exact analysis of the self avoiding random walks on two infinite families of fractals abstract we introduce two infinite families of fractals that we name the family and the koch family according to their first members which are the plane filling lattice and the koch fractal curve respectively the fractal dimension d f of family varies from 2 to 1 and from 1 465 to 1 in the case of the koch family when the fractal enumerator b an odd integer varies from 3 to we have calculated exactly the critical exponents of the self avoiding random walks saws on these fractals our results render it possible to perform a complete and exact study of the fractal to euclidean crossover which in this case occurs when b it turns out that all critical exponents when d f 1 b tend to the corresponding euclidean values with a unique correction term of the type constant ln b

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

reversible jump mcmc for joint detection and estimation of sources in colored noise this paper presents a novel bayesian solution to the difficult problem of joint detection and estimation of sources impinging on a single array of sensors in spatially colored noise with arbitrary covariance structure robustness to the noise covariance structure is achieved by integrating out the unknown covariance matrix in an appropriate posterior distribution the proposed procedure uses the reversible jump markov chain monte carlo mcmc method to extract the desired model order and direction of arrival parameters we show that the determination of model order is consistent provided a particular hyperparameter is within a specified range simulation results support the effectiveness of the method

strongly consistent model order selection for estimating 2 d sinusoids in colored noise the problem of jointly estimating the number as well as the parameters of 2 d sinusoidal signals observed in the presence of an additive colored noise field is considered we begin by establishing the strong consistency of the nonlinear least squares estimator of the parameters of 2 d sinusoids when the number of sinusoidal signals assumed in the field is incorrect based on these results we prove the strong consistency of a new family of model order selection rules

subspace based fault detection robust to changes in the noise covariances the detection of changes in the eigenstructure of a linear time invariant system by means of a subspace based residual function has been proposed previously while enjoying some success in its applicability in particular in the context of vibration monitoring the robustness of this framework against changes in the noise properties has not been properly addressed yet in this paper a new robust residual is proposed and the robustness of its statistics against changes in the noise covariances is shown the complete theory for hypothesis testing for fault detection is derived and a numerical illustration is provided

theta point exponent for polymer chain in random media using field theoretic arguments for self avoiding walks on dilute lattices with site occupation concentrationp we show that the point size exponent of polymer chains remains unchanged for small disorder concentration p p c at the percolation thresholdp p c using a flory type approximation we conjecture that 5 d b 7 whered b is the percolation backbone dimension it shows that the upper critical dimensionality for the point transition atp p c shifts to a dimensiond c 3 we also propose that the point varies practically linearly withp for 1 p p c

estimating the number of sinusoids in additive white noise the test proposed uses the eigenvector decomposition of the estimated autocorrelation matrix and is based on matrix perturbation analysis the estimator is shown to be able to resolve closely spaced sinusoids at lower signal to noise ratios than heuristic tests simulation results for two closely spaced sinusoids are detailed several unanswered questions are discussed

joint bayesian model selection and estimation of noisy sinusoids via reversible jump mcmc in this paper the problem of joint bayesian model selection and parameter estimation for sinusoids in white gaussian noise is addressed an original bayesian model is proposed that allows us to define a posterior distribution on the parameter space all bayesian inference is then based on this distribution unfortunately a direct evaluation of this distribution and of its features including posterior model probabilities requires evaluation of some complicated high dimensional integrals we develop an efficient stochastic algorithm based on reversible jump markov chain monte carlo methods to perform the bayesian computation a convergence result for this algorithm is established in simulation it appears that the performance of detection based on posterior model probabilities outperforms conventional detection schemes

a wavelet based approach for the identification of linear time varying dynamical systems a novel procedure is developed for the identification of linear discrete models of dynamical systems from noisy data of particular interest is the application of the methodology to time varying systems the procedure is based on a representation of the governing differential equations with respect to a wavelet basis and the formulation of an inverse algebraic problem in the associated subspace the effect of noisy data is considered and numerical simulations demonstrating the applicability of the method to single and multi degree of freedom dynamical systems are presented

detection and diagnosis of abrupt changes in modal characteristics of nonstationary digital signals corresp new instrumental tests for detecting and diagnosing changes in the poles of a signal having unknown time varying zeros are proposed numerical results for nonstationary scalar signals are given the extension of these tests to the vector case may be used for vibration monitoring

changing spectrum estimation abstract an autoregressive ar model with time varying coefficients is used for the modeling of non stationary covariance time series a stochastically perturbed linear constraint model is presented as a model of time varying ar coefficients the overall model for the time series is fitted by using the kalman filter and akaike s aic criterion an estimate of a changing spectrum is obtained by the fitted model and the fixed interval smoother examples are given to illustrate the procedure

realization and reduction of markovian models from nonstationary data the realization of markovian models for nonstationary processes generated by time invariant linear systems is considered a model is obtained by constructing an orthogonal finite step predictor for the process optimal model approximation by order reduction is naturally defined in this framework the construction and reduction of markovian models from multiple data records and the numerical considerations involved are illustrated by examples

