an iterative algorithm for computing mean first passage times of markov chains abstract mean first passage times are an essential ingredient in both the theory and the applications of markov chains in the literature they have been expressed in elegant closed form formulas these formulas involve explicit full matrix inversions and if computed directly may incur numerical instability in this paper we present a new iterative algorithm for computing mean first passage times in a manner that does not rely on explicit full matrix inversions results regarding the convergence behavior of this algorithm are also developed

spherical prediction variance properties of central composite and box behnken designs for quadratic regression on the hypercube a single number criterion such as a g efficiency that is based on the prediction variance is often included as one of the criteria when selecting a response surface design as an alternative to the single number criterion approach the variance dispersion graph presented by giovannitti jensen and myers is a graphical technique for evaluating prediction variance properties throughout the experimental region three properties of interest are the maximum minimum and average spherical prediction variances given the spherical radius as an alternative to the computer based approach requiring an optimization algorithm to evaluate these properties the maximum minimum and spherical prediction variances for central composite and box behnken designs can be determined analytically and are functions only of the radius and the design parameters these functions yield the exact values of the spherical prediction variance properties of central composite and box behnke

basic soules matrices and their applications abstract in this paper we study the properties of the basic soules matrices in r n n which are a special subclass of the n n soules matrices generated via the basic soules basis the basic soules basis has the sign pattern n and it corresponds to the vector e n r n of all 1 s the basic soules matrices are up to a multiple by a positive scalar symmetric and doubly stochastic we begin by investigating the permanents of basic soules matrices next for a nonsingular basic soules matrix a r n n we show that the matrix a a 1 which is known to be a nonsingular m matrix has a basic soules basis of eigenvectors furthermore we obtain explicit formulas for the eigenvalues of a a 1 in terms of the eigenvalues of a finally let a r n n be a basic soules matrix of spectral radius 1 and set q i a by investigating the sign pattern of the off diagonal entries of the group inverse q of q we determine when the perron root is a concave function in each of the off diagonal entries at a

multiple comparisons with a control in response surface methodology quadratic response surface methodology often focuses on finding the levels of some coded predictor variables x x l x 2 x k that optimize the expected value of a response variable y typically the experimenter starts from some best guess or control combination of the predictors usually coded to x 0 and performs an experiment varying them in a region around this center point the question of interest addressed here is whether any x in the experimental region provides an e y preferable to that of the control and if so by what amount this article approaches the question via simultaneous confidence intervals for e y x e y 0 for all x within a specified distance of 0 exact results for the quadratic regression case k 1 are obtained using existing results for linear regression a conservative solution for rotatable designs in k 1 predictors is obtained using a result of casella and strawderman several examples are provided

a large sample confidence region useful in characterizing the stationary point of a quadratic response surface a second order response surface model is often used to approximate the relationship between a response variable and a set of explanatory variables the nature of the stationary point of the surface can be determined by considering the eigenvalues of the matrix of the model s second order terms since the elements of this matrix are estimated from the data however it follows that the eigenvalues are random variables hence the sampling properties of these eigenvalues should be considered in characterizing the nature of the stationary point in this article it is shown how a confidence region around these eigenvalues can be used to aid in the characterization of the stationary point and in an improved ridge analysis of the response surface the delta method is used to construct an approximate confidence region for these eigenvalues box and draper 1987 gave a result that simplifies the calculation of such a confidence region for rotatable or nearly rotatable designs a simulation study was performed to

a reordering for the pagerank problem we describe a reordering particularly suited to the pagerank problem which reduces the computation of the pagerank vector to that of solving a much smaller system and then using forward substitution to get the full solution vector we compare the theoretical rates of convergence of the original pagerank algorithm to that of the new reordered pagerank algorithm showing that the new algorithm can do no worse than the original algorithm we present results of an experimental comparison on five datasets which demonstrate that the reordered pagerank algorithm can provide a speedup of as much as a factor of 6 we also note potential additional benefits that result from the proposed reordering

a measure of rotatability for response surface designs a measure that quantifies the amount of rotatability in a given response surface design is introduced in this article the measure which is expressible as a percentage takes the value 100 if and only if the design is rotatable one of the main advantages of this measure is that it can be used to repair a nonrotatable design by the addition of experimental runs that maximize the percent rotatability over a spherical region of interest four numerical examples are given to illustrate the applications of this measure

