colored group field theory random matrix models generalize to group field theories gft whose feynman graphs are dual to higher dimensional topological spaces the perturbative development of the usual gft s is rather involved combinatorially and plagued by topological singularities which we discuss in great detail in this paper thus very difficult to control and unsatisfactory

addendum to a renormalizable 4 dimensional tensor field theory this note fills a gap in the article ben geloun and rivasseau commun math phys 318 69 109 2013 we provide the proof of eq 82 of lemma 5 in ben geloun and rivasseau commun math phys 318 69 109 2013 and thereby complete its power counting analysis with a more precise next to leading order estimate

irreducible unitary representations of su 2 2 we give an explicit classification of the irreducible unitary representations of the simple lie group su 2 2

the 1 n expansion of tensor models beyond perturbation theory we analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor using a version of the loop vertex expansion which we call the mixed expansion we show that the cumulants write as explicit series in 1 n plus bounded rest terms the mixed expansion recasts the problem of determining the subleading corrections in 1 n into a simple combinatorial problem of counting trees decorated by a finite number of loop edges

common structure of techniques for choosing smoothing parameters in regression problems on tente de relier deux methodes de choix du parametre de lissage l une basee sur la mesure du risque et l autre sur le degre d ajustement de la regression aux donnees

regularized iterative image restoration with ringing reduction linear space invariant image restoration algorithms often introduce ringing effects near sharp intensity transitions it is shown that these artifacts are attributable to the regularization of the ill posed image restoration problem two possible methods to reduce the ringing effects in restored images are proposed the first method incorporates deterministic a priori knowledge about the original image into the restoration algorithm the second method locally regulates the severity of the noise magnification and the ringing phenomenon depending on the edge information in the image a regularized iterative image restoration algorithm is proposed in which both ringing reduction methods are included by making use of the theory of the projections onto convex sets and the concept of norms in a weighted hilbert space both the numerical performance and the visual evaluation of the results are improved by the use of ringing reduction

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

locally monotonic regression the concept of local monotonicity appears in the study of the set of root signals of the median filter and provides a measure of the smoothness of the signal the median filter is a suboptimal smoother under this measure of smoothness since a filter pass does necessarily yield a locally monotonic output even if a locally monotonic output does result there is no guarantee that it will possess other desirable properties such as optimal similarity to the original signal locally monotonic regression is a technique for the optimal smoothing of finite length discrete real signals under such a criterion a theoretical framework in which the existence of locally monotonic regression is proved and algorithms for their computation are given regression is considered as an approximation problem in r sub n the criterion of approximation is derived from a semimetric and the approximating set is the collection of signals sharing the property of being locally monotonic

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

on the finite amplitudes for open graphs in abelian dynamical colored boulatov ooguri models in the work ben geloun and bonzom 2011 int j theor phys 50 2819 it has been proved that the radiative corrections of the 2 point function in the su 2 boulatov tensor model generates a marginal in the renormalization group sense contribution of the form of a laplacian such a term which was missing in the initial boulatov model action should be added in that action before discussing the renormalization analysis of this model in this work by linearizing the group manifold we prove that the amplitudes associated with feynman graphs with external legs of the colored boulatov model over u 1 3 endowed with a laplacian dynamics are all convergent we conjecture that the same feature happens for the corresponding boulatov model over su 2 higher rank models are also discussed

nonnegative primitive matrices with exponent 2 abstract a nonnegative matrix m with zero trace is primitive if for some positive integer k m k is positive the exponent exp m of the primitive matrix is the smallest such k by treating the digraph g whose adjacency matrix is the primitive matrix m we will show that the minimum number of positive entries of m is 3 n 3 when exp m 2 we will also show that for a symmetric n n matrix m if exp m 2 the minimum number of positive entries of m is 3 n 2 or 3 n 3 according to n

primitive graphs with given exponents and minimum number of edges a graph g v e on n vertices is primitive if there is a positive integer k such that for each pair of vertices u v of g there is a walk of length k from u to v the minimum value of such an integer k is the exponent exp g of g in this paper we find the minimum number h n k of edges of a simple graph g on n vertices with exponent k and we characterize all graphs which have h n k edges when k is 3 or even

wielandt s proof of the exponent inequality for primitive nonnegative matrices the proof of the exponent inequality found in wielandt s unpublished diaries of a result announced without proof in his well known paper on nonnegative irreducible matrices a facsimile a transcription a translation and a commentary are presented

