field theory conjecture for loop erased random walks we give evidence that the functional renormalization group frg developed to study disordered systems may provide a field theoretic description for the loop erased random walk lerw allowing to compute its fractal dimension in a systematic expansion in e 4 d up to two loop the frg agrees with rigorous bounds correctly reproduces the leading logarithmic corrections at the upper critical dimension d 4 and compares well with numerical studies we obtain the universal subleading logarithmic correction in d 4 which can be used as a further test of the conjecture

local inequalities for plurisubharmonic functions the main objective of this paper is to prove a new inequality for plurisubharmonic functions estimating their supremum over a ball by their supremum over a measurable subset of the ball we apply this result to study local properties of polynomial algebraic and analytic functions the paper has much in common with an earlier paper br of the author

functional renormalization group for anisotropic depinning and relation to branching processes in this article we review basic facts about disordered syst ems especially the existence of many metastable states and and the resulting failure of dimensional reduction besides techniques based on the gaussian variational method and replica symmetry breaking rsb the functional renormalization group frg is the only general method capable of attacking strongly disordered systems we explain the basic ideas of the latter method and why it is difficult to implement we finally review current progress fo r elastic manifolds in disorder

width distribution for random walk interfaces roughening of a one dimensional interface is studied under the assumption that the interface configurations are continuous periodic random walks the distribution of the square of the width of interface mathit w 2 is found to scale as p mathit w 2 mathit w 2 mathrm mathrm ensuremath 1 ensuremath phi mathit w 2 mathit w 2 where mathit w 2 is the average of mathit w 2 we calculate the scaling function ensuremath phi x exactly and compare it both to exact enumerations for a discrete slope surface evolution model and to ensuremath phi s obtained in monte carlo simulations of equilibrium and driven interfaces of chemically reacting systems

amplitude and kinematic corrections of migrated images for nonunitary imaging operators obtaining migrated images with meaningful amplitudes is a challenging problem when the migration operator is not unitary one possible solution to this problem is iterative inversion however inversion is an expensive process that can be rather difficult to apply especially with 3d data in this paper i propose estimating migrated images similar to the least squares inverse images by approximating the inverse hessian thus avoiding the need for iterative inversion the inverse hessian is approximated with a bank of nonstationary matching filters these filters are not exact impulse responses and are limited in their ability to mimic the full effects of least squares inversion tests on two data sets show that this filtering approach gives results similar to iterative least squares inversion at a lower cost this technique is flexible enough to be applied to images migrated from zero offset or angle domain common image point gathers

hyperbolic polynomials and interior point methods for convex programming hyperbolic polynomials have their origins in partial differential equations we show in this paper that they have applications in interior point methods for convex programming each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone we give an explicit representation of this cone in terms of polynomial inequalities the function fx log px is a logarithmically homogeneous self concordant barrier function for the hyperbolicity cone with barrier parameter equal to the degree of p the function fx possesses striking additional properties that are useful in designing long step interior point methods for example we show that the long step primal potential reduction methods of nesterov and todd and the surface following methods of nesterov and nemirovskii extend to hyperbolic barrier functions we also show that there exists a hyperbolic barrier function on every homogeneous cone

small amplitude limit cycles and the distribution of zeros of families of analytic functions we estimate the expected number of limit cycles of a planar polynomial vector field situated in a neighbourhood of the origin provided that the field in a larger neighbourhood is close enough to a linear center our main tool is a distributional inequality for the number of zeros of some families of univariate holomorphic functions depending analytically on a parameter we obtain this inequality by methods of pluripotential theory this inequality also implies versions of a strong law of large numbers and the central limit theorem for a probabilistic scheme associated with the distribution of zeros

size distributions of shocks and static avalanches from the functional renormalization group interfaces pinned by quenched disorder are often used to model jerky self organized critical motion we study static avalanches or shocks defined here as jumps between distinct global minima upon changing an external field we show how the full statistics of these jumps is encoded in the functional renormalizationgroup fixed point functions this allows us to obtain the size distribution p s of static avalanches in an expansion in the internal dimension d of the interface near and above d 4 this yields the mean field distribution p s s 3 2 e s 4sm where sm is a large scale cutoff in some cases calculable resumming all one loop contributions we find p s s exp c s sm 1 2 b 4 s sm where b c and are obtained to first order in 4 d our result is consistent to o with the relation a2 2 d where is the static roughness exponent often conjectured to hold at depinning our calculation applies to all static universality classes including random bond random field and random periodic disorders extended to long range elastic systems it yields a different size distribution for the case of contact line elasticity with an exponent compatible with 2 1 d to o 2 d we discuss consequences for avalanches at depinning and for sandpile models relations to burgers turbulence and the possibility that the relation be violated to higher loop order finally we show that the avalanche size distribution on a hyperplane of codimension one is in mean field valid close to and above d 4 given by p s k1 3 s s where k is the bessel k function thus hyper plane 4

