a general theory of canonical induction formulae abstract so far there exist three independent constructions of two different canonical versions of brauer s induction theorem for complex characters due to v snaith p symonds and the author canonical in this context means functorial with respect to restrictions along group homomorphisms in this article we axiomatize the situation in which the above canonical induction formulae are constructed mackey functors and related structures arise in this way naturally as a convenient language this approach allows us to construct canonical induction formulae for arbitrary mackey functors in particular we obtain canonical induction formulae for the brauer character ring the group of projective characters the ring of trivial source modules and the ring of linear source modules in most cases it is not difficult to construct such formulae over the rational numbers a much more subtle question is whether the constructed formula comes from a canonical induction formula defined over the integers we give a sufficient condition in the general framework of mackey functors for a canonical induction formula to be integral as an application we show how canonical induction formulae allow the construction of functorial maps on representation rings in terms of functorial maps on subrings as for example the span of linear characters in the case of the canonical brauer induction formula this will be used in a subsequent article in the case of adams operations and chern classes

image restoration by matching gradient distributions the restoration of a blurry or noisy image is commonly performed with a map estimator which maximizes a posterior probability to reconstruct a clean image from a degraded image a map estimator when used with a sparse gradient image prior reconstructs piecewise smooth images and typically removes textures that are important for visual realism we present an alternative deconvolution method called iterative distribution reweighting idr which imposes a global constraint on gradients so that a reconstructed image should have a gradient distribution similar to a reference distribution in natural images a reference distribution not only varies from one image to another but also within an image depending on texture we estimate a reference distribution directly from an input image for each texture segment our algorithm is able to restore rich mid frequency textures a large scale user study supports the conclusion that our algorithm improves the visual realism of reconstructed images compared to those of map estimators

exact operator solution of the calogero sutherland model the wave functions of the calogero sutherland model are known to be expressible in terms of jack polynomials a formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived the creation operators that enter in this formula of rodrigues type for the jack polynomials involve dunkl operators

multi observation blind deconvolution with an adaptive sparse prior this paper describes a robust algorithm for estimating a single latent sharp image given multiple blurry and or noisy observations the underlying multi image blind deconvolution problem is solved by linking all of the observations together via a bayesian inspired penalty function which couples the unknown latent image along with a separate blur kernel and noise variance associated with each observation all of which are estimated jointly from the data this coupled penalty function enjoys a number of desirable properties including a mechanism whereby the relative concavity or sparsity is adapted as a function of the intrinsic quality of each corrupted observation in this way higher quality observations may automatically contribute more to the final estimate than heavily degraded ones while troublesome local minima can largely be avoided the resulting algorithm which requires no essential tuning parameters can recover a sharp image from a set of observations containing potentially both blurry and noisy examples without knowing a priori the degradation type of each observation experimental results on both synthetic and real world test images clearly demonstrate the efficacy of the proposed method

correspondence functors and lattices abstract a correspondence functor is a functor from the category of finite sets and correspondences to the category of k modules where k is a commutative ring a main tool for this study is the construction of a correspondence functor associated to any finite lattice t we prove for instance that this functor is projective if and only if the lattice t is distributive moreover it has quotients which play a crucial role in the analysis of simple functors the special case of total orders yields some more specific and complete results

removing atmospheric turbulence via space invariant deconvolution to correct geometric distortion and reduce space and time varying blur a new approach is proposed in this paper capable of restoring a single high quality image from a given image sequence distorted by atmospheric turbulence this approach reduces the space and time varying deblurring problem to a shift invariant one it first registers each frame to suppress geometric deformation through b spline based nonrigid registration next a temporal regression process is carried out to produce an image from the registered frames which can be viewed as being convolved with a space invariant near diffraction limited blur finally a blind deconvolution algorithm is implemented to deblur the fused image generating a final output experiments using real data illustrate that this approach can effectively alleviate blur and distortions recover details of the scene and significantly improve visual quality

the dade group of a p group let p be a prime number this paper solves the question of the structure of the group d p of endo permutation modules over an arbitrary finite p group p that was open after dade s original papers in 1978 19 20 and it gives a proof of the conjectures proposed in 4 and 10 this leads to a presentation of d p by explicit generators and relations generalizing the presentation obtained by dade when p is abelian

