image filtering edge detection and edge tracing using fuzzy reasoning we characterize the problem of detecting edges in images as a fuzzy reasoning problem the edge detection problem is divided into three stages filtering detection and tracing images are filtered by applying fuzzy reasoning based on local pixel characteristics to control the degree of gaussian smoothing filtered images are then subjected to a simple edge detection algorithm which evaluates the edge fuzzy membership value for each pixel based on local image characteristics finally pixels having high edge membership are traced and assembled into structures again using fuzzy reasoning to guide the tracing process the filtering detection and tracing algorithms are tested on several test images comparison is made with a standard edge detection technique

a new two dimensional fast cosine transform algorithm the discrete cosine transform 2 d dct is based on a one dimensional fast cosine transform 1 d fct algorithm instead of computing the 2 d transform using the row column method the 1 d algorithm is extended by means of the vector radix approach derivation based on both the sequence splitting and kronecker matrix product method are discussed the sequence splitting approach has the advantage that all the underlying operations are shown clearly while the matrix product representations are more compact and readily generalized to higher dimensions the bit reversal operations are placed before the recursive additions so that the recursive operations can be performed in a very regular manner this greatly simplifies the indexing problem in the software implementation of the algorithms the vector radix algorithm saves 25 multiplications as compared with the row column method

level spacing distributions and the bessel kernel scaling models of randomn n hermitian matrices and passing to the limitn leads to integral operators whose fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order for the gaussian unitary ensemble and for many others as well the kernel one obtains by scaling in the bulk of the spectrum is the sine kernel frac sin pi x y pi x y rescaling the gue at the edge of the spectrum leads to the kernel frac ai x ai y ai x ai y x y where ai is the airy function in previous work we found several analogies between properties of this airy kernel and known properties of the sine kernel a system of partial differential equations associated with the logarithmic differential of the fredholm determinant when the underlying domain is a union of intervals a representation of the fredholm determinant in terms of a painleve transcendent in the case of a single interval and also in this case asymptotic expansions for these determinants and related quantities achieved with the help of a differential operator which commutes with the integral operator in this paper we show that there are completely analogous properties for a class of kernels which arise when one rescales the laguerre or jacobi ensembles at the edge of the spectrum namely frac j alpha sqrt x sqrt y j alpha sqrt y sqrt x j alpha sqrt x j alpha sqrt y 2 x y wherej z is the bessel function of order in the cases 1 2 these become after a variable change the kernels which arise when taking scaling limits in the bulk of the spectrum for the gaussian orthogonal and symplectic ensembles in particular an asymptotic expansion we derive will generalize ones found by dyson for the fredholm determinants of these kernels

correlated wishart ensembles and chaotic time series we study the correlated wishart ensembles in the context of time series analysis we are interested in the statistics of eigenlevels viz variables associated with independent eigenmodes in the system the motivation of this work is to study the effect of time series correlations on the wishart ensembles in this connection we derive the level density and the two point function for the correlated wishart ensembles by using the binary correlation method using our analytic results we analyze spectra of autocovariance matrices derived from single variable stationary time series we consider the stochastic time series of gaussian variables with exponentially decaying correlations and time series of chaotic maps viz the arnold map the standard map and the stadium billiard map in both cases correlated time series are encountered and analyzed under the framework of random matrix theory it is shown that the eigenlevel statistics for the chaotic maps follow closely those of correlated wishart ensembles it is indicated that the presence of collective modes in the spectra of autocovariance matrices is related to the integrability of the system

on the computation of two dimensional dct a new fast algorithm for the type ii two dimensional 2 d discrete cosine transform dct is presented it shows that the 2 d dct can be decomposed into cosine cosine cosine sine sine cosine and sine sine sequences that can be further decomposed into a number of similar sequences compared with other reported algorithms the proposed one achieves savings on the number of arithmetic operations and has a recursive computational structure that leads to a simplification of the input output indexing process furthermore the new algorithm supports transform sizes p sub 1 2 sup m1 spl times p sub 2 2 sup m2 where p sub 1 and p sub 2 are arbitrarily odd integers which provides a wider range of choices on transform sizes for various applications