on single and double soules matrices abstract until now the concept of a soules basis matrix of sign pattern n consisted of an orthogonal matrix r r n n generated in a certain way from a positive n vector which has the property that for any diagonal matrix diag 1 n with 1 n 0 the symmetric matrix a r r t has nonnegative entries only in the present paper we introduce the notion of a pair of double soules basis matrices of sign pattern n which is a pair of matrices p q each in r n n which are not necessarily orthogonal and which are generated in a certain way from two positive vectors but such that pq t i and such that for any of the aforementioned diagonal matrices the matrix a p q t also has nonnegative entries only we investigate the interesting properties which such matrices a have as a preamble to the above investigation we show that the iterates a k r k r k t generated in the course of the qr algorithm when it is applied to a r r t where r is a soules basis matrix of sign pattern n are again symmetric matrices generated by the soules basis matrices r k of sign pattern n which are themselves modified as the algorithm progresses our work here extends earlier works by soules and elsner et al

transfer matrix renormalization group method for general markov random fields abstract we seek the numerical calculation of partition functions of general markov random fields mrfs on an infinitely long twisted cylindrical lattice by using the transfer matrix renormalization group tmrg method the tmrg is a variant of the density matrix renormalization group dmrg which automatically truncates the hilbert space so that the properties of large systems can be precisely calculated while the dimension of the renormalized hilbert space remains constant we apply the tmrg to the decimation of the fundamental transfer matrix that we have proposed previously for general mrfs instead of the standard s e scheme for tmrg we propose a new e s e scheme and propose an alternative method for selecting the renormalized basis specifically the new e s e scheme keeps those singular value decomposition svd components of the fundamental transfer matrix that are relevant for the perron state and truncates the other irrelevant ones results for the ising model show that our method exhibits very impressive accuracy under a rather restricted computational resource simulations for another four general mrfs demonstrate that our tmrg method is superior to the classical monte carlo method in accuracy computational speed and in the possibility of treating a much larger system

perron eigenvector of the tsetlin matrix abstract we consider the move to position k linear search scheme where the sequence of record requests is a markov chain formulas are derived for the stationary distribution of the permutation chain for k 1 2 n 1 and n where n is the number of records certain identities for the perron complement are established in the process

simplifying multivariate second order response surfaces by fitting constrained models using automatic differentiation multivariate regression models for second order polynomial response surfaces are proposed the fitted surfaces for each response variable are constrained so that when expressed in their canonical forms they have features in common such as common stationary points or common sets of eigenvectors this can greatly reduce the number of parameters required and make the set of surfaces easier to interpret together at the cost of a greater computational burden however the use of automatic differentiation within the package matlab is shown to be easy and to reduce this burden considerably we describe the models and how to fit them and derive standard errors and report a small simulation study and an application to a dataset

conditional and unconditional cramer rao bounds for near field source localization near field source localization problem by a passive antenna array makes the assumption that the time varying sources are located near the antenna in this context the far field assumption i e planar wavefront is of course no longer valid and one has to consider a more complicated model parameterized by the bearing as in the far field case and by the distance named range between the source and a reference coordinate system one can find a plethora of estimation schemes in the literature but their ultimate performance in terms of mean square error mse have not been fully investigated to characterize these performance the cramer rao bound crb is a popular mathematical tool in signal processing the main cause for this is that the mse of several high resolution direction of arrival algorithms are known to achieve the crb under quite general weak conditions in this correspondence we derive and analyze the so called conditional and unconditional crbs for a single time varying near field source in each case we obtain non matrix closed form expressions our approach has two advantages i due to the fact that one has to inverse the fisher information matrix the computational cost for a large number of snapshots in the case of the conditional crb and or for a large number of sensors in the case of the unconditional crb of a matrix based crb can be high while our approach is low and ii some useful information can be deduced from the behavior of the bound in particular an explicit relationship between the conditional and the unconditional crbs is provided and one shows that closer is the source from the array and or higher is the signal carrier frequency better is the range estimation

a covariance approximation method for near field direction finding using a uniform linear array most narrowband high resolution bearing estimation algorithms were proposed based on the assumption of a far field source environment when this assumption is violated i e some sources are in the near field these algorithms generally provide unsatisfactory performances a new algorithm is proposed to handle this near field problem using a uniform linear array the received signal covariance matrix for near field sources is viewed as a corrupted measurement of the ideal signal covariance matrix for far field sources located at the same bearings taking this viewpoint the authors reconstruct a far field approximation ffa covariance matrix from the received covariance matrix to reduce the corruptions therefore existing high resolution bearing estimation techniques can be directly applied to estimate the bearings of the near field sources the properties of the proposed approach are investigated in detail simulation results demonstrating the effectiveness of this approach are included

