derivation of the matrix product ansatz for the heisenberg chain from the algebraic bethe ansatz we derive a matrix product representation of the bethe ansatz state for the xxx and xxz spin heisenberg chains using the algebraic bethe ansatz in this representation the components of the bethe eigenstates are expressed as traces of products of matrices which act on the tensor product of auxiliary spaces by changing the basis in we derive explicit finite dimensional representations for the matrices these matrices are the same as those appearing in the recently proposed matrix product ansatz by alcaraz and lazo 2006 j phys a math gen 39 11335 apart from normalization factors we also discuss the close relation between the matrix product representation of the bethe eigenstates and the six vertex model with domain wall boundary conditions korepin 1982 commun math phys 86 391 and show that the change of basis corresponds to a mapping from the six vertex model to the five vertex model

an mdl algorithm for detecting more sources than sensors using outer products of array output 1991 2012 ieee in this paper we propose an algorithm for detecting the number m of gaussian sources received by an array of a number n n m of sensors this algorithm is based on the minimum description length mdl principle using the outer products of the array output we show that as long as the covariance matrix of the array output has the full rank n the covariance matrix of a vectorized outer product of the array output has the full rank n squared which meets a validity condition of the mdl algorithm we show by simulation that the mdl algorithm can perform substantially better than some relevant algorithms a necessary identifiability condition is also obtained for uncorrelated sources

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

colored noise induced chaotic array synchronization the effect of a time correlated gaussian noise on one dimensional arrays consisting of diffusively coupled chaotic cells is analyzed a resonance effect between the time scale of the chaotic attractor and the colored gaussian noise has been found as well depending on the number of cells coupling and noise strength an improvement of the synchronization or a poor synchronization between cells within the array can occur for some values of the time correlation these nonlinear cooperative effects are studied in terms of a linear stability analysis around the uniform synchronized behavior

robust adaptive beamforming based on the eigenstructure method in a linearly constrained beamformer with imperfect arrays the authors investigate the cause of cancelling the desired signal from a viewpoint based on the eigenstructure properties of the array covariance matrix based on this cause they propose a robust beamforming algorithm as an adaptive algorithm of the proposed beamformer the present a data domain signal subspace updating algorithm

the slˆ n k wznw fusion ring a combinatorial construction and a realisation as quotient of quantum cohomology abstract a simple combinatorial construction of the sl n k wznw fusion ring also known as verlinde algebra is given as a byproduct of the construction one obtains an isomorphism between the fusion ring and a particular quotient of the small quantum cohomology ring of the grassmannian gr k k n we explain how our approach naturally fits into known combinatorial descriptions of the quantum cohomology ring by establishing what one could call a boson fermion correspondence between the two rings we also present new recursion formulae for the structure constants of both rings the fusion coefficients and the gromov witten invariants

synchronous chaos in coupled oscillator systems we investigate the synchronization of chaotic oscillations in coupled oscillator systems both theoretically and in analog electronic circuits particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift invariant symmetry these cases include the well studied cases of nearest neighbor diffusive coupling and all to all or global coupling an approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit when the oscillators are coupled through a single coordinate scalar coupling this stability criterion is illustrated numerically in a set of coupled r ossler like oscillators synchronization experiments with coupled r ossler like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems

boxed plane partitions as an exactly solvable boson model plane partitions naturally appear in many problems of statistical physics and quantum field theory for instance in the theory of faceted crystals and of topological strings on calabi yau threefolds in this paper a connection is made between the exactly solvable model with the boson dynamical variables and a problem of enumeration of boxed plane partitions three dimensional young diagrams placed into a box of a finite size the scalar product of the introduced model gives the macmahon enumeration formula while the correlation functions of the model may be considered as the generating functionals of the young diagrams with the fixed heights of its certain columns the evaluation of the scalar product and the correlation functions is based on the yang baxter algebra the analytical answers are obtained in terms of determinants and they can also be expressed through the schur functions

the determination of optimum structures for the state space representation of multivariate stochastic processes when identifying a model for a multivariate stationary stochastic process an important problem is that of determining the structure of the state variable model several overlapping parameterizations can usually be fitted to a given process and the question arises as to which structure leads to the most accurate parameter estimates the accuracy of parameter estimates is often measured by the determinant of the fisher information matrix we show that all admissible structures will give asymptotically the same value to this criterion for finite data some structures may still be better than others and two heuristic structure estimation methods are analyzed some simulation results are also presented

