the semiclassical limit of the two dimensional quantum yang mills model the semiclassical limit of the quantum yang mills partition function on a compact oriented surface is related to the symplectic volume of the moduli space of flat connections by using an explicit expression for the symplectic form this gives an independent proof of some recent results of witten and forman

some rigorous results for yang mills theories on a cylinder using an approach based on the canonical formalism the yang mills theories on a cylinder are rigorously analyzed in this way the moduli space a g can be explicitly described with a being the space of connections and g the group of gauge transformations in particular a g0 g0 being the group of the pointed gauge transformations is diffeomorphic to the structure group of the theory g whereas a g is g modulo the group of inner automorphisms it is also proven that a g is a principal fiber bundle with structure group g0

on quantum gauge theories in two dimensions two dimensional quantum yang mills theory is studied from three points of view i by standard physical methods ii by relating it to the largek limit of three dimensional chern simons theory and two dimensional conformal field theory iii by relating its weak coupling limit to the theory of reidemeister ray singer torsion the results obtained from the three points of view agree and give formulas for the volumes of the moduli spaces of representations of fundamental groups of two dimensional surfaces

adaptive image contrast enhancement using generalizations of histogram equalization this paper proposes a scheme for adaptive image contrast enhancement based on a generalization of histogram equalization he he is a useful technique for improving image contrast but its effect is too severe for many purposes however dramatically different results can be obtained with relatively minor modifications a concise description of adaptive he is set out and this framework is used in a discussion of past suggestions for variations on he a key feature of this formalism is a cumulation function which is used to generate a grey level mapping from the local histogram by choosing alternative forms of cumulation function one can achieve a wide variety of effects a specific form is proposed through the variation of one or two parameters the resulting process can produce a range of degrees of contrast enhancement at one extreme leaving the image unchanged at another yielding full adaptive equalization

wilson loops in two dimensional space time regarded as white noise abstract wilson loops are formally defined as e i c a x dx where c is a closed curve and a is the electromagnetic vector potential in this paper the case of two dimensional euclidean space time is investigated a satisfies the equation a f f being generalized white noise a rigorous definition of wilson loops is given and the n loop schwinger functions which are shown to satisfy seiler s axioms are explicitly calculated

the semiclassical limit for gauge theory on s 2 it is shown that the yang mills measurez h 1 e s h d whereh 0 describing gauge fields on the two sphere converges to a probability measure on the moduli space of yang mills connections ons2 ash 0

variational approach for the fusion of exposure bracketed pairs when taking pictures of a dark scene with artificial lighting ambient light is not sufficient for most cameras to obtain both accurate color and detail information the exposure bracketing feature usually available in many camera models enables the user to obtain a series of pictures taken in rapid succession with different exposure times the implicit idea is that the user picks the best image from this set but in many cases none of these images is good enough in general good brightness and color information are retained from longer exposure settings whereas sharp details are obtained from shorter ones in this paper we propose a variational method for automatically combining an exposure bracketed pair of images within a single picture that reflects the desired properties of each one we introduce an energy functional consisting of two terms one measuring the difference in edge information with the short exposure image and the other measuring the local color difference with a warped version of the long exposure image this method is able to handle camera and subject motion as well as noise and the results compare favorably with the state of the art

a functional integral approaches to the makeenko migdal equations makeenko and migdal phys lett b 88 1 135 137 1979 gave heuristic identities involving the expectation of the product of two wilson loop functionals associated to splitting a single loop at a self intersection point kazakov and kostov nucl phys b 176 1 199 215 1980 reformulated the makeenko migdal equations in the plane case into a form which made rigorous sense nevertheless the first rigorous proof of these equations and their generalizations was not given until the fundamental paper of levy 2017 subsequently driver kemp and hall commun math phys 351 2 741 774 2017 gave a simplified proof of levy s result and then with driver gabriel kemp and hall commun math phys 352 3 967 978 2017 we showed that these simplified proofs extend to the yang mills measure over arbitrary compact surfaces all of the proofs to date are elementary but tricky exercises in finite dimensional integration by parts the goal of this article is to give a rigorous functional integral proof of the makeenko migdal equations guided by the original heuristic machinery invented by makeenko and migdal although this stochastic proof is technically more difficult it is conceptually clearer and explains why the makeenko migdal equations are true it is hoped that this paper will also serve as an introduction to some of the problems involved in making sense of quantizing yang mill s fields