complex wishart matrices and conductance in mesoscopic systems exact results it is noted that the hypothesis of independent random complex elements for the off diagonal blocks say m2 and m3 of the transfer matrix describing conductance in a mesoscopic wire allows the eigenvalue distribution of the matrix product m3 m3 or m2 m2 to be computed exactly exact expressions in terms of double wronskian and toeplitz determinants are derived for the distribution of the smallest and second smallest eigenvalue of this and similar random matrix products

statistical properties of random density matrices statistical properties of ensembles of random density matrices are investigated we compute traces and von neumann entropies averaged over ensembles of random density matrices distributed according to the bures measure the eigenvalues of the random density matrices are analysed we derive the eigenvalue distribution for the bures ensemble which is shown to be broader then the quarter circle distribution characteristic of the hilbert schmidt ensemble for measures induced by partial tracing over the environment we compute exactly the two point eigenvalue correlation function

exact minimum eigenvalue distribution of an entangled random pure state a recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved in fact the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems they also provide a rare exactly solvable case for the distribution of the minimum of a set of nstrongly correlated random variables for all values of n and not just for large n

gradient estimation using wide support operators one of the fastest methods of localizing edges in images is based on small gradient kernels such as sobel prewitt and roberts although small gradient kernels provide a fast way of computing the gradients they have little control over noise edge location and edge orientation they are known to be only sensitive to step edges and fail to detect smooth boundaries on the other hand large kernels provide superior noise suppression characteristics but they suffer from wide response area around edges they cause edges of neighboring objects to merge due to their wide support problems associated with large gradient kernels prevent their widespread usage this paper presents a fuzzy topology based method to facilitate the use of larger gradient kernels the new method effectively limits the response area around the edge and prevents neighboring objects to affect each other synthetic images are used to show the superior noise suppression properties and response characteristics to both step and ramp edges natural images are also used to assess the performance of the newly proposed topological gradient estimation qualitatively

a two dimensional fast cosine transform a two dimensional fast cosine transform algorithm 2 d fct is developed for 2m 2ndata points this algorithm is an extended version of the 1 d fct algorithm introduced in a recent paper but with significantly reduced computations for a 2 d field the rationale for this 2 d fct is a 2 d decomposition of data sequences into 2 d subblocks with reduced dimension halves rather than serial one dimensional separable treatment for the columns and rows of the data sets computer simulation for the 2 d fct algorithms using a smaller block of data and finite word precision proves to be excellent in comparison with the direct 2 d discrete cosine transform 2 d dct an example of a 4 4 2 d inverse fast cosine transform 2 d ifct algorithm development is presented in this paper together with a signal flow graph

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

recursion for the smallest eigenvalue density of β wishart laguerre ensemble the statistics of the smallest eigenvalue of wishart laguerre ensemble is important from several perspectives the smallest eigenvalue density is typically expressible in terms of determinants or pfaffians these results are of utmost significance in understanding the spectral behavior of wishart laguerre ensembles and among other things unveil the underlying universality aspects in the asymptotic limits however obtaining exact and explicit expressions by expanding determinants or pfaffians becomes impractical if large dimension matrices are involved for the real matrices beta 1 edelman has provided an efficient recurrence scheme to work out exact and explicit results for the smallest eigenvalue density which does not involve determinants or matrices very recently an analogous recurrence scheme has been obtained for the complex matrices beta 2 in the present work we extend this to beta wishart laguerre ensembles for the case when exponent alpha in the associated laguerre weight function lambda alpha e beta lambda 2 is a non negative integer while beta is positive real this also gives access to the smallest eigenvalue density of fixed trace beta wishart laguerre ensemble as well as moments for both cases moreover comparison with earlier results for the smallest eigenvalue density in terms of certain hypergeometric function of matrix argument results in an effective way of evaluating these explicitly exact evaluations for large values of n the matrix dimension and alpha also enable us to compare with tracy widom density and large deviation results of katzav and castillo we also use our result to obtain the density of the largest of the proper delay times which are eigenvalues of the wigner smith matrix and are relevant to the problem of quantum chaotic scattering

