mass concentration and aging in the parabolic anderson model with doubly exponential tails we study the non negative solution u u x t to the cauchy problem for the parabolic equation partial t u vardelta u xi u on mathbb z d times 0 infty with initial data u x 0 mathsf 1 0 x here vardelta is the discrete laplacian on mathbb z d and xi xi z z in mathbb z d is an i i d random field with doubly exponential upper tails we prove that for large t and with large probability most of the total mass u t sum x u x t of the solution resides in a bounded neighborhood of a site z t that achieves an optimal compromise between the local dirichlet eigenvalue of the anderson hamiltonian vardelta xi and the distance to the origin the processes t mapsto z t and t mapsto tfrac 1 t log u t are shown to converge in distribution under suitable scaling of space and time aging results for z t as well as for the solution to the parabolic problem are also established the proof uses the characterization of eigenvalue order statistics for vardelta xi in large sets recently proved by the first two authors

detecting singular patterns in 2d vector fields using weighted laurent polynomial in this paper we propose a method for detecting patterns of interest in vector fields our method detects patterns in a scale and rotation invariant manner it works by approximating the vector field data locally using a laurent polynomial weighted by radial basis functions the proposed representation is able to model both analytic and non analytic flow fields invariance to scale and rotation is achieved by combining the linearity properties of the model coefficients and a scale space parameter of the radial basis functions promising detection results are obtained on a variety of fluid flow sequences

anderson parabolic model for a quasi stationary medium we study the anderson parabolic model for a random medium which is a product of an i i d space like random field and a white noise the model has long range space time correlations and is intermediate between the stationary case and the turbulent one which were studied in previous works under some natural assumptions on the distribution of the space potential we prove existence and uniqueness and derive the long time asymptotics for the annealed moments and the semi annealed ones for which expectation is taken only w r t the white noise a conjecture for the fully quenched case is discussed on a simplified model

population growth in random media ii wavefront propagation in this second part of a two part presentation we continue with the model introduced in part i in this part the initial configuration has one particle at each site to the left of 0 and no particle elsewhere the expected number of particles observed at a site moving at speed has an exponential growth rate speed growth rate that is computed explicitly the result reveals two characteristic wavefront speeds 1 the speed of the front of zero growth rightmost particle and 2 the speed of the front of maximal growth the latter speed exhibits a phase transition changing from zero to positive as the drift in the migration crosses a threshold the qualitative shape of the growth rate as a function of changes as well in particular below the threshold there appears a linear piece which corresponds to the system exhibiting an intermittency effect

delocalising the parabolic anderson model through partial duplication of the potential the parabolic anderson model on mathbb z d with i i d potential is known to completely localise if the distribution of the potential is sufficiently heavy tailed at infinity in this paper we investigate a modification of the model in which the potential is partially duplicated in a symmetric way across a plane through the origin in the case of potential distribution with polynomial tail decay we exhibit a surprising phase transition in the model as the decay exponent varies for large values of the exponent the model completely localises as in the i i d case by contrast for small values of the exponent we show that the model may delocalise more precisely we show that there is an event of non negligible probability on which the solution has non negligible mass on two sites

long time tails in the parabolic anderson model with bounded potential we consider the parabolic anderson problem t u u u on 0 z d with random i i d potential z z zd and the initial condition u 0 1 our main assumption is that esssup 0 0 depending on the thickness of the distribution prob 0 close to its essential supremum we identify both the asymptotics of the moments of u t 0 and the almost sure asymptotics of u t 0 as t in terms of variational problems as a by product we establish lifshitz tails for the random schrodinger operator at the bottom of its spectrum in our class of distributions the lifshitz exponent ranges from d 2 to the power law is typically accompanied by lower order corrections

localization criteria for anderson models on locally finite graphs we prove spectral and dynamical localization for anderson models on locally finite graphs using the fractional moment method our theorems extend earlier results on localization for the anderson model on d we establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently large disorder

on the spectrum of two layer approach and multiplex pagerank abstract in this paper we present some results about the spectrum of the matrix associated with the computation of the multiplex pagerank defined by the authors in a previous paper these results can be considered as a natural extension of the known results about the spectrum of the google matrix in particular we show that the eigenvalues of the transition matrix associated with the multiplex network can be deduced from the eigenvalues of a block matrix containing the stochastic matrices defined for each layer we also show that as occurs in the classic pagerank the spectrum is not affected by the personalization vectors defined on each layer but depends on the parameter that controls the teleportation we also give some analytical relations between the eigenvalues and we include some small examples illustrating the main results

rotational invariance based on fourier analysis in polar and spherical coordinates in this paper polar and spherical fourier analysis are defined as the decomposition of a function in terms of eigenfunctions of the laplacian with the eigenfunctions being separable in the corresponding coordinates the proposed transforms provide effective decompositions of an image into basic patterns with simple radial and angular structures the theory is compactly presented with an emphasis on the analogy to the normal fourier transform the relation between the polar or spherical fourier transform and the normal fourier transform is explored as examples of applications rotation invariant descriptors based on polar and spherical fourier coefficients are tested on pattern classification problems