image editing with spatiograms transfer histogram equalization is a well known method for image contrast enhancement nevertheless as histograms do not include any information on the spatial repartition of colors their application to local image editing problems remains limited to cope with this lack of spatial information spatiograms have been recently proposed for tracking purposes a spatiogram is an image descriptor that combines a histogram with the mean and the variance of the position of each color in this paper we address the problem of local retouching of images by proposing a variational method for spatiogram transfer more precisely a reference spatiogram is used to modify the color value of a given region of interest of the processed image experiments on shadow removal and inpainting demonstrate the strength of the proposed approach

perceptual color correction through variational techniques in this paper we present a discussion about perceptual based color correction of digital images in the framework of variational techniques we propose a novel image functional whose minimization produces a perceptually inspired color enhanced version of the original the variational formulation permits a more flexible local control of contrast adjustment and attachment to data we show that a numerical implementation of the gradient descent technique applied to this energy functional coincides with the equation of automatic color enhancement ace a particular perceptual based model of color enhancement moreover we prove that a numerical approximation of the euler lagrange equation reduces the computational complexity of ace from o n2 to o nlogn where n is the total number of pixels in the image

the nottingham group for p 2 abstract in this paper i consider the nottingham group over a finite field of characteristic 2 i obtain a number of results previously known only for nottingham groups in odd characteristic for example i obtain information on the derived series and i prove that the nottingham group is hereditarily just infinite as a pro 2 group as a consequence the nottingham group over any finite field of characteristic 2 is not analytic over any pro 2 ring

sewing yang mills measures and moduli spaces over compact surfaces consider a closed surface obtained by pasting two surfaces 1and 2along some of their boundary components a formula is derived expressing quantum yang mills functional integrals for in terms of the corresponding integrals for the surfaces i using this a formula is derived which expresses the symplectic volume measure on the moduli space of flatsu 2 connections over a closed riemann surface in terms of the corresponding volume measures for the surfaces 1and 2 when the latter have one boundary component each

the large n limit for two dimensional yang mills theory the analysis of the large n limit of u n yang mills theory on a surface proceeds in two stages the analysis of the wilson loop functional for a simple closed curve and the reduction of more general loops to a simple closed curve in the case of the 2 sphere the first stage has been treated rigorously in the recent work of dahlqvist and norris which shows that the large n limit of the wilson loop functional for a simple closed curve in s2 exists and that the associated variance goes to zero we give a rigorous treatment of the second stage of analysis in the case of the 2 sphere dahlqvist and norris independently performed such an analysis using a similar but not identical method specifically we establish the existence of the limit and the vanishing of the variance for arbitrary loops with a finite number of simple crossings the proof is based on the makeenko migdal equation for the yang mills measure on surfaces as established rigorously by driver gabriel hall and kemp together with an explicit procedure for reducing a general loop in s2 to a simple closed curve the methods used here also give a new proof of these results in the plane case as a variant of the methods used by levy we also consider loops on an arbitrary surface sigma we put forth two natural conjectures about the behavior of wilson loop functionals for topologically trivial simple closed curves in sigma under the weaker of the conjectures we establish the existence of the limit and the vanishing of the variance for topologically trivial loops with simple crossings that satisfy a smallness assumption under the stronger of the conjectures we establish the same result without the smallness assumption

