hochschild cohomology and atiyah classes abstract in this paper we prove that on a smooth algebraic variety the hkr morphism twisted by the square root of the todd genus gives an isomorphism between the sheaf of poly vector fields and the sheaf of poly differential operators both considered as derived gerstenhaber algebras in particular we obtain an isomorphism between hochschild cohomology and the cohomology of poly vector fields which is compatible with the lie bracket and the cupproduct the latter compatibility is an unpublished result by kontsevich our proof is set in the framework of lie algebroids and so applies without modification in much more general settings as well

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

a robust hybrid method for nonrigid image registration a nonrigid registration method is proposed to automatically align two images by registering two sets of sparse features extracted from the images motivated by the paradigm of robust point matching rpm algorithms 1 2 which were originally proposed for shape registration we develop robust hybrid image matching rhim algorithm by alternatively optimizing feature correspondence and spatial transformation for image registration our rhim algorithm is built to be robust to feature extraction errors a novel dynamic outlier rejection approach is described for removing outliers and a local refinement technique is applied to correct non exactly matched correspondences arising from image noise and deformations experimental results demonstrate the robustness and accuracy of our method

eigenvalues of cartan matrices of principal 3 blocks of finite groups with abelian sylow 3 subgroups abstract let a be the principal 3 block of a finite group g with an abelian sylow 3 subgroup p let c a be the cartan matrix of a and we denote by c a the unique largest eigenvalue of c a the value c a is called the frobenius perron eigenvalue of c a we shall prove that c a is a rational number if and only if a and the principal 3 block of n g p are morita equivalent this generalizes earlier wada s theorem in 2007 where he proves it only for the case that the order of p is nine while we prove it for the case that p is an arbitrary finite abelian 3 group the result presented here uses the classification of finite simple groups

the mukai pairing ii the hochschild kostant rosenberg isomorphism abstract we continue the study of the hochschild structure of a smooth space that we began in our previous paper examining implications of the hochschild kostant rosenberg theorem the main contributions of the present paper are we introduce a generalization of the usual notions of mukai vector and mukai pairing on differential forms that applies to arbitrary manifolds we give a proof of the fact that the natural chern character map k 0 x hh 0 x becomes after the hkr isomorphism the usual one k 0 x h i x x i and we present a conjecture that relates the hochschild and harmonic structures of a smooth space similar in spirit to the tsygan formality conjecture

broue s conjecture holds for principal 3 blocks with elementary abelian defect group of order 9 abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he conjectures that for any prime p if a finite group g has an abelian sylow p subgroup p then the derived categories of the principal p blocks of g and of the normalizer ng p of p in g are equivalent we prove in this paper that broue inage kus conjecture holds for the principal 3 block of an arbitrary finite group g with an elementary abelian sylow 3 subgroup p of order 9 by using initiated works for the case where g is simple which are due to puig okuyama waki miyachi and the authors the result depends on the classification of finite simple groups

formality for lie algebroids using dolgushev s generalization of fedosov s method for deformation quantization we give a positive answer to a question of p xu can one prove a formality theorem for lie algebroids as a direct application of this result we obtain that any triangular lie bialgebroid is quantizable

cellular algebras and cartan matrices abstract let a be a finite dimensional algebra over a field k and let c be the cartan matrix of a usually the eigenvalues of c being integers do not imply the semisimplicity of a however we prove that a cellular algebra a is semisimple if and only if det c 1 and all eigenvalues of c are integers moreover we use cartan matrices to classify the cellular algebras with the property that the determinant of the cartan matrix equals a given prime p and all eigenvalues are integers we also give a classification of cellular nakayama algebras with integral eigenvalues of their cartan matrices finally we show that if a is a cellular algebra then its trivial extension t a is also a cellular algebra in particular if a non simple connected cellular algebra a is quasi hereditary then the cartan matrix of t a has at least one non integral eigenvalue the main tool used in this paper is the well known perron frobenius theory on non negative matrices

on equivalences between blocks of group algebras reduction to the simple components abstract a conjecture of michel broue states that if d is an abelian sylow p subgroup of a finite group g and h n g d then the principal blocks of g and h are rickard equivalent the structure of groups with abelian sylow p subgroups as determined by p fong and m e harris raises the following question assuming that broue s conjecture holds for the simple components of g under what conditions does it hold for g itself due to the structure of g this problem requires mainly the lifting of rickard complexes to p extensions of the simple components and the construction of complexes over wreath products we give here these reduction steps which may be regarded as a clifford theory of tilting complexes

căldăraru s conjecture and tsygan s formality in this paper we complete the proof of caldararu s conjecture on the compatibility between the module structures on differential forms over poly vector fields and on hochschild homology over hochschild cohomology in fact we show that twisting with the square root of the todd class gives an isomorphism of precalculi between these pairs of objects our methods use formal geometry to globalize the local formality quasi isomorphisms introduced by kontsevich and shoikhet the existence of the latter was conjectured by tsygan we also rely on the fact recently proved by the first two authors that shoikhet s quasi isomorphism is compatible with cap products after twisting with a maurer cartan element

