replacement policy t can be found analytically or numerically another numerical example for replacement model is also given

foliations of multiprojective spaces and a conjecture of bernstein and lunts we use foliations of multiprojective spaces defined by hamiltonian functions on the underlying affine space to prove the three dimensional case of a conjecture of bernstein and lunts according to which the symbol of a generic first order differential operator gives rise to a hypersurface of the cotangent bundle which does not contain involutive conical subvarieties apart from the zero section and fibres of the bundle

extensions of modules over weyl algebras in this paper we calculate some ext groups of singular modules over the complex weyl algebra an in particular we determine conditions under which ext is an infinite dimensional vector space when n 2 or 3

geometric and algebraic reduction for singular momentum maps this paper concerns the reduction of singular constraint sets of symplectic manifolds it develops a geometric reduction procedure as well as continues the work of sniatycki and patrick on reduction a la dirac the relationships among the dirac geometric and sniatycki weinstein algebraic reduction procedures are studied primary emphasis is placed on the case where the constraints are given by the vanishing of a singular momentum map associated to the hamiltonian action of a compact lie group specifically an explicit local normal form is given for the momentum map which is used to show that these various reductions are all well defined and a necessary and sufficient condition for them to agree is derived related conditions are investigated and shown to be sufficient in the case of torus actions numerous examples are computed illustrating the results some discussion and examples are given for the noncompact case

weighted level set evolution based on local edge features for medical image segmentation level set methods have been widely used to implement active contours for image segmentation applications due to their good boundary detection accuracy in the context of medical image segmentation weak edges and inhomogeneities remain important issues that may hinder the accuracy of any segmentation method based on active contours implemented using level set methods this paper proposes a method based on active contours implemented using level set methods for segmentation of such medical images the proposed method uses a level set evolution that is based on the minimization of an objective energy functional whose energy terms are weighted according to their relative importance in detecting boundaries this relative importance is computed based on local edge features collected from the adjacent region located inside and outside of the evolving contour the local edge features employed are the edge intensity and the degree of alignment between the image s gradient vector flow field and the evolving contour s normal we evaluate the proposed method for segmentation of various regions in real mri and ct slices x ray images and ultra sound images evaluation results confirm the advantage of weighting energy forces using local edge features to reduce leakage these results also show that the proposed method leads to more accurate boundary detection results than the state of the art edge based level set segmentation methods particularly around weak edges

lifting ore sets of noetherian filtered rings and applications abstract let r be a filtered ring such that the rees ring r of r is left noetherian it is observed that if t is a left ore set of the associated graded ring g r consisting of homogeneous elements then the saturated set s s r s t is a left ore set of r this lifting property is used to obtain local global results on r which simplify some microlocal global results in the literature if g r is positively graded and commutative then certain structure sheaves on r are constructed

flux maximizing geometric flows several geometric active contour models have been proposed for segmentation in computer vision and image analysis the essential idea is to evolve a curve in 2d or a surface in 3d under constraints from image forces so that it clings to features of interest in an intensity image recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented however it is still unclear how to apply these techniques to images of narrow elongated structures such as blood vessels where intensity contrast may be low and reliable region statistics cannot be computed to address this problem we derive the gradient flows which maximize the rate of increase of flux of an appropriate vector field through a curve in 2d or a surface in 3d the key idea is to exploit the direction of the vector field along with its magnitude the calculations lead to a simple and elegant interpretation which is essentially parameter free and has the same form in both dimensions we illustrate its advantages with several level set based segmentations of 2d and 3d angiography images of blood vessels

filtrations on simple artinian rings abstract filtrations on simple artinian rings are related to pseudo valuations by conditions on the associated graded rings

