multicomponent f x seismic random noise attenuation via vector autoregressive operators we propose an extension of the traditional frequency space f x random noise attenuation method to three component seismic records for this purpose we develop a three component vector autoregressive var model in the f x domain that is applied to the multicomponent spatial samples of each individual temporal frequency var model parameters are estimated using the least squares minimization of forward and backward prediction errors var modeling effectively identifies the potential coherencies between various components of a multicomponent signal we use the squared coherence spectrum of var models as an indicator to determine these coherencies synthetic and real data examples are provided to show the effectiveness of the proposed method

five dimensional interpolation recovering from acquisition constraints although 3d seismic data are being acquired in larger volumes than ever before the spatial sampling of these volumes is not always adequate for certain seismic processes this is especially true of marine and land wide azimuth acquisitions leading to the development of multidimensional data interpolation techniques simultaneous interpolation in all five seismic data dimensions inline crossline offset azimuth and frequency has great utility in predicting missing data with correct amplitude and phase variations although there are many techniques that can be implemented in five dimensions this study focused on sparse fourier reconstruction the success of fourier interpolation methods depends largely on two factors 1 having efficient fourier transform operators that permit the use of large multidimensional data windows and 2 constraining the spatial spectrum along dimensions where seismic amplitudes change slowly so that the sparseness and band limitation assumptions remain valid fourier reconstruction can be performed when enforcing a sparseness constraint on the 4d spatial spectrum obtained from frequency slices of five dimensional windows binning spatial positions into a fine 4d grid facilitates the use of the fft which helps on the convergence of the inversion algorithm this improves the results and computational efficiency the 5d interpolation can successfully interpolate sparse data improve avo analysis and reduce migration artifacts target geometries for optimal interpolation and regularization of land data can be classified in terms of whether they preserve the original data and whether they are designed to achieve surface or subsurface consistency

stochastic calculus of variations abstract a theory of stochastic calculus of variations is presented which generalizes the ordinary calculus of variations to stochastic processes generalizations of the euler equation and noether s theorem are obtained and several conservation laws are discussed an application to nelson s probabilistic framework of quantum mechanics is also given

computationally attractive reconstruction of bandlimited images from irregular samples an efficient method for the reconstruction of bandlimited images and the approximation of arbitrary images from nonuniform sampling values is developed the novel method is based on the observation that the reconstruction problem can be formulated as linear system of equations using two dimensional 2 d trigonometric polynomials where the matrix is of block toeplitz type with toeplitz blocks this system is solved iteratively by the conjugate gradient cg method we show that the use of so called adaptive weights in the establishment of the block toeplitz matrix can be seen as efficient preconditioning the superiority of the new method over conventional approaches is demonstrated by numerical experiments

wave equation trace interpolation spatial aliasing in multichannel seismic data can be overcome by solving an inversion in which the model is the section that would be recorded in a well sampled zero offset experiment and the data are seismic data after normal moveout nmo the formulation of the linear relation between the data and the model is based on the wave equation and on fourier analysis of aliasing a processing sequence in which one treats missing data as zero data and performs partial migration before stacking is equivalent to application of the transpose of the operator that actually needs to be inverted the inverse of that operator cannot be uniquely determined but it can be estimated using spatial spectral balancing in a conjugate gradient iterative scheme the first iteration is conventional processing including prestack partial migration as shown in a field data example in which severe spatial aliasing was simulated a few more iterations are necessary to achieve significantly better results

quantum classical correspondence via a deformed kinetic operator we propose an approach to quantum classical correspondence based on a deformation of the momentum and kinetic operators of quantum mechanics making use of the factorization method we construct classical versions of the momentum and kinetic operators which in addition to the standard quantum expressions contain terms that are functionals of the n particle density we show that this implementation of quantum classical correspondence is related to witten s deformation of the exterior derivative and laplacian introduced in the context of supersymmetric quantum mechanics the corresponding deformed action is also shown to be related to the fisher information finally we briefly consider the possible relevance of our approach to the construction of kinetic energy density functionals