model order selection based on information theoretic criteria design of the penalty information theoretic criteria itc have been widely adopted in engineering and statistics for selecting among an ordered set of candidate models the one that better fits the observed sample data the selected model minimizes a penalized likelihood metric where the penalty is determined by the criterion adopted while rules for choosing a penalty that guarantees a consistent estimate of the model order are known theoretical tools for its design with finite samples have never been provided in a general setting in this paper we study model order selection for finite samples under a design perspective focusing on the generalized information criterion gic which embraces the most common itc the theory is general and as case studies we consider a the problem of estimating the number of signals embedded in additive white gaussian noise awgn by using multiple sensors b model selection for the general linear model glm which includes e g the problem of estimating the number of sinusoids in awgn the analysis reveals a trade off between the probabilities of overestimating and underestimating the order of the model we then propose to design the gic penalty to minimize underestimation while keeping the overestimation probability below a specified level for the considered problems this method leads to analytical derivation of the optimal penalty for a given sample size a performance comparison between the penalty optimized gic and common aic and bic is provided demonstrating the effectiveness of the proposed design strategy

hamilton s law of variable mass system and time finite element formulations for time varying structures based on the law summary traditional principles of mechanics are primarily conceived for constant mass systems which are only valid if mass is gained or lost at null velocity with respect to an inertial reference frame for variable mass systems thus the numerical algorithms for time varying structures based on these principles are only suitable for this special case in this paper hamilton s law of variable mass system is derived based on meshchersky s fundamental equation and two classes of novel time finite element formulations for linear systems with arbitrary continuous time varying parameters are developed based on the previous law the formulations are verified extensively through numerical examples in which the convergence and effectiveness of algorithms are evaluated numerical examples demonstrate that compared with the algorithms for time varying structures that developed based on traditional principles of mechanics the proposed algorithms provide extended capabilities in both time varying mass problems that mass is gained or lost at any velocity such as rocket problem and moving mass problems such as vehicle bridge interaction problem besides the time varying stiffness and damping problems the proposed algorithms have a wider range of application in particular hamilton s law of variable mass system provides a solid theoretical foundation for further research on the algorithm design for time varying structures copyright 2014 john wiley sons ltd

the fractal dimension of the minimum path in two and three dimensional percolation the authors calculate the fractal dimension d min of the shortest path l between two points on a percolation cluster where l approximately rd min and r is the pythagorean distance between the points they find d min 1 130 or 0 002 for d 2 and 1 34 or 0 01 for d 3

self avoiding walks in quenched random environments the self avoiding walk in a quenched random environment is studied using realspace and field theoretic renormalization and flory arguments these methods indicate that the system is described for d de by a strong disorder fixed point corresponding to a glass state in which the polymer is confined to the lowest energy path this fixed point is characterized by scaling laws for the size of the walk l n with n the number of steps and the fluctuations in the free energy af l the bound 1 co pore and suggests that this inequality holds for d 2 and 3 although pure cannot be excluded particularly for d 2 for d d c there is a transition between strong and weak disorder phases at which pure the strong disorder fixed point for saws on percolation clusters is discussed the analogy with directed walks is emphasized

map model order selection rule for 2 d sinusoids in white noise we consider the problem of jointly estimating the number as well as the parameters of two dimensional 2 d sinusoidal signals observed in the presence of an additive white gaussian noise field existing solutions to this problem are based on model order selection rules and are derived for the parallel one dimensional 1 d problem these criteria are then adapted to the 2 d problem using heuristic arguments employing asymptotic considerations we derive a maximum a posteriori map model order selection criterion for jointly estimating the parameters of the 2 d sinusoids and their number the proposed model order selection rule is strongly consistent as an example the model order selection criterion is applied as a component in an algorithm for parametric estimation and synthesis of textured images

output only identification and dynamic analysis of time varying mechanical structures under random excitation a comparative assessment of parametric methods this article addresses the problem of parametric time domain identification and dynamic analysis for time varying tv mechanical structures under unobservable random excitation the methods presented are based on time dependent autoregressive moving average tarma models and are classified according to the mathematical structure imposed on the tv parameter evolution as unstructured parameter evolution stochastic parameter evolution and deter ministic parameter evolution the features and relative merits of each class are outlined a representativ e method from each is then assessed through its application to the identification and dynamic analysis o f a laboratory tv structure consisting of a beam with a mass moving on it the results are mutually compared and contrasted to those obtained through frozen configuration multiple experiment bas eline identification

maximum likelihood parameter estimation of superimposed signals by dynamic programming the problem of fitting a model composed of a number of superimposed signals to noisy data using the maximum likelihood criterion is considered it is shown using the cramer rao bound for the estimation accuracy that in many instances useful models for the composite signal can be restricted without loss of generality to component signals that directly interact only with one or two of their closest neighbors in parameter space it is shown that for such models the global extremum of the criterion can be found efficiently by dynamic programming the computation requirements are linear in the number of signals rather than exponential as in the case of exhaustive search the technique applies for arbitrary sampling of the signals the dynamic programming method is easily adapted to determining the number of signals as well as is demonstrated using the minimum description length principle computer simulation results are given for several examples

detection and localization of multiple sources via the stochastic signals model a method for the detection of coherent and noncoherent signals based on the application of j rissanen s 1978 minimum description length principle for model selection to the stochastic signals model is presented the detection and localization are done simultaneously with the location estimator coinciding with the maximum likelihood estimator derived by j f bohme 1986 the proposed method outperforms the method of m wax and i ziskind 1989 especially in the threshold region simulation results demonstrating the improved performance are included

