delocalization of two dimensional random surfaces with hard core constraints we study the fluctuations of random surfaces on a two dimensional discrete torus the random surfaces we consider are defined via a nearest neighbor pair potential which we require to be twice continuously differentiable on a possibly infinite interval and infinity outside of this interval no convexity assumption is made and we include the case of the so called hammock potential when the random surface is uniformly chosen from the set of all surfaces satisfying a lipschitz constraint our main result is that these surfaces delocalize having fluctuations whose variance is at least of order log n where n is the side length of the torus we also show that the expected maximum of such surfaces is of order at least log n the main tool in our analysis is an adaptation to the lattice setting of an algorithm of richthammer who developed a variant of a mermin wagner type argument applicable to hard core constraints we rely also on the reflection positivity of the random surface model the result answers a question mentioned by brascamp et al on the hammock potential and a question of velenik

co registration and distortion correction of diffusion and anatomical images based on inverse contrast normalization diffusion mri provides quantitative information about microstructural properties which can be useful in neuroimaging studies of the human brain echo planar imaging epi sequences which are frequently used for acquisition of diffusion images are sensitive to inhomogeneities in the primary magnetic b0 field that cause localized distortions in the reconstructed images we describe and evaluate a new method for correction of susceptibility induced distortion in diffusion images in the absence of an accurate b0 fieldmap in our method the distortion field is estimated using a constrained non rigid registration between an undistorted t1 weighted anatomical image and one of the distorted epi images from diffusion acquisition our registration framework is based on a new approach inversion inverse contrast normalization for very simple registration which exploits the inverted contrast relationship between t1 and t2 weighted brain images to define a simple and robust similarity measure we also describe how inversion can be used for rigid alignment of diffusion images and t1 weighted anatomical images our approach is evaluated with multiple in vivo datasets acquired with different acquisition parameters compared to other methods inversion shows robust and consistent performance in rigid registration and shows improved alignment of diffusion and anatomical images relative to normalized mutual information for non rigid distortion correction

stability and asymptoticity of volterra difference equations a progress report we survey some of the fundamental results on the stability and asymptoticity of linear volterra difference equations the method of z transform is heavily utilized in equations of convolution type an example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty it is shown that the two notions are equivalent if the kernel decays exponentially for equations of nonconvolution type liapunov functions are used to find explicit criteria for stability moreover the resolvent matrix is defined to produce a variation of constants formula the study of asymptotic equivalence for difference equations with infinite delay is carried out in section 6 finally we state some problems

on homogenization and scaling limit of some gradient perturbations of a massless free field we study the continuum scaling limit of some statistical mechanical models defined by convex hamiltonians which are gradient perturbations of a massless free field by proving a central limit theorem for these models we show that their long distance behavior is identical to a new homogenized continuum massless free field we shall also obtain some new bounds on the 2 point correlation functions of these models

asymptotic behavior of volterra difference equations abstract in this paper we investigate boundedness and stability properties of some classes of discrete volterra equations the main tool in this work is the use of a representation formula which allows us to express the solution of discrete volterra equations in terms of the resolvent matrix of the corresponding system of volterra difference equations

stability analysis of discrete recurrence equations of volterra type with degenerate kernels abstract stability criteria are derived for difference equations of volterra type with degenerate kernels the main tool in this analysis is the use of the new representation formula which allows us to express the solution of discrete volterra equation with degenerate kernel in terms of the fundamental matrix of the corresponding first order system of the difference equations

boundedness of discrete volterra equations abstract investigation of the boundedness of the solutions of volterra equations with discrete time by means of the direct liapunov method and comparison theorems is performed boundedness conditions of solutions of some particular classes of equations are derived using such conditions stability of direct quadrature methods for second kind volterra equations is analyzed

boundedness of solutions of difference systems with delays we give sufficient conditions for the boundedness of all solutions of some classes of systems of difference equations with delays by comparison of their norms with the solution of certain auxiliary scalar difference equations

motion by mean curvature from the ginzburg landau interface model we consider the scalar field t with a reversible stochastic dynamics which is defined by the standard dirichlet form relative to the gibbs measure with formal energy the potential v is even and strictly convex we prove that under a suitable large scale limit the t field becomes deterministic such that locally its normal velocity is proportional to its mean curvature except for some anisotropy effects as an essential input we prove that for every tilt there is a unique shift invariant ergodic gibbs measure for the field

high dimensional lipschitz functions are typically flat a homomorphism height function on the d dimensional torus mathbb z n d is a function on the vertices of the torus taking integer values and constrained to have adjacent vertices take adjacent integer values a lipschitz height function is defined similarly but may also take equal values on adjacent vertices for each of these models we consider the uniform distribution over all such functions with predetermined values at some fixed vertices boundary conditions our main result is that in high dimensions and with zero boundary values the random function obtained is typically very flat having bounded variance at any fixed vertex and taking at most c log n 1 d values with high probability this result matches up to constants a lower bound of benjamini yadin and yehudayoff our results extend to any dimension d ge2 if one replaces the torus mathbb z n d by an enhanced version of it the torus mathbb z n d times mathbb z 2 d 0 for some fixed d 0 consequently we establish one side of a conjectured roughening transition in two dimensions the full transition is established for a class of tori with nonequal side lengths including for example the n times lfloor frac 1 10 log n rfloor torus in another case of interest we find that when the dimension d is taken to infinity while n remains fixed the random function takes at most r values with high probability where r 5 for the homomorphism model and r 4 for the lipschitz model suitable generalizations are obtained when n grows with d our results have consequences also for the related model of uniform 3 coloring and establish that for certain boundary conditions a uniformly sampled proper 3 coloring of mathbb z n d will be nearly constant on either the even or odd sublattice our proofs are based on the construction of a combinatorial transformation suitable to the homomorphism model and on a careful analysis of the properties of a class of cutsets which we term odd cutsets for the lipschitz model our results rely also on a bijection of yadin this work generalizes results of galvin and kahn refutes a conjecture of benjamini yadin and yehudayoff and answers a question of benjamini haggstrom and mossel