width distribution of contact lines on a disordered substrate we have studied the roughness of a contact line on a disordered substrate by measuring its width distribution which characterizes the roughness completely the measured distribution is in excellent agreement with the distribution calculated in previous works extended here to the case of open boundary conditions this type of analysis which is performed here on experimental data provides a strong confirmation that the joanny de gennes model is not sufficient to describe the dynamics of the contact line at the depinning threshold

subunit balls for symbols of pseudodifferential operators abstract in this work we shall study a definition of subunit ball for non negative symbols of sub elliptic pseudodifferential operators extending in phase space the one given by stein nagel and wainger in the differential operator case using microlocal methods introduced by fefferman and phong we prove that these balls can be straightened by means of a canonical transformation to contain and be contained in boxes of certain sizes which we give in terms of the size of the symbol after microlocalizing the symbol in section 3 we define classes of subunit symbols and study some of their basic properties then we define the subunit ball in the last section the main structure theorems in the n n dimensional elliptic case and in the 1 1 and 2 2 dimensional nonelliptic nondegenerate cases are stated and proved

a comparison of imaging conditions for wave equation shot profile migration the application of a deconvolution imaging condition in wave equation shot profile migration is important to provide illumination compensation and amplitude recovery particularly if the aim is to successfully recover a measure of the medium reflectivity an imaging condition that destroys amplitudes is unacceptable we study a set of imaging conditions with illumination compensation the imaging conditions are evaluated by the quality of the output amplitudes and artifacts produced in numerical experiments using a vertically inhomogeneous velocity model the best of all imaging conditions we tested is the one that divides the crosscorrelation of upgoing and downgoing wavefields by the autocorrelation of the downgoing wavefield also known as the illumination map in an application to marmousi data unconditional division by autocorrelation turned out to be unstable effective stabilization was achieved by smoothing the illumination map

on the self concordance of the universal barrier function let k be a regular convex cone in hbox bbb r n and let f x be its universal barrier function let d kf x h ldots h be the k th order directional derivative at the point x in k 0 and direction h in hbox bbb r n we show that for every m ge3 there exists a constant c m 0 depending only on m such that d mf x h ldots h le c m d 2f x h h m 2 for m 3 this is the self concordance inequality of nesterov and nemirovskii our proof uses a powerful recent result of bourgain

first principles derivation of static avalanche size distributions we study the energy minimization problem for an elastic interface in a random potential plus a quadratic well as the position of the well is varied the ground state undergoes jumps called shocks or static avalanches we introduce an efficient and systematic method to compute the statistics of avalanche sizes and manifold displacements the tree level calculation i e mean field limit is obtained by solving a saddle point equation graphically it can be interpreted as the sum of all tree graphs the 1 loop corrections are computed using results from the functional renormalization group at the upper critical dimension the shock statistics is described by the brownian force model bfm the static version of the so called alessandro beatrice bertotti montorsi abbm model in the nonequilibrium context of depinning this model can itself be treated exactly in any dimension and its shock statistics is that of a levy process contact is made with classical results in probability theory on the burgers equation with brownian initial conditions in particular we obtain a functional extension of an evolution equation introduced by carraro and duchon which recursively constructs the tree diagrams in the field theory

migration of primaries and multiples using an imaging condition for amplitude normalized separated wavefields abstractmigration of primary and multiple reflections leads to enhanced subsurface illumination and to increased image resolution a joint migration approach using the complete wavefield requires properly imaged primaries and multiples of all orders in recent works primaries and multiples have therefore been imaged separately using the upgoing and downgoing pressure wavefields obtained by decomposing dual sensor streamer data the matches between the corresponding depth images are still not found to be sufficiently accurate so new and more appropriate imaging conditions need to be found we reviewed the classical imaging approach used in one way wave equation migration with the aim of extending it for simultaneous migration of primaries and all orders of multiples based on rayleigh s reciprocity theorem and well known theoretical developments we derived a new imaging condition described in terms of the upgoing pressure wavefield and a filtered version of the downgoing vertical velocity wavefield t