self avoiding walks on fractals studied by the monte carlo renormalization group the authors have applied the monte carlo renormalization group mcrg method to study the problem of self avoiding walks on the sierpinski gasket family of fractals each member of the family is labelled by an integer b 2 or b or infinity and when b to infinity both the fractal df and spectral ds dimension approach their euclidean value 2 they have calculated the critical exponent nu associated with the mean square end to end distance up to b 80 their mcrg results deviate at most 0 03 from the available exact results for 2 or b or 9 the obtained data show clearly that nu monotonically decreases with b and crosses the euclidean value nu 3 4 at b approximately 27 that is before entering the fractal to euclidean crossover region that occurs in the limit b to infinity

a model selection rule for sinusoids in white gaussian noise the model selection problem for sinusoidal signals has often been addressed by employing the akaike 1974 information criterion aic and the minimum description length principle mdl the popularity of these criteria partly stems from the intrinsically simple means by which they can be implemented they can however produce misleading results if they are not carefully used the aic and mdl have a common form in that they comprise two terms a data term and a penalty term the data term quantifies the residuals of the model and the penalty term reflects the desideratum of parsimony while the data terms of the aic and mdl are identical the penalty terms are different in most of the literature the aic and mdl penalties are however both obtained by apportioning an equal weight to each additional unknown parameter be it phase amplitude or frequency by contrast we demonstrate that the penalties associated with the amplitude and phase parameters should be weighted differently than the penalty attached to the frequencies following the bayesian methodology we derive a model selection criterion for sinusoidal signals in gaussian noise which also contains the log likelihood and the penalty terms the simulation results disclose remarkable improvement in our selection rule over the commonly used mdl and aic

detection estimation of very close emitters performance breakdown ambiguity and general statistical analysis of maximum likelihood estimation we reexamine the well known problem of threshold behavior or performance breakdown in the detection estimation of very closely spaced emitters in this extreme regime we analyze the performance for maximum likelihood estimation mle of directions of arrival doa for two close gaussian sources over the range of sample volumes and signal to noise ratios snrs where the correct number of sources is reliably estimated by information theoretic criteria itc but where one of the doa estimates is severely erroneous outlier we show that random matrix theory rmt applied to the evaluation of theoretical mle performance gives a relatively simple and accurate analytical description of the threshold behavior of mle and itc in particular the introduced single cluster criterion provides accurate ambiguity bounds for the outliers

estimation of stationary structural system parameters from non stationary random vibration data a locally stationary model method abstract stationary structural system building natural frequency and damping parameters are estimated from a long non stationary ambient vibration time series record the non stationary vibration record is decomposed into continuous not necessarily equal duration stationary time series segments by a locally stationary autoregressive ar model method estimates of the stationary structural system parameters are extracted from each of the locally stationary ar models the final estimate of the structural system parameters is a time duration weighted average of the estimates in each stationary segment under reasonable conditions the theoretical variance of the structural system parameter estimates decreases with the duration of the long non stationary record the results of the analysis of a long duration non stationary record are compared with the results of an earlier approach in which the long duration non stationary record was decomposed into relatively short fixed duration vibration records and analyzed as stationary time series 1 the variances of the damping parameter estimates achieved by the current method are one half to one quarter of those obtained by the earlier method the sample variance of the structural system parameter estimates decreases with the reciprocal of the duration of the overall non stationary record

theory of self avoiding walks on percolation fractals a phenomenological approach which takes into account the basic geometry and topology of percolation fractal structures and of self avoiding walks saw is used to derive a new expression for the flory exponent describing the average radius of gyration of saws on fractals we focus on the radius of gyration and discuss the importance of the intrinsic fractal dimensions of percolation clusters in determining the lower and upper critical dimensions of saws the mean field version of our new formula corresponds to the aharony and harris expression who used the standard flory approach for its derivation

merging sensor data from multiple measurement set ups for non stationary subspace based modal analysis processing sensor data from multiple non simultaneously recorded measurement set ups for structural analysis is often achieved by merging identification results obtained from records corresponding to different sensor pools since pole matching and eigenvector gluing might not be consistent in some cases the question arises to merge the data first and then process them globally subspace identification algorithms have proven efficient for performing output only modal analysis of mechanical systems subject to uncontrolled unmeasured and non stationary excitation the purpose of this paper is to investigate as to how subspace based output only modal analysis algorithms can be adapted to handle the multi patch measurements set up numerical results obtained on both laboratory and real application examples are reported which show the relevance and usefulness of the proposed algorithm

robust full bayesian learning for radial basis networks we propose a hierarchical full bayesian model for radial basis networks this model treats the model dimension number of neurons model parameters regularization parameters and noise parameters as unknown random variables we develop a reversible jump markov chain monte carlo mcmc method to perform the bayesian computation we find that the results obtained using this method are not only better than the ones reported previously but also appear to be robust with respect to the prior specification in addition we propose a novel and computationally efficient reversible jump mcmc simulated annealing algorithm to optimize neural networks this algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function it performs a global search in the joint space of the parameters and number of parameters thereby surmounting the problem of local minima to a large extent we show that by calibrating the full hierarchical bayesian prior we can obtain the classical akaike information criterion bayesian information criterion and minimum description length model selection criteria within a penalized likelihood framework finally we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible jump mcmc simulated annealing method