residual analysis for feature detection it is shown that in a very simple form residual analysis achieves results that are at least as good as if not better than those obtained by other techniques there are many ways for extensions of the method for example moving average filters of regularization can be used to obtain the residual images also the strength of the correlation measured by d sub rr o can be used to eliminate noise weak edges etc a more ambitious extension is by considering smoothing filters that leave invariant the function representing the reflectance from smooth surfaces

entanglement and localization transitions in eigenstates of interacting chaotic systems the entanglement and localization in eigenstates of strongly chaotic subsystems are studied as a function of their interaction strength excellent measures for this purpose are the von neumann entropy havrda charv at tsallis entropies and the averaged inverse participation ratio all the entropies are shown to follow a remarkably simple exponential form which describes a universal and rapid transition to nearly maximal entanglement for increasing interaction strength an unexpectedly exact relationship between the subsystem averaged inverse participation ratio and purity is derived that prescribes the transition in the localization as well

induced measures in the space of mixed quantum states we analyse several product measures in the space of mixed quantum states in particular we study measures induced by the operation of partial tracing the natural rotationally invariant measure on the set of all pure states of a n k composite system induces a unique measure in the space of n n mixed states or in the space of k k mixed states if the reduction takes place with respect to the first subsystem for k n the induced measure is equal to the hilbert schmidt measure which is shown to coincide with the measure induced by singular values of non hermitian random gaussian matrices pertaining to the ginibre ensemble we compute several averages with respect to this measure and show that the mean entanglement of n n pure states behaves as lnn 1 2

statistical distribution of quantum entanglement for a random bipartite state we compute analytically the statistics of the renyi and von neumann entropies standard measures of entanglement for a random pure state in a large bipartite quantum system the full probability distribution is computed by first mapping the problem to a random matrix model and then using a coulomb gas method we identify three different regimes in the entropy distribution which correspond to two phase transitions in the associated coulomb gas the two critical points correspond to sudden changes in the shape of the coulomb charge density the appearance of an integrable singularity at the origin for the first critical point and the detachment of the rightmost charge largest eigenvalue from the sea of the other charges at the second critical point analytical results are verified by monte carlo numerical simulations a short account of part of these results appeared recently in nadal et al phys rev lett 104 110501 2010

measuring dynamical randomness of quantum chaos by statistics of schmidt eigenvalues we study statistics of entanglement generated by quantum chaotic dynamics using an ensemble of the very large number 10 7 of quantum states obtained from the temporally evolving coupled kicked tops we verify that the estimated one body distribution of the squared schmidt eigenvalues for the quantum chaotic dynamics can agree surprisingly well with the analytical one for the universality class of the random matrices described by the fixed trace ensemble fte in order to quantify this agreement we introduce the l 1 norm of the difference between the one body distributions for the quantum chaos and fte and use it as an indicator of the dynamical randomness as we increase the scaled coupling constant the l 1 difference decreases when the effective planck constant is not small enough the decrease saturates which implies quantum suppression of dynamical randomness on the other hand when the effective planck constant is small enough the decrease of the l 1 difference continues until it is masked by statistical fluctuation due to finiteness of the ensemble furthermore we carry out two statistical analyses the 2 goodness of fit test and an autocorrelation analysis on the difference between the distributions to seek for dynamical remnants buried under the statistical fluctuation we observe that almost all fluctuating deviations are statistical however even for well developed quantum chaos unexpectedly we find a slight nonstatistical deviation near the largest schmidt eigenvalue in this way the statistics of schmidt eigenvalues enables us to measure dynamical randomness of quantum chaos with reference to the random matrix theory of fte