cone free primal dual path following and potential reduction polynomial time interior point methods we present a framework for designing and analyzing primal dual interior point methods for convex optimization we assume that a self concordant barrier for the convex domain of interest and the legendre transformation of the barrier are both available to us we directly apply the theory and techniques of interior point methods to the given good formulation of the problem as is without a conic reformulation using the very usual primal central path concept and a less usual version of a dual path concept we show that many of the advantages of the primal dual interior point techniques are available to us in this framework and therefore they are not intrinsically tied to the conic reformulation and the logarithmic homogeneity of the underlying barrier function

imaging the total wavefields by reflectivity estimation using amplitude normalized wavefield decomposition field data example abstractto combine imaging information of up and downgoing wavefields using primaries and multiples we have developed an imaging framework based on the subsurface impulse response the latter is expressed at every depth level by a fredholm integral equation defined in terms of the amplitude normalized upgoing pressure and downgoing vertical velocity wavefields the subsurface impulse response can be obtained by inverting the matrix form of the integral equation by performing a multidimensional deconvolution mdd of the upgoing components by the downgoing components this procedure gives the reflectivity matrix by assuming locally reacting media or lateral shift invariance we can describe how the mdd can reduce to simpler deconvolution imaging conditions based on an example acquired with dual sensor towed streamers and simultaneous sources we have developed a real data application of imaging the total up and downgoing wavefields by reflectivity inversion the total upgoing wavefield used in the im

markov s inequality and polynomial mappings markov s inequality is a certain estimate for the norm of the derivative of a polynomial in terms of the degree and the norm of this polynomial it has many interesting applications in approximation theory constructive function theory and in analysis for instance to sobolev inequalities or whitney type extension problems one of the purposes of this paper is to give a solution to an old problem studied among others by baran and ple niak and concerning the invariance of markov s inequality under polynomial mappings polynomial images we also address the issue of preserving markov s inequality when taking polynomial preimages lastly we give a sufficient condition for a subset of a markov set to be a markov set

theory of true amplitude one way wave equations and true amplitude common shot migration one way wave operators are powerful tools for forward modeling and migration here we describe a recently developed true amplitude implementation of modified one way operators and present some numerical examples by true amplitude one way forward modeling we mean that the solutions are dynamically correct as well as kinematically correct that is ray theory applied to these equations yields the upward and downward traveling eikonal equations of the full wave equation and the amplitude satisfies the transport equation of the full wave equation the solutions of these equations are used in the standard wave equation migration imaging condition the boundary data for the downgoing wave is also modified from the one used in the classic theory because the latter data is not consistent with a point source for the full wave equation when the full wave form solutions are replaced by their ray theoretic approximations the imaging formula reduces to the common shot kirchhoff inversion formula in this sense

width distribution of curvature driven interfaces a study of universality one dimensional interfaces with curvature driven growth kinetics are investigated we calculate the steady state distribution p mathit w 2 of the square of the width of the interface mathit w 2 and show that as in the case for random walk interfaces the result can be written in a scaling form mathit w 2 p mathit w 2 ensuremath phi mathit w 2 mathit w 2 where mathit w 2 is the average of mathit w 2 the scaling function ensuremath phi x is found to be distinct from that of random walk interfaces but as our monte carlo simulations indicate this function is universal for curvature driven growth it is argued that comparison of scaling functions can be a useful method for distinguishing between universality classes of growth processes

graphs of zeros of analytic families let f f be a family of holomorphic functions in a domain d c depending holomorphically on u c we study the distribution of zeros of f in a subdomain r d whose boundary is a closed non singular analytic curve as an application we obtain several results about distributions of zeros of families of generalized exponential polynomials and displacement maps related to certain ode s

higher correlations universal distributions and finite size scaling in the field theory of depinning recently we constructed a renormalizable field theory up to two loops for the quasi static depinning of elastic manifolds in a disordered environment here we explore further properties of the theory we show how higher correlation functions of the displacement field can be computed drastic simplifications occur unveiling much simpler diagrammatic rules than anticipated this is applied to the universal scaled width distribution the expansion in d 4 epsilon predicts that the scaled distribution coincides to the lowest orders with the one for a gaussian theory with propagator g q 1 q d 2 zeta zeta being the roughness exponent the deviations from this gaussian result are small and involve higher correlation functions which are computed here for different boundary conditions other universal quantities are defined and evaluated we perform a general analysis of the stability of the fixed point we find that the correction to scaling exponent is omega epsilon and not epsilon 3 as used in the analysis of some simulations a more detailed study of the upper critical dimension is given where the roughness of interfaces grows as a power of a logarithm instead of a pure power