a filtration of the modular representation functor abstract let f and k be algebraically closed fields of characteristics p 0 and 0 respectively for any finite group g we denote by k r f g k z g 0 f g the modular representation algebra of g over k where g 0 f g is the grothendieck group of finitely generated f g modules with respect to exact sequences the usual operations induction inflation restriction and transport of structure with a group isomorphism between the finitely generated modules of group algebras over f induce maps between modular representation algebras making k r f an inflation functor we show that the composition factors of k r f are precisely the simple inflation functors s c v i where c ranges over all nonisomorphic cyclic p groups and v ranges over all nonisomorphic simple k out c modules moreover each composition factor has multiplicity 1 we also give a filtration of k r f

simple modules over green biset functors we present three examples of green biset functors for which their simple modules can be parametrized these are particular cases of a conjecture by serge bouc classifying the simple modules over a green biset functor a that generalizes the classification of simple biset functors we also prove this conjecture under certain hypothesis for a

a ghost ring for the left free double burnside ring and an application to fusion systems abstract for a finite group g we define a ghost ring and a mark homomorphism for the double burnside ring b g g of left free g g bisets in analogy to the case of the burnside ring b g the ghost ring has a much simpler ring structure and after tensoring with q one obtains an isomorphism of q algebras as an application of a key lemma we obtain a very general formula for the brauer construction applied to a tensor product of two p permutation bimodules m and n in terms of brauer constructions of the bimodules m and n over a field of characteristic 0 we determine the simple modules of the left free double burnside algebra and prove semisimplicity results for the bifree double burnside algebra these results carry over to results about biset functor categories finally we apply the ghost ring and mark homomorphism to fusion systems on a finite p group we extend a remarkable bijection due to ragnarsson and stancu between saturated fusion systems and certain idempotents of the bifree double burnside algebra over z p to a bijection between all fusion systems and a larger set of idempotents in the bifree double burnside algebra over q

tornehave morphisms iii the reduced tornehave morphism and the burnside unit functor abstract we shall show that a morphism anticipated by tornehave induces and helps to explain bouc s isomorphism relating a quotient of the burnside unit functor measuring a difference between real and rational representations of finite 2 groups and a quotient of the kernel of linearization measuring a difference between rhetorical and rational 2 biset functors

alcahestic subalgebras of the alchemic algebra and a correspondence of simple modules the unified treatment of the five module theoretic notions transfer inflation transport of structure by an isomorphism deflation and restriction is given by the theory of biset functors introduced by bouc in this paper we construct the algebra realizing biset functors as representations the algebra has a presentation similar to the well known mackey algebra we adopt some natural constructions from the theory of mackey functors and give two new constructions of simple biset functors we also obtain a criterion for semisimplicity in terms of the biset functor version of the mark homomorphism the criterion has an elementary generalization to arbitrary finite dimensional algebras over a field

endo p permutation modules this paper introduces the notion of endo p permutation kg module i give a characterization of indecomposable endo p permutation modules with vertex p via their source modules which are exactly the indecomposable endo permutation modules whose classes in the dade group d p are g stable in particular when the normalizer of p controls p fusion i give a classification of sources of endo p permutation modules using the recent classification of the dade group

idempotents of double burnside algebras l enriched bisets and decomposition of p biset functors abstract let r be a unital commutative ring and g be a finite group with order invertible in r we introduce new idempotents t s g in the double burnside algebra r b g g of g over r indexed by conjugacy classes of minimal sections t s of g i e sections such that s t these idempotents are orthogonal and their sum is equal to the identity it follows that for any biset functor f over r the evaluation f g splits as a direct sum of specific r modules indexed by minimal sections of g up to conjugation the restriction of these constructions to the biset category of p groups where p is a prime number invertible in r leads to a decomposition of the category of p biset functors over r as a direct product of categories f l indexed by atoric p groups l up to isomorphism we next introduce the notions of l enriched biset and l enriched biset functor for an arbitrary finite group l and show that for an atoric p group l the category f l is equivalent to the category of l enriched biset functors defined over elementary abelian p groups finally the notion of vertex of an indecomposable p biset functor is introduced when p r and when r is a field of characteristic different from p the objects of the category f l are characterized in terms of vertices of their composition factors

