conditional intensity and gibbsianness of determinantal point processes the papangelou intensities of determinantal or fermion point processes are investigated these exhibit a monotonicity property expressing the repulsive nature of the interaction and satisfy a bound implying stochastic domination by a poisson point process we also show that determinantal point processes satisfy the so called condition which is a general form of gibbsianness under a continuity assumption the gibbsian conditional probabilities can be identified explicitly

a novel fuzzy logic approach to contrast enhancement abstract contrast enhancement is one of the most important issues of image processing pattern recognition and computer vision the commonly used techniques for contrast enhancement fall into two categories 1 indirect methods of contrast enhancement and 2 direct methods of contrast enhancement indirect approaches mainly modify histogram by assigning new values to the original intensity levels histogram specification and histogram equalization are two popular indirect contrast enhancement methods however histogram modification technique only stretches the global distribution of the intensity the basic idea of direct contrast enhancement methods is to establish a criterion of contrast measurement and to enhance the image by improving the contrast measure the contrast can be measured globally and locally it is more reasonable to define a local contrast when an image contains textual information fuzzy logic has been found many applications in image processing pattern recognition etc fuzzy set theory is a useful tool for handling the uncertainty in the images associated with vagueness and or imprecision in this paper we propose a novel adaptive direct fuzzy contrast enhancement method based on the fuzzy entropy principle and fuzzy set theory we have conducted experiments on many images the experimental results demonstrate that the proposed algorithm is very effective in contrast enhancement as well as in preventing over enhancement

volumes of balls in large riemannian manifolds we prove two lower bounds for the volumes of balls in a riemannian manifold if m n g is a complete riemannian manifold with lling radius at least r then it contains a ball of radius r and volume at least n r n if m n hyp is a closed hyperbolic manifold and if g is another metric on m with volume no greater than n vol m hyp then the universal cover of m g contains a unit ball with volume greater than the volume of a unit ball in hyperbolic n space

a variational principle in the dual pair of reproducing kernel hilbert spaces and an application given a positive definite bounded linear operator a on the hilbert space mathcal h 0 l2 e we consider a reproducing kernel hilbert space mathcal h with a reproducing kernel a x y here e is any countable set and a x y x y e is the representation of a w r t the usual basis of mathcal h 0 imposing further conditions on the operator a we also consider another reproducing kernel hilbert space mathcal h with a kernel function b x y which is the representation of the inverse of a in a sense so that mathcal h mathcal h 0 mathcal h becomes a rigged hilbert space we investigate the ratios of determinants of some partial matrices of a and b we also get a variational principle on the limit ratios of these values we apply this relation to show the gibbsianness of the determinantal point process or fermion point process defined by the operator a i a 1 on the set e

hard and soft packing radius theorems singular spaces are playing an increasingly important role in riemannian geometry in particular this is true of the so called alexandrov spaces i e finite hausdorff dimensional complete inner metric spaces with a lower curvature bound in the local triangle comparison sense interest in alexandrov spaces is largely explained by the fact that the natural process of taking gromov hausdorff limits is closed in alexandrov geometry but not in riemannian geometry this simple observation has become a powerful tool in riemannian geometry see for example fy gp2 or gpw and pe in this paper we use a new means to obtain results in riemannian geometry by studying alexandrov spaces the operation of forming spherical suspensions of positively curved spaces an operation which is also closed in alexandrov geometry but not in riemannian geometry will be applied to prove a differentiable sphere theorem which is unlike all previous solutions to the following basic problem

a nonlinear image contrast sharpening approach based on munsell s scale contrast is a measure of the variation in intensity or gray value in a specified region of an image the region can be most or all of the image giving rise to a global concept of contrast the region might on the other hand be a small window in which case the concept of contrast is a locally defined expression in this work we introduce a nonlinear local contrast enhancement method this method utilizes the munsell value scale which is based upon human visual perception use of the munsell value scale allows for the partitioning of the gray scale into ten discrete subintervals subsequent local processing occurs within each of these subintervals inside each subinterval this method constructs a contrast enhancement function that is a smooth approximation to the threshold step function and which maps a given subinterval into itself this function then thresholds the gray values in a subinterval in a smooth manner about a locally computed quantity called the mean edge gray value by enhancing the contrast in this way the original shades of gray are preserved that is the groupings of the gray values by subinterval are preserved as a result no gray value distortion is introduced into the image

on the filling radius of positively curved alexandrov spaces it was shown by f wilhelm that gromov s filling radius of any positively curved closed riemannian manifolds are less than that of the round sphere unless they are isometric to each other in this short paper we adapt his proof to see that the same is true for any positively curved closed alexandrov spaces as well

the length of a shortest geodesic loop at a point in this paper we prove that given a point p m n where m n is a closed riemannian manifold of dimension n the length of a shortest geodesic loop lp m n at this point is bounded above by 2nd where d is the diameter of m n moreover we show that on a closed simply connected riemannian manifold m n with a nontrivial second homotopy group there either exist at least three geodesic loops of length less than or equal to 2d at each point of m n or the length of a shortest closed geodesic on m n is bounded from above by 4d