fast three dimensional discrete cosine transform a fast three dimensional discrete cosine transform algorithm 3d fct and a fast 3d inverse cosine transform 3d ifct algorithm are presented suitable for analysis of 3d data points many existing algorithms for three dimensional data points make use of either the 1d cosine transform or both the 2d and 1d cosine transforms existing algorithms based on the 1d discrete cosine transform dct apply the separable 1d transform to the data points in the x y and z directions respectively while those based on 2d and 1d transforms apply the 2d cosine transform for the x y planes and then the 1d cosine transform in the z direction the proposed 3d dct algorithms handle the 3d data points directly and have been shown to be computationally efficient they involve a 3d decomposition process where a data volume is recursively decomposed in each dimension until unit data cubes are obtained the algorithms are presented in the form of a signal flow graph which captures the various computations involved a complexity analysis along with empirical results is included demonstrating the performance of the proposed direct 3d dct algorithms as 3d fct and ifct are symmetric and relatively fast they can be used in any application requiring a real time symmetric codec such as video conferencing online multiparty video games and three dimensional graphics rendering

optimal edge detectors for ramp edges it is argued that the best way to model an edge is by assuming all ideal mathematical function passed through a low pass filter and and immersed in noise using techniques similar to those developed by j canny 1983 1986 and l a spacek 1986 optimal filters are derived for ramp edges of various slopes the optimal nonrecursive filter for ideal step edges is then derived as a limiting case of the filters for ramp edges because there are no step edges in images edge detection is improved when the ramp filter is used instead of the filters developed for step edges for practical purposes some convolution masks are given which can be used directly for edge detection without the need to go into the details of the subject

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

a fast 4 4 dct algorithm for the recursive 2 d dct the authors present an efficient algorithm for the computation of the 4 4 discrete cosine transform dct the algorithm is based on the decomposition of the 4 4 dct into four 4 point 1 d dcts thus only 1 d transformations and some additions are required it is shown that the proposed algorithm requires only 16 multiplications which is half the number needed for the conventional row column method since the 2 sup m 2 sup m dct can be computed using the 4 4 dct recursively for any m the proposed algorithm leads to a fast algorithm for the computation of the 2 d dct

directional filtering in edge detection two dimensional 2 d edge detection can be performed by applying a suitably selected optimal edge half filter in n directions computationally such a two dimensional n directional filter can be represented by a pair of real masks that is by one complex number matrix regardless of the number of filtering directions n specific calculations of the edge strength were conducted using a 2 d tridirectional filter based on a petrou kittler 1991 one dimensional 1 d detector optimized for the ramp edges which are characteristic of posterior eye capsule images that were used here as a test set in applications to image segmentation tridirectional filtering results in co occurrence arrays of low dimensionality

the distribution and moments of the smallest eigenvalue of a random matrix of wishart type abstract given a random rectangular m n matrix with elements from a normal distribution what is the distribution of the smallest singular value to pose an equivalent question in the language of multivariate statistics what is the distribution of the smallest eigenvalue of a matrix from the central wishart distribution in the null case we give new results giving the distribution as a simple recursion this includes the more difficult case when n m is an even integer without resorting to zonal polynomials and hypergeometric functions of matrix arguments with the recursion one can obtain exact expressions for the density and the moments of the distribution in terms of functions usually no more complicated than polynomials exponentials and at worst ordinary hypergeometric functions we further elaborate on the special cases when n m 0 1 2 and 3 and give a numerical table of the expected values for 2 m 25 and 0 n m 25

spectral statistics for the difference of two wishart matrices in this work we consider the weighted difference of two independent complex wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite dimension scenario using two distinct approaches the first derivation involves the use of unitary group integral while the second one relies on applying the derivative principle the latter relates the joint probability density of eigenvalues of a matrix drawn from a unitarily invariant ensemble to the joint probability density of its diagonal elements exact closed form expressions for an arbitrary order correlation function are also obtained and spectral densities are contrasted with monte carlo simulation results analytical results for moments as well as probabilities quantifying positivity aspects of the spectrum are also derived additionally we provide a large dimension asymptotic result for the spectral density using the stieltjes transform approach for algebraic random matrices finally we point out the relationship of these results with the corresponding results for difference of two random density matrices and obtain some explicit and closed form expressions for the spectral density and absolute mean