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

translation invariant models for non commutative gauge fields motivated by the recent construction of a translation invariant renormalizable non commutative model for a scalar field 1 we introduce models for non commutative u 1 gauge fields along the same lines more precisely we include some extra terms into the action with the aim of getting rid of the uv ir mixing

generalised conservation laws in non local field theories we propose a geometrical treatment of symmetries in non local field theories where the non locality is due to a lack of identification of field arguments in the action we show that the existence of a symmetry of the action leads to a generalized conservation law in which the usual conserved current acquires an additional non local correction term obtaining a generalization of the standard noether theorem we illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of bose einstein condensates we expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity

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

general choice of the regularization functional in regularized image restoration the determination of the regularization parameter is an important issue in regularized image restoration since it controls the trade off between fidelity to the data and smoothness of the solution a number of approaches have been developed in determining this parameter in this paper a new paradigm is adopted according to which the required prior information is extracted from the available data at the previous iteration step i e the partially restored image at each step we propose the use of a regularization functional instead of a constant regularization parameter the properties such a regularization functional should satisfy are investigated and two specific forms of it are proposed an iterative algorithm is proposed for obtaining a restored image the regularization functional is defined in terms of the restored image at each iteration step therefore allowing for the simultaneous determination of its value and the restoration of the degraded image both proposed iteration adaptive regularization functionals are shown to result in a smoothing functional with a global minimum so that its iterative optimization does not depend on the initial conditions the convergence of the algorithm is established and experimental results are shown

non perturbative deformation quantization of cartan domains abstract we construct families of non commuting c algebras of quantized functions for bounded irreducible hermitian symmetric spaces for this procedure we use algebras of toeplitz operators defined with respect to a perturbation of the ordinary bergman metric we prove the deformation quantization conditions for these algebras

positive energy representations holomorphic discrete series and finite dimensional irreps let g be a semi simple non compact lie group with unitary lowest highest weight representations we consider explicitly the relation among three types of representations of g positive energy unitary lowest weight representations holomorphic discrete series representations and non unitary finite dimensional irreps we consider mainly the conformal groups soo n 2 treating in full detail the cases n 1 3 4

mayer expansions and the hamilton jacobi equation we review the derivation of wilson s differential equation in infinitely many variables which describes the infinitesimal change in an effective potential of a statistical mechanical model or quantum field theory when an infinitesimal integration out is performed we show that this equation can be solved for short times by a very elementary method when the initial data are bounded and analytic the resulting series solutions are generalizations of the mayer expansion in statistical mechanics the differential equation approach gives a remarkable identity for connected parts and precise estimates which include criteria for convergence of iterated mayer expansions applications include the yukawa gas in two dimensions past the 4 threshold and another derivation of some earlier results of gopfert and mack

some classes of renormalizable tensor models we identify new families of renormalizable tensor models from anterior renormalizable tensor models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property mainly a version of the rank 3 tensor model as defined by ben geloun and samary ann henri poincare 14 1599 2013 e print arxiv 1201 0176 hep th 10 1007 s00023 012 0225 5 and the grosse wulkenhaar model in 4d and 2d generate three different classes of renormalizable models the proof of the renormalizability is fully performed for the first reduced model the same procedure can be applied for the remaining cases interestingly we find that due to the peculiar behavior of anisotropic wave function renormalizations the rank 3 tensor model reduced to a matrix model generates a simple super renormalizable vector model

renormalizable models in rank d geq 2 tensorial group field theory classes of renormalizable models in the tensorial group field theory framework are investigated the rank d tensor fields are defined over d copies of a group manifold g d u 1 d or g d su 2 d with no symmetry and no gauge invariance assumed on the fields in particular we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form p 2a a in 0 1 this study is tailored for models equipped with laplacian dynamics on gd case a 1 but also for more exotic nonlocal models in quantum topology case 0 a 1 a generic model can be written dim g d phi k d a where k is the maximal valence of its interactions using a multi scale analysis for the generic situation we identify several classes of renormalizable actions including matrix model actions in this specific instance we find a tower of renormalizable matrix models parametrized by k geq 4 in a second part of this work we study the uv behavior of the models up to maximal valence of interaction k 6 all rank d geq 3 tensor models proved renormalizable are asymptotically free in the uv all matrix models with k 4 have a vanishing function at one loop and very likely reproduce the same feature of the grosse wulkenhaar model commun math phys 256 305 2005

markov random field models for directional field and singularity extraction in fingerprint images a bayesian formulation is proposed for reliable and robust extraction of the directional field in fingerprint images using a class of spatially smooth priors the spatial smoothness allows for robust directional field estimation in the presence of moderate noise levels parametric template models are suggested as candidate singularity models for singularity detection the parametric models enable joint extraction of the directional field and the singularities in fingerprint impressions by dynamic updating of feature information this allows for the detection of singularities that may have previously been missed as well as better aligning the directional field around detected singularities a criteria is presented for selecting an optimal block size to reduce the number of spurious singularity detections the best rates of spurious detection and missed singularities given by the algorithm are 4 9 and 7 1 respectively based on the nist 4 database

a study of methods of choosing the smoothing parameter in image restoration by regularization the method of regularization is portrayed as providing a compromise between fidelity to the data and smoothness with the tradeoff being determined by a scalar smoothing parameter various ways of choosing this parameter are discussed in the case of quadratic regularization criteria they are compared algebraically and their statistical properties are comparatively assessed from the results of all extensive simulation study based on simple images

