extended stochastic gradient identification algorithms for hammerstein wiener armax systems an extended stochastic gradient algorithm is developed to estimate the parameters of hammerstein wiener armax models the basic idea is to replace the unmeasurable noise terms in the information vector of the pseudo linear regression identification model with the corresponding noise estimates which are computed by the obtained parameter estimates the obtained parameter estimates of the identification model include the product terms of the parameters of the original systems two methods of separating the parameter estimates of the original parameters from the product terms are discussed the average method and the singular value decomposition method to improve the identification accuracy an extended stochastic gradient algorithm with a forgetting factor is presented the simulation results indicate that the parameter estimation errors become small by introducing the forgetting factor

parameter identification of multi input single output systems based on fir models and least squares principle by means of auxiliary models finite impulse response fir models this paper develops an identification algorithm for multi input single output stochastic systems the basic idea is to estimate the fir model parameters of each fictitious subsystem submodel with the fir model orders increasing and to use auxiliary models to predict estimate the outputs of the submodels and further to use the pade approximation method to produce the parameter estimates of submodels some simulation results are given

multi innovation least squares identification methods based on the auxiliary model for miso systems for multi input single output output error systems a difficulty in identification is that the information vector in the identification model obtained contains unknown inner intermediate variables thus the standard least squares methods cannot be applied directly in this paper we present a multi innovation least squares identification algorithm based on the auxiliary model its basic idea is to replace the unknown inner variables with their estimates computed by an auxiliary model convergence analysis indicates that the parameter estimation error converges to zero under persistent excitation the algorithm proposed has significant computational advantage over existing identification algorithms a simulation example is included

the asymptotics of a bessel kernel determinant which arises in random matrix theory in random matrix theory the local correlations of the laguerre and jacobi unitary ensemble in the hard edge scaling limit can be described in terms of the bessel kernel b x y xyj x yj y j y xj x x2 y2 x y 0 1 in particular the so called hard edge gap probabilities p r can be expressed as the fredholm determinants of the corresponding integral operator b restricted to the finite interval 0 r using operator theoretic methods we are going to compute their asymptotics as r i e we show that p r det i b l2 0 r exp r24 r 22logr g 1 2 2 where g stands for the barnes g function in fact this asymptotic formula will be proved for all complex parameters satisfying re 1

large deviations for the hbox sine _ beta and hbox sch _ tau processes the hbox sine beta process is the bulk point process limit of the gaussian beta ensemble for beta 1 2 and 4 this process gives the limit of the goe gue and gse random matrix models the hbox sch tau process is obtained similarly as the bulk scaling limit of the spectrum of certain discrete one dimensional random schrodinger operators both point processes have asymptotically constant average density in our chosen normalization one expects close to tfrac 1 2 pi lambda points in a large interval of length lambda we prove large deviation principles for the average densities of the processes identifying the rate function in both cases our approach is based on the representation of the counting functions using coupled systems of stochastic differential equations our techniques work for the full range of parameter values the results are novel even in the classical beta 1 2 and 4 cases for the hbox sine beta process they are consistent with the existing rigorous results on large gap probabilities and confirm the physical predictions made using log gas arguments

gap probability of the circular unitary ensemble with a fisher hartwig singularity and the coupled painleve v system we consider the circular unitary ensemble with a fisher hartwig singularity of both jump type and root type at z 1 a rescaling of the ensemble at the fisher hartwig singularity leads to the confluent hypergeometric kernel by studying the asymptotics of the toeplitz determinants we show that the probability of there being no eigenvalues in a symmetric arc about the singularity on the unit circle for a random matrix in the ensemble can be explicitly evaluated via an integral of the hamiltonian of the coupled painleve v system in dimension four this leads to a painleve type representation of the confluent hypergeometric kernel determinant moreover the large gap asymptotics including the constant terms are derived by evaluating the total integral of the hamiltonian in particular we reproduce the large gap asymptotics of the confluent hypergeometric kernel determinant obtained by deift krasovsky and vasilevska and the sine kernel determinant as a special case including the constant term conjectured earlier by dyson

