extension of finite volume compressible flow solvers to multi dimensional variable density zero mach number flows when attempting to compute unsteady variable density flows at very small or zero mach number using a standard finite volume compressible flow solver one faces at least the following difficulties i spatial pressure variations vanish as the mach numberm

transmission of vector quantized data over a noisy channel in the transmission of vector quantized data the vector quantizer and the communication system are usually designed separately with such an approach the channel noise results in significant degradations in the performance of the vector quantizer to solve this problem we should properly create the mapping from the codebook of the quantizer to the channel signal set of the communication system this paper proposes a new approach to construct such a mapping based on the ordering property of the self organizing feature map sofm we use the neighborhood structure of the sofm and the neighborhood structure of the channel signal set to construct the mapping simulation results confirm that the proposed approach is robust with respect to channel noise

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

estimating bounds for quadratic assignment problems associated with hamming and manhattan distance matrices based on semidefinite programming quadratic assignment problems qaps with a hamming distance matrix for a hypercube or a manhattan distance matrix for a rectangular grid arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems in this paper we consider the issue of how to obtain lower bounds for those two classes of qaps based on semidefinite programming sdp by exploiting the data structure of the distance matrix b we first show that for any permutation matrix x the matrix y alpha e xbx t is positive semidefinite where alpha is a properly chosen parameter depending only on the associated graph in the underlying qap and e ee t is a rank 1 matrix whose elements have value 1 this results in a natural way to approximate the original qaps via sdp relaxation based on the matrix splitting technique our new sdp relaxations have a smaller size compared with other sdp relaxations in the literature and can be solved efficiently by most open source sdp solvers experimental results show that for the underlying qaps of size up to n 200 strong bounds can be obtained effectively

a spectral element basin model for the shallow water equations abstract a spectral element model is built for the shallow water equations in complex geometry it is proved to be an efficient computational model in solving oceanic problems in particular the equatorial rossby modon s reflection process is simulated

semi implicit extension of a godunov type scheme based on low mach number asymptotics i one dimensional flow a single scale multiple space scale asymptotic analysis provides detailed insight into the low mach number limit behavior of solutions of the compressible euler equations we use the asymptotics as a guideline for developing a low mach number extension of an explicit higher order shock capturing scheme this semi implicit scheme involves multiple pressure variables large scale differencing and averaging procedures that are discretized versions of standard operations in multiple scales asymptotic analysis advection and acoustic wave propagation are discretized explicitly and upwind and only one scalar elliptic equation is to be solved implicitly at each time step this equation is a pressure correction equation for incompressible flows when the mach number is zero in the low mach number limit the time step is restricted by a courant number based essentially on the maximum flow velocity for moderate and large mach numbers the scheme reduces to the underlying explicit higher order shock capturing algorithm

a fast learning algorithm for gabor transformation an adaptive learning approach for the computation of the coefficients of the generalized nonorthogonal 2 d gabor 1946 transform representation is introduced the algorithm uses a recursive least squares rls type algorithm the aim is to achieve minimum mean squared error for the reconstructed image from the set of the gabor coefficients the proposed rls learning offers better accuracy and faster convergence behavior when compared with the least mean squares lms based algorithms applications of this scheme in image data reduction are also demonstrated

a semi spectral primitive equation ocean circulation model using vertical sigma and orthogonal curvilinear horizontal coordinates abstract we describe a new diabatic primitive equation model for studying regional and basin scale ocean circulation processes the model features coordinate transformations that efficiently incorporate moderately irregular basin geometries and large variations in bottom topography and permits the inclusion of both thermal and wind forcing a novel semi spectral solution procedure in which the vertical structure of the model variables is represented as a finite sum of user specifiable structure functions e g chebyshev polynomials provides faster than algebraic convergence of the vertical approximation scheme model performance is assessed on a variety of test problems drawn from coastal and large scale oceanography including unforced linear wave propagation in both regular and irregular geometries non linear flow over rough bottom topography and eddy mean flow interaction in a wind driven midlatitude ocean basin computational efficiency of the model is found to be comparable to other existing primitive equation ocean models despite the utilization of the higher order spectral methods

the hadamard transform a tool for index assignment we show that the channel distortion for maximum entropy encoders due to noise on a binary symmetric channel is minimized if the vector quantizer can be expressed as a linear transform of a hypercube the index assignment problem is regarded as a problem of linearizing the vector quantizer we define classes of index assignments with related properties within which the best index assignment is found by sorting not searching two powerful algorithms for assigning indices to the codevectors of nonredundant coding systems are presented one algorithm finds the optimal solution in terms of linearity whereas the other finds a very good but suboptimal solution in a very short time