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

noncommutative deformations of type a kleinian singularities abstract the type a kleinian singularities are the surfaces of the form c 2 g where g is a finite cyclic subgroup of sl2 c the standard noncommutative analog is the fixed ring of the weyl algebra a1 c under the induced action of g these fixed rings are however only part of a large family of algebras whose associated graded ring is the coordinate ring of such a singularity the structure of these algebras is studied with reference to the structure of the associated singularity and to the structure of primitive factor rings of u s l 2 c

reflexive ideals in iwasawa algebras let g be a torsionfree compact p adic analytic group we give sufficient conditions on p and g which ensure that the iwasawa algebra og of g has no non trivial two sided reflexive ideals consequently these conditions imply that every non zero normal element in og is a unit we show that these conditions hold in the case when g is an open subgroup of and p is arbitrary using a previous result of the first author we show that there are only two prime ideals in og when g is a congruence subgroup of the zero ideal and the unique maximal ideal these statements partially answer some questions asked by the first author and brown

harmonic active contours we propose a segmentation method based on the geometric representation of images as 2 d manifolds embedded in a higher dimensional space the segmentation is formulated as a minimization problem where the contours are described by a level set function and the objective functional corresponds to the surface of the image manifold in this geometric framework both data fidelity and regularity terms of the segmentation are represented by a single functional that intrinsically aligns the gradients of the level set function with the gradients of the image and results in a segmentation criterion that exploits the directional information of image gradients to overcome image inhomogeneities and fragmented contours the proposed formulation combines this robust alignment of gradients with attractive properties of previous methods developed in the same geometric framework 1 the natural coupling of image channels proposed for anisotropic diffusion and 2 the ability of subjective surfaces to detect weak edges and close fragmented boundaries the potential of such a geometric approach lies in the general definition of riemannian manifolds which naturally generalizes existing segmentation methods the geodesic active contours the active contours without edges and the robust edge integrator to higher dimensional spaces non flat images and feature spaces our experiments show that the proposed technique improves the segmentation of multi channel images images subject to inhomogeneities and images characterized by geometric structures like ridges or valleys

on noncommutative noetherian schemes abstract the main aim of this paper is to better understand the localization technique for certain noetherian rings like enveloping algebras of nilpotent lie algebras for such rings r we also give a conjectural definition of certain sheaves which should be affine objects naturally generalizing the classically defined structure sheaves in commutative theory the corresponding sheaves associated to some r modules might carry particularly interesting information e g for representation theory of semisimple lie groups next we generalize one important theorem of p f smith on localization in noetherian artin rees rings as an interesting corollary we obtain that every prime ideal of height 1 in the enveloping algebra of the lie algebra sl 2 over a field of characteristic zero is localizable finally we provide a number of concrete useful calculations for our main example the enveloping algebra of the three dimensional heisenberg lie algebra and thus test both the proposed ideas and methods in particular we introduce the notion of a weakly normal element generalizing the notion of a normal element

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

lie algebra modules with finite dimensional weight spaces i let g denote a reductive lie algebra over an algebraically closed field of characteristic zero and let 4 denote a cartan subalgebra of g in this paper we study finitely generated g modules that decompose into direct sums of finite dimensional 4 weight spaces we show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of irreducible modules those we call torsion free modules we also show that if g is a simple lie algebra that admits a torsion free module then g is of type a or c

vanishing of certain equivariant distributions on spherical spaces we prove vanishing of mathfrak z eigen distributions on a split real reductive group which change according to a non degenerate character under the left action of the unipotent radical of the borel subgroup and are equivariant under the right action of a spherical subgroup this is a generalization of a result by shalika that concerned the group case shalika s result was crucial in the proof of his multiplicity one theorem we view our result as a step in the study of multiplicities of quasi regular representations on spherical varieties as an application we prove non vanishing of spherical bessel functions

regularized laplacian zero crossings as optimal edge integrators we view the fundamental edge integration problem for object segmentation in a geometric variational framework first we show that the classical zero crossings of the image laplacian edge detector as suggested by marr and hildreth inherently provides optimal edge integration with regard to a very natural geometric functional this functional accumulates the inner product between the normal to the edge and the gray level image gradient along the edge we use this observation to derive new and highly accurate active contours based on this functional and regularized by previously proposed geodesic active contour geometric variational models we also incorporate a 2d geometric variational explanation to the haralick edge detector into the geometric active contour framework