asymptotics for the fredholm determinant of the sine kernel on a union of intervals in the bulk scaling limit of the gaussian unitary ensemble of hermitian matrices the probability that an interval of lengths contains no eigenvalues is the fredholm determinant of the sine kernel frac sin x y pi x y over this interval a formal asymptotic expansion for the determinant ass tends to infinity was obtained by dyson in this paper we replace a single interval of lengths bysj wherej is a union ofm intervals and present a proof of the asymptotics up to second order the logarithmic derivative with respect tos of the determinant equals a constant expressible in terms of hyperelliptic integrals timess plus a bounded oscillatory function ofs zero ifm 1 periodic ifm 2 and in general expressible in terms of the solution of a jacobi inversion problem pluso 1 also determined are the asymptotics of the trace of the resolvent operator which is the ratio in the same model of the probability that the set contains exactly one eigenvalue to the probability that it contains none the proofs use ideas from orthogonal polynomial theory

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

parameter identification of systems with preload nonlinearities based on the finite impulse response model and negative gradient search abstract this paper considers identification problems of a class of nonlinear systems by introducing a switching function and the finite impulse response model we obtain the identification model of a preload nonlinear system and develop a stochastic gradient algorithm to the parameters of the system furthermore a stochastic gradient algorithm with a forgetting factor is given to improve the identification accuracy a simulation results indicate that the forgetting factor can improve the parameter estimation accuracy

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

technical communique analysis of an output error identification algorithm an output error based algorithm proposed by landau and recently analysed by dugard and landau is shown to have a certain robustness property specifically it is proved that the parameters of the system transfer function can be estimated consistently with that algorithm even if the noise is not correctly modelled this fact was noticed empirically by dugard and landau but a theoretical analysis was not provided

iterative solutions of the generalized sylvester matrix equations by using the hierarchical identification principle abstract in this paper by extending the well known jacobi and gauss seidel iterations for ax b we study iterative solutions of matrix equations axb f and generalized sylvester matrix equations axb cxd f including the sylvester equation ax xb f as a special case and present a gradient based and a least squares based iterative algorithms for the solution it is proved that the iterative solution always converges to the exact solution for any initial values the basic idea is to regard the unknown matrix x to be solved as the parameters of a system to be identified and to obtain the iterative solutions by applying the hierarchical identification principle finally we test the algorithms and show their effectiveness using a numerical example

parameter estimation of dual rate stochastic systems by using an output error method in this note a new gradient based recursive algorithm for estimating parameters of dual rate sampled data systems is presented the basic idea is by using an output error method to identify the single rate models and the unknown noise free outputs true outputs directly from dual rate input output data further convergence properties of the proposed algorithm in parameter and output estimation are analyzed and the result is illustrated and tested with an experimental water level system

on iterative solutions of general coupled matrix equations in this paper we study coupled matrix equations which are encountered in many systems and control applications first we extend the well known jacobi and gauss seidel iterations and present a large family of iterative methods which are then applied to develop iterative solutions to coupled sylvester matrix equations the basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified and to obtain the iterative solutions by applying a hierarchical identification principle next we generalize the sylvester equations to general coupled matrix equations and propose a gradient based iterative algorithm for the solutions using a block matrix inner product the star star product we prove that the iterative algorithm always converges to the unique solutions for any initial values one advantage of the algorithms proposed is that they require less storage space in implementation than existing numerical methods finally we test the algorithms and show their effectiveness using numerical examples

the residual based interactive stochastic gradient algorithms for controlled moving average models this paper derives a residual based interactive stochastic gradient isg parameter estimation algorithm for controlled moving average cma models and studied the performance of the residual based isg algorithm under weaker conditions on statistical properties of the noise compared with the residual based extended stochastic gradient algorithm for identifying cma models the proposed isg algorithm can give highly accurate parameter estimates by the simulation example

performance analysis of the am sg parameter estimation for multivariable systems the auxiliary model based stochastic gradient am sg parameter estimation method is an important identification one this paper analyzes the performances of the am sg estimation algorithm for multiple input single output systems i e multivariable systems under the strong persistent excitation condition the analysis and simulation results indicate that the parameter estimation errors converge to zero