adaptive gabor transformation for image processing an algorithm that computes the gabor coefficients of an image is presented an adaptive filter that uses the complex least mean square algorithm for their computation is proposed and its numerical characteristics are discussed it is shown that the filter is stable under certain conditions because the gabor transformation seems to be an excellent tool for image compression the efficiency of information coding using the gabor coefficients is investigated and compared with coding that uses the coefficients of the discrete cosine transformation dct properties of both transformations are discussed

multirate based fast parallel algorithms for 2 d dht based real valued discrete gabor transform novel algorithms for the multirate and fast parallel implementation of the 2 d discrete hartley transform dht based real valued discrete gabor transform rdgt and its inverse transform are presented in this paper a 2 d multirate based analysis convolver bank is designed for the 2 d rdgt and a 2 d multirate based synthesis convolver bank is designed for the 2 d inverse rdgt the parallel channels in each of the two convolver banks have a unified structure and can apply the 2 d fast dht algorithm to speed up their computations the computational complexity of each parallel channel is low and is independent of the gabor oversampling rate all the 2 d rdgt coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process the computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2 d discrete gabor transforms the results indicate that the proposed algorithms are the fastest which make them attractive for real time image processing

the spectral element method for the shallow water equations on the sphere the spectral element method is implemented for the shallow water equations in spherical geometry and its performance is compared with other models this is the first step in evaluating the suitability of spectral elements for climate modeling the potential advantages and disadvantages of spectral elements over more conventional models used for climate studies are discussed the method requires that the sphere be tiled with rectangles for which we make use of the gnomonic projection to map the sphere onto the cube to measure the performance of the method relative to other models results are presented from a standard suite of shallow water test cases for the sphere these results confirm the spectral accuracy of the method

an error control scheme for transmission of vector quantization data over noisy channels this paper presents an error control scheme for transmitting vector quantized data over noisy channels first we review a self organizing feature map sofm based approach to construct the mapping from the codebook of the quantizer to the channel signal set of the communication system this approach is robust with respect to channel noise even if we do not use any error control scheme in the communication system afterwards a new trellis type quantizer namely the trellis coded kohonen 1984 map tckm is presented the design process of the tckm which is based on the neighborhood structure of sofms is simpler than that of conventional trellis coded vector quantizers tcvqs simulation results show that the performance of tckms is comparable with that of tcvqs last we introduce the error control scheme based on the concepts of the above two applications of sofms simulation results show that the proposed error control scheme is more robust with respect to channel noise the advantage of our approaches mentioned above is that the design processes of transmission systems are predefined before the construction of the codebook thus different codebooks with the same neighborhood structure can share the same design

a multiscale pressure splitting of the shallow water equations abstract direct representation of the free surface in ocean circulation models leads to a number of computational difficulties that are due to the fast time scales associated with free surface waves these fast time scales generally result in severe time step restrictions when the free surface is advanced using an explicit scheme and may result in large phase errors when the free surface is treated implicitly with a large time step a multiple scale analysis of the shallow water equations is used to analyze this stiffness and to guide the construction of a computational methodology that overcomes the associated difficulties specifically we explore a class of fractional step methods that utilize coarsened grids in the propagation of long wave data the behavior of the corresponding schemes is examined in detail in light of one dimensional model problems based on finite difference or spectral element discretizations

convergence analysis of lms filters with uncorrelated gaussian data statistical analysis of the least mean squares lms adaptive algorithm with uncorrelated gaussian data is presented exact analytical expressions for the steady state mean square error mse and the performance degradation due to weight vector misadjustment are derived necessary and sufficient conditions for the convergence of the algorithm to the optimal wiener solution within a finite variance are derived it is found that the adaptive coefficient which controls the rate of convergence of the algorithm must be restricted to an interval significantly smaller than the domain commonly stated in the literature the outcome of this paper therefore places fundamental limitations on the mse performance and rate of convergence of the lms adaptive scheme

improved semidefinite programming bounds for quadratic assignment problems with suitable symmetry semidefinite programming sdp bounds for the quadratic assignment problem qap were introduced in zhao et al j comb optim 2 71 109 1998 empirically these bounds are often quite good in practice but computationally demanding even for relatively small instances for qap instances where the data matrices have large automorphism groups these bounds can be computed more efficiently as was shown in klerk and sotirov math program a 122 2 225 246 2010 continuing in the same vein we show how one may obtain stronger bounds for qap instances where one of the data matrices has a transitive automorphism group to illustrate our approach we compute improved lower bounds for several instances from the qap library qaplib