fourier reconstruction of nonuniformly sampled aliased seismic data there are numerous methods for interpolating uniformly sampled aliased seismic data but few can handle the combination of nonuniform sampling and aliasing we combine the principles of fourier reconstruction of nonaliased nonuniformly sampled data with the ideas of frequency wavenumber f k interpolation of aliased uniformly sampled data in a new two step algorithm in the first step we estimate the fourier coefficients at the lower nonaliased temporal frequencies from the nonuniformly sampled data the coefficients are then used in the second step as an a priori model to distinguish between aliased and nonaliased energy at the higher aliased temporal frequencies by using a nonquadratic model penalty in the inversion both the artifacts in the fourier domain from nonuniform sampling and the aliased energy are suppressed the underlying assumption is that events are planar therefore the algorithm is applied to seismic data in overlapping spatiotemporal windows

fourier reconstruction of marine streamer data in four spatial coordinates many methods exist for interpolation of seismic data in one and two spatial dimensions but few can interpolate properly in three or four spatial dimensions marine multi streamer data typically are sampled relatively well in the midpoint and absolute offset coordinates but not in the azimuth because the crossline shot coordinate is significantly under sampled we approach the problem of interpolation of marine streamer data in four spatial dimensions by splitting the problem into a 1d interpolation along the densely sampled streamers and a 3d fourier reconstruction for the remaining spatial coordinates in fourier reconstruction the fourier coefficients that synthesize the nonuniformly sampled seismic data are estimated in a least squares inversion the method is computationally efficient requires no subsurface information and can handle uniform grids with missing data as well as nonuniform grids or random sampling the output grid of the 1d interpolation in the first step is arbitrary when the output grid has uniform inline midpoints spacing the 3d fourier reconstruction in the second step is performed in the crossline midpoint absolute offset and azimuth coordinates when the first step outputs to uniform absolute offset the 3d fourier reconstruction handles the crossline inline midpoint and the azimuth coordinates in both cases the main innovation is the inclusion of the azimuthal coordinate in the fourier reconstruction the azimuth multiplicity must be increased for the method to be successful which means that overlap shooting is required we have tested the algorithm on synthetic streamer data for which the proposed method outperforms an approach where the azimuthal coordinate is ignored potential applications are interpolation of marine streamer data to decrease the crossline source sampling for the benefit of 3d multiple prediction and regularization to reduce sampling related differences in processing of time lapse data

fisher and jaynesian statistics compared in the description of classical fluids fisher statistics provides an information measure which like that of shannon is a functional of a distribution f the latter solves an euler equation to minimize the functional to make comparison with statistical derivations of extended thermodynamics calculations by frieden plastino and collaborators are specialized to the case where f is a phase space distribution approximating a solution of the liouville equation the euler equations are solved subject to conditions specifying values of internal energy and fluxes e g of heat and momentum the solution is compared with that of jaynes which with information theory provides an entropy model the fisher and jaynes entropies are identical only in equilibrium the distributions agree in linear approximation for a restricted set of variables this set is large enough to embrace all those needed in the classical non equilibrium description of simple fluids fisher euler solutions are not unique in non equilibrium

fisher based thermodynamics its legendre transform and concavity properties it is shown that the legendre transform structure of thermodynamics can be replicated without any change if one replaces the entropy s by fisher s information measure i also the important thermodynamic property of concavity is shown to be obeyed by i by this use of the fisher information measure we develop a thermodynamics that seems to be able to treat equilibrium and nonequilibrium situations in a manner entirely similar to the conventional one

malliavin calculus and euclidean quantum mechanics i functional calculus abstract we give a rigorous version of the functional calculus developed by r feynman in relation to his path integral formulation of quantum mechanics our approach is euclidean but distinct from the one founded on the feynman kac formula it uses two basic ingredients a new probabilistic interpretation of the classical heat equation introduced recently in the framework of euclidean quantum mechanics and an infinite dimensional differential calculus adapted to functionals of the diffusion processes relevant for this interpretation

generalizations of the heisenberg and schrodinger uncertainty relations in this paper releasing the restriction on operators which are self adjoint we propose a heisenberg type uncertainty relation and a schrodinger type uncertainty relation with any pair of operators on a hilbert space a generalization of luo s theorem s luo heisenberg uncertainty relation for mixed states phys rev a 72 042110 2005 is investigated

