a continuous analogue of the fisher hartwig formula for piecewise continuous symbols abstract the fisher hartwig formula alluded to describes the asymptotic behavior of large toeplitz determinants generated by piecewise continuous functions the purpose of the present paper is to establish an analogue of this formula for truncated wiener hopf integral operators under the assumption that these are of the form identity plus trace operator

a higher order split step fourier parabolic equation sound propagation solution scheme a three dimensional cartesian parabolic equation model with a higher order approximation to the square root helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides the higher order approximation includes cross terms with the free space square root helmholtz operator and the medium phase speed anomaly it can be implemented with a split step fourier algorithm to solve for sound pressure in the model two idealized ocean waveguide examples are presented to demonstrate the performance of this numerical technique

local rademacher complexity for multi label learning we analyze the local rademacher complexity of empirical risk minimization based multi label learning algorithms and in doing so propose a new algorithm for multi label learning rather than using the trace norm to regularize the multi label predictor we instead minimize the tail sum of the singular values of the predictor in multi label learning benefiting from the use of the local rademacher complexity our algorithm therefore has a sharper generalization error bound compared with methods that minimize over all singular values concentrating on the tail singular values results in better recovery of the low rank structure of the multi label predictor which plays an important role in exploiting label correlations we propose a new conditional singular value thresholding algorithm to solve the resulting objective function moreover a variance control strategy is employed to reduce the variance of variables in optimization empirical studies on real world data sets validate our theoretical results and demonstrate the effectiveness of the proposed algorithm for multi label learning

riemann hilbert approach to a generalised sine kernel and applications we investigate the asymptotic behavior of a generalized sine kernel acting on a finite size interval q q we determine its asymptotic resolvent as well as the first terms in the asymptotic expansion of its fredholm determinant further we apply our results to build the resolvent of truncated wiener hopf operators generated by holomorphic symbols finally the leading asymptotics of the fredholm determinant allows us to establish the asymptotic estimates of certain oscillatory multidimensional coupled integrals that appear in the study of correlation functions of quantum integrable models

extensions of kmeans type algorithms a new clustering framework by integrating intracluster compactness and intercluster separation kmeans type clustering aims at partitioning a data set into clusters such that the objects in a cluster are compact and the objects in different clusters are well separated however most kmeans type clustering algorithms rely on only intracluster compactness while overlooking intercluster separation in this paper a series of new clustering algorithms by extending the existing kmeans type algorithms is proposed by integrating both intracluster compactness and intercluster separation first a set of new objective functions for clustering is developed based on these objective functions the corresponding updating rules for the algorithms are then derived analytically the properties and performances of these algorithms are investigated on several synthetic and real life data sets experimental studies demonstrate that our proposed algorithms outperform the state of the art kmeans type clustering algorithms with respect to four metrics accuracy randindex fscore and normal mutual information

asymptotics of toeplitz hankel and toeplitz hankel determinants with fisher hartwig singularities we study the asymptotics in n for n dimensional toeplitz determinants whose symbols possess fisher hartwig singularities on a smooth background we prove the general nondegenerate asymptotic behavior as conjectured by basor and tracy we also obtain asymptotics of hankel determinants on a nite interval as well as determinants of toeplitz hankel type our analysis is based on a study of the related system of orthogonal polynomials on the unit circle using the riemann hilbert approach

multi view intact space learning it is practical to assume that an individual view is unlikely to be sufficient for effective multi view learning therefore integration of multi view information is both valuable and necessary in this paper we propose the multi view intact space learning misl algorithm which integrates the encoded complementary information in multiple views to discover a latent intact representation of the data even though each view on its own is insufficient we show theoretically that by combing multiple views we can obtain abundant information for latent intact space learning employing the cauchy loss a technique used in statistical learning as the error measurement strengthens robustness to outliers we propose a new definition of multi view stability and then derive the generalization error bound based on multi view stability and rademacher complexity and show that the complementarity between multiple views is beneficial for the stability and generalization misl is efficiently optimized using a novel iteratively reweight residuals irr technique whose convergence is theoretically analyzed experiments on synthetic data and real world datasets demonstrate that misl is an effective and promising algorithm for practical applications