the universality classes in the parabolic anderson model we discuss the long time behaviour of the parabolic anderson model the cauchy problem for the heat equation with random potential on mathbb z d we consider general i i d potentials and show that exactly four qualitatively different types of intermittent behaviour can occur these four universality classes depend on the upper tail of the potential distribution 1 tails at that are thicker than the double exponential tails 2 double exponential tails at studied by gartner and molchanov 3 a new class called almost bounded potentials and 4 potentials bounded from above studied by biskup and konig the new class 3 which contains both unbounded and bounded potentials is studied in both the annealed and the quenched setting we show that intermittency occurs on unboundedly increasing islands whose diameter is slowly varying in time the characteristic variational formulas describing the optimal profiles of the potential and of the solution are solved explicitly by parabolas respectively gaussian densities our analysis of class 3 relies on two large deviation results for the local times of continuous time simple random walk one of these results is proved by brydges and the first two authors in bhk04 and is also used here to correct a proof in bk01

uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation for independent translation invariant irreducible percolation models it is proved that the infinite cluster when it exists must be unique the proof is based on the convexity or almost convexity and differentiability of the mean number of clusters per site which is the percolation analogue of the free energy the analysis applies to both site and bond models in arbitrary dimension including long range bond percolation in particular uniqueness is valid at the critical point of one dimensional 1 x y 2 models in spite of the discontinuity of the percolation density there corollaries of uniqueness and its proof are continuity of the connectivity functions and except possibly at the critical point of the percolation density related to differentiability of the free energy are inequalities which bound the specific heat critical exponent in terms of the mean cluster size exponent and the critical cluster size distribution exponent e g 1 2 1 1

a combined approach for evaluating papers authors and scientific journals an integrated model for ranking scientific publications together with authors and journals recently presented in bini del corso romani etna 2008 is closely analyzed the model which relies on certain adjacency matrices h k and f obtained from the relations of citation authorship and publication provides the ranking by means of the perron vector of a stochastic matrix obtained by combining h k and f some perturbation theorems concerning the perron vector previously introduced by the authors are extended to more general cases and a counterexample to a property previously addressed by the authors is presented the theoretical results confirm the consistency and effectiveness of our model some paradigmatic examples are reported together with some results obtained on a real set of data

brownian motion in a poissonian potential we study here ad dimensional brownian motion in a random potentialv obtained as the sum of translations of a given fixed non negative shape function at the points of a poisson cloud of constant intensityv we are interested in the larget behavior for typical cloud configurations of the brownian path in timet under the influence of the natural feynman kac weight associated tov in particular we show that the location at timet of the process tends to be concentrated near points of suitably low local eigenvalue of 1 2 v which lie almost at distancet from the origin near these points one can find in the cloud a big hole or clearing of size const logt 1 d with volume like a ball of radiusr 0 d v logt 1 d

a characterization of the anderson metal insulator transport transition we investigate the anderson metal insulator transition for random schrodinger operators we define the strong insulator region to be the part of the spectrum where the random operator exhibits strong dynamical localization in the hilbert schmidt norm we introduce a local transport exponent e and set the weak metallic transport region to be the part of the spectrum with nontrivial transport i e e 0 we prove that these insulator and metallic regions are complementary sets in the spectrum of the random operator and that the local transport exponent e provides a characterization of the metal insulator transport transition moreover we show that if there is such a transition then e has to be discontinuous at a transport mobility edge more precisely we show that if the transport is nontrivial then e 1 2d where d is the space dimension these results follow from a proof that slow transport of quantum waves in random media implies the starting hypothesis for the authors bootstrap multiscale analysis we also conclude that the strong insulator region coincides with the part of the spectrum where we can perform a bootstrap multiscale analysis proving that the multiscale analysis is valid all the way up to a transport mobility edge

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

branching random walk in random environment phase transitions for local and global growth rates let n be the infinite particle system on whose evolution is as follows at each unit of time each particle independently is replaced by a new generation the size of a new generation descending from a particle at sitex has distributionf x and each of its members independently jumps to sitex 1 with probability 1 h 2 h 0 1 the sequence f x is i i d with uniformly bounded second moment and is kept fixed during the evolution the initial configuration 0 is shift invariant and ergodic two quantities are considered

localization for a class of one dimensional quasi periodic schrodinger operators we prove for small and satisfying a certain diophantine condition the operator h varepsilon 2 delta frac 1 2 pi cos 2 pi j alpha theta j in mathbb z has pure point spectrum for almost all a similar result is established at low energy for h frac d 2 dx 2 k 2 cos 2 pi x cos 2 pi alpha x theta providedk is sufficiently large

geometric characterization of intermittency in the parabolic anderson model we consider the parabolic anderson problem tu u x u on r z d with localized initial condition u 0 x 0 x and random i i d potential under the assumption that the distribution of 0 has a double exponential or slightly heavier tail we prove the following geometric characterisation of intermittency with probability one as t 1 the overwhelming contribution to the total mass p x u t x comes from a slowly increasing number of islands which are located far from each other these islands are local regions of those high exceedances of the eld in a box of side length 2t log 2 t for which the local principal dirichlet eigenvalue of the random operator is close to the top of the spectrum in the box we also prove that the shape of in these regions is non random and that u t is close to the corresponding positive eigenfunction this is the geometric picture suggested by localization theory for the anderson hamiltonian