modeling and parameter identification of systems with multisegment piecewise linear characteristics this paper deals with the modeling and parameter identification of nonlinear systems having multi segment piecewise linear characteristics the decomposition of the corresponding mapping provides a new form of multi segment nonlinearity representation leading to an output equation where all the parameters to be estimated are separated hence an iterative method with internal variable estimation can be applied for parameter identification using input output data records the only required a priori knowledge of the nonlinear characteristic represents the limits for the domain partition the proposed model of given static nonlinearity is also incorporated into the hammerstein model examples of parameter identification for static and dynamic systems with multi segment piecewise linear characteristics are presented

multidimensional scaling by iterative majorization using radial basis functions abstract this paper considers the use of radial basis functions for modelling the non linear transformation of a data set obtained by a multidimensional scaling analysis this approach has two advantages over conventional nonmetric multidimensional scaling it reduces the number of parameters to estimate and it provides a transformation that may be used on an unseen test set a scheme based on iterative majorization is proposed for obtaining the parameters of the network

brief estimation of an n l n hammerstein wiener model estimation of a single input single output block oriented model is studied the model consists of a linear block embedded between two static nonlinear gains hence it is called n l n hammerstein wiener model first the model structure is motivated and the disturbance model is discussed the paper then concentrates on parameter estimation a relaxation iteration scheme is proposed by making use of a model structure in which the error is bilinear in parameters this leads to a simple algorithm which minimizes the original loss function the convergence and consistency of the algorithm are studied in order to reduce the variance error the obtained linear model is further reduced using frequency weighted model reduction simulation study will be used to illustrate the method

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

extreme gaps between eigenvalues of random matrices this paper studies the extreme gaps between eigenvalues of random matrices we give the joint limiting law of the smallest gaps for haar distributed unitary matrices and matrices from the gaussian unitary ensemble in particular the kth smallest gap normalized by a factor n 4 3 has a limiting density proportional to x3k 1e x3 concerning the largest gaps normalized by n logn they converge in lp to a constant for all p 0 these results are compared with the extreme gaps between zeros of the riemann zeta function

a latent class unfolding model for analyzing single stimulus preference ratings a multidimensional unfolding model is developed that assumes that the subjects can be clustered into a small number of homogeneous groups or classes the subjects that belong to the same group are represented by a single ideal point since it is not known in advance to which group of class a subject belongs a mixture distribution model is formulated that can be considered as a latent class model for continuous single stimulus preference ratings a gem algorithm is described for estimating the parameters in the model the m step of the algorithm is based on a majorization procedure for updating the estimates of the spatial model parameters a strategy for selecting the appropriate number of classes and the appropriate number of dimensions is proposed and fully illustrated on some artificial data the latent class unfolding model is applied to political science data concerning party preferences from members of the dutch parliament finally some possible extensions of the model are discussed

observable state space realizations for multivariable systems this paper derives two canonical state space forms i e the observer canonical form and the observability canonical form from multiple input multiple output systems described by difference equations the state space model is expressed by the first order difference equation and is equivalent to the input output representation more specifically by setting the different state variables the difference equations or the input output representations can be transformed into two observable canonical forms and the canonical state space model can be also transformed into the difference equations finally two examples are given

some identities for determinants of structured matrices abstract in this paper we establish several relations between the determinants of the following structured matrices hankel matrices symmetric toeplitz hankel matrices and toeplitz matrices using known results for the asymptotic behavior of toeplitz determinants these identities are used in order to obtain fisher hartwig type results on the asymptotics of certain skew symmetric toeplitz determinants and certain hankel determinants

hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems according to the hierarchical identification principle a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems i e multivariable oema like models which is different from multivariable carma like models as there exist unmeasurable noise free outputs and unknown noise terms in the information vector matrix of the corresponding identification model this paper is by means of the auxiliary model identification idea to replace the unmeasurable variables in the information vector matrix with the estimated residuals and the outputs of the auxiliary model a numerical example is provided

hierarchical least squares based iterative estimation algorithm for multivariable box jenkins like systems using the auxiliary model abstract this paper presents a hierarchical least squares iterative algorithm to estimate the parameters of multivariable box jenkins like systems by combining the hierarchical identification principle and the auxiliary model identification idea the key is to decompose a multivariable systems into two subsystems by using the hierarchical identification principle as there exist the unmeasurable noise free outputs and noise terms in the information vector the solution is using the auxiliary model identification idea to replace the unmeasurable variables with the outputs of the auxiliary model and the estimated residuals a numerical example is given to show the performance of the proposed algorithm