random bures mixed states and the distribution of their purity ensembles of random density matrices determined by various probability measures are analysed a simple and efficient algorithm to generate at random density matrices distributed according to the bures measure is proposed this procedure may serve as an initial step in performing the bayesian approach to quantum state estimation based on the bures prior we study the distribution of purity of random mixed states the moments of the distribution of purity are determined for quantum states generated with respect to the bures measure this calculation serves as an exemplary application of the deform and study approach in the theory of integrable systems leading to one of painleves transcendents

distribution of the smallest eigenvalue in the correlated wishart model wishart random matrix theory is of major importance for the analysis of correlated time series the distribution of the smallest eigenvalue for wishart correlation matrices is particularly interesting in many applications in the complex and in the real case we calculate it exactly for arbitrary empirical eigenvalues i e for fully correlated gaussian wishart ensembles to this end we derive certain dualities of matrix models in ordinary space we thereby completely avoid the otherwise unsurmountable problem of computing a highly nontrivial group integral our results are compact and much easier to handle than previous ones furthermore we obtain a new universality for the distribution of the smallest eigenvalue on the proper local scale

increasing subsequences and the hard to soft edge transition in matrix ensembles our interest is in the cumulative probabilities pr l t l for the maximum length of increasing subsequences in poissonized ensembles of random permutations random fixed point free involutions and reversed random fixed point free involutions it is shown that these probabilities are equal to the hard edge gap probability for matrix ensembles with unitary orthogonal and symplectic symmetry respectively the gap probabilities can be written as a sum over correlations for certain determinantal point processes from these expressions a proof can be given that the limiting form of pr l t l in the three cases is equal to the soft edge gap probability for matrix ensembles with unitary orthogonal and symplectic symmetry respectively thereby reclaiming theorems due to baik deift johansson and baik rains

edge and line feature extraction based on covariance models image segmentation based on contour extraction usually involves three stages of image operations feature extraction edge detection and edge linking this paper is devoted to the first stage a method to design feature extractors used to detect edges from noisy and or blurred images the method relies on a model that describes the existence of image discontinuities e g edges in terms of covariance functions the feature extractor transforms the input image into a log likelihood ratio image such an image is a good starting point of the edge detection stage since it represents a balanced trade off between signal to noise ratio and the ability to resolve detailed structures for 1 d signals the performance of the edge detector based on this feature extractor is quantitatively assessed by the so called average risk measure the results are compared with the performances of 1 d edge detectors known from literature generalizations to 2 d operators are given applications on real world images are presented showing the capability of the covariance model to build edge and line feature extractors finally it is shown that the covariance model can be coupled to a mrf model of edge configurations so as to arrive at a maximum a posteriori estimate of the edges or lines in the image

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

entanglement of random vectors we analytically calculate the average value of the ith largest schmidt coefficient for random pure quantum states schmidt coefficients i e eigenvalues of the reduced density matrix are expressed in the limit of large hilbert space size and for arbitrary bipartite splitting as an implicit function of index i

distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles the ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra it does not require the knowledge of density of states and is therefore quite convenient to compute in analyzing the spectrum of a general system the wigner surmise like results for the ratio distribution are known for the invariant classes of gaussian random matrices however for the crossover ensembles which are useful in modeling systems with partially broken symmetries corresponding results have remained unavailable so far in this work we derive exact results for the distribution and average of the ratio of two consecutive level spacings in the gaussian orthogonal to unitary crossover ensemble using a 3 3 random matrix model this crossover is useful in modeling time reversal symmetry breaking in quantum chaotic systems although based on a 3 3 matrix model our results can also be applied in the study of large spectra provided the symmetry breaking parameter facilitating the crossover is suitably scaled we substantiate this claim by considering gaussian and laguerre crossover ensembles comprising large matrices moreover we apply our result to investigate the violation of time reversal invariance in the quantum kicked rotor system

generic neighborhood operators a method that treats linear neighborhood operators within a unified framework that enables linear combinations concatenations resolution changes or rotations of operators to be treated in a canonical manner is presented various families of operators with special kinds of symmetries such as translation rotation magnification are explicitly constructed in 1 d 2 d and 3 d a concept of order is defined and finite orthonormal bases of functions closely connected with the operators of various orders are constructed linear transformations between the various representations are considered the method is based on two fundamental assumptions a decrease of resolution should not introduce spurious detail and the local operators should be self similar under changes of resolution these assumptions merely sum up the even more general need for homogeneity isotropy scale invariance and separability of independent dimensions of front end processing in the absence of a priori information