performance analysis of higher order esprit for localization of near field sources most existing array processing techniques for estimating the directions of arrival doas or signal copy rely heavily on the plane wave assumption of far field sources when the sources are located relatively close to the array these techniques may no longer perform satisfactorily in this paper we present an asymptotic performance analysis of an esprit like method for passive localization of nearfield sources the algorithm which is based on fourth order cumulants is formulated for observations collected from a single uniformly spaced linear array we examine the least squares version of the algorithm and derive the expressions for the asymptotic variance of the estimated doas relative to a reference sensor and estimated ranges of the sources we also derive an algorithm independent bound on the asymptotic variance of the estimated parameters this bound can be used as a measure against the theoretically predicted algorithmic performance some insight into the achievable performance of this algorithm is obtained by numerical evaluation of the bound for several test cases of interest and the results are compared with those obtained by numerical evaluation of the theoretically predicted performance monte carlo simulations are used to verify the theoretical analysis

bounds for the perron root of nonnegative matrices and spectral radius of iteration matrices abstract new bounds for the perron root a of a nonnegative matrix a are proposed we prove that min 1 i n r i a b r i b a max 1 i n r i a b r i b where b is an arbitrary matrix with row sums r i b k b i k 0 i 1 n the bounds of h minc 1 and shulin liu 6 are both special cases of this result and based on this result we also get some bounds for the spectral radius of iteration matrices

inequalities for permanents involving perron complements abstract let a r n n and let and be nonempty complementary subsets of 1 n of increasing integers for a we define the generalized perron complement of a in a at as the matrix p a a a a i a 1 a for the classes of the nonnegative matrices and of the positive semidefinite matrices we study the relationship between the permanents of the whole matrices and the permanents of their perron complement our conditions which hold in many cases of interest are such that the value of the permanent increases as we pass from the whole matrix to its generalized perron complement for nonnegative and irreducible matrices we also study the relationship between the maximum circuit geometric mean of the entire matrix and the maximum circuit geometric mean of its perron complements

efficient application of music algorithm under the coexistence of far field and near field sources this correspondence is concerned with source localization and classification for scenarios where both the far field and near field narrowband sources may coexist we propose an efficient music based solution that requires neither a multidimensional search nor high order statistics hos we also derive the stochastic cramer rao bound crb for the problem under consideration the performance of the proposed method is compared with an existing method and with the crb

standard errors for the multiple roots in quadratic response surface models in this article we develop the asymptotic distribution for the eigenvalues of a quadratic response surface by using the result of eaton and tyler to extend the results of carter chinchilli and campbell and bisgaard and ankenman to the case including nondistinct eigenvalues in particular we suggest a method for estimating the confidence regions for multiple roots

i optimal design of mixture experiments abstractin mixture experiments the factors under study are proportions of the ingredients of a mixture the special nature of the factors necessitates specific types of regression models and specific types of experimental designs although mixture experiments usually are intended to predict the response s for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients little research has been done concerning their i optimal design this is surprising given that i optimal designs minimize the average variance of prediction and therefore seem more appropriate for mixture experiments than the commonly used d optimal designs which focus on a precise model estimation rather than precise predictions in this article we provide the first detailed overview of the literature on the i optimal design of mixture experiments and identify several contradictions for the second order and the special cubic model we present continuous i optimal designs and contrast the

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

on perron complements of inverse n0 matrices abstract in this paper we show that the perron complements of irreducible n 0 matrices are n 0 matrices we also demonstrate the perron complements of irreducible inverse n 0 matrices are inverse n 0 matrices with a little restriction in addition we give some related inequalities about inverse n 0 matrices

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

threshold conditions for sis epidemic models on edge weighted networks abstract we consider the disease dynamics of a susceptible infected susceptible model in weighted random and regular networks by using the pairwise approximation we build an edge based compartment model from which the condition of epidemic outbreak is obtained our results suggest that there exists a remarkable difference between the linear and nonlinear transmission rate for a linear transmission rate the epidemic threshold is completely determined by the mean weight which is different from the susceptible infected recovered model framework while for a nonlinear transmission rate the epidemic threshold is not only related to the mean weight but also closely related to the heterogeneity of weight distribution