maximum relative height of elastic interfaces in random media the distribution of the maximal relative height mrh of self affine one dimensional elastic interfaces in a random potential is studied we analyze the ground state configuration at zero driving force and the critical configuration exactly at the depinning threshold both for the random manifold and random periodic universality classes these configurations are sampled by exact numerical methods and their mrh distributions are compared with those with the same roughness exponent and boundary conditions but produced by independent fourier modes with normally distributed amplitudes using pickands theorem we derive an exact analytical description for the right tail of the latter after properly rescaling the mrh distributions we find that corrections from the gaussian independent modes approximation are in general small as previously found for the average width distribution of depinning configurations in the large size limit all corrections are finite except for the ground state in the random periodic class whose mrh distribution becomes for periodic boundary conditions indistinguishable from the airy distribution we find that the mrh distributions are in general sensitive to changes of boundary conditions

on local behavior of holomorphic functions along complex submanifolds of ℂ n in this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of n as a corollary we present multi dimensional generalizations of an important result of coman and poletsky on bernstein type inequalities on transcendental curves in 2

delayed shot 3d depth migration for 3d seismic imaging in structurally complex areas the use of migration by wavefield extrapolation has become widespread by its very nature this family of migration methods operates on data sets that satisfy a wave equation in the context of a single physically realizable field experiment such as a common shot record however common shot migration of data recorded over dipping structures requires a migration aperture much larger than the recording aperture resulting in extra computations a different type of wave equation record the response to a linear or planar source can be synthesized from all the common shot records synthesizing these records from common shot records involves slant stack processing or applying delays to the various shots we call these records delayed shot records delayed shot records don t suffer from the aperture problems of common shot records since their recording aperture is the length of the seismic survey consequently delayed shot records hold potential for eff

functional renormalization group and the field theory of disordered elastic systems we study elastic systems such as interfaces or lattices pinned by quenched disorder to escape triviality as a result of dimensional reduction we use the functional renormalization group difficulties arise in the calculation of the renormalization group functions beyond one loop order even worse observables such as the two point correlation function exhibit the same problem already at one loop order these difficulties are due to the nonanalyticity of the renormalized disorder correlator at zero temperature which is inherent to the physics beyond the larkin length characterized by many metastable states as a result two loop diagrams which involve derivatives of the disorder correlator at the nonanalytic point are naively ambiguous we examine several routes out of this dilemma which lead to a unique renormalizable field theory at two loop order it is also the only theory consistent with the potentiality of the problem the beta function differs from previous work and the one at depinning by novel anomalous terms for interfaces and random bond disorder we find a roughness exponent zeta 0 208 298 04epsilon 0 006 858epsilon 2 epsilon 4 d for random field disorder we find zeta epsilon 3 and compute universal amplitudes to order o epsilon 2 for periodic systems we evaluate the universal amplitude of the two point function we also clarify the dependence of universal amplitudes on the boundary conditions at large scale all predictions are in good agreement with numerical and exact results and are an improvement over one loop finally we calculate higher correlation functions which turn out to be equivalent to those at depinning to leading order in epsilon

remez type inequality on sets with cusps abstract a remez type inequality is proved for a large family of sets with cusps in r n including compact fat and semialgebraic or subanalytic sets

universal interface width distributions at the depinning threshold the scaling properties of driven elastic interfaces in random media play an important role in a wide variety of physical situations ranging from stochastic surface growth to domain walls in disordered magnetic materials the spreading of fluids on rough substrates and the dynamics of cracks 1 2 these problems share many features with critical phenomena and provide a challenge for theoretical approaches to disordered systems and nonequilibrium phenomena 3 8 here we study interfaces described by a scalar height function h x where x is the d dimensional internal coordinate we measure the deviation from the mean position as u x 5h x 2 h where iii stands for the spatial average over all x of a given interface cf fig 1 the mean square width of a single interface w 2 n u x o5 u 2 can be used to characterize its roughness and explore universal properties after averaging over the ensemble of interfaces w 2 grows with the lateral extension l of the system as w 2