flowers on riemannian manifolds in this paper we will present two upper bounds for the length of a smallest flower shaped geodesic net in terms of the volume and the diameter of a manifold minimal geodesic nets are critical points of the length functional on the space of graphs immersed into a riemannian manifold let mn be a closed riemannian manifold of dimension n we prove that there exists a minimal geodesic net that consists of one vertex and at most 2n 1 geodesic loops based at that vertex of total length 2n d where d is the diameter of mn we also show that there exists a minimal geodesic net that consists of one vertex and at most 3 n 1 2 loops of total length leq2 n 1 2 3 n 1 3 fill rad m n leq2 n 1 frac 5 2 3 n 1 3 n 1 n n vol m n frac 1 n where fill rad mn denotes the filling radius and vol mn denotes the volume of mn

gibbsianness of fermion random point fields we consider fermion or determinantal random point fields on euclidean space d given a bounded translation invariant and positive definite integral operator j on l2 d we introduce a determinantal interaction for a system of particles moving on d as follows the n points located at x1 x n d have the potential energy given by where j x y is the integral kernel function of the operator j we show that the gibbsian specification for this interaction is well defined when j is of finite range in addition and for d 2 if the intensity is small enough we show that the fermion random point field corresponding to the operator j i j 1 is a gibbs measure admitted to the specification

gromov hyperbolic spaces and the sharp isoperimetric constant in this article we exhibit the largest constant in a quadratic isoperimetric inequality which ensures that a geodesic metric space is gromov hyperbolic as a particular consequence we obtain that euclidean space is a borderline case for gromov hyperbolicity in terms of the isoperimetric function we prove similar results for the linear filling radius inequality our results strengthen and generalize theorems of gromov papasoglu and others

dirichlet forms and diffusion processes for fermion random point fields abstract we construct the dirichlet forms and the associated diffusion processes on the configuration space of particles moving on the euclidean space r d for which certain fermion random point fields are invariant

geodesic loops and periodic geodesics on a riemannian manifold diffeomorphic to s 3 let m n be a closed 2 connected riemannian manifold such that 3 m n 0 in this paper we prove that either there exists a periodic geodesic on m n of length 6d where d is the diameter of m n or at each point p m n there exists a geodesic loop of length 2d

adaptive contrast enhancement and de enhancement abstract two different interpolative schemes for adaptive contrast enhancement have been presented for speeding up the contrast enhancement algorithm proposed by beghdadi and negrate to reduce the enhancement of noise in relatively flat regions present in the image an adaptive power variation technique is used in which the degree of contrast enhancement is varied depending on the severity of brightness change in a region a contrast transformation function is proposed which can be used for adaptive enhancement as well as de enhancement of images

length of geodesics on a two dimensional sphere let m be an arbitrary riemannian manifold diffeomorphic to s 2 let x y be two arbitrary points of m we prove that for every k 1 2 3 ldots there exist k distinct geodesics between x and y of length less than or equal to 4k 2 2k 1 d where d denotes the diameter of m to prove this result we demonstrate that for every riemannian metric on s 2 there are two not mutually exclusive possibilities either every two points can be connected by many short geodesics of index 0 or the resulting riemannian sphere can be swept out by short meridians

quasi invariance and integration by parts for determinantal and permanental processes abstract determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent their atoms exhibit mutual attraction of repulsion thus these processes are very far from the uncorrelated situation encountered in poisson models we establish a quasi invariance result we show that if atom locations are perturbed along a vector field the resulting process is still a determinantal respectively permanental process the law of which is absolutely continuous with respect to the original distribution based on this formula following bismut approach of malliavin calculus we then give an integration by parts formula

random point fields associated with certain fredholm determinants i fermion poisson and boson point processes we introduce certain classes of random point fields including fermion and boson point processes which are associated with fredholm determinants of certain integral operators and study some of their basic properties limit theorems correlation functions palm measures etc also we propose a conjecture on an analogue of the determinant and permanent

random point fields associated with certain fredholm determinants ii fermion shifts and their ergodic and gibbs properties we construct and study a family of probability measures on the configuration space over countable discrete space associated with nonnegative definite symmetric operators via determinants under a mild condition they turn out unique gibbs measures also some ergodic properties including the entropy positivity are discussed in the lattice case

on the spread of positively curved alexandrov spaces it was proved by f wilhelm that gromov s filling radius of closed positively curved manifolds with a uniform lower bound on sectional curvature attains the maximum with the round sphere recently the author proved that this is also the case for closed finite dimensional alexandrov spaces with a positive lower curvature bound these were proved as a corollary of a comparison theorem for the invariant called spread of those spaces in this paper we extend the latter result to infinite dimensional alexandrov spaces

asymptotics of plancherel measures for symmetric groups 1 1 plancherel measures given a finite group g by the corresponding plancherel measure we mean the probability measure on the set g of irreducible representations of g which assigns to a representation g the weight dim g for the symmetric group s n the set s n is the set of partitions of the number n which we shall identify with young diagrams with n squares throughout this paper the plancherel measure on partitions arises naturally in representation theoretic combinatorial and probabilistic problems for example the plancherel distribution of the first part of a partition coincides with the distribution of the longest increasing subsequence of a uniformly distributed random permutation 31 we denote the plancherel measure on partitions of n by mn

lower bounds on the energy of maps on demontre que pour la metrique standard sur rp n l application identite est minimisante de l energie dans sa classe d homotopie

moment formulae for general point processes abstract the goal of this paper is to generalize most of the moment formulae obtained in 12 more precisely we consider a general point process and show that the quantities relevant to our problem are the so called papangelou intensities when the papangelou intensities of are well defined we show some general formulae to recover the moment of order n of the stochastic integral of the point process we will use these extended results to introduce a divergence operator and study a random transformation of the point process