principal components algorithms for arma spectrum estimation principal components algorithms are presented for the problem of fitting an arma model to a given segment of a sample sequence of a discrete time stochastic process and the model is used to estimate the process power spectrum to reduce the effects of finite wordlength errors balanced state pace parameterization of the arma model is used instead of the more popular difference equation parameterization model identification is formulated as a problem of selecting a partial state to span approximately an apparently large dimensional information interface between the past and the future of the process different criteria are used to measure the quality of the approximation which leads to principal components algorithms for the problem that are based on singular value decomposition

music like doa estimation without estimating the number of sources this paper presents a new direction of arrival doa estimation algorithm where doa estimation is realized in the framework of beamforming by introducing a new optimization problem the new optimization problem aims to minimize the variance of the array output subject to retaining the output power at the look direction and precluding a trivial solution the proposed algorithm is equivalent to the multiple signal classification music algorithm in some special cases it is therefore named as the music like method however different from the classical music algorithm the new method is not based on subspace decomposition and the number of sources is hence not required for direction finding this enables us to avoid performance deterioration caused by incorrect source number estimation the effectiveness and advantage of the proposed algorithm is theoretically investigated and computational complexity is also addressed to verify the theoretical analysis computer simulations are implemented and comparisons with other algorithms are made

on the critical behaviour of self avoiding walks for pt i see ibid vol 22 p 1839 1989 for the self avoiding walk problem the coefficients of the chain generating function and of the generating function for the sum of square end to end distances have been extended to 20 terms for the triangular lattice to 27 terms for the diamond lattice to 21 terms for the simple cubic lattice and to 16 terms for the bcc lattice precise estimates of the critical points are obtained and for the exponents we find that gamma 1 161 or 0 002 and nu 0 592 or 0 003 encompasses all the three dimensional lattice data

monogenic hopf algebras over discrete valuation rings with low ramification abstract let k be an extension of q p with absolute ramification index 1 e p 1 let r o k and let k be the residue field of r we show that any monogenic finite abelian local hopf algebra with local dual lifts to r and we construct all such lifts for h an r hopf algebra arising from one of these lifts we realize spech as the kernel of an isogeny of one dimensional formal groups we then obtain a complete list of fields l for which l k is an h k galois object

bounds on maximum likelihood ratio part ii application to antenna array detection estimation with imperfect wavefront coherence the multiple hypothesis testing problem of the detection estimation of an unknown number of independent gaussian point sources is adequately addressed by likelihood ratio lr maximization over the set of admissible covariance matrix models we introduce nonasymptotic lower and upper bounds for the maximum lr since lr optimization is generally a nonconvex multiextremal problem any practical solution could now be tested against these bounds enabling a high probability of recognizing nonoptimal solutions we demonstrate that in many applications the lower bound is quite tight with approximate maximum likelihood ml techniques often unable to approach this bound the introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace based direction of arrival doa estimation techniques we also demonstrate that by proper lr maximization we can extend the range of signal to noise ratio snr values and or number of data samples wherein accurate parameter estimates are produced yet when the snr and or sample size falls below a certain limit for a given scenario we show that ml estimation suffers from a discontinuity in the parameter estimates a phenomenon that cannot be eliminated within the ml paradigm

activation detection in functional mri using subspace modeling and maximum likelihood estimation a statistical method for detecting activated pixels in functional mri fmri data is presented in this method the fmri time series measured at each pixel is modeled as the sum of a response signal which arises due to the experimentally controlled activation baseline pattern a nuisance component representing effects of no interest and gaussian white noise for periodic activation baseline patterns the response signal is modeled by a truncated fourier series with a known fundamental frequency but unknown fourier coefficients the nuisance subspace is assumed to be unknown a maximum likelihood estimate is derived for the component of the nuisance subspace which is orthogonal to the response signal subspace an estimate for the order of the nuisance subspace is obtained from an information theoretic criterion a statistical test is derived and shown to be the uniformly most powerful ump test invariant to a group of transformations which are natural to the hypothesis testing problem the maximal invariant statistic used in this test has an f distribution the theoretical f distribution under the null hypothesis strongly concurred with the experimental frequency distribution obtained by performing null experiments in which the subjects did not perform any activation task applications of the theory to motor activation and visual stimulation fmri studies are presented

statistical model based damage detection and localization subspace based residuals and damage to noise sensitivity ratios the vibration based structural health monitoring problem is addressed as the double task of detecting damages modeled as changes in the eigenstructure of a linear dynamic system and localizing the detected damages within a fem of the monitored structure the proposed damage detection algorithm is based on a residual generated from a stochastic subspace based covariance driven identification method and on the statistical local approach to the design of detection algorithms this algorithm basically computes a global test which performs a sensitivity analysis of the residuals to the damages relative to uncertainties and noises how this residual relates to some residuals for damage localization and model updating is discussed damage localization is stated as a detection problem this problem is addressed by plugging aggregated sensitivities of the modes and mode shapes w r t fem structural parameters in the above setting this results in directional tests which perform the same type of damage to noise sensitivity analysis of the residual as for damage detection how the sensitivity aggregation mechanism relates to sub structuring is outlined numerical results obtained on one example are reported