split radix algorithms for arbitrary order of polynomial time frequency transforms the polynomial time frequency transform is one of important tools for estimating the coefficients of the polynomial phase signals ppss with the maximum likelihood method the transform converts a one dimensional 1 d data sequence into a multidimensional output array from which the phase coefficients of the data sequence are estimated a prohibitive computational load is generally needed for high order polynomial phase signals although the 1 d fast fourier transform fft algorithm can be used based on the split radix concept this paper derives a fast algorithm for arbitrary order of polynomial time frequency transforms to significantly reduce the computational complexity comparisons on the computational complexity needed by various algorithms are also made to show the merits of the proposed algorithm

fast algorithm for the 3 d dct ii recently many applications for three dimensional 3 d image and video compression have been proposed using 3 d discrete cosine transforms 3 d dcts among different types of dcts the type ii dct dct ii is the most used in order to use the 3 d dcts in practical applications fast 3 d algorithms are essential therefore in this paper the 3 d vector radix decimation in frequency 3 d vr dif algorithm that calculates the 3 d dct ii directly is introduced the mathematical analysis and the implementation of the developed algorithm are presented showing that this algorithm possesses a regular structure can be implemented in place for efficient use of memory and is faster than the conventional row column frame rcf approach furthermore an application of 3 d video compression based 3 d dct ii is implemented using the 3 d new algorithm this has led to a substantial speed improvement for 3 d dct ii based compression systems and proved the validity of the developed algorithm

random pure states quantifying bipartite entanglement beyond the linear statistics we analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions n and m framing the problem in terms of random matrices with a fixed trace constraint we establish for arbitrary n m a general relation between the n point densities and the cross moments of the eigenvalues of the reduced density matrix i e the so called schmidt eigenvalues and the analogous functionals of the eigenvalues of the wishart laguerre ensemble of the random matrix theory this allows us to derive explicit expressions for two level densities and also an exact expression for the variance of von neumann entropy at finite n m then we focus on the moments e k a of the schmidt number k the reciprocal of the purity this is a random variable supported on 1 n which quantifies the number of degrees of freedom effectively contributing to the entanglement we derive a wealth of analytical results for e k a for n 2 and 3 and arbitrary m and also for square n m systems by spotting for the latter a connection with the probability p x min gue sqrt 2n that the smallest eigenvalue x min gue of an n n matrix belonging to the gaussian unitary ensemble is larger than sqrt 2n as a by product we present an exact asymptotic expansion for p x min gue sqrt 2n for finite n as our results are corroborated by numerical simulations whenever possible with excellent agreement

on optimal infinite impulse response edge detection filters the authors outline the design of an optimal computationally efficient infinite impulse response edge detection filter the optimal filter is computed based on canny s high signal to noise ratio good localization criteria and a criterion on the spurious response of the filter to noise an expression for the width of the filter which is appropriate for infinite length filters is incorporated directly in the expression for spurious responses the three criteria are maximized using the variational method and nonlinear constrained optimization the optimal filter parameters are tabulated for various values of the filter performance criteria a complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented the approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions the implementation is very simple and computationally efficient has a constant time of execution for different sizes of the operator and is readily amenable to real time hardware implementation

exact results and universal asymptotics in the laguerre random matrix ensemble for various values of the parameters in the laguerre random matrix ensemble the distribution of the smallest eigenvalue and the scaled n level distribution function are calculated exactly in terms of generalized hypergeometric functions in certain cases these functions are expressed as multidimensional integrals from which asymptotic formulas are calculated and predictions of universal behavior verified

purity distribution for bipartite random pure states analytic expressions for the probability density distribution of the linear entropy and the purity are derived for bipartite pure random quantum states the explicit distributions for a state belonging to a product of hilbert spaces of dimensions p and q are given for p 3 and any q 3 as well as for p q 4