maximum likelihood stochastic gradient estimation for hammerstein systems with colored noise based on the key term separation technique this paper considers the identification problems of hammerstein finite impulse response moving average fir ma systems using the maximum likelihood principle and stochastic gradient method based on the key term separation technique in order to improve the convergence rate a maximum likelihood multi innovation stochastic gradient algorithm is presented the simulation results show that the proposed algorithms can effectively estimate the parameters of the hammerstein fir ma systems

asymptotics of the airy kernel determinant the authors use riemann hilbert methods to compute the constant that arises in the asymptotic behavior of the airy kernel determinant of random matrix theory

brief identification of linear systems with hard input nonlinearities of known structure this paper studies identification of systems with input nonlinearities of known structure for input nonlinearities parameterized by one parameter a deterministic approach is proposed based on the idea of separable least squares the identification problem is shown to be equivalent to an one dimensional minimization problem the method is very effective for several common static and nonstatic input nonlinearities for a general input nonlinearity a correlation analysis based identification algorithm is presented which is shown to be convergent

recursive identification method for miso wiener hammerstein model a simple technique for recursive identification of the wiener hammerstein model with extension to the multi input single output miso case is presented we use a new transformation of the input output difference equation where parameters to be estimated are those of each subsystem of the initial and unique realization after that a weighted extended least squares method is employed to estimate recursively and separately parameters of the linear subsystems and the static nonlinear element the convergence analysis of the proposed procedure is also studied finally a numerical example is provided to show the efficiency of the algorithm

multi innovation stochastic gradient algorithm for multiple input single output systems using the auxiliary model in order to reduce computational burden and improve the convergence rate of identification algorithms an auxiliary model based multi innovation stochastic gradient am misg algorithm is derived for the multiple input single output systems by means of the auxiliary model identification idea and multi innovation identification theory the basic idea is to replace the unknown outputs of the fictitious subsystems in the information vector with the outputs of the auxiliary models and to present an auxiliary model based stochastic gradient algorithm and then to derive the am misg algorithm by expanding the scalar innovation to innovation vector and introducing the innovation length the simulation example shows that the proposed algorithms work quite well

data filtering based recursive least squares algorithm for hammerstein systems using the key term separation principle this paper concerns parameter identification of hammerstein output error moving average systems with a two segment piecewise nonlinearity by combining the key term separation principle and the data filtering technique we transfer the hammerstein model into two regression identification models and present a data filtering based recursive least squares method to estimate the parameters of these two identification models the proposed algorithm achieves a higher computational efficiency than the standard approach by using covariance matrices of smaller dimensions from the two identification models instead of one identification model in the standard approach

dyson s constant in the asymptotics of the fredholm determinant of the sine kernel we prove that the asymptotics of the fredholm determinant of i k where k is the integral operator with the sine kernel open image in new window on the interval 0 are given by

auxiliary model based least squares identification methods for hammerstein output error systems abstract the difficulty in identification of a hammerstein a linear dynamical block following a memoryless nonlinear block nonlinear output error model is that the information vector in the identification model contains unknown variables the noise free true outputs of the system in this paper an auxiliary model based least squares identification algorithm is developed the basic idea is to replace the unknown variables by the output of an auxiliary model convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition the simulation results show the effectiveness of the proposed algorithms

hierarchical least squares identification methods for multivariable systems for multivariable discrete time systems described by transfer matrices we develop a hierarchical least squares iterative hlsi algorithm and a hierarchical least squares hls algorithm based on a hierarchical identification principle we show that the parameter estimation error given by the hlsi algorithm converges to zero for the deterministic cases and that the parameter estimates by the hls algorithm consistently converge to the true parameters for the stochastic cases the algorithms proposed have significant computational advantage over existing identification algorithms finally we test the proposed algorithms on an example and show their effectiveness