graphical tools for assessing the sensitivity of response surface designs to model misspecification when comparing different designs for an experiment optimality criteria and other measures often depend on the correctness of the assumed model in this article we develop and illustrate an approach for comparing designs given the potential effect of bias due to an underspecified model we illustrate this approach using graphical summaries of the expected mean squared error emse that allow assessment of the robustness of designs to model misspecification for response surface designs in cuboidal regions the excellent performance of the central composite designs when the quadratic model is correct is tempered when bias is present the box behnken designs demonstrate superiority in the presence of missing cubic terms for a screening design scenario the amount of bias present leads to different conclusions as to which design is best

passive localization of near field sources with a polarization sensitive array the least squares virtual esprit algorithm ls vespa is extended to jointly estimate the direction of arrival doa and ranges of multiple near field sources impinging on an array of crossed dipoles the algorithm utilizes fourth order cumulants for direct estimation of the arrival angle and range parameters via the eigenvalues of certain constructed matrices compared with several existing algorithms the loss of array aperture is effectively avoided as a result the proposed method can estimate doas and ranges of n 1 polarized near field sources using n dual polarization sensors simulation results show that the proposed method outperforms a fourth order statistics based esprit like method

inverse m matrices ii this is an update of the 1981 survey by the first author in the meantime a considerable amount has been learned about the very special structure of the important class of inverse m matrices developments since the earlier survey are emphasized but we have tried to be somewhat complete and some results have not previously been published some proofs are given where appropriate and references are given for others after some elementary preliminaries results are grouped by certain natural categories

uncoupling the perron eigenvector problem abstract for a nonnegative irreducible matrix a with spectral radius this paper is concerned with the determination of the unique normalized perron vector which satisfies a 62 0 j j 1 it is explained how to uncouple a large matrix a into two or more smaller matrices say p 11 p 22 p kk such that this sequence of smaller matrices has the following properties 1 each p ii is also nonnegative and irreducible so that each pii has a unique perron vector i 2 each pii has the same spectral radius as a 3 it is possible to determine the i s completely independently of each other so that one can execute the computation of the i s parallel 4 it is easy to couple the smaller perron vectors i back together in order to produce the perron vector for the original matrix a

a optimality for regression designs abstract use is made of a result of horn amer j math 76 1954 620 630 on the existence of a symmetric matrix with prescribed diagonal elements and eigenvalues a necessary and sufficient condition is then given for the existence of an a optimal design for a regression experiment in the dorogovcev selected transl math statist probab 10 1971 35 41 setting

some closer bounds of perron root basing on generalized perron complement this paper is concerned with the bounds of the perron root r a of a nonnegative irreducible matrix a two new methods utilizing the relationship between the perron root of a nonnegative irreducible matrix and its generalized perron complements are presented the former method is efficient because it gives the bounds for r a only by calculating the row sums of the generalized perron complement p t a a a or even the row sums of submatrices a a a b a a b and a b a and the latter gives the closest bounds just in this paper of r a the results obtained by these methods largely improve the classical bounds numerical examples are given to illustrate the procedure and compare it with others which shows that these methods are effective

enhanced puma for direction of arrival estimation and its performance analysis direction of arrival doa estimation is a problem of significance in many applications in practice due to the occurrence of coherent signals and or when the number of available snapshots is small it is a challenge to find doas accurately this problem is revisited here through a new enhanced principal singular vector utilization for modal analysis epuma doa estimation approach which improves the threshold performance by first generating p k doa candidates for k sources where p geq k and then judiciously selecting k of them the asymptotic variance of epuma is theoretically derived and numerical results are provided to validate the asymptotic analysis and illustrate the practical merits of epuma

maximum likelihood source localization and unknown sensor location estimation for wideband signals in the near field in this paper we derive the maximum likelihood ml location estimator for wideband sources in the near field of the sensor array the ml estimator is optimized in a single step as opposed to other estimators that are optimized separately in relative time delay and source location estimations for the multisource case we propose and demonstrate an efficient alternating projection procedure based on sequential iterative search on single source parameters the proposed algorithm is shown to yield superior performance over other suboptimal techniques including the wideband music and the two step least squares methods and is efficient with respect to the derived cramer rao bound crb from the crb analysis we find that better source location estimates can be obtained for high frequency signals than low frequency signals in addition large range estimation error results when the source signal is unknown but such unknown parameter does not have much impact on angle estimation in some applications the locations of some sensors may be unknown and must be estimated the proposed method is extended to estimate the range from a source to an unknown sensor location after a number of source location frames the location of the uncalibrated sensor can be determined based on a least squares unknown sensor location estimator

