analysis of the linearization around a critical point of an infinite dimensional hamiltonian system partial differential equations that conserve energy can often be written as infinite dimensional hamiltonian systems of the following general form du dt je u where j x x is a symplectic matrix i e jj 1 and e x r is a c 2 functional defined on some hilbert space x

a prediction error and stepwise regression estimation algorithm for non linear systems the identification of non linear systems based on a narmax non linear autoregressive moving average model with exogenous inputs model representation is considered and a combined stepwise regression prediction error estimation algorithm is derived the stepwise regression routine determines the model structure by detecting significant terms in the model while the prediction error algorithm provides optimal estimates of the final model parameters implementation of the algorithms is discussed in detail and several simulated examples and industrial applications are included to illustrate that parsimonious models of non linear systems can be identified using the algorithm

on instability of excited states of the nonlinear schrodinger equation we introduce a new notion of linear stability for standing waves of the nonlinear schrodinger equation nls which requires not only that the spectrum of the linearization be real but also that the generalized kernel be not degenerate and that the signature of all the positive eigenvalues be positive we prove that excited states of the nls are not linearly stable in this more restrictive sense we then give a partial proof that this more restrictive notion of linear stability is a necessary condition to have orbital stability

an adaptive orthogonal search algorithm for model subset selection and non linear system identification a new adaptive orthogonal search aos algorithm is proposed for model subset selection and non linear system identification model structure detection is a key step in any system identification problem this consists of selecting significant model terms from a redundant dictionary of candidate model terms and determining the model complexity model length or model size the final objective is to produce a parsimonious model that can well capture the inherent dynamics of the underlying system in the new aos algorithm a modified generalized cross validation criterion called the adjustable prediction error sum of squares apress is introduced and incorporated into a forward orthogonal search procedure the main advantage of the new aos algorithm is that the mechanism is simple and the implementation is direct and easy and more importantly it can produce efficient model subsets for most non linear identification problems

multivariate adaptive regression splines a new method is presented for flexible regression modeling of high dimensional data the model takes the form of an expansion in product spline basis functions where the number of basis functions as well as the parameters associated with each one product degree and knot locations are automatically determined by the data this procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties unlike recursive partitioning however this method produces continuous models with continuous derivatives it has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables in addition the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions

model structure selection by cross validation two criteria for choosing between different model structures are proposed their derivation is within a natural cross validatory assessment context and is fairly assumption free in particular the two criteria can be used for discriminating between non nested model structures and more importantly the true system is not required to belong to the considered set of models should the true system belong to the model set the two proposed criteria will asymptotically reduce to some well known structure selection criteria this is believed to be a desirable feature of our proposals on the other hand it provides a nice cross validation interpretation of some well known model structure selection rules also the cross validation interpretation helps one to choose which criteria to use in a given application the paper also has a second purpose somewhat decoupled from that mentioned above it contains an extensive survey of the literature that is useful in its own right

nonparametric identification of nonlinear time series selecting significant lags abstract in this article we suggest a nonparametric procedure for selecting significant lags in the model description of a general nonlinear stationary time series the procedure can be applied to both the conditional mean and the conditional variance and is valid for heteroscedastic series the procedure is illustrated by simulations and sunspot data lynx data and blowfly data are analyzed it is indicated that projectors can be used in conjunction with the procedure for selecting significant lags to check the adequacy of an additive time series model

perturbation expansion and nth order fermi golden rule of the nonlinear schrodinger equations in this paper we consider generalized nonlinear schrodinger equations with external potentials we find the expressions for the fourth and the sixth order fermi golden rules fgrs conjectured in gang and sigal rev math phys 17 1143 1207 2005 geom funct anal 16 no 7 1377 1390 2006 the fgr is a key condition in a study of the asymptotic dynamics of trapped solitons

flexible parsimonious smoothing and additive modeling a simple method is presented for fitting regression models that are nonlinear in the explanatory variables despite its simplicity or perhaps because of it the method has some powerful characteristics that cause it to be competitive with and often superior to more sophisticated techniques especially for small data sets in the presence of high noise

harnack estimates for conjugate heat kernel on evolving manifolds in this article we derive harnack estimates for conjugate heat kernel in an abstract geometric flow our calculation involves a correction term mathcal d when mathcal d is nonnegative we are able to obtain a harnack inequality our abstract formulation provides a unified framework for some known results in particular including corresponding results of ni j geom anal 14 1 87 100 2004 perelman arxiv math dg 0211159 2002 and tran arxiv 1211 6448 2012 as special cases moreover it leads to new results in the setting of ricci harmonic flow and mean curvature flow in lorentzian manifolds with nonnegative sectional curvature

monotone volume formulas for geometric flows we consider a closed manifold m with a riemannian metric gij t evolving by t gij 2sij where sij t is a symmetric two tensor on m g t we prove that if sij satises the tensor inequality d sij x 0 for all vector elds x on m where d sij x is dened in 1 6 then one can construct a forwards and a backwards reduced volume quantity the former being non increasing the latter being non decreasing along the ow t gij 2sij in the case where sij rij the ricci curvature of m the result corresponds to perelman s well known reduced volume monotonicity for the ricci