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

generalization of the bollobas riordan polynomial for tensor graphs tensor models are used nowadays for implementing a fundamental theory of quantum gravity we define here a polynomial t encoding the supplementary topological information this polynomial is a natural generalization of the bollobas riordan polynomial used to characterize matrix graphs and is different from the gur u polynomial r gur u ann henri poincare 11 565 2010 10 1007 s00023 010 0035 6 defined for a particular class of tensor graphs the colorable ones the polynomial t is defined for both colorable and non colorable graphs and it is proved to satisfy the deletion contraction relation a non trivial example of a non colorable graphs is analyzed

simultaneous iterative image restoration and evaluation of the regularization parameter a nonlinear regularized iterative image restoration algorithm is proposed according to which only the noise variance is assumed to be known in advance the algorithm results from a set theoretic regularization approach where a bound of the stabilizing functional and therefore the regularization parameter are updated at each iteration step sufficient conditions for the convergence of the algorithm are derived and experimental results are shown

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

the exponent set of symmetric primitive 0 1 matrices with zero trace abstract we prove that the exponent set of symmetric primitive 0 1 matrices with zero trace the adjacency matrices of the simple graphs is 2 3 2 n 4 s where s is the set of all odd numbers in n 2 n 1 2 n 5 we also obtain a characterization of the symmetric primitive matrices with zero trace whose exponents attain the upper bound 2 n 4

piecewise and local image models for regularized image restoration using cross validation we describe two broad classes of useful and physically meaningful image models that can be used to construct novel smoothing constraints for use in the regularized image restoration problem the two classes termed piecewise image models pims and focal image models lims respectively capture unique image properties that can be adapted to the image and that reflect structurally significant surface characteristics members of the pim and lim classes are easily formed into regularization operators that replace differential type constraints we also develop an adaptive strategy for selecting the best pim or lim for a given problem from among the defined class and we explain the construction of the corresponding regularization operators considerable attention is also given to determining the regularization parameter via a cross validation technique and also to the selection of an optimization strategy for solving the problem several results are provided that illustrate the processes of model selection parameter selection and image restoration the overall approach provides a new viewpoint on the restoration problem through the use of new image models that capture salient image features that are not well represented through traditional approaches

polchinski s exact renormalisation group for tensorial theories gausian universality and power counting in this paper we use the exact renormalisation in the context of tensor models and group field theories as a byproduct we rederive gausian universality for random tensors and provide a general power counting for abelian tensorial field theories with a closure constraint leading us to a only five renormalisable theories

methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation the application of regularization to ill conditioned problems necessitates the choice of a regularization parameter which trades fidelity to the data with smoothness of the solution the value of the regularization parameter depends on the variance of the noise in the data the problem of choosing the regularization parameter and estimating the noise variance in image restoration is examined an error analysis based on an objective mean square error mse criterion is used to motivate regularization two approaches for choosing the regularization parameter and estimating the noise variance are proposed the proposed and existing methods are compared and their relationship to linear minimum mean square error filtering is examined experiments are presented that verify the theoretical results

lie group convolution algebras as deformation quantizations of linear poisson structures introduction let l be a finite dimensional lie algebra over the real numbers r and let l be its dual vector space it is well known 24 that the lie algebra structure on l defines a natural poisson structure on l in fact this was already known to lie 24 and these poisson structures are exactly what are now called the linear poisson structures given a manifold m equipped with a poisson structure one can seek deformation quantizations in the direction of as first studied in 3 these are loosely speaking one parameter families h ler of deformations of the pointwise multiplication on c m or an appropriate subalgebra such that

elementary representations and intertwining operators for su 2 2 i the structure of the group su 2 2 and of its lie algebra is studied in detail the results will be applied in subsequent parts devoted to the explicit construction of elementary representations of su 2 2 induced from different parabolic subgroups and of the intertwining operators between these representations a summary of some results of parts ii and iii is given

