well posedness for the schrodinger korteweg de vries system we study well posedness of the cauchy problem associated to the schrodinger korteweg de vries system we obtain local well posedness for weak initial data where the best result obtained is for data in the sobolev space l 2 r x h 3 4 this result implies in particular the global well posedness in the energy space h 1 r x h 1 r both results considerably improve the previous ones by bekiranov ogawa and ponce 1997 guo and miao 1999 and tsutsumi 1993

stochastic decision making in the minority game abstract a discussion is presented of the effects of stochasticity in the decision making of agents in the minority game both simulational and analytic results are reported and discussed for both additive and multiplicative noise as a function of the ratio d of information dimension to number of agents a phase transition separates a low d non ergodic phase from a high d ergodic phase for additive noise the critical dc is temperature independent but for multiplicative noise dc t decreases with t additive noise does not affect the asymptotic behaviour for d dc but is relevant below dc multiplicative noise has consequence for all d

dynamical solution of the on line minority game we solve the dynamics of the on line minority game mg with general types of decision noise using generating functional techniques a la de dominicis and the temporal regularization procedure of bedeaux et al the result is a macroscopic dynamical theory in the form of closed equations for correlation and response functions defined via an effective continuous time single trader process which are exact in both the ergodic and in the non ergodic regime of the mg our solution also explains why although one cannot formally truncate the kramers moyal expansion of the process after the fokker planck term upon doing so one still finds the correct solution that the previously proposed diffusion matrices for the fokker planck term are incomplete and how previously proposed approximations of the market volatility can be traced back to ergodicity assumptions

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

continuous time dynamics of the thermal minority game we study the continuous time dynamics of the thermal minority game we find that the dynamical equations of the model reduce to a set of stochastic differential equations for an interacting disordered system with nontrivial random diffusion this is the simplest microscopic description which accounts for all the features of the system within this framework we study the phase structure of the model and find that its macroscopic properties strongly depend on the initial conditions

on the minority game analytical and numerical studies abstract we investigate further several properties of the minority game we have recently introduced we explain the origin of the phase transition and give an analytical expression of 2 n in the n 2 m region the ability of the players to learn a given payoff is also analyzed and we show that the darwinian evolution process tends to a self organized state in particular the lifetime distribution is a power law with exponent 2 furthermore we study the influence of identical players on their gain and on the systems performance finally we show that large brains always take advantage of small brains

accurate and computationally efficient tensor based subspace approach for multidimensional harmonic retrieval in this paper parameter estimation for r dimensional r d sinusoids with r 2 in additive white gaussian noise is addressed with the use of tensor algebra and principal singular vector utilization for modal analysis the sinusoidal parameters at one dimension are first accurately estimated according to an iterative procedure which utilizes the linear prediction property and weighted least squares the damping factors and frequencies in the remaining dimensions are then solved such that pairing of the r d parameters is automatically achieved algorithm modification for a single r d tone is made and it is proved that the frequency estimates are asymptotically unbiased while their variances approach cramer rao lower bound at sufficiently high signal to noise ratio conditions computer simulations are also included to compare the proposed approach with conventional r d harmonic retrieval schemes in terms of mean square error performance and computational complexity

minority game with sk interactions a batch minority game with fake random history and additional sk like quenched interaction is introduced and analysed a mixing parameter quantifies the admixture and dictates the relative dominance of the two contributions if 0 agent decisions are based on their strategies and point scores alone as in the pure minority game whereas for 0 the agents also communicate with each other directly and update their points accordingly keeping the minority game dynamics in which the agents points are updated in parallel at each time step the aim is to understand what happens if instead of simply using the normal strategy based decisions the agents also take account of an effective field generated by the other agents it is shown that the sk interaction introduces a noise term which is broader than that in the normal minority game and which furthermore kills the normal phase transition it is also shown that the same effect would occur if instead of an sk interaction gaussian distributed quenched random fields are added by calculating order parameters in the time translational invariant phase we show that the system is persistent in a ergodic phase both simulational and analytical results are presented

the cauchy problem for the schrodinger kdv system abstract in this paper we prove that in the general case i e not necessarily vanishing the cauchy problem for the schrodinger korteweg de vries system is locally well posed in l 2 h 3 4 and if 0 then it is locally well posed in h s h 3 4 with 3 16 s 1 4 these results improve the corresponding results of corcho and linares 2007 5 idea of the proof is to establish some bilinear and trilinear estimates in the space g s f s where g s and f s are dyadic bourgain type spaces related to the schrodinger operator i t x 2 and the airy operator t x 3 respectively but with a modification on f s in low frequency part of functions with a weaker structure related to the maximal function estimate of the airy operator

