kernels regularization and differential equations many common machine learning methods such as support vector machines or gaussian process inference make use of positive definite kernels reproducing kernel hilbert spaces gaussian processes and regularization operators in this work these objects are presented in a general unifying framework and interrelations are highlighted with this in mind we then show how linear stochastic differential equation models can be incorporated naturally into the kernel framework and vice versa many kernel machines can be interpreted in terms of differential equations we focus especially on ordinary differential equations also known as dynamical systems and it is shown that standard kernel inference algorithms are equivalent to kalman filter methods based on such models in order not to cloud qualitative insights with heavy mathematical machinery we restrict ourselves to finite domains implying that differential equations are treated via their corresponding finite difference equations

analytical inversion of symmetric tridiagonal matrices in this paper we present an analytical formula for the inversion of symmetrical tridiagonal matrices the result is of relevance to the solution of a variety of problems in mathematics and physics as an example the formula is used to derive an exact analytical solution for the one dimensional discrete poisson equation with dirichlet boundary conditions

a strongly polynomial algorithm for controlled queues we consider the problem of computing optimal policies of finite state finite action markov decision processes mdps a reduction to a continuum of constrained mdps cmdps is presented such that the optimal policies for these cmdps constitute a path in a graph defined over the deterministic policies this path contains in particular an optimal policy of the original mdp we present an algorithm based on this new approach that finds this path and thus an optimal policy in the general case this path might be exponentially long in the number of states and actions we prove that the length of this path is polynomial if the mdp satisfies a coupling property thus we obtain a strongly polynomial algorithm for mdp s that satisfies the coupling property we prove that discrete time versions of controlled m m 1 queues induce mdp s that satisfy the coupling property the only previously known polynomial algorithm for controlled m m 1 queues in the expected average cost model is based on linear programming and is not known to be strongly polynomial our algorithm works both for the discounted and expected average cost models and the running time does not depend on the discount factor

application of a nonlinear computational aeroacoustics code to the gust airfoil problem a time domain solution of the gust airfoil problem is obtained using a high accuracy computational aeroacoustics code to solve the nonlinear euler equations for computational efficiency the equations are cast in chain rule curvilinear form and a structured multiblock solver is used on a distributed memory parallel computer cluster to fully investigate the performance of this solver a test matrix of benchmark problems is computed two airfoil geometries and four gust reduced frequencies these results are compared to benchmark solutions both on the airfoil surface and in the flow domain

blind equalization of digital communication channels using high order moments the authors describe algorithms for blind equalization of digital communication channels of the quadrature amplitude modulation qam type these algorithms are based on the fourth order statistical moments of the received data sequence the first of the two is a linear least squares type algorithm the second algorithm is of the nonlinear least squares type the algorithms use the fourth order statistical moments of the symbol sequence to explicitly estimate the channel impulse response the estimated impulse response is used in turn to construct a linear mean square error equalizer the performance of this equalizer is not optimal in any sense but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large

bounds for entries of the inverse matrix of a tridiagonal matrix inequalities for the moduli of entries of the inverse matrix of a tridiagonal matrix are obtained these results are applicable to a relatively large family of matrices which occur in many branches of numerical analysis applied mathematics and engineering

regularization theory and neural networks architectures we had previously shown that regularization principles lead to approximation schemes that are equivalent to networks with one layer of hidden units called regularization networks in particular s

gaussian mixture density modeling of non gaussian source for autoregressive process a new approach is taken to model non gaussian sources of ar processes using gaussian mixture densities that are known to be effective for approximating wide varieties of probability distributions a maximum likelihood estimation algorithm is derived for estimating the ar parameters by solving a generalized normal equation and a clustering algorithm is used for estimating the parameters of gaussian mixture density of the source signals the correlation matrix of the generalized normal equation is not toeplitz but is symmetric and in general positive definite higher order statistics of skewness and kurtosis are used for identifying the source distribution as being gaussian or non gaussian and consequently determining the parameter estimation technique between the conventional method and the proposed method experiments on non gaussian source ar processes demonstrate that under high snr conditions snr spl ges 20 db the proposed algorithm outperforms the conventional ar estimation algorithm and the cumulant based algorithm by an order of magnitude reduction of average estimation errors the proposed algorithm also has very low estimation errors with short data records finally a maximum likelihood prediction method is formulated for non gaussian source ar processes that has shown potential in achieving higher efficiency signal coding than linear predictive coding