large deviations for brownian motion in a random scenery we prove large deviations principles in large time for the brownian occupation time in random scenery frac 1 t int 0 t xi b s ds the random field is constant on the elements of a partition of d into unit cubes these random constants say left lbrace xi j j in mathbb z d right rbrace consist of i i d bounded variables independent of the brownian motion bs s 0 this model is a time continuous version of kesten and spitzer s random walk in random scenery we prove large deviations principles in quenched and annealed settings

correlation structure of intermittency in the parabolic anderson model consider the cauchy problem u x t t u x t x d t 0 with initial condition u x 0 1 and with the anderson hamiltonian here is the discrete laplacian 0 is a diffusion constant and x x d is an i i d random field taking values in gartner and molchanov 1990 have shown that if the law of 0 is nondegenerate then the solution u is asymptotically intermittent in the present paper we study the structure of the intermittent peaks for the special case where the law of 0 is in the vicinity of the double exponential prob 0 s exp e s s here 0 is a parameter that can be thought of as measuring the degree of disorder in the field our main result is that for fixed x y d and t the correlation coefficient of u x t and u y t converges to w 2 l2 z d w x z w y z in this expression while w d is given by w v d with v the unique centered ground state i e the solution in l2 with minimal l 2 norm of the 1 dimensional nonlinear equation v 2 v log v 0 the uniqueness of the ground state is actually proved only for large but is conjectured to hold for any 0 empty it turns out that if the right tail of the law of 0 is thicker or thinner than the double exponential then the correlation coefficient of u x t and u y t converges to x y resp the constant function 1 thus the double exponential family is the critical class exhibiting a nondegenerate correlation structure

the fourier argand representation an optimal basis of steerable patterns computing the convolution between a 2d signal and a corresponding filter with variable orientations is a basic problem that arises in various tasks ranging from low level image processing e g ridge edge detection to high level computer vision e g pattern recognition through decades of research there still lacks an efficient method for solving this problem in this paper we investigate this problem from the perspective of approximation by considering the following problem what is the optimal basis for approximating all rotated versions of a given bivariate function surprisingly solely minimising the l 2 approximation error leads to a rotation covariant linear expansion which we name fourier argand representation this representation presents two major advantages 1 rotation covariance of the basis which implies a strong steerability rotating by an angle alpha corresponds to multiplying each basis function by a complex scalar e ik alpha 2 optimality of the fourier argand basis which ensures a few number of basis functions suffice to accurately approximate complicated patterns and highly direction selective filters we show the relation between the fourier argand representation and the radon transform leading to an efficient implementation of the decomposition for digital filters we also show how to retrieve accurate orientation of local structures patterns using a fast frequency estimation algorithm

parabolic problems for the anderson model the objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics in particular in hydrodynamics on a qualitative level intermittent random fields are distinguished by the appearance of sparsely distributed sharp peaks which give the main contribution to the formation of the statistical moments the paper deals with the cauchy problem t u t x hu t x u 0 x t0 x 0 t x d for the anderson hamiltonianh x x d where is a generally unbounded spatially homogeneous random potential this first part is devoted to some basic problems using percolation arguments a complete answer to the question of existence and uniqueness for the cauchy problem in the class of all nonnegative solutions is given in the case of i i d random variables necessary and sufficient conditions for intermittency of the fieldsu t ast are found in spectral terms ofh rough asymptotic formulas for the statistical moments and the almost sure behavior ofu t x ast are also derived

distances in the highly supercritical percolation cluster on the supercritical percolation cluster with parameter p the distances between two distant points of the axis are asymptotically increased by a factor 1 1 p2 o 1 p with respect to the usual distance the proof is based on an apparently new connection with the tasep totally asymmetric simple exclusion process

absence of diffusion in the anderson tight binding model for large disorder or low energy we prove that the green s function of the anderson tight binding hamiltonian decays exponentially fast at long distances on v with probability 1 we must assume that either the disorder is large or the energy is sufficiently low our proof is based on perturbation theory about an infinite sequence of block hamiltonians and is related to kam methods

transition from the annealed to the quenched asymptotics for a random walk on random obstacles in this work we study a natural transition mechanism describing the passage from a quenched almost sure regime to an annealed in average one for a symmetric simple random walk on random obstacles on sites having an identical and independent law the transition mechanism we study was first proposed in the context of sums of identical independent random exponents by ben arous bogachev and molchanov in probab theory related fields 132 2005 579 612 let p x t be the survival probability at time t of the random walk starting from site x and let l t be some increasing function of time we show that the empirical average of p x t over a box of side l t has different asymptotic behaviors depending on l t there are constants 0 1 a law of large numbers is satisfied and the empirical survival probability decreases like the annealed one if l t e td d 2 with y 2 also a central limit theorem is satisfied if l t t the averaged survival probability decreases like the quenched survival probability if t l t and log l t t d d 2 we obtain an intermediate regime furthermore when the dimension d 1 it is possible to describe the fluctuations of the averaged survival probability when l t e td d 2 with y 2 it is shown that they are infinitely divisible laws with a levy spectral function which explodes when x 0 as stable laws of characteristic exponent a 2 these results show that the quenched and annealed survival probabilities correspond to a low and high temperature behavior of a mean field type phase transition mechanism

