robust multitask multiview tracking in videos various sparse representation based methods have been proposed to solve tracking problems and most of them employ least squares lss criteria to learn the sparse representation in many tracking scenarios traditional ls based methods may not perform well owing to the presence of heavy tailed noise in this paper we present a tracking approach using an approximate least absolute deviation lad based multitask multiview sparse learning method to enjoy robustness of lad and take advantage of multiple types of visual features such as intensity color and texture the proposed method is integrated in a particle filter framework where learning the sparse representation for each view of the single particle is regarded as an individual task the underlying relationship between tasks across different views and different particles is jointly exploited in a unified robust multitask formulation based on lad in addition to capture the frequently emerging outlier tasks we decompose the representation matrix to two collaborative components that enable a more robust and accurate approximation we show that the proposed formulation can be effectively approximated by nesterov s smoothing method and efficiently solved using the accelerated proximal gradient method the presented tracker is implemented using four types of features and is tested on numerous synthetic sequences and real world video sequences including the cvpr2013 tracking benchmark and alov data set both the qualitative and quantitative results demonstrate the superior performance of the proposed approach compared with several state of the art trackers

on the pre lie algebra of specified feynman graphs we study the pre lie algebra of specified feynman graphs v t and we define a pre lie structure on its doubling space f t we prove that f t is pre lie module on v t and we find some relations between the two pre lie structures also we study the enveloping algebras of two pre lie algebras denoted respectively by d t and h t and we prove that d t is a module bialgebra on h t we study the pre lie algebra of specified feynman graphs v t and we define a pre lie structure on its doubling space f t we prove that f t is pre lie module on v t and we find some relations between the two pre lie structures also we study the enveloping algebras of two pre lie algebras denoted respectively by d t and h t and we prove that d t is a module bialgebra on h t

the fate of the wilson fisher fixed point in non commutative ϕ4 in this article we study non commutative vector sigma model with the most general 4 interaction on moyal weyl spaces we compute the 2 and 4 point functions to all orders in the large n limit and then apply the approximate wilson renormalization group recursion formula to study the renormalized coupling constants of the theory the non commutative wilson fisher fixed point interpolates between the commutative wilson fisher fixed point of the ising universality class which is found to lie at zero value of the critical coupling constant a of the zero dimensional reduction of the theory and a novel strongly interacting fixed point which lies at infinite value of a corresponding to maximal non commutativity beyond which the two sheeted structure of a as a function of the dilation parameter disappears

parametric representation of covariant noncommutative qft models we extend the parametric representation of renormalizable non commutative quantum field theories to a class of theories which we call covariant because their power counting is definitely more difficult to obtain this class of theories is important since it includes gauge theories which should be relevant for the quantum hall effect

noncommutative poisson bialgebras abstract in this paper we introduce the notion of a noncommutative poisson bialgebra and establish the equivalence between matched pairs manin triples and noncommutative poisson bialgebras using quasi representations and the corresponding cohomology theory of noncommutative poisson algebras we study coboundary noncommutative poisson bialgebras which leads to the introduction of the poisson yang baxter equation a skew symmetric solution of the poisson yang baxter equation naturally gives a coboundary noncommutative poisson bialgebra rota baxter operators more generally o operators on noncommutative poisson algebras and noncommutative pre poisson algebras are introduced by which we construct skew symmetric solutions of the poisson yang baxter equation in some special noncommutative poisson algebras obtained from these structures

restricted range approximation by splines and variational inequalities error estimates are obtained for the approximation of nonnegative functions from below by nonnegative splines the maximum norm results are of the same order as the jackson type estimates for unconstrained approximation by splines the l 2 results are used to estimate the rate of convergence of the ritz method for certain variational inequalities the more general problem of approximating functions f in the set w g in c a b l x leqq g x leqq u x x in a b by splines in w is also discussed