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

the caldeira leggett quantum master equation in wigner phase space continued fraction solution and application to brownian motion in periodic potentials the continued fraction method of solving classical fokker planck equations has been adapted to tackle quantum master equations of the caldeira leggett type this was done taking advantage of the phase space wigner representation of the quantum density matrix the approach differs from those in which some continued fraction expression is found for a certain quantity in that the full solution of the master equation is obtained by continued fraction methods this allows us to study in detail the effects of the environment fluctuations and dissipation on several classes of nonlinear quantum systems we apply the method to the canonical problem of quantum brownian motion in periodic potentials both for cosine and ratchet potentials lacking inversion symmetry

inversion of tridiagonal matrices this paper presents a simple algorithm for inverting nonsymmetric tridiagonal matrices that leads immediately to closed forms when they exist ukita s theorem is extended to characterize the class of matrices that have tridiagonal inverses

analytical inversion of general periodic tridiagonal matrices in this paper we present an analytical forms for the inversion of general periodic tridiagonal matrices and provide some very simple analytical forms which immediately lead to closed formulae for some special cases such as symmetric or perturbed toeplitz for both periodic and non periodic tridiagonal matrices an efficient computational algorithm for finding the inverse of any general periodic tridiagonal matrices from the analytical form is given it is suited for implementation using computer algebra systems such as maple matlab macsyma and mathematica an example is also given to illustrate the algorithm

non symbolic algorithms for the inversion of tridiagonal matrices a representation for the entries of the inverse of general tridiagonal matrices is based on the determinants of their principal submatrices it enables us to introduce through the linear recurrence relations satisfied by such determinants a simple algorithm for the entries of the inverse of any tridiagonal nonsingular matrix reduced as well as unreduced the numerical approach is preserved here without invoking the symbolic computation for tridiagonal diagonally dominant matrices a scaling transformation on the recurrences allows us to give another algorithm to avoid overflow and underflow

a fast and reliable numerical solver for general bordered k tridiagonal matrix linear equations to improve on the shortcomings observed in symbolic algorithms introduced recently for related matrices a reliable numerical solver is proposed for computing the solution of the matrix linear equation a x b the n n matrix coefficient a is a nonsingular bordered k tridiagonal matrix the particular structure of a is exploited through an incomplete or full givens reduction depending on the singularity of its associated k tridiagonal matrix then adapted back substitution and sherman morrison s formula can be applied specially the inverse of the matrix a is computed moreover for a wide range of matrices a the solution of the vector linear equation a x b can be computed in o n time numerical comparisons illustrate the results

high accuracy large step explicit runge kutta hale rk schemes for computational aeroacoustics in many realistic calculations the computational grid spacing required to resolve the mean flow gradients is much smaller than the grid spacing required to resolve the unsteady propagating waves of interest because of this the high temporal resolution provided by existing optimized time marching schemes can be excessive due to the small time step required for stability in regions of clustered grid in this work explicit fourth order accurate runge kutta time marching schemes are optimized to increase the inviscid stability limit rather than the accuracy at large time steps single and multiple step optimized schemes are developed and analyzed the resulting schemes are validated on several realistic benchmark problems

inversion of jacobi s tridiagonal matrix abstract this paper gives a simple algorithm for finding the explicit inverse of a general jacobi tridiagonal matrix a few illustrations are also provided to demonstrate the applicability of our algorithm

a reliable givens lu approach for solving opposite bordered tridiagonal linear systems abstract a fast and reliable numerical solver is proposed to handle determined opposite bordered tridiagonal linear systems a x b a precise sequence of givens rotations on the nonsingular matrix coefficient a allows us to work with a simpler linear system this equivalent system which admits always a trivial lu factorization can be solved in linear time for large order matrices of use in applications the main advantage of this solver with respect to other special algorithms proposed is its stability and risk free performance as it is checked with comparative examples its extension to manage opposite bordered tridiagonal matrix equations is straightforward