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

effective action for the yukawa 2 quantum field theory using a rigorous version of the renormalization group we construct the effective action for they2 model the construction starts with integrating out the bosonic field which eliminates the large fields problem studying the soobtained purely fermionic theory proceeds by a series of convergent perturbation expansions we show that the continuum limit of the effective action exists and its perturbation expansion is borel summable

bubble divergences from twisted cohomology we consider a class of lattice topological field theories among which are the weak coupling limit of 2d yang mills theory and 3d riemannian quantum gravity whose dynamical variables are flat discrete connections with compact structure group on a cell 2 complex in these models it is known that the path integral measure is ill defined because of a phenomenon known as bubble divergences in this paper we extend recent results of the authors to the cases where these divergences cannot be understood in terms of cellular cohomology we introduce in its place the relevant twisted cohomology and use it to compute the divergence degree of the partition function we also relate its dominant part to the reidemeister torsion of the complex thereby generalizing previous results of barrett and naish guzman the main limitation to our approach is the presence of singularities in the representation variety of the fundamental group of the complex we illustrate this issue in the well known case of two dimensional manifolds

on the number of arcs in primitive digraphs with large exponents a digraph g is called primitive if for some positive integer k there is a walk of length exactly k from each vertex u to each vertex v possibly u again if g is primitive the smallest such k is called the exponent of g denoted by exp g for any real number r 0 r 1 let f n r be the maximum number of arcs in a primitive digraph with n vertices having exponent greater than or equal to r2n2 we show that f n r n2 is asymptotically 1 r 2 3 whenever r 2 2

perceptual evaluation of the mean square error choice of regularization parameter a formal perceptual study shows that the perceptually optimal choice of regularization parameter varies from the minimum mean square error parameter as a function of the original image the point spread function and the signal to noise ratio snr however further studies show that this variation has only a slight effect on the perceived quality of the restoration

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

generalized deterministic annealing we develop a general formalism for computing high quality low cost solutions to nonconvex combinatorial optimization problems expressible as distributed interacting local constraints for problems of this type generalized deterministic annealing gda avoids the performance related sacrifices of current techniques gda exploits the localized structure of such problems by assigning k state neurons to each optimization variable the neuron values correspond to the probability densities of k state local markov chains and may be updated serially or in parallel the markov model is derived from the markov model of simulated annealing sa although it is greatly simplified theorems are presented that firmly establish the convergence properties of gda as well as supplying practical guidelines for selecting the initial and final temperatures in the annealing process a benchmark image enhancement application is provided where the performance of gda is compared to other optimization methods the empirical data taken in conjunction with the formal analytical results suggest that gda enjoys significant performance advantages relative to current methods for combinatorial optimization

double exponential sinc collocation method for solving the energy eigenvalues of harmonic oscillators perturbed by a rational function we show that the double exponential sinc collocation method provides an efficient uniformly accurate solution to the one dimensional time independent schrodinger equation for a general class of rational potentials of the form v x p x q x the derived algorithm is based on the discretization of the hamiltonian of the schrodinger equation using sinc expansions this discretization results in a generalized eigenvalue problem the eigenvalues of which correspond to approximations of the energy values of the starting hamiltonian a systematic numerical study is conducted beginning with test potentials with known eigenvalues and moving to rational potentials of increasing degree

nonlinear image estimation using piecewise and local image models we introduce a new approach to image estimation based on a flexible constraint framework that encapsulates meaningful structural image assumptions piecewise image models pims and local image models lims are defined and utilized to estimate noise corrupted images pims and lims are defined by image sets obeying certain piecewise or local image properties such as piecewise linearity or local monotonicity by optimizing local image characteristics imposed by the models image estimates are produced with respect to the characteristic sets defined by the models thus we propose a new general formulation for nonlinear set theoretic image estimation detailed image estimation algorithms and examples are given using two pims piecewise constant pico and piecewise linear pili models and two lims locally monotonic lomo and locally convex concave loco models these models define properties that hold over local image neighborhoods and the corresponding image estimates may be inexpensively computed by iterative optimization algorithms forcing the model constraints to hold at every image coordinate of the solution defines a nonlinear regression problem that is generally nonconvex and combinatorial however approximate solutions may be computed in reasonable time using the novel generalized deterministic annealing gda optimization technique which is particularly well suited for locally constrained problems of this type results are given for corrupted imagery with signal to noise ratio snr as low as 2 db demonstrating high quality image estimation as measured by local feature integrity and improvement in snr

adaptive nonlinear image restoration by a modified kalman filtering approach an adaptive nonlinear kalman type filter is presented for the restoration of two dimensional images degraded by general image formation system degradations and additive white noise a vector difference equation model is used to model the degradation process the object plane distribution function is partitioned into disjoint regions based on the amount of spatial activity in the image and difference equation models are used to characterize this nonstationary object plane distribution function features of the restoration filter include the ability to account for the response of the human visual system to additive noise in an image a two dimensional interpolation scheme to improve the estimates of the initial states in each region and a nearest neighbor algorithm to choose the previous state of vector for the state of pixel i j

