model structure simplification of nonlinear systems via immersion this paper concerns the simplification of model structures of nonlinear systems while preserving their input output maps the basic technique is an immersion of a system which is a mapping of the initial state from the original system to another system of an identical input output map the necessary and sufficient conditions are presented for the immersibility of a given system into a state space representation of such particular structures as rational functions or polynomials with respect to the state the conditions are so mild that many types of nonlinear systems can be represented by rational or polynomial model structures moreover it is also shown that a polynomial state space representation can always be constructed to be at most quadratic with respect to the state

superposition rules for nonlinear coupled first order differential equations pairs of coupled nonlinear differential equations of the polynomial type have been studied no higher powers than quadratic were considered lie s theorem provides a superposition rule exists if certain operators generate a finite dimensional lie algebra the lie algebras possible were divided into twenty categories for each case the general form of the coupled differential equations is obtained the coupled differential equations are then separated where possible solutions are obtained expressed in terms of a finite number of particular solutions

the perturbed galerkin method for cauchy singular integral equations with constant coefficients we have considered the numerical solution of cauchy singular integral equations with constant coefficients via a polynomial based galerkin method l 2 and uniform convergence results are proved under holder continuity conditions on the kernel and right hand side and taking into account the quadrature errors produced when inner products are replaced by numerical quadratures these results generalize those of miel who considered only the case of equations of the first kind with index 0

on the numerical resolution of the generalized airfoil equation with possio kernel in this paper we consider the so called generalized airfoil singular integral equation with a smooth input function and present ad hoc quadrature rules to compute efficiently the elements of collocation and galerkin matrices

diverging moments and parameter estimation heavy tailed distributions are enjoying increased popularity and are becoming more readily applicable as the arsenal of analytical and numerical tools grows they play key roles in modeling approaches in networking finance and hydrology to name but a few areas the tail parameter is of central importance because it governs both the existence of moments of positive order and the thickness of the tails of the distribution some of the best known tail estimators such as those of koutrouvelis and hill are either parametric or show a lack of robustness or accuracy this article develops a shift and scale invariant nonparametric estimator for both upper and lower bounds for orders with finite moments the estimator builds on the equivalence between tail behavior and the regularity of the characteristic function at the origin and achieves its goal by deriving a simplified wavelet analysis that is particularly suited to characteristic functions

on determining the radar threshold for non gaussian processes from experimental data the problem of detecting radar signals embedded in clutter is an area of great interest in many radar applications it is important to set thresholds to achieve a false alarm probability p sub f of 10 sup 5 or lower using conventional monte carlo techniques where thresholds are set based on raw percentiles an extremely large number of samples is required we use the generalized pareto distribution to approximate the extreme tail of the distributions and propose the ordered sample least squares osls method for estimating its parameters

universal formats for nonlinear ordinary differential systems it is shown that very general nonlinear ordinary differential systems embracing all that arise in practice may first be brought down to polynomial systems where the nonlinearities occur only as polynomials in the dependent variables by introducing suitable new variables into the original system second that polynomial systems are reducible to riccati systems where the nonlinearities are quadratic at most third that riccati systems may be brought to elemental universal formats containing purely quadratic terms with simple arrays of coefficients that are all zero or unity the elemental systems have representations as novel types of matrix riccati equations different starting systems and their associated riccati systems differ from one another at the final elemental level in order and in initial data but not in format

brief paper diagonal stability of a class of cyclic systems and its connection with the secant criterion we consider a class of systems with a cyclic interconnection structure that arises among other examples in dynamic models for certain biochemical reactions we first show that a secant criterion for local stability derived earlier in the literature is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices we then revisit a recent generalization of this criterion to output strictly passive systems and recover the same stability condition using our diagonal stability result as a tool for constructing a lyapunov function using this procedure for lyapunov construction we exhibit classes of cyclic systems with sector nonlinearities and characterize their global stability properties

value at risk estimation with wavelet based extreme value theory evidence from emerging markets abstract this paper introduces wavelet based extreme value theory evt for univariate value at risk estimation wavelets and evt are combined for volatility forecasting to estimate a hybrid model in the first stage wavelets are used as a threshold in generalized pareto distribution and in the second stage evt is applied with a wavelet based threshold this new model is applied to two major emerging stock markets the istanbul stock exchange ise and the budapest stock exchange bux the relative performance of wavelet based evt is benchmarked against the riskmetrics ewma arma garch generalized pareto distribution and conditional generalized pareto distribution models the empirical results show that the wavelet based extreme value theory increases predictive performance of financial forecasting according to number of violations and tail loss tests the superior forecasting performance of the wavelet based evt model is also consistent with basel ii requirements and this new model can be used by financial institutions as well