robust vector quantization by a linear mapping of a block code in this paper we propose a novel technique for vector quantizer design where the reconstruction vectors are given by a linear mapping of a binary block code lmbc the lmbc framework provides a relation between the index bits and the reconstruction vectors through mapping properties we define a framework show its flexibility and give optimality conditions we consider source optimized vector quantization vq where the objective is to directly obtain a vq with inherent good channel robustness properties several instructive theoretical results and properties of the distortion experienced due to channel noise are demonstrated these results are used to guide the design process both optimization algorithms and a block code selection procedure are devised experimental results for gauss markov sources show that quantization performance close to an unconstrained vq is obtained with a short block code which implies a constrained vq the resulting vqs have better channel noise robustness than conventional vqs designed with the generalized lloyd algorithm gla and splitting initialization even when a post processing index assignment algorithm is applied to the gla based vq we have thus demonstrated a unique method for direct design resulting in an inherent good index assignment combined with small losses in quantization performance

a study of vector quantization for noisy channels several issues related to vector quantization for noisy channels are discussed an algorithm based on simulated annealing is developed for assigning binary codewords to the vector quantizer code vectors it is shown that this algorithm could result in dramatic performance improvements as compared to randomly selected codewords a modification of the simulated annealing algorithm for binary codeword assignment is developed for the case where the bits in the codeword are subjected to unequal error probabilities resulting from unequal levels of error protection an algorithm for the design of an optimal vector quantizer for a noisy channel is briefly discussed and its robustness under channel mismatch conditions is studied numerical results for a stationary first order gauss markov source and a binary symmetric channel are provided it is concluded that the channel optimized vector quantizer design algorithm if used carefully can result in a fairly robust system with no additional delay the case in which the communication channel is nonstationary as in mobile radio channels is studied and some preliminary ideas for quantizer design are presented

pseudo gray coding a pseudo gray code is an assignment of n bit binary indexes to 2 points in a euclidean space so that the hamming distance between two points corresponds closely to the euclidean distance pseudo gray coding provides a redundancy free error protection scheme for vector quantization vq of analog signals when the binary indexes are used as channel symbols on a discrete memoryless channel and the points are signal codevectors binary indexes are assigned to codevectors in a way that reduces the average quantization distortion introduced in the reproduced source vectors when a transmitted index is corrupted by channel noise a globally optimal solution to this problem is generally intractable due to an inherently large computational complexity a locally optimal solution the binary switching algorithm is introduced based on the objective of minimizing a useful upper bound on the average system distortion the algorithm yields a significant reduction in average distortion and converges in reasonable running times the sue of pseudo gray coding is motivated by the increasing need for low bit rate vq based encoding systems that operate on noisy channels such as in mobile radio speech communications

the generalized gabor scheme of image representation in biological and machine vision a scheme suitable for visual information representation in a combined frequency position space is investigated through image decomposition into a finite set of two dimensional gabor elementary functions gef the scheme is generalized to account for the position dependent gabor sampling rate oversampling logarithmic frequency scaling and phase quantization characteristic of the visual system comparison of reconstructed signal highlights the advantages of the generalized gabor scheme in coding typical bandlimited images it is shown that there exists a tradeoff between the number of frequency components used per position and the number of such clusters sampling rate utilized along the spatial coordinate

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

stability analysis of operator splitting for large scale ocean modeling the ocean plays a crucial role in the earth s climate system and an improved understanding of that role will be aided greatly by high resolution simulations of global ocean circulation over periods of many years for such simulations the computational requirements are extremely demanding and maximum efficiency is essential however the governing equations typically used for ocean modeling admit wave velocities having widely varying magnitudes and this situation can create serious problems with the efficiency of numerical algorithms one common approach to resolving these problems is to split the fast and slow dynamics into separate subproblems the fast motions are nearly independent of depth and it is natural to try to model these motions with a two dimensional system of equations these fast equations could be solved with an implicit time discretization or with an explicit method with short time steps the slow motions would then be modeled with a three dimensional system that is solved explicitly with long time steps that are determined by the slow wave speeds however if the splitting is inexact then the equations that model the slow motions might actually contain some fast components so the stability of explicit algorithms for the slow equations could come into doubt in this paper we discuss some general features of the operator splitting problem and we then describe an example of such a splitting and show that instability can arise in that case

minimax nonredundant channel coding the distortion of a message due to channel noise can be alleviated significantly without redundant error control bits by judicious assignment of binary indices to message symbols the nonredundant coding gain relies only on a notion of distance between symbols in this paper we consider the index assignment problem and adopt a minimax design criterion instead of the usual mean squared error mse measure the problem is found to be np hard and an effective heuristic polynomial time algorithm is presented for computing approximate solutions the minimax criterion yields greatly improved worst case performance while maintaining good average performance in addition the familiar mse criterion is shown likewise to yield an np hard index assignment task the mse problem is a special case of the classical quadratic assignment problem for which computationally and theoretically useful results are available from the discrete mathematics literature

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined