cointegration and speed of convergence to equilibrium this paper is concerned with the time profile of the effects of shocks on cointegrating relations in the context of a multivariate var p model it considers alternative methods of characterizing and estimating such a time profile and in particular proposes the application of the persistence profile approach introduced in lee and pesaran 1993 it is shown that the estimator of the persistence profile of the cointegrating relations is root t consistent with a limiting normal distribution the paper also shows that the persistence profile approach is invariant to the way shocks in the underlying var model are orthogonalized which is not true of the traditional impulse response analysis the theoretical framework is applied to an exchange rate and interest rate data set and it is found that the persistence profile of the purchasing power parity ppp relation converges to zero very slowly while the persistence profile of the uncovered interest parity uip relation converges to zero reasonably quickly

new lp relaxations for minimum cycle path tree cover problems abstract given an undirected complete graph g v e with nonnegative edge weight function obeying the triangle inequality a set c 1 c 2 c k of cycles is called a cycle cover if v i 1 k v c i where v c i represents the set of vertices in c i and its cost is given by the maximum weight of the cycles the minimum cycle cover problem mccp aims to find a cycle cover of cost at most with the minimum number of cycles we propose new lp relaxations for mccp as well as its variants called the minimum path cover problem mpcp and the minimum tree cover problem where the cycles are replaced by paths or trees moreover we give new lp relaxations for a special case of the rooted version of mccp mpcp we show that these lp relaxations have significantly better integrality gaps than the previous relaxations

inference in dynamic models containing surprise variables abstract some new results on calculating moving average representation mar coefficients and their limiting distribution from estimated vector arma processes are presented the technique is applied to the problem of estimating the coefficients of unanticipated or surprise variables in a single equation for a multi period expectations horizon the method naturally conditions the expectations on all past values of the process and avoids the necessity of using two step regression procedures and adjusting the resulting standard errors

on the reducibility of linear quasi periodic systems with liouvillean basic frequencies and multiple eigenvalues abstract in this paper we consider the linear quasi periodic system x a p t x x r d where a is a d d constant matrix of elliptic type and has multiple eigenvalues p t is analytic quasi periodic with respect to t with basic frequencies 1 where is irrational and is a small perturbation parameter under suitable non resonant condition non degeneracy condition and 0 r where lim sup n ln q n 1 q n q n is the sequence of denominations of the best rational approximations for r q 0 r r r is the initial radius of analytic strip it is proved that for most sufficiently small this system can be reduced to a constant system x a x where a is a constant matrix close to a as some applications we apply our results to quasi periodic hill s equations three dimensional skew symmetric systems and n coupled schrodinger equations to study the lyapunov stability of the equilibrium and the existence of quasi periodic solutions

consistent estimation of equations with composite moving average disturbance terms abstract the paper examines the circumstances under which an equation with a composite ma disturbance term can be consistently estimated by single equation non linear least squares the composite disturbance may arise as a result of the dependent or an explanatory variable being unobservable either because it is subject to measurement error or because it is a desired or expected variable it may also arise as a result of substituting out an explanatory variable from an equation or because a vector ma process is specified for the structural form of a linear simultaneous equation model the argument of the paper relies on some results relating to the sum of finite ma processes presented in nelson 1975a and darroch and mcdonald 1981

almost reducibility and non perturbative reducibility of quasi periodic linear systems in this paper we prove that a quasi periodic linear differential equation in sl 2 with two frequencies 1 is almost reducible provided that the coefficients are analytic and close to a constant in the case that is diophantine we get the non perturbative reducibility we also obtain the reducibility and the rotations reducibility for an arbitrary irrational under some assumption on the rotation number and give some applications for schrodinger operators our proof is a generalized kam type iteration adapted to all irrational

new approximation algorithms for the minimum cycle cover problem given an undirected weighted graph g v e with nonnegative weight function obeying the triangle inequality a set c 1 c 2 ldots c k of cycles is called a cycle cover if v subseteq bigcup i 1 k v c i and its cost is given by the maximum weight of the cycles the minimum cycle cover problem aims to find a cycle cover of cost at most lambda with the minimum number of cycles an o n 2 24 5 approximation algorithm and an o n 5 14 3 approximation algorithm are given by yu and liu theor comput sci 654 45 58 2016 however the original proofs for approximation ratios are incomplete in this paper we first present a corrected simplified analysis on the 24 5 approximation algorithm then we give a new o n 3 approximation algorithm that achieves the same ratio 14 3 and has much simpler proof on the approximation ratio moreover we derive an improved 32 7 approximation algorithm that runs in o n 5

