a wide band equivalent source reconstruction method exploiting the stoer bulirsch algorithm with the adaptive frequency sampling conventional equivalent source reconstruction methods are only operating at a single frequency point each time however for wide band radiators their computation cost of the source reconstruction increases with the number of frequency points in this communication a wide band equivalent source reconstruction method wb srm based on the neville type stoer bulirsch sb algorithm is developed since the sb algorithm is a recursive tabular method it can perform the interpolation over a broadband using a single rational function without any singularity issue supported by the adaptive frequency sampling afs scheme the number of required sampling data is significantly reduced which leads to much better computational efficiency during the afs process three fitting models fm are considered two are triangle rules and another one is rhombus rule in this communication a bisection searching strategy is performed furthermore to achieve high order accuracy the nystrom method is implemented numerical examples are presented to validate the proposed wb srm and demonstrate its accuracy and applications

frequency estimation for closely spaced sinsoids simple approximations to the cramer rao lower bound simple approximate formulas for the evaluation of the cramer ran lower bound crlb of unbiased frequency estimates for the deterministic and stochastic cases of multiple snapshots of two closely spaced cisoids in complex noise are introduced these are based on general expressions recently published by stoica and nehorai also explored along the same lines is the case of a single snapshot com prising either one real sinusoid in real noise or two cisoids in complex noise these formulas though simple are accurate to within a few percent where the number of data points per snapshot is greater than about 6 it is felt that they add insight into the behavior of the crlb and cover many of the situations commonly cited in the literature

energy weighted linear predictive spectral estimation a new method combining robustness and high resolution a new method for estimating the ar process coefficients for spectral estimation is introduced the m selected coefficients achieve the minimum square error in fitting a recursion among the estimated covariance elements of the data which would be satisfied exactly if the statistics were known exactly and the data process fit the model assumptions mth order ar this minimization is shown to be identical to minimizing the average one step prediction error with adaptive weights determined by the energy of the measured data as in the burg algorithm forward and backward sweeps are averaged and the levinson recursion is employed spectra computed from short deterministic and noisy data are compared with computed burg spectra and show improvement in bias resolution and robustness of peak detection

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

bispectrum estimation a parametric approach higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality estimation of the bispectrum which is a third order spectrum has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non gaussianness of processes existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations the paper proposes a parametric approach to bispectrum estimation based on a non gaussian white noise driven autoregressive ar model the ar parameter estimates are obtained by solving the third order recursion equations which may be toeplitz in form but not symmetric it is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids the method provides significantly better resolution

from taubes currents to almost kahler forms the taubes current is introduced by taubes in j symplectic geom 9 161 250 2011 as an intermediate step to construct almost kahler forms in this paper we prove that an almost complex structures being almost kahler structure in dimension four is the equivalent of the existence of taubes currents precisely we show that taubes currents could be regularized to almost kahler forms up to small perturbations of cohomology classes on any 4 dimensional almost complex manifold m j a similar result is established for higher dimensions under the assumption of almost kahler an application to donaldson s tamed to compatible question is provided

an optimum tapered burg algorithm for linear prediction and spectral analysis several problems associated with the burg algorithm are for the most part alleviated by the use of an appropriate energy taper used in the derivation of the algorithm the tapered burg technique uses a weighted forward backward least squares fit to the parameters of the all pole model subject to levinson s recursion constraint based on a minimum average variance of the estimated frequency of a real sinusoid an optimum taper is derived finally the performance of the optimally tapered burg technique is compared with the least squares yule walker and the usual burg techniques

linear prediction approach for efficient frequency estimation of multiple real sinusoids algorithms and analyses based on the linear prediction property of sinusoidal signals two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed in order to achieve accurate frequency estimation the first algorithm uses a generalized unit norm constraint while the second method employs a monic constraint the weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner for the case of a single real tone with sufficiently large data samples both estimators provide nearly identical frequency estimates and their performance approaches crame spl acute r rao lower bound crlb for white gaussian noise before the threshold effect occurs algorithms for closed form single tone frequency estimation are also devised computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the crlb for different frequencies observation lengths and signal to noise ratio snr conditions

closed characteristics on non compact hypersurfaces in r 2n viterbo demonstrated that any 2n 1 dimensional compact hypersur face m r 2n of contact type has at least one closed characteristic this result proved the weinstein conjecture for the standard symplectic space r 2n various extensions of this theorem have been obtained since all for compact hypersurfaces in this paper we consider non compact hypersurfaces m r 2n coming from mechanical hamiltonians and prove an analogue of viterbo s result the main result provides a strong connection between the top half homology groups hi m i n 2n 1 and the existence of closed characteristics in the non compact case including the compact case

a generalized least squares method for frequency estimation the application of the generalized least squares gls method to the estimation of the frequencies of sinusoids in additive colored noise is discussed an iterative algorithm is proposed starting from the assumption that the parameter vector in the model of the sinusoids is symmetric the algorithm utilizes an adaptive strategy for contracting the poles of the estimated signal model expressions for the probability limit and the asymptotic variance of the estimates are derived for the single sinusoid case possible convergence points and the asymptotic behavior of the algorithm in the case of low snrs signal to noise ratios are analyzed extensive simulation results show that the algorithm represents a simple and reliable tool for practical applications

periodic solutions of lagrangian systems on a compact manifold abstract let m be a smooth n dimensional manifold and let tm be its tangent bundle we consider a time periodic lagrangian of period t l t tm r and we seek t periodic solutions of the lagrange equations which in local coordinates are d dt l q t q q l q t q q 0 i 1 n our main result states that if the fundamental group of m is finite then has infinitely many t periodic solutions provided that l t satisfies certain physically reasonable assumptions

homotopy equivalence of nearby lagrangians and the serre spectral sequence we construct using relatively basic techniques a spectral sequence for exact lagrangians in cotangent bundles similar to the one constructed by fukaya seidel and smith that spectral sequence was used to prove that exact relative spin lagrangians in simply connected cotangent bundles with vanishing maslov class are homology equivalent to the base a similar result was also obtained by nadler the ideas in that paper were extended by abouzaid who proved that vanishing maslov class alone implies homotopy equivalence in this paper we present a short proof of the fact that any exact lagrangian with vanishing maslov class is homology equivalent to the base and that the induced map on fundamental groups is an isomorphism when the fundamental group of the base is pro finite this implies homotopy equivalence

convergence of yang mills higgs fields in this paper we study the convergence of yang mills higgs ymh fields defined on fiber bundles over riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the underlying surface is allowed to vary we show that away from the nodes the ymh fields converges up to gauge to a smooth ymh field modulo finitely many harmonic spheres while near the nodes where the conformal structure degenerates the ymh fields converges to a pair consisting of a flat connection and a twisted geodesic with potential in particular we generalize the recent compactness results on both harmonic maps from surfaces and twisted holomorphic curves to general ymh fields

regularity and estimates for j holomorphic discs attached to a maximal totally real submanifold we prove that pseudo holomorphic discs attached to a maximal totally real submanifold inherit their regularity to the boundary from the regularity of the submanifold and of the almost complex structure the proof is based on the computation of an explicit lower bound for the kobayashi metric in almost complex manifolds which also yields explicit estimates of holderian norms of such discs

planar near field to far field transformation using an equivalent magnetic current approach an alternative method is presented for computing far field antenna patterns from near field measurements the method utilizes the near field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna and these currents are used to ascertain the far fields under certain approximations the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near field measurements are made an electric field integral equation efie is developed to relate the near fields to the equivalent magnetic currents the method of moments is used to transform the integral equation into a matrix one the matrix equation is solved with the conjugate gradient method and in the case of a rectangular matrix a least squares solution for the currents is found without explicitly computing the normal form of the equation near field to far field transformation for planar scanning may be efficiently performed under certain conditions numerical results are presented for several antenna configurations

multichannel ar spectrum estimation the optimum approach in the reflection coefficient domain a new approach for multichannel autoregressive ar spectrum estimation is introduced based on an iterative gradient algorithm in the context of dynamic programming the approach is shown to be optimum in the reflection coefficient domain whereas the multichannel ar nuttall strand algorithm is shown to be suboptimum the approach guarantees a stable multichannel ar filter and a nonnegative spectrum matrix estimate it is demonstrated via simulation examples that such drawbacks of the nuttall strand method as frequency bias and line splitting may be alleviated by the optimum approach however the improved performance is achieved at the expense of considerably more computational effort and time the single channel fougere descent method may be seen as a special case of the proposed multichannel ar approach

a recursive maximum likelihood algorithm for arma line enhancement optimal filtering of narrow band signals corrupted by noise requires an infinite impulse response iir filter a recursive maximum likelihood algorithm is proposed for adaptively adjusting the coefficients of an iir line enhancer the performance of this adaptive iir filter is analyzed and compared to that of a finite impulse response filter preliminary simulation results are presented to illustrate the behavior of the proposed algorithm under various signal to noise conditions

spectral estimation of quasi periodic data a computationally efficient algorithm for estimating the autocorrelation function and or the power spectrum of periodic quasi periodic time series when information about its period is available is described the autocorrelation matrix obtained from the sample covariance matrix using this method is a good approximation of the maximum likelihood estimate of the autocorrelation matrix simulation results involving sinusoids in noise and speech data are presented