new error estimates for galerkin method to an airfoil equation in this paper we consider new error estimates under the weighted chebyshev norm for galerkin method to an airfoil equation galerkin discretisation is discussed the smoothness conditions of the input functions are improved i e they need to be holder continuous with 12 m 1

attracting subspaces in a hyper spherical representation of autonomous dynamical systems in this work we focus on the possibility to recast the ordinary differential equations odes governing the evolution of deterministic autonomous dynamical systems conservative or damped and generally non linear into a parameter free universal format we term such a representation hyper spherical since the new variables are a radial norm having physical units of inverse of time and a normalized state vector with possibly complex valued dimensionless components here we prove that while the system evolves in its physical space the mirrored evolution in the hyper spherical space is such that the state vector moves monotonically towards fixed attracting subspaces one at a time correspondingly the physical space can be split into attractiveness regions we present the general concepts and provide an example of how such a transformation of odes can be achieved for a class of mechanical like systems where the physical variables are a set of configurational degrees of freedom and the associated velocities in a phase space representation a one dimensional case model motion in a bi stable potential is adopted to illustrate the procedure in this work we focus on the possibility to recast the ordinary differential equations odes governing the evolution of deterministic autonomous dynamical systems conservative or damped and generally non linear into a parameter free universal format we term such a representation hyper spherical since the new variables are a radial norm having physical units of inverse of time and a normalized state vector with possibly complex valued dimensionless components here we prove that while the system evolves in its physical space the mirrored evolution in the hyper spherical space is such that the state vector moves monotonically towards fixed attracting subspaces one at a time correspondingly the physical space can be split into attractiveness regions we present the general concepts and provide an example of how such a transformation of odes can be achieved for a class of mechanical like systems where the physical variables are a set of configurational degrees of freedom and the associat

limit theory for the sample covariance and correlation functions of moving averages abstract document describes a moving average process which have regularly varying tail probabilities with index alpha 0 the limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite variance but an infinite fourth moment furthermore in the infinite variance case 0 alpha 2 the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices alpha and alpha 2 respectively this result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process author

the confounding effects of distribution mixtures on some basic methods for handling stable paretian distributions abstract the belief that the distributions of many business and economic variables are stable paretian sp generated a large literature on sp financial modelling in contrast some recent studies appear to have shown that the major financial variables thought to be sp are not sp however practically all these earlier studies assume that the variable under consideration has a single or pure sp distribution whereas many business economic variables come from distribution mixtures this paper investigates the applicability of some basic sp methods to mixtures of sp distributions our results show that current sp parameter estimation procedures and sp hypothesis tests are all very unreliable for sp mixtures our results imply that i earlier findings on testing the sp hypothesis for various business economic variables are unreliable and whether major financial variables are sp remains an important unanswered question ii new methods need to be developed to handle sp mixtures

predictive likelihood inference with applications summary conditional and marginal predictive likelihood are defined and used in predicting un observed or missing data a distinction is made between predictive and estimative goals of a data analysis such methodology and distinctions are illustrated in the context of outlier theory and mixed model ano va the prediction of unobserved or missing data is considered from a likelihood perspective a general predictive likelihood is proposed for such purposes and contrasted with parametric likelihood the resulting maximum likelihood predictor is also compared with the limiting imputation from the em algorithm the new methodology is illustrated and contrasted with estimative likelihood analysis in the context of outlier theory and mixed model ano va predictions are proposed that are based on conditional and marginal predictive likelihoods for the unobserved data which are predictive adaptations of the methods developed by kalbfleisch and sprott 1970 1973 these authors were concerned with the elimination of nuisance parameters in order to make inference about another set of structural parameters prediction in the frame work of parametric distributions involves the elimination of all parameters in such a way that inference about the unobserved data is possible therefore in the predictive setting all para meters are nuisance parameters and the unobserved data now play a role similar to that of the structural parameters various predictive approaches to statistical inference have been advocated principally by geisser 1971 1975 stone 1974 aitchison and dunsmore 1975 and guttman 1970 a survey is provided by geisser 1980 and a brief overview in a parametric setting is presented in the next section following this a conditional likelihood approach is developed and shown to be closely related to the lauritzen 1974 hinkley 1979 likelihood method but specified in a manner allowing for a wider range of applicability a marginal predictive likelihood procedure is also specified which when applicable essentially agrees with the conditional likelihood procedure for the examples considered for a general account of likelihood based inference see fraser