connection formulae for painleve v functions ii the d function bose gas problem abstract we continue our study of those painleve v equations which admit a one parameter family of solutions analytic at the origin and solve the global problem of connecting the 2 parameter expansion about t 0 with the 2 parameter expansion valid for t i a special case of our results is applied to the study of the one particle reduced density matrix of the one dimensional gas of impenetrable bosons we also use our results to obtain a 2 parameter connection formula for a class of painleve iii functions

leading order cross term correction of three dimensional parabolic equation models the issue of handling a leading order cross multiplied term in three dimensional 3d parabolic equation pe based models is addressed in particular numerical results obtained incorporating a leading order cross term correction in an existing 3d pe model written in cylindrical coordinates based on higher order pade approximations in both depth and azimuth and a splitting operator technique are reported note that the numerical algorithm proposed in this paper could be used in the future to update any 3d pe codes that neglect cross terms and use a splitting numerical technique the 3d penetrable wedge benchmark problem is chosen to illustrate the accuracy of the now fully wide angle enhanced 3d pe model the comparisons with a 3d reference solution based on the image source clearly show that handling the leading order cross term in the 3d pe computation is sufficient to remove the phase errors inherent to any 3d pe models that neglect cross terms in their formulations

discriminative embedded clustering a framework for grouping high dimensional data in many real applications of machine learning and data mining we are often confronted with high dimensional data how to cluster high dimensional data is still a challenging problem due to the curse of dimensionality in this paper we try to address this problem using joint dimensionality reduction and clustering different from traditional approaches that conduct dimensionality reduction and clustering in sequence we propose a novel framework referred to as discriminative embedded clustering which alternates them iteratively within this framework we are able not only to view several traditional approaches and reveal their intrinsic relationships but also to be stimulated to develop a new method we also propose an effective approach for solving the formulated nonconvex optimization problem comprehensive analyses including convergence behavior parameter determination and computational complexity together with the relationship to other related approaches are also presented plenty of experimental results on benchmark data sets illustrate that the proposed method outperforms related state of the art clustering approaches and existing joint dimensionality reduction and clustering methods

a three dimensional parabolic equation model of sound propagation using higher order operator splitting and pade approximants an alternating direction implicit adi three dimensional fluid parabolic equation solution method with enhanced accuracy is presented the method uses a square root helmholtz operator splitting algorithm that retains cross multiplied operator terms that have been previously neglected with these higher order cross terms the valid angular range of the parabolic equation solution is improved the method is tested for accuracy against an image solution in an idealized wedge problem computational efficiency improvements resulting from the adi discretization are also discussed

counting free fermions on a line a fisher hartwig asymptotic expansion for the toeplitz determinant in the double scaling limit we derive an asymptotic expansion for a wiener hopf determinant arising in the problem of counting one dimensional free fermions on a line segment at zero temperature this expansion is an extension of the result in the theory of toeplitz and wiener hopf determinants known as the generalized fisher hartwig conjecture the coefficients of this expansion are conjectured to obey certain periodicity relations which renders the expansion explicitly periodic in the counting parameter we present two methods to calculate these coefficients and verify the periodicity relations order by order the matrix riemann hilbert problem and the painleve v equation we show that the expansion coefficients are polynomials in the counting parameter and list explicitly first several coefficients

zero temperature correlation functions for the impenetrable fermion gas we calculate the long time and distance asymptotics of the one particle correlation functions in the model of impenetrable spin 1 2 fermions in 1 1 dimensions we consider the spin disordered zero temperature regime which occurs when the limit t 0 is taken at a positive chemical potential the asymptotic expressions are found from the asymptotic solution of the matrix riemann hilbert problem related to the determinant representation of the correlation functions