exponential splitting for nonautonomous linear discrete time systems in banach spaces in this paper we consider some concepts of exponential splitting for nonautonomous linear discrete time systems these concepts are generalizations of some well known concepts of uniform and nonuniform exponential dichotomies connections between these concepts are presented and some illustrating examples prove that these are distinct

pseudo almost periodic solutions of neutral integral and differential equations with applications abstract the existence and uniqueness of pseudo almost periodic solutions to general neutral integral equations with deviations are obtained for this pseudo almost periodic functions in two variables are considered the results extend the corresponding ones to the convolution type integral equations they are used to study pseudo almost periodic solutions of general neutral differential equations and to the so called scalar neutral logistic equation version

existence and roughness of the exponential dichotomy for skew product semiflow in banach spaces abstract in this paper we introduce a concept of exponential dichotomy for skew product semiflow in infinite dimensional banach spaces which is an extension of the classic concept for evolution operators this concept is used to study the roughness property of the skew product semiflow also we introduce the concept of discrete skew product and give a necessary and sufficient condition for this discrete skew product to have a discrete dichotomy after that we give necessary and sufficient conditions for the existence of exponential dichotomy for skew product semiflow moreover we prove that the exponential dichotomy for skew product semiflow is not destroyed by small perturbation finally we apply these results to parabolic partial differential equations and functional differential equations

on reducibility for a class of n dimensional quasi periodic systems with a small parameter in this paper we consider the reducibility of a class of n dimensional real analytic quasi periodic systems with a small parameter x a q t x x r n we prove that if the basic frequencies of q and the eigenvalues of a satisfy some non resonance conditions then for most of the sufficiently small parameters in the sense of lebesgue measure the system is reducible without any non degeneracy assumption with respect to the parameter moreover under some assumptions we obtain a similar result for nonlinear quasi periodic systems

prediction in dynamic models with time dependent conditional variances abstract this paper considers forecasting the conditional mean and variance from a single equation dynamic model with autocorrelated disturbances following an arma process and innovations with time dependent conditional heteroskedasticity as represented by a linear garch process expressions for the minimum mse predictor and the conditional mse are presented we also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with garch 1 1 innovations these results are then used in the construction of ex ante prediction confidence intervals by means of the cornish fisher asymptotic expansion an empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results

asymptotic integration of ordinary different systems an extension and a new proof of hartman and wintner s theorem on asymptotic integration are given

the floquet theory and the state density of quasi periodic schrodinger operators abstract we study the floquet solutions of quasi periodic schrodinger operators on flows which satisfy a diophantine condition using these solutions we show that the resolvent of such an operator is smooth with respect to certain derivations in the c algebra associated with the flow and that every projection corresponding to a spectral gap has a finite localization length based on these results we derive a formula which quantizes the integral components of the integrated density of states for the operator on each spectral gap

asymptotic distributions of impulse response functions in short panel vector autoregressions this paper establishes the asymptotic distributions of the impulse response functions in panel vector autoregressions with a fixed time dimension it also proves the asymptotic validity of a bootstrap approximation to their sampling distributions the autoregressive parameters are estimated using the gmm estimators based on the first differenced equations and the error variance is estimated using an extended analysis of variance type estimator contrary to the time series setting we find that the gmm estimator of the autoregressive coefficients is not asymptotically independent of the error variance estimator the asymptotic dependence calls for variance correction for the orthogonalized impulse response functions simulation results show that the variance correction improves the coverage accuracy of both the asymptotic confidence band and the studentized bootstrap confidence band for the orthogonalized impulse response functions

robust nonuniform dichotomies and parameter dependence abstract we establish the robustness of linear cocycles with an exponential dichotomy under sufficiently small lipschitz perturbations in the sense that the existence of an exponential dichotomy for a given cocycle persists under these perturbations we consider cocycles in banach spaces as well as the general case of nonuniform exponential dichotomies and also the general case of an exponential behavior e c n given by an arbitrary sequence n including the usual exponential behavior n n as a very special case moreover we show that the projections of the exponential dichotomies obtained from the perturbation vary continuously with the parameter and in fact that they are locally lipschitz on finite dimensional parameters

a note on the asymptotic distribution of impulse response functions of estimated var models with orthogonal residuals abstract a simple closed form expression is given for the covariance matrix of the asymptotic distribution of the coefficients of a moving average representation with orthogonal residuals computed from an estimated vector autoregressive process

approximation algorithms for min max cycle cover problems as a fundamental optimization problem the vehicle routing problem has wide application backgrounds and has been paid lots of attentions in past decades in this paper we study its applications in data gathering and wireless energy charging for wireless sensor networks by devising improved approximation algorithms for it and its variants the key ingredients in the algorithm design include exploiting the combinatorial properties of the problems and making use of tree decomposition and minimum weighted maximum matching techniques specifically given a metric complete graph g and an integer k 0 we consider rootless uncapacitated rooted and capacitated rooted min max cycle cover problems in g with an aim to find k rootless or rooted edge disjoint cycles covering the vertices in v such that the maximum cycle weight among the k cycles is minimized for each of the mentioned problems we develop an improved approximate solution that is for the rootless min max cycle cover problem we develop a 5 1 over 3 epsilon approximation algorithm for the uncapacitated rooted min max cycle cover problem we devise a 6 1 over 3 epsilon approximation algorithm and for the capacitated rooted min max cycle cover problem we propose a 7 epsilon approximation algorithm these algorithms improve the best existing approximation ratios of the corresponding problems 6 epsilon 7 epsilon and 13 epsilon respectively where epsilon is a constant with 0 we finally evaluate the performance of the proposed algorithms through experimental simulations experimental results show that the actual approximation ratios delivered by the proposed algorithms are always no more than 2 much better than their analytical counterparts

upper quantum lyapunov exponent and anosov relations for quantum systems driven by a classical flow we generalize the definition of quantum anosov properties and the related lyapunov exponents to the case of quantum systems driven by a classical flow i e skew product systems we show that the skew anosov properties can be interpreted as regular anosov properties in an enlarged hilbert space in the framework of a generalized floquet theory this extension allows us to describe the hyperbolicity properties of almost periodic quantum parametric oscillators and we show that their upper lyapunov exponents are positive and equal to the lyapunov exponent of the corresponding classical parametric oscillators as second example we show that the configurational quantum cat system satisfies quantum anosov properties

quasi genericity of bifurcations to high dimensional invariant tori for maps we consider a family of maps in a banach spacee near the situation when the derivative at the fixed point has two pairs of complex eigenvalues lying on the unit circle the other part of the spectrum being strictly inside the unit disc we focus our attention on the region of the parameter space where the truncated normal form of the maps shows a bifurcation of a family of invariantt 1 circles into a family of invariantt 2 tori we show that this problem needs a 3 dimensional parameter unfolding and that for the complete maps bifurcation occurs at points where is the rotation number on the non normally hyperbolict 1 circle ande 2i are the eigenvalues of the constant matrix conjugated to the non contracting part of the linearization on the normal fiber bundle overt 1 making some non resonance and diophantine assumptions on leading to a positive measure cantor set int 2 we show that in paraboloidal regions of the 3 dim parameter space we have clean bifurcations as for the truncated normal form the complement of these regions forms a set of bubbles such as the ones obtained by chenciner in chen for a codimension 2 problem for maps in 2 the main tool here is a generalization for a matrix function ont 1 close to a constant of the quasi conjugacy to a constant modulo a minimum of additional parameters moved quasi conjugacy for the infinite dimensional case we use ac decoupling result on the angular dependent linear parts into a contraction still angular dependent and another part quasi conjugated to a constant matrix this type of analysis applies for a wide range of problems where truncated normal forms of the maps give bifurcations fromt n tot n 1 tori and this needs a n 1 dimensional parameter unfolding

poincare type theorems for non autonomous systems in this paper we establish analytic equivalence theorems of poincare and poincare dulac type for analytic non autonomous differential systems based on the dichotomy spectrum of their linear part as applications of the theorem normal forms linearize for two illustrative examples

asymptotic distributions of impulse responses step responses and variance decompositions of estimated linear dynamic models formulas are derived for computing asymptotic covariance matrices of sets of impulse responses step responses or variance decompositions of estimated dynamic simultane ous equations models in vector autoregressive moving average varma form com puted covariances would be used to test linear restrictions on sets of impulse responses step responses or variance decompositions the results unify and extend previous formulas to handle any model in varma form provide accurate computations based on analytic derivatives and provide insights into the structures of the asymptotic covariances following the lead of sims 1980 impulse responses step responses and variance decompositions have become standard tools for examining the empiri cal validity of economic theories or interpreting the forecasting and policy implications of estimated linear dynamic models runkle 1987 demonstrated the importance of accounting for sampling variability in these exercises he computed confidence bounds for impulse responses and variance decomposi tions derived from estimated vector autoregressive var models with sto chastic simulations and asymptotic normal approximations the two methods produced comparable results but the simulations took about 160 times longer to compute than normal approximations based on numerical derivatives whereas runkle only reported confidence bounds for individual impulse re sponses and decomposed variances of var models the present paper derives equations for computing full asymptotic covariance matrices of sets of impulse responses step responses or variance decompositions of estimated dynamic simultaneous equations models in autoregressive moving average form the computed covariances may be used to jointly test multiple linear restrictions or linear approximations of differentiable nonlinear restrictions on sets of im pulse responses step responses or variance decompositions of estimated mod els because the derived computational equations are based on analytical derivatives they have at least two advantages they lead to more accurate and often faster computations than those based on numerical derivatives they provide insight into the structures of asymptotic covariances of the estimated quantities by allowing for various identifying restrictions the paper extends and unifies results of schmidt 1973 evans and wells 1986 and liutkepohl 1988 1989

cauchy matrix for linear almost periodic systems and some consequences abstract a novel method to construct the fundamental matrix for a linear almost periodic system is proposed provided that the diagonal terms satisfy an average separation condition and the off diagonal coefficients are l small the idea is to transform the system in a set of riccati type equations and use exponential dichotomy and its consequences it is shown that the method yields easy computation procedures with simple and direct conditions depending on the coefficients finally our result enables us to obtain i explicit almost periodic matrices q t q 1 t and q t which diagonalize the original system and ii sufficient conditions for the stability two illustrative examples are shown

improved approximation algorithms for some min max and minimum cycle cover problems given an undirected weighted graph g v e a set c1 c2 ck of cycles is called a cycle cover of the vertex subset v if vi 1kv ci and its cost is given by the maximum weight of the cycles the min max cycle cover problem mmccp is to find a minimum cost cycle cover of v with at most k cycles the rooted min max cycle cover problem rmmccp is to find a minimum cost cycle cover of vd with at most k cycles each of which contains one vertex in d the minimum cycle cover problem mccp aims to find a cycle cover of v of cost at most with the minimum number of cycles we propose approximation algorithms for mmccp and rmmccp with performance ratios 5 and 6 respectively these results improve the previous algorithms in term of both approximation ratios and running times for mccp we obtain a 143 approximation algorithm that has the same time complexity as the previous best 5 approximation algorithm moreover we transform a approximation algorithm for tsp into approximation algorithms for mmccp rmmccp and mccp with ratios 4 4 1 and 4 respectively

on the reducibility of linear differential equations with quasiperiodic coefficients the system x a eq t x in rd is considered where a is a constant matrix and q a quasiperiodic analytic matrix with r basic frequencies the eigenvalues of a are arbitrary including the purely imaginary case suppose that the set formed by the eigenvalues of a and the basic frequencies of q satisfies a nonresonant condition then there is a positive measure cantorian set e such that for e e the system is reducible to constant coefficients by means of a quasiperiodic change of variables provided a nondegeneracy condition holds this condition prevents locking at resonance

nearly efficient estimation of time series models with predetermined but not exogenous instruments particularly under the assumption of rational expectations a model may have serially correlated errors and those errors may be uncorrelated with contemporaneous and lagged values of a predetermined instrument yet the instruments may not be strictly exogenous this paper proposes a method for transforming such a model to one without serial correlation while keeping the instrument predetermined standard theory of instrumental variables estimation then applies furthermore it turns out that for transformations of the class proposed asymptotic distribution theory is the same whether the serial correlation properties of the errors are known a priori or estimated as the number of lagged values of the predetermined variables used as instruments increases the asymptotic variance of the standard instrumental variables estimator applied to the transformed model approaches that of the optimal estimator proposed by hansen and sargent 8 in a number of recently developed macroeconomic models behavioral equations arise in which error terms can be asserted on the basis of economic arguments to be uncorrelated with some set of instrumental variables at a certain set of dates but not to be uncorrelated with the instruments at all dates examples of such