composition factors of functors abstract let x be a family of finite groups satisfying certain conditions and k be a field we study composition factors radicals and socles of biset and related functors defined on x over k for such a functor m and for a group h in x we construct bijections between some classes of maximal respectively simple subfunctors of m and some classes of maximal respectively simple k out h submodules of m h we use these bijections to relate the multiplicity of a simple functor s h v in m to the multiplicity of v in a certain k out h module related to m h we then use these general results to study the structure of one of the important biset and related functors namely the burnside functor b k which assigns to each group g in x its burnside algebra b k g k z b g where b g is the burnside ring of g we find the radical and the socle of b k in most cases of x and k for example if k is of characteristic p 0 and x is a family of finite abelian p groups we find the radical and the socle series of b k considered as a biset functor on x over k we finally study restrictions of functors to nonfull subcategories for example we find some conditions forcing a simple deflation functor to remain simple as a mackey functor for an inflation functor m defined on abelian groups over a field of characteristic zero we also obtain a criterion for m to be semisimple in terms of the images of inflation and induction maps on m

on the representation types of category algebras of finite ei categories abstract a finite ei category is a small category with finitely many morphisms such that every endomorphism is an isomorphism they include finite groups finite posets and free categories of finite quivers as special cases in this paper we consider category algebras of finite ei categories with two or three objects describe some criteria for finite representation type and classify the representation types for certain classes of finite ei categories with extra properties

foncteurs d ensembles munis d une double action resume sommaire 1 introduction 2 notations generalites 3 ensembles munis d une double action 3 1 notations 3 2 formule de mackey 3 3 decomposition d un morphisme 3 4 sous categories 3 4 1 ensembles p q libres 3 4 2 groupes reductifs 4 foncteurs simples 5 une theorie de vortex et de source 6 une seconde theorie de vortex et source 7 le foncteur de burnside 7 1 un homomorphisme deb g dans end g 7 2 les sous foncteurs du foncteur de burnside en caracteristique 0 7 2 1 premier exemple 7 2 2 les constantesmg n 7 2 3 lesb groupes 7 2 4 les sous foncteurs deb 7 2 5 exemples deb groupes 8 exemples de foncteurs simples 8 1 le cas des foncteurs de mackey globaux 8 2 les foncteurssh k 8 3 certains foncteurs simples en caracteristique 0 9 l algebreegg end g egg 9 1 une base naturelle 9 2 multiplication 9 3 semi simplicite 10 le foncteur des representations complexes 10 1 caracteres 10 2 sous foncteurs et decomposition 10 3 semi simplicite

polynomial ideals and classes of finite groups the object of this note is to discuss the properties of some polynomials on a countable set of indeterminates attached to any finite group which generalize the eulerian functions of a group defined by p hall 1936 quart j math 7 134 151 in particular i will define some classes of finite groups associated to prime ideals of the polynomial ring and i will show that each finite group has a unique largest quotient in such a class of groups this work is a generalization of the notion of the b group introduced in an earlier paper bouc 1996 j algebra183 664 736 through a systematic use of the polynomial formalism of section 7 2 5 there for the reader s convenience however this paper is self contained and the proofs of the results already stated are included

generalized correspondence functors abstract a generalized correspondence functor is a functor from the category of finite sets and t generalized correspondences to the category of all k modules where t is a finite distributive lattice and k a commutative ring we parametrize simple generalized correspondence functors using the notions of t module and presheaf of posets as an application we prove finiteness and stabilization results in particular when k is a field any finitely generated correspondence functor has finite length and when k is noetherian any subfunctor of a finitely generated functor is finitely generated

the functor of p permutation modules for abelian groups let k be a field of characteristic p where p is a prime number let pp k g be the grothendieck group of p permutation kg modules where g is a finite group and let cpp k g be pp k g tensored with the field of complex numbers c in this article we find all the composition factors of the biset functor cpp k restricted to the category of abelian groups

rational p biset functors abstract in this paper i give several characterizations of rational biset functors over p groups which are independent of the knowledge of genetic bases for p groups i also introduce a construction of new biset functors from known ones which is similar to the yoneda construction for representable functors and to the dress construction for mackey functors and i show that this construction preserves the class of rational p biset functors this leads to a characterization of rational p biset functors as additive functors from a specific quotient category of the biset category to abelian groups finally i give a description of the largest rational quotient of the burnside p biset functor when p is odd this is simply the functor r q of rational representations but when p 2 it is a non split extension of r q by a specific uniserial functor which happens to be closely related to the functor of units of the burnside ring