positive definite toeplitz completion in doa estimation for nonuniform linear antenna arrays ii partially augmentable arrays this paper considers the problem of direction of arrival doa estimation for multiple uncorrelated plane waves incident on so called fully augmentable sparse linear arrays in situations where a decision is made on the number of existing signal sources m prior to the estimation stage we investigate the conditions under which doa estimation accuracy is effective in the maximum likelihood sense in the case where m is less than the number of antenna sensors m a new approach called music maximum entropy equalization is proposed to improve doa estimation performance in the preasymptotic region of finite sample size n and signal to noise ratio a full sized positive definite p d toeplitz matrix is constructed from the m spl times m direct data covariance matrix and then alternating projections are applied to find a p d toeplitz matrix with m variate signal eigensubspace signal subspace truncations when m spl ges m cramer rao bound analysis suggests that the minimal useful sample size n is rather large even for arbitrarily strong signals it is demonstrated that the well known direct augmentation approach daa cannot approach the accuracy of the corresponding cramer rao bound even asymptotically as n spl rarr spl infin and therefore needs to be improved we present a new estimation method whereby signal subspace truncation of the daa augmented matrix is used for initialization and is followed by a local maximum likelihood optimization routine the accuracy of this method is demonstrated to be asymptotically optimal for the various superior scenarios m spl ges m presented

theta point exponent for polymer chains on percolation fractals we derive a new expression for the flory exponent describing the average radius of gyration of polymer chains at the theta point for this we make use of the appropriate distribution function for the radius of gyration we start from euclidean lattices and extend the results to percolation fractals by taking into account the basic geometry and the topology of such structures we show that such basic features have a very prominent effect on the flory exponent of the chain polymer on fractals at the theta point

a smoothness priors time varying ar coefficient modeling of nonstationary covariance time series a smoothness priors time varying ar coefficient model approach for the modeling of nonstationary in the covariance time series is shown smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each ar coefficient the unknown white noise variances are hyperparameters of the ar coefficient distribution the critical computation is of the likelihood of the hyperparameters of the bayesian model this computation is facilitated by a state space representation kalman filter implementation the best difference equation order best ar model order best hyperparameter model locally in time is selected using the minimum aic method also an instantaneous spectral density is defined in terms of the instantaneous ar model coefficients and a smoothed estimate of the instantaneous time series variance an earthquake record is analyzed the changing spectral analysis of the original data and of simulations from a time varying ar coefficient model of that data are shown

automatic determination of the number of targets present when using the time reversal operator acoustical time reversal mirrors have been shown to provide a highly accurate means of studying and focusing on acoustical sources the dort method is a derivation of the time reversal process which allows for focusing on multiple targets an important step in this process is the determination of the number of targets or sources present this is achieved by examining the eigenvalues of the time reversal operator tro the number of significant eigenvalues is then chosen as the number of sources present however as mentioned in n mordant c prada and m fink j acoust soc am 105 2634 2642 1999 and c prada m tanter and m fink in proceedings of the ieee symposium 1997 pp 679 683 factors such as low signal to noise ratio snr small data sample array configuration and the target location may result in the eigenvalues corresponding to the targets no longer being distinguishable from the background noise eigenvalues this paper proposes a robust method of automatically determining the

detection estimation of more uncorrelated gaussian sources than sensors in nonuniform linear antenna arrays ii partially augmentable arrays previous studies dealing with direction of arrival doa estimation for uncorrelated planes waves incident on nonuniform m sensor arrays assumed that the number of signal sources m was known or had already been estimated in the conventional case m m traditional detection techniques such as akaike s information criterion aic and minimum description length mdl that are based on the equality of several smallest eigenvalues in the covariance matrix may be applied although we demonstrate that these results can be misleading for nonuniform arrays in the superior case m spl ges m these standard techniques are not applicable we introduce a new approach to the detection problem for fully augmentable arrays whose set of intersensor differences is complete we show that the well known direct augmentation approach applied to the sample covariance matrix is not a solution by itself since the resulting toeplitz matrix is generally not positive definite for realistic sample volumes we propose a transformation of this augmented matrix into a positive definite toeplitz matrix t sub spl mu with the proper number of equal minimum eigenvalues that are appropriate for the candidate number of sources spl mu comparison of the results of these best fit transformations over the permissible range of candidates then allows us to select the most likely number of sources m spl circ using traditional criteria and yields uniquely defined doas simulation results demonstrate the high performance of this method since detection techniques for superior scenarios have not been previously described in the literature we compare our method with the standard aic and mdl techniques in a conventional case with similar cramer rao bound crb and find that it has a similar detection performance