multidimensional de aliased cadzow reconstruction of seismic records abstractwe tested a strategy for beyond alias interpolation of seismic data using cadzow reconstruction the strategy enables cadzow reconstruction to be used for interpolation of regularly sampled seismic records first in the frequency space f x domain we generated a hankel matrix from the spatial samples of the low frequencies to perform interpolation at a given frequency the spatial samples were interlaced with zero samples and another hankel matrix was generated from the zero interlaced data next the rank reduced eigen decomposition of the hankel matrix at low frequencies was used for beyond alias preconditioning of the hankel matrix at a given frequency finally antidiagonal averaging of the conditioned hankel matrix produced the final interpolated data in addition the multidimensional extension of the proposed algorithm was explained the proposed method provides a unifying thread between reduced rank cadzow reconstruction and beyond alias f x prediction error interpolation synthetic an

diffusion processes with singular drift fields a class of stochastic differential equations with highly singular drift fields is considered using a purely probabilistic approach we can show the unattainability of the nodal set moreover a global existence and uniqueness theorem for diffusion processes with singular drift fields is established the finite action condition of carlen and zheng can be modified we relate our results to the diffusions which describe the time evolution of quantum systems in stochastic mechanics

oc seislet seislet transform construction with differential offset continuation many of the geophysical data analysis problems such as signal noise separation and data regularization are conveniently formulated in a transform domain in which the signal appears sparse classic transforms such as the fourier transform or the digital wavelet transform dwt fail occasionally in processing complex seismic wavefields because of the nonstationarity of seismic data in time and space dimensions we present a sparse multiscale transform domain specifically tailored to seismic reflection data the new wavelet like transform the oc seislet transform uses a differential offset continuation oc operator that predicts prestack reflection data in offset midpoint and time coordinates it provides a high compression of reflection events its compression properties indicate the potential of oc seislets for applications such as seismic data regularization or noise attenuation results of applying the method to synthetic and field data examples demonstrate that the oc seislet transform can recon

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

quantum covariance quantum fisher information and the uncertainty relations in this paper the relation between quantum covariances and quantum fisher informations is studied this study is applied to generalize a recently proved uncertainty relation based on quantum fisher information the proof given here considerably simplifies the previously proposed proofs and leads to more general inequalities

multistep autoregressive reconstruction of seismic records linear prediction filters in the f x domain are widely used to interpolate regularly sampled data we study the problem of reconstructing irregularly missing data on a regular grid using linear prediction filters we propose a two stage algorithm first we reconstruct the unaliased part of the data spectrum using a fourier method minimum weighted norm interpolation then prediction filters for all the frequencies are extracted from the reconstructed low frequencies the latter is implemented via a multistep autoregressive msar algorithm finally these prediction filters are used to reconstruct the complete data in the f x domain the applicability of the proposed method is examined using synthetic and field data examples

beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data we propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform in a first pass the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data the aforementioned coefficients are divided into two groups of scales alias free and alias contaminated scales the alias free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the alias contaminated scale coefficients the mask function is incorporated into the inversion via a minimum norm least squares algorithm that determines the curvelet coefficients of the desired alias free data once the alias free coefficients are determined the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions the proposed method can be used to reconstruct regularly and irregularly sampled seismic data we believe that our exposition leads to a clear unifying thread between f x and f k beyond alias interpo

reconstruction of multidimensional bandlimited signals from nonuniform and generalized samples this paper addresses the problem of multidimensional signal reconstruction from nonuniform or generalized samples typical solutions in the literature for this problem utilize continuous filtering the key result of the current paper is a multidimensional interpolation identity which establishes the equivalence of two multidimensional processing operations one of these uses continuous domain filters whereas the other uses discrete processing this result has obvious benefits in the context of the afore mentioned problem the results here expand and generalize earlier work by other authors on the one dimensional 1 d case potential applications include two dimensional 2 d images and video signals

interpolation and extrapolation using a high resolution discrete fourier transform we present an iterative nonparametric approach to spectral estimation that is particularly suitable for estimation of line spectra this approach minimizes a cost function derived from bayes theorem the method is suitable for line spectra since a long tailed distribution is used to model the prior distribution of spectral amplitudes since the data themselves are used as constraints phase information can also be recovered and used to extend the data outside the original window the objective function is formulated in terms of hyperparameters that control the degree of fit and spectral resolution noise rejection can also be achieved by truncating the number of iterations spectral resolution and extrapolation length are controlled by a single parameter when this parameter is large compared with the spectral powers the algorithm leads to zero extrapolation of the data and the estimated fourier transform yields the periodogram when the data are sampled at a constant rate the algorithm uses one levinson recursion per iteration for irregular sampling the algorithm uses one cholesky decomposition per iteration the performance of the algorithm is illustrated with three different problems that arise in geophysical data 1 harmonic retrieval from a time series contaminated with noise 2 linear event detection from a finite aperture array of receivers 3 interpolation extrapolation of gapped data the performance of the algorithm as a spectral estimator is tested with the kay and marple 1981 data set