existence and robustness of nonuniform h k μ ν dichotomies for nonautonomous impulsive differential equations abstract for the linear nonautonomous impulsive differential equation we propose a new notion called the nonuniform h k dichotomy which extends the notion of dichotomy of uniform and nonuniform types and is related to the theory of nonuniform hyperbolicity we establish a sufficient criterion for the existence of the nonuniform h k dichotomy in terms of appropriate lyapunov exponents for the linear perturbation we develop the robustness or roughness of nonuniform h k dichotomies in the sense that a nonuniform h k dichotomy persists under a sufficiently small linear perturbation

existence and global exponential stability of almost periodic solution for cellular neural networks with variable coefficients and time varying delays in this paper we study cellular neural networks with almost periodic variable coefficients and time varying delays by using the existence theorem of almost periodic solution for general functional differential equations introducing many real parameters and applying the lyapunov functional method and the technique of young inequality we obtain some sufficient conditions to ensure the existence uniqueness and global exponential stability of almost periodic solution the results obtained in this paper are new useful and extend and improve the existing ones in previous literature

econometric analysis of linearized singular dynamic stochastic general equilibrium models in this paper i propose an alternative to calibration of linearized singular dynamic stochastic general equilibrium models given an a theoretical econometric model as a representative of the data generating process i will construct an information measure which compares the conditional distribution of the econometric model variables with the corresponding singular conditional distribution of the theoretical model variables the singularity problem will be solved by using convolutions of both distributions with a non singular distribution this information measure will then be maximized to the deep parameters of the theoretical model which links these parameters to the parameters of the econometric model and provides an alternative to calibration this approach will be illustrated by an application to a linearized version of the stochastic growth model of king plosser and rebelo

input output admissibility and exponential trichotomy of difference equations abstract we propose a new method for the study of the asymptotic behavior of difference equations in infinite dimensional spaces providing characterizations for the property of uniform exponential trichotomy we deduce the structure of the stable unstable and bounded subspace and prove the uniqueness of the projection families we introduce a new admissibility concept with respect to a discrete input output system and prove that this is a necessary and sufficient condition for the existence of uniform exponential trichotomy throughout the paper there is no assumption on the coefficients and the obtained results are applicable to any class of difference equations

large sample estimation and testing procedures for dynamic equation systems abstract joint two step estimation procedures which have the same asymptotic properties as the maximum likelihood ml estimator are developed for the final equation transfer function and structural form of a multivariate dynamic model with normally distributed vector moving average errors the ml estimator under fixed and known initial values is obtained by iterating the procedure until convergence the asymptotic distribution of the two step estimators is used to construct large sample testing procedures for the different forms of the model

robustness of general dichotomies abstract for a linear equation v a t v we consider general dichotomies that may exhibit stable and unstable behaviors with respect to arbitrary asymptotic rates e c t for some function t this includes as a special case the usual exponential behavior when t t we also consider the general case of nonuniform exponential dichotomies we establish the robustness of the exponential dichotomies in banach spaces in the sense that the existence of an exponential dichotomy for a given linear equation persists under sufficiently small linear perturbations we also establish the continuous dependence with the perturbation of the constants in the notion of dichotomy

exponential dichotomy roughness on banach spaces in the present paper we extend existing results on exponential dichotomy roughness for linear ode systems to infinite dimensional banach space we give new conditions for the existence of exponential dichotomy roughness in infinite dimensional space and in the finite interval case we also improve previous results by indicating the exact values of the dichotomic constants of the perturbed equation

exponential dichotomy and dichotomy radius for difference equations abstract the aim of this paper is to provide a new approach concerning the characterization of exponential dichotomy of difference equations by means of admissible pair of sequence spaces we classify the classes of input and output spaces respectively and deduce necessary and sufficient conditions for exponential dichotomy applicable for a large variety of systems by an example we show that the obtained results are the most general in this topic as an application we deduce a general lower bound for the dichotomy radius of difference equations in terms of input output operators acting on sequence spaces which are invariant under translations

nonuniform almost reducibility of nonautonomous linear differential equations abstract we prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be written as diagonal system with a perturbation which is small enough moreover we show that the diagonal terms are contained in the nonuniform exponential dichotomy spectrum for this purpose we introduce the concepts of nonuniform almost reducibility and nonuniform contractibility which are generalizations of these notions originally defined in a uniform context

smoothness of spectral subbundles and reducibility of quasi periodic linear differential systems abstract in this paper we study linear differential systems 1 x a t x where a is an n n matrix valued function defined on the k torus t k and t t is a given irrational twist flow on t k first we show that if a c n t k where n 0 1 2 then the spectral subbundles are of class c n on t k next we assume that a is sufficiently smooth on t k and satisfies a suitable small divisors inequality we show that if 1 satisfies the full spectrum assumption then there is a quasi periodic linear change of variables x p t y that transforms 1 to a constant coefficient system y by finally we study the case where the matrix a t in 1 is the jacobian matrix of a nonlinear vector field x evaluated along a quasi periodic solution x t of 2 x x we give sufficient conditions in terms of smoothness and small divisors inequalities in order that there is a coordinate system z defined in the vicinity of h the hull of so that the linearized system 1 can be represented in the form z dz where d is a constant matrix our results represent substantial improvements over known methods because we do not require that a be close to a constant coefficient system

a dynamical systems result on asymptotic integration of linear differential systems abstract we are interested in the asymptotic integration of linear differential systems of the form x t r t x where is diagonal and r l p t 0 for p 1 2 our dichotomy condition is in terms of the spectrum of the omega limit set our results include examples that are not covered by the hartman wintner theorem

exponential dichotomy integral separation and diagonalizability of linear systems of ordinary differential equations abstract this paper is concerned with linear systems of ordinary differential equations a criterion for integral separation in terms of exponential dichotomy is given as corollaries we obtain the roughness theorem for integral separation and the new result that an upper triangular system on a half line is integrally separated if and only if the system corresponding to its diagonal is we then show that a diagonal system on a half line is integrally separated if and only if a certain perturbed system is diagonalizable using this result we are able to deduce that the interior of the set of diagonalizable systems on a half line is the set of systems with integral separation and that the interior for the whole line is the set of systems which are integrally separated on both half lines

large sample estimation and testing procedures for dynamic equation systems abstract in 1980 palm and zellner presented a number of joint or system estimation and testing procedures for the final equations transfer functions and structural equations of a multivariate dynamic model with normally distributed vector moving average errors in this paper we show that there is a flaw in their argument which renders most of the procedures invalid possible alternative procedures are described

on the reducibility of a class of finitely differentiable quasi periodic linear systems abstract in this paper we consider the following system x a e q t x where a is a constant matrix with different eigenvalues and q t is quasi periodic with frequencies 1 2 r moreover q q t q t has continuous partial derivatives b q j b for j 1 2 r where b 9 4 r 1 z and the moduli of continuity of b q j b satisfy a condition of finiteness condition on an integral which is more general than a holder condition under suitable hypothesis of non resonance conditions and non degeneracy conditions we prove that for most sufficiently small e the system can be reducible to a constant coefficient differentiable equation by means of a quasi periodic homeomorphism

existence and stability of almost periodic solutions in impulsive neural network models abstract the existence and global exponential stability of an almost periodic solution of an impulsive neural network model with distributed delays is considered in a matrix setting the approach transforms the original network into a matrix analysis problem where a set of sufficient conditions based on spectral radius is presented a concrete hopfield model shows the advantages in comparison with a classical norm approach

a parameterization method for the computation of invariant tori and their whiskers in quasi periodic maps rigorous results abstract in this paper we prove rigorous results on persistence of invariant tori and their whiskers the proofs are based on the parameterization method of x cabre e fontich r de la llave the parameterization method for invariant manifolds i manifolds associated to non resonant subspaces indiana univ math j 52 2 2003 283 328 x cabre e fontich r de la llave the parameterization method for invariant manifolds ii regularity with respect to parameters indiana univ math j 52 2 2003 329 360 the invariant manifolds results proved here include as particular cases of the usual strong stable and strong unstable manifolds but also include other non resonant manifolds the method lends itself to numerical implementations whose analysis and implementation is studied in a haro r de la llave a parameterization method for the computation of invariant tori and their whiskers in quasi periodic maps numerical algorithms preprint 2005 a haro r de la llave a parameterization method for the computation of invariant tori and their whiskers in quasi periodic maps numerical implementation and examples preprint 2005 the results are stated as a posteriori results namely that if one has an approximate solution which is not degenerate then one has a true solution not too far from the approximate one this can be used to validate the results of numerical computations