estimating the bearings of near field cyclostationary signals by exploiting favorable characteristics of a uniform linear array ula the far field approximation ffa method reduces the deterioration of most high resolution bearing estimation techniques due to the invalidity of the planar wavefront assumption when near field sources exist we first present a new technique that provides better performance than existing bearing estimation techniques for cyclostationary signals then the proposed technique incorporating with the ffa method is proposed to estimate signal bearings in the presence of near field sources without revising the planar wavefront assumption several simulation examples confirm the theoretical work and show the effectiveness of the proposed technique

asymptotic performance analysis of direction finding algorithms based on fourth order cumulants in the narrow band array processing context the use of higher order statistics has been often advocated because consistent and asymptotically unbiased parameter estimates can be obtained without it being necessary to know to model or to estimate the spatial covariance of the noise as long as it is normally distributed however experimentation shows that this noise insensitivity is traded for increased variability of the parameter estimates the main purpose of this contribution is to derive and work out closed form expressions of the asymptotic covariance of music like direction of arrival estimates based on two fourth order cumulant matrices the diagonal slice and the contracted quadricovariance this is compared with the standard covariance based music estimate establishing on a rational basis the domain of applicability of higher order statistics for doa estimation in particular the actual impact of the noise variance and of the dynamic range of the sources is investigated this asymptotic performance analysis is achieved within a general framework which we believe to be of general interest

graphical assessment of the prediction capability of response surface designs measures of the quality of prediction at locations on the surface of a hyperspherc are presented these measures are used to form a graphical method of assessing the overall prediction capability of an experimental design throughout the region of interest a plot of the spherical variance and the maximum and minimum prediction variances for locations on a sphere against the radius of the sphere a vuriance dispersion graph is used to give a comprehensive picture of the behavior of the prediction variances throughout a region and hence of the quality of the predicted responses obtained with a particular design such plots are used to investigate and compare the prediction capabilities of certain response surface designs currently available to the researcher

comparison of design optimality criteria of reduced models for response surface designs in the hypercube results from the comparison of d g and a efficiencies and the scaled average prediction variance iv criterion are presented for the central composite small composite notz hoke box draper and computer generated designs these design optimality criteria are evaluated over the cuboidal design region for three four and five design variables

on perron complements of totally nonnegative matrices abstract an n n matrix is called totally nonnegative if every minor of a is nonnegative the problem of interest is to describe the perron complement of a principal submatrix of an irreducible totally nonnegative matrix we show that the perron complement of a totally nonnegative matrix is totally nonnegative only if the complementary index set is based on consecutive indices we also demonstrate a quotient formula for perron complements analogous to the so called quotient formula for schur complements and verify an ordering between the perron complement and schur complement of totally nonnegative matrices when the perron complement is totally nonnegative

confidence intervals and an improved ridge analysis of response surfaces the user of rsm techniques gains considerable insight into the nature of the stationary point and the nature of the underlying response surface from estimates of the eigenvalues of the matrix of pure and mixed quadratic regression coefftcients b this article presents and illustrates methodology for constructing conservative confidence limits on the eigenvalues of this matrix as well as the mean response at a constrained optimum when a confidence interval about an eigenvalue of b includes zero a change in the strategy of analysis is required one is suggested and illustrated

schur complements and its applications to symmetric nonnegative and z matrices in linear algebra appl 177 1992 137 smith proved that if h is a hermitian semidefinite matrix and a is a nonsingular principal submatrix then the eigenvalues of the schur complement h a interlace those of h in this paper we refine the latter result and use it to derive eigenvalues interlacing results on an irreducible symmetric nonnegative matrix that involve perron complements for an irreducible symmetric nonnegative matrix we give lower and upper bounds for its spectral radius and also a lower bound for the maximal spectral radius of its principal submatrices of a fixed order we apply our results to an irreducible symmetric z matrix and to the adjacency matrix or the general laplacian matrix of a connected weighted graph the equality cases for the bounds for spectral radii or least eigenvalues are also examined

the schur complement of ph matrices abstract in this paper we consider the class of p h matrices a subclass of h matrices and using scaling characterization we show that this class is closed under taking the schur complement we show that under certain conditions the perron complement of a p h matrix is a p h matrix we also present a way of constructing a scaling matrix for the given p h matrix and we give eigenvalue localization for the schur complement of a p h matrix using only the entries of the original matrix we illustrate this by numerical examples

a weighted linear prediction method for near field source localization this paper proposes a low computational cost method for the near field narrowband source localization problem which does not require multidimensional search or high order statistics the proposed method is based on the second order statistics sos of the outputs of a uniform linear array ula more precisely the range and angle parameters are estimated through a weighted linear prediction lp algorithm applied to a properly chosen array output correlation sequence detailed performance analysis and derivation of the optimal weightings are provided simulation results are finally presented to validate the theoretical analysis results and to assess the performance of the proposed method