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

the exponent and circumdiameter of primitive digraphs abstract the exponent d of a primitive digraph d is the smallest m such that for each ordered pair of not necessarily distinct vertices u v there exists a u v walk of length m if d is the set of all cycle lengths then the circumdiameter of d denoted dc d is the maximum over all ordered pairs of not necessarily distinct vertices u v of the length of a shortest u v walk that intersects cycles of all lengths it is well known that d d dc d in which d is the frobenius schur index several new sufficient conditions and families of digraphs for which equality holds in the above upper bound are given and some families of digraphs d for which d d dc d 1 are defined additional sufficient conditions for equality in the above upper bound for d and a new upper bound for dc d are given for digraphs with large exponent that is digraphs on n vertices having d n 1 2 1 2 2 the circumdiameter and bounds on the exponent for the digraph of a leslie matrix are found

a note on the eigenvalues of a primitive matrix with large exponent abstract let a be a primitive stochastic matrix of order n 7 and exponent at least n 1 2 1 2 2 we describe the general form of the characteristic polynomial of a and prove that a must have at least 2 n 4 4 complex eigenvalues of modulus at greater than 1 2 sin n 1 2 n 1 observe that this last quantity tends to 1 as n both combinatorial and algebraic arguments are used to establish the result

construction and borel summability of infrared φ 4 4 by a phase space expansion we construct the thermodynamic limit of the critical massless 4 model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion this expansion requires in a natural way the introduction of effective or running constants and the infrared asymptotic freedom of the model i e the decay of the running coupling constant plays a crucial role we prove also that the correlation functions of the model are the borel sums of their perturbation expansion

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

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

corrected loop vertex expansion for φ24 theory this paper is an extended erratum to 1 in which the classic construction and borel summability of the 4 euclidean quantum eld theory was revisited combining a multi scale analysis with the constructive method called loop vertex expansion lve unfortunately we discovered an important error in the method of 1 we explain the mistake and provide a new correct construction of the 4 theory according to the lve

continuous point symmetries in group field theories we discuss the notion of symmetries in non local field theories characterized by integro differential equations of motion from a geometric perspective we then focus on group field theory gft models of quantum gravity and provide a general analysis of their continuous point symmetry transformations including the generalized conservation laws following from them

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

primitive digraphs with smallest large exponent abstract a primitive digraph d on n vertices has large exponent if its exponent d satisfies n d w n where n w n 2 2 and w n n 1 2 1 it is shown that the minimum number of arcs in a primitive digraph d on n 5 vertices with exponent equal to n is either n 1 or n 2 explicit constructions are given for fixed n even and odd for a primitive digraph on n vertices with exponent n and n 2 arcs these constructions extend to digraphs with some exponents between n and w n a necessary and sufficient condition is presented for the existence of a primitive digraph on n vertices with exponent n and n 1 arcs together with some number theoretic results this gives an algorithm that determines for fixed n whether the minimum number of arcs is n 1 or n 2

generalized constructive tree weights the loop vertex expansion lve is a quantum field theory qft method which explicitly computes the borel sum of feynman perturbation series this lve relies in a crucial way on symmetric tree weights which define a measure on the set of spanning trees of any connected graph in this paper we generalize this method by defining new tree weights they depend on the choice of a partition of a set of vertices of the graph and when the partition is non trivial they are no longer symmetric under permutation of vertices nevertheless we prove they have the required positivity property to lead to a convergent lve in fact we formulate this positivity property precisely for the first time our generalized tree weights are inspired by the brydges battle federbush work on cluster expansions and could be particularly suited to the computation of connected functions in qft several concrete examples are explicitly given

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

fast digital locally monotonic regression locally monotonic regression is the optimal counterpart of iterated median filtering in a previous paper restrepo and bovik see ibid vol 41 no 9 p 2796 2810 1993 developed an elegant mathematical framework in which they studied locally monotonic regressions in r sup n the drawback is that the complexity of their algorithms is exponential in n we consider digital locally monotonic regressions in which the output symbols are drawn from a finite alphabet and by making a connection to viterbi decoding provide a fast o a sup 2 spl alpha n algorithm that computes any such regression where a is the size of the digital output alphabet a stands for lomo degree and n is the sample size this is linear in n and it renders the technique applicable in practice

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