kernel optimum nearly analytical discretization kond algorithm applied to parabolic and hyperbolic equations abstract two applications of the kernel optimum nearly analytical discretization kond algorithm to the parabolic and the hyperbolic type equations are presented in detail to lead to novel numerical schemes with very high numerical accuracy it is demonstrated numerically that the two dimensional kond p scheme for the parabolic type yields much less numerical error by over 2 3 orders measured quantitatively by the root mean square deviation from analytical solutions and reduces the cpu time to about 1 5 for a common numerical accuracy compared with the conventional explicit scheme of reference it is also demonstrated numerically that the kond h scheme for the hyperbolic type yields much less diffusive error and has fairly high stability for both of the linear and the nonlinear wave propagations compared with other conventional schemes origins of numerical errors in data processing in general numerical schemes are discussed

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

radiated noise from airfoils in realistic mean flows the long term objective of the research described is to use computational aeroacoustics methodology and parallel computers to increase the understanding of broadband blade noise in a systematic progression toward simulations of completely realistic configurations and conditions some simplified problems that address the important features of the flow are investigated a two dimensional navier stokes code implemented using the message passing library and fortran 90 on the ibm sp2 is used to perform the calculations results are presented for the interaction of a vortical gust and naca airfoils including nonlinear effects the influence of gust frequency and airfoil thickness is described a multigrid method is used to obtain converged steady state solutions before the gust is introduced in a source region inside the domain

on the inverses of general tridiagonal matrices in this work the sign distribution for all inverse elements of general tridiagonal h matrices is presented in addition some computable upper and lower bounds for the entries of the inverses of diagonally dominant tridiagonal matrices are obtained based on the sign distribution these bounds greatly improve some well known results due to ostrowski 1952 23 shivakumar and ji 1996 26 nabben 1999 21 22 and recently given by peluso and politi 2001 24 peluso and popolizio 2008 25 and so forth it is also stated that the inverse of a general tridiagonal matrix may be described by 2n 2 parameters k k 2n and k k 1n 1 instead of 2n 2 ones as given by el mikkawy 2004 3 el mikkawy and karawia 2006 4 and huang and mccoll 1997 10 according to these results a new symbolic algorithm for finding the inverse of a tridiagonal matrix without imposing any restrictive conditions is presented which improves some recent results finally several applications to the preconditioning technology the numerical solution of differential equations and the birth death processes together with numerical tests are given

a finite difference frequency domain numerical scheme for the solution of the gust response problem abstract a numerical method is developed for solving subsonic flows with convected three dimensional vortical waves around lifting airfoils the first order method that is presented fully accounts for the distortion effects of the nonuniform mean flow on the convected vorticity the unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the lagrangian coordinates of the mean flow and an irrotational field whose potential satisfies a nonconstant coefficient inhomogeneous convective wave equation using an elliptic coordinate transformation the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the mach number and reduced frequency extensive comparisons are made with known solutions to unsteady vortical flow problems and it is seen that the agreement is in general very good for reduced frequencies ranging from zero to four

parameter estimation for autoregressive gaussian mixture processes the emax algorithm the problem of estimating parameters of discrete time non gaussian autoregressive ar processes is addressed the subclass of such processes considered is restricted to those whose driving noise samples are statistically independent and identically distributed according to a gaussian mixture probability density function pdf because the likelihood function for this problem is typically unbounded in the vicinity of undesirable degenerate parameter estimates the maximum likelihood approach is not fruitful hence an alternative approach is taken whereby a finite local maximum of the likelihood surface is sought this approach which is termed the quasimaximum likelihood qml approach is used to obtain estimates of the ar parameters as well as the means variances and weighting coefficients that define the gaussian mixture pdf a technique for generating solutions to the qml problem is derived using a generalized version of the expectation maximization principle this technique which is referred to as the emax algorithm is applied in four illustrative examples its performance is compared directly with that of previously proposed algorithms based on the same data model and that of conventional least squares techniques