eigenvalue bounds on restrictions of reversible nearly uncoupled markov chains in this paper we analyze decompositions of reversible nearly uncoupled markov chains into rapidly mixing subchains we state upper bounds on the 2nd eigenvalue for restriction and stochastic complementation chains of reversible markov chains as well as a relation between them we illustrate the obtained bounds analytically for bunkbed graphs and furthermore apply them to restricted markov chains that arise when analyzing conformation dynamics of a small biomolecule

a graphical approach for evaluating response surface designs in terms of the mean squared error of prediction one of the fundamental purposes of response surface methodology is to develop a relatively simple linear model to explain a more complex phenomenon since the proposed model is only an approximation analysts almost always must address the potential of bias due to model misspecification this article proposes a graphical approach for evaluating response surface designs in terms of the mean squared error of prediction in particular this article develops measures of the maximum and minimum mean squared error of prediction over the surface of spheres through a region of interest these measures are then plotted against radius the resulting plots reveal at a glance how a response surface design performs in the presence of model misspecification these plots are used to investigate the performances of several common response surface designs

mismatch of near field bearing range spatial geometry in source localization by a uniform linear array many near field source localization algorithms intentionally simplifies the exact spatial geometry among the emitter and the sensors in order to speed up the signal processing involved for example the fresnel approximation is a second order taylor series approximation such intentional approximation introduces a systemic error in the algorithm s modeling of the actual objective reality from which the measured data arise a mismatch thus exists between the algorithm s presumptions versus the data it processes this modeling mismatch will introduce a systematic bias in the bearing range estimates of the near field source localization algorithm this bias is non random and adds towards the random estimation errors due to the additive and or multiplicative noises the open literature currently offers no rigorous mathematical analysis on this issue this proposed project aims to fill this literature gap by deriving explicit formulas of the degrading effects in three dimensional source localization due to approximating the source sensor geometry by any order of the taylor s series expansion

inverses of perron complements of inverse m matrices the concept of the perron complement of a nonnegative and irreducible matrix was introduced by meyer in 1989 and it was used by him to construct an algorithm for computing the stationary distribution vector for markov chains here we consider properties of the perron complement of an n n matrix k which is an inverse of an irreducible m matrix we first show that the perron complements of k are inverses of m matrices and that the inverses of associated principal submatrices of k are sandwiched between the inverses of the perron complements of k and the inverses of the corresponding schur complements of k we then investigate the directed graph of the inverse of the perron complements of such matrices k

center points in second order response surface designs previous approaches for selecting the number of center points in a second order response surface design are explained and an integrated variance criterion is offered calculations extending results in the literature are made for various composite and box behnken designs for 2 k 8 the results are compared and discussed and indicate that fewer center points than initially recommended are generally appropriate

asymptotics of the partition function of a general markov random field on an infinite rectangular lattice abstract we investigate theoretically and numerically the asymptotics of the partition function of a general markov random field mrf on an infinite rectangular lattice we first propose the general local energy function lef parameterized mrf then we prove that the thermodynamic limit of the free energy of the mrf can be exactly characterized by the perron root of the fundamental transfer matrix of a particular markov additive process map this matrix possesses a special structure and many interesting properties that enable parallel computation of the perron root and may be beneficial for deriving an analytical form of the free energy we also develop another transfer matrix for numerical computation of the desired perron root specifically the former is a site to site transfer matrix on a twisted cylindrical lattice while the latter is the one associated with a row to row transition on a vertical strip numerical results show that our methods exhibit consistent finite size scaling behavior even for small values of the lattice width this study reveals that the fundamental transfer matrix is an alternative direction of research on the analysis of the partition function of general mrfs within the scope of matrix algebra

localization of perron roots abstract this paper is concerned with the localization of the perron root of a nonnegative irreducible matrix a a new localization method that utilizes the relationship between the perron root of a nonnegative matrix and the estimates of the row sums of its generalized perron complement is presented the method is efficient because it gives the bounds on a only by computing the estimates of the row sums of the generalized perron complement rather than the generalized perron complement itself several numerical examples are given to illustrate the effectiveness of our method