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

block time and frequency domain modified covariance algorithms for spectral analysis block modified covariance algorithms are proposed for autoregressive parametric spectral estimation first the authors develop the block modified covariance algorithm bmca which can be implemented either in the time or in the frequency domain with the latter being more efficient in high order cases a block algorithm is also developed for the energy weighted combined forward and backward prediction this algorithm is called energy weighted bmca ewbmca and its performance is analogous to that of the weighted covariance method proposed by nikias and scott 1983 time varying convergence factors designed to minimize the error energy from one iteration to the next are given for both algorithms in addition three updating schemes are presented namely block by block sample by sample and sample by sample with time scale separation the performance of the proposed algorithms is examined with stationary and nonstationary narrowband and broadband processes and also with sinusoids in noise lastly the authors discuss the computational complexity of the proposed algorithms and give performance comparisons to existing modified covariance algorithms

minimum cross entropy spectral analysis the principle of minimum cross entropy minimum directed divergence minimum discrimination information minimum relative entropy is summarized discussed and applied to the classical problem of estimating power spectra given values of the autocorrelation function this new method differs from previous methods in its explicit inclusion of a prior estimate of the power spectrum and it reduces to maximum entropy spectral analysis as a special case the prior estimate can be viewed as a means of shaping the spectral estimator cross entropy minimization yields a family of shaped spectral estimators consistent with known autocorrelations results are derived in two equivalent ways once by minimizing the cross entropy of underlying probability densities and once by arguments concerning the cross entropy between the input and output of linear filters several example minimum cross entropy spectra are included

symplectic manifolds with contact type boundaries an example of a 4 dimensional symplectic manifold with disconnected boundary of contact type is constructed a collection of other results about symplectic manifolds with contact type boundaries are derived using the theory ofj holomorphic spheres in particular the following theorem of eliashberg floer mcduff is proved if a neighbourhood of the boundary of v is symplectomorphic to a neighbourhood ofs2n 1 in standard euclidean space and if vanishes on all 2 spheres inv thenv is diffeomorphic to the ballb2n

universal coding information prediction and estimation a connection between universal codes and the problems of prediction and statistical estimation is established a known lower bound for the mean length of universal codes is sharpened and generalized and optimum universal codes constructed the bound is defined to give the information in strings relative to the considered class of processes the earlier derived minimum description length criterion for estimation of parameters including their number is given a fundamental information theoretic justification by showing that its estimators achieve the information in the strings it is also shown that one cannot do prediction in gaussian autoregressive moving average arma processes below a bound which is determined by the information in the data

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

object tracking from image sequences using adaptive models in fuzzy particle filter this paper describes a vision based system for tracking objects from image sequences the proposed system has the standard architecture with a particle filter which is a popular algorithm to track objects in real time many tracking algorithms have a great difficulty in tracking objects robustly by reason of complex background and rapid changes under a real complex environment such as a traffic road to make a robust algorithm for object tracking we propose the method that uses the adaptive autoregressive model as a state transition model and the adaptive appearance mixture model as an observation model but in case of changing the state of a tracked object suddenly the adaptive models may not make the optimal parameters for accurate states at current time because the noise variance of the adaptive models in this case is larger than that in normal case it has an effect on the accuracy of an object tracking algorithm thus we propose a fuzzy particle filter to overcome problems from the occurrence of the unexpected improper variances due to several causes in this paper as the process noises and the observation noises in a fuzzy particle filter are considered as fuzzy variables by using the possibility theory a fuzzy particle filter with fuzzy noises is used to manage uncertainty in various noise models also we make possibility measure as using the fuzzy relation equation which is defined by these fuzzy variables and then the states are estimated by using a fuzzy expected value operator also because the proposed algorithm applies several functions to improve the accuracy of tracking an object the performance of tracking speed deteriorates to resolve this problem to some extent we consider the fact that a fuzzy particle filter has a little bit of an effect on the number of particles consequently we propose the method which can adjust the number of particles by using the result from a measurement step in order to improve the speed for an object tracking in the proposed algorithm the experiments of this paper show that the proposed method is efficient and has many advantages for an object tracking in real environments