eigenvalues of cartan matrices of principal 2 blocks with abelian defect groups abstract let g be a finite group with an abelian sylow 2 subgroup p let c b be the cartan matrix of the principal 2 block b of g we show that the frobenius perron eigenvalue b of c b is a rational integer if and only if b and its brauer correspondent block b of n g p are morita equivalent by using a classification of finite simple groups with an abelian sylow 2 subgroup in this case we can take the brauer character table b of b as a unimodular eigenvector matrix u b of c b over a complete discrete valuation ring r

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

a proof of the tsygan formality conjecture for chains abstract we extend the kontsevich formality l morphism u t poly r d d poly r d to an l morphism of l modules over t poly r d u c a a r d a c r d the construction of the map u is given in kontsevich type integrals the conjecture that such an l morphism exists is due to boris tsygan formality conjecture for chains math qa 9904132 as an application we obtain an explicit formula for isomorphism a a a a a a a is the kontsevich deformation quantization of the algebra a by a poisson bivector field and is the poisson bracket we also formulate a conjecture extending the kontsevich theorem on cup products to this context the conjecture implies a generalization of the duflo formula and many other things

registration of images with varying topology using embedded maps this paper presents registration via embedded maps rem a deformable registration algorithm for images with varying topology the algorithm represents 3 d images as 4 d manifolds in a riemannian space referred to as embedded maps registration is performed as a surface evolution matching one embedded map to another using a diffusion process the approach differs from those existing in that it takes an a priori estimation of image regions where topological changes are present for example lesions and generates a dense vector field representing both the shape and intensity changes necessary to match the images the algorithm outputs both a diffeomorphic deformation field and an intensity displacement which corrects the intensity difference caused by topological changes multiple sets of experiments are conducted on magnetic resonance imaging mri with lesions from oasis and adni datasets these images are registered to either a brain template or images of healthy individuals an exemplar case registering a template to an mri with tumor is also given the resulting deformation fields were compared with those obtained using diffeomorphic demons where topological changes are not modeled these sets of experiments demonstrate the efficacy of our proposed rem method for registration of brain mri with severe topological differences

the principal 3 blocks of four and five dimensional projective special linear groups in non defining characteristic abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he has conjectured that for any prime p if a finite group g has an abelian sylow p subgroup p then the principal p blocks of g and the normalizer ng p of p in g are derived equivalent let q be a power of a prime such that q 2 or 5 mod 9 in this paper we show that broue s conjecture is true for p 3 and for g psl4 q and g psl5 q in these cases g has elementary abelian sylow 3 subgroups of order 9 what we prove here is the following in the case g psl4 q all the principal 3 blocks of g are morita even puig equivalent independently of infinitely many q in the case g psl5 q all the principal 3 blocks of g are morita even puig equivalent to the principal 3 block of ng p independently of infinitely many q

on global deformation quantization in the algebraic case abstract we give a proof of yekutieli s global algebraic deformation quantization result which does not rely on the choice of local sections of the bundle of affine coordinate systems instead we use an argument inspired by algebraic de rham cohomology

a formality theorem for hochschild chains abstract we prove tsygan s formality conjecture for hochschild chains of the algebra of functions on an arbitrary smooth manifold m using the fedosov resolutions proposed in math qa 0307212 and the formality quasi isomorphism for hochschild chains of r y 1 y d proposed in paper math qa 0010321 by shoikhet this result allows us to describe traces on the quantum algebra of functions on an arbitrary poisson manifold

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

eigenvalues and elementary divisors of cartan matrices of cyclic blocks with l b 5 and tame blocks abstract we give a conjecture on relation between eigenvalues and elementary divisors of the cartan matrix of a p block b of a finite group then we prove the conjecture is true for cyclic blocks with l b 5 and for tame blocks

derived geometry of the first formal neighborhood of a smooth analytic cycle abstract if x is a smooth scheme of characteristic zero or a complex analytic manifold and s is a locally split infinitesimal thickening of x we compute explicitly the derived self intersection of x in s