revisiting bayesian blind deconvolution blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation because this problem is fundamentally ill posed strong priors on both the sharp image and blur kernel are required to regularize the solution space while this naturally leads to a standard map estimation framework performance is compromised by unknown trade off parameter settings optimization heuristics and convergence issues stemming from non convexity and or poor prior selections to mitigate some of these problems a number of authors have recently proposed substituting a variational bayesian vb strategy that marginalizes over the high dimensional image space leading to better estimates of the blur kernel however the underlying cost function now involves both integrals with no closed form solution and complex function valued arguments thus losing the transparency of map beyond standard bayesian inspired intuitions it thus remains unclear by exactly what mechanism these methods are able to operate rendering understanding improvements and extensions more difficult to elucidate these issues we demonstrate that the vb methodology can be recast as an unconventional map problem with a very particular penalty prior that conjoins the image blur kernel and noise level in a principled way this unique penalty has a number of useful characteristics pertaining to relative concavity local minima avoidance normalization and scale invariance that allow us to rigorously explain the success of vb including its existing implementational heuristics and approximations it also provides strict criteria for learning the noise level and choosing the optimal image prior that perhaps counter intuitively need not reflect the statistics of natural scenes in so doing we challenge the prevailing notion of why vb is successful for blind deconvolution while providing a transparent platform for introducing enhancements and extensions moreover the underlying insights carry over to a wide variety of other bilinear models common in the machine learning literature such as independent component analysis dictionary learning sparse coding and non negative matrix factorization

understanding blind deconvolution algorithms blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown recent algorithms have afforded dramatic progress yet many aspects of the problem remain challenging and hard to understand the goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally we explain the previously reported failure of the naive map approach by demonstrating that it mostly favors no blur explanations we show that using reasonable image priors a naive simulations map estimation of both latent image and blur kernel is guaranteed to fail even with infinitely large images sampled from the prior on the other hand we show that since the kernel size is often smaller than the image size a map estimation of the kernel alone is well constrained and is guaranteed to succeed to recover the true blur the plethora of recent deconvolution techniques makes an experimental evaluation on ground truth data important as a first step toward this experimental evaluation we have collected blur data with ground truth and compared recent algorithms under equal settings additionally our data demonstrate that the shift invariant blur assumption made by most algorithms is often violated

diagonal p permutation functors abstract let k be an algebraically closed field of positive characteristic p and let f be an algebraically closed field of characteristic 0 we consider the f linear category f p p k of finite groups in which the set of morphisms from g to h is the f linear extension f t h g of the grothendieck group t h g of p permutation k h k g bimodules with twisted diagonal vertices the f linear functors from f p p k to f mod are called diagonal p permutation functors they form an abelian category f p p k we study in particular the functor f t sending a finite group g to the grothendieck group f t g of p permutation kg modules and show that f t is a semisimple object of f p p k equal to the direct sum of specific simple functors parametrized by isomorphism classes of pairs p s of a finite p group p and a generator s of a p subgroup acting faithfully on p this leads to a precise description of the evaluations of these simple functors in particular we show that the simple functor indexed by the trivial pair 1 1 is isomorphic to the functor sending a finite group g to f k 0 k g where k 0 k g is the grothendieck group of projective kg modules

subset selection in noise based on diversity measure minimization we develop robust methods for subset selection based on the minimization of diversity measures a bayesian framework is used to account for noise in the data and a maximum a posteriori map estimation procedure leads to an iterative procedure which is a regularized version of the focal underdetermined system solver focuss algorithm the convergence of the regularized focuss algorithm is established and it is shown that the stable fixed points of the algorithm are sparse we investigate three different criteria for choosing the regularization parameter quality of fit sparsity criterion l curve the l curve method as applied to the problem of subset selection is found not to be robust and we propose a novel modified l curve procedure that solves this problem each of the regularized focuss algorithms is evaluated through simulation of a detection problem and the results are compared with those obtained using a sequential forward selection algorithm termed orthogonal matching pursuit omp in each case the regularized focuss algorithm is shown to be superior to the omp in noisy environments