auxiliary model based rels and mi els algorithm for hammerstein oema systems this paper considers the identification problem for hammerstein output error moving average oema systems an auxiliary model based recursive extended least squares rels algorithm and an auxiliary model based multi innovation extended least squares mi els algorithm are presented using the multi innovation identification theory the basic idea is to express the system output as a linear combination of the parameters by using the key term separation principle and auxiliary model method the proposed algorithms can give highly accurate parameter estimates the simulation results show the effectiveness of the proposed algorithms

differentiability of kruskal s stress at a local minimum it is shown that kruskal s multidimensional scaling loss function is differentiable at a local minimum or to put it differently that in multidimensional scaling solutions using kruskal s stress distinct points cannot coincide

the widom dyson constant for the gap probability in random matrix theory in the bulk scaling limit for the gaussian unitary ensemble in random matrix theory the probability that there are no eigenvalues in the interval 0 2s is given by p s det i k s where k s is the trace class operator with kernel k s x y sin x y p x y acting on l 2 0 2s in the analysis of the asymptotic behavior of p s as s there is particular interest in the constant term known as the widom dyson constant we present a new derivation of this constant which can be adapted to calculate similar critical constants in other problems arising in random matrix theory

two stage least squares based iterative identification algorithm for controlled autoregressive moving average carma systems a two stage least squares based iterative two stage lsi identification algorithm is derived for controlled autoregressive moving average carma systems the basic idea is to decompose a carma system into two subsystems and to identify each subsystem respectively because the dimensions of the involved covariance matrices in each subsystem become small the proposed algorithm has a high computational efficiency the simulation results indicate that the proposed algorithm is effective

asymptotics of tracy widom distributions and the total integral of a painleve ii function the tracy widom distribution functions involve integrals of a painleve ii function starting from positive infinity in this paper we express the tracy widom distribution functions in terms of integrals starting from minus infinity there are two consequences of these new representations the first is the evaluation of the total integral of the hastings mcleod solution of the painleve ii equation the second is the evaluation of the constant term of the asymptotic expansions of the tracy widom distribution functions as the distribution parameter approaches minus infinity for the gue tracy widom distribution function this gives an alternative proof of the recent work of deift its and krasovsky the constant terms for the goe and gse tracy widom distribution functions are new

asymptotics of level spacing distributions for random matrices asymptotic formulas for the probability of finding exactly n eigenvalues in an interval of length s for large s and fixed n are given for random matrices taken from the gaussian ensembles 1 2 4 these exact results are compared with the predictions of a continuum coulomb gas model due to dyson

combined parameter and output estimation of dual rate systems using an auxiliary model for a dual rate sampled data system an auxiliary model based identification algorithm for combined parameter and output estimation is proposed the basic idea is to use an auxiliary model to estimate the unknown noise free output true output of the system and directly to identify the parameters of the underlying fast single rate model from the dual rate input output data it is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance and that the output estimates uniformly converge to the true outputs an example is included

brief parameter identification of a class of hammerstein plants we consider parameter identification of plants that can be described by a piecewise affine nonlinear element in series with linear dynamics the identification scheme is based on a suitable plant parametrization obtained by an orthogonal expansion of the nonlinearity then a persistently exciting pe input sequence is generated to ensure the convergence of the estimated model to the true one

brief a random least trimmed squares identification algorithm the least trimmed squares lts estimator is a well known robust estimator in terms of protecting the estimate from the outliers its high computational complexity is however a problem in practice in this paper we propose a random lts algorithm which has a low computational complexity that can be calculated a priori as a function of the required error bound and the confidence interval moreover if the number of data points goes to infinite the algorithm becomes a deterministic one that converges to the true lts in some probability sense

hierarchical gradient based identification of multivariable discrete time systems in this paper we use a hierarchical identification principle to study identification problems for multivariable discrete time systems we propose a hierarchical gradient iterative algorithm and a hierarchical stochastic gradient algorithm and prove that the parameter estimation errors given by the algorithms converge to zero for any initial values under persistent excitation the proposed algorithms can be applied to identification of systems involving non stationary signals and have significant computational advantage over existing identification algorithms finally we test the proposed algorithms by simulation and show their effectiveness