brownian asymptotics in a poissonian environment we consider a brownian motion moving in a random potential obtained by translating a given fixed non negative shape function at the points of a poisson cloud we derive the almost sure principal long time behavior of the expectation of the natural feynman kac functional which is insensitive to the detail of the shape function we also study the situation of hard obstacles where brownian motion is killed once it comes within distancea of a point of the cloud the nature of the results then changes between the case whena is small or large in connection with the presence or absence of an infinite component in the complement of the obstacles

on the chemical distance for supercritical bernoulli percolation we prove large deviation estimates at the correct order for the graph distance of two sites lying in the same cluster of an independent percolation process we improve earlier results of gartner and molchanov and grimmett and marstrand and answer affirmatively a conjecture of kozlov

constructive proof of localization in the anderson tight binding model we prove that for large disorder or near the band tails the spectrum of the anderson tight binding hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues the corresponding eigenfunctions are exponentially well localized these results hold in arbitrary dimension and with probability one in one dimension we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder our techniques extend to other physical systems which exhibit localization phenomena such as infinite systems of coupled harmonic oscillators or random schrodinger operators in the continuum

the schrodinger equation with a quasi periodic potential we consider the schrodinger equation dx2 v e cosx cos cix 0 v eqi where e is small and a satisfies the diophantine inequality lp qcl c q2 forp qez q 0 we look for solutions of the form ikx ikx in x im ax 0 m x e q x e 2m ne inxne e if we try to solve for v v mn we are led to the schrodinger equation on the lattice z2 h k q ba v k q en where a is the discrete laplacian without diagonal terms and v k is some 2 potential on z we have two main results 4 for e sufficiently small h k has pure point spectrum for almost every k 2 for e sufficiently small the operator d dx 2 e cosx cos ax has no point spectrum to prove our results we must get decay estimates on the green s function e h 1 the decay of the eigenfunction follows from this in general we must keep track of small divisors which can make the green s function large this is accomplished by a kam kolmogorov arnold moser type of multiscale perturbation analysis

gibbs measures on mutually interacting brownian paths under singularities we are interested in the analysis of gibbs measures defined on two independent brownian paths in d interacting through a mutual self attraction this is expressed by the hamiltonian 2dv x y dx dy with two probability measures and representing the occupation measures of two independent brownian motions we will be interested in a class of potentials v that are singular e g dirac or coulomb type interactions in 3 or the correlation function of the parabolic anderson problem with white noise potential the mutual interaction of the brownian paths inspires a compactification of the quotient space of orbits of product measures which is structurally different from the self interacting case introduced in 27 owing to the lack of shift invariant structure in the mutual interaction we prove a strong large deviation principle for the product measures of two brownian occupation measures in such a compactification and derive asymptotic path behavior under gibbs measures on wiener paths arising from mutually attracting singular interactions for the spatially smoothened parabolic anderson model with white noise potential our analysis allows a direct computation of the annealed lyapunov exponents and a strict ordering of them implies the intermittency effect present in the smoothened model 2017 wiley periodicals inc

robust rotation angle estimator the conventional method of estimating the rotation angle of a pattern using the principal axes is not suitable for circular symmetric patterns since their eigenvalues are similar in both directions in the paper a robust method of estimating a rotation angle using the phase information of zernike moments is presented the experimental results show that the proposed method estimates the rotation angle of the circular symmetric patterns more accurately than the principal axes method even in the presence of noise

on the moments and the interface of the symbiotic branching model in this paper we introduce a critical curve separating the asymptotic behavior of the moments of the symbiotic branching model introduced by etheridge and fleischmann stochastic process app 114 2004 127 160 into two regimes using arguments based on two different dualities and a classical result of spitzer trans amer math soc 87 1958 187 197 on the exit time of a planar brownian motion from a wedge we prove that the parameter governing the model provides regimes of bounded and exponentially growing moments separated by subexponential growth the moments turn out to be closely linked to the limiting distribution as time tends to infinity the limiting distribution can be derived by a self duality argument extending a result of dawson and perkins ann probab 26 1998 1088 1138 for the mutually catalytic branching model as an application we show how a bound on the 35th moment improves the result of etheridge and fleischmann stochastic process appl 114 2004 127 160 on the speed of the propagation of the the interface of the symbiotic branching model

sharp estimates for the personalized multiplex pagerank abstract pagerank can be understood as the stationary distribution of a markov chain that occurs in a two layer network with the same set of nodes in both layers the physical layer and the teleportation layer in this paper we present some bounds for the extension of this two layer approach to multiplex networks establishing sharp estimates for this multiplex pagerank and locating the possible values of the personalized pagerank for each node of a network several examples are shown to compare the values obtained for both algorithms the classic and the two layer pagerank

brownian survival and lifshitz tail in perturbed lattice disorder abstract we consider the annealed asymptotics for the survival probability of brownian motion among randomly distributed traps the configuration of the traps is given by independent displacements of the lattice points we determine the long time asymptotics of the logarithm of the survival probability up to a multiplicative constant as applications we show the lifshitz tail effect of the density of states of the associated random schrodinger operator and derive a quantitative estimate for the strength of intermittency in the parabolic anderson problem

parabolic problems for the anderson model i intermittency and related topics the objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics in particular in hydrodynamics on a qualitative level intermittent random fields are distinguished by the appearance of sparsely distributed sharp peaks which give the main contribution to the formation of the statistical moments the paper deals with the cauchy problem t u t x hu t x u 0 x t 0 x 0 t x d for the anderson hamiltonianh x x d where is a generally unbounded spatially homogeneous random potential this first part is devoted to some basic problems using percolation arguments a complete answer to the question of existence and uniqueness for the cauchy problem in the class of all nonnegative solutions is given in the case of i i d random variables necessary and sufficient conditions for intermittency of the fieldsu t ast are found in spectral terms ofh rough asymptotic formulas for the statistical moments and the almost sure behavior ofu t x ast are also derived

the rough membership functions on four types of covering based rough sets and their applications abstract pawlak s rough membership functions not only give numerical characterizations of pawlak s rough set approximations but also establishes the relationships between pawlak s rough sets and fuzzy sets or probabilistic rough sets however it is noteworthy that pawlak s rough membership functions have limitations when handling incomplete data that exist widely in the real world as will be shown in this paper one way to overcome this is to construct rough membership functions for covering based rough sets in this paper we first use an example in evidence based medicine to illustrate how to use pawlak s rough membership function on numerically characterizing decisions under the circumstances where data are complete then we construct covering based rough membership functions for four types of covering based rough sets which were examined by zhu and wang in ieee transactions on knowledge and data engineering 19 8 2007 1131 1144 and information sciences 201 2012 80 92 and use them to characterize these covering based rough sets numerically finally we present theoretical backgrounds for these covering based rough membership functions and illustrate how to apply them on numerically characterizing decisions under the circumstances where data are incomplete

2d partial unwinding a novel non linear phase decomposition of images this paper aims at proposing a novel 2d non linear phase decomposition of images which performs the image processing tasks better than the traditional fourier transformation linear phase decomposition but further it has additional mathematical properties allowing more effective image analysis including adaptive decomposition components and positive instantaneous phase derivatives 1d unwinding blaschke decomposition has recently been proposed and studied through factorization it expresses arbitrary 1d signal into an infinite linear combination of blaschke products it offers fast converging positive frequency decomposition in the form of rational approximation however in the multi dimensional cases the usual factorization mechanism does not work as a consequence there is no genuine unwinding decomposition for multi dimensions in this paper a 2d partial unwinding decomposition based on algebraic transforms reducing multi dimensions to the 1d case is proposed and analyzed the result shows that the fast convergence offers efficient image reconstruction the tensor type decomposing terms are mutually orthogonal giving rise to 2d positive frequency decomposition the comparison results show that the proposed method outperforms the standard greedy algorithm and the most commonly used methods in the fourier category an application in watermarking is presented to demonstrate its potential in applications

quenched asymptotics for brownian motion of renormalized poisson potential and for the related parabolic anderson models let bs be a d dimensional brownian motion and dx be an independent poisson field on rd the almost sure asymptotics for the logarithmic moment generating function loge0exp t0v bs ds t are investigated in connection with the renormalized poisson potential of the form v x rd1 y x p dy dy x rd the investigation is motivated by some practical problems arising from the models of brownian motion in random media and from the parabolic anderson models

rotation invariant hog descriptors using fourier analysis in polar and spherical coordinates the histogram of oriented gradients hog is widely used for image description and proves to be very effective in many vision problems rotation invariant analysis is necessary or preferred popular solutions are mainly based on pose normalization or learning neglecting some intrinsic properties of rotations this paper presents a method to build rotation invariant hog descriptors using fourier analysis in polar spherical coordinates which are closely related to the irreducible representation of the 2d 3d rotation groups this is achieved by considering a gradient histogram as a continuous angular signal which can be well represented by the fourier basis 2d or spherical harmonics 3d as rotation invariance is established in an analytical way we can avoid discretization artifacts and create a continuous mapping from the image to the feature space in the experiments we first show that our method outperforms the state of the art in a public dataset for a car detection task in aerial images we further use the princeton shape benchmark and the shrec 2009 generic shape benchmark to demonstrate the high performance of our method for similarity measures of 3d shapes finally we show an application on microscopic volumetric data

strong clumping of super brownian motion in a stable catalytic medium a typical feature of the long time behavior of continuous super brownian motion in a stable catalytic medium is the development of large mass clumps or clusters at spatially rare sites we describe this phenomenon by means of a functional limit theorem under renormalization the limiting process is a poisson point field of mass clumps with no spatial motion component and with infinite variance the mass of each cluster evolves independently according to a non markovian continuous process trapped at mass zero which we describe explicitly by means of a brownian snake construction in a random medium we also determine the survival probability and asymptotic size of the clumps

anomalous thermostat and intraband discrete breathers abstract we investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice including quenched disorder the coupling between both parts is bilinear elimination of the harmonic degrees of freedom leads to a nonlinear langevin equation with memory kernels t and noise term t for the anharmonic coordinates q t q t for zero temperature i e for t 0 we prove that the support of the fourier transform of t and of the time averaged velocity velocity correlation functions k t of the anharmonic system cannot overlap as a consequence the asymptotic solutions can be constant periodic quasiperiodic or almost periodic and possibly weakly chaotic for a sinusoidal trajectory q t with frequency we find that the energy e t transferred to the harmonic system up to time t is proportional to t if equals one of the phonon frequencies it is 2 we prove that there is a zero measure set l such that for in its full measure complement r l it is 0 i e there is no energy dissipation under certain conditions l contains a subset l such that for l the dissipation rate is nonzero and may be subdissipative 0 1 or superdissipative 1 2 compared to ordinary dissipation 1 consequently the harmonic bath does act as an anomalous thermostat in variance with the common belief that elimination of a macroscopically large number of degrees of freedom always generates dissipation forcing convergence to equilibrium intraband discrete breathers are such solutions which do not relax we prove for arbitrary anharmonicity and small but finite coupling that intraband discrete breathers with frequency exist for all in a cantor set c k of finite lebesgue measure this is achieved by estimating the contribution of small denominators appearing for g t related to t for c k the small denominators do not lead to divergencies such that g t is a smooth and bounded function in t

brownian confinement and pinning in a poissonian potential ii we study the behavior of ad dimensional brownian motion in a soft repulsive poissonian potential over long time intervals 0 t we introduce certaint and configuration dependent scales which grow almost linearly witht for typical configurations with probability tending to 1 ast goes to the size of displacements of the process is bounded above by these scales confinement effect the proof involves calculations beyond leading order to this end we use a coarse grained picture of the environment method of enlargement of obstacles and of the path a backbone of excursions between clearings and forest parts in the environment these coarse grained pictures are also used in the sequel 11 to the present article when proving the pinning effect

discrete spherical harmonic oscillator transforms on the cartesian grids using transformation coefficients the analog harmonic oscillators are well studied in quantum physics including their energy states wavefunctions orthogonal properties and eigenfunctions of the fourier transform in addition the continuous solutions in different dimension and coordinate systems are known some discrete equivalents of the 1d wavefunctions were also studied however in the 3d spherical coordinate system the discrete equivalents of the 3d wavefunctions are not established in this paper we focus on the spherical harmonic oscillator wavefunctions shows the spherical harmonic oscillator transforms shots and their discrete implementation the shows can be synthesized by linear combinations of the hermite gaussian functions with proper transformation coefficients we find that computing the coefficients can be speeded up using the fast fourier transforms or some recursive relations these coefficients relate the hermite transforms with the shots some applications of the discrete shows and the discrete shots are introduced first the shows are exactly the eigenfunctions of the 3d dft also the shots can be used to derive the spherical harmonic oscillator descriptor shod which is a rotational invariant descriptor we find that the shod is not only compatible with the existing rotational descriptors for the spherically sampled data but also outperforms the existing rotational descriptors for 3d cartesian sampled bandlimited input data besides the shots can be used to decompose 3d signals into spherical components hence 3d signal reconstruction is done using partially chosen spherical component and 3d data compression for mri data is demonstrated using shots for medical applications

extremal theory for spectrum of random discrete schrodinger operator i asymptotic expansion formulas we consider the spectral problem for the random schrodinger operator on the multidimensional lattice torus increasing to the whole of lattice with an i i d potential anderson hamiltonian we obtain the explicit almost sure asymptotic expansion formulas for the extreme eigenvalues and eigenfunctions in the intermediate rank case provided the upper distributional tails of potential decay at infinity slower than the double exponential function for the fractional exponential tails including weibull s and gaussian distributions extremal type limit theorems for eigenvalues are proved and the strong influence of parameters of the model on a specification of normalizing constants is described in the proof we use the finite rank perturbation arguments based on the cluster expansion for resolvents

localization in general one dimensional random systems we discuss two ways of extending the recent ideas of localization from discrete schrodinger operators jacobi matrices to the continuum case one case allows us to prove localization in the goldshade molchanov pastur model for a larger class of functions than previously the other method studies the model v wherev is a random constant in each hyper cube we extend wegner s result on the lipschitz nature of the ids to this model

a rigorous replica trick approach to anderson localization in one dimension leth v onl2 wherev x x are i i d r v s and letg l x y e i x hl e i 1 y whereh l denotes the operatorh restricted to l l 1 l with dirichlet boundary conditions we use a supersymmetric replica trick to prove that e g l 0 x e i eta 2 leqq k eta 2 exp m log eta sigma x for somem 0 0 k uniformly inl ande this estimate together with the usual necessary estimate on the density of states implies zero conductivity and gives exponential localization by the frohlich martinelli scoppola and spencer method