nonlinear model order reduction via lifting transformations and proper orthogonal decomposition this paper presents a structure exploiting nonlinear model reduction method for systems with general nonlinearities first the nonlinear model is lifted to a model with more structure via variable

a coupled electromechanical analysis of a piezoelectric layer bonded to an elastic substrate part ii numerical solution and applications this two part contribution presents a novel and efficient method to analyze the two dimensional 2 d electromechanical fields of a piezoelectric layer bonded to an elastic substrate which takes into account the fully coupled electric and mechanical behaviors in part i we have obtained a system of governing integro differential equations for the structure via a variational principle this part presents a numerical solution algorithm of the integro differential equations and the numerical results of some applications a numerical algorithm for solving the system of four integro differential equations with strongly singular kernels is developed the convergence of the numerical algorithm is discussed the numerical results suggest that the fully coupled electromechanical analysis is helpful for a better understanding of the performance of the piezoelectric sensor and actuator the interfacial normal stress is much higher than the interfacial shear stress suggesting that the interfacial normal stress causes a delamination initiation

on the weighted galerkin method of numerical solution of cauchy type singular integral equations the well known weighted galerkin method for the direct numerical solution of cauchy type singular integral equations of the first and the second kind based on the approximation of the unknown function by a finite series of appropriate orthogonal polynomials is shown to be identical to the corresponding method based on the reduction of the cauchy type singular integral equation to an equivalent fredholm integral equation of the second kind and the application to the latter of the weighted galerkin method this result permits the direct transfer of the whole set of convergence and rate of convergence results for the weighted galerkin method of numerical solution of fredholm integral equations with regular kernels to the case of cauchy type singular integral equations an application to the case where chebyshev polynomials are used is also made and the available convergence results for the direct weighted galerkin method are rederived with essentially no analysis

on stability and trajectory boundedness of lotka volterra systems with polytopic uncertainty a new approach is proposed to study the stability property of the feasible equilibrium point and the trajectory boundedness of the lotka volterra lv dynamics in the presence of polytopic uncertainties stability analysis of general lv systems is not straightforward in comparison with its cooperative counterpart it is shown that under specific conditions the trajectory of the cooperative counterpart of the lv system can be considered as an upper bound for the trajectory of the corresponding dynamics consequently the stability of the cooperative counterpart of the lv system leads to boundedness of the trajectory the obtained results are extended for the lv systems with polytopic uncertainties it is shown that under specific conditions there is a region which the trajectory of the system belongs to it as time tends to infinity also the stability of lv systems with polytopic uncertainty is investigated the obtained results are confirmed through some numerical application based examples

on bayesian modeling of fat tails and skewness abstract we consider a bayesian analysis of linear regression models that can account for skewed error distributions with fat tails the latter two features are often observed characteristics of empirical datasets and we formally incorporate them in the inferential process a general procedure for introducing skewness into symmetric distributions is first proposed even though this allows for a great deal of flexibility in distributional shape tail behavior is not affected applying this skewness procedure to a student t distribution we generate a skewed student distribution which displays both flexible tails and possible skewness each entirely controlled by a separate scalar parameter the linear regression model with a skewed student error term is the main focus of the article we first characterize existence of the posterior distribution and its moments using standard improper priors and allowing for inference on skewness and tail parameters for posterior inference with this model we suggest

a parametric solution for simple stress strength model of failure with an application abstract estimation of p r s is considered for the simple stress strength model of failure using the pareto and power distributions together with their combined form a useful parametric solution is obtained and is illustrated numerically it is shown that these models are also applicable when only the tails of distributions for r and s are considered an application to the failure study concerning the fractures is also included

the galerkin method for singular integral equations revisited abstract in an earlier work the author has obtained error bounds for the galerkin method for solving cauchy singular integral equations discovering that the usually neglected constants contain the riemann zeta function when evaluated in the supremum norm the aim of this investigation is twofold to show that the occurrence of the riemann zeta function in the error bound for the chebyshev norm is sharp and secondly to use this result to obtain a class of forcing functions for which the method does not yield an approximate solution differing from the analytical one by at most a prescribed error tolerance these counterexamples indicate that in practical situations for functions exhibiting a behavior similar to the one presented here galerkin s method might not lead to an acceptable solution