spectra of sparse regular graphs with loops we derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary lengths the implications of our results for the structural and dynamical properties of network models are discussed by showing how loops influence the size of the spectral gap and the propensity for synchronization analytical formulas for the spectrum are obtained for specific lengths of the loops

analytical inversion of general tridiagonal matrices in this paper we give a complete analysis for general tridiagonal matrix inversion for both non block and block cases and provide some very simple analytical formulae which immediately lead to closed forms for some special cases such as symmetric or toeplitz tridiagonal matrices

efficient blind system identification of non gaussian autoregressive models with hmm modeling of the excitation we have previously proposed a blind system identification method that exploits the underlying dynamics of non gaussian signals in li and andersen blind identification of non gaussian autoregressive models for efficient analysis of speech signals proceedings of the international conference on acoustics speech and signal processing icassp may 2006 vol 1 pp i 1205 i 1208 the signal model being identified is an autoregressive ar model driven by a discrete state hidden markov process an exact expectation maximization em algorithm was derived for the joint estimation of the ar parameters and the hidden markov model hmm parameters in this paper we extend the system model by introducing an additive measurement noise the identification of the extended system model becomes much more complicated since the system output is now hidden we propose an exact em algorithm that incorporates a novel switching kalman smoother which obtains nonlinear minimum mean square error mmse estimates of the system output based on the state information given by the hmm filter the exact em algorithms for both models are obtainable only by appropriate constraints in the model design and have better convergence properties than algorithms employing generalized em algorithm or empirical iterative schemes the proposed methods also enjoy good data efficiency since only second order statistics are involved in the computation the signal models are general and suitable to numerous signals such as speech and baseband communication signals this paper describes the two system identification algorithms in an integrated form and provides supplementary results to the noise free model and new results to the extended model with applications in speech analysis and channel equalization

adjoint sensitivity formulation for discontinuous galerkin discretizations in unsteady inviscid flow problems this paper presents an unsteady discrete adjoint algorithm for high order implicit discontinuous galerkin discretizations in time dependent inviscid flow problems the major function of the adjoint approach is to obtain the sensitivity information in a time dependent functional output which in turn is used to drive an unsteady shape optimization process to deliver a minimum of the objective functional a gradient based optimization strategy is investigated in which the sensitivity derivatives of the objective functional with respect to input variables are formulated in the context of high order discontinuous galerkin discretizations while special emphasis is given to the variations and linearizations of curvilinear boundary elements implicit temporal discretizations consisting of a second order backward euler scheme and a fourth order implicit runge kutta scheme are considered exclusively in this work where the corresponding adjoint problem is required to be solved in a backward time integration manner due to the associated transpose operation two numerical examples for the unsteady shape design techniques are presented to verify the derived sensitivity formulations and to demonstrate the performance of the adjoint approach the first involves an inverse shape optimization case by matching a time dependent target pressure profile for a two dimensional periodic vortical gust impinging on a rae 2822 airfoil and the second considers minimization of the acoustic noise produced by subsonic flow over a naca0012 airfoil with a 0 03c thick blunt trailing edge

the importance of the unsteady kutta condition when modelling gust aerofoil interaction abstract the kutta condition is applied to aerofoils with sharp trailing edges to allow for viscous effects to be considered within a simplified system of equations that are inviscid this paper discusses in detail the inclusion of an unsteady kutta condition at a sharp trailing edge during gust aerofoil interaction and illustrates how the analytic solution for the far field noise generated by this interaction changes if the unsteady kutta condition is neglected or more precisely if the unsteady pressure is permitted to be singular at the trailing edge the analytic solution both with and without the unsteady kutta condition is compared with numerical results that have no imposed unsteady kutta condition importantly the results agree well only when the unsteady kutta condition is neglected in the analytic solution this paper highlights where the far field acoustics are most affected by neglecting the unsteady kutta condition for a variety of singularities that can occur in the unsteady pressure at the trailing edge and shows that results permitting different behaviour in the unsteady surface pressure at the trailing edge could give significantly different far field noise predictions even though the surface pressure elsewhere along the aerofoil surface agrees with benchmark solutions

