the spectrum of a magnetic schrodinger operator with randomly located delta impurities we consider a single band approximation to the random schrodinger operator in an external magnetic field the spectrum of such an operator has been characterized in the case where delta impurities are located on the sites of a lattice in this paper we generalize these results by letting the delta impurities have random positions as well as strengths they are located in squares of a lattice with a general bounded distribution we characterize the entire spectrum of this operator when the magnetic field is sufficiently high we show that the whole spectrum is pure point the energy coinciding with the first landau level is infinitely degenerate and that the eigenfunctions corresponding to other landau band energies are exponentially localized

an optimal wegner estimate and its application to the global continuity of the integrated density of states for random schrodinger operators we prove that the integrated density of states ids of random schrodinger operators with anderson type potentials on l 2 r d for d geq1 is locally holder continuous at all energies with the same holder exponent 0 alpha leq1 as the conditional probability measure for the single site random variable as a special case we prove that if the probability distribution is absolutely continuous with respect to lebesgue measure with a bounded density then the ids is lipschitz continuous at all energies the single site potential u in l 0 infty r d must be nonnegative and compactly supported the unperturbed hamiltonian must be periodic and satisfy a unique continuation principle we also prove analogous continuity results for the ids of random anderson type perturbations of the landau hamiltonian in two dimensions all of these results follow from a new wegner estimate for local random hamiltonians with rather general probability measures

an adaptable multilayer fractional fourier transform approach for image registration a novel adaptable accurate way for calculating polar fft and log polar fft is developed in this paper named multilayer fractional fourier transform mlfft mlfft is a necessary addition to the pseudo polar fft for the following reasons it has lower interpolation errors in both polar and log polar fourier transforms it reaches better accuracy with the nearly same computing complexity as the pseudo polar fft it provides a mechanism to increase the accuracy by increasing the user defined computing level this paper demonstrates both mlfft itself and its advantages theoretically and experimentally by emphasizing applications of mlfft in image registration with rotation and scaling our experiments suggest two major advantages of mlfft 1 scaling up to 5 and arbitrary rotation angles or scales up to 10 without rotation can be recovered by mlfft while currently the result recovered by the state of the art algorithms is the maximum scaling of 4 2 no iteration is needed to obtain large rotation and scaling values of images by mlfft hence it is more efficient than the pseudopolar based fft methods for image registration

new characterizations of the region of complete localization for random schrodinger operators we study the region of complete localization in a class of random operators which includes random schrodinger operators with anderson type potentials and classical wave operators in random media as well as the anderson tight binding model we establish new characterizations or criteria for this region of complete localization given either by the decay of eigenfunction correlations or by the decay of fermi projections these are necessary and sufficient conditions for the random operator to exhibit complete localization in this energy region using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity

the absolute continuity of the integrated density of states for magnetic schrodinger operators with certain unbounded random potentials the object of the present study is the integrated density of states of a quantum particle in multi dimensional euclidean space which is characterized by a schrodinger operator with magnetic field and a random potential which may be unbounded from above and below in case that the magnetic field is constant and the random potential is ergodic and admits a so called one parameter decomposition we prove the absolute continuity of the integrated density of states and provide explicit upper bounds on its derivative the density of states this local lipschitz continuity of the integrated density of states is derived by establishing a wegner estimate for finite volume schrodinger operators which holds for rather general magnetic fields and different boundary conditions examples of random potentials to which the results apply are certain alloy type and gaussian random potentials besides we show a diamagnetic inequality for schrodinger operators with neumann boundary conditions

microlocalization percolation and anderson localization for the magnetic schrodinger operator with a random potential abstract we study the spectral properties of the magnetic schrodinger operator with a random potential using results from microlocal analysis and percolation we show that away from the landau levels the spectrum is almost surely pure point with at least exponentially decaying eigenfunctions moreover it is shown that the rate of decay is proportional to b