counting eigenvalues via the krein signature in infinite dimensional hamiltonian systems spectra of nonlinear waves in infinite dimensional hamiltonian systems are investigated we establish a connection via the krein signature between the number of negative directions of the second variation of the energy and the number of potentially unstable eigenvalues of the linearization about a nonlinear wave we apply our results to determine the effect of symmetry breaking on the spectral stability of nonlinear waves in weakly coupled nonlinear schrodinger equations

term and variable selection for non linear system identification the purpose of variable selection is to pre select a subset consisting of the significant variables or to eliminate the redundant variables from all the candidate variables of a system under study prior to model term detection it is required that the selected significant variables alone should sufficiently represent the system generally not all the model terms which are produced by combining different variables make an equal contribution to the system output and terms which make little contribution can be omitted a parsimonious representation which contains only the significant terms can often be obtained without the loss of representational accuracy by eliminating the redundant terms based on these observations a new variable and term selection algorithm is proposed in this paper the term detection algorithm can be applied to the general class of non linear modelling problems which can be expressed as a linear in the parameters form the variable selection procedure is based on locally linea

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

long time existence and bounded scalar curvature in the ricci harmonic flow abstract in this paper we study the long time existence of the ricci harmonic flow in terms of scalar curvature and weyl tensor which extends cao s result 6 in the ricci flow in dimension four we also study the integral bound of the riemann curvature for the ricci harmonic flow generalizing a recently result of simon 38

bifurcations from the endpoints of the essential spectrum in the linearized nonlinear schrodinger problem we study bifurcations of eigenvalues from the endpoints of the essential spectrum in the linearized nonlinear schrodinger problem in three dimensions we show that a resonance and an eigenvalue of positive energy at the endpoint may bifurcate only to a real eigenvalue of positive energy while an eigenvalue of negative energy at the endpoint may also bifurcate to complex eigenvalues

the logarithmic sobolev inequalities along geometric flow and applications abstract for some class of geometric flows we obtain the logarithmic sobolev inequalities and their equivalence up to different factors directly and also obtain the long time non collapsing and non inflated properties which generalize the results in the case of ricci flow or list ricci flow or harmonic ricci flow as applications for mean curvature flow in lorentzian space with nonnegative sectional curvature and twisted kahler ricci flow on fano manifolds we get the results above

harnack estimates for nonlinear backward heat equations in geometric flows let m be a closed riemannian manifold with a family of riemannian metrics gij t evolving by a geometric flow tgij 2sij where sij t is a family of smooth symmetric two tensors we derive several differential harnack estimates for positive solutions to the nonlinear backward heat type equation f t f flog f asf where a and are constants and s gijsij is the trace of sij our abstract formulation provides a unified framework for some known results proved by various authors and moreover leads to new harnack inequalities for a variety of geometric flows

stable manifolds for all monic supercritical focusing nonlinear schrodinger equations in one dimension keywords critical schrodinger equation stable manifolds modulation theory spectral theory klein gordon equations non linear schrodinger blow up rate standing waves nonintegrable equations invariant manifolds stability theory solitary waves ground states instability reference epfl article 155183doi 10 1090 s0894 0347 06 00524 8 record created on 2010 11 19 modified on 2017 05 12

identification of mimo non linear systems using a forward regression orthogonal estimator abstract an orthogonal least squares estimator which was originally derived for single input single output systems is extended to multi input multi output non linear systems the estimator can provide information about the structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner multivariable non linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included

spectra of positive and negative energies in the linearized nls problem we study the spectrum of the linearized nls equation in three dimensions in association with the energy spectrum we prove that unstable eigenvalues of the linearized nls problem are related to negative eigenvalues of the energy spectrum while neutrally stable eigenvalues may have both positive and negative energies the nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum we derive bounds on the number of unstable eigenvalues of the linearized nls problem and study bifurcations of embedded eigenvalues of positive and negative energies we develop the l 2 scattering theory for the linearized nls operators and recover results of grillakis 5 with a fermi golden rule c

on asymptotic stability in energy space of ground states for nonlinear schrodinger equations we consider nonlinear schrodinger equations iu t delta u beta u 2 u 0 text for t x in mathbb r times mathbb r d where d 3 and is smooth we prove that symmetric finite energy solutions close to orbitally stable ground states converge to a sum of a ground state and a dispersive wave as t assuming the so called the fermi golden rule fgr hypothesis we improve the sign condition required in a recent paper by gang zhou and i m sigal

fast orthogonal identification of nonlinear stochastic models and radial basis function neural networks a new fast orthogonal estimation algorithm is derived for a wide class of nonlinear stochastic models including training radial basis function neural networks the selection of significant regressors and the estimation of unknown parameters in the presence of nonlinear noise sources are considered and simulated examples are included to demonstrate the efficiency of the new procedure