the analytic inversion of any finite symmetric tridiagonal matrix we use the theory of orthogonal polynomials to write down explicit expressions for the polynomials of the first and second kind associated with a given infinite symmetric tridagonal matrix h the green s function is the inverse of the infinite symmetric tridiagonal matrix h zi by calculating the inverse of the finite symmetric tridiagonal matrix we can find the analytical form of the inverse of the finite symmetric tridiagonal matrix

bayesian classification with gaussian processes we consider the problem of assigning an input vector to one of m classes by predicting p c x for c 1 m for a two class problem the probability of class one given x is estimated by spl sigma y x where spl sigma y 1 1 e sup y a gaussian process prior is placed on y x and is combined with the training data to obtain predictions for new x points we provide a bayesian treatment integrating over uncertainty in y and in the parameters that control the gaussian process prior the necessary integration over y is carried out using laplace s approximation the method is generalized to multiclass problems m 2 using the softmax function we demonstrate the effectiveness of the method on a number of datasets

efficient computation of gaussian process regression for large spatial data sets by patching local gaussian processes this paper develops an efficient computational method for solving a gaussian process gp regression for large spatial data sets using a collection of suitably defined local gp regressions the conventional local gp approach first partitions a domain into multiple non overlapping local regions and then fits an independent gp regression for each local region using the training data belonging to the region two key issues with the local gp are 1 the prediction around the boundary of a local region is not as accurate as the prediction at interior of the local region and 2 two local gp regressions for two neighboring local regions produce different predictions at the boundary of the two regions creating undesirable discontinuity in the prediction we address these issues by constraining the predictions of local gp regressions sharing a common boundary to satisfy the same boundary constraints which in turn are estimated by the data the boundary constrained local gp regressions are solved by a finite element method our approach shows competitive performance when compared with several state of the art methods using two synthetic data sets and three real data sets

gaussian processes for classification mean field algorithms we derive a mean field algorithm for binary classification with gaussian processes that is based on the tap approach originally proposed in statistical physics of disordered systems the theory also yields an approximate leave one out estimator for the generalization error which is computed with no extra computational cost we show that from the tap approach it is possible to derive both a simpler naive mean field theory and support vector machines svms as limiting cases for both mean field algorithms and support vector machines simulation results for three small benchmark data sets are presented they show that one may get state of the art performance by using the leave one out estimator for model selection and the built in leave one out estimators are extremely precise when compared to the exact leave one out estimate the second result is taken as strong support for the internal consistency of the mean field approach

mimo ar system identification and blind source separation for gmm distributed sources the problem of blind source separation bss and system identification for multiple input multiple output mimo auto regressive ar mixtures is addressed in this paper two new time domain algorithms for system identification and bss are proposed based on the gaussian mixture model gmm for sources distribution both algorithms are based on the generalized expectation maximization gem method for joint estimation of the mimo ar model parameters and the gmm parameters of the sources the first algorithm is derived under the assumption of unstructured input signal statistics while the second algorithm incorporates the prior knowledge about the structure of the input signal statistics due to the statistically independent source assumption these methods are tested via simulations using synthetic and audio signals the system identification performances are tested by comparison between the state transition matrix estimation using the proposed algorithms and the well known multidimensional yule walker solution followed by an instantaneous bss method the results show that the proposed algorithms outperform the yule walker based approach the bss performances were compared to other convolutive bss methods the results show that the proposed algorithms achieve higher signal to interference ratio sir compared to the other tested methods

recursive maximum likelihood algorithm for dependent observations a recursive maximum likelihood algorithm rml is proposed that can be used when both the observations and the hidden data have continuous values and are statistically dependent between different time samples the algorithm recursively approximates the probability density functions of the observed and hidden data by analytically computing the integrals with respect to the state variables where the parameters are updated using gradient steps a full convergence proof is given based on the ordinary differential equation approach which shows that the algorithm converges to a local minimum of the kullback leibler divergence between the true and the estimated parametric probability density functions a result that is useful even for a miss specified parametric model compared to other rml algorithms proposed in the literature this contribution extends the state space model and provides a theoretical analysis in a nontrivial statistical model that was not analyzed so far we further extend the rml analysis to constrained parameter estimation problems two examples including nonlinear state space models are given to highlight this contribution

