algebraic approach to system identification a variety of identification procedures exists for estimating the parameters of an autoregressive moving average arma process from noise free excitation and noise contaminated response data in this paper an identification procedure is proposed for the more realistic situation in which both the excitation and response are contaminated by white noises the method is based upon the null space characterization of an associated data matrix some of the more important algebraic properties possessed by this data matrix are first established in the ideal noise free data case in particular it is found that an overordering of the arma model will not impair the identification of the underlying system in the more realistic noise contaminated data case an approximation of the data matrix s null space is affected by using an eigenvalue eigenvector decomposition by incorporating this null space approximation the deleterious effects of the noise are significantly reduced thereby giving rise to improved modeling performance this improvement is demonstrated by means of a standard example in which the proposed identification method is shown to produce a better modeling behavior than does the classical least squares method the corresponding iterative generalized least squares method and a commonly employed instrumental variable method

a bias correction method for identification of linear dynamic errors in variables models this paper considers the problem of identifying linear systems where the input is observed in white noise but the output is observed in colored noise which also includes process disturbances an efficient method is developed which can perform unbiased parameter estimation without utilizing a prefilter the developed method is characterized by attractive features direct use of the observed data without prefiltering no need to evaluate autocorrelation functions for the input noise no need to identify a high order augmented system and provision of a direct unbiased estimate of the system parameters without parameter extraction computer simulations are presented to illustrate its superior performance including its significantly reduced computational complexity

energy method for boltzmann equation abstract a basic simple energy method for the boltzmann equation is presented here it is based on a new macro micro decomposition of the boltzmann equation as well as the h theorem this allows us to make use of the ideas from hyperbolic conservation laws and viscous conservation laws to yield the direct energy method as an illustration we apply the method for the study of the time asymptotic nonlinear stability of the global maxwellian states previous energy method starting with grad and finishing with ukai involves the spectral analysis and regularity of collision operator through sophisticated weighted norms

classical solutions to the boltzmann equation for molecules with an angular cutoff an important class of collision kernels in the boltzmann theory are governed by the inverse power law in which the intermolecular potential between two particles is an inverse power of their distance under the grad angular cutoff assumption global in time classical solutions near maxwellians are constructed in a periodic box for all soft potentials with 3 0

on the approximability of numerical taxonomy fitting distances by tree metrics we consider the problem of fitting an n n distance matrix d by a tree metric t let varepsilon be the distance to the closest tree metric under the l infty norm that is varepsilon min t parallel t d parallel infty first we present an o n2 algorithm for finding a tree metric t such that parallel t d parallel infty leq 3 varepsilon second we show that it is cal np hard to find a tree metric t such that parallel t d parallel infty frac 9 8 varepsilon this paper presents the first algorithm for this problem with a performance guarantee

the frisch scheme in dynamic system identification abstract the use of the frisch scheme in the identification of linear dynamic systems is investigated in order to describe the whole family of models that can explain given input output noisy sequences unlike the algebraic case it is shown that in general only a single model is compatible with the data these results are first proposed for single input single output systems and then generalized to the multivariable case

on the hardness of inferring phylogenies from triplet dissimilarities this work considers the problem of reconstructing a phylogenetic tree from triplet dissimilarities which are dissimilarities defined over taxon triplets triplet dissimilarities are possibly the simplest generalization of pairwise dissimilarities and were used for phylogenetic reconstructions in the past few years we study the hardness of finding a tree best fitting a given triplet dissimilarity table under the norm we show that the corresponding decision problem is np hard and that the corresponding optimization problem cannot be approximated in polynomial time within a constant multiplicative factor smaller than 1 4 on the positive side we present a polynomial time constant rate approximation algorithm for this problem we also address the issue of best fit under maximal distortion which corresponds to the largest ratio between matching entries in two triplet dissimilarity tables we show that it is np hard to approximate the corresponding optimization problem within any constant multiplicative factor

on subspace methods for blind identification of single input multiple output fir systems blind identification of single input multiple output simo fir systems based on second order statistics has attracted a great deal of research effort we focus on subspace estimation procedures which exploit the structure of the range space of certain matrix valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations general subspace identifiability results are obtained based on properties of minimal polynomial bases of rational subspaces several subspace estimation procedures are then derived these estimators are all based on a weighted least square solution of an overdetermined system of linear equations an asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting

a constructive algorithm for realizing a distance matrix the natural metric of a weighted graph is the length of the shortest paths between all pairs of vertices the investigated problem consists in a representation of a given metric by a graph such that the total length of the graph is minimized for that purpose we give a constructive algorithm based on a technique of reduction fusion and deletion we then show some results on a set of various distance matrices whose optimal realization is known

optimal instrumental variable estimation and approximate implementations the accuracy properties of instrumental variables iv methods are investigated extensions such as prefiltering of data and use of additional instruments are included in the analysis the parameter estimates are shown to be asymptotically gaussian distributed an explicit expression is given for the covariance matrix of their distribution the covariance matrix is then taken as a multivariable measure of accuracy it is shown how it can be optimized by an appropriate selection of instruments and prefilter the so obtained optimal instrumental variable estimates cannot be used directly since the true system and the statistical properties of the disturbance must be known in order to compute the optimal instruments and prefilters a multistep procedure consisting of three or four simple steps is then proposed as a way to overcome this difficulty this procedure includes modeling of the disturbance as an arma process using a statistically efficient method such as a prediction error method the statistical properties of the estimates obtained with the multistep procedure are also analyzed those estimates are shown to be asymptotically gaussian distributed as well the covariance matrix of the estimation errors is compared to that corresponding to a prediction error method for some model structures these two approaches give the same asymptotic accuracy the conclusion is that the multistep procedure which is quite easy to implement and also has nice uniqueness properties can be viewed as an interesting alternative to prediction error methods

efficient algorithms for inverting evolution evolution can be mathematically modelled by a stochastic process that operates on the dna of species such models are based on the established theory that the dna sequences or genomes of all extant species have been derived from the genome of the common ancestor of all species by a process of random mutation and natural selection a stochastic model of evolution can be used to construct phylogenies or evolutionary trees for a set of species maximum likelihood estimation mle methods seek the evolutionary tree which is most likely to have produced the dna under consideration while these methods are intellectually satisfying they have not been widely accepted because of their computational intractability in this paper we address the intractability of mle methods as follows we introduce a metric on stochastic process models of evolution we show that this metric is meaningful by proving that in order for any algorithm to distinguish between two stochastic models that are close according to this metric it needs to be given many observations we complement this result with a simple and efficient algorithm for inverting the stochastic process of evolution that is for building a tree from observations on two state characters we will use the same techniques in a subsequent paper to solve the problem for multistate characters and hence for building a tree from dna sequence data the tree we build is provably close in our metric to the tree generating the data and gets closer as more observations become available though there have been many heuristics suggested for the problem of finding good approximations to the most likely tree our algorithm is the first one with a guaranteed convergence rate and further this rate is within a polynomial of the lower bound rate we establish ours is also the first polynomial time algorithm that is proven to converge at all to the correct tree

o sqrt logn approximation to sparsest cut in tilde o n 2 time this paper shows how to compute o sqrt log n approximations to the sparsest cut and balanced separator problems in tilde o n 2 time thus improving upon the recent algorithm of arora rao and vazirani proceedings of the 36th annual acm symposium on theory of computing 2004 pp 222 231 their algorithm uses semidefinite programming and requires tilde o n 9 5 time our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs the existence of expander flows was also established by arora rao and vazirani proceedings of the 36th annual acm symposium on theory of computing 2004 pp 222 231

skeletal shape abstraction from examples learning a class prototype from a set of exemplars is an important challenge facing researchers in object categorization although the problem is receiving growing interest most approaches assume a one to one correspondence among local features restricting their ability to learn true abstractions of a shape in this paper we present a new technique for learning an abstract shape prototype from a set of exemplars whose features are in many to many correspondence focusing on the domain of 2d shape we represent a silhouette as a medial axis graph whose nodes correspond to partsrdquo defined by medial branches and whose edges connect adjacent parts given a pair of medial axis graphs we establish a many to many correspondence between their nodes to find correspondences among articulating parts based on these correspondences we recover the abstracted medial axis graph along with the positional and radial attributes associated with its nodes we evaluate the abstracted prototypes in the context of a recognition task