topology optimization of fluid structure interaction problems in poroelasticity abstract this paper presents a method for applying topology optimization to fluid structure interaction problems in saturated poroelastic media the method relies on a multiple scale method applied to periodic media the resulting model couples the stokes flow in the pores of the structure with the deformation of the elastic skeleton through a macroscopic darcy type flow law the method allows to impose pressure loads for static problems through a one way coupling while transient problems are fully coupled modeling the interaction between fluid and solid the material distribution is determined by topology optimization in order to optimize the performance of a shock absorber and test the pressure loading capabilities and optimization of an internally pressurized lid

non monotonic random schrodinger operators the anderson model abstract we prove exponential localization at all energies for one dimensional continuous anderson type models with single site potentials of changing sign a periodic background potential is allowed the main problem arises from non monotonicity i e the operator does not depend monotonically in the form sense on the random parameters we show that the method of two parameter spectral averaging recently devised by buschmann and stolz to prove localization for poisson and random displacement models can be modified to work for the type of anderson model considered here

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

a new proof of localization in the anderson tight binding model we give a new proof of exponential localization in the anderson tight binding model which uses many ideas of the frohlich martinelli scoppola and spencer proof but is technically simpler particularly the probabilistic estimates

extended edge states in finite hall systems we study edge states of a random schrodinger operator for an electron submitted to a magnetic field in a finite macroscopic two dimensional system of linear dimensions equal to l the y direction is l periodic and in the x direction the electron is confined by two smoothly increasing parallel boundary potentials we prove that with large probability for an energy range in the first spectral gap of the bulk hamiltonian the spectrum of the full hamiltonian consists only on two sets of eigenenergies whose eigenfuntions have average velocities which are strictly positive negative uniformly with respect to the size of the system our result gives a well defined meaning to the notion of edge states for a finite cylinder with two boundaries and extends previous studies on systems with only one boundary

collinear segment detection using ht neighborhoods in this paper geometrical analysis is used to extract novel straight line segment features from the wings around the peaks of the hough transform ht based on these features a practical segment detection method is proposed which has the ability to determine complete straight line segment parameters including the location of the center length slope and the euclidean distance to the origin the proposed method does not rely on edge point verification in the image space i e the complete set of segment features are determined only using the information embodied in the ht data the proposed method can distinguish between highly collinear straight line segments segment detection is robust to disturbing edge points especially ones collinear with the object a predefined collinear segment resolution that provides a theoretical criterion to determine straight line contiguity is derived image processing and analysis experiments show consistent robust performance

landau hamiltonians with random potentials localization and the density of states we prove the existence of localized states at the edges of the bands for the two dimensional landau hamiltonian with a random potential of arbitrary disorder provided that the magnetic field is sufficiently large the corresponding eigenfunctions decay exponentially with the magnetic field and distance we also prove that the integrated density of states is lipschitz continuous away from the landau energies the proof relies on a wegner estimate for the finite area magnetic hamiltonians with random potentials and exponential decay estimates for the finitearea green s functions the proof of the decay estimates for the green s functions uses fundamental results from two dimensional bond percolation theory

dequantizing image orientation we address the problem of computing a local orientation map in a digital image we show that standard image gray level quantization causes a strong bias in the repartition of orientations hindering any accurate geometric analysis of the image in continuation a simple dequantization algorithm is proposed which maintains all of the image information and transforms the quantization noise in a nearby gaussian white noise we actually prove that only gaussian noise can maintain isotropy of orientations mathematical arguments are used to show that this results in the restoration of a high quality image isotropy in contrast with other classical methods it turns out that this property can be obtained without smoothing the image or increasing the signal to noise ratio snr as an application it is shown in the experimental section that thanks to this dequantization of orientations such geometric algorithms as the detection of nonlocal alignments can be performed efficiently we also point out similar improvements of orientation quality when our dequantization method is applied to aliased images

extracting straight lines this paper presents a new approach to the extraction of straight lines in intensity images pixels are grouped into line support regions of similar gradient orientation and then the structure of the associated intensity surface is used to determine the location and properties of the edge the resulting regions and extracted edge parameters form a low level representation of the intensity variations in the image that can be used for a variety of purposes the algorithm appears to be more effective than previous techniques for two key reasons 1 the gradient orientation rather than gradient magnitude is used as the initial organizing criterion prior to the extraction of straight lines and 2 the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements

dynamical delocalization in random landau hamiltonians we prove the existence of dynamical delocalization for random landau hamiltonians near each landau level since typically there is dynamical localization at the edges of each disordered broadened landau band this implies the existence of at least one dynamical mobility edge at each landau band namely a boundary point between the localization and delocalization regimes which we prove to converge to the corresponding landau level as either the magnetic field goes to infinity or the disorder goes to zero in this article we prove the existence of dynamical delocalization for random landau hamiltonians near each landau level more precisely we prove that for these two dimensional hamiltonians there exists at least one energy e near each landau level such that e 1 where e the local transport exponent introduced in gk5 is a measure of the rate of transport in wave packets with spectral support near e since typically there is dynamical localization at the edges of each disordered broadened landau band this implies the existence of at least one dynamical mobility edge at each landau band namely a boundary point between the localization and delocalization regimes which we prove to converge to the corresponding landau level as either the magnetic field goes to infinity or the disorder goes to zero random landau hamiltonians are the subject of intensive study due to their links with the integer quantum hall e ect kli for which von klitzing received the 1985 nobel prize in physics they describe an electron moving in a very thin flat conductor with impurities under the influence of a constant magnetic field perpendicular to the plane of the conductor and play an important role in the understanding of the quantum hall e ect l aoa t h nt ku be avss bees laughlin s argument l as pointed out by halperin h uses the assumption that under weak disorder and strong magnetic field the energy spectrum consists of bands of extended states separated

asymptotic expansion for the density of states of the magnetic schrodinger operator with a random potential we study the asymptotics for the density of states of the magnetic schrodinger operator with a random potential by using the methods of effective hamiltonian complex dilation and complex translation we obtain in the large magnetic field limit the asymptotic expansion for the density of states measure considered as a distribution

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

advanced hough transform using a multilayer fractional fourier method the hough transform ht is a commonly used technique for the identification of straight lines in an image the hough transform can be equivalently computed using the radon transform rt by performing line detection in the frequency domain through use of central slice theorem in this research an advanced radon transform is developed using a multilayer fractional fourier transform a cartesian to polar mapping and 1 d inverse fourier transforms followed by peak detection in the sinogram the multilayer fractional fourier transform achieves a more accurate sampling in the frequency domain and requires no zero padding at the stage of cartesian to polar coordinate mapping our experiments were conducted on mix shape images noisy images mixed thickness lines and a large data set consisting of 751 000 handwritten chinese characters the experimental results have shown that our proposed method outperforms all known representative line detection methods based on the standard hough transform or the fourier transform

a fast hough transform for segment detection the authors describe a new algorithm for the fast hough transform fht that satisfactorily solves the problems other fast algorithms propose in the literature erroneous solutions point redundance scaling and detection of straight lines of different sizes and needs less storage space by using the information generated by the algorithm for the detection of straight lines they manage to detect the segments of the image without appreciable computational overhead they also discuss the performance and the parallelization of the algorithm and show its efficiency with some examples

the quantum hall effect for electrons in a random potential we assume the existence of sufficiently localised states near the edges of each landau band we then prove that the hall conductivity is quantised and the parallel conductivity vanishes when the filling factor stays close to an integer the hall integer is a topological invariant given by the landau band index

wegner estimate and anderson localization for random magnetic fields we consider a two dimensional magnetic schrodinger operator with a spatially stationary random magnetic field we assume that the magnetic field has a positive lower bound and that it has fourier modes on arbitrarily short scales we prove the wegner estimate at arbitrary energy i e we show that the averaged density of states is finite throughout the whole spectrum we also prove anderson localization at the bottom of the spectrum