a deformation of affine hecke algebra and integrable stochastic particle system we introduce a deformation of the affine hecke algebra of type which describes the commutation relations of the divided difference operators found by lascoux and schutzenberger and the multiplication operators making use of its representation we construct an integrable stochastic particle system it is a generalization of the q boson system due to sasamoto and wadati we also construct eigenfunctions of its generator using the propagation operator as a result we get the same eigenfunctions for the boson process obtained by povolotsky

detection of coherent signals using weighted subspace smoothing a new approach to detecting the number of coherent signals incident upon a uniformly spaced linear array is presented the approach combines a modified spatial smoothing scheme and a modified mdl criterion the modified spatial smoothing scheme referred to as weighted subspace smoothing is actually a generalization of the post smoothing approach proposed by krim and proakis in 1994 it is shown that the noise eigenvalues obtained with weighted subspace smoothing are more accurate than those obtained with the original spatial smoothing we thus attempt to improve the detection performance using these more accurate eigenvalues a novel modification of the minimum description length mdl criterion is proposed to accomplish this computer simulations are presented to study the performance improvement of this new approach

the influence of noise on the logistic model the behavior of the logistic system which is generated by the functionf x ax 1 x changes in an interesting way if it is perturbed by external noise it turns out that the chaotic behavior which was predicted by li and yorke for orbits of period 3 becomes visible and that a sequence of mergence transitions occurs at the critical parameter the change of the invariant probability density and the lyapunov exponents are examined numerically the power spectrum for the period 3 orbit for different fluctuations is calculated and a recursion formula for the time evolution of the probability density is presented as a discrete time analog of a chapman kolmogorov equation

nonparametric detection of signals by information theoretic criteria performance analysis and an improved estimator determining the number of sources from observed data is a fundamental problem in many scientific fields in this paper we consider the nonparametric setting and focus on the detection performance of two popular estimators based on information theoretic criteria the akaike information criterion aic and minimum description length mdl we present three contributions on this subject first we derive a new expression for the detection performance of the mdl estimator which exhibits a much closer fit to simulations in comparison to previous formulas second we present a random matrix theory viewpoint of the performance of the aic estimator including approximate analytical formulas for its overestimation probability finally we show that a small increase in the penalty term of aic leads to an estimator with a very good detection performance and a negligible overestimation probability

on information theoretic criteria for determining the number of signals in high resolution array processing an important problem in high resolution array processing is the determination of the number of signals arriving at the array information theoretic criteria provide a means to achieve this two commonly used criteria are the akaike information criterion aic and minimum descriptive length mdl criterion while the aic tends to overestimate even at a high signal to noise ratio snr the mdl criterion tends to underestimate at low or moderate snr by excluding irrelevant parameters a new log likelihood function has been chosen utilizing this new log likelihood function gives a set of more accurate estimates of the eigenvalues and in the establishment of modified information theoretic criteria which moderate the performance of the aic and the mdl criterion computer simulations confirm that the modified criteria have superior performance

boxed skew plane partition and integrable phase model we study the relation between the boxed skew plane partition and the integrable phase model we introduce a generalization of a scalar product of the phase model and calculate it in two ways the first one in terms of the skew schur functions and the other one by use of the commutation relations of operators in both cases a generalized scalar product is expressed as a determinant we show that a special choice of the spectral parameters of a generalized scalar product gives the generating function of the boxed skew plane partition

paper selecting the best linear transfer function model statistics currently used to determine the best model order based on the covariance of the parameter estimates or the instrumental product moment matrix are critically examined particularly for their applicability to situations where input and output units differ or where there is a large or small steady state gain a normalization process is advocated which extends the usefulness and reliability of the statistics in these situations a procedure for comparing determinant statistics for models of different orders is described which simplifies current methods the improved procedures and statistics are compared using simulated data and an instrumental variable estimation method confirming their worth

non parametric detection of the number of signals hypothesis testing and random matrix theory detection of the number of signals embedded in noise is a fundamental problem in signal and array processing this paper focuses on the non parametric setting where no knowledge of the array manifold is assumed first we present a detailed statistical analysis of this problem including an analysis of the signal strength required for detection with high probability and the form of the optimal detection test under certain conditions where such a test exists second combining this analysis with recent results from random matrix theory we present a new algorithm for detection of the number of sources via a sequence of hypothesis tests we theoretically analyze the consistency and detection performance of the proposed algorithm showing its superiority compared to the standard minimum description length mdl based estimator a series of simulations confirm our theoretical analysis