algebraic renormalisation of regularity structures we give a systematic description of a canonical renormalisation procedure of stochastic pdes containing nonlinearities involving generalised functions this theory is based on the construction of a new class of regularity structures which comes with an explicit and elegant description of a subgroup of their group of automorphisms this subgroup is sufficiently large to be able to implement a version of the bphz renormalisation prescription in this context this is in stark contrast to previous works where one considered regularity structures with a much smaller group of automorphisms which lead to a much more indirect and convoluted construction of a renormalisation group acting on the corresponding space of admissible models by continuous transformations our construction is based on bialgebras of decorated coloured forests in cointeraction more precisely we have two hopf algebras in cointeraction coacting jointly on a vector space which represents the generalised functions of the theory two twisted antipodes play a fundamental role in the construction and provide a variant of the algebraic birkhoff factorisation that arises naturally in perturbative quantum field theory

preordered forests packed words and contraction algebras abstract we introduce the notions of preordered and heap preordered forests generalizing the construction of ordered and heap ordered forests we prove that the algebras of preordered and heap preordered forests are hopf for the cut coproduct and we construct a hopf morphism to the hopf algebra of packed words moreover we define another coproduct on the preordered forests given by the contraction of edges finally we give a combinatorial description of morphism defined on hopf algebras of forests with values in the hopf algebras of shuffles or quasi shuffles

integrable renormalization i the ladder case in recent years a hopf algebraic structure underlying the process of renormalization in quantum field theory was found it led to a birkhoff factorization for regularized hopf algebra characters i e for feynman rules in this work we would like to show that this birkhoff factorization finds its natural formulation in terms of a classical r matrix coming from a rota baxter structure underlying the target space of the regularized hopf algebra characters working in the rooted tree hopf algebra the simple case of the hopf subalgebra of ladder trees is treated in detail the extension to the general case i e the full hopf algebra of rooted trees or feynman graphs is briefly outlined

a lie theoretic approach to renormalization motivated by recent work of connes and marcolli based on the connes kreimer approach to renormalization we augment the latter by a combinatorial lie algebraic point of view our results rely both on the properties of the dynkin idempotent one of the fundamental lie idempotents in the theory of free lie algebras and on properties of hopf algebras encapsulated in the notion of associated descent algebras besides leading very directly to proofs of the main combinatorial aspects of the renormalization procedures the new techniques give rise to an algebraic approach to the galois theory of renormalization in particular they do not depend on the geometry underlying the case of dimensional regularization and the riemann hilbert correspondence this is illustrated with a discussion of the bphz renormalization scheme

hopf algebras of rooted forests cocyles and free rota baxter algebras the hopf algebra and the rota baxter algebra are the two algebraic structures underlying the algebraic approach of connes and kreimer to renormalization of perturbative quantum field theory in particular the hopf algebra of rooted trees serves as the baby model of feynman graphs in their approach and can be characterized by certain universal properties involving a hochschild 1 cocycle decorated rooted trees have also been applied to study feynman graphs we will continue the study of universal properties of various spaces of decorated rooted trees with such a 1 cocycle leading to the concept of a cocycle hopf algebra we further apply the universal properties to equip a free rota baxter algebra with the structure of a cocycle hopf algebra

fast low rank modifications of the thin singular value decomposition this paper develops an identity for additive modivations of a singular value decomposition svd to reflect updates downdates shifts and edits of the data matrix this sets the stage for fast and ememory efficient sequential algorithms for tracking singular values and subspaces in conjunction with a fast solution for the pseudo inverse of a submatrix of an orthogonal matrix we develop a scheme for computing a thin svd of streaming data in a single pass with linear time complexity a rank r think svd of a p x q matrix can be computed in o pqr time for r less than or equal sqroot min p q linear algebra and its applications

parametric representation of rank d tensorial group field theory abelian models with kinetic term sum_s p_s mu we consider the parametric representation of the amplitudes of abelian models in the so called framework of rank d tensorial group field theory these models are called abelian because their elds live on

constructive renormalization for φ24 theory with loop vertex expansion in this paper we construct the two dimensional euclidean 4 quantum field theory using the method of loop vertex expansion we reproduce the results of standard constructive theory for example the borel summability of the schwinger functions in the coupling constant our method should be also suitable for the future construction of grosse wulkenhaar models on non commutative space time