split step finite difference and split step lanczos algorithms for solving alternative higher order parabolic equations recently porter and jensen j acoust soc am 94 1510 1516 1993 reported on a seemingly benign propagation problem in which two wide angle split step parabolic equations pes performed poorly compared to other pes that is for a source and receiver located within a leaky surface duct anomalously high transmission losses were predicted for ranges at which the leakage energy is refracted back into the duct moreover both equations displayed greater sensitivity to the choice of reference wave number than the standard pe in this paper a new propagation operator is formulated that retains the computational efficiency of the split step algorithm but is considerably more accurate two rapid numerical solution algorithms valid in both two and three dimensions are then introduced and applied to the leaky surface duct to implement the simplest second order method a tridiagonal finite difference system of equations is solved at each range step in addition to the usual split step fourier computations higher order procedures instead involve applying the lanczos algorithm solely to the higher order terms in the wide angle expansion thereby circumventing the convergence difficulties associated with the direct lanczos evaluation of the helmholtz propagator hermansson et al ieee j light technol 10 772 776 1992

a 3 d split step fourier algorithm based on a discrete spectral representation of the propagation equation a propagation method self consistent in the discrete domain for the simulation of large distance scenarios in a 3 d inhomogeneous atmosphere is proposed first a spectral representation of the field in a discrete 3 d domain over an infinite perfect ground is introduced in cylindrical coordinates a discrete spectral propagator is then derived as in 2 d methods the inhomogeneous atmosphere is considered in the spatial domain using phase screens an explicit numerical scheme is introduced for directive sources a sectoral propagation is proposed to reduce the computation time by limiting the computation domain the method is tested by simulation scenarios involving refractive effects in both vertical and azimuthal directions the 3 d refractive effects are shown to be properly simulated

deformed graph laplacian for semisupervised learning graph laplacian has been widely exploited in traditional graph based semisupervised learning ssl algorithms to regulate the labels of examples that vary smoothly on the graph although it achieves a promising performance in both transductive and inductive learning it is not effective for handling ambiguous examples shown in fig 1 this paper introduces deformed graph laplacian dgl and presents label prediction via dgl lpdgl for ssl the local smoothness term used in lpdgl which regularizes examples and their neighbors locally is able to improve classification accuracy by properly dealing with ambiguous examples theoretical studies reveal that lpdgl obtains the globally optimal decision function and the free parameters are easy to tune the generalization bound is derived based on the robustness analysis experiments on a variety of real world data sets demonstrate that lpdgl achieves top level performance on both transductive and inductive settings by comparing it with popular ssl algorithms such as harmonic functions anchorgraph regularization linear neighborhood propagation laplacian regularized least square and laplacian support vector machine

a wide angle initial field for parabolic equation models numerical predictions of underwater sound propagation are routinely carried out by applying marching algorithms to solve parabolic equations these equations require initial field data to begin marching process for many applications a suitably normalized gaussian or sinc function of depth z is used e r robinson and d h wood j acoust soc am suppl 1 81 s10 1987 these functions however do not model correctly the vertical wavenumber kz spectrum associated with the farfield of a point source in this paper a new starting field is presented that matches the proper k variation over the full spectral aperture needed by wide angle parabolic equation models the new field in the z domain is obtained numerically via a discrete fourier transform of its bandlimited spectrum because of this efficient distribution of energy in the kz domain a larger step size z can be used than that required by the gaussian initial field h m garon j s hanna and p v rost j acoust soc am suppl

quantum fluctuations of one dimensional free fermions and fisher hartwig formula for toeplitz determinants we revisit the problem of finding the probability distribution of a fermionic number of one dimensional spinless free fermions on a segment of a given length the generating function for this probability distribution can be expressed as a determinant of a toeplitz matrix we use the recently proven generalized fisher hartwig conjecture on the asymptotic behavior of such determinants to find the generating function for the full counting statistics of fermions on a line segment unlike the method of bosonization the fisher hartwig formula correctly takes into account the discreteness of charge furthermore we numerically check the precision of the generalized fisher hartwig formula find that it has a higher precision than rigorously proven so far and conjecture the form of the next order correction to the existing formula