a multi class approach for ranking graph nodes after the phenomenal success of the pagerank algorithm many researchers have extended the pagerank approach to ranking graphs with richer structures in addition to the simple linkage structure indeed in some scenarios we have to deal with networks modeling multi parameters data where each node has additional features and there are important relationships between such features this paper addresses the need of a systematic approach to deal with multi parameter data we propose models and ranking algorithms that can be applied to a large variety of networks bibliographic data patent data twitter and social data healthcare data we focus on several aspects not previously addressed in the literature 1 we propose different models for ranking multi parameters data and a class of numerical algorithms for efficiently computing the ranking score of such models 2 we analyze stability and convergence of the proposed numerical schemes and we derive a fast and stable ranking algorithm 3 we analyze the robustness of our models when data are incomplete the comparison of the rank on the incomplete data with the rank on the full structure shows that our models compute consistent rankings whose correlation is up to 60 when just 10 of the links of the attributes are maintained

comparison of krylov subspace methods on the pagerank problem pagerank algorithm plays a very important role in search engine technology and consists in the computation of the eigenvector corresponding to the eigenvalue one of a matrix whose size is now in the billions the problem incorporates a parameter a that determines the difficulty of the problem in this paper the effectiveness of stationary and nonstationary methods are compared on some portion of real web matrices for different choices of a we see that stationary methods are very reliable and more competitive when the problem is well conditioned that is for small values of a however for large values of the parameter a the problem becomes more difficult and methods such as preconditioned bicgstab or restarted preconditioned gmres become competitive with stationary methods in terms of mflops count as well as in number of iterations necessary to reach convergence

moment asymptotics for the parabolic anderson problem with a perturbed lattice potential abstract the parabolic anderson problem with a random potential obtained by attaching a long tailed potential around a randomly perturbed lattice is studied the moment asymptotics of the total mass of the solution is derived the results show that the total mass of the solution concentrates on a small set in the space of configuration

mild solution to parabolic anderson model in gaussian and poisson potential we consider the parabolic anderson model in a special random homogeneous potential that is generated by the gaussian and poisson random medium together in our model the coefficient v x is not holder continuous with positive probability and thus the model is unlikely to have a path wise solution we construct a mild solution for the parabolic anderson model with random potential of the form v x rdk y x dy w dy where and w denote the independent standard poisson point process and centred gaussian field respectively the case where the potential switches in sign and the poisson field is absent is handled as well

on chemical distances and shape theorems in percolation models with long range correlations in this paper we provide general conditions on a one parameter family of random infinite subsets of z d to contain a unique infinite connected component for which the chemical distances are comparable to the euclidean distance in addition we show that these conditions also imply a shape theorem for the corresponding infinite connected component by verifying these conditions for specific models we obtain novel results about the structure of the infinite connected component of the vacant set of random interlacements and the level sets of the gaussian free field as a byproduct we obtain alternative proofs to the corresponding results for random interlacements in the work of cern and popov on the internal distance in the interlacement set electron j probab 17 29 1 25 2012 and while our main interest is in percolation models with long range correlations we also recover results in the spirit of the work of antal and pisztora on the chemical distance for supercritical bernoulli percolation ann probab 24 2 1036 1048 1996 for bernoulli percolation finally as a corollary we derive new results about the chemical diameter of the largest connected component in the complement of the trace of the random walk on the torus

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

on absence of diffusion near the bottom of the spectrum for a random schrodinger operator on l 2 bf r nu we consider a random schrodinger operator onl2 v of the form h omega delta v omega v omega x sigma chi c i x q i omega ci being a covering of v with unit cubes around the sites of v and qi i i d random variables with values in 0 1 we assume that theqi s are continuously distributed with bounded densityf q and that 0 p q0 1 2 1 then we show that an ergodic mean of the quantity dx x 2 exp ith x 2 t 1 vanishes provided ge h where is well localized around the origin andge is a positivec function with support in 0 e e e f our estimate ofe f is such that the set x v v x e f may contain with probability one an infinite cluster of cubes ci which are nearest neighbours the proof is based on the technique introduced by frohlich and spencer for the analysis of the anderson model

upper bound on the energy gap in terms of the localization in tight binding systems we present an upper bound on the energy gap above the ground energy in terms of the variance of the particle position in one particle tight binding systems our inequality gives a complementary relationship between the energy gap and the localization of the particle that is the energy gap narrows as the ground state spreads spatially while the energy gap can broaden as the ground state becomes localized we first consider the ground state in one dimensional tight binding systems and relate the energy gap to the variance of the particle position in the ground state we then extend the result to higher dimensional systems we compare our upper bound with the exact energy gap as calculated numerically in one and two dimensions this comparison confirms that our upper bound places a tight restriction on the energy gap

a two cities theorem for the parabolic anderson model the parabolic anderson problem is the cauchy problem for the heat equation partial derivative t u t z delta u t z xi z u t z on 0 infinity x z d with random potential xi z z is an element of z d we consider independent and identically distributed potentials such that the distribution function of z converges polynomially at infinity if u is initially localized in the origin that is if u 0 z 1 0 z we show that as time goes to infinity the solution is completely localized in two points almost surely and in one point with high probability we also identify the asymptotic behavior of the concentration sites in terms of a weak limit theorem