efficient computation of tridiagonal matrices largest eigenvalue abstract this paper proposes a method for a fast estimation of the largest eigenvalue of an asymmetric tridiagonal matrix the proposed method is based on the power method and the computation of the square of the original matrix the matrix square is computed through a proposed fast algorithm designed specifically for tridiagonal matrices implementations for compressed column ccs and compressed row storage crs formats are provided discussed and compared to a standard scientific library we investigate the roundoff numerical errors showing that the proposed method provides errors no greater than the usual power method we provide numerical results with simulations in c c implementation in order to demonstrate the effectiveness of the proposed method

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

graph laplacians and their convergence on random neighborhood graphs given a sample from a probability measure with support on a submanifold in euclidean space one can construct a neighborhood graph which can be seen as an approximation of the submanifold the graph laplacian of such a graph is used in several machine learning methods like semi supervised learning dimensionality reduction and clustering in this paper we determine the pointwise limit of three different graph laplacians used in the literature as the sample size increases and the neighborhood size approaches zero we show that for a uniform measure on the submanifold all graph laplacians have the same limit up to constants however in the case of a non uniform measure on the submanifold only the so called random walk graph laplacian converges to the weighted laplace beltrami operator

blind mimo ar system identification and source separation with finite alphabet in this paper a new method for system identification and blind source separation in a multiple input multiple output mimo system is proposed the mimo channel is modeled by a multi dimensional autoregressive ar system the transmitted signals are assumed to take values from a finite alphabet modeled by the gaussian mixture model gmm with infinitesimal variances the expectation maximization em algorithm for estimation of the mimo ar model parameters is derived the performance of the proposed algorithm in terms of probability of error in signal detection and root mean squared error rmse of the system parameters and system transfer function estimates is evaluated via simulations it is shown that the obtained probability of error is very close to the probability of error of the optimal algorithm which assumes known channel state information

time domain inflow boundary condition for turbulence airfoil interaction noise prediction using synthetic turbulence modeling abstract the present paper deals with development of the synthetic turbulence inflow boundary condition stibc to predict inflow broadband noise generated by interaction between turbulence and an airfoil a cascade of airfoils in the time domain the stibc is derived by combining inflow boundary conditions that have been successfully applied in external and internal computational aeroacoustics caa simulations with a synthetic turbulence model the random particle mesh rpm method based on a digital filter is used as the synthetic turbulence model gaussian and liepmann spectra are used to define the filters for turbulence energy spectra the linearized euler equations are used as governing equations to evaluate the suitability of the stibc in time domain caa simulations first the velocity correlations and energy spectra of the synthesized turbulent velocities are compared with analytic ones the comparison results reveal that the stibc can reproduce a turbulent velocity field satisfying the required statistical characteristics of turbulence particularly the liepmann filter representing a non gaussian filter is shown to be effectively described by superposing the gaussian filters each gaussian filter has a different turbulent kinetic energy and integral length scale second two inflow noise problems are numerically solved using the stibc the turbulence airfoil interaction and the turbulence a cascade of airfoils interaction problems the power spectrum of noise due to an isolated flat plate airfoil interacting with incident turbulence is predicted and its result is successfully validated against amiet s analytic model amiet 1975 4 the prediction results of the upstream and downstream acoustic power spectra from a cascade of flat plates are then compared with cheong s analytic model cheong et al 2006 30 these comparisons are also in excellent agreement on the basis of these illustrative computation results the stibc is expected to be applied to investigate more complicated inflow noise problems including the effects of non uniform mean flow nonlinear interaction and real airfoil shapes