the graded centers of derived discrete algebras abstract we describe in the paper the graded centers of the bounded derived categories of the derived discrete algebras in particular we prove that if a is a derived discrete algebra then the reduced part of the graded center of the bounded derived category of a is nontrivial if and only if a has infinite global dimension moreover we show that the nilpotent part of the graded center is controlled by the objects for which the auslander reiten translation coincides with a power of the suspension functor

a generalized skew information and uncertainty relation a generalized skew information is defined and a generalized uncertainty relation is established with the help of a trace inequality which was recently proven by fujii in addition we prove the trace inequality conjectured by luo and zhang finally we point out that theorem 1 in s luo and q zhang ieee trans inf theory vol 50 pp 1778 1782 no 8 aug 2004 is incorrect in general by giving a simple counter example

locally finite triangulated categories abstract a k linear triangulated category a is called locally finite provided x ind a dim k hom a x y for any indecomposable object y in a it has auslander reiten triangles in this paper we show that if a connected triangulated category has auslander reiten triangles and contains loops then its auslander reiten quiver is of the form l n download download full size image by using this we prove that the auslander reiten quiver of any locally finite triangulated category a is of the form z g where is a dynkin diagram and g is an automorphism group of z for most automorphism groups g the triangulated categories with z g as their auslander reiten quivers are constructed in particular a triangulated category with l n as its auslander reiten quiver is constructed

on sampling functions and fourier reconstruction methods random sampling can lead to algorithms in which the fourier reconstruction is almost perfect when the underlying spectrum of the signal is sparse or band limited conversely regular sampling often hampers the fourier data recovery methods however 2d signals that are band limited in one spatial dimension can be recovered by designing a regular acquisition grid that minimizes the mixing between the unknown spectrum of the well sampled signal and aliasing artifacts this concept can be easily extended to higher dimensions and used to define potential strategies for acquisition guided fourier reconstruction the wavenumber response of various sampling operators is derived and sampling conditions for optimal fourier reconstruction are investigated using synthetic and real data examples

quantization from an exponential distribution of infinitesimal action abstract a statistical model of quantization based on an exponential distribution of infinitesimal action is proposed a trajectory which does not extremize the action along an infinitesimal short segment of path is allowed to occur with a very small probability following an exponential law planck s constant is argued to give the average deviation from the infinitesimal stationary action

variational approach to dequantization we present a dequantization procedure based on a variational approach whereby quantum fluctuations latent in the quantum momentum are suppressed this is done by adding generic local deformations to the quantum momentum operator which give rise to a deformed kinetic term quantifying the amount of fuzziness caused by such fluctuations considered as a functional of such deformations the deformed kinetic term is shown to possess a unique minimum which is seen to be the classical kinetic energy furthermore we show that extremization of the associated deformed action functional introduces an essential nonlinearity to the resulting field equations which are seen to be the classical hamilton jacobi and continuity equations thus a variational procedure determines the particular deformation that has the effect of suppressing the quantum fluctuations resulting in dequantization of the system

a dynamical uncertainty principle in von neumann algebras by operator monotone functions suppose that a1 an are observables selfadjoint matrices and is a state density matrix in this case the standard uncertainty principle proved by robertson gives a bound for the quantum generalized variance namely for det cov aj ak using the commutators aj ak this bound is trivial when n is odd recently a dierent inequality of robertson type has been proved by the authors with the help of the theory of operator monotone functions in this case the bound makes use of the commutators a j and is non trivial for any n in the present paper we generalize this new result to the von neumann algebra case nevertheless the proof appears to simplify all the existing ones