rational cherednik algebras and hilbert schemes ii representations and sheaves let h c be the rational cherednik algebra of type a n 1 with spherical subalgebra u c e h c e then u c is filtered by order of differential operators with associated graded ring gr u c mathbb c mathfrac h mathfrac h w where is the n th symmetric group using the z algebra construction from gs it is also possible to associate to a filtered h c or u c module hat m on the hilbert scheme hilb n using this technique we study the representation theory of u c and h c and we relate it to hilb n and to the resolution of singularities hilb n mathfrac h mathfrac h w for example we prove the following if c 1 n so that l c triv is the unique one dimensional simple h c module then hat e l c triv mathcal o z n where z n 1 0 is the punctual hilbert scheme if c 1 n k for k in mathbb n then under a canonical filtration on the finite dimensional module l c triv gr e l c triv has a natural bigraded structure that coincides with that on h 0 z n mathscr l k where mathscr l mathcal o hilb n 1 this confirms conjectures of berest etingof and ginzburg beg2 conjectures 7 2 7 3 under mild restrictions on c the characteristic cycle of hat e c equals sum k z where k are kostka numbers and the z are known irreducible components of 1 mathfrak h w

a geometric process maintenance model with preventive repair abstract in this paper a geometric process maintenance model with preventive repair is studied a maintenance policy t n is applied by which the system will be repaired whenever it fails or its operating time reaches t whichever occurs first and the system will be replaced by a new and identical one following the n th failure the long run average cost per unit time is determined an optimal policy t n could be determined numerically or analytically for minimizing the average cost a new class of lifetime distribution which takes into account the effect of preventive repair is studied that is applied to determine the optimal policy t n

integrated active contours for texture segmentation we address the issue of textured image segmentation in the context of the gabor feature space of images gabor filters tuned to a set of orientations scales and frequencies are applied to the images to create the gabor feature space a two dimensional riemannian manifold of local features is extracted via the beltrami framework the metric of this surface provides a good indicator of texture changes and is used therefore in a beltrami based diffusion mechanism and in a geodesic active contours algorithm for texture segmentation the performance of the proposed algorithm is compared with that of the edgeless active contours algorithm applied for texture segmentation moreover an integrated approach extending the geodesic and edgeless active contours approaches to texture segmentation is presented we show that combining boundary and region information yields more robust and accurate texture segmentation results

subspaces of non commutative spaces this paper concerns the closed points closed subspaces open subspaces weakly closed and weakly open subspaces and effective divisors on a non commutative space

subjective surfaces a geometric model for boundary completion we present a geometric model and a computational method for segmentation of images with missing boundaries in many situations the human visual system fills in missing gaps in edges and boundaries building and completing information that is not present boundary completion presents a considerable challenge in computer vision since most algorithms attempt to exploit existing data a large body of work concerns completion models which postulate how to construct missing datas these models are often trained and specific to particular images in this paper we take the following alternative perspective we consider a given reference point within the image and then develop an algorithm which tries to build missing information on the basis of the given point of view and the available information as boundary data to the algorithm starting from this point of view a surface is constructed it is then evolved with the mean curvature flow in the metric induced by the image until a piecewise constant solution is reached we test the computational model on modal completion amodal completion and texture segmentation we extend the geometric model and the algorithm to 3d in order to extract shapes from low signal noise ratio ultrasound image volumes results in 3d echocardiography and 3d fetal echography are also presented

scale space analysis and active contours for omnidirectional images a new generation of optical devices that generate images covering a larger part of the field of view than conventional cameras namely catadioptric cameras is slowly emerging these omnidirectional images will most probably deeply impact computer vision in the forthcoming years provided that the necessary algorithmic background stands strong in this paper we propose a general framework that helps define various computer vision primitives we show that geometry which plays a central role in the formation of omnidirectional images must be carefully taken into account while performing such simple tasks as smoothing or edge detection partial differential equations pdes offer a very versatile tool that is well suited to cope with geometrical constraints we derive new energy functionals and pdes for segmenting images obtained from catadioptric cameras and show that they can be implemented robustly using classical finite difference schemes various experimental results illustrate the potential of these new methods on both synthetic and natural images

on involutive homogeneous varieties and representations of weyl algebras abstract this paper is concerned with the geometry of minimal involutive homogeneous varieties in complex affine 2 n space and its application to the study of the representation theory of the n th complex weyl algebra a n the main results are the existence of minimal involutive homogeneous varieties of any given codimension and of a n modules that have these varieties for characteristic variety we also determine conditions on the codimensions of a n modules m and n under which ext 1 m n is a finite dimensional vector space

a generic cubic surface contains no involutive curve abstract in 1988 j bernstein and v lunts invent math 94 223 243 proved that a generic surface in p 3 of degree 4 or greater would not contain a curve which supported a module over the second weyl algebra it is known that quadric surfaces and planes always do this paper shows that a generic cubic surface does not

bernstein inequality and holonomic modules abstract in this paper we study the representation theory of filtered algebras with commutative associated graded whose spectrum has finitely many symplectic leaves examples are provided by the algebras of global sections of quantizations of symplectic resolutions quantum hamiltonian reductions and spherical symplectic reflection algebras we introduce the notion of holonomic modules for such algebras we show that provided the algebraic fundamental groups of all leaves are finite the generalized bernstein inequality holds for the simple modules and turns into equality for holonomic simples under the same finiteness assumption we prove that the associated variety of a simple holonomic module is equi dimensional we also prove that if the regular bimodule has finite length then any holonomic module has finite length this allows one to reduce the bernstein inequality for arbitrary modules to simple ones we prove that the regular bimodule has finite length for the global sections of quantizations of symplectic resolutions for quantum hamiltonian reductions and for rational cherednik algebras the paper contains a joint appendix by the author and etingof that motivates the definition of a holonomic module in the case of global sections of a quantization of a symplectic resolution

gelfand kirillov dimension and associated graded modules abstract let s a 0sa be a filtered algebra over a field k and m ma a filtered s module with associated graded module gr m m a m a 1 over gr s s a s a 1 we consider conditions which ensure that gr m and m have the same gelfand kirillov dimension and show that this equality holds in particular if gr s is an affine commutative k algebra

a generalisation of the calogero moser system abstract a generalised calogero moser many body system in which the particles possess extra internal degrees of freedom is introduced and solved by the method of olshanetsky and perelomov further the hierarchy of flows commuting with this system is obtained from a hierarchy of linear systems possessing sl n symmetry by the usual method of reduction thus they are shown to be integrable

comparisons and bounds for expected lifetimes of reliability systems sharp bounds on expectations of lifetimes of coherent and mixed systems composed of elements with independent and either identically or non identically distributed lifetimes are expressed in terms of expected lifetimes of components similar evaluations are concluded for the respective mean residual lifetimes in the iid case improved inequalities dependent on a concentration parameter connected to the gini dispersion index are obtained the results can be used to compare systems with component lifetimes ordered in the convex ordering in the inid case some refined bounds are derived in terms of the expected lifetimes of series systems of smaller sizes and the expected lifetime of single unit for the equivalent systems with iid components the latter can be further simplified in the case of weak schur concavity and schur convexity of the system generalized domination polynomial

on irreducible representations of compact p adic analytic groups we prove that the canonical dimension of a coadmissible representation of a semisimple p adic lie group in a p adic banach space is either zero or at least half the dimension of a nonzero coadjoint orbit to do this we establish analogues for p adically completed enveloping algebras of bernstein s inequality for modules over weyl algebras the beilinson bernstein localisation theorem and quillen s lemma about the endomorphism ring of a simple module over an enveloping algebra