a generalized majorization method for least souares multidimensional scaling of pseudodistances that may be negative the usual convergence proof of the smacof algorithm model for least squares multidimensional scaling critically depends on the assumption of nonnegativity of the quantities to be fitted called the pseudodistances when this assumption is violated erratic convergence behavior is known to occur three types of circumstances in which some of the pseudodistances may become negative are outlined nonmetric multidimensional scaling with normalization on the variance metric multidimensional scaling including an additive constant and multidimensional scaling under the city block distance model a generalization of the smacof method is proposed to resolve the difficulty that is based on the same rationale frequently involved in robust fitting with least absolute residuals

on the convergence of an iterative algorithm used for hammerstein system identification an analytical counterexample to the general convergence of an interative algorithm used for identification of hammerstein systems is given numerical illustration is also included

parameter bounds for discrete time hammerstein models with bounded output errors in this note we present a two stage procedure for deriving parameters bounds in hammerstein models when the output measurement errors are bounded first using steady state input output data parameters of the nonlinear part are tightly bounded then for a given input transient sequence we evaluate tight bounds on the unmeasurable inner signal which together with noisy output measurements are used for bounding the parameters of the linear dynamic block

gradient based and least squares based iterative algorithms for matrix equations axb cxtd f abstract this paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation axb cx t d f the basic idea is to decompose the matrix equation system under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving ax b and axb f the analysis shows that when the matrix equation has a unique solution under the sense of least squares the iterative solution converges to the exact solution for any initial values a numerical example verifies the proposed theorems

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

gradient based iterative algorithms for solving a class of matrix equations in this note we apply a hierarchical identification principle to study solving the sylvester and lyapunov matrix equations in our approach we regard the unknown matrix to be solved as system parameters to be identified and present a gradient iterative algorithm for solving the equations by minimizing certain criterion functions we prove that the iterative solution consistently converges to the true solution for any initial value and illustrate that the rate of convergence of the iterative solution can be enhanced by choosing the convergence factor or step size appropriately furthermore the iterative method is extended to solve general linear matrix equations the algorithms proposed require less storage capacity than the existing numerical ones finally the algorithms are tested on computer and the results verify the theoretical findings

data visualization by multimensional scaling a deterministic annealing approach abstract multidimensional scaling addresses the problem how proximity data can be faithfully visualized as points in a low dimensional euclidean space the quality of a data embedding is measured by a stress function which compares proximity values with euclidean distances of the respective points the corresponding minimization problem is non convex and sensitive to local minima we present a novel deterministic annealing algorithm for the frequently used objective sstress and for sammon mapping derived in the framework of maximum entropy estimation experimental results demonstrate the superiority of our optimization technique compared to conventional gradient descent methods

iterative least squares solutions of coupled sylvester matrix equations abstract in this paper we present a general family of iterative methods to solve linear equations which includes the well known jacobi and gauss seidel iterations as its special cases the methods are extended to solve coupled sylvester matrix equations in our approach we regard the unknown matrices to be solved as the system parameters to be identified and propose a least squares iterative algorithm by applying a hierarchical identification principle and by introducing the block matrix inner product the star product for short we prove that the iterative solution consistently converges to the exact solution for any initial value the algorithms proposed require less storage capacity than the existing numerical ones finally the algorithms are tested on computer and the results verify the theoretical findings

random sorting networks local statistics via random matrix laws this paper finds the bulk local limit of the swap process of uniformly random sorting networks the limit object is defined through a deterministic procedure a local version of the edelman greene algorithm applied to a two dimensional determinantal point process with explicit kernel the latter describes the asymptotic joint law near 0 of the eigenvalues of the corners in the antisymmetric gaussian unitary ensemble in particular the limiting law of the first time a given swap appears in a random sorting network is identified with the limiting distribution of the closest to 0 eigenvalue in the antisymmetric gue moreover the asymptotic gap in the bulk between appearances of a given swap is the gaudin mehta law the limiting universal distribution for gaps between eigenvalues of real symmetric random matrices the proofs rely on the determinantal structure and a double contour integral representation for the kernel of random poissonized young tableaux of arbitrary shape