strongly consistent coefficient estimate for errors in variables models for the single input single output siso errors in variables system it is assumed that the system input is an arma process and that the driven noise of the system input and the observation noise are jointly gaussian the two dimensional observation made on system input and output is represented as a two dimensional 2d arma system of minimum phase driven by a sequence of 2d i i d gaussian random vectors innovation representation it is shown that the resulting arma system is identifiable i e its coefficients are uniquely defined under reasonable conditions recursive algorithms are proposed for estimating coefficients of the arma representation including those contained in the original siso system the estimates are proved to be convergent to the true values with probability one and the convergence rate is derived as well the theoretical results are justified by numerical simulation

global existence to boltzmann equation with external force in infinite vacuum in this paper we give a condition on the bicharacteristic which guarantees the global existence of the mild solution to the boltzmann equation with an external force for the hard sphere model and potentials with angular cutoff in infinite vacuum this generalizes the previous results to the case when the force can have arbitrary strength the constructive condition on the bicharacteristic is used to obtain the pointwise estimates on the collision operator so that the global existence comes from the contraction mapping theorem

object recognition as many to many feature matching object recognition can be formulated as matching image features to model features when recognition is exemplar based feature correspondence is one to one however segmentation errors articulation scale difference and within class deformation can yield image and model features which don t match one to one but rather many to many adopting a graph based representation of a set of features we present a matching algorithm that establishes many to many correspondences between the nodes of two noisy vertex labeled weighted graphs our approach reduces the problem of many to many matching of weighted graphs to that of many to many matching of weighted point sets in a normed vector space this is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure many to many vector correspondences established by the earth mover s distance framework are mapped back into many to many correspondences between graph nodes empirical evaluation of the algorithm on an extensive set of recognition trials including a comparison with two competing graph matching approaches demonstrates both the robustness and efficacy of the overall approach

identification of closed loop linear systems via cyclic spectral analysis given noisy input output time domain data the problem of closed loop system identification given noisy time domain input output measurements is considered it is assumed that the various disturbances affecting the system are zero mean stationary whereas the closed loop system operates under an external cyclostationary input which is not measured noisy measurements of the direct input and output of the plant are assumed to be available the closed loop system must be stable but it is allowed to be unstable in open loop no knowledge about the linear feedback mechanism is assumed two identification algorithms are investigated using cyclic spectral analysis of noisy input output data for both approaches the open loop transfer function is first estimated using the cyclic spectrum and cyclic cross spectrum of the input output data these transfer function estimates are then used as data for the proposed algorithms both classes of parameter estimators are shown to be weakly consistent in any stationary noise both at input as well as output asymptotic performance analysis of the proposed parameter estimators is also provided computer simulation examples are presented in support of the proposed approaches

subspace algorithms for the identification of multivarible dynamic errors in variables models abstract we consider the problem of identifying multivariable finite dimensional linear time invariant systems from noisy input output measurements apart from the fact that both the measured input and output are corrupted by additive white noise the output may also be contaminated by a term which is caused by a white input process noise furthermore all these noise processes are allowed to be correlated with each other we shall develop a solution to this problem in the framework of subspace identification and we shall show that our algorithms give consistent estimates when the system is operating in open or closed loop two realistic simulation studies are presented to demonstrate the practical applicability of the proposed algorithms 1997 elsevier science ltd

stability of the boltzmann equation with potential forces on torus abstract in this paper we are concerned with the stability of solutions to the cauchy problem of the boltzmann equation with potential forces on torus it is shown that the natural steady state with the symmetry of origin is asymptotically stable in the sobolev space with exponential rate in time for any initially smooth periodic origin symmetric small perturbation which preserves the same total mass momentum and mechanical energy for the non symmetric steady state it is also shown that it is stable in l 1 norm for any initial data with the finite total mass mechanical energy and entropy

on the uniqueness of prediction error models for systems with noisy input output data abstract this paper addresses the uniqueness problem of the prediction error pe identification for a class of linear systems with noisy input and output data necessary and sufficient conditions are derived for the corresponding pe loss function to have asymptotically a unique global minimum the results indicate that a pe algorithm may give very bad parameter estimates for systems not satisfying these conditions such a possibility is illustrated by a numerical example while the pe method is used as a vehicle for illustration the derived conditions for global uniqueness or identifiability apply to any consistent estimation method based on second order data

bias correction in least squares identification abstract the least squares method in system identification leads generally to biased parameter estimates a conceptually simple modification is to estimate the bias and to compute compensated parameter estimates when white output noise is the only disturbance this principle compensated least squares cls can readily be used to obtain consistent estimates the main purpose of the paper is to investigate the accuracy of the parameter estimates obtained when the cls method is used it is proved that the estimates are asymptotically gaussian distributed an explicit expression for the covariance matrix is given it is also shown that a commonly used instrumental variable method gives asymptotically better accuracy than the compensated least squares method

variance reduction in covariance based realization algorithm with application to closed loop data abstract the covariance based realization algorithm cobra one branch of subspace methods enables the estimation of multivariable models using a large number of data points due to the use of finite size covariance matrices in addition the covariance pre processing allows cobra to ignore any high order noise dynamics and focus on the estimation of the low order deterministic model however subspace methods and cobra in particular are not maximum likelihood methods in this paper an in depth study on the statistical behavior of the noise effects is conducted an approach is provided to reduce the variance of an estimate obtained by cobra via the choice of optimal row and column weighting matrices for closed loop implementation of cobra a two stage procedure is proposed with the estimate on an intermediate instrument at the first stage a least length perturbation of a scalar accuracy function is used to obtain an analytic solution for the optimal weighting matrices the resulting instruments produced by the first stage are used for the identification at the second stage to extract the plant model simulation examples are given to illustrate the efficiency of the proposed two stage cobra method on the basis of closed loop data and compared with other subspace methods

upgma and the normalized equidistant minimum evolution problem upgma unweighted pair group method with arithmetic mean is a widely used clustering method here we show that upgma is a greedy heuristic for the normalized equidistant minimum evolution neme problem that is finding a rooted tree that minimizes the minimum evolution score relative to the dissimilarity matrix among all rooted trees with the same leaf set in which all leaves have the same distance to the root we prove that the neme problem is np hard in addition we present some heuristic and approximation algorithms for solving the neme problem including a polynomial time algorithm that yields a binary rooted tree whose neme score is within o log2n of the optimum

on closed loop system identification using polyspectral analysis given noisy input output time domain data parametric models of linear systems operating in closed loop can be consistently identified from time domain noisy input output measurements using cumulant spectra without requiring parametric modeling of noise two algorithms are proposed and their asymptotic performance is analyzed

optimal decay estimates on the linearized boltzmann equation with time dependent force and their applications although the decay in time estimates of the semi group generated by the linearized boltzmann operator without forcing have been well established there is no corresponding result for the case with general external force this paper is mainly concerned with the optimal decay estimates on the solution operator in some weighted sobolev spaces for the linearized boltzmann equation with a time dependent external force no time decay assumption is made on the force the proof is based on both the energy method through the macro micro decomposition and the lp lq estimates from the spectral analysis the decay estimates thus obtained are applied to the study on the global existence of the cauchy problem to the nonlinear boltzmann equation with time dependent external force and source precisely for space dimension n 3 the global existence and decay rates of solutions to the cauchy problem are obtained under the condition that the force and source decay in time with some rates this time decay restriction can be removed for space dimension n 5 moreover the existence and asymptotic stability of the time periodic solution are given for space dimension n 5 when the force and source are time periodic with the same period

combinatorics of distance based tree inference several popular methods for phylogenetic inference or hierarchical clustering are based on a matrix of pairwise distances between taxa or any kind of objects the objective is to construct a tree with branch lengths so that the distances between the leaves in that tree are as close as possible to the input distances if we hold the structure topology of the tree fixed in some relevant cases e g ordinary least squares the optimal values for the branch lengths can be expressed using simple combinatorial formulae here we define a general form for these formulae and show that they all have two desirable properties first the common tree reconstruction approaches least squares minimum evolution when used in combination with these formulae are guaranteed to infer the correct tree when given enough data consistency second the branch lengths of all the simple nearest neighbor interchange rearrangements of a tree can be calculated optimally in quadratic time in the size of the tree thus allowing the efficient application of hill climbing heuristics the study presented here is a continuation of that by mihaescu and pachter on branch length estimation mihaescu r pachter l 2008 proc natl acad sci usa 105 13206 13211 the focus here is on the inference of the tree itself and on providing a basis for novel algorithms to reconstruct trees from distances

global stability of boltzmann equation with large external potential for a class of large oscillation data abstract in this paper we investigate the stability of boltzmann equation with large external potential in t 3 for a class of initial data with large oscillations in l x v around the local maxwellian we prove the existence of a global solution to the boltzmann equation provided the initial perturbation is suitably small in l 2 norm the large time behavior of the boltzmann solution with exponential decay rate is also obtained this seems to be the first result on the perturbation theory of large amplitude non constant equilibriums for large amplitude initial data

an improved bias compensation approach for errors in variables model identification parametric estimation of the dynamic errors in variables models is considered in this paper in particular a bias compensation approach is examined in a generalized framework sufficient conditions for uniqueness of the identified model are presented subsequently a statistical accuracy analysis of the estimation algorithm is carried out the asymptotic covariance matrix of the system parameter estimates depends on a user chosen filter and a certain weighting matrix it is shown how these can be tuned to boost the estimation performance the numerical simulation results suggest that the covariance matrix of the estimated parameter vector is very close to the cramer rao lower bound for the estimation problem

worst case identification of errors in variables models in closed loop a worst case identification method in frequency domain is proposed to cope with the identification of errors in variables models eivms in closed loop with a priori bound for the disturbing noises of an eivm in closed loop a frequency domain normalized coprime factor model ncfm with perturbation is derived and thus the identification of the eivm becomes that of the ncfm by employing the v gap metric as an optimization criterion the worst case error for an identified nominal ncfm is easily quantified and the parameter optimization can be effectively solved by linear matrix inequalities lmis during the parameter optimization the derivative of the nominal ncfm is constrained to some degree to reduce the effect of overfitting phenomenon different from other eivm identification methods we use v gap metric to characterize the disturbing noises and quantify the worst case error for the nominal ncfm as a result the identification result is not a deterministic model but a model set moreover this model set can be perfectly combined with the robust controller design finally a numerical simulation is presented to verify the proposed method

suppression of bursting abstract we investigate the possibility of using a single small amplitude control input and feedback to stabilize equilibrium sets in a class of highly nonlinear o 2 symmetric dynamical systems possessing structurally stable heteroclinic cycles the leading order behavior near the equilibria is bilinear and homogeneous in the state variables while nonlinearities representing the symmetry breaking effect of the controller are crucial after a series of simplifying transformations we use ideas from optimal control theory to construct a stabilizing controller this study is motivated by the desire to stabilize the burst sweep cycle in low dimensional models of a turbulent boundary layer in the last two sections we apply the techniques to the 10 dimensional system of aubry et al 1988 kw bilinear systems dynamical systems heteroclinic cycles normal forms optimal control symmetry

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

provably fast and accurate recovery of evolutionary trees through harmonic greedy triplets we give a greedy learning algorithm for reconstructing an evolutionary tree based on a certain harmonic average on triplets of terminal taxa after the pairwise distances between terminal taxa are estimated from sequence data the algorithm runs in smallbigo numtaxa 2 time using smallbigo numtaxa work space where numtaxa is the number of terminal taxa these time and space complexities are optimal in the sense that the size of an input distance matrix is numtaxa 2 and the size of an output tree is numtaxa moreover in the jukes cantor model of evolution the algorithm recovers the correct tree topology with high probability using sample sequences of length polynomial in 1 numtaxa 2 the logarithm of the error probability and 3 the inverses of two small parameters

stochastic system identification with noisy input using cumulant statistics addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated it is assumed that the input is non gaussian and the noises are gaussian the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation an optimization algorithm is presented strong consistency of the proposed parameter estimators is proved under certain sufficient conditions both single input single output and multiple input multiple output cases are investigated finally simulation results are presented to illustrate the proposed approach

combined instrumental variable and subspace fitting approach to parameter estimation of noisy input output systems the paper considers the problem of estimating the parameters of linear discrete time systems from noise corrupted input output measurements under fairly general conditions the output and input noises may be auto correlated and they may be cross correlated as well by using the instrumental variable iv principle a covariance matrix is obtained the singular vectors of which bear complete information on the parameters of the system under study a weighted subspace fitting wsf procedure is then employed on the sample singular vectors to derive estimates of the parameters of the system the combined iv wsf method proposed in the present paper is noniterative and simple to use its large sample statistical performance is analyzed in detail and the theoretical results so obtained are used to predict the behavior of the method in samples with practical lengths several numerical examples are included to show the agreement between the theoretically predicted and the empirically observed performances