sce a manifold regularized set covering method for data partitioning cluster analysis plays a very important role in data analysis in these years cluster ensemble as a cluster analysis tool has drawn much attention for its robustness stability and accuracy many efforts have been done to combine different initial clustering results into a single clustering solution with better performance however they neglect the structure information of the raw data in performing the cluster ensemble in this paper we propose a structural cluster ensemble sce algorithm for data partitioning formulated as a set covering problem in particular we construct a laplacian regularized objective function to capture the structure information among clusters moreover considering the importance of the discriminative information underlying in the initial clustering results we add a discriminative constraint into our proposed objective function finally we verify the performance of the sce algorithm on both synthetic and real data sets the experimental results show the effectiveness of our proposed method sce algorithm

non equilibrium 1d many body problems and asymptotic properties of toeplitz determinants non equilibrium bosonization technique facilitates the solution of a number of important many body problems out of equilibrium including the fermi edge singularity the tunneling spectroscopy and full counting statistics of interacting fermions forming a luttinger liquid we generalize the method to non equilibrium hard core bosons tonks girardeau gas and establish interrelations between all these problems the results can be expressed in terms of fredholm determinants of the toeplitz type we analyze the long time asymptotics of such determinants using szeg and fisher hartwig theorems our analysis yields dephasing rates as well as power law scaling behavior with exponents depending not only on the interaction strength but also on the non equilibrium state of the system

a wide angle split step algorithm for the parabolic equation in this paper we describe a new wide angle parabolic equation based on an operator splitting that permits the use of a marching type fourier transform solution method the equation was first presented by feit and fleck appl opt 17 3990 3998 1978 for studying propagation within optical fibers existing computer codes which numerically solve the standard parabolic equation of ocean acoustics by the split step algorithm of tappert and hardin are easily modified to accommodate the wide angle capability of the new equation in addition since the new wide angle equation is less sensitive to the value of the reference wavenumber the effects of phase errors are greatly reduced the results of a simple error analysis indicate that improved accuracy can be achieved by the new wide angle equation for propagation conditions typical of deep ocean environments this is supported by our numerical experience a summary of which is presented in the paper for test cases where the variation of the acoustic index

comparisons of laboratory scale measurements of three dimensional acoustic propagation with solutions by a parabolic equation model in this paper laboratory scale measurements of long range across slope acoustic propagation in a three dimensional 3 d wedge like environment are compared to numerical solutions in a previous work it was shown that the experimental data contain strong 3 d effects like mode shadow zones and multiple mode arrivals in qualitative agreement with theoretical and numerical predictions in the present work the experimental data are compared with numerical solutions obtained using a fully 3 d parabolic equation based model a subspace inversion approach is used for the refinement of some of the parameters describing the model experiment the inversion procedure is implemented in a bayesian framework based on the exhaustive search over the parameter space the comparisons are performed both in the time and in the frequency domain using the maximum a posteriori estimates of the refined parameters as input in the 3 d model a very good quantitative agreement is achieved between the numerical predictions provided by the 3 d parabolic equation model and the experimental data

the fisher hartwig conjecture and generalizations abstract we discuss the status of the fisher hartwig conjecture concerning the asymptotic expansion of a class of toeplitz determinants with singular generating functions a counterexample is given for a nonrational generating function and we formulate a generalized fisher hartwig conjecture

operator valued riemann hilbert problem for correlation functions of the xxz spin chain the generating functional of correlation functions for the xxz spin chain is considered in the thermodynamic limit we derive a system of integro difference equations that prescribe this functional on the basis of this system we establish the operator valued riemann hilbert problem for correlation functions of the xxz spin chain

ensemble clustering by means of clustering embedding in vector spaces ensemble clustering is a recently evolving research direction in cluster analysis and has found several different application domains in this work the complex ensemble clustering problem is reduced to the well known euclidean median problem by clustering embedding in vector spaces the euclidean median problem is solved by the weiszfeld algorithm and an inverse transformation maps the euclidean median back into the clustering domain in the experiment study different evaluation strategies are considered the proposed embedding strategy is compared to several state of art ensemble clustering algorithms and demonstrates superior performance highlightsthis paper presents a novel approach to solving the ensemble clustering problem an embedding method successful for strings and graphs is adapted to clusterings an extensive experiment study is presented the proposed method is superior to several state of the art related algorithms