mean squared error sampling and reconstruction in the presence of noise one of the main goals of sampling theory is to represent a continuous time function by a discrete set of samples here we treat the class of sampling problems in which the underlying function can be specified by a finite set of samples our problem is to reconstruct the signal from nonideal noisy samples which are modeled as the inner products of the signal with a set of sampling vectors contaminated by noise to mitigate the effect of the noise and the mismatch between the sampling and reconstruction vectors the samples are linearly processed prior to reconstruction considering a statistical reconstruction framework we characterize the strategies that are mean squared error mse admissible meaning that they are not dominated in terms of mse by any other linear reconstruction we also present explicit designs of admissible reconstructions that dominate a given inadmissible method adapting several classical estimation approaches to our particular sampling problem we suggest concrete admissible reconstruction methods and compare their performance the results are then specialized to the case in which the samples are processed by a digital correction filter

quantization from hamilton jacobi theory with a random constraint abstract we propose a method of quantization based on hamilton jacobi theory in the presence of a random constraint due to the fluctuations of a set of hidden random variables given a lagrangian it reproduces the results of canonical quantization yet with a unique ordering of operators if the lagrange multiplier that arises in the dynamical system with constraint can only take binary values 2 with equal probability

uncertainty principle with quantum fisher information in this paper we prove a lower bound for the determinant of the covariance matrix of quantum mechanical observables which was conjectured by gibilisco et al and has the interpretation of uncertainty the lower bound is given in terms of the commutator of the state and the observables and quantum fisher information generated by an operator monotone function

seismic trace interpolation in the f x domain interpolation of seismic traces is an effective means of improving migration when the data set exhibits spatial aliasing a major difficulty of standard interpolation methods is that they depend on the degree of reliability with which the various geological events can be separated in this respect a multichannel interpolation method is described which requires neither a priori knowledge of the directions of lateral coherence of the events nor estimation of these directions the method is based on the fact that linear events present in a section made of equally spaced traces may be interpolated exactly regardless of the original spatial interval without any attempt to determine their true dips the predictability of linear events in the f x domain allows the missing traces to be expressed as the output of a linear system the input of which consists of the recorded traces the interpolation operator is obtained by solving a set of linear equations whose coefficients depend only on the spectrum of the spatial prediction filter defined by the recorded traces synthetic examples show that this method is insensitive to random noise and that it correctly handles curvatures and lateral amplitude variations assessment of the method with a real data set shows that the interpolation yields an improved migrated section

monotone metrics on matrix spaces abstract the study of monotone inner products under stochastic mappings on the space of matrices was initiated by morozova and chentsov motivated by information geometry they did not show a monotone metric but proposed several candidates the main result of the present paper is to provide an abundance of monotone metrics by means of operator monotone functions and to characterize them it turns out that there is a correspondence between monotone metrics and operator means in the sense of kubo and ando it follows that all proposals of morozova and chentsov are indeed monotone metrics

calabi yau objects in triangulated categories we introduce the calabi yau cy objects in a hom finite krull schmidt triangulated k category and notice that the structure of the minimal consequently all the cy objects can be described the relation between indecomposable cy objects and auslander reiten triangles is provided finally we classify all the cy modules of self injective nakayama algebras determining this way the self injective nakayama algebras admitting indecomposable cy modules in particular this result recovers the algebras whose stable categories are calabi yau which have been obtained in bs

quantum equilibrium and the origin of absolute uncertainty what is randomness probability certainty knowledge these are old and difficult questions and we shall not focus on them here nonetheless we shall obtain sharp striking conclusions concerning the relationship between these concepts

fisher information matrix of husimi distribution we calculate the fisher information matrix of husimi distribution in the fock bargmann representation it turns out that the fisher information of the position and that of the momentum move in opposite directions and that a weighted trace of the fisher information matrix is a constant independent of the husimi distribution this may be interpreted as a kind of uncertainty relation in the spirit of heisenberg uncertainty principle from the statistical inference point of view

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

super resolution from unregistered and totally aliased signals using subspace methods in many applications the sampling frequency is limited by the physical characteristics of the components the pixel pitch the rate of the analog to digital aid converter etc a low pass filter is usually applied before the sampling operation to avoid aliasing however when multiple copies are available it is possible to use the information that is inherently present in the aliasing to reconstruct a higher resolution signal if the different copies have unknown relative offsets this is a nonlinear problem in the offsets and the signal coefficients they are not easily separable in the set of equations describing the super resolution problem thus we perform joint registration and reconstruction from multiple unregistered sets of samples we give a mathematical formulation for the problem when there are m sets of n samples of a signal that is described by l expansion coefficients we prove that the solution of the registration and reconstruction problem is generically unique if mn ges l m 1 we describe two subspace based methods to compute this solution their complexity is analyzed and some heuristic methods are proposed finally some numerical simulation results on one and two dimensional signals are given to show the performance of these methods

double weave 3d seismic acquisition part 2 seismic modeling and subsurface fold analyses abstractthe compatibility of 3d double weave acquisition designs with sparse fourier reconstruction algorithms was examined using simple modeled seismic data zigzag and orthogonal double weave acquisitions and random acquisition all had successful 5d sparse fourier interpolation results however the simplicity and regularity of double weave acquisition made it a more attractive alternative to random acquisition the subsurface fold analysis of double weave acquisition reveals nonuniform distribution of midpoint sampling in comparison with random and traditional orthogonal acquisition layouts this can be alleviated by either using larger bin sizes or introducing random shifts to the shot receiver lines of double weave acquisition layouts zigzag double weave acquisition reveals a more uniform offset azimuth distribution compared with orthogonal double weave random and traditional orthogonal acquisitions

an informational characterization of schrodinger s uncertainty relations heisenberg s uncertainty relations employ commutators of observables to set fundamental limits on quantum measurement the information concerning incompatibility non commutativity of observables is well included but that concerning correlation is missing schrodinger s uncertainty relations remedy this defect by supplementing the correlation in terms of anti commutators however both heisenberg s uncertainty relations and schrodinger s uncertainty relations are expressed in terms of variances which are not good measures of uncertainty in general situations e g when mixed states are involved by virtue of the wigner yanase skew information we will establish an uncertainty relation along the spirit of schrodinger from a statistical inference perspective and propose a conjecture the result may be interpreted as a quantification of certain aspect of the celebrated wigner araki yanase theorem for quantum measurement which states that observables not commuting with a conserved quantity cannot be measured exactly

minimum weighted norm interpolation of seismic records in seismic data processing we often need to interpolate and extrapolate data at missing spatial locations the reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired we propose a wavefield reconstruction scheme for spatially band limited signals the method entails solving an inverse problem where a wavenumber domain regularization term is included the regularization term constrains the solution to be spatially band limited and imposes a prior spectral shape the numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix vector multiplications implemented via the fast fourier transform fft is adopted the algorithm can be used to perform multidimensional reconstruction in any spatial domain

improvement of uncertainty relations for mixed states we study a possible improvement of uncertainty relations the heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables the schrodinger uncertainty relation improves the heisenberg uncertainty relation by adding the correlation in terms of anti commutator however both relations are insensitive whether the state used is pure or mixed we improve the uncertainty relations by introducing additional terms which measure the mixtureness of the state for the momentum and position operators as conjugate observables and for the thermal state of quantum harmonic oscillator it turns out that the equalities in the improved uncertainty relations hold

uncertainty principle and quantum fisher information ii heisenberg and schrodinger uncertainty principles give lower bounds for the product of variances var a var b if the observables a b are not compatible namely if the commutator a b is not zero in this paper we prove an uncertainty principle in schrodinger form where the bound for the product of variances var a var b depends on the area spanned by the commutators i a and i b with respect to an arbitrary quantum version of the fisher information

incompleteness of trajectory based interpretations of quantum mechanics trajectory based approaches to quantum mechanics include the de broglie bohm interpretation and nelson s stochastic interpretation it is shown that the usual route to establishing the validity of such interpretations via a decomposition of the schr dinger equation into a continuity equation and a modified hamilton jacobi equation fails for some quantum states a very simple example is provided by a quantum particle in a box described by a wavefunction that is initially uniform over the interior of the box for this example there is no corresponding continuity or modified hamilton jacobi equation and the space time dependence of the wavefunction has a known fractal structure examples with finite average energies are also constructed

seismic data interpolation and denoising in the frequency wavenumber domain i introduce a unified approach for denoising and interpolation of seismic data in the frequency wavenumber f k domain first an angular search in the f k domain is carried out to identify a sparse number of dominant dips not only using low frequencies but over the whole frequency range then an angular mask function is designed based on the identified dominant dips the mask function is utilized with the least squares fitting principle for optimal denoising or interpolation of data the least squares fit is directly applied in the time space domain the proposed method can be used to interpolate regularly sampled data as well as randomly sampled data on a regular grid synthetic and real data examples are provided to examine the performance of the proposed method