a n type dunkl operators and new spin calogero sutherland models a new family of an type dunkl operators preserving a polynomial subspace of finite dimension is constructed using a general quadratic combination of these operators and the usual dunkl operators several new families of exactly and quasi exactly solvable quantum spin calogero sutherland models are obtained these include in particular three families of quasi exactly solvable elliptic spin hamiltonians

the coset poset and probabilistic zeta function of a finite group abstract we investigate the topological properties of the poset of proper cosets xh in a finite group g of particular interest is the reduced euler characteristic which is closely related to the value at 1 of the probabilistic zeta function of g our main result gives divisibility properties of this reduced euler characteristic

a study of a simple p permutation functor abstract in this article we are going to give a description of a simple p permutation functor s 1 c we can prove the existence of an isomorphism between this functor and the functor which sends a group to the image of the cartan homomorphism this fact allows us to link the evaluation of s 1 c with the image of the cartan matrix of comack k g and gives us an explicit formula for the dimension of this evaluation

partial deconvolution with inaccurate blur kernel most non blind deconvolution methods are developed under the error free kernel assumption and are not robust to inaccurate blur kernel unfortunately despite the great progress in blind deconvolution estimation error remains inevitable during blur kernel estimation consequently severe artifacts such as ringing effects and distortions are likely to be introduced in the non blind deconvolution stage in this paper we tackle this issue by suggesting 1 a partial map in the fourier domain for modeling kernel estimation error and 2 a partial deconvolution model for robust deblurring with inaccurate blur kernel the partial map is constructed by detecting the reliable fourier entries of estimated blur kernel and partial deconvolution is applied to wavelet based and learning based models to suppress the adverse effect of kernel estimation error furthermore an e m algorithm is developed for estimating the partial map and recovering the latent sharp image alternatively experimental results show that our partial deconvolution model is effective in relieving artifacts caused by inaccurate blur kernel and can achieve favorable deblurring quality on synthetic and real blurry images

blind image deconvolution using machine learning for three dimensional microscopy in this work we propose a novel method for the regularization of blind deconvolution algorithms the proposed method employs example based machine learning techniques for modeling the space of point spread functions during an iterative blind deconvolution process a prior term attracts the point spread function estimates to the learned point spread function space we demonstrate the usage of this regularizer within a bayesian blind deconvolution framework and also integrate into the latter a method for noise reduction thus creating a complete blind deconvolution method the application of the proposed algorithm is demonstrated on synthetic and real world three dimensional images acquired by a wide field fluorescence microscope where the need for blind deconvolution algorithms is indispensable yielding excellent results

new algebraic quantum many body problems we develop a systematic procedure for constructing quantum many body problems whose spectrum can be partially or totally computed by purely algebraic means the exactly solvable models include rational and hyperbolic potentials related to root systems in some cases with an additional external field the quasi exactly solvable models can be considered as deformations of the previous ones which share their algebraic character

normalizability of one dimensional quasi exactly solvable schrodinger operators we completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi exactly solvable schrodinger operator on the line methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi exactly solvable hamiltonians and explicit normalizability conditions in general coordinate systems

a remark on the dade group and the burnside group abstract the object of this note is to show that the formula for tensor induction of relative syzygies in the dade group stated in s bouc j reine angew math 523 2000 113 can be viewed as a special case of a functorial homomorphism from the dual b of the burnside group to the subgroup d of the dade group generated by relative syzygies it follows that there exists a short exact sequence of functors 0 r q b d d tors 0 where r q is the functor of rational representations this may be viewed as an improvement from q to z of theorem d of invent math 139 2000 275

correspondence functors and finiteness conditions abstract we investigate the representation theory of finite sets the correspondence functors are the functors from the category of finite sets and correspondences to the category of k modules where k is a commutative ring they have various specific properties which do not hold for other types of functors in particular if k is a field and if f is a correspondence functor then f is finitely generated if and only if the dimension of f x grows exponentially in terms of the cardinality of the finite set x moreover in such a case f has actually finite length also if k is noetherian then any subfunctor of a finitely generated functor is finitely generated