an analysis of the projection method for robust adaptive beamforming two causes of performance degradation in adaptive beamforming are perturbation error and sample covariance error these causes were discussed by feldman and griffihs see ieee trans signal processing vol 42 p 867 april 1994 which proposed an approach termed the projection method to reduce the sensitivity of the beamformer performance to both types of error this paper contains an analysis of the expected performance of the beamformer when it is implemented either with or without using the projection method based on a second order taylor series expansion of an approximate expression for the signal to interference plus noise ratio sinr at the beamformer output the analysis provides accurate results when either perturbation error or sample covariance error occurs a less accurate analysis based on a zeroth order taylor series expansion includes results presented by jablon 1986 and chang and yeh see ibid vol 40 no 11 p 1336 1992 as special cases

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

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

k theoretic boson fermion correspondence and melting crystals we study non hermitian integrable fermion and boson systems from the perspectives of grothendieck polynomials the models considered in this article are the five vertex model as a fermion system and the non hermitian phase model as a boson system both models are characterized by different solutions satisfying the same yang baxter relation from our previous works on the identification between the wavefunctions of the five vertex model and grothendieck polynomials we introduce skew grothendieck polynomials and derive the addition theorem among them using these relations we derive the wavefunctions of the non hermitian phase model as a determinant form which can also be expressed as grothendieck polynomials namely we establish a k theoretic boson fermion correspondence at the level of wavefunctions as a by product the partition function of the statistical mechanical model of a three dimensional 3d melting crystal is exactly calculated by use of the scalar products of the wavefunctions of the phase model the resultant expression can be regarded as a k theoretic generalization of the macmahon function describing the generating function of the plane partitions which interpolates the generating functions of two dimensional 2d and 3d young diagrams

combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice we introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in a finite lattice we introduce the l operator related to the uq sl2 r matrix and construct the wavefunctions and their duals we prove the exact correspondence between the wavefunctions and symmetric polynomials which is a quantum group deformation of the grothendieck polynomials this is proved by combining the matrix product method and an analysis on the domain wall boundary partition functions as applications of the correspondence between the wavefunctions and symmetric polynomials we derive several properties of the symmetric polynomials such as the determinant pairing formulas and the branching formulas by analyzing the domain wall boundary partition functions and the matrix elements of the b operators

schur polynomials and the yang baxter equation we describe a parametrized yang baxter equation with nonabelian parameter group that is we show that there is an injective map g mapsto r g from rm gl 2 mathbb c times rm gl 1 mathbb c to end v otimes v where v is a two dimensional vector space such that if g h in g then r 12 g r 13 gh r 23 h r 23 h r 13 gh r 12 g here r i j denotes r applied to the i j components of v otimes v otimes v the image of this map consists of matrices whose nonzero coefficients a 1 a 2 b 1 b 2 c 1 c 2 are the boltzmann weights for the non field free six vertex model constrained to satisfy a 1 a 2 b 1 b 2 c 1 c 2 0 this is the exact center of the disordered regime and is contained within the free fermionic eight vertex models of fan and wu as an application we show that with boundary conditions corresponding to integer partitions the six vertex model is exactly solvable and equal to a schur polynomial s times a deformation of the weyl denominator this generalizes and gives a new proof of results of tokuyama and hamel and king

a pencil music algorithm for finding two dimensional angles and polarizations using crossed dipoles the authors study the problem of finding two dimensional 2 d angles of wave arrival and wave polarizations using a uniform rectangular array of crossed dipoles the method presented effectively exploits the redundancy in this array via 2 d moving window smoothing to handle coherent sources and to achieve optimum noise sensitivity the method combines the computational advantages of the music and matrix pencil approaches the method is shown in simulation to be nearly optimum compared with the cramer rao bound

the sos model partition function and the elliptic weight functions we generalized a recent observation khoroshkin and pakuliak 2005 theor math phys 145 1373 that the partition function of the six vertex model with domain wall boundary conditions can be obtained from a calculation of projections of the product of total currents in the quantum affine algebra in its current realization a generalization is done for the elliptic current algebra enriquez and felder 1998 commun math phys 195 651 enriquez and rubtsov 1997 ann sci ecole norm sup 30 821 the projections of the product of total currents in this case are calculated explicitly and are presented as integral transforms of a product of the total currents it is proved that the integral kernel of this transform is proportional to the partition function of the sos model with domain wall boundary conditions

symmetry classes of alternating sign matrices under one roof in a previous article math co 9712207 we derived the alternating sign matrix asm theorem from the izergin korepin determinant for a partition function for square ice with domain wall boundary here we show that the same argument enumerates three other symmetry classes of alternating sign matrices vsasms vertically symmetric asms even htsasms half turn symmetric asms and even qtsasms quarter turn symmetric asms the vsasm enumeration was conjectured by mills the others by robbins math co 0008045 we introduce several new types of asms uasms asms with a u turn side uuasms two u turn sides osasms off diagonally symmetric asms oosasms off diagonally off antidiagonally symmetric and uosasms off diagonally symmetric with u turn sides uasms generalize vsasms while uuasms generalize vhsasms vertically and horizontally symmetric asms and another new class vhpasms vertically and horizontally perverse osasms oosasms and uosasms are related to the remaining symmetry classes of asms namely dsasms diagonally symmetric dasasms diagonally anti diagonally symmetric and tsasms totally symmetric asms we enumerate several of these new classes and we provide several 2 enumerations and 3 enumerations our main technical tool is a set of multi parameter determinant and pfaffian formulas generalizing the izergin korepin determinant for asms and the tsuchiya determinant for uasms solv int 9804010 we evaluate specializations of the determinants and pfaffians using the factor exhaustion method

coherence enhancement in nonlinear systems subject to multiplicative ornstein uhlenbeck noise we show that for two biologically relevant models with self sustained oscillations under the action of a multiplicative ornstein uhlenbeck process their coherence response behaves nonmonotonically with the process correlation time there is a correlation time for which the quality factor is optimized this phenomenon is a consequence of the interplay between the correlation time and the system s periodicity this relation is evidenced through a power law relation with an exponent close to 1 2

roundoff induced coalescence of chaotic trajectories numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term or signal may synchronize after a finite time we study the process of synchronization as function of precision of calculations two generic behaviors of the average coalescence time are identified exponential or linear in both cases no synchronization occurs if iterations are done with em infinite precision

vertex models tasep and grothendieck polynomials we examine the wavefunctions and their scalar products of a one parameter family of integrable five vertex models at a special point of the parameter the model investigated is related to an irreversible interacting stochastic particle system the so called totally asymmetric simple exclusion process tasep by combining the quantum inverse scattering method with a matrix product representation of the wavefunctions the on off shell wavefunctions of the five vertex models are represented as a certain determinant form up to some normalization factors we find that the wavefunctions are given by grothendieck polynomials which are a one parameter deformation of schur polynomials introducing a dual version of the grothendieck polynomials and utilizing the determinant representation for the scalar products of the wavefunctions we derive a generalized cauchy identity satisfied by the grothendieck polynomials and their duals several representation theoretical formulae for the grothendieck polynomials are also presented as a byproduct the relaxation dynamics such as green functions for the periodic tasep are found to be described in terms of the grothendieck polynomials

nonlinear dynamic elements with noisy sinusoidal forcing enhancing response via nonlinear coupling we consider a network of nonlinear dynamic elements with nonlinear global coupling subject to noise and a time periodic signal the system response characterized by its signal to noise ratio is computed via approximate analytic techniques and precise numerical simulations we find that cooperative effects arising from the noise and coupling lead to an enhancement of the response of the network over that of a single element

nested arrays in two dimensions part ii application in two dimensional array processing this paper explores the practical application of a new class of two dimensional arrays namely the two dimensional nested arrays in array processing problems like two dimensional direction of arrival estimation nested arrays constitute a class of two dimensional arrays with physical sensors on lattice s whose difference co array gives rise to a virtual two dimensional array with o mn elements although the number of physical sensors used is m n the structure of the two dimensional nested array was proposed in a companion paper and several issues related to the geometrical orientation of the difference co array in the two dimensional space were addressed in this paper the practical aspects of the application of the nested array in two dimensional array processing are considered which can enable us to exploit the increased degrees of freedom offered by the co array under the constraint of a fixed total number of physical sensors the optimal structure of the 2d nested array is solved which maximizes the number of elements in the virtual co array this provides closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors it is shown that one can obtain o n2 virtual elements in the co array using only n physical sensors to exploit the increased degrees of freedom large number of virtual sensors offered by the virtual array for two dimensional doa estimation of more sources than sensors a novel algorithm based on the concept of two dimensional spatial smoothing is proposed and several issues related to identifiability in two dimensional doa estimation problem which is a fundamental issue in two dimensions are addressed the validity of the proposed methods is verified through several numerical examples

chaos noise and synchronization reconsidered in a recent paper maritan and banavar phys rev lett 72 1451 1994 reported the synchronization of identical chaotic systems by additive noise we relate such a synchronization to the maximum lyapunov exponent of a single system and discuss the underlying mechanisms of the effect in the case of the lorenz equations the nonvanishing mean of the noise mimics a parameter change leading to synchronization for the logistic map a state dependence of the fluctuations is induced by the boundary conditions

symmetric functions and wavefunctions of xxz type six vertex models and elliptic felderhof models by izergin korepin analysis we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an elliptic extension of the trigonometric felderhof model we show that the wavefunctions can be expressed as one parameter deformations of an elliptic analog of the vandermonde determinant and elliptic symmetric functions we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an

on the performance of signal subspace processing part i narrow band systems this paper presents an analytical evaluation of detection determination of the number of sources and estimation performances of narrow band signal subspace processing for multiple source direction finding the probabilities of underestimating and overestimating the number of sources are derived under asymptotic conditions and around the threshold regions in terms of the choice of a penalty function and signal noise and array parameters for the cases of at most two closely spaced sources in the spatially white noise a scalar measure is introduced for the evaluation of the quality of the estimated signal subspace based on the statistics of this measure performance thresholds are demonstrated for the signal to noise ratio angle separation and correlation between two equipowered sources

quantum integrability and generalised quantum schubert calculus abstract we introduce and study a new mathematical structure in the generalised quantum cohomology theory for grassmannians namely we relate the schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six vertex model our approach offers a new perspective on already established and well studied special cases for example equivariant k theory and in addition allows us to formulate a conjecture on the so far unknown case of quantum equivariant k theory

low complexity and high resolution line spectral estimation using cyclic minimization the line spectral estimation problem has applications in radar wireless communications spectroscopy and power electronics among others the signal is modeled as a sparse linear combination of complex sinusoids and the problem target is to estimate the number of sinusoids in the mixture and respective parameters of each individual sinusoid such as magnitude phase and frequency in this work we first introduce a novel formulation of the rank function which involves the solution of a multi convex optimization problem using the multi convex reformulation of the rank function an over parameterization of the line estimation problem is proposed together with a cyclic minimization procedure to obtain a solution the cyclic method iterates between the optimization of the signal subspace and null space and stops when the two are orthogonal every limit point of the sequence of iterates is shown to be a stationary point of the original problem numerical experiments show that only a small number of iterations is required for convergence the signal subspace optimization is a semidefinite program sdp and the null space optimization has a closed form solution the cost per iteration of a general purpose interior point method ipm to solve the sdp is a quartic function of the problem dimension it is shown that by exploiting the problem structure the cost per iteration of the ipm may be reduced to a cubic function of the problem dimension comparable to the cost of the alternating direction method of multipliers admm however contrarily to the latter the former achieves the precision necessary for fine frequency localization a large set of numerical experiments show the effectiveness of the proposed approach

derivation of a matrix product representation for the asymmetric exclusion process from the algebraic bethe ansatz we derive using the algebraic bethe ansatz a generalized matrix product ansatz for the asymmetric exclusion process asep on a one dimensional periodic lattice in this matrix product ansatz the components of the eigenvectors of the asep markov matrix can be expressed as traces of products of non commuting operators we derive the relations between the operators involved and show that they generate a quadratic algebra our construction provides explicit finite dimensional representations for the generators of this algebra

calculation of norms of bethe wave functions a class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered eigenfunctions of the hamiltonians are known for these models norms of these eigenfunctions in the finite box are calculated in the present paper these models include in particular the quantum nonlinear schrodinger equation and the heisenbergxxz model

statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing the performances of the akaike 1974 information criterion and the minimum descriptive length criterion methods are examined the events which lead to erroneous decisions are considered and on the basis of these events the probabilities of error for the two criteria are derived the probabilities of the first two events are derived based on the asymptotic distribution of the sample eigenvalues of an estimated hermitian matrix it is further shown that the probabilities of missing and false alarm for these two criteria can be evaluated to a close approximation although the derivation of the probabilities of error is based on an asymptotic analysis the results are confirmed to be in very close agreement with computer simulation results

k theoretic analogues of factorial schur p and q functions abstract we introduce two families of symmetric functions generalizing the factorial schur p and q functions due to ivanov we call them k theoretic analogues of factorial schur p and q functions we prove various combinatorial expressions for these functions e g as a ratio of pfaffians a sum over set valued shifted tableaux and a sum over excited young diagrams as a geometric application we show that these functions represent the schubert classes in the k theory of torus equivariant coherent sheaves on the maximal isotropic grassmannians of symplectic and orthogonal types this generalizes a corresponding result for the equivariant cohomology given by the authors we also discuss a remarkable property enjoyed by these functions which we call the k theoretic q cancellation property we prove that the k theoretic p functions form a formal basis of the ring of functions with the k theoretic q cancellation property

detection of the number of signals a predicted eigen threshold approach a novel method for detecting the number of signals incident upon an array of sensors is described the method is based on finding upper thresholds for the observed eigenvalues of the correlation matrix of the array output the asymptotic normality of the multifold eigenvalue estimate is used to derive a prediction formula for the thresholds due to the fact that the detection error of the method can be controlled by a parameter t the performance of the method is superior to the mdl minimum description length under low snr signal to noise ratio and superior to an aic akaike information criterion under high snr the distribution functions of both missing and false alarm errors are evaluated so that the performance of the method can be analyzed and so that t can be chosen simulation results are presented to confirm the analysis

refined cauchy littlewood identities and six vertex model partition functions iii deformed bosons abstract we study hall littlewood polynomials using an integrable lattice model of t deformed bosons working with row to row transfer matrices we review the construction of hall littlewood polynomials of the a n root system within the framework of this model introducing appropriate double row transfer matrices we extend this formalism to hall littlewood polynomials based on the b c n root system and obtain a new combinatorial formula for them we then apply our methods to prove a series of refined cauchy and littlewood identities involving hall littlewood polynomials the last two of these identities are new and relate infinite sums over hyperoctahedrally symmetric hall littlewood polynomials with partition functions of the six vertex model on finite domains

nested arrays a novel approach to array processing with enhanced degrees of freedom a new array geometry which is capable of significantly increasing the degrees of freedom of linear arrays is proposed this structure is obtained by systematically nesting two or more uniform linear arrays and can provide o n2 degrees of freedom using only n physical sensors when the second order statistics of the received data is used the concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically it is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors this cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors in minimum input minimum output mimo radar the degrees of freedom are increased by constructing a longer virtual array through active sensing the method proposed here however does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting to utilize the degrees of freedom of the nested co array a novel spatial smoothing based approach to doa estimation is also proposed which does not require the inherent assumptions of the traditional techniques based on fourth order cumulants or quasi stationary signals as another potential application of the nested array a new approach to beamforming based on a nonlinear preprocessing is also introduced which can effectively utilize the degrees of freedom offered by the nested arrays the usefulness of all the proposed methods is verified through extensive computer simulations

detection of number of sources via exploitation of centro symmetry property forward backward fb averaging is a technique which can be employed in sensor array signal processing for exploiting a so called centro symmetry property of the signal subspace to improve parameter estimation accuracy although fb averaging effectively doubles the number of data samples it also introduces correlation among these data vectors this correlation complicates not only the performance analysis but also the detection of the number of sources when fb averaging is employed existing detection procedures such as sequential hypothesis sh likelihood ratio tests minimum description length mdl and an information criterion aic must be modified to correctly account for this preprocessing of the data herein proper exploitation of the centro symmetry property of the fb averaged covariance is described and a rigorous analysis is conducted it is shown that the general scheme of existing methods is still applicable to the fb averaging case but that the parameters e g degrees of freedom need to be adjusted

q bosons toda lattice pieri rules and baxter q operator we use the pieri rules to recover the q boson model and show it is equivalent to a discretized version of the relativistic toda chain we identify its semi infinite transfer matrix and the corresponding baxter q matrix with half vertex operators related by an duality transformation we observe that the scalar product of two higher spin xxz wave functions can be expressed with a gaudin determinant

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

determinant formula for the six vertex model the partition function of a six vertex model with domain wall boundary conditions is considered on the finite lattice the authors show that the partition function satisfies a recursive relation they solve the recursion relation by a determinant formula this gives a determinant representation for the partition function they use the quantum inverse scattering method qism

on a family of symmetric rational functions abstract this paper is about a family of symmetric rational functions that form a one parameter generalization of the classical hall littlewood polynomials we introduce two sets of skew and non skew functions that are akin to the p and q hall littlewood polynomials we establish a a combinatorial formula that represents our functions as partition functions for certain path ensembles in the square grid b symmetrization formulas for non skew functions c identities of cauchy and pieri type d explicit formulas for principal specializations e two types of orthogonality relations for non skew functions our construction is closely related to the half infinite volume finite magnon sector limit of the higher spin six vertex or xxz model with both sets of functions representing higher spin six vertex partition functions and or transfer matrices for certain domains