quantum fractals in boxes a quantum wave with probability density confined by dirichlet boundary conditions in a d dimensional box of arbitrary shape and finite surface area evolves from the uniform state for almost all positions the graph of the evolution of p is a fractal curve with dimension for almost all times t the graph of the spatial probability density p is a fractal hypersurface with dimension when d 1 there are in addition to these generic time and space fractals infinitely many special quantum revival times when p is piecewise constant and infinitely many special spacetime slices for which the dimension of p is 5 4 if the surface of the box is a fractal with dimension simple arguments suggest that the dimension of the time fractal is and that of the space fractal is

a robertson type uncertainty principle and quantum fisher information let a1 an be complex self adjoint matrices and let be a density matrix the robertson uncertainty principle det cov ah aj det i 2 tr a h aj gives a bound for the quantum generalized variance in terms of the commutators ah aj the right side matrix is antisymmetric and therefore the bound is trivial equal to zero in the odd case n 2m 1 let f be an arbitrary normalized symmetric operator monotone function and let h i f be the associated quantum fisher information we have conjectured the inequality det cov ah aj det f 0 hi a h i a j i f

seismic trace interpolation in the fourier transform domain a data adaptive interpolation method is designed and applied in the fourier transform domain f k or f kx ky for spatially aliased data the method makes use of fast fourier transforms and their cyclic properties thereby offering a significant cost advantage over other techniques that interpolate aliased data the algorithm designs and applies interpolation operators in the f k or f kx ky domain to fill zero traces inserted in the data in the t x or t x y domain at locations where interpolated traces are needed the interpolation operator is designed by manipulating the lower frequency components of the stretched transforms of the original data this operator is derived assuming that it is the same operator that fills periodically zeroed traces of the original data but at the lower frequencies and corresponds to the f k or f kx ky domain version of the well known f x or f x y domain trace interpolators the method is applicable to 2d and 3d data recorded sparsely in a horizontal plane the most comm

how to distinguish quantum covariances using uncertainty relations abstract to each operator monotone function it is possible to associate a quantum version of the classical covariance we show that i only for regular quantum covariances one can prove non trivial uncertainty relations ii the usual quantum covariance gives the best inequalities in this setting

seismic data interpolation using a fast generalized fourier transform we have found a fast and efficient method for the interpolation of nonstationary seismic data the method uses the fast generalized fourier transform fgft to identify the space wavenumber evolution of nonstationary spatial signals at each temporal frequency the nonredundant nature of fgft renders a big computational advantage to this interpolation method a least squares fitting scheme is used next to retrieve the optimal fgft coefficients representative of the ideal interpolated data for randomly sampled data on a regular grid we seek a sparse representation of fgft coefficients to retrieve the missing samples in addition to interpolate the regularly sampled seismic data at a given frequency we use a mask function derived from the fgft coefficients of the low frequencies synthetic and real data examples can be used to examine the performance of the method

weakly non local fluid mechanics the schrodinger equation a weakly non local extension of ideal fluid dynamics is derived from the second law of thermodynamics it is proved that in the reversible limit the additional pressure term can be derived from a potential the requirement of the additivity of the specific entropy function determines the quantum potential uniquely the relation to other known derivations of the schrodinger equation stochastic fisher information exact uncertainty is clarified

multidimensional interpolation using a model constrained minimum weighted norm interpolation abstractfourier based minimum weighted norm interpolation mwni has been widely used to regularize land seismic data however it has difficulty interpolating regular missing data that are spatially aliased minimizing the aliasing artifacts is still a technical challenge in mwni i have developed a novel method to address the aliasing problem in mwni using a prior model as constraints the prior model was constructed by a linear interpolation along dominant dips to produce a fully regular initial model the spectral weights derived from this initial model are typically not aliased and can be used to constrain the least squares inversion in mwni frequency by frequency to overcome the aliasing artifacts this new interpolation scheme expands the capability of conventional mwni to handle spatially aliased data that are often associated with steeply dipping structures and it reconstructs more reliable interpolation results decimation tests of a simple 2d synthetic data set and a complex 3d synthetic sal