regularized motion blur kernel estimation with adaptive sparse image prior learning this paper proposes a regularized negative log marginal likelihood minimization method for motion blur kernel estimation which is the core problem of blind motion deblurring in contrast to existing approaches the proposed method treats the blur kernel as a deterministic parameter in a directed graphical model wherein the sharp image is sparsely modeled by using a three layer hierarchical bayesian prior and the inverse noise variance is supposed distributed to the gamma hyper prior by borrowing the ideas of mean filed approximation and iteratively reweighted least squares the posterior distributions of the sharp image the inverse noise variance and the hyper parameters involved in the image prior as well as the deterministic model parameters including the motion blur kernel and those involved in the hyper priors are all estimated automatically for each blind motion deblurring problem it is worthy to note that the new approach relies on a strict minimization objective function and learns a more adaptive sparse image prior while with considerably less implementation heuristics compared with existing motion blur kernel estimation approaches experimental results on both benchmark and real world motion blurred images demonstrate that the proposed method has achieved state of the art or even better performance than the current blind motion deblurring approaches in terms of the image deblurring quality the results also show that the proposed approach is robust to the size of the motion blur kernel to a great extent a new motion blur kernel estimation method is proposed for blind image deblurring the new method is formulated in a unified and rigorous optimization perspective sparse image priors are learned adaptively for each blind deblurring problem the noise variance is automatically estimated unlike state of the art vb methods the method achieves better performance in terms of deblurring effectiveness

expansivity and roquette groups we prove the non existence of expansive subgroups with trivial global core in different families of roquette groups this study is motivated by the importance of expansive subgroups in the theory of stabilizing bisets highlighted in 4

robust multichannel blind deconvolution via fast alternating minimization blind deconvolution which comprises simultaneous blur and image estimations is a strongly ill posed problem it is by now well known that if multiple images of the same scene are acquired this multichannel mc blind deconvolution problem is better posed and allows blur estimation directly from the degraded images we improve the mc idea by adding robustness to noise and stability in the case of large blurs or if the blur size is vastly overestimated we formulate blind deconvolution as an l1 regularized optimization problem and seek a solution by alternately optimizing with respect to the image and with respect to blurs each optimization step is converted to a constrained problem by variable splitting and then is addressed with an augmented lagrangian method which permits simple and fast implementation in the fourier domain the rapid convergence of the proposed method is illustrated on synthetically blurred data applicability is also demonstrated on the deconvolution of real photos taken by a digital camera

on the depth of subgroups and group algebra extensions we investigate notions of depth for inclusions of rings b a in particular for group algebra extensions rh rg for finite groups h g and a non zero commutative ring r a group theoretic or combinatorial notion of depth for h in g is defined and used to show that rh rg has always finite depth we compare the depths of h g and rh rg and investigate how the depth varies with r

fields of experts we develop a framework for learning generic expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks the approach provides a practical method for learning high order markov random field mrf models with potential functions that extend over large pixel neighborhoods these clique potentials are modeled using the product of experts framework that uses non linear functions of many linear filter responses in contrast to previous mrf approaches all parameters including the linear filters themselves are learned from training data we demonstrate the capabilities of this field of experts model with two example applications image denoising and image inpainting which are implemented using a simple approximate inference scheme while the model is trained on a generic image database and is not tuned toward a specific application we obtain results that compete with specialized techniques

representations of the double burnside algebra and cohomology of the extraspecial p group ii abstract let e be the extraspecial p group of order p 3 and exponent p where p is an odd prime we determine the mod p cohomology h x f p of a summand x in the stable splitting of p completed classifying space be in the previous paper hida and yagita 2014 7 we determined this cohomology modulo nilpotence in this paper we consider the whole of the cohomology moreover we consider the stable splittings of bg for some finite groups with sylow p subgroup e related to the three dimensional linear group l 3 p

blind deconvolution with model discrepancies blind deconvolution is a strongly ill posed problem comprising of simultaneous blur and image estimation recent advances in prior modeling and or inference methodology led to methods that started to perform reasonably well in real cases however as we show here they tend to fail if the convolution model is violated even in a small part of the image methods based on variational bayesian inference play a prominent role in this paper we use this inference in combination with the same prior for noise image and blur that belongs to the family of independent non identical gaussian distributions known as the automatic relevance determination prior we identify several important properties of this prior useful in blind deconvolution namely enforcing non negativity of the blur kernel favoring sharp images over blurred ones and most importantly handling non gaussian noise which as we demonstrate is common in real scenarios the presented method handles discrepancies in the convolution model and thus extends applicability of blind deconvolution to real scenarios such as photos blurred by camera motion and incorrect focus

