on global diffeomorphisms of euclidian space as is well known the first attempt at characterizing global diffeomorphisms of ir goes back to the 1906 work of hadamard l since that time progress in the global diffeomorphism problem has been rather slow notable contributions are those of levy 2 who generalized hadamard s theorem to banach spaces and of banach and mazur 3 and caccioppoli 4 who proved the so called properness criterion saying that a proper local homeomorphism of a banach space is a global homeomorphism the standard proofs of the theorems of hadamard and levy and of banach mazur and caccioppoli rely upon ideas of what is now called covering space theory via the important homotopy lifting property of coverings see e g 5 this approach makes it clear that it is only lack of compactness of ir that allows for the existence of noninjective local homeomorphisms when n l 2 the complex exponential when n 2 being the most famous example the theorems mentioned above were found again by various authors sometimes in special cases and sometimes in a different framework but always through some variant of the same argument a synthesis was made by rheinboldt 6 in 1969 part of his results were rediscovered five years later by plastock 7 and given a somewhat simpler exposition for the special case of banach spaces other contributions were made by meisters and olech 8 global homeomorphisms of bounded domains in i meyer 9 complementing the work of levy and radulescu and radulescu lo expanding upon plastock s results many other articles have been devoted to special cases where extra hypotheses are introduced consistently with the problem at hand for instance polynomial mappings only are relevant to the jacobian conjecture of algebraic geometry and hypotheses about the spectrum of the derivative at each point come up in a natural way in global stability questions for differential equations the new results presented in this paper have been obtained through arguments from critical point theory and differential topology here the central notion is that of admissible flow given a mapping f ii ir the main property of what we call an f admissible flow q ir x ii f o i f o is that for every x e ir f o the function t jf q t x l where 1 1 is the euclidean norm is strictly increasing and tends to 0 resp 00 as t tends to co resp 00 the basic feature we prove is that a local diffeomorphism f is a global one if and only if f o zi and there is an f admissible flow this statement makes it clear that 0 plays a special role regarding f admissibility and the condition f o 0 cannot be eliminated as examples will show the introduction of f admissibility followed the author s remark that in hilbert space hadamard s theorem could be derived from the mountain pass theorem of ambrosetti and

kalman filtering with intermittent observations on the boundedness of the expected error covariance this paper addresses the stability of a kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator we give a necessary condition and a sufficient condition with a trivial gap between them for the boundedness of the expected value of the estimation error covariance these conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order markov process hence we extend the class of systems for which these conditions are known in two directions namely by including degenerate systems and by considering network models more general than i i d and gilbert elliott we show that these conditions recover known results from the literature when evaluated for non degenerate systems under the assumption of i i d or gilbert elliott packet loss models

the periodic boundary value problem for semilinear elastic beam equations the resonance case this paper discusses the existence of generalized solutions to periodic boundary value problems for semilinear elastic beam equations under a resonance condition the argument presented makes use of the global inverse theorem and galerkin s method

unscented kalman filter over unreliable communication networks with markovian packet dropouts the paper investigates the stability of the discrete time modified unscented kalman filter mukf in transmitting measurement outputs to the filter via a network since the communication channel states do not always vary in time the arrival of the observations is modeled as a two state time homogeneous markov process k the stability of the estimation error covariance matrices at packet reception times is analyzed sufficient conditions related to hk and the initial conditions for the peak covariance stability and the usual covariance stability are given also the relationship between the different types of stability notions is illustrated for systems with i i d observation dropouts numerical example is given to illustrate the effectiveness of the techniques developed

finding domains of invertibility for smooth functions by means of attraction basins abstract the problem of finding a large domain in r n where a locally invertible smooth function is one to one had been approached in different ways none of them exhaustive the present paper considers an auxiliary ordinary differential equation built upon c 1 which has an asymptotically stable equilibrium at the point around which we invert on the basin of attraction of this point the function is proved to be one to one a sufficient condition for injectivity on a compact ball b is derived the condition involves the values of and its jacobian matrix d on the boundary b this criterion of invertibility is easily generalized to more general domains

stability analysis of networked sampled data linear systems with markovian packet losses we consider the stability properties of sampled data networked linear systems with markovian packet losses a binary markov chain is used to characterize the packet loss phenomenon of the network we show that the sampled data system under consideration can be considered as a randomly sampled system with an i i d random sampling period necessary and sufficient conditions for the stochastic stability properties are established those conditions are based on the relationships of stability properties between the systems evolving in deterministic continuous time deterministic discrete time and random discrete time in addition the asymptotic stability of the system is also studied by using lyapunov exponent method

global homeomorphisms and covering projections on metric spaces for a large class of metric spaces with nice local structure which includes banach finsler manifolds and geodesic spaces of curvature bounded above we give sufficient conditions for a local homeomorphism to be a covering projection we first obtain a general condition in terms of a path continuation property as a consequence we deduce several conditions in terms of path liftings involving a generalized derivative and in particular we obtain an extension of hadamard global inversion theorem in this context next we prove that in the case of quasi isometric mappings some of these sufficient conditions are also necessary finally we give an application to the existence of global implicit functions

riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices until recently it was believed that a necessary and sufficient condition for convergence of the riccati difference equation of optimal filtering was that the system be both delectable and stabilizable recently it has been shown that the stabilizability condition can be removed but convergence has only established under restrictive assumptions including the requirement that the state transition matrix be nonsingular the present paper generalizes these results in several directions first properties of the algebraic riccati equation are established for the case of singular state transition matrix second several assumptions previously imposed in establishing convergence of the riccati difference equation for systems with unreachable modes on the unit circle are relaxed including replacing observability by detectability weakening the conditions on the initial covariance and allowing the state transition matrix to be singular third results on the convergence and properties of the riccati equations are expressed as both necessary and sufficient conditions whereas previous results were only sufficient these extensions mean that the results have wider applicability including fixed lag smoothing problems and filtering for systems with time delays the implications of the results in the dual problem of optimal control are also studied

polyhedral lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the jacobian is non singular for a vast class of dynamical networks including chemical reaction networks crns with monotonic reaction rates the existence of a polyhedral lyapunov function plf implies structural i e parameter free local stability global structural stability is ensured under the additional assumption that each of the variables chemical species concentrations in crns is subject to a spontaneous infinitesimal dissipation this paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation showing that the existence of a plf structurally ensures global convergence if and only if the system jacobian passes a structural non singularity test it is also shown that if the jacobian is structurally non singular under positivity assumptions for the system partial derivatives the existence of an equilibrium is guaranteed for systems subject to positivity constraints it is shown that if the system admits a plf under structural non singularity assumptions global convergence within the positive orthant is structurally ensured while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise linear in rate lyapunov function

on estimation error outage for scalar gauss markov signals sent over fading channels measurements of a scalar linear gauss markov process are sent over a fading channel the fading channel is modeled as independent and identically distributed random variables with known realization at the receiver the optimal estimator at the receiver is the kalman filter in contrast to the classical kalman filter theory given a random channel the kalman gain and the error covariance become random then the probability distribution function of expected estimation error and its outage probability can be chosen for estimation quality assessment in this paper and in order to get the estimation error outage we provide means to characterize the stationary probability density function of the random expected estimation error furthermore and for the particular case of the i i d rayleigh fading channels upper and lower bounds for the outage probability are derived which provide insight and simpler means for design purposes we also show that the bounds are tight for the high snr regime and that the outage probability decreases linearly with the inverse of the average channel snr

effects of diversity and procrastination in priority queuing theory the different power law regimes empirical analyses show that after the update of a browser or the publication of the vulnerability of a software or the discovery of a cyber worm the fraction of computers still using the older browser or software version or not yet patched or exhibiting worm activity decays as a power law ensuremath sim 1 t ensuremath alpha with 0l ensuremath alpha ensuremath le 1 over a time scale of years we present a simple model for this persistence phenomenon framed within the standard priority queuing theory of a target task which has the lowest priority compared to all other tasks that flow on the computer of an individual we identify a time deficit control parameter ensuremath beta and a bifurcation to a regime where there is a nonzero probability for the target task to never be completed the distribution of waiting time mathcal t until the completion of the target task has the power law tail ensuremath sim 1 t 1 2 resulting from a first passage solution of an equivalent wiener process taking into account a diversity of time deficit parameters in a population of individuals the power law tail is changed into 1 t ensuremath alpha with ensuremath alpha 0 5 ensuremath infty including the well known case 1 t we also study the effect of procrastination defined as the situation in which the target task may be postponed or delayed even after the individual has solved all other pending tasks this regime provides an explanation for even slower apparent decay and longer persistence

global invertibility of nonsmooth mappings on etend le theoreme de hadamard d inversibilite globale a la classe des applications localement continues de lipschitz

theory of earthquakes interevent times applied to financial markets abstract we analyze the probability density function pdf of waiting times between financial loss exceedances the empirical pdfs are fitted with the self excited hawkes conditional poisson process with a long power law memory kernel the hawkes process is the simplest extension of the poisson process that takes into account how past events influence the occurrence of future events by analyzing the empirical data for 15 different financial assets we show that the formalism of the hawkes process used for earthquakes can successfully model the pdf of interevent times between successive market losses

local inversion theorems without assuming continuous differentiability in 6 it is proved that if d c r is open and f d r is frechet differentiable on d and f x e isom r r for every x e d then f is a local diffeomorphism on d we shall extend this theorem for infinite dimensional banach spaces e and mappings f d e d c e open f it where t d e is compact and i d e i x x for every x e d we shall also prove a generalization of the hadamard levi theorem for such mappings our methods are purely analytical since the single instrument we are using for establishing the results of the present paper is the topological degree theory our methods are different from 6 even in the finite dimensional case since we not use the results from s

global inversion of nonsmooth mappings using pseudo jacobian matrices we study the global inversion of a continuous nonsmooth mapping f r n r n which may be non locally lipschitz to this end we use the notion of pseudo jacobian map associated to f introduced by jeyakumar and luc and we consider a related index of regularity for f we obtain a characterization of global inversion in terms of its index of regularity furthermore we prove that the hadamard integral condition has a natural counterpart in this setting providing a sufficient condition for global invertibility

global univalence and global inversion theorems in banach spaces on etablit de nouveaux theoremes d inversion globaux on obtient des variantes globales du theoreme des fonctions implicite on demontre une generalisation du theoreme de hurwitz sur des suites de fonctions analytiques univalentes

diversity effects in kalman filtering over rayleigh fading channels a scalar first order gauss markov signal is sent over d parallel i i d rayleigh fading channels using uncoded transmission assuming perfect channel estimation at the receiver the optimal mmse estimator is the kalman filter with random instantaneous estimation error variance statistical characteristics of the instantaneous estimation error variance are studied to characterize the estimation quality one such characteristic is the estimation error outage which probabilistically depicts how often the value of the instantaneous estimation error variance exceeds a certain threshold in this paper we study the effect of channel diversity on the estimation error outage probability we show that for a certain range of outage thresholds the estimation error outage probability decreases with inverse of d th power of the average signal to noise ratio at the receiver side this means that analogous to the context of digital communication over fading channels our result implies a diversity order of d in estimating the input process

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

consistent estimators in generalized linear mixed models abstract a simple method based on simulated moments is proposed for estimating the fixed effects and variance components in a generalized linear mixed model glmm it is shown that the method is not only computationally attractive but also leads to consistent estimators on the other hand simulation shows that the method can be quite inefficient

periodic solutions for 2kth boundary value problem with resonance abstract in this paper a non variational version of a max min principle is extended and some unique existence results for the periodic boundary value problem of the higher order nonconservative systems with resonance u 2 k t j 1 k a j u 2 j 1 t 1 k 1 g u t e t are obtained

an improved stability condition for kalman filtering with bounded markovian packet losses in this paper we consider the peak covariance stability of kalman filtering subject to packet losses the length of consecutive packet losses is governed by a time homogeneous finite state markov chain we establish a sufficient condition for peak covariance stability and show that this stability check can be recast as a linear matrix inequality lmi feasibility problem compared with the literature the stability condition given in this paper is invariant with respect to similarity state transformations moreover our condition is proved to be less conservative than the existing results numerical examples are provided to demonstrate the effectiveness of our result

mean square stability for kalman filtering with markovian packet losses this paper studies the stability of kalman filtering over a network subject to random packet losses which are modeled by a time homogeneous ergodic markov process for second order systems necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure while for certain classes of higher order systems necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices all stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the markov process their implications and relationships with related results in the literature are discussed

on kalman filtering for conditionally gaussian systems with random matrices abstract we consider linear stochastic systems with additive white gaussian noise with the added generality that the system matrices are random and adapted to the observation process the main result of this paper is that in order for the standard kalman filter to generate the conditional mean and conditional covariance of the conditionally gaussian distributed state it is sufficient for the random matrices to be finite with probability one at each time instant this generalizes the best previous results available to date to our knowledge which require the more stringent hypothesis that the entries of the random matrices should possess finite second moments at each time instant a significant application of the results of this paper is to the problem of recursive identification of the unknown parameters of a controlled linear stochastic system in such problems the observation matrix is typically generated by complicated nonlinear feedback as for example in adaptive control and the finiteness of the second moments is difficult if not impossible to establish while the finiteness with probability one has been established in many applications

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

on a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage in this note we consider the following problem suppose a set of sensors is jointly trying to estimate a process one sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors what is the sensor schedule that results in the minimum error covariance we describe a stochastic sensor selection strategy that is easy to implement and is computationally tractable the problem described above comes up in many domains out of which we discuss two in the sensor selection problem there are multiple sensors that cannot operate simultaneously e g sonars in the same frequency band thus measurements need to be scheduled in the sensor coverage problem a geographical area needs to be covered by mobile sensors each with limited range thus from every position the sensors obtain a different view point of the area and the sensors need to optimize their trajectories the algorithm is applied to these problems and illustrated through simple examples

diffeomorphisms with banach space domains so f is a local diffeomorphism at every point by the inverse function theorem the aim of this paper is to find a sufficient condition for f to be injective and so a global diffeomorphism x f x theorem 2 l and a sufficient condition for f to be bijective and so a global diffeomorphism onto y theorem 3 1 this last condition is also necessary in the particular case x y r in these theorems the key role is played by nonnegative auxiliary scalar coercive functions that is continuous mappings k x r with k x a as llxll a as far as we know the use of such auxiliary functions in these questions is new first we find some corollaries to the aforementioned theorems the author hopes that suitable auxiliary functions adapted to particular problems may lead to new consequences in order to briefly discuss the results and some of their relations with the literature let us consider the case where x is a hilbert space with scalar product and k e c this simplifies the formulas a little however our results will be formulated and proved for banach spaces where we will ask for k to be locally lipschitz continuous and to have the right directional derivatives only these last assumptions are not made to quibble about this matter but are related to the nondifferentiability of the map x y ix in general banach spaces in this paper we use the hypothesis that the operator norm 11 f i x 11 is bounded on bounded sets i e sup iif ii vr o r w 1 2 il4 5 r

gossip and distributed kalman filtering weak consensus under weak detectability the paper presents the gossip interactive kalman filter gikf for distributed kalman filtering for networked systems and sensor networks where intersensor communication and observations occur at the same time scale the communication among sensors is random each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link we show that under a weak distributed detectability condition 1 the gikf error process remains stochastically bounded irrespective of the instability of the random process dynamics and 2 the network achieves weak consensus i e the conditional estimation error covariance at a uniformly randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semidefinite matrices independent of the initial state to prove these results we interpret the filtering states estimates and error covariances at each node in the gikf as stochastic particles with local interactions we analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched random riccati equation the switching being dictated by a nonstationary markov chain on the network graph

an application of a global inversion theorem to an existence and uniqueness theorem for a class of nonlinear systems of differential equations abstract in this paper a class of systems of nonlinear differential equations at resonance is considered with the use of a global inversion theorem which is an extended form of a non variational version of a max min principle we prove that this class of equations possesses a unique 2 periodic solution under a rather weaker condition for existence and uniqueness than those given in papers j chen w li periodic solution for 2 k th boundary value problem with resonance j math anal appl 314 2006 661 671 f cong periodic solutions for 2 k th order ordinary differential equations with nonresonance nonlinear anal 32 1998 787 793 f cong periodic solutions for second order differential equations appl math lett 18 2005 957 961 w li periodic solutions for 2 k th order ordinary differential equations with resonance j math anal appl 259 2001 157 167 w li h li a min max theorem and its applications to nonconservative systems int j math math sci 17 2003 1101 1110 w li z shen a constructive proof of existence and uniqueness of 2 periodic solution to duffing equation nonlinear anal 42 2000 1209 1220 this result extends the results known so far

an understanding of human dynamics in urban subway traffic from the maximum entropy principle abstract we studied the distribution of entry time interval in beijing subway traffic by analyzing the smart card transaction data and then deduced the probability distribution function of entry time interval based on the maximum entropy principle both theoretical derivation and data statistics indicated that the entry time interval obeys power law distribution with an exponential cutoff in addition we pointed out the constraint conditions for the distribution form and discussed how the constraints affect the distribution function it is speculated that for bursts and heavy tails in human dynamics when the fitted power exponent is less than 1 0 it cannot be a pure power law distribution but with an exponential cutoff which may be ignored in the previous studies

stability of a random riccati equation with markovian binary switching this paper is concerned with the boundedness of the solution of a random riccati difference equation arising from kalman filtering with observation losses characterized by a markovian binary jump parameter a new sufficient condition for stability in the peak covariance sense is obtained which has a simpler form and is shown to be less conservative for systems with the observability index of two than existing works meanwhile we give some conditions under which the covariance matrix is bounded or unbounded in the usual sense then the equivalence between the peak covariance stability and the usual covariance stability is established for systems with the observability index of one and independent and identically distributed i i d observation losses