geodesic active fields a geometric framework for image registration in this paper we present a novel geometric framework called geodesic active fields for general image registration in image registration one looks for the underlying deformation field that best maps one image onto another this is a classic ill posed inverse problem which is usually solved by adding a regularization term here we propose a multiplicative coupling between the registration term and the regularization term which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem then the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem this proposed approach for registration shares close similarities with the well known geodesic active contours model in image segmentation where the segmentation term the edge detector function is coupled with the regularization term the length functional via multiplication as well as a matter of fact our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by caselles kimmel sapiro the energy of the deformation field is measured with the polyakov energy weighted by a suitable image distance borrowed from standard registration models we investigate three different weighting functions the squared error and the approximated absolute error for monomodal images and the local joint entropy for multimodal images as compared to specialized state of the art methods tailored for specific applications our geometric framework involves important contributions firstly our general formulation for registration works on any parametrizable smooth and differentiable surface including nonflat and multiscale images in the latter case multiscale images are registered at all scales simultaneously and the relations between space and scale are intrinsically being accounted for second this method is to the best of our knowledge the first reparametrization invariant registration method introduced in the literature thirdly the multiplicative coupling between the registration term i e local image discrepancy and the regularization term naturally results in a data dependent tuning of the regularization strength finally by choosing the metric on the deformation field one can freely interpolate between classic gaussian and more interesting anisotropic tv like regularization

remarks on derived equivalences of ricci flat manifolds after a finite etale cover any ricci flat kahler manifold decomposes into a product of complex tori irreducible holomorphic symplectic manifolds and calabi yau manifolds we present results indicating that this decomposition is an invariant of the derived category the main idea to distinguish the derived category of an irreducible holomorphic symplectic manifold from that of a calabi yau manifold is that point sheaves do not deform in certain non commutative deformations of the former whereas they do for the latter on the way we prove a conjecture of c ld raru on the module structure of the hochschild kostant rosenberg isomorphism for manifolds with trivial canonical bundle as a direct consequence of recent work by calaque van den bergh and ramadoss

formality theorems for hochschild chains in the lie algebroid setting in this paper we prove lie algebroid versions of tsygan s formality conjecture for hochschild chains both in the smooth and holomorphic settings in the holomorphic setting our result implies a version of tsygan s formality conjecture for hochschild chains of the structure sheaf of any complex manifold and in the smooth setting this result allows us to describe quantum traces for an arbitrary poisson lie algebroid the proofs are based on the use of kontsevich s quasi isomorphism for hochschild cochains of r y 1 y d shoikhet s quasi isomorphism for hochschild chains of r y 1 y d and fedosov s resolutions of the natural analogues of hochschild co chain complexes associated with a lie algebroid

geodesics based image registration applications to biological and medical images depicting concentric ring patterns in many biological or medical applications images that contain sequences of shapes are common the existence of high inter individual variability makes their interpretation complex in this paper we address the computer assisted interpretation of such images and we investigate how we can remove or reduce these image variabilities the proposed approach relies on the development of an efficient image registration technique we first show the inadequacy of state of the art intensity based and feature based registration techniques for the considered image datasets then we propose a robust variational method which benefits from the geometrical information present in this type of images in the proposed non rigid geodesics based registration the successive shapes are represented by a level set representation which we rely on to carry out the registration the successive level sets are regarded as elements in a shape space and the corresponding matching is that of the optimal geodesic path the proposed registration scheme is tested on synthetic and real images the comparison against results of state of the art methods proves the relevance of the proposed method for this type of images

a counterexample to a conjecture of wada abstract wada conjectured in 2007 that the largest eigenvalue of the cartan matrix c of a block of a finite group is rational if and only if all eigenvalues of c are rational we provide a counterexample to this conjecture and discuss related questions

rationality of eigenvalues of cartan matrices in finite groups abstract we study the case in which eigenvalues and elementary divisors of a cartan matrix of a p block b of a finite group coincide in several cases we prove the coincidence occurs if and only if the perron frobenius eigenvalue of the cartan matrix is equal to the order of a defect group of b

eigenvector matrices of cartan matrices for finite groups abstract let c b be the cartan matrix of a p block b of a finite group g we show that there is a unimodular eigenvector matrix u b of c b over a discrete valuation ring r if all eigenvalues of c b are integers when b is a cyclic block a tame block a p block of a p solvable group or the principal 3 block with elementary abelian defect group of order 9

deformation quantization in algebraic geometry abstract we study deformation quantizations of the structure sheaf o x of a smooth algebraic variety x in characteristic 0 our main result is that when x is d affine any formal poisson structure on x determines a deformation quantization of o x canonically up to gauge equivalence this is an algebro geometric analogue of kontsevich s celebrated result

a fast diffeomorphic image registration algorithm abstract this paper describes dartel which is an algorithm for diffeomorphic image registration it is implemented for both 2d and 3d image registration and has been formulated to include an option for estimating inverse consistent deformations nonlinear registration is considered as a local optimisation problem which is solved using a levenberg marquardt strategy the necessary matrix solutions are obtained in reasonable time using a multigrid method a constant eulerian velocity framework is used which allows a rapid scaling and squaring method to be used in the computations dartel has been applied to intersubject registration of 471 whole brain images and the resulting deformations were evaluated in terms of how well they encode the shape information necessary to separate male and female subjects and to predict the ages of the subjects