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

on learning vector valued functions in this letter we provide a study of learning in a hilbert space of vectorvalued functions we motivate the need for extending learning theory of scalar valued functions by practical considerations and establish some basic results for learning vector valued functions that should prove useful in applications specifically we allow an output space y to be a hilbert space and we consider a reproducing kernel hilbert space of functions whose values lie in y in this setting we derive the form of the minimal norm interpolant to a finite set of data and apply it to study some regularization functionals that are important in learning theory we consider specific examples of such functionals corresponding to multiple output regularization networks and support vector machines for both regression and classification finally we provide classes of operator valued kernels of the dot product and translation invariant type

classification of digital amplitude phase modulated signals in time correlated non gaussian channels in this paper a new algorithm is proposed for the classification of digital amplitude phase modulated signals in flat fading channels with time correlated non gaussian noise the first order statistics of the additive noise is modeled by a gaussian mixture distribution and an autoregressive ar process is used to model the time correlation the proposed classifier involves the use of a whitening filter necessary to reduce the complexity of the classification process and maximum likelihood classification for the estimation of the whitening filter coefficients a new blind technique that is based on the use of a robust h filter is developed after whitening the received signal following a composite hypothesis testing approach the unknown fading and noise distribution parameters are estimated results are presented which show that when the noise process is time correlated non gaussian the proposed classifier outperforms maximum likelihood classifiers developed under the assumption that the noise process is either white non gaussian or white gaussian it is also shown that when the noise process is white gaussian the proposed classifier s performance closely approaches that of the maximum likelihood classifier developed for white gaussian noise channels

a potential theoretic method for far field sound radiation calculations abstract the far field acoustic radiation due to the interaction of upstream unsteady vortical disturbances with an airfoil in subsonic compressible flow is calculated using potential theory a kirchhoff surface is placed in the near field surrounding the airfoil and the pressure on this surface is calculated from the unsteady flow field obtained using a second order finite difference code the governing equation is reduced to the helmholtz equation in the frequency domain and the solution is written in terms of an integral over the kirchhoff surface involving the free space green s function and an unknown single layer density function the single layer density is then determined from the boundary condition on the kirchhoff surface this method is presented as an alternative to classical kirchhoff methods it has the advantage of being able to accommodate arbitrarily shaped kirchhoff surfaces and is also readily extendable to three dimensional problems numerical results are presented for thin symmetric and loaded airfoils thin airfoil results are compared to the analytical solution and thick airfoil results are checked for numerical convergence and compared to results obtained from a time domain euler solver

symbolic algorithms for the inverses of general k tridiagonal matrices two symbolic algorithms for inverting k tridiagonal matrices have been recently found by el mikkawy and atlan 2014 2015 these two algorithms are mainly based on the doolittle lu factorization of the k tridiagonal matrix in the current paper we present a new explicit analytic expression for the inverses of general tridiagonal matrices at first by using a block diagonalization technique we then relate k tridiagonal matrix inversion to tridiagonal matrix inversion meanwhile an efficient algorithm is derived for computing the inverses of nonsingular k tridiagonal matrices with the help of any algorithm for computing the inverses of tridiagonal matrices three examples are given in order to illustrate the performance and efficiency of the proposed algorithms

prefactored small stencil compact schemes abstract a new type of prefactored compact schemes is presented that obtains high order accuracy while using a very small stencil size these schemes require fewer boundary stencils and offer simpler boundary condition implementation than the existing compact schemes results are shown for linear and nonlinear 1 d benchmark problems and a 2 d linear benchmark problem boundary stencils for both exterior and interior multiblock boundaries are given and boundary condition specification is described and demonstrated

a numerical solver for general bordered tridiagonal matrix equations abstract to overcome several limitations of symbolic algorithms introduced recently for matrices of large order a fast numerical solver is proposed for the matrix linear equation a x b where the n n coefficient matrix a is a general nonsingular bordered tridiagonal matrix its sparse structure is preserved through partial givens reduction in particular the matrix inverse of a can be computed for a wide range of bordered tridiagonal linear systems a x b the solution is computed in linear time using back substitution and sherman morrison s formula numerical comparisons illustrate the results