renormalization in quantum field theory and the riemann hilbert problem i the hopf algebra structure of graphs and the main theorem this paper gives a complete selfcontained proof of our result announced in 6 showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the riemann hilbert problem we shall first show that for any quantum field theory the combinatorics of feynman graphs gives rise to a hopf algebra which is commutative as an algebra it is the dual hopf algebra of the enveloping algebra of a lie algebra whose basis is labelled by the one particle irreducible feynman graphs the lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa the corresponding lie group g is the group of characters of we shall then show that using dimensional regularization the bare unrenormalized theory gives rise to a loop where c is a small circle of complex dimensions around the integer dimension d of space time our main result is that the renormalized theory is just the evaluation at z d of the holomorphic part of the birkhoff decomposition of we begin to analyse the group g and show that it is a semi direct product of an easily understood abelian group by a highly non trivial group closely tied up with groups of diffeomorphisms the analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title

extended compressed tracking via random projection based on msers and online ls svm learning the compressed tracking algorithm ct tracker is a well known visual tracking method that models a target object s appearance through sparse random projection however the tracking results are not stable and robust due to the randomness of random projection to solve this problem a more stable and robust approach is proposed for visual tracking based on maximally stable extremal regions msers sparse random projection and online least squares svm classifier ls svm learning to obtain a relatively stable appearance model the stable connected components of an object based on msers in image feature space are extracted with the fusion of msers and sparse random projection we model adaptive object appearance to adapt the variation of appearance additionally an online closed form ls svm is employed to quickly and robustly predict the target object location in a tracking by detection framework experimental results on benchmark sequences show the stability and robustness of the proposed algorithm compared with the existing ct based trackers and other state of the art trackers highlightsa more stable and robust approach is proposed for visual tracking relying on maximally stable extremal regions msers sparse random projection and online least squares svm classifier ls svm learning with the fusion of msers and sparse random projection the stable adaptive object appearance is modeled to adapt the variation of appearance an online closed form ls svm is employed to quickly and robustly predict the target object location

a combinatorial hopf algebra for nonlinear output feedback control systems abstract in this work a combinatorial description is provided of a faa di bruno type hopf algebra which naturally appears in the context of fliess operators in nonlinear feedback control theory it is a connected graded commutative and non cocommutative hopf algebra defined on rooted circle trees a cancellation free forest formula for its antipode is given

non commutative hopf algebra of formal diffeomorphisms abstract this paper deals with two hopf algebras which are the non commutative analogues of two different groups of formal power series the first group is the set of invertible series with the group law being multiplication of series while the second is the set of formal diffeomorphisms with the group law being a composition of series the motivation to introduce these hopf algebras comes from the study of formal series with non commutative coefficients invertible series with non commutative coefficients still form a group and we interpret the corresponding new non commutative hopf algebra as an alternative to the natural hopf algebra given by the co ordinate ring of the group which has the advantage of being functorial in the algebra of coefficients for the formal diffeomorphisms with non commutative coefficients this interpretation fails because in this case the composition is not associative anymore however we show that for the dual non commutative algebra there exists a natural co associative co product defining a non commutative hopf algebra moreover we give an explicit formula for the antipode which represents a non commutative version of the lagrange inversion formula and we show that its coefficients are related to planar binary trees then we extend these results to the semi direct co product of the previous hopf algebras and to series in several variables finally we show how the non commutative hopf algebras of formal series are related to some renormalization hopf algebras which are combinatorial hopf algebras motivated by the renormalization procedure in quantum field theory and to the renormalization functor given by the double tensor algebra on a bi algebra

parametric representation of noncommutative field theory in this paper we investigate the schwinger parametric representation for the feynman amplitudes of the recently discovered renormalizable phi 4 4 quantum field theory on the moyal non commutative mathbb r 4 space this representation involves new hyperbolic polynomials which are the non commutative analogs of the usual kirchoff or symanzik polynomials of commutative field theory but contain richer topological information

perturbative quantum field theory via vertex algebras in this paper we explain how perturbative quantum field theory can be formulated in terms of a version of vertex algebras our starting point is the wilson zimmermann operator product expansion ope following ideas of a previous paper s hollands e print arxiv 0802 2198 we consider a consistency essentially associativity condition satisfied by the coefficients in this expansion we observe that the information in the ope coefficients can be repackaged straightforwardly into vertex operators and that the consistency condition then has essentially the same form as the key condition in the theory of vertex algebras we develop a general theory of perturbations of the algebras that we encounter similar in nature to the hochschild cohomology describing the deformation theory of ordinary algebras the main part of the paper is devoted to the question how one can calculate the perturbations corresponding to a given interaction lagrangian such as 4 in practice using the consistency condition an

holder continuous rough paths by fourier normal ordering we construct in this article an explicit geometric rough path over arbitrary d dimensional paths with finite 1 variation for any alpha in 0 1 the method may be coined as fourier normal ordering since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest fourier frequencies in doing so there appear non trivial tree combinatorics which are best understood by using the structure of the hopf algebra of decorated rooted trees in connection with the chen or multiplicative property and of the hopf shuffle algebra in connection with the shuffle or geometric property holder continuity is proved by using besov norms the method is well suited in particular in view of applications to probability theory see the companion article 34 for the construction of a rough path over multidimensional fractional brownian motion with hurst index 1 4 or 35 for a short survey in that case

normal coordinates and primitive elements in the hopf algebra of renormalization we introduce normal coordinates on the infinite dimensional group g introduced by connes and kreimer in their analysis of the hopf algebra of rooted trees we study the primitive elements of the algebra and show that they are generated by a simple application of the inverse poincare lemma given a closed left invariant 1 form on g for the special case of the ladder primitives we find a second description that relates them to the hopf algebra of functionals on power series with the usual product either approach shows that the ladder primitives are given by the schur polynomials the relevance of the lower central series of the dual lie algebra in the process of renormalization is also discussed leading to a natural concept of k primitiveness which is shown to be equivalent to the one already in the literature

renormalisation of noncommutative ϕ 4 theory by multi scale analysis in this paper we give a much more efficient proof that the real euclidean 4 model on the four dimensional moyal plane is renormalisable to all orders we prove rigorous bounds on the propagator which complete the previous renormalisation proof based on renormalisation group equations for non local matrix models on the other hand our bounds permit a powerful multi scale analysis of the resulting ribbon graphs here the dual graphs play a particular role because the angular momentum conservation is conveniently represented in the dual picture choosing a spanning tree in the dual graph according to the scale attribution we prove that the summation over the loop angular momenta can be performed at no cost so that the power counting is reduced to the balance of the number of propagators versus the number of completely inner vertices in subgraphs of the dual graph

renormalization in quantum field theory and the riemann hilbert problem ii the β function diffeomorphisms and the renormalization group we showed in part i that the hopf algebra of feynman graphs in a given qft is the algebra of coordinates on a complex infinite dimensional lie group g and that the renormalized theory is obtained from the unrenormalized one by evaluating at 0 the holomorphic part of the riemann hilbert decomposition 1 of the loop g provided by dimensional regularization we show in this paper that the group g acts naturally on the complex space x of dimensionless coupling constants of the theory more precisely the formula g 0 gz 1 z 3 3 2 for the effective coupling constant when viewed as a formal power series does define a hopf algebra homomorphism between the hopf algebra of coordinates on the group of formal diffeomorphisms to the hopf algebra this allows first of all to read off directly without using the group g the bare coupling constant and the renormalized one from the riemann hilbert decomposition of the unrenormalized effective coupling constant viewed as a loop of formal diffeomorphisms this shows that renormalization is intimately related with the theory of non linear complex bundles on the riemann sphere of the dimensional regularization parameter it also allows to lift both the renormalization group and the function as the asymptotic scaling in the group g this exploits the full power of the riemann hilbert decomposition together with the invariance of under a change of unit of mass this not only gives a conceptual proof of the existence of the renormalization group but also delivers a scattering formula in the group g for the full higher pole structure of minimal subtracted counterterms in terms of the residue

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

algebras of distributions suitable for phase space quantum mechanics i the twisted product of functions on r2n is extended to a algebra of tempered distributions that contains the rapidly decreasing smooth functions the distributions of compact support and all polynomials and moreover is invariant under the fourier transformation the regularity properties of the twisted product are investigated a matrix presentation of the twisted product is given with respect to an appropriate orthonormal basis which is used to construct a family of banach algebras under this product

dimensional regularization in position space and a forest formula for epstein glaser renormalization we reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time ordered products as solutions to the induction scheme of epstein glaser this closed expression which we call the epstein glaser forest formula is analogous to zimmermann s forest formula for bph renormalization for scalar fields the resulting renormalization method is always applicable we compute several examples we also analyze the hopf algebraic aspects of the combinatorics our starting point is the main theorem of renormalization of stora and popineau and the arising renormalization group as originally defined by stuckelberg and petermann

on the invariance of residues of feynman graphs we use simple iterated one loop graphs in massless yukawa theory and qed to pose the following question what are the symmetries of the residues of a graph under a permutation of places to insert subdivergences the investigation confirms partial invariance of the residue under such permutations the highest weight transcendental is invariant under such a permutation for qed this result is gauge invariant i e the permutation invariance holds for any gauge computations are done making use of the hopf algebra structure of graphs and employing ginac to automate the calculations

rota baxter operators on sl 2 c and solutions of the classical yang baxter equation we explicitly determine all rota baxter operators of weight zero on sl 2 c under the cartan weyl basis for the skew symmetric operators we give the corresponding skew symmetric solutions of the classical yang baxter equation in sl 2 c confirming the related study by semenov tian shansky in general these rota baxter operators give a family of solutions of the classical yang baxter equation in the six dimensional lie algebra sl 2 c ad sl 2 c they also give rise to three dimensional pre lie algebras which in turn yield solutions of the classical yang baxter equation in other six dimensional lie algebras

hopf algebras cyclic cohomology and the transverse index theorem in this paper we solve a longstanding internal problem of noncommutative geometry namely the computation of the index of transversally elliptic operators on foliations we show that the computation of the local index formula for transversally hypoelliptic operators can be settled thanks to a very specific hopf algebra associated to each integer codimension this hopf algebra reduces transverse geometry to a universal geometry of affine nature the structure of this hopf algebra its relation with the lie algebra of formal vector fields as well as the computation of its cyclic cohomology are done in the present paper in which we also show that under a suitable unimodularity condition the cosimplicial space underlying the hochschild cohomology of a hopf algebra carries a highly nontrivial cyclic structure

parametric representation of a translation invariant renormalizable noncommutative model we construct here the parametric representation of a translation invariant renormalizable scalar model on the noncommutative moyal space of even dimension d this representation of the feynman amplitudes is based on some integral form of the noncommutative propagator all types of graphs planar and non planar are analyzed the role played by noncommutativity is explicitly shown this parametric representation established allows us to calculate the power counting of the model furthermore the space dimension d is just a parameter in the formulae obtained this paves the road for the dimensional regularization of this noncommutative model

free tri dendriform family algebras abstract in this paper we first prove that a rota baxter family algebra indexed by a semigroup amounts to an ordinary rota baxter algebra structure on the tensor product with the semigroup algebra we show that the same phenomenon arises for dendriform and tridendriform family algebras then we construct free dendriform family algebras in terms of typed decorated planar binary trees finally we generalize typed decorated rooted trees to typed valently decorated schroder trees and use them to construct free tridendriform family algebras

background foreground modeling based on spatiotemporal sparse subspace clustering background estimation and foreground segmentation are important steps in many high level vision tasks many existing methods estimate background as a low rank component and foreground as a sparse matrix without incorporating the structural information therefore these algorithms exhibit degraded performance in the presence of dynamic backgrounds photometric variations jitter shadows and large occlusions we observe that these backgrounds often span multiple manifolds therefore constraints that ensure continuity on those manifolds will result in better background estimation hence we propose to incorporate the spatial and temporal sparse subspace clustering into the robust principal component analysis rpca framework to that end we compute a spatial and temporal graph for a given sequence using motion aware correlation coefficient the information captured by both graphs is utilized by estimating the proximity matrices using both the normalized euclidean and geodesic distances the low rank component must be able to efficiently partition the spatiotemporal graphs using these laplacian matrices embedded with the rpca objective function these laplacian matrices constrain the background model to be spatially and temporally consistent both on linear and nonlinear manifolds the solution of the proposed objective function is computed by using the linearized alternating direction method with adaptive penalty optimization scheme experiments are performed on challenging sequences from five publicly available datasets and are compared with the 23 existing state of the art methods the results demonstrate excellent performance of the proposed algorithm for both the background estimation and foreground segmentation

quantum field theory on quantized bergman domain we present an oscillator realization of discrete series representations of group su 2 2 we give formulas for the coherent state star product quantization of a bergman domain d a formulation of a regularized noncommutative scalar field on a quantized d is given

robust visual tracking via consistent low rank sparse learning object tracking is the process of determining the states of a target in consecutive video frames based on properties of motion and appearance consistency in this paper we propose a consistent low rank sparse tracker clrst that builds upon the particle filter framework for tracking by exploiting temporal consistency the proposed clrst algorithm adaptively prunes and selects candidate particles by using linear sparse combinations of dictionary templates the proposed method learns the sparse representations of image regions corresponding to candidate particles jointly by exploiting the underlying low rank constraints in addition the proposed clrst algorithm is computationally attractive since temporal consistency property helps prune particles and the low rank minimization problem for learning joint sparse representations can be efficiently solved by a sequence of closed form update operations we evaluate the proposed clrst algorithm against 14 14 state of the art tracking methods on a set of 25 25 challenging image sequences experimental results show that the clrst algorithm performs favorably against state of the art tracking methods in terms of accuracy and execution time

qed hopf algebras on planar binary trees abstract in this paper we describe the hopf algebras on planar binary trees used to renormalize the feynman propagators of quantum electrodynamics and the coaction which describes the renormalization procedure both structures are related to some semi direct coproduct of hopf algebras

decomposition spaces incidence algebras and mobius inversion i basic theory abstract this is the first in a series of papers devoted to the theory of decomposition spaces a general framework for incidence algebras and mobius inversion where algebraic identities are realised by taking homotopy cardinality of equivalences of groupoids a decomposition space is a simplicial groupoid satisfying an exactness condition weaker than the segal condition expressed in terms of active and inert maps in just as the segal condition expresses composition the new exactness condition expresses decomposition and there is an abundance of examples in combinatorics after establishing some basic properties of decomposition spaces the main result of this first paper shows that to any decomposition space there is an associated incidence coalgebra spanned by the space of 1 simplices and with coefficients in groupoids we take a functorial viewpoint throughout emphasising conservative ulf functors these induce coalgebra homomorphisms reduction procedures in the classical theory of incidence coalgebras are examples of this notion and many are examples of decalage of decomposition spaces an interesting class of examples of decomposition spaces beyond segal spaces is provided by hall algebras the waldhausen s construction of an abelian or stable infinity category is shown to be a decomposition space in the second paper in this series we impose further conditions on decomposition spaces to obtain a general mobius inversion principle and to ensure that the various constructions and results admit a homotopy cardinality in the third paper we show that the lawvere menni hopf algebra of mobius intervals is the homotopy cardinality of a certain universal decomposition space two further sequel papers deal with numerous examples from combinatorics note the notion of decomposition space was arrived at independently by dyckerhoff and kapranov 17 who call them unital 2 segal spaces our theory is quite orthogonal to theirs the definitions are different in spirit and appearance and the theories differ in terms of motivation examples and directions

etude de l algebre de lie double des arbres enracines decores the double lie algebra ld of rooted trees decorated by a set d is introduced generalising the construction of connes and kreimer it is shown that it is a simple lie algebra its derivations and its automorphisms are described as well as some central extensions finally the category of lowest weight modules is introduced and studied

multi orientable group field theory group field theories gfts are quantum field theories over group manifolds they can be seen as a generalization of matrix models gft feynman graphs are tensor graphs generalizing ribbon graphs or combinatorial maps these graphs are not always dual to manifolds in order to simplify the topological structure of these various singularities colored gft was recently introduced and intensively studied we propose here a different simplification of gft which we call multi orientable gft we study the relation between multi orientable gft feynman graphs and colorable graphs we prove that tadfaces and some generalized tadpoles are absent some feynman amplitude computations are performed a few remarks on the renormalizability of both multi orientable and colorable gft are made a generalization from three dimensional to four dimensional theories is also proposed

eigentracking robust matching and tracking of articulated objects using a view based representation this paper describes an approach for tracking rigid and articulated objects using a view based representation the approach builds on and extends work on eigenspace representations robust estimation techniques and parameterized optical flow estimation first we note that the least squares image reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation second we define a subspace constancy assumption that allows us to exploit techniques for parameterized optical flow estimation to simultaneously solve for the view of an object and the affine transformation between the eigenspace and the image to account for large affine transformations between the eigenspace and the image we define a multi scale eigenspace representation and a coarse to fine matching strategy finally we use these techniques to track objects over long image sequences in which the objects simultaneously undergo both affine image motions and changes of view in particular we use this eigentracking technique to track and recognize the gestures of a moving hand