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

the most efficient implementation of the iqml algorithm the work by clark and scharf 1992 showed a new implementation of the iqml iterative quadratic maximum likelihood algorithm which requires at each iteration computational flops of order n sup 2 where n is the dimension of signal vector or length of data sequence they also indicated that the implementation of other related algorithms such as the steiglitz mcbride 1965 algorithm would also require order n sup 2 computations the present author gives a better way of implementation which requires computational flops of the order n this better way of implementation is shown in detail for the iqml algorithm following the same idea shown in the present paper one can also straightforwardly design the order n implementation of the steiglitz mcbride algorithm the present implementation is also the most efficient in that no implementation can be made less than order n sup 2

a generalized weighted linear predictor frequency estimation approach for a complex sinusoid based on linear prediction and weighted least squares three simple iterative algorithms for frequency estimation of a complex sinusoid in additive white noise are devised the proposed approach which utilizes the first order as well as higher order linear prediction terms simultaneously but does not require phase unwrapping can be considered as a generalized version of the weighted linear predictor frequency estimator in particular convergence as well as mean and variance analysis of the most computationally efficient frequency estimator namely gwlp 2 are provided computer simulations are included to contrast the performance of the proposed algorithms with several conventional computationally attractive frequency estimators and crame spl acute r rao lower bound for different frequencies observation lengths and signal to noise ratios

scattering for the quartic generalised korteweg de vries equation abstract we show that the quartic generalised kdv equation u t u x x x u 4 x 0 is globally well posed for data in the critical scale invariant space h x 1 6 r with small norm and locally well posed for large norm improving a result of grunrock a grunrock a bilinear airy estimate with application to gkdv 3 differential integral equations 18 12 2005 1333 1339 as an application we obtain scattering results in h x 1 r h x 1 6 r for the radiation component of a perturbed soliton for this equation improving the asymptotic stability results of martel and merle y martel f merle asymptotic stability of solitons for subcritical generalized kdv equations arch ration mech anal 157 3 2001 219 254

irrelevance of memory in the minority game by means of extensive numerical simulations we show that all the distinctive features of the minority game introduced by challet and zhang physica a 256 514 1998 are completely independent of the memory of the agents the only crucial requirement is that all the individuals must possess the same information irrespective of whether this information is true or false

an algorithm for pole zero modeling and spectral analysis an explicit connection between fitting exponential models and pole zero models to observed data is made the fitting problem is formulated as a constrained nonlinear minimization problem this problem is then solved using a simplified iterative algorithm the algorithm is applied to simulated data and the performance of the algorithm is compared to previous results

the extended least squares criterion minimization algorithms and applications the least squares ls estimation criterion on one hand and the total ls tls constrained tls ctls and structured tls stls criteria on the other hand can be viewed as opposite limiting cases of a more general criterion which we term extended ls xls the xls criterion distinguishes measurement errors from modeling errors by properly weighting and balancing the two error sources in the context of certain models termed pseudo linear we derive two iterative algorithms for minimizing the xls criterion one is a straightforward alternating coordinates minimization and the other is an extension of an existing ctls algorithm the algorithms exhibit different tradeoffs between convergence rate computational load and accuracy the xls criterion can be applied to popular estimation problems such as identifying an autoregressive ar with exogenous noise arx system from noisy input output measurements or estimating the parameters of an ar process from noisy measurements we demonstrate the convergence properties and performance of the algorithms with examples of the latter

sharp well posedness and ill posedness results for a quadratic non linear schrodinger equation abstract we establish that the quadratic non linear schrodinger equation iu t u xx u 2 where u r r c is locally well posed in h s r when s 1 and ill posed when s 1 previous work in c kenig g ponce l vega quadratic forms for the 1 d semilinear schrodinger equation trans amer math soc 346 1996 3323 3353 had established local well posedness for s 3 4 the local well posedness is achieved by an iteration using a modification of the standard x s b spaces the ill posedness uses an abstract and general argument relying on the high to low frequency cascade present in the non linearity and a computation of the first non linear iterate

three phases of the minority game we define three phases of the minority game according to the value 2m n 2m n the ratio of the number of entries in a strategy to the number of agents the time sequence of the population in one room has distinct feature in different phase it shows quasi periodic structure in the first phase where c2 c2 the system is able to reach its best performance in reducing the population variance the crucial factor which hinders the system to reach its best performance in the first and second phases is the number of agents who switch strategy at the same time when c2 c2 the constraint that bound 2m predictions in a strategy is small so that too many agents will switch to a better strategy simultaneously as a result they form a majority group and are more likely to lose we give analytical approximate formulas for the population variance in the first and third phases we have also determined the phase changing point c1 c1