a modified algorithm for the perron root of a nonnegative matrix abstract an algorithm of diagonal transformation for the perron root of nonnegative matrices is proposed by duan and zhang f duan k zhang an algorithm of diagonal transformation for perron root of nonnegative irreducible matrices appl math comput 175 2006 762 772 this method can be used for all nonnegative irreducible matrices in this paper an improved algorithm which is based on this method is proposed the new algorithm inherits all the above mentioned advantages of the original algorithm and has higher efficiency it is testified by numerical testing that the efficiency of the new algorithm is improved greatly

near field multiple source localization by passive sensor array the localization of multiple near field sources in a spatially white gaussian noise environment is studied a modified two dimensional 2 d version of the multiple signal classification music algorithm is used to localize the signal sources range and bearing a global optimum maximum likelihood searching approach to localize these sources is discussed it is shown that in the single source situation the covariances of both the 2 d music estimator and the maximum likelihood estimator mle approach the cramer rao lower bound as the number of snapshots increases to infinity in the multiple source situation it is observed that for a high signal to noise ratio snr and a large number of snapshots the root mean square errors rmses of both localization techniques are relatively small however for low snr and or small number of snapshots the performance of the mle is much superior that of the modified 2 d music

an index of rotatability an index of rotatability is suggested that will enable the experimenter to obtain an immediate appreciation of the overall shape of specified variance contours for symmetrical second order designs values of the index are tabulated for the central composite designs for two to eight factors three designs of roquemore 1976 are assessed via the index comparisons are made with an entirely different index suggested by khuri 1988 it is concluded that both indexes are useful and sensibly consistent

standard errors for the eigenvalues in second order response surface models in the interpretation of the geometry of second order response surface models standard errors and confidence intervals for the eigenvalues of the second order coefficient matrix play an important role in this article we propose a new method for estimating the standard errors and hence approximate confidence intervals of these eigenvalues the method is simple in both concept and execution it involves the refitting of a full quadratic model after rotating the coordinate system to coincide with the canonical axes the estimated standard errors of the pure quadratic terms from this refitting are then used as approximate standard errors of the eigenvalues because this approach is based on the canonical form it is geometrically intuitive and easily taught our method is intended as a way for practitioners to get quick estimates of the standard errors of the eigenvalues in our justification of the approach we show that it is equivalent to using the delta method proposed by carter chinchilli and camp

stochastic resonance in discrete time nonlinear ar 1 models this paper deals with stochastic resonance this nonlinear physical phenomenon generally occurs in bistable systems excited by random input noise plus a sinusoid through its internal dynamics such a system forces cooperation between the input noise and the input sine provided the existence of fine tuning between the power noise and the dynamics the system reacts periodically at the frequency of the sine of particular interest is the fact that the local output signal to noise ratio presents a maximum when plotted against the input noise power the system resounds stochastically continuous time systems have already been studied we study the ability of intrinsically discrete time systems general nonlinear ar 1 models to produce stochastic resonance it is then suggested that such discrete systems can be used in signal processing

perron complement and perron root for a nonnegative irreducible matrix a this paper is concerned with the estimation and determination of the unique perron root or spectral radius of a we present a new method that utilizes the relation between perron roots of the nonnegative matrix and its generalized perron complement several numerical examples are given to show that our method is effective at least for some classes of nonnegative matrices

an algorithm of diagonal transformation for perron root of nonnegative irreducible matrices abstract it is always to use diagonal transformation for the estimation of nonnegative matrix s perron root however it is invalid for some matrices or a long distance of bounds generated sometimes so the application of this method is limitation therefore in this paper a condition of a diagonal transformation is researched and a new method is proposed for nonnegative irreducible matrices this method can be used for all nonnegative irreducible matrices and its convergence is proved in theory it is convenient to compute by this method and it is easy to get the precision you wanted it is proved by numerical testing that this method is valid and efficient

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

compound d and d s optimum designs for determining the order of a chemical reaction estimation of the order of a chemical reaction is often at least as important as estimation of the rate of the reaction locally optimum experimental designs are found for the order and the rate separately and together compound d optimum designs provide a method for designing experiments with specified efficiency for rate or order determination a relationship between the compound designs and d optimum designs for both rate and order aids interpretation of the plots of design efficiencies bayesian designs incorporating prior uncertainty are exemplified monte carlo sampling of the prior is used to design an experiment for the esterification of acetic anhydride

response surface designs in flexible regions abstract when both variance and bias errors are present the choice of an experimental design to fit a response surface depends on the choice of the region of interest box and draper 1959 1963 and draper and lawrence 1965a 1966 investigated spherical and cuboidal regions respectively both of these regions can however be regarded as special cases of a more general flexible region family depending on a single parameter in this manner the sensitivity of the design criterion can be studied and more general results can be obtained the problem is set out here for k predictor variables and specific designs are provided for k 2 predictor variables when variance and bias errors are of roughly the same order a broad rule of thumb that emerges from this work is that for practical situations involving both variance and bias errors and for designs of the composite type used for fitting a second order surface the design points should be near the boundary of the region of interest over which a uni