estimating the stable index alpha in order to measure tail thickness a critique stable laws are often fit to outlier prone data and if the index alpha is estimated to be much less than two then the normal law is rejected in favor of an infinite variance stable law this paper derives the theoretical properties of such a procedure when the true distribution is stable the distribution of the m l e of alpha is non regular if alpha 2 when the true distribution is not stable the estimate of alpha is not a robust measure of the rate of decrease of the tail probabilities a more robust procedure is developed and a statistic for describing and comparing the tail shapes of arbitrary samples is proposed

adaptive threshold estimation via extreme value theory determining a detection threshold to automatically maintain a low false alarm rate is a challenging problem in a number of different applications the underlying parametric assumptions of most automatic target detection algorithms are invalid therefore thresholds derived using these incorrect distribution assumptions do not produce desirable results when applied to real sensor data monte carlo methods for threshold determination work well but tend to perform poorly when targets are present in order to mitigate these effects we propose an algorithm using extreme value theory through the use of the generalized pareto distribution gpd and a kolmogorov smirnov statistical test unlike previous work based on gpd estimates this algorithm incorporates a way to adaptively maintain low false alarm rates in the presence of targets both synthetic and real world detection results demonstrate the usefulness of this algorithm

scaling stability and distribution of the high frequency returns of the ibex35 index abstract in this paper we perform a statistical analysis of the high frequency returns of the ibex35 madrid stock exchange index we find that its probability distribution seems to be stable over different time scales a stylized fact observed in many different financial time series however an in depth analysis of the data using maximum likelihood estimation and different goodness of fit tests rejects the levy stable law as a plausible underlying probabilistic model the analysis shows that the normal inverse gaussian distribution provides an overall fit for the data better than any of the other subclasses of the family of generalized hyperbolic distributions and certainly much better than the levy stable laws furthermore the right resp left tail of the distribution seems to follow a power law with exponent 4 60 resp 4 28 finally we present evidence that the observed stability is due to temporal correlations or non stationarities of the data

detection of dependent heavy tailed signals this paper examines the problem of detection of dependent alpha stable signals measurements of several phenomena exhibit non gaussian heavy tailed behavior in their probability density functions p d f we use the class of alpha stable distributions to characterize these signals when two sensors make simultaneous measurements of such phenomena these heavy tailed realizations are dependent across sensors the intersensor dependence is modeled using copulas we consider a two sided test in the neyman pearson framework and present an asymptotic analysis of the generalized likelihood test glrt both nested and non nested models are considered in the analysis the performance of the proposed scheme is evaluated numerically on simulated data as well as indoor seismic data with appropriately selected models our results demonstrate that a high probability of detection can be achieved for false alarm probabilities of the order of 10 4

discrete projection methods for cauchy singular integral equations with constant coefficients we consider proving the mean square and uniform convergence of various discrete galerkin and collocation methods for cauchy singular integral equations with constant coefficients for galerkin s method the convergence rates improve those given in an earlier paper while for collocation methods the results appear to be new in particular we consider product quadrature methods for equations with discontinuous coefficients and develop and prove the convergence of a new algorithm for equations of the first kind with index zero and logarithmically singular kernels

further convergence results for the weighted galerkin method of numerical solution of cauchy type singular integral equations the convergence of the weighted lalerkin method based on chcbvshen or jacobi polvnoinials for the direct numerical solution of one dimensional real cauchv tvpe singular integral equations of the first and of the second kind on a finite interval is proved under sufficientlv weak continuitv assumptions for the kernels and the right side functions of thc integral equations

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

galerkin methods for singular integral equations the approximate solution of a singular integral equation by galerkin s method is studied we discuss the theoretical aspects of such problems and give error bounds for the approximate solution

a passivity based approach to stability of spatially distributed systems with a cyclic interconnection structure a class of distributed systems with a cyclic interconnection structure is considered these systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially heterogeneous patterns in this paper a class of cyclic systems in which addition of diffusion does not have a destabilizing effect is identified for these systems global stability results hold if the ldquosecantrdquo criterion is satisfied in the linear case it is shown that the secant condition is necessary and sufficient for the existence of a decoupled quadratic lyapunov function which extends a recent diagonal stability result to partial differential equations for reaction diffusion equations with nondecreasing coupling nonlinearities global asymptotic stability of the origin is established all of the derived results remain true for both linear and nonlinear positive diffusion terms similar results are shown for compartmental systems