univariate splines equivalence of moduli of smoothness and applications several results on equivalence of moduli of smoothness of univariate splines are obtained for example it is shown that for any 1 k r 1 0 m r 1 and 1 p the inequality n v k v s v n 1 p k s n 1 p 1 v min k m 1 is satisfied where s c m 1 1 is a piecewise polynomial of degree r on a quasi uniform i e the ratio of lengths of the largest and the smallest intervals is bounded by a constant partition of an interval similar results for chebyshev partitions and weighted ditzian totik moduli of smoothness are also obtained these results yield simple new constructions and allow considerable simplification of various known proofs in the area of constrained approximation by polynomials and splines

the ponzano regge model and parametric representation we give a parametric representation of the effective noncommutative field theory derived from a kappa deformation of the ponzano regge model and define a generalized kirchhoff polynomial with kappa correction terms obtained in a kappa linear approximation we then consider the corresponding graph hypersurfaces and the question of how the presence of the correction term affects their motivic nature we look in particular at the tetrahedron graph which is the basic case of relevance to quantum gravity with the help of computer calculations we verify that the number of points over finite fields of the corresponding hypersurface does not fit polynomials with integer coefficients hence the hypersurface of the tetrahedron is not polynomially countable this shows that the correction term can change significantly the motivic properties of the hypersurfaces with respect to the classical case

renormalization of multiple zeta values abstract multiple zeta values mzvs in the usual sense are the special values of multiple variable zeta functions at positive integers their extensive studies are important in both mathematics and physics with broad connections and applications in contrast very little is known about the special values of multiple zeta functions at non positive integers since the values are usually undefined we define and study multiple zeta functions at integer values by adapting methods of renormalization from quantum field theory and following the hopf algebra approach of connes and kreimer this definition of renormalized mzvs agrees with the convergent mzvs and extends the work of ihara kaneko zagier on renormalization of mzvs with positive arguments we further show that the important quasi shuffle stuffle relation for usual mzvs remains true for the renormalized mzvs

from rota baxter algebras to pre lie algebras rota baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics rota baxter algebras provide a construction of pre lie algebras from associative algebras in this paper we give all rota baxter operators of weight 1 on complex associative algebras in dimension 3 and their corresponding pre lie algebras

deformations of associative rota baxter operators abstract rota baxter operators and more generally o operators on associative algebras are important in probability combinatorics associative yang baxter equation and splitting of algebras using a method of uchino we construct an explicit graded lie algebra whose maurer cartan elements are given by o operators this allows us to construct cohomology for an o operator this cohomology can also be seen as the hochschild cohomology of a certain algebra with coefficients in a suitable bimodule next we study linear and formal deformations of an o operator which are governed by the above defined cohomology we introduce nijenhuis elements associated with an o operator which give rise to trivial deformations as applications we conclude deformations of weight zero rota baxter operators associative r matrices and averaging operators

birkhoff type decompositions and the baker campbell hausdorff recursion we describe a unification of several apparently unrelated factorizations arising from quantum field theory vertex operator algebras combinatorics and numerical methods in differential equations the unification is given by a birkhoff type decomposition that was obtained from the baker campbell hausdorff formula in our study of the hopf algebra approach of connes and kreimer to renormalization in perturbative quantum field theory there we showed that the birkhoff decomposition of connes and kreimer can be obtained from a certain baker campbell hausdorff recursion formula in the presence of a rota baxter operator we will explain how the same decomposition generalizes the factorization of formal exponentials and uniformization for lie algebras that arose in vertex operator algebra and conformal field theory and the even odd decomposition of combinatorial hopf algebra characters as well as the lie algebra polar decomposition as used in the context of the approximation of matrix exponentials in ordinary differential equations