target oriented wave equation inversion a target oriented strategy can be applied to estimate a wave equation least squares inverse lsi image by explicitly computing the wave equation hessian the lsi image is obtained as the solution of a nonstationary least squares inverse filtering problem the rows of the hessian are the nonstationary filters containing information about the acquisition geometry the velocity model and the band limited characteristics of the seismic data by exploiting the sparsity and the structure of the hessian matrix a large number of iterations necessary to achieve convergence can be computed cheaply the results on a structurally complex model show the improvements of the lsi image versus the migrated image

subsurface reflectivity estimation from imaging of primaries and multiples using amplitude normalized separated wavefields abstractseveral studies have shown the benefits of including multiple reflections together with primaries in the structural imaging of subsurface reflectors however to characterize the reflector properties there is a need to compensate for propagation effects due to multiple scattering and to properly combine the information from primaries and all orders of multiples from this perspective and based on the wave equation and rayleigh s reciprocity theorem recent works have suggested computing the subsurface image from the green s function reflection response or reflectivity by inverting a fredholm integral equation in the frequency space domain by following claerbout s imaging principle and assuming locally reacting media the integral equation may be reduced to a trace by trace deconvolution imaging condition for a complex overburden and considering that the structure of the subsurface is angle dependent this trace by trace deconvolution does not properly solve the fredholm integral equation we

smoothing imaging condition for shot profile migration amplitudes in shot profile migration can be improved if the imaging condition incorporates a division deconvolution in the time domain of the upgoing wavefield by the downgoing wavefield this division can be enhanced by introducing an optimal wienerfilterwhichassumesthatthenoisepresentinthedatahas a white spectrum this assumption requires a damping parameter related to the signal to noise ratio often chosen by trial and error in practice the damping parameter replaces the small valuesofthespectrumofthedowngoingwavefieldandavoidsdivision by zero the migration results can be quite sensitive to the damping parameter and in most applications the upgoing and downgoing wavefields are simply multiplied alternatively the division can be made stable by filling the small values of the spectrumwithanaverageoftheneighboringpoints thisaveraging is obtained by running a smoothing operator on the spectrum ofthedowngoingwavefield thisoperationcalledthesmoothing imaging condition our results show that where the spectrum of the downgoing wavefield is high the imaging condition with dampingandsmoothingyieldssimilarresults thuscorrectingfor illumination effects where the spectrum is low the smoothing imaging condition tends to be more robust to the noise level present in the data thus giving better images than the imaging condition with damping in addition our experiments indicate that the parameterization of the smoothing imaging condition i e choice of window size for the smoothing operator is easy and repeatable from one data set to another making it a valuable additiontoourimagingtoolbox

level spacing for non monotone anderson models we prove localization and probabilistic bounds on the minimum level spacing for a random block anderson model without monotonicity using a sequence of narrowing energy windows and associated schur complements we obtain detailed probabilistic information about the microscopic structure of energy levels of the hamiltonian as well as the support and decay of eigenfunctions

dynamical selection of critical exponents in renormalized field theories there are in general one or few fixed points that are accessible by the renormalization group flow they can be identified from the fixed point equations exceptionally an infinite family of fixed points exists parameterized by a scaling exponent itself a function of a nonrenormalizing parameter here we report a different scenario with an infinite family of fixed points of which seemingly only one is chosen by the renormalization group flow this dynamical selection takes place in systems with an attractive interaction v as in standard 4 theory but where the potential v at large goes to zero as e g the attraction by a defect

on the complexity of a practical interior point method the theory of self concordance in convex optimization has been used to analyze the complexity of interior point methods based on newton s method for large problems it may be impractical to use newton s method here we analyze a truncated newton method in which an approximation to the newton search direction is used in addition practical interior point methods often include enhancements such as extrapolation that are absent from the theoretical algorithms analyzed previously we derive theoretical results that apply to such an algorithm one similar to a sophisticated computer implementation of a barrier method the results for a single barrier subproblem are a satisfying extension of the results for newton s method when extrapolation is used in the overall barrier method however our results are more limited we indicate by both theoretical arguments and examples why more elaborate results may be difficult to obtain

on local behavior of analytic functions we prove local inequalities for analytic functions defined on a convex body in r n which generalize well known classical inequalities for polynomials

nodal sets of eigenfunctions on riemannian manifolds soit m n une variete connexe compacte a metrique riemannienne c soit le laplacien de m soit f une fonction propre reelle de de valeur propre on demontre que la fonction propre f s annule au plus a l ordre c 1 2 pour tout point dans m