algebraic recasting of nonlinear systems of odes into universal formats it is sometimes desirable to produce for a nonlinear system of odes a new representation of simpler structural form but it is well known that this goal may imply an increase in the dimension of the system this is what happens if in this new representation the vector field has a lower degree of nonlinearity or a smaller number of nonlinear contributions until now both issues have been treated separately rather unsystematically and in some cases at the expense of an excessive increase in the number of dimensions we unify here the treatment of both issues in a common algebraic framework this allows us to proceed algorithmically in terms of simple matrix operations

on the robustness of nonlinearity tests to moment condition failure abstract this paper investigates the consequences of testing nonlinearities in data that suffer from moment condition failure simulation experiments indicate that tests designed to have maximal power against misspecification of the conditional variance seem to be especially sensitive to the nonexistence of moments the relationship between findings of nonlinearity and moment condition failure is further investigated in a sample of daily stock returns the empirical study shows that evidence of nonlinearity in stock returns cannot all be attributed to the nonrobustness of nonlinearity tests to moment condition failure however it is shown that most tests of nonlinearity are not reliable in testing situations involving heavy tailed data

sinc nystrom method for numerical solution of one dimensional cauchy singular integral equation given on a smooth arc in the complex plane on developpe une methode numerique basee sur les fonctions sinc pour la solution approchee d une equation integrale singuliere de cauchy a une dimension sur un arc regulier du plan complexe

semi nonparametric var forecasts for hedge funds during the recent crisis abstract the need to provide accurate value at risk var forecasting measures has triggered an important literature in econophysics although these accurate var models and methodologies are particularly demanded for hedge fund managers there exist few articles specifically devoted to implement new techniques in hedge fund returns var forecasting this article advances in these issues by comparing the performance of risk measures based on parametric distributions the normal student s t and skewed t semi nonparametric snp methodologies based on gram charlier gc series and the extreme value theory evt approach our results show that normal student s t and skewed t based methodologies fail to forecast hedge fund var whilst snp and evt approaches accurately success on it we extend these results to the multivariate framework by providing an explicit formula for the gc copula and its density that encompasses the gaussian copula and accounts for non linear dependences we show that the var obtained by the meta gc accurately captures portfolio risk and outperforms regulatory var estimates obtained through the meta gaussian and student s t distributions

consistent order determination for processes with infinite variance summary order determination for autoregressive processes when the residuals have a distribution belonging to the domain of attraction of an infinite variance stable law is examined the use of the fpe criterion of bhansali and downham 1977 is shown to provide a consistent estimator of the order with any a 0 order determination for moving average processes is considered a procedure based on autoregressive estimates of the inverse correlations see bhansali 1983 is shown to provide a consistent estimator of the order consistency of the estimated autoregressive and moving average parameters of an arbitrary order is established the question of consistent discrimination between autoregressive and moving average models is also considered the finite sample behaviour of the discrimination procedure is investigated by means of a simulation study

forecasting the value at risk of chinese stock market using the harq model and extreme value theory abstract using intraday data of the csi300 index this paper discusses value at risk var forecasting of the chinese stock market from the perspective of high frequency volatility models first we measure the realized volatility rv with 5 minute high frequency returns of the csi300 index and then model it with the newly introduced heterogeneous autoregressive quarticity harq model which can handle the time varying coefficients of the har model second we forecast the out of sample var of the csi300 index by combining the harq model and extreme value theory evt finally using several popular backtesting methods we compare the var forecasting accuracy of harq model with other traditional har type models such as har har j char and shar the empirical results show that the novel harq model can beat other har type models in forecasting the var of the chinese stock market at various risk levels

galerkin s method for operator equations with nonnegative index with application to cauchy singular integral equations abstract we consider solving operator equation 1 hu ku f where h and k are bounded linear operators between two real hilbert spaces h1 and h2 operator h is assumed to have a finite dimensional nullspace n h and a bounded right inverse h1 h2 h1 and k is compact it follows that dim n h k dim n h so that to obtain uniqueness the m additional conditions 2 u k 1 bk k 1 2 h dim n h m are imposed where the k k 1m are an orthonormal basis for n h to solve 1 and 2 these equations are converted to an equivalent equation of the second kind to which galerkin s method is applied using the basis 1 2 m m 1 n it was shown that this method is equivalent to the method of weighted residuals when h 1 h the adjoint of h the results are applied to obtain convergence proofs of some numerical methods for solving several classes of cauchy singular integral equations whose kernels are only square integrable