many closed symplectic manifolds have infinite hofer zehnder capacity we exhibit many examples of closed symplectic manifolds on which there is an autonomous hamiltonian whose associated flow has no nonconstant periodic orbits the only previous explicit example in the literature was the torus t2n n 2 with an irrational symplectic structure the underlying smooth manifolds of our examples include for instance the k3 surface and also infinitely many smooth manifolds homeomorphic but not diffeomorphic to it infinitely many minimal four manifolds having any given finitely presented group as their fundamental group and simply connected minimal four manifolds realizing all but finitely many points in the first quadrant of the geography plane below the line corresponding to signature 3 the examples are constructed by performing symplectic sums along suitable tori and then perturbing the symplectic form in such a way that hypersurfaces near the neck in the symplectic sum have no closed characteristics we conjecture that any closed symplectic four manifold with b 1 admits symplectic forms with a similar property

polyfolds cobordisms and the strong weinstein conjecture abstract we prove the strong weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres

the birkhoff lewis fixed point theorem and a conjecture of v i arnold abstract the following conjecture of v i arnold is proved every measure preserving diffeomorphism of the torus t2 which is homologeous to the identity and which leaves the center of mass invariant possesses at least 3 fixed points the proof of this global fixed point theorem does not make use of the generating function technique the theorem is a consequence of the statement that a hamiltonian vector field on a torus t2n which depends periodically on time possesses at least 2n 1 forced oscillations these periodic solutions are are found using the classical variational principle by means of two qualitative statements for general flows a second conjecture of v i arnold proved concerns a birkhoff lewis type fixed point theorem for symplectic maps additional keywords periodic functions variational principles equations reprints author

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

reconstruction of equivalent currents distribution over arbitrary three dimensional surfaces based on integral equation algorithms a technique for the determination of the equivalent currents distribution from a known radiated field is described this inverse radiation problem is solved through an integral equation algorithm that allows the characterization of antennas of complex geometry both for near field to far field nf ff transformation purposes as well as for diagnostic tasks the algorithm is based on the representation of the radiating structure by means of a set of equivalent currents over a three dimensional 3d surface that can be fitted to the arbitrary geometry of the antenna the innovative formulation uses an integral equation involving the electric field due to the currents tangential components to the represented antenna 3d surface for that purpose both the magnetic and electric equivalent currents are considered in the integral equations regularization techniques are also introduced to improve the convergence of the proposed iterative solution the paper concludes with several results related to the practical verification of the equivalence principle and the characterization of a horn antenna

classification of natural textures by means of two dimensional orthogonal masks an approach to texture classification in which each local neighborhood is transformed reversibly into a minimal set of uncorrelated features is described these features are found to represent local average as well as first and second order derivative information of the texture comparison to other techniques of similar complexity using identical classification procedures shows the superiority of the proposed approach moreover this approach leads directly to a real time parallel implementation

improved spectrum performance via a data adaptive weighted burg technique a new method for generating autoregressive ar parameters for spectral estimation is introduced and shown to be a data adaptive weighted burg dab technique the respective ar coefficient estimates minimize a weighted measure of the squared forward and backward linear predictive errors with weights that are proportional to the common energy of the forward and backward process realizations and result in a stable filter representation spectra are computed comparing the new method to other weighted burg techniques e g rectangular hamming and optimum parabolic weighting and demonstrate performance improvements in frequency bias and resolution no evidence of a line splitting tendency is exhibited however somewhat greater spectral variability is exhibited by the dab method in processing nonsinusoidal signals the provision of asymptotically unbiased ar parameter estimates is presented

asymptotic analysis of a fast algorithm for efficient multiple frequency estimation based on an asymptotic analysis of the contraction mapping cm method of li and kedem 1993 a bandwidth shrinkage rule is proposed for fast and accurate estimation of the frequencies of multiple sinusoids from noisy measurements the cm frequency estimates are defined as the fixed points of a contractive mapping formed by the lag one autocorrelation coefficient calculated from the output of a parametric filter applied to the observed time series with bandwidth parameters judiciously chosen according to the asymptotic analysis the algorithm is shown to be able to accommodate possibly poor initial values of precision o n sup 1 3 and converge to a final estimate whose accuracy is arbitrarily close to o n sup 3 2 the optimal error rate for frequency estimation under the gaussian assumption the total computational complexity of the algorithm is shown to be o n log n which is comparable to that of n point fast fourier transform fft a novelty in the asymptotic analysis is that it accommodates closely spaced frequencies by allowing not only the filter bandwidth but also the frequency separation to be functions of the sample size n this enables an assessment of the accuracy of the frequency estimates for given bandwidths and initial values in situations where some or all of the frequencies are close to each other

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

two dimensional ar spectral estimation using a two dimensional minimum free energy method we present a 2 d extension of the minimum free energy mfe autoregressive parameter and spectral estimation technique mfe can outperform the multidimensional levinson algorithm producing superior spectral estimation of 2 d sinusoids in white gaussian noise mfe spectral estimates are found to be comparable to modified covariance method estimates mfe also outperforms the conventional fourier method for closely spaced sinusoids at low signal to noise ratio and low data set size

solvability of dirac type equations abstract this paper develops a weighted l 2 method for the half dirac equation for dirac bundles over closed riemann surfaces we give a sufficient condition for the solvability of the half dirac equation in terms of a curvature integral applying this to the dolbeault dirac operator we establish an automatic transversality criteria for holomorphic curves in kahler manifolds on compact riemannian manifolds we give a new perspective on some well known results about the first eigenvalue of the dirac operator and improve the estimates when the dirac bundle has a z 2 grading on riemannian manifolds with cylindrical ends we obtain solvability in the l 2 spaces with suitable exponential weights while allowing mild negativity of the curvature

periodic orbits in magnetic fields and ricci curvature of lagrangian systems where da f on the space of closed curves on the manifold mn here a is a 1 form i e f is an exact 2 form this functional is a natural generalization of the usual functional of length and its closed extremals correspond to periodic trajectories of the motion of particles on the riemannian manifold mn when the kinetic energy is defined by the metric tensor and the form f defines a magnetic field also this functional corresponds to the periodic orbits for other problems of classical mechanics and mathematical physics as it was shown in n2 n3 ns when the lagrangian function

iterative filtering for multiple frequency estimation it is well known that prony s least squares estimator gives inconsistent estimates for multiple frequency estimation in a recent attempt to diminish this problem dragosevic and stankovic 1989 couple the least squares method of autoregressive ar estimation with an iterative filtering scheme discussed by kay 1988 using an all pole filter but the inconsistency still persists this paper attacks the chronic inconsistency with a general approach of parametric filtering that unifies and extends the previous work it is shown that the inconsistency can be eliminated with an appropriately parametrized filter the clue for the correct parametrization comes from a formula for the bias of the least squares ar estimator the fact of the matter is that as long as a filter satisfies the parametrization requirement consistent estimates can be obtained from the least squares ar estimator on the basis of the filtered data in particular the all pole filter considered by dragosevic and stankovic can be easily reparametrized so that it too satisfies the parametrization requirement and thus leads to a consistent estimator experimental results show that the modified method has a higher resolution than the discrete fourier transform and that its overall performance is quite remarkable

a c 2 smooth counterexample to the hamiltonian seifert conjecture in r 4 we construct a proper c 2 smooth function on r 4 such that its hamiltonian flow has no periodic orbits on at least one regular level set this result can be viewed as a c 2 smooth counterexample to the hamiltonian seifert conjecture in dimension four

stationary points of the recursive generalized least squares algorithm for adaptive notch filtering possible convergence points of the generalized least squares adaptive notch filtering algorithm are analytically derived for the multiple sinusoid case showing explicitly the dependence of the asymptotic bias on the pole contraction factor signal to noise ratio and the true model parameters the results for symmetric and nonsymmetric parameterization are compared

multilevel fast multipole accelerated inverse equivalent current method employing rao wilton glisson discretization of electric and magnetic surface currents the radiation of any object in a homogeneous environment can be described by a set of equivalent sources different types of equivalent sources are feasible and all of them have their own benefits equivalent current methods are especially advantageous for irregular measurement grids of arbitrary shape and if a priori information about the object shall be used also they can immediately provide diagnostic information about the object in this paper a very flexible equivalent current method is presented which has been derived from a general purpose boundary integral equation solver as such the method works with arbitrary triangular surface meshes and rao wilton glisson basis functions where electric and or magnetic surface current densities can be assumed high efficiency is achieved since the multilevel fast multipole method has been adapted to speed up the inverse solution process results obtained from simulations and measurements are presented where large scale problems with dimensions up to 75 wavelengths are considered

unbiased estimation of a sinusoid in colored noise via adapted notch filters standard notch models for the estimation of a sinusoid in noise are characterized by two poles on the unit circle and two zeros aligned with the poles these models provide biased estimates of the unknown frequency the bias increasing with the zero pole distance on the other hand keeping the zeros far from the poles has the beneficial effect of making the identification algorithm less sensitive to the adopted initialization in this paper we remove the pole zero alignment constraint the extra degree of freedom thus obtained is used to alleviate the traditional trade off between unbiasedness of the estimates and robustness against poor initializations the proposed technique applies to the case of both white and colored additive noise