universal crossing of the self avoiding walk critical exponent nu at the euclidean value 3 4 for several different fractal families we find that the end to end distance critical exponent nu is close to the euclidean value 3 4 for self avoiding walks saws on fractals that are composed of homogeneous parts of size bh approximately 26 more precisely we find that saws on fractals with smaller homogeneous parts b 3 4 while nu 27 we establish this result in the case of three quite different fractal families the sierpinski gasket sg family the plane filling pf family and the checkerboard cb family of fractals in the case of the first two families sg and pf the relevant values for nu were found previously by applying the monte carte renormalization group mcrg method but the specific value bh was not recognized on the other hand for the cb fractals only the exact renormalization group rg results were known previously for 3 or b or 9 where b is an odd integer that serves as the fractal enumerator in this paper we extend the sequence of the known results for the cb family up to b 81 by generalizing the mcrg method the new results have revealed the occurrence of the aforementioned crossing of the euclidean value 3 4 we discuss the significance of the crossing within the current knowledge of saws on fractals

non stationary functional series tarma vibration modelling and analysis in a planar manipulator abstract the problem of non stationary stochastic vibration modelling and analysis is considered through a paradigm involving vibration analysis in a periodically varying manipulator a parametric functional series method based upon time dependent autoregressive moving average tarma models is applied for the first time within the vibration analysis context and comparisons with both pure tar and non parametric fourier based analysis are made these focus on achievable time dependent spectrum accuracy resolution and tracking as well as on estimated modal parameter accuracy the functional series tarma method is shown to lead unambiguously to a physically meaningful tarma 4 5 p 3 representation while the pure tar method leads to a tar 12 p 3 representation the tarma 4 5 p 3 model is shown to achieve superior spectral and modal parameter accuracy while avoiding the problem of estimated false modal modes of its tar 12 p 3 counterpart the tarma 4 5 p 3 model also attains lower parametric complexity and superior values of the model fit criteria the study demonstrates the facets and capabilities of the functional series tarma method for non stationary vibration analysis indicating that the tarma model s direct relationship with the underlying physical system constitutes an important asset of the method

input output versus output only data processing for structural identification application to in flight data analysis the problem of structural model identification under both known and unknown input excitations is addressed in flight data analysis is an important instance of that problem input output and output only eigenstructure identification methods are described and compared within two classes of methods subspace based and prediction error in particular different types of relevant projections for handling the known and unknown inputs are discussed the relevance of the methods is emphasized through numerical results obtained on real flight test data sets

scaling theory for the statistics of self avoiding walks on random lattices the authors study self avoiding walks saw on randomly diluted quenched lattices with direct configurational averaging over the moments of the saw distribution function a scaling function representation of rn the average end to end distance of n step walks is studied here both for saw on a the infinite percolation cluster and b any cluster they have shown that at the percolation threshold nu p nu p 1 beta p 2 nu p where beta p and nu p are the percolation order parameter and correlation length exponents respectively the authors also propose a scaling function representation for the total number of n step saw configuration gn approximately mu nngamma 1 for infinite cluster averaging which gives gamma p gamma d nu p nu for all cluster averaging gamma will remain unchanged

quantifying uncertainty in material damage from vibrational data the response of a vibrating beam to a force depends on many physical parameters including those determined by material properties damage caused by fatigue or cracks results in local reductions in stiffness parameters and may drastically alter the response of the beam data obtained from the vibrating beam are often subject to uncertainties and or errors typically modeled using probability densities the goal of this paper is to estimate and quantify the uncertainty in damage modeled as a local reduction in stiffness using uncertain data we present various frameworks and methods for solving this parameter determination problem we also describe a mathematical analysis to determine and compute useful output data for each method we apply the various methods in a specified sequence that allows us to interface the various inputs and outputs of these methods in order to enhance the inferences drawn from the numerical results obtained from each method numerical results are presented using both simulated and experimentally obtained data from physically damaged beams

comparison of some instrumental variable methods consistency and accuracy aspects a general analysis of various instrumental variable methods is given the investigation includes methods for open loop operation as well as methods designed for closed loop operation the instrumental variables are formed as different combinations of inputs delayed inputs delayed outputs filtered inputs and external setpoint variations necessary conditions as well as sufficient conditions for consistency are explicitly derived and discussed the paper also includes some simple counter examples to general consistency for some common instrumental variable methods also asymptotic accuracy properties are reviewed it is e g studied how the use of filters will influence the covariance matrix of the parameter estimates

asymptotic map criteria for model selection the two most popular model selection rules in signal processing literature have been akaike s 1974 criterion aic and rissanen s 1978 principle of minimum description length mdl these rules are similar in form in that they both consist of data and penalty terms their data terms are identical but the penalties are different mdl being more stringent toward overparameterization aic penalizes for each additional model parameter with an equal incremental amount of penalty regardless of the parameter s role in the model in most of the literature on model selection mdl appears in a form that also suggests equal penalty for every unknown parameter this mdl criterion we refer to as naive mdl in this paper we show that identical penalization for every parameter is not appropriate and that the penalty has to depend on the model structure and type of model parameters the approach to showing this is bayesian and it relies on large sample theory we derive maximum a posteriori map rules for several different families of competing models and obtain forms that are similar to aic and naive mdl for some families however we find that the derived penalties are different in those cases our extensive simulations show that the map rule outperforms aic and naive mdl

joint model order selection and parameter estimation of chirps with harmonic components we consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp and estimating its parameters i e its initial frequency and frequency rate given time samples of the observed signal common model order criteria select the number of harmonics based on the maximum likelihood estimator we develop exact and approximated maximum likelihood estimators of these parameters to avoid an exhaustive search in the initial frequency frequency rate space involved by those estimators we propose an alternative low complexity two step estimation method the first step separates the signal to its harmonic components then in the second step the parameters of interest are estimated using least squares method given the phases of the harmonic components the method is compared to the exact and approximated maximum likelihood estimators and to the well known high order ambiguity function based method numerical simulations and real data examples demonstrate that the proposed low complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal to noise ratio since the estimates obtained by the proposed method achieve the cramer rao lower bound at these signal to noise ratios