two dimensional poroelastic acoustical foam shape design for absorption coefficient maximization by topology optimization method optimal shape design of a two dimensional poroelastic acoustical foam is formulated as a topology optimization problem for a poroelastic acoustical system consisting of an air region and a poroelastic foam region two different physical regions are continuously changed in an iterative design process to automatically account for the moving interfaces between two regions we propose a new unified model to analyze the whole poroelastic acoustical foam system with one set of governing equations biot s equations are modified with a material property interpolation from a topology optimization method with the unified analysis model we carry out two dimensional optimal shape design of a poroelastic acoustical foam by a gradient based topology optimization setting the specific objective is the maximization of the absorption coefficient in low and middle ranges of frequencies with different amounts of a poroelastic material the performances of the obtained shapes are compared with those of well known wedge s

topology optimization using a mixed formulation an alternative way to solve pressure load problems abstract a shortcoming of the traditional density based approach to topology optimization is the handling of design dependent loads that relate to boundary data such as for example pressure loads previous works have introduced spline and iso density curves or alternative parametrization schemes to determine the load surfaces in this work we suggest a new way to solve pressure load problems in topology optimization using a mixed displacement pressure formulation for the underlying finite element problem we define the void phase to be an incompressible hydrostatic fluid in this way we can transfer pressure loads through the fluid without any needs for special load surface parametrizations the method is easily implemented in the standard density approach and is demonstrated to work efficiently for both 2d and 3d problems by extending the method to a three phase solid fluid void design method we also demonstrate design of water containing dams

extended hough transform for linear feature detection improving the accuracy of line segment detection reduces the complexity of subsequent high level processing common in cartographic feature detection we developed a new extension to the hough transform and reported on its application to building extraction we expanded the hough space by a third parameter the horizontal or vertical coordinate of the image space to provide incremental information as to the length of the lineal feature being sought using this extended ht transform allowed us to more accurately detect the true length of a line segment in addition we used a bayesian probabilistic approach to process our extended hough space that further increased the accuracy of our extended hough transform

combining local filtering and multiscale analysis for edge ridge and curvilinear objects detection this paper presents a general method for detecting curvilinear structures like filaments or edges in noisy images this method relies on a novel technique the feature adapted beamlet transform fabt which is the main contribution of this paper it combines the well known beamlet transform bt introduced by donoho with local filtering techniques in order to improve both detection performance and accuracy of the bt moreover as the desired feature detector is chosen to belong to the class of steerable filters our transform requires only o n log n operations where n n 2 is the number of pixels besides providing a fast implementation of the fabt on discrete grids we present a statistically controlled method for curvilinear objects detection to extract significant objects we propose an algorithm in four steps 1 compute the fabt 2 normalize beamlet coefficients 3 select meaningful beamlets thanks to a fast energy based minimization and 4 link beamlets together in order to get a list of objects we present an evaluation on both synthetic and real data and demonstrate substantial improvements of our method over classical feature detectors

intermixture of extended edge and localized bulk energy levels in macroscopic hall systems we study the spectrum of a random schrodinger operator for an electron subjected to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to l the y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials the eigenvalues of the hamiltonian are classified according to their associated quantum mechanical diamagnetic current in the y direction here we look at an interval of energies inside the first landau band of the random operator for the infinite plane in this energy interval with large probability there exist l eigenvalues with positive or negative currents of 1 between each of these there exist l2 eigenvalues with infinitesimal current e b log l 2 we explain the relevance of this analysis of boundary diamagnetic currents to the integer quantum hall effect

infinite degeneracy for a landau hamiltonian with poisson impurities we consider a single band approximation to the random schrodinger operator in an external magnetic field the random potential consists of delta functions of random strengths whose positions have a poisson distribution we prove that if the magnetic field is sufficiently high compared to the density of scatterers then with probability one there exists an infinitely degenerate eigenenergy coinciding with the first landau level in the absence of a random potential

lsd a fast line segment detector with a false detection control we propose a linear time line segment detector that gives accurate results a controlled number of false detections and requires no parameter tuning this algorithm is tested and compared to state of the art algorithms on a wide set of natural images