recursive autoregressive spectral estimation by minimization of the free energy a digital signal processing technique applicable to power spectrum estimation designated as the minimum free energy method is described with no a priori model assumption and no attempt to extract special features such as sinusoids one can obtain high resolution even with high noise contamination of the measured signal the technique is demonstrated by modification of the burg recursive method of spectral analysis a recursive minimum free energy method in which the reflection coefficient is chosen at each step is proposed for minimizing the free energy the burg energy measure minus the product of a temperature and an information entropy the method produces a spectral estimator more impervious to high noise contamination than the burg method and diminishes the burg tendency to produce spurious peaks

near field to near far field transformation for arbitrary near field geometry utilizing an equivalent electric current and mom presented here is a method for computing near and far field patterns of an antenna from its near field measurements taken over an arbitrarily shaped geometry this method utilizes near field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna this electric current once determined can be used to ascertain the near and the far field this method demonstrates the concept of analytic continuity i e once the value of the electric field is known for one region in space from a theoretical perspective its value for any other region can be extrapolated it is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near field measurements are made in this approach the measured data need not satisfy the nyquist sampling criteria an electric field integral equation is developed to relate the near field to the equivalent electric current a moment method procedure is employed to solve the integral equation by transforming it into a matrix equation a least squares solution via singular value decomposition is used to solve the matrix equation computations with both synthetic and experimental data where the near field of several antenna configurations are measured over various geometrical surfaces illustrate the accuracy of this method

fast antenna diagnosis algorithm using oblate spheroidal nonuniform grids a fast algorithm for the diagnosis of large antennas is developed the algorithm is based on the rayleigh sommerfeld rs backpropagation method accelerated by a multilevel nonuniform grid algorithm comparison between the field distributions reconstructed from measurements and the desired ones can be used for the localization of antenna defects and geometrical distortions the optimal performance is obtained by using oblate spheroidal grids which are tailored to both the measurement and antenna surfaces further acceleration can be achieved for particular cases via optimal sampling on the antenna surface the algorithm s performance is demonstrated for the example of a parabolic reflector with a number of surface distortions and compared to that achieved with spherical grids the accuracy and error controllability are studied in comparison to the direct rs integral computation

adaptive notch filtering for the retrieval of sinusoids in noise in this paper an adaptive notch filter is developed employing a frequency domain and time domain analysis for the enhancement and tracking of sinusoids in additive noise colored or white the notch filter is implemented as a constrained infinite impulse response filter with the constraint enforced by a single parameter termed the debiasing parameter the resulting notch filter requires few parameters facilitates the formation of the desired band rejection filter response and also leads to various useful implementations cascade parallel for the adaptation of the filter coefficients the stochastic gauss newton algorithm is used the convergence of this updating procedure is established by studying the associated differential equation also it is shown that the structure present in the problem enables truncation of the gradient thereby reducing the complexity of adapting the filter coefficients simulation results are presented to substantiate the analysis and to demonstrate the potential of the notch filtering technique

reconstruction of the field distribution on slot array antennas using the gerchberg papoulis algorithm a method to reconstruct the field distribution on slot array antennas is presented the field on each slot is reconstructed with high spatial resolution by extrapolating the invisible region of the plane wave spectrum pws using the gerchberg papoulis g p algorithm the information of the slot positions angles and lengths is exploited in the g p algorithm to enhance the accuracy and resolution of the reconstructed field the proposed algorithm is validated through the source reconstruction of a k band radial line slot antenna rlsa from the near field on planar and spherical scanning surfaces

generalized counterexamples to the seifert conjecture using the theory of plugs and the self insertion construction due to the second author we prove that a foliation of any codimension of any manifold can be modified in a real analytic or piecewise linear fashion so that all minimal sets have codimension 1 in particular the 3 sphere s 3 has a real analytic dynamical system such that all limit sets are 2 dimensional we also prove that a 1 dimensional foliation of a manifold of dimension at least 3 can be modified in a piecewise linear fashion so that there are no closed leaves but all minimal sets are 1 dimensional these theorems provide new counterexamples to the seifert conjecture which asserts that every dynamical system on s 3 with no singular points has a periodic trajectory

periodic solutions on hypersurfaces and a result by c viterbo on considere un champ vectoriel hamiltonien x j h x x h x sur x r 2n h etant une fonction lisse dont le gradient h est defini par rapport a la metrique euclidienne on cherche des solutions periodiques sur une surface d energie donnee s x r 2n h x const supposee reguliere

existence and classification of overtwisted contact structures in all dimensions we establish a parametric extension h principle for overtwisted contact structures on manifolds of all dimensions which is the direct generalization of the 3 dimensional result from 12 it implies in particular that any closed manifold admits a contact structure in any given homotopy class of almost contact structures