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

modular subspace based system identification from multi setup measurements subspace identification algorithms are efficient for output only eigenstructure identification of linear mimo systems the problem of merging sensor data obtained from moving and nonsimultaneously recorded measurement setups under varying excitation is considered to address the problem of dimension explosion when retrieving the system matrices of the complete system a modular and scalable approach is proposed adapted to a large class of subspace methods observability matrices are normalized and merged to retrieve global system matrices

monogenic hopf orders and associated orders of valuation rings abstract let r be a complete discrete valuation ring of mixed characteristic with perfect residue field and let h be a finite local commutative r hopf algebra we consider when there exists a finite extension of the field of fractions of r whose valuation ring is a galois h object if this occurs then h is monogenic conversely if h is also cocommutative and h is monogenic then there exists a valuation ring which is a galois h object to prove this result we represent h as the kernel of an isogeny of a special type between formal groups over r we deduce that if a is a finite abelian r hopf algebra such that both a and its dual are local then a is the associated order of a valuation ring if and only if the dual of a is monogenic

a combined order selection and parameter estimation algorithm for undamped exponentials we propose an approximate maximum likelihood parameter estimation algorithm combined with a model order estimator for superimposed undamped exponentials in noise the algorithm combines the robustness of fourier based estimators and the high resolution capabilities of parametric methods we use a combination of a wald 1945 statistic and a map test for order selection and initialize an iterative maximum likelihood descent algorithm recursively based on estimates at higher candidate model orders experiments using simulated data and synthetic radar data demonstrate improved performance over mdl map and aic in places of practical interest

order estimation and discrimination between stationary and time varying tvar autoregressive models for a set of t independent observations of the same n variate correlated gaussian process we derive a method of estimating the order of an autoregressive ar model of this process regardless of its stationary or time varying nature we also derive a test to discriminate between stationary ar models of order m ar m and time varying autoregressive models of order m tvar m we demonstrate that within this technique the number t of independent identically distributed data samples required for order estimation and discrimination just exceeds the maximum possible order mmax which in many cases is significantly fewer than the dimension of the problem n

a smooth transition model for multiple regime time series this study deals with the problem of fitting a time series modeled by a smooth transition regression function this model extends the standard linear piecewise model within the piecewise model the regression function parameters change abruptly at the changepoints in the smooth transition model parametric transition functions are introduced that allow for gradual changes of the regression function around the changepoints this model can very accurately reproduce both nonregular and smooth random processes moreover it allows the extraction of information about the changes in the regression function through the transition function parameters the estimation of the model is performed through a fully bayesian framework prior distributions are set for each parameter and the full joint posterior distribution is expressed the computation of standard bayesian estimates involves intractable multi dimensional integrals therefore a reversible jump markov chain monte carlo algorithm is derived to sample the joint posterior distributions a comparative simulation study shows that the smooth transition approach achieves competitive performances and provides more sparse representations of standard test functions finally the smooth transition framework is applied to estimate real world electrical transients which allows the extraction of the relevant features for signal classification

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

flory approximant for self avoiding walks on fractals a flory approximant for the exponent describing the end to end distance of a self avoiding walk saw on fractals is derived the approximant involves the fractal dimensionalities of the backbone and of the minimal path and the exponent describing the resistance of the fractal the approximant yields values which are very close to those available from exact and numerical calculations

where two fractals meet the scaling of a self avoiding walk on a percolation cluster the scaling properties of self avoiding walks on a d dimensional diluted lattice at the percolation threshold are analyzed by a field theoretical renormalization group approach to this end we reconsider the model of y meir and a b harris phys rev lett 63 2819 1989 and argue that via renormalization its multifractal properties are directly accessible while the former first order perturbation did not agree with the results of other methods our analytic result gives an accurate description of the available mc and exact enumeration data in a wide range of dimensions 2 ensuremath leqslant d ensuremath leqslant 6

on board component fault detection and isolation using the statistical local approach we describe both the key principles and real application examples of a unified theory which allows us to perform the on board incipient fault detection and isolation tasks involved in monitoring for condition based maintenance this theory is known under the name of local approach and it is especially suited to component faults it aims at transforming complex detection problems concerning a parameterized stochastic process into the universal problem of monitoring the mean of a gaussian vector based on a small deviation assumption the key tools are the first order taylor expansion and the asymptotic gaussianity of a convenient parameter estimating function ml ls iv and subspace identification methods are addressed in this perspective in the case of dynamic processes given in state space form the approach may also call for observer based state estimation or state elimination experiments concerning both simulated and real data for linear and nonlinear dynamical processes are reported how the key principles and features of the local approach compare with those of other approaches is discussed