und unite and divide method in fourier and radon domains for line segment detection in this paper we extend our previously proposed line detection method to line segmentation using a so called unite and divide und approach the methodology includes two phases namely the union of spectra in the frequency domain and the division of the sinogram in radon space in the union phase given an image its sinogram is obtained by parallel 2d multilayer fourier transforms cartesian to polar mapping and 1d inverse fourier transform in the division phase the edges of butterfly wings in the neighborhood of every sinogram peak are firstly specified with each neighborhood area corresponding to a window in image space by applying the separated sinogram of each such windowed image we can extract the line segments the division phase identifies the edges of butterfly wings in the neighborhood of every sinogram peak such that each neighborhood area corresponds to a window in image space line segments are extracted by applying the separated sinogram of each windowed image our experiments are conducted on benchmark images and the results reveal that the und method yields higher accuracy has lower computational cost and is more robust to noise compared to existing state of the art methods

edge and impurity effects on quantization of hall currents we consider the edge hall conductance and show it is invariant under perturbations located in a strip along the edge decaying perturbations far from the edge are also allowed this enables us to prove for the edge conductances a general sum rule relating currents due to the presence of two different media located respectively on the left and on the right half plane as a particular interesting case we put forward a general quantization formula for the difference of edge hall conductances in semi infinite samples with and without a confining wall it implies in particular that the edge hall conductance takes its ideal quantized value under a gap condition for the bulk hamiltonian or under some localization properties for a random bulk hamiltonian provided one first regularizes the conductance we shall discuss this regularization issue our quantization formula also shows that deviations from the ideal value occurs if a semi infinite distribution of impurity potentials is repulsive enough to produce current carrying surface states on its boundary

topology optimization of non linear elastic structures and compliant mechanisms abstract a linear elastic response is assumed in most structural topology optimization problems while this assumption is valid for a wide variety of problems it is not valid for structures undergoing large displacements the elastic structural analysis used here accommodates geometric and material non linearities the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities the filtering scheme is embedded in the structural analysis to resolve the non existent solution to the solid void topology problem in this way we know precisely what optimization problem is being solved the structural topology optimization formulation is also used to design compliant mechanisms

localization for some continuous random schrodinger operators we study the spectrum of random schrodinger operators acting onl2 r d of the following type h delta w sum x in mathbb z d t x v x the t x x in mathbb z d are i i d random variables under weak assumptions onv we prove exponential localization forh at the lower edge of its spectrum in order to do this we give a new proof of the wegner estimate that works without sign assumptions onv

comment on extended hough transform for linear feature detection recently cha et al presented an efficient extended hough transform eht method to detect lines each line segment with desired length instead of performing the voting process twice for each edge pixel in the eht method this comment presents a simple modification such that each edge pixel in the edge map only needs to perform the voting processing once this modification leads to 16 execution time improvement ratio when compared to the eht method and it is very close to the theoretical execution time improvement ratio 14

bootstrap multiscale analysis and localization in random media we introduce an enhanced multiscale analysis that yields subexponentially decaying probabilities for bad events for quantum and classical waves in random media we obtain exponential decay for the resolvent of the corresponding random operators in boxes of side l with probability higher than 1 e l for any 0 1 the starting hypothesis for the enhanced multiscale analysis only requires the verification of polynomial decay of the finite volume resolvent at some sufficiently large scale with probability bigger than 1 d is the dimension note that from the same starting hypothesis we get conclusions that are valid for any 0 1 this is achieved by the repeated use of a bootstrap argument as an application we use a generalized eigenfunction expansion to obtain strong dynamical localization of any order in the hilbert schmidt norm and better estimates on the behavior of the eigenfunctions

linear response theory for magnetic schrodinger operators in disordered media abstract we justify the linear response theory for an ergodic schrodinger operator with magnetic field within the noninteracting particle approximation and derive a kubo formula for the electric conductivity tensor to achieve that we construct suitable normed spaces of measurable covariant operators where the liouville equation can be solved uniquely if the fermi level falls into a region of localization we recover the well known kubo str eda formula for the quantum hall conductivity at zero temperature