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

taubes s proof of the weinstein conjecture in dimension three does every smooth vector field on a closed three manifold for example the three sphere have a closed orbit no according to counterexamples by k kuperberg and others on the other hand there is a special class of vector fields called reeb vector fields which are associated to contact forms the three dimensional case of the weinstein conjecture asserts that every reeb vector field on a closed oriented three manifold has a closed orbit this conjecture was recently proved by taubes using seiberg witten theory we give an introduction to the weinstein conjecture the main ideas in taubes s proof and the bigger picture into which it fits taubes s proof of the weinstein conjecture is the culmination of a large body of work both by taubes and by others in an attempt to make this story accessible to nonspecialists much of the present article is devoted to background and context and taubes s proof itself is only partially explained hopefully this article will help prepare the reader to learn the full story from taubes s paper 62 more exposition of this subject which was invaluable in the preparation of this article can be found in the online video archive from the june 2008 msri hot topics workshop 44 and in the article by auroux 5 below in 1 3 we introduce the statement of the weinstein conjecture and discuss some examples in 4 6 we discuss a natural strategy for approaching the weinstein conjecture which proves it in many but not all cases and provides background for taubes s work in 7 we give an overview of the big picture surrounding taubes s proof of the weinstein conjecture readers who already have some familiarity with the weinstein conjecture may wish to start here in 8 9 we recall necessary material from seiberg witten theory in 10 we give an outline of taubes s proof and in 11 we explain some more details of it to conclude in 12 we discuss some further results and open problems related to the weinstein conjecture 1 statement of the weinstein conjecture the weinstein conjecture asserts that certain vector fields must have closed orbits before stating the conjecture at the end of this section we first outline its origins this is discussion is only semi historical because only a sample of the relevant works will be cited and not always in chronological order 1 1 closed orbits of vector fields let y be a closed manifold in this article all manifolds and all objects defined on them are smooth unless otherwise stated 2000 mathematics subject classification 57r17 57r57 53d40 partially supported by nsf grant dms 0806037

strong consistency of the contraction mapping method for frequency estimation some statistical properties in regard to the contraction mapping cm method are discussed one of the requirements in this method is that the filter be parameterized to satisfy a certain fundamental property the parameterization clearly depends on the normalized noise spectrum which theoretically has to be known or estimated a priori if this information is available one can first whiten the noise with a linear filter and then apply the cm method to the filtered data in this way the parameterization only needs to be done under the white noise assumption and filters like the ar 2 can be used by the cm method in applications however prewhitening may not always be necessary

further simulation results on tapered and energy weighted burg methods in this correspondence we report about a simulation study of the tapered and energy weighted burg methods for sinusoidal signals we confirm swingler s results about the frequency estimation error and extend them for frequency resolution we also discuss some drawbacks of the energy weighted burg methods on the basis of the results reported in this correspondence we show that the optimum tapered burg method results in the best performance

the sources reconstruction method for amplitude only field measurements an extension of the sources reconstruction method srm for antenna diagnostics using amplitude only field measurements is presented while previous works limit the application to canonical domain cases the combination of the srm capabilities for handling with arbitrary geometry domains jointly with phase retrieval techniques allows antenna diagnostics extension to complex geometry antenna and field acquisition domains the consideration of the radiation inverse problem with a general integral equation formulation using arbitrary geometry field and currents domains and field phaseless information supposes a challenging ill posed problem that is solved using iterative minimization techniques for non linear problems different examples are presented from simple to general antenna diagnostics cases

examples of symplectic structures in this paper we construct symplectic forms tilde omega k k geqq 0 on a compact manifold tilde y which have the same homotopy theoretic invariants but which are not diffeomorphic

a parameter estimation approach to estimation of frequencies of sinusoids it is shown that with uniform sampling a sample of the sum of m sinusoids at time nt can be uniquely expressed as a linear combination of the 2m samples at times n 1 t n 2m t the 2m coefficients of linear combination are also the coefficients of a 2m order polynomial whose roots are e pmj omega i omega i being the frequencies of the sinusoids given the samples of sinusoids plus noise a consistent estimate of the 2m coefficients are obtained by the instrumental variable method of parameter estimation it is also possible to track time varying frequencies by a recursive algorithm that exponentially weighs out the past data simulation examples of one and two sinusoids are given