dyson s constants in the asymptotics of the determinants of wiener hopf hankel operators with the sine kernel let k alpha pm stand for the integral operators with the sine kernels frac sin x y pi x y pm frac sin x y pi x y acting on l2 0 dyson conjectured that the asymptotics of the fredholm determinants of i k alpha pm are given by log det i k alpha pm frac alpha 2 4 mp frac alpha 2 frac log alpha 8 frac log 2 24 pm frac log 2 4 frac 3 2 zeta 1 o 1 as in this paper we are going to give a proof of these two asymptotic formulas

compensation of the rls algorithm for output nonlinearities it is shown how the recursive least squares rls algorithm can be modified to compensate for a priori known errors of linearity in the output measurement a novel signal model is used for this purpose only the nonlinear effects are modeled by an output error model and much of the output measurements are used directly in the regression vector the main benefit with this approach is that the advantages of the rls like quick initial convergence for infinite impulse response models can be retained for small linearity errors at the same time the output nonlinearity is allowed to be noninvertible this can be important to treat for example small deadzones and also to avoid the amplification of additive measurement disturbances such amplification can result from inversion of the output nonlinearity simulations illustrate the performance of the algorithm

monodromy dependence and connection formulae for isomonodromic tau functions we discuss an extension of the jimbo miwa ueno differential 1 form to a form closed on the full space of extended monodromy data of systems of linear ordinary differential equations with rational coefficients this extension is based on the results of m bertola generalizing a previous construction by b malgrange we show how this 1 form can be used to solve a long standing problem of evaluation of the connection formulae for the isomonodromic tau functions which would include an explicit computation of the relevant constant factors we explain how this scheme works for fuchsian systems and in particular calculate the connection constant for the generic painleve vi tau function the result proves the conjectural formula for this constant proposed by iorgov lisovyy and tykhyy we also apply the method to non fuchsian systems and evaluate constant factors in the asymptotics of the painleve ii tau function

on integrals of the tronquee solutions and the associated hamiltonians for the painleve ii equation abstract we consider a family of tronquee solutions of the painleve ii equation q s 2 q s 3 s q s 2 1 2 1 2 which is characterized by the stokes multipliers s 1 e 2 i s 2 s 3 e 2 i with being a free parameter these solutions include the well known generalized hastings mcleod solution as a special case if 0 we derive asymptotics of integrals of the tronquee solutions and the associated hamiltonians over the real axis for 1 2 and 0 with the constant terms evaluated explicitly our results agree with those already known in the literature if the parameters and are chosen to be special values some applications of our results in random matrix theory are also discussed

the tunneling method for global optimization in multidimensional scaling this paper focuses on the problem of local minima of the stress function it turns out that unidimensional scaling is particularly prone to local minima whereas full dimensional scaling with euclidean distances has a local minimum that is global for intermediate dimensionality with euclidean distances it depends on the dissimilarities how severe the local minimum problem is for city block distances in any dimensionality many different local minima are found a simulation experiment is presented that indicates under what conditions local minima can be expected we introduce the tunneling method for global minimization and adjust it for multidimensional scaling with general minkowski distances the tunneling method alternates a local search step in which a local minimum is sought with a tunneling step in which a different configuration is sought with the same stress as the previous local minimum in this manner successively better local minima are obtained and experimentation so far shows that the last one is often a global minimum

parameter estimation methods for nonlinear systems this paper discusses parameter estimation problems of nonlinear system modeling two model transformation based estimation methods are proposed the basic idea is to transform a complex nonlinear optimization problem into a linear or simple nonlinear optimization problem which is easy to solve then according to the gradient search principle and the newton method a gradient based iterative algorithm and a newton iterative algorithm are derived to determine the parameters of the nonlinear systems finally a numerical example is provided

a bias corrected estimator for nonlinear systems with output error type model structures parametric identification of linear time invariant lti systems with output error oe type of noise model structures has a well established theoretical framework different algorithms like instrumental variables based approaches or prediction error methods pems have been proposed in the literature to compute a consistent parameter estimate for linear oe systems although the prediction error method provides a consistent parameter estimate also for nonlinear output error noe systems it requires to compute the solution of a nonconvex optimization problem therefore an accurate initialization of the numerical optimization algorithms is required otherwise they may get stuck in a local minimum and as a consequence the computed estimate of the system might not be accurate in this paper we propose an approach to obtain in a computationally efficient fashion a consistent parameter estimate for output error systems with polynomial nonlinearities the performance of the method is demonstrated through a simulation example