modal analysis using co prime arrays we address the problem of estimating mode parameters from noisy observations of a linear combination of the corresponding modes this problem arises in line spectrum estimation vibration analysis speech processing system identification and direction of arrival estimation our results differ from standard results of modal analysis to the extent that we consider co prime samplings in space or equivalently co prime samplings in time our main result is a characterization of the orthogonal subspace for this problem this is the subspace that is orthogonal to the signal subspace spanned by the columns of the generalized vandermonde matrix of modes in co prime samplings this characterization is derived in a form that allows us to adapt modern methods of subspace signal processing to co prime sampled signals several numerical examples are presented to demonstrate the application of the proposed modal estimation method we state and prove theorems on identifiability of the modes and calculate a cramer rao bound that allows us to analyze the performance of co prime arrays that are subsamplings of uniform linear arrays of the same apertures

dynamics of the batch minority game with inhomogeneous decision noise we study the dynamics of a version of the batch minority game with random external information and with different types of inhomogeneous decision noise additive and multiplicative using generating functional techniques a la de dominicis the control parameters in this model are the ratio ensuremath alpha p n of the number p of possible values for the external information over the number n of trading agents and the statistical properties of the agents decision noise parameters the presence of decision noise is found to have the general effect of damping macroscopic oscillations which explains why in certain parameter regions it can effectively reduce the market volatility as observed in earlier studies in the limit n ensuremath rightarrow ensuremath infty we i solve the first few time steps of the dynamics for any ensuremath alpha ii calculate the location ensuremath alpha c of the phase transition signaling the onset of anomalous response and iii solve the statics for ensuremath alpha g ensuremath alpha c we find that ensuremath alpha c is not sensitive to additive decision noise but we arrive at nontrivial phase diagrams in the case of multiplicative noise our theoretical results find excellent confirmation in numerical simulations

generating functional analysis of the dynamics of the batch minority game with random external information we study the dynamics of the batch minority game with random external information using generating functional techniques introduced by de dominicis the relevant control parameter in this model is the ratio a5 p n of the number p of possible values for the external information over the number n of trading agents in the limit n we calculate the location a c of the phase transition signaling the onset of anomalous response and solve the statics for a a c exactly the temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times for a a c the stationary state is shown to be nonunique for a 0 we analyze our equations in leading order in a and find asymptotic solutions with diverging volatility s5o a 21 2 as regularly observed in simulations but also asymptotic solutions with vanishing volatility s5o a 1 2 the former however are shown to emerge only if the agents initial strategy valuations are below a specific critical value

comments on a weighted least squares method for the design of stable 1 d and 2 d iir digital filters with reply for original paper by lu et al see ieee trans signal processing vol 46 p 1 10 1998 january the iterative procedure by lu et al for designing iir filters is recognized as the sanathanan koerner or steiglitz mcbride iteration which was proposed originally in 1963 and 1965 respectively for system identification purposes we re examine some claims and issues related to lu et al s paper in view of various properties that have been deduced for the steiglitz mcbride iteration in the identification literature in particular the steiglitz mcbride procedure is known not to minimize a least squares distance measure contrary to lu et al s claim it can however provide good models and remain stable during successive iterations under specific conditions which are reviewed a reply is given by lu et al

total least squares for affinely structured matrices and the noisy realization problem structured rank deficient matrices arise in many applications in signal processing system identification and control theory the author discusses the structured total least squares stls problem which is the problem of approximating affinely structured matrices i e matrices affine in the parameters by similarly structured rank deficient ones while minimizing an l sub 2 error criterion it is shown that the optimality conditions lead to a nonlinear generalized singular value decomposition which can be solved via an algorithm that is inspired by inverse iteration next the author concentrates on the so called l sub 2 optimal noisy realization problem which is equivalent with approximating a given data sequence by the impulse response of a finite dimensional time invariant linear system of a given order this can be solved as a structured total least squares problem it is shown with some simple counter examples that classical algorithms such as the steiglitz mcbride 1965 iterative quadratic maximum likelihood and cadzow s 1988 iteration do not converge to the optimal l sub 2 solution despite misleading claims in the literature

on the complexity of iqml algorithms the authors study the computational complexity of two methods for solving least squares and maximum likelihood modal analysis problems in particular they consider the steiglitz mcbride and iterative quadratic maximum likelihood iqml algorithms j h mcclellan and d lee ibid vol 39 no 2 p 509 12 1991 have shown the iterations of the two methods to be equivalent however they suggest that the steiglitz mcbride algorithm may be computationally preferable a method for reducing the dimension of the matrix inversion required at each iteration of iqml is provided the resulting reduction in the computation makes the computational complexity of iqml commensurate with that of the steiglitz mcbride algorithm

crowd effects and volatility in markets with competing agents abstract we present analytic and numerical results for two models namely the minority model and the bar attendance model which offer simple paradigms for a competitive marketplace both models feature heterogeneous agents with bounded rationality who act using inductive reasoning we find that the effects of crowding are crucial to the understanding of the macroscopic fluctuations or volatility in the resulting dynamics of these systems

parametric identification using weighted null space fitting in identification of dynamical systems the prediction error method with a quadratic cost function provides asymptotically efficient estimates under gaussian noise but in general it requires solving a nonconvex optimization problem which may imply convergence to nonglobal minima an alternative class of methods uses a nonparametric model as intermediate step to obtain the model of interest weighted null space fitting wnsf belongs to this class starting with the estimate of a nonparametric arx model with least squares then the reduction to a parametric model is a multistep procedure where each step consists of the solution of a quadratic optimization problem which can be obtained with weighted least squares the method is suitable for both open and closed loop data and can be applied to many common parametric model structures including output error armax and box jenkins the price to pay is the increase of dimensionality in the nonparametric model which needs to tend to infinity as function of the sample size for certain asymptotic statistical properties to hold in this paper we conduct a rigorous analysis of these properties namely consistency and asymptotic efficiency also we perform a simulation study illustrating the performance of wnsf and identify scenarios where it can be particularly advantageous compared with state of the art methods

maximum likelihood binary shift register synthesis from noisy observations we consider the problem of estimating the feedback coefficients of a linear feedback shift register based on noisy observations the problem of determining feedback coefficients in the absence of noise is now classical massey s 1969 algorithm in the current approach to the problem of estimation with noisy observations the coefficients are endowed with a probabilistic model gradient ascent updates to coefficient probabilities are computed using recursions developed by means of the expectation maximization em algorithm reduced complexity approximations are also developed by reducing the number forward probability terms propagated at each stage while suffering from a local maximum problem typical of many maximum likelihood ml procedures the method does exhibit convergence

comparative study of iqml and mode direction of arrival estimators we present a comparative study of using the iterative quadratic maximum likelihood iqml and the method of direction estimation mode for direction of arrival doa estimation of narrowband incident signals with a uniform linear array the conditions for local convergence and the theoretical performance of iqml are derived although the doa estimates obtained via mode are asymptotically statistically efficient we show that those obtained via iqml are almost always inconsistent and have much larger mean squared errors we also show that the amount of computations required by iqml is usually much larger than that required by mode especially for low signal to noise ratio snr and a large number of snapshots

parametric identification of transfer functions in the frequency domain a survey this paper gives a survey of frequency domain identification methods for rational transfer functions in the laplace s or z domain the interrelations between the different approaches are highlighted through a study of the equivalent cost functions the properties of the various estimators are discussed and illustrated by several examples

optimal identification of discrete time systems from impulse response data an optimal method om for estimation of the parameters of rational transfer functions from prescribed impulse response data is presented the multidimensional nonlinear fitting error minimization problem has been theoretically decoupled into two subproblems of reduced computational complexities the proposed approach is applicable for identifying rational models with arbitrary numbers of poles and zeros the nonlinear denominator subproblem possesses weighted quadratic structure which is utilized to formulate an efficient iterative minimization algorithm the optimal numerator is found noniteratively with a linear least squares approach that utilizes the optimized denominator both the decoupled subcriteria of om posses global optimality properties the steiglitz mcbride 1960 sm method is also decoupled for arbitrary numbers of poles and zeros dsm g it is demonstrated that the denominator subproblem of dsm g is theoretically optimal for another existing decoupled sm method dsm j it has been shown that only the numerator is theoretically optimal

exact equivalence of the steiglitz mcbride iteration and iqml the exact equivalence of the steiglitz mcbride mode 1 algorithm and the iterative quadratic maximum likelihood algorithm iqml is demonstrated other methods published earlier by l l scharf et al 1986 and by a g evans and r fischl 1973 are also known to give the same equations and answer as iqml hence all these methods are equivalent to the steiglitz mcbride iteration since the iqml method was originally formulated to solve a multiple measurement case an extended version of the steiglitz mcbride mode 1 algorithm applicable to the multiple measurement case is also stated and shown to be equivalent to the general form of iqml

statistical mechanics of systems with heterogeneous agents minority games we study analytically a simple game theoretical model of heterogeneous interacting agents we show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz such a stationary state differs from the nash equilibrium where each agent maximizes her own utility the latter turns out to be characterized by a replica symmetry broken structure numerical results fully agree with our analytical findings

two dimensional modal analysis based on maximum likelihood the authors present a method for estimating the parameters of 2 d damped harmonic modal signals in additive gaussian noise this method applies in the cases of single or multiexperiment data and incoherent or coherent signals both synthesis and analysis models for the data are developed central to these models are the signal and orthogonal subspaces under the assumption of distinct modes in one of the two dimensions there exists an invertible function between the parameters of these two subspaces this function can be used to express the optimization problem given by maximum likelihood in terms of the orthogonal subspace the resulting problem can be solved by any of several methods including total least squares and iterative quadratic maximum likelihood iqml