iterative inverse filtering approach to the estimation of frequencies of noisy sinusoids a signal modeling approach is proposed to reduce the problem of estimating frequencies of noisy sinusoids to the parameter estimation problem both white and colored noise are considered the maximum likelihood approach leads to an algorithm computationally inefficient for low values of signal to noise ratio based on the equation error formulation an iterative inverse filtering algorithm is derived in the case of colored noise and a generalized least squares algorithm in the case of white noise it is shown on the basis of numerous experimental results that the iterative inverse filtering algorithm provides highly accurate estimates of unknown frequencies for low values of signal to noise ratio even in the case of a small number of sampling points

radial field retrieval in spherical scanning for current reconstruction and nf ff transformation a near field to far field nf ff transformation is addressed for the case of spherical scanning using equivalent magnetic currents emcs and matrix methods it is based on the decoupling of the field components and the iterative retrieval of the radial component of the electric field the technique is applied for far field calculation as well as for the estimation of the current distribution of the antenna under test aut using spherical near field facilities results from measured near field data of several antennas are presented and compared to those of the analytical solution via a spherical wave mode expansion method

periodic fourth order cubic nls local well posedness and non squeezing property abstract in this paper we consider the cubic fourth order nonlinear schrodinger equation 4nls under the periodic boundary condition we prove two results one is the local well posedness in h s t with 1 3 s 0 for the cauchy problem of the wick ordered 4nls the other one is the non squeezing property for the flow map of 4nls in the symplectic phase space l 2 t to prove the former we used the ideas introduced in 36 and 27 and to prove the latter we used the ideas in 8

adaptive ar modeling in white gaussian noise autoregressive ar modeling is widely used in signal processing the coefficients of an ar model can be easily obtained with a least mean square lms prediction error filter however it is known that this filter gives a biased solution when the input signal is corrupted by white gaussian noise treichler 1979 suggested the spl gamma lms algorithm to remedy this problem and proved that the mean weight vector can converge to the wiener solution in this paper we develop a new algorithm that extends works of vijayan et al 1990 for adaptive ar modeling in the presence of white gaussian noise by theoretical analysis we show that the performance of the new algorithm is superior to the spl gamma lms filter simulations are also provided to support our theoretical results

frequency estimation performance of several weighted burg algorithms the frequency estimation performance of a set of weighted burg algorithms is investigated for single complex and real sinusoids in noise it is demonstrated that in the complex case an extension of ibrahim s 1987 1989 modification of kaveh and lipert s 1983 optimum tapered burg algorithm meets the cramer rao lower bound for a sufficiently high signal to noise ratio and a sufficiently large model order this is in contrast with the original burg method in the case of a real sinusoid the same algorithm most closely approaches this bound making it the technique of choice for both applications spectral resolution is addressed briefly

hamiltonian collapsing of irrational lagrangian submanifolds with small first betti number among the main symplectic invariants of a closed lagrange submanifoldl of the cotangent of n is the tubular radiusr l defined as the smallest tube d r n 1 of n t n in whichl can be pushed by an hamiltonian diffeotopy of n we show here using pseudo holomorphic techniques that such a submanifold cannot collapse if the first betti number ofl is smaller than 3 and if the maslov class ofl does not vanish in other words r l is then strictly positive and one can actually give an explicit lower bound in terms of the liouville and maslov classes ofl

efficient near field far field transformation for nonredundant sampling representation on arbitrary surfaces in near field antenna measurements a nonredundant sampling representation on arbitrary surfaces in near field antenna measurements together with a direct near field far field transformation is described the utilized sampling criterion depends on the electrical size of the antenna under test aut along with the separation between the aut and the measurement surface the minimum number of samples required is directly linked with the number of unknowns in the linear system of equations derived considering spherical expansion of radiated aut fields equivalent plane wave sources are used to represent the aut fields plane wave translations can be directly performed for any arbitrary measurement grid with the same efficiency thus nonredundant sampling representations can be utilized on any scan surface in contrast other fast field transformation techniques would lose their efficiency the proposed sampling is applied to near field measurements and synthetic data using a variety of antennas and the results are compared to the case of standard sampling remarkable decrease in the number of measurement points is observed with a negligible change in the accuracy of the transformed pattern thereby greatly reducing the measurement time and the computational effort