galerkin solution of a singular integral equation with constant coefficients galerkin methods are used to approximate the singular integral equation email protected x email protected 1 email protected t email protected 1 1k t x f t dt f x 10 are constants in this case f is decomposed as f x 1 x a 1 x bu x where email protected 0 0 is a small enough constant

recurrent and feedforward polynomial modeling of coupled time series we present two methods for the prediction of coupled time series the first one is based on modeling the series by a dynamic system with a polynomial format this method can be formulated in terms of learning in a recurrent network for which we give a computationally effective algorithm the second method is a purely feedforward network procedure whose architecture derives from the recurrence relations for the derivatives of the trajectories of a ricatti format dynamic system it can also be used for the modeling of discrete series in terms of nonlinear mappings both methods have been tested successfully against chaotic series

estimating tails of probability distributions we study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold a key idea is the use of pickands generalised pareto distribution and its fitting in most cases by the method of maximum likelihood the results cover all three limiting types of extreme value theory we propose a new estimator for an index of regular variation and show that it often performs better than hill s estimator we give new results for estimating the endpoint of a distribution extending earlier work by hall and by smith and weissman finally we give detailed results for the domain of attraction of exp e x and show that in most cases our proposed estimator is more efficient than two others one based on the exponential distribution and the other due to davis and resnick we also touch briefly on the problem of large deviations from a statistical point of view the results make extensive use of existing work on rates of convergence

algebraic structures and invariant manifolds of differential systems algebraic tools are applied to find integrability properties of odes bilinear nonassociative algebras are associated to a large class of polynomial and nonpolynomial systems of differential equations since all equations in this class are related to a canonical quadratic differential system the lotka volterra system these algebras are classified up to dimension 3 and examples for dimension 4 and 5 are given their subalgebras are associated to nonlinear invariant manifolds in the phase space these manifolds are calculated explicitly more general algebraic invariant surfaces are also obtained by combining a theorem of walcher and the lotka volterra canonical form applications are given for lorenz model lotka may leonard and rikitake systems

stability analysis of quasi polynomial dynamical systems with applications to biological network models we study asymptotic stability properties of a class of quasi polynomial dynamical systems this class of nonlinear systems is a special class of interconnected systems arising in several biochemical and biological system applications and can be represented using quasi polynomial dynamical systems it is known that a special class of such systems can be embedded into a higher dimensional space and cast in lotka volterra canonical form we characterize a class of quasi polynomial dynamical systems with asymptotic stability properties for all initial conditions in the positive orthant the key advantage of the proposed method is that it is algebraic such that asymptotic stability conditions can be derived in terms of as they are usually in biological network models parameters of the system we apply our results to parameterized models of three different biological systems the generalized mass action gma model an oscillating biochemical network and a reduced order model of the glycolysis pathway and show that one can apply our proposed method to verify asymptotic stability for each case in terms of underlying parameters

geometrizing rates of convergence ii consider estimating a functional t f of an unknown distribution f in mathbf f from data x 1 cdots x n i i d f let omega varepsilon denote the modulus of continuity of the functional t over mathbf f computed with respect to hellinger distance for well behaved loss functions l t we show that inf t n sup mathbf f e fl t n t f is equivalent to l omega n 1 2 to within constants whenever t is linear and mathbf f is convex the same conclusion holds in three nonlinear cases estimating the rate of decay of a density estimating the mode and robust nonparametric regression we study the difficulty of testing between the composite infinite dimensional hypotheses h 0 t f leq t and h 1 t f geq t delta our results hold in the cases studied because the difficulty of the full infinite dimensional composite testing problem is comparable to the difficulty of the hardest simple two point testing subproblem

input output linearization of nonlinear systems using multivariable legendre polynomials this contribution presents a new approach for the numeric computation of the input output linearizing feedback law which is obtained exactly in an analytical form by using a state space embedding technique the nonlinear system to be controlled is described by a higher order system with solely polynomial nonlinearities consequently the nonlinearities of this system can be represented by multivariable legendre polynomials so that the derivation of the input output linearizing feedback controller can be accomplished using the operational matrices of multiplication and of differentiation for legendre polynomials

nonlinear action of lie groups and superposition principles for