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

the volume of the moduli space of flat connections on a nonorientable 2 manifold we compute the riemannian volume of the moduli space of flat connections on a nonorientable 2 manifold for a natural class of metrics we also show that witten s volume formula for these moduli spaces may be derived using haar measure and we give a new proof of witten s volume formula for the moduli space of flat connections on a 2 manifold using haar measure

the symplectic nature of fundamental groups of surfaces soit 7b g la categorie des groupes de lie g avec une forme bilineaire symetrique non singuliere b sur l algebre de lie soit le groupe fondamental d une surface orientee close de genre 1 et soit 7b s la categorie des out espaces symplectiques alors la correspondance g b hom g g b definit un foncteur 7b g 7b s ou b est la structure symplectique sur hom g g definie par b

index subgroups of the nottingham group abstract it is known that every countably based pro p group embeds as a closed subgroup into the nottingham group j j f p at the same time the subgroup structure of j remains rather mysterious in this paper we introduce the class of so called index subgroups of j and study their fundamental properties two main applications are given i we prove that a certain infinite subclass of index subgroups provides new examples of hereditarily just infinite pro p groups of finite width ii we determine which hausdorff dimensions occur for index subgroups and subsequently show that the hausdorff spectrum of j begins with a proper interval

some hereditarily just infinite subgroups of j abstract this work examines the commutator structure of some closed subgroups of the wild group of automorphisms of a local field with perfect residue field a group we call j in particular we establish a new approach to evaluating commutators in j and using this method investigate the normal subgroup structure of some classes of index subgroups of j as introduced by klopsch we provide new proofs of fesenko s results that lead to a proof that the torsion free group t t k 1 a k t qk 1 a k f p is hereditarily just infinite and by extending his work we also demonstrate the existence of a new class of hereditarily just infinite subgroups of j which have non trivial torsion

small volume limits of 2 d yang mills by examining the lattice gauge approximation we show that the small volume limit of the 2 dimensional yang mills functional integral is the natural symplectic measure on the moduli space of flat connections

a comprehensive framework for image inpainting inpainting is the art of modifying an image in a form that is not detectable by an ordinary observer there are numerous and very different approaches to tackle the inpainting problem though as explained in this paper the most successful algorithms are based upon one or two of the following three basic techniques copy and paste texture synthesis geometric partial differential equations pdes and coherence among neighboring pixels we combine these three building blocks in a variational model and provide a working algorithm for image inpainting trying to approximate the minimum of the proposed energy functional our experiments show that the combination of all three terms of the proposed energy works better than taking each term separately and the results obtained are within the state of the art

a symplectic structure for connections on surfaces with boundary for compact surfaces with one boundary component and semisimple gauge groups we construct a closed gauge invariant 2 form on the space of flat connections whose boundary holonomy lies in a fixed conjugacy class this form descends to the moduli space under the action of the full gauge group and provides an explicit description of a symplectic structure for this moduli space

yang mills on surfaces with boundary quantum theory and symplectic limit the quantum field measure for gauge fields over a compact surface with boundary with holonomy around the boundary components specified is constructed loop expectation values for general loop configurations are computed for a compact oriented surface with one boundary component let be the moduli space of flat connections with boundary holonomy lying in a conjugacy class in the gauge group g we prove that a certain natural closed 2 form on introduced in an earlier work by c king and the author is a symplectic structure on the generic stratum of for generic we then prove that the quantum yang mills measure with the boundary holonomy constrained to lie in converges in a natural sense to the corresponding symplectic volume measure in the classical limit we conclude with a detailed treatment of the case and determine the symplectic volume of this moduli space

a variational model for histogram transfer of color images in this paper we propose a variational formulation for histogram transfer of two or more color images we study an energy functional composed by three terms one tends to approach the cumulative histograms of the transformed images the other two tend to maintain the colors and geometry of the original images by minimizing this energy we obtain an algorithm that balances equalization and the conservation of features of the original images as a result they evolve while approaching an intermediate histogram between them this intermediate histogram does not need to be specified in advance but it is a natural result of the model finally we provide experiments showing that the proposed method compares well with the state of the art

the moduli space of flat connections on oriented surfaces with boundary abstract a 2 form is constructed on the space of connections on a principal bundle over an oriented surface with boundary this induces a symplectic structure for the moduli space of flat connections with boundary holonomies lying in prescribed conjugacy classes the yang mills quantum field measure is described for this situation this measure converges to the normalized symplectic volume measure in the classical limit