removing motion blur with space time processing although spatial deblurring is relatively well understood by assuming that the blur kernel is shift invariant motion blur is not so when we attempt to deconvolve on a frame by frame basis this is because in general videos include complex multilayer transitions indeed we face an exceedingly difficult problem in motion deblurring of a single frame when the scene contains motion occlusions instead of deblurring video frames individually a fully 3 d deblurring method is proposed in this paper to reduce motion blur from a single motion blurred video to produce a high resolution video in both space and time unlike other existing approaches the proposed deblurring kernel is free from knowledge of the local motions most importantly due to its inherent locally adaptive nature the 3 d deblurring is capable of automatically deblurring the portions of the sequence which are motion blurred without segmentation and without adversely affecting the rest of the spatiotemporal domain where such blur is not present our method is a two step approach first we upscale the input video in space and time without explicit estimates of local motions and then perform 3 d deblurring to obtain the restored sequence

the composition factors of the functor of permutation modules the grothendieck group of permutation modules for a finite group g becomes a biset functor when g is allowed to vary all the composition factors of this biset functor are determined

on the ideals and essential algebras of shifted functors of linear representations abstract we present a study on the shifted green biset functors k r f g of linear f representations with coefficients over k for fields k and f of characteristic zero and a finite group g we provide a criterion for the vanishing of their essential algebras and we prove that the condition of uniqueness of minimal groups for simple modules holds for these functors we give a parametrization of a family of simple k r q g modules we also prove the semisimplicity of the category of c r c g modules by means of an equivalence with a category of modules over a semisimple algebra

tensor product of correspondence functors abstract as part of the study of correspondence functors the present paper investigates their tensor product and proves some of its main properties in particular the correspondence functor associated to a finite lattice has the structure of a commutative algebra in the tensor category of all correspondence functors and a converse also holds

borel smith functions and the dade group we show that there is an exact sequence of biset functors over p groups 0 cb jb d 0 where cb is the biset functor for the group of borel smith functions b is the dual of the burnside ring functor d is the functor for the subgroup of the dade group generated by relative syzygies and the natural transformation is the transformation recently introduced by the first author in s bouc a remark on the dade group and the burnside group j algebra 279 2004 180 190 we also show that the kernel of mod 2 reduction of is naturally equivalent to the functor b of units of the burnside ring and obtain exact sequences involving the torsion part of d mod 2 reduction of cb and b

mackey functors induction from restriction functors and coinduction from transfer functors abstract boltje s plus constructions extend two well known constructions on mackey functors the fixed point functor and the fixed quotient functor in this paper we show that the plus constructions are induction and coinduction functors of general module theory as an application we construct simple mackey functors from simple restriction functors and simple transfer functors we also give new proofs for the classification theorem for simple mackey functors and semisimplicity theorem of mackey functors

a conjecture on b groups in this note i propose the following conjecture a finite group g is nilpotent if and only if its largest quotient b group beta g is nilpotent i give a proof of this conjecture under the additional assumption that g be solvable i also show that this conjecture is equivalent to the following the kernel of restrictions to nilpotent subgroups is a biset subfunctor of the burnside functor

fibered biset functors abstract the theory of biset functors introduced by serge bouc gives a unified treatment of operations in representation theory that are induced by permutation bimodules in this paper by considering fibered bisets we introduce and describe the basic theory of fibered biset functors which is a natural framework for operations induced by monomial bimodules the main result of this paper is the classification of simple fibered biset functors

the ideals of the slice burnside p biset functor abstract let g be a finite group and k be a field of characteristic zero our purpose is to investigate the ideals of the slice burnside functor k it turns out that they are the subfunctors f of k such that for any finite group g the evaluation f g is an ideal of the algebra k g this allows for a determination of the full lattice of ideals of the slice burnside p biset functor k p

maximal subgroups of direct products we determine all maximal subgroups of the direct product g n of n copies of a group g if g is finite we show that the number of maximal subgroups of g n is a quadratic function of n if g is perfect but grows exponentially otherwise we deduce a theorem of wiegold about the growth behaviour of the number of generators of g n