unique additive information measures boltzmann gibbs shannon fisher and beyond abstract it is proved that the only additive and isotropic information measure that can depend on the probability distribution and also on its first derivative is a linear combination of the boltzmann gibbs shannon and fisher information measures power law equilibrium distributions are found as a result of the interaction of the two terms the case of second order derivative dependence is investigated and a corresponding additive information measure is given

topological conformal field theories and calabi yau categories abstract this is the first of two papers which construct a purely algebraic counterpart to the theory of gromov witten invariants at all genera these gromov witten type invariants depend on a calabi yau a category which plays the role of the target in ordinary gromov witten theory when we use an appropriate a version of the derived category of coherent sheaves on a calabi yau variety this constructs the b model at all genera when the fukaya category of a compact symplectic manifold x is used it is shown under certain assumptions that the usual gromov witten invariants are recovered the assumptions are that open closed gromov witten theory can be constructed for x and that the natural map from the hochschild homology of the fukaya category of x to the ordinary homology of x is an isomorphism

spreading lengths of hermite polynomials the renyi shannon and fisher spreading lengths of the classical or hypergeometric orthogonal polynomials which are quantifiers of their distribution all over the orthogonality interval are defined and investigated these information theoretic measures of the associated rakhmanov probability density which are direct measures of the polynomial spreading in the sense of having the same units as the variable share interesting properties invariance under translations and reflections linear scaling and vanishing in the limit that the variable tends towards a given definite value the expressions of the renyi and fisher lengths for the hermite polynomials are computed in terms of the polynomial degree the combinatorial multivariable bell polynomials which are shown to characterize the finite power of an arbitrary polynomial play a relevant role for the computation of these information theoretic lengths indeed these polynomials allow us to design an error free computing approach for the entropic moments weighted l q norms of hermite polynomials and subsequently for the renyi and tsallis entropies as well as for the renyi spreading lengths sharp bounds for the shannon length of these polynomials are also given by means of an information theoretic based optimization procedure moreover the existence of a linear correlation between the shannon length as well as the second order renyi length and the standard deviation is computationally proved finally the application to the most popular quantum mechanical prototype system the harmonic oscillator is discussed and some relevant asymptotical open issues related to the entropic moments mentioned previously are posed

fisher information and kinetic energy functionals a dequantization approach we strengthen the connection between information theory and quantum mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed the dequantization procedure results in a decomposition of the quantum kinetic energy as the sum of a classical term and a purely quantum term the purely quantum term which results from the quantum fluctuations is essentially identical to the fisher information the classical term is complementary to the fisher information and in this sense it plays a role analogous to that of the shannon entropy we demonstrate the kinetic energy decomposition for both stationary and nonstationary states and employ it to shed light on the nature of kinetic energy functionals

3d interpolation of irregular data with a pocs algorithm seismic surveys generally have irregular areas where data cannot be acquired these data should often be interpolated a projection onto convex sets pocs algorithm using fourier transforms allows interpolation of irregularly populated grids of seismic data with a simple iterative method that produces high quality results the original 2d image restoration method the gerchberg saxton algorithm is extended easily to higher dimensions and the 3d version of the process used here produces much better interpolations than typical 2d methods the only parameter that makes a substantial difference in the results is the number of iterations used and this number can be overestimated without degrading the quality of the results this simplicity is a significant advantage because it relieves the user of extensive parameter testing although the cost of the algorithm is several times the cost of typical 2d methods the method is easily parallelized and still completely practical

schrodinger equation from an exact uncertainty principle an exact uncertainty principle formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position leads from the classical equations of motion to the schrodinger equation

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

noetherian hereditary abelian categories satisfying serre duality norwegian univ sci technol dept math sci n 7491 trondheim norway limburgs univ ctr dept wni b 3590 diepenbeek belgium reiten i norwegian univ sci technol dept math sci n 7491 trondheim norway

geometry of the schrodinger equation and stochastic mass transportation the schrodinger equation is deduced from a geometric principle lagrange hamilton jacobi and hamilton formalisms are defined almost analogously to the deterministic case which can be identified as geometric optic the form of these formalisms is identical to the deterministic formalisms furthermore it will be shown how the deterministic case is superficial to the stochastic one if planck s constant is very small an elementary proof of heisenberg s uncertainty relation finishes the paper

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159