fractal properties of the percolating backbone in three dimensions a recursive algorithm to determine the backbone of the two dimensional percolating cluster is adjusted to measure the fractal properties of the backbone of the three dimensional percolating cluster the specific properties measured are the fractal dimensionality of the backbone dbbf 1 75 or 0 04 the chemical dimensionality dt 1 26 or 0 03 and the minimum path dimensionality dmin 1 39 or 0 03

single sample modal identification of a nonstationary stochastic process gauss markov processes excited by nonstationary noises are encountered in the modeling of vibrating systems we prove that the classical instrumental variable method as well as the ho kalman realization algorithm for identifying the pole part modal characteristics of the model are consistent when used on a single sample of the nonstationary signal

nonstationary consistency of subspace methods in this paper we study ldquononstationary consistencyrdquo of subspace methods for eigenstructure identification i e the ability of subspace algorithms to converge to the true eigenstructure despite nonstationarities in the excitation and measurement noises note that such nonstationarities may result in having time varying zeros for the underlying system so the problem is nontrivial in particular likelihood and prediction error related methods do not ensure consistency under such situation because estimation of poles and estimation of zeros are tightly coupled we show in turn that subspace methods ensure such consistency our study carefully separates statistical from nonstatistical arguments therefore enlightening the role of statistical assumptions in this story

duality for hopf orders in this paper we use duality to construct new classes of hopf orders in the group algebra kc p3 where k is a finite extension of q p and c p3 denotes the cyclic group of order p 3 included in this collection is a subcollection of hopf orders which are realizable as galois groups

glrt based threshold detection estimation performance improvement and application to uniform circular antenna arrays the problem of estimating the number of independent gaussian sources and their parameters impinging upon an antenna array is addressed for scenarios that are problematic for standard techniques namely under threshold conditions where subspace techniques such as music experience an abrupt and dramatic performance breakdown we propose an antenna geometry invariant method that adopts the generalized likelihood ratio test glrt methodology supported by a maximum likelihood ratio lower bound analysis that allows erroneous solutions outliers to be found and rectified detection estimation performance in both uniform circular and linear antenna arrays is shown to be significantly improved compared with conventional techniques but limited by the performance breakdown phenomenon that is intrinsic to all such maximum likelihood ml techniques

state space formulation a solution to modal parameter estimation abstract as an alternative to fourier techniques based on transfer function fitting modal parameters identification methods derived from a state space formulation of the dynamic equation have been recently studied and developed this formulation leads to the solution of the modal problem via multi dimensional arma model parameters identification in this paper the transition from the dynamic equation to the arma model is described and the algorithms of identification are explained for the very common case of uncontrolled and unmeasured excitation these techniques the qualities of which have been established during extensive processing of offshore structures measurements have been generalized to more complex excitation models such as those of turbo alternators several examples illustrate these different application domains

series studies of self avoiding walks near the theta point on 2d critical percolation clusters the thermally weighted average end to end distance rn of interacting self avoiding walks saws are obtained enumerating all the finite n stepped saw configurations on the infinite percolation cluster of bond diluted square lattice at the percolation threshold averaging over 250 percolation clusters and enumerating all the possible saws on them for n up to 31 rn is fitted to a scaling form r2n approximately n2 nu theta f nphi tau t theta theta is the temperature interval away from the theta point phi is the crossover exponent and nu theta is the tricritical size exponent the best fit is obtained for theta approximately 0 71 compared to theta 0 approximately 1 54 on a pure square lattice nu approximately 0 74 compared to nu theta phi 4 mod 7 approximately 0 57 in two dimensions and phi approximately 0 20 they also obtain an estimate for of saw size exponent nu c for collapsed phase on the percolation cluster

svd based information theoretic criteria for detection of the number of damped undamped sinusoids and their performance analysis following the information theoretic approach to model selection the authors develop criteria for detection of the number of damped undamped sinusoids these criteria are matched to the singular value decomposition svd based methods such as modified forward backward and forward backward linear prediction so well that the extra computations needed over and above those required for computing the svd are marginal next an analytical framework for analyzing the performance of these criteria is developed in the development of the analysis some approximations which become better for large signal to noise ratio are made simulations are used to verify the usefulness of the analysis and to compare the performance of the method with that of j j fuchs 1988

model selection for sinusoids in noise statistical analysis and a new penalty term detection of the number of sinusoids embedded in noise is a fundamental problem in statistical signal processing most parametric methods minimize the sum of a data fit likelihood term and a complexity penalty term the latter is often derived via information theoretic criteria such as minimum description length mdl or via bayesian approaches including bayesian information criterion bic or maximum a posteriori map while the resulting estimators are asymptotically consistent empirically their finite sample performance is strongly dependent on the specific penalty term chosen in this paper we elucidate the source of this behavior by relating the detection performance to the extreme value distribution of the maximum of the periodogram and of related random fields based on this relation we propose a combined detection estimation algorithm with a new penalty term our proposed penalty term is sharp in the sense that the resulting estimator achieves a nearly constant false alarm rate a series of simulations support our theoretical analysis and show the superior detection performance of the suggested estimator