frequency radial duality based photoacoustic image reconstruction photoacoustic image reconstruction algorithms are usually slow due to the large sizes of data that are processed this paper proposes a method for exact photoacoustic reconstruction for the spherical geometry in the limiting case of a continuous aperture and infinite measurement bandwidth that is faster than existing methods namely 1 backprojection method and 2 the norton linzer method s j norton and m linzer ultrasonic reflectivity imaging in three dimensions exact inverse scattering solution for plane cylindrical and spherical apertures biomedical engineering ieee trans bme 28 202 220 1981 the initial pressure distribution is expanded using a spherical fourier bessel series the proposed method estimates the fourier bessel coefficients and subsequently recovers the pressure distribution a concept of frequency radial duality is introduced that separates the information from the different radial basis functions by using frequencies corresponding to the bessel zeros this approach pro

simplicity of eigenvalues in the anderson model we give a transparent and intuitive proof that all eigenvalues of the anderson model in the region of localization are simple

remark on the absence of absolutely continuous spectrum for d dimensional schrodinger operators with random potential for large disorder or low energy we show that there is no absolutely continuous part in the spectrum of the anderson tight binding model for large disorder or low energy the proof is based on the exponential decay of the green s function proved by frohlich and spencer the extension of this result to the continuous case is also discussed

errata and comments on generic orthogonal moments jacobi fourier moments for invariant image description abstract ping et al z ping h ren j zou y sheng and w bo generic orthogonal moments jacobi fourier moments for invariant image description pattern recognition 40 4 2007 1245 1254 made a landmark contribution to the theory of two dimensional orthogonal moments confined to the unit disk by unifying the radial kernels of existing polynomial based circular orthogonal moments under the roof of shifted jacobi polynomials however the work contains some errata that result mainly from the confusion between the two slightly different definitions of shifted jacobi polynomials in the literature taking into account the great importance and the high impact of the work in the pattern recognition community this paper points out the confusing points corrects the errors and gives some other relevant comments the corrections developed in this paper are illustrated by some experimental evidence

exact asymptotics in a mean field model with random potential for a mean field operator with a random potential asymptotic properties of the eigenvalues and eigenfunctions are studied and applied to investigate the longerm behavior of the solutions of a corresponding large system of differential equations the total mass of the system is approximately concentrated in the record point of the random potential complete localization a more detailed inspection of the peaks shows that there is a phase transition only in the case of a moderate increase of time relatively to the growth of the space size the model behaves similarly to the system without diffusion but also in the non moderate case the asymptotic height of peaks can exactly be described

fast generic polar harmonic transforms generic polar harmonic transforms have recently been proposed to extract rotation invariant features from images and their usefulness has been demonstrated in a number of pattern recognition problems however direct computation of these transforms from their definition is inefficient and is usually slower than some efficient computation strategies that have been proposed for other methods this paper presents a number of novel computation strategies to compute these transforms rapidly the proposed methods are based on the inherent recurrence relations among complex exponential and trigonometric functions used in the definition of the radial and angular kernels of these transforms the employment of these relations leads to recursive and addition chain based strategies for fast computation of harmonic function based kernels experimental results show that the proposed method is about 10 times faster than direct computation and 5 times faster than fast computation of zernike moments using the q recursive strategy thus among all existing rotation invariant feature extraction methods polar harmonic transforms are the fastest

analyticity of the density of states and replica method for random schrodinger operators on a lattice we analyze the density of states and some aspects of the replica method for anderson s tight binding model on a lattice of arbitrary dimension with diagonal disorder we give heuristic arguments for the conjectures that the classical value of the exponent of the localization length is 1 2 and that the upper critical dimension d c loc is bounded by 4 d c loc 6

stationary parabolic anderson model and intermittency this paper is devoted to the analysis of the large time behavior of the solutions of the anderson parabolic problem frac partial u partial t kappa delta u xi x u when the potential x is a homogeneous ergodic random field on d our goal is to prove the asymptotic spatial intermittency of the solution and for this reason we analyze the large time properties of all the moments of the positive solutions this provides an extension to the continuous space d of the work done originally by gartner and molchanov in the case of the lattice d in the process of our moment analysis we show that it is possible to exhibit new asymptotic regimes by considering a special class of generalized gaussian fields interpolating continuously between the exponent 2 which is found in the case of bona fide continuous gaussian fields x and the exponent 3 2 appearing in the case of a one dimensional white noise finally we also determine the precise almost sure large time asymptotics of the positive solutions

intermittency type estimates for some nondegenerate spde s in this paper we prove some intermittency type estimates for the stochastic partial differential equation du mathscr l u dt mathscr m lu circ dw l t where mathscr l is a strongly elliptic second order partial differential operator and the mathscr m l s are first order partial differential operators here the w l s are standard wiener processes and circ denotes stratonovich integration we assume for simplicity that u 0 cdot equiv 1 our interest here is the behavior of mathbb e lbrack u t x p rbrack for large time and large p more specifically our interest is the growth of p 2t 1 log mathbb e lbrack u t x p rbrack as t then p become large