phase coexistence of gradient gibbs states we consider the scalar gradient fields a b with b denoting the nearest neighbor edges in mathbb z 2 that are distributed according to the gibbs measure proportional to hbox e beta h eta nu d eta here h bv b is the hamiltonian v is a symmetric potential 0 is the inverse temperature and is the lebesgue measure on the linear space defined by imposing the loop condition eta b 1 eta b 2 eta b 3 eta b 4 for each plaquette b1 b2 b3 b4 in mathbb z 2 for convex v funaki and spohn have shown that ergodic infinite volume gibbs measures are characterized by their tilt we describe a mechanism by which the gradient gibbs measures with non convex v undergo a structural order disorder phase transition at some intermediate value of inverse temperature at the transition point there are at least two distinct gradient measures with zero tilt i e e b 0

stability of finite delay difference systems the stability of finite delay difference systems has recently been discussed in l in this paper we consider the delay difference systems with infinite delay of the following form x n 1 g n x s s 1 1 1 n g n x 1 where 1 is an integer or w we assume g n 0 0 forn l l l so that 1 has the zero solution x n 0 clearly for any given integer n l 1 and a given bounded initial function 4 l 1 1 no rk there is a unique solution of l denoted by x n n 4 such that it satisfies 1 for all integers n 2 n and x n no 4 444 forn f l l no for any integer m 2 co let 2 m m 1 i and 2 z the integer set if m a for any n e z define ii411 tlnl sup l s 15 s 5 n and for any h 0 let c n 4 z rk i nl h in the sequel we always assume that the variables n r and s take integer values and the corresponding intervals are discrete intervals

on the absence of spontaneous symmetry breaking and of crystalline ordering in two dimensional systems we develop a unified approach based on araki s relative entropy concept to proving absence of spontaneous breaking of continuous internal symmetries and translation invariance in two dimensional statistical mechanical systems more precisely we show that under rather general assumptions on the interactions all equilibrium states of a two dimensional system have all the symmetries compact internal and spatial of the dynamics except possibly rotation invariance rotation invariance remains unbroken if connected correlations decay more rapidly than the inverse square distance we also prove that two dimensional systems with a non compact internal symmetry group like anharmonic crystals typically do not have gibbs states

a survey stability and boundedness of volterra difference equations abstract volterra difference equations arise in the modeling of many real phenomena in this survey stability and boundedness problems of some volterra nonlinear difference equations are investigated stability conditions and boundedness are formulated in terms of the characteristics of equations

stability of difference volterra equations direct liapunov method and numerical procedure abstract a procedure to construct liapunov functionals for discrete volterra equations is proposed using this procedure stability conditions are derived for general volterra difference equations some applications of the proposed procedure for obtaining stability conditions for linear multistep methods for volterra integro differential equations are presented

on the symmetry of the gibbs states in two dimensional lattice systems under fairly general conditions if a two dimensional classical lattice system has an internal symmetry groupg which is a compact connected lie group then all gibbs states areg invariant

equilibrium fluctuations for nabla_ varphi interface model we study the large scale space time fluctuations of an interface which is modeled by a massless scalar field with reversible langevin dynamics for a strictly convex interaction potential we prove that on a large space time scale these fluctuations are governed by an infinite dimensional ornstein uhlenbeck process its effective diffusion type covariance matrix is characterized through a variational formula

a central limit theorem for convex sets we show that there exists a sequence varepsilon n searrow0 for which the following holds let k n be a compact convex set with a non empty interior let x be a random vector that is distributed uniformly in k then there exist a unit vector in n t0 and 0 such that sup a subset mathbb r left textit prob langle x theta rangle in a frac 1 sqrt 2 pi sigma int ae frac t t 0 2 2 sigma 2 dt right leq varepsilon n qquad ast where the supremum runs over all measurable sets a and where denotes the usual scalar product in n furthermore under the additional assumptions that the expectation of x is zero and that the covariance matrix of x is the identity matrix we may assert that most unit vectors satisfy with t0 0 and 1 corresponding principles also hold for multi dimensional marginal distributions of convex sets

a perspective on the numerical treatment of volterra equations abstract we discuss the properties and numerical treatment of various types of volterra and abel volterra integral and integro differential equations

general theorems for stability and boundedness for nonlinear functional discrete systems abstract we consider the nonlinear functional discrete system x n 1 g n x s 0 s n def g n x and obtain sufficient conditions for stability properties of the zero solution and for the boundedness of solutions

phase structure of two dimensional spin models and percolation for a class of classical spin models in 2d satisfying a certain continuity constraint it is proven that some of their correlations do not decay exponentially the class contains discrete and continuous spin systems with abelian and non abelian symmetry groups for the discrete models our results imply that they show either long range order or are in a soft phase characterized by powerlike decay of correlations for the continuous models only the second possibility exists the continuous models include a version of the plane rotator o 2 model for this model we rederive modulo two conjectures the frohlich spencer result on the existence of the kosterlitz thouless phase in a very simple way the proof is based on percolation theoretic and topological arguments