successive overrelaxation for laplacian support vector machine semisupervised learning ssl problem which makes use of both a large amount of cheap unlabeled data and a few unlabeled data for training in the last few years has attracted amounts of attention in machine learning and data mining exploiting the manifold regularization mr belkin et al proposed a new semisupervised classification algorithm laplacian support vector machines lapsvms and have shown the state of the art performance in ssl field to further improve the lapsvms we proposed a fast laplacian svm flapsvm solver for classification compared with the standard lapsvm our method has several improved advantages as follows 1 flapsvm does not need to deal with the extra matrix and burden the computations related to the variable switching which make it more suitable for large scale problems 2 flapsvm s dual problem has the same elegant formulation as that of standard svms this means that the kernel trick can be applied directly into the optimization model and 3 flapsvm can be effectively solved by successive overrelaxation technology which converges linearly to a solution and can process very large data sets that need not reside in memory in practice combining the strategies of random scheduling of subproblem and two stopping conditions the computing speed of flapsvm is rigidly quicker to that of lapsvm and it is a valid alternative to plapsvm

large time and distance asymptotics of field correlation function of impenetrable bosons at finite temperature abstract asymptotics of the temperature time dependent correlation function of two fields one dimensional bosons with infinite point like repulsion is calculated

a higher order tangent linear parabolic equation solution of three dimensional sound propagation a higher order square root operator splitting algorithm is employed to derive a tangent linear solution for the three dimensional parabolic wave equation due to small variations of the sound speed in the medium the solution shown in this paper unifies other solutions obtained from less accurate approximations examples of three dimensional acoustic ducts are presented to demonstrate the accuracy of the solution future work on the applications of associated adjoint models for acoustic inversions is proposed and discussed

toeplitz and wiener hopf determinants with piecewise continuous symbols abstract the asymptotics for determinants of toeplitz and wiener hopf operators with piecewise continuous symbols are obtained in this paper if w is the wiener hopf operator defined on l2 0 with piecewise continuous symbol having a finite number of discontinuities at r then under appropriate conditions it is shown that det w g r2k where g exp log 0 r 1 2 log r r and k is a completely determined constant an analogous result is obtained for toeplitz operators the main point of the paper is to obtain a result in the wiener hopf case since the toeplitz case had been treated earlier in the toeplitz case it was discovered that one could obtain asymptotics fairly easily for symbols with several singularities if for each singularity one could find a single example of a symbol with a singularity of that kind whose associated asymptotics were known fortunately in the toeplitz case such asymptotics were known the difficulty in the wiener hopf case is that there was not a single singular case where the determinant was explicitly known this problem was overcome by using the fact that wiener hopf determinants when discretized become toeplitz determinants whose entries depend on the size of the matrix no theorem on toeplitz matrices can be applied directly but these theorems are modified to obtain the desired results

asymptotics of toeplitz determinants and the emptiness formation probability for the xy spin chain we study an asymptotic behaviour of a special correlator known as the emptiness formation probability efp for the one dimensional anisotropic xy spin 1 2 chain in a transverse magnetic field this correlator is essentially the probability of formation of a ferromagnetic string of length n in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models for the xy spin chain the correlator can be expressed as the determinant of a toeplitz matrix and its asymptotical behaviours for n throughout the phase diagram are obtained using known theorems and conjectures on toeplitz determinants we find that the decay is exponential everywhere in the phase diagram of the xy model except on the critical lines i e where the spectrum is gapless in these cases a power law prefactor with a universal exponent arises in addition to an exponential or gaussian decay the latter gaussian behaviour holds on the critical line corresponding to the isotropic xy model while at the critical value of the magnetic field the efp decays exponentially at small anisotropy one has a crossover from the gaussian to the exponential behaviour we study this crossover using the bosonization approach