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

a logarithmic image prior for blind deconvolution blind deconvolution consists in the estimation of a sharp image and a blur kernel from an observed blurry image because the blur model admits several solutions it is necessary to devise an image prior that favors the true blur kernel and sharp image many successful image priors enforce the sparsity of the sharp image gradients ideally the l 0 l0 norm is the best choice for promoting sparsity but because it is computationally intractable some methods have used a logarithmic approximation in this work we also study a logarithmic image prior we show empirically how well the prior suits the blind deconvolution problem our analysis confirms experimentally the hypothesis that a prior should not necessarily model natural image statistics to correctly estimate the blur kernel furthermore we show that a simple maximum a posteriori formulation is enough to achieve state of the art results to minimize such formulation we devise two iterative minimization algorithms that cope with the non convexity of the logarithmic prior one obtained via the primal dual approach and one via majorization minimization

a characterization of finite ei categories with hereditary category algebras abstract in this paper we give an explicit algorithm to construct the ordinary quiver of a finite ei category for which the endomorphism groups of all objects have orders invertible in the field k we classify all finite ei categories with hereditary category algebras characterizing them as free ei categories in a sense which we define for which all endomorphism groups of objects have invertible orders some applications on the representation types of finite ei categories are derived

the group of endo permutation modules the group d p of all endo permutation modules for a finite p group p is a finitely generated abelian group we prove that its torsion free rank is equal to the number of conjugacy classes of non cyclic subgroups of p we also obtain partial results on its torsion subgroup we determine next the structure of q otimes d viewed as a functor which turns out to be a simple functor s e q indexed by the elementary group e of order p 2 and the trivial out e module q finally we describe a rather strange exact sequence relating q otimes d p q otimes b p and q otimes r p where b p is the burnside ring and r p is the grothendieck ring of qp modules

rhetorical biset functors rational p biset functors and their semisimplicity in characteristic zero rhetorical biset functors can be defined for any family of finite groups that is closed under subquotients up to isomorphism the rhetorical p biset functors almost coincide with the rational p biset functors we show that over a field with characteristic zero the rhetorical biset functors are semisimple and furthermore they admit a character theory involving primitive characters of automorphism groups of cyclic groups

quasi exactly solvable problems and sl 2 algebra recently discovered quasi exactly solvable problems of quantum mechanics are shown to be related to the existence of the finite dimensional representations of the groupsl 2 q whereq r c it is proven that the bilinear formh a j j b j stand for the generators allows one to generate a set of quasi exactly solvable problems of different types including those that are already known we get in particular problems in which the spectral riemannian surface containing an infinite number of sheets is split off one or two finite sheet pieces in the general case the transitionh h d2 dx2 v x is realized with the aim of the elliptic functions all known exactly solvable quantum problems with known spectrum and factorized riemannian surface can be obtained in this approach

ring of subquotients of a finite group i linearization abstract we introduce the ring g of subquotients of a finite group g as an abelian group it is free on the set of conjugacy classes of subquotients of the group g the ring g integrally extends the burnside ring and there is a linearization map with range the grothendieck ring of the mackey algebra

the functor of rational representations for p groups abstract let k be a field of characteristic p 0 let c p k be the category whose objects are the finite p groups morphisms are the k linear combinations of bisets and composition of morphisms is obtained by k linear extension from the usual product of bisets let f p k denote the category of k linear functors from c p k to the category of k vector spaces this paper investigates the structure of the functor kr q mapping a p group p to kr q p k z r q p as an object of f p k where r q p is the grothendieck group of the category of finite dimensional q p modules the main result is an explicit description of the lattice of all subfunctors of kr q in particular for p odd it is shown that kr q is a uniserial object in f p k for p 2 the lattice of subfunctors of kr q can be described as the lattice of closed subsets of a graph whose vertices are the 2 groups of normal 2 rank 1 in both cases a composition series of kr q is obtained which leads to a formula giving the dimension of the evaluations sq k p of the simple objects sq k of f p k associated to p groups q of normal p rank 1 different from cp this formula can be phrased in terms of rational representations of p but also in terms of the geometry of the lattice of subgroups of p using the notions of basic subgroups and origins for example if p 2 the dimension of s 1 k p is equal to the number of absolutely irreducible q p modules