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

stochastic complementation uncoupling markov chains and the theory of nearly reducible systems a concept called stochastic complementation is an idea which occurs naturally although not always explicitly in the theory and application of finite markov chains this paper brings this idea to the forefront with an explicit definition and a development of some of its properties applications of stochastic complementation are explored with respect to problems involving uncoupling procedures in the theory of markov chains furthermore the role of stochastic complementation in the development of the classical simon ando theory of nearly reducible system is presented

crb based design of linear antenna arrays for near field source localization this paper is devoted to the cramer rao bound crb on the angle and range of a narrow band near field source localized by means of an arbitrary linear array using the exact expression of the time delay parameter first we prove that the conditional and unconditional crbs are proportional for an arbitrary parametrization of the steering vector that may include but is not limited to the source doa range or polarization then a taylor expansion of the crb is conducted to obtain accurate nonmatrix closed form expressions of the crb on angle and range in contrast to the existing expressions our expressions are simple interpretable and more general because the sensors are only constrained to be placed along some axis our analysis leads to the characterization and design of a class of centro symmetric linear arrays with improved near field angle and range estimation capabilities

a general approach to ridge analysis with confidence intervals in response surface methodology ridge analysis is a graphical technique for interpreting response surfaces particularly those of three or more dimensions standard ridge analysis techniques employ a second order polynomial regression model an approach to ridge analysis is presented here that generalizes its current scope this approach allows the use of a general regression model for the response surface within the class of linear models conservative or approximate simultaneous confidence intervals about the optimal mean responses for varying radii can be obtained these simultaneous confidence intervals form a guidance band to aid the experimenter in determining optimal levels of operation a variety of explanatory variable constraints including mixture constraints can also be imposed for the standard quadratic model these confidence intervals can be easily modified to obtain confidence bounds about the maximum or minimum eigenvalues of b the matrix of second order regression coefficients

mixed response surface models with heterogeneous within block error variances the experimental error variance in a response surface model with a block effect has traditionally been assumed to be constant in some experimental situations however this variance may be different for the different blocks that compose the associated design this article discusses the analysis of a response surface model with a random block effect and heterogeneous error variances among the blocks the model includes interactions between the fixed polynomial effects and the block effect procedures for estimating and testing the fixed effects and the random effects in the model are described in particular anova based procedures for testing equality of the error variances and testing the random effects are introduced

the lower and upper bounds on perron root of nonnegative irreducible matrices let a be an nxn nonnegative irreducible matrix let a a be the principal submatrix of a based on the nonempty ordered subset a of 1 2 n and define the generalized perron complement of a a by p t a a a i e p t a a a a b a b a ti a a 1a a b t r a a this paper gives the upper and lower bounds on the perron root of a an upper bound on perron root is derived from the maximum of the given parameter t 0 and the maximum of the row sums of p t 0 a a a synchronously a lower bound on perron root is expressed by the minimum of the given parameter t 0 and the minimum of the row sums of p t 0 a a a it is also shown how to choose the parameter t after a to get tighter upper and lower bounds of r a several numerical examples are presented to show that our method compared with the methods in l z lu m k ng locations of perron roots linear algebra appl 392 2004 103 117 is more effective

deterministic performance bounds on the mean square error for near field source localization this correspondence investigates lower bounds on estimator s mean square error applied to the passive near field source localization more precisely we focus on the so called threshold prediction for which these bounds are known to be useful we give closed form expressions of the mcaulay seidman the hammersley chapman robbins the mcaulay hofstetter bounds and also a recently proposed bound the so called todros tabrikian bound for the deterministic observation model i e parameterized mean and the stochastic observation model i e parameterized covariance matrix finally numerical simulations are given to assess the efficiency of these lower bounds to approximate the estimator s mean square error and to predict the threshold effect

total nonnegativity of the extended perron complement abstract a real matrix is called totally nonnegative if all of its minors are nonnegative in this paper the extended perron complement of a principal submatrix in a matrix a is investigated in extension of known results it is shown that if a is irreducible and totally nonnegative and the principal submatrix consists of some specified consecutive rows then the extended perron complement is totally nonnegative also inequalities between minors of the extended perron complement and the schur complement are presented