recursive identification for multi input multi output hammerstein wiener system abstractin this paper an identification method based on the recursive auxiliary variable least squares algorithm is proposed for a multi input multi output hammerstein wiener system with process noise in the proposed identification method the system is converted into the multivariate regression form under the condition that the nonlinear block in the output part is invertible then the auxiliary variable is constructed the parameters of the regression equations are identified and the system parameter matrices can be obtained by matrix composition of the parameter product matrix a theoretical analysis showed that the proposed method has uniform convergence when the process noise is white and has a finite variance the effectiveness of the proposed method is validated through the experiments

on the analysis of incomplete spectra in random matrix theory through an extension of the jimbo miwa ueno differential abstract several distribution functions in the classical unitarily invariant matrix ensembles are prime examples of isomonodromic tau functions as introduced by jimbo miwa and ueno jmu in the early 1980s 45 recent advances in the theory of tau functions 41 based on earlier works of b malgrange and m bertola have allowed to extend the original jimbo miwa ueno differential form to a 1 form closed on the full space of extended monodromy data of the underlying lax pairs this in turn has yielded a novel approach for the asymptotic evaluation of isomonodromic tau functions including the exact computation of all relevant constant factors we use this method to efficiently compute the tail asymptotics of soft edge hard edge and bulk scaled distribution and gap functions in the complex wishart ensemble provided each eigenvalue particle has been removed independently with probability 1 0 1

convergence of stochastic gradient estimation algorithm for multivariable arx like systems this paper studies the convergence of the stochastic gradient identification algorithm of multi input multi output arx like systems i e multivariable arx like systems by using the stochastic martingale theory this arx like model contains a characteristic polynomial and differs from the conventional multivariable arx system the results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions the simulation results validate the proposed convergence theorem

iterative algorithm for parameter identification of hammerstein systems with two segment nonlinearities this paper deals with parameter identification of hammerstein systems having two segment polynomial nonlinearities the application of a simple decomposition technique and using switching sequences provide a special form of a hammerstein model that is linear in parameters this model is used in an iterative algorithm enabling simultaneous estimation of all of the model parameters to demonstrate the feasibility of the identification method more illustrative examples are included

from gap probabilities in random matrix theory to eigenvalue expansions we present a method to derive asymptotics of eigenvalues for trace class integral operators acting on a single interval which belongs to the ring of integrable operators its et al 1990 int j mod phys b 4 1003 37 our emphasis lies on the behavior of the spectrum of k as and i is fixed we show that this behavior is intimately linked to the analysis of the fredholm determinant as and in a stokes type scaling regime concrete asymptotic formulae are obtained for the eigenvalues of airy and bessel kernels in random matrix theory

identification of hammerstein nonlinear armax systems two identification algorithms an iterative least squares and a recursive least squares are developed for hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by armax carma models the basic idea is to replace unmeasurable noise terms in the information vectors by their estimates and to compute the noise estimates based on the obtained parameter estimates convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition the simulation results validate the algorithms proposed

large deformations of the tracy widom distribution i non oscillatory asymptotics we analyze the left tail asymptotics of deformed tracy widom distribution functions describing the fluctuations of the largest eigenvalue in invariant random matrix ensembles after removing each soft edge eigenvalue independently with probability 1 gamma in 0 1 as gamma varies a transition from tracy widom statistics gamma 1 to classical weibull statistics gamma 0 was observed in the physics literature by bohigas et al phys rev e 79 031117 2009 we provide a description of this transition by rigorously computing the leading order left tail asymptotics of the thinned goe gue and gse tracy widom distributions in this paper we obtain the asymptotic behavior in the non oscillatory region with gamma in 0 1 fixed for the goe gue and gse distributions and gamma uparrow 1 at a controlled rate for the gue distribution this is the first step in an ongoing program to completely describe the transition between tracy widom and weibull statistics as a corollary to our results we obtain a new total integral formula involving the ablowitz segur solution to the second painleve equation