a simple robust controller for the approximate regulation of almost periodic signals for linear systems by using a delay line as a signal generator we design a simple robust controller for the approximate regulation i e approximate asymptotic tracking and rejection of almost periodic signals for linear systems as opposed to the related existing results our controller design does not require online parameter tuning besides the usual assumptions about stabilizability detectability and nonexistence of transmission zeros for the plant the controller design algorithm of this paper only requires knowledge of the desired tracking accuracy based on this information alone we can only design a robust controller achieving in the presence of unknown trigonometric polynomial disturbances and additive perturbations to the plant and the controller here is the output of the plant and is an arbitrary almost periodic reference signal taken from an infinite dimensional generalized sobolev space of almost periodic functions in this paper we also study robust output regulation in the limiting case where it turns out that due to the general loss of exponential closed loop stability asymptotic tracking rejection can also be lost as unless the exogenous signals are smooth enough this last result extends some recent theorems on nonrobust open loop output regulation for infinite dimensional exosystems the results of this paper are new and potentially useful for finite dimensional plants but the main results are also true for infinite dimensional systems with bounded control and observation operators

polynomial time approximation schemes for euclidean traveling salesman and other geometric problems we present a polynomial time approximation scheme for euclidean tsp in fixed dimensions for every fixed c 1 and given any n nodes in r 2 a randomized version of the scheme finds a 1 1 c approximation to the optimum traveling salesman tour in o n log n o c time when the nodes are in r d the running time increases to o n log n o d c d 1 for every fixed c d the running time is n poly log n that is nearly linear in n the algorithmm can be derandomized but this increases the running time by a factor o n d the previous best approximation algorithm for the problem due to christofides achieves a 3 2 aproximation in polynomial time we also give similar approximation schemes for some other np hard euclidean problems minimum steiner tree k tsp and k mst the running times of the algorithm for k tsp and k mst involve an additional multiplicative factor k the previous best approximation algorithms for all these problems achieved a constant factor approximation we also give efficient approximation schemes for euclidean min cost matching a problem that can be solved exactly in polynomial time all our algorithms also work with almost no modification when distance is measured using any geometric norm such as e p for p 1 or other minkowski norms they also have simple parallel i e nc implementations

studying co movements in large multivariate data prior to multivariate modelling abstract for non stationary vector autoregressive models var hereafter or var with moving average varma hereafter we show that the presence of common cyclical features or cointegration leads to a reduction of the order of the implied univariate autoregressive integrated moving average arima hereafter models this finding can explain why we identify parsimonious univariate arima models in applied research although var models of typical order and dimension used in macroeconometrics imply non parsimonious univariate arima representations next we develop a strategy for studying interactions between variables prior to possibly modelling them in a multivariate setting indeed the similarity of the autoregressive roots will be informative about the presence of co movements in a set of multiple time series our results justify both the use of a panel setup with homogeneous autoregression and heterogeneous cross correlated vector moving average errors and a factor structure and the use of cross sectional aggregates of arima series to estimate the homogeneous autoregression

embedding of analytic quasi periodic cocycles into analytic quasi periodic linear systems and its applications in this paper we prove that any analytic quasi periodic cocycle close to constant is the poincare map of an analytic quasi periodic linear system close to constant which bridges both methods and results in quasi periodic linear systems and cocycles we also show that the almost reducibility of an analytic quasi periodic linear system is equivalent to the almost reducibility of its corresponding poincare cocycle by the local embedding theorem and the equivalence we transfer the recent local almost reducibility results of quasi periodic linear systems hou and you in invent math 190 209 260 2012 to quasi periodic cocycles and the global reducibility results of quasi periodic cocycles avila in almost reducibility and absolute continuity 2010 avila et al in geom funct anal 21 1001 1019 2011 to quasi periodic linear systems finally we give a positive answer to a question of avila et al geom funct anal 21 1001 1019 2011 and use it to study point spectrum of long range quasi periodic operator with liouvillean frequency the embedding also holds for some nonlinear systems