loop vertex expansion for φ2k theory in zero dimension in this paper we extend the method of loop vertex expansion to interactions with degree higher than 4 as an example we provide through this expansion an explicit proof that the free energy of 2k scalar theory in zero dimension is borel le roy summable of order k 1 we detail the computations in the case of a 6 interaction in this paper we extend the method of loop vertex expansion to interactions with degree higher than 4 as an example we provide through this expansion an explicit proof that the free energy of 2k scalar theory in zero dimension is borel le roy summable of order k 1 we detail the computations in the case of a 6 interaction

constrained spline smoothing several results on constrained spline smoothing are obtained in particular we establish a general result showing how one can constructively smooth any monotone or convex piecewise polynomial function ppf or any q monotone ppf q geq 3 with one additional degree of smoothness to be of minimal defect while keeping it close to the original function in the mathbb l p quasi norm it is well known that approximating a function by ppfs of minimal defect splines avoids introduction of artifacts which may be unrelated to the original function thus it is always preferable on the other hand it is usually easier to construct constrained ppfs with as few requirements on smoothness as possible our results allow us to obtain shape preserving splines of minimal defect with equidistant or chebyshev knots the validity of the corresponding jackson type estimates for shape preserving spline approximation is summarized in particular we show that the mathbb l p estimates p geq 1 can be immediately derived from the mathbb l infty estimates

on the stability of some groups of formal diffeomorphisms by the birkhoff decomposition abstract let g be the group of one parameter identity tangent diffeomorphisms on the line whose coefficients are formal laurent series in the parameter e with a pole of finite order at 0 it is well known that the birkhoff decomposition can be defined in such a group we investigate the stability of the birkhoff decomposition in subgroups of g and give a formula for this decomposition these results are strongly related to renormalization in quantum field theory since it was proved by a connes and d kreimer that after dimensional regularization the unrenormalized effective coupling constants are the image by a formal identity tangent diffeomorphism of the coupling constants of the theory in the massless 6 3 theory this diffeomorphism is in g and its birkhoff decomposition gives directly the bare coupling constants and the renormalized coupling constants

deformations and homotopy theory of relative rota baxter lie algebras we determine the l infty algebra that controls deformations of a relative rota baxter lie algebra and show that it is an extension of the dg lie algebra controlling deformations of the underlying mathsf lie mathsf rep pair by the dg lie algebra controlling deformations of the relative rota baxter operator consequently we define the cohomology of relative rota baxter lie algebras and relate it to their infinitesimal deformations a large class of relative rota baxter lie algebras is obtained from triangular lie bialgebras and we construct a map between the corresponding deformation complexes next the notion of a homotopy relative rota baxter lie algebra is introduced we show that a class of homotopy relative rota baxter lie algebras is intimately related to pre lie infty algebras

an algebraic birkhoff decomposition for the continuous renormalization group this paper aims at presenting the first steps towards a formulation of the exact renormalization group equation in the hopf algebra setting of connes and kreimer it mostly deals with some algebraic preliminaries allowing us to formulate perturbative renormalization within the theory of differential equations the relation between renormalization formulated as a change of boundary condition for a differential equation and an algebraic birkhoff decomposition for rooted trees is explicited

power counting theorem for non local matrix models and renormalisation solving the exact renormalisation group equation a la wilson polchinski perturbatively we derive a power counting theorem for general matrix models with arbitrarily non local propagators the power counting degree is determined by two scaling dimensions of the cut off propagator and various topological data of ribbon graphs as a necessary condition for the renormalisability of a model the two scaling dimensions have to be large enough relative to the dimension of the underlying space in order to have a renormalisable model one needs additional locality properties typically arising from orthogonal polynomials which relate the relevant and marginal interaction coefficients to a finite number of base couplings the main application of our power counting theorem is the renormalisation of field theories on noncommutative d in matrix formulation

renormalization of tensorial group field theories abelian u 1 models in four dimensions we tackle the issue of renormalizability for tensorial group field theories tgft including gauge invariance conditions with the rigorous tool of multi scale analysis to prepare the ground for applications to quantum gravity models in the process we define the appropriate generalization of some key qft notions including connectedness locality and contraction of high subgraphs we also define a new notion of wick ordering corresponding to the subtraction of maximal melonic tadpoles we then consider the simplest examples of dynamical 4 dimensional tgft with gauge invariance conditions for the abelian u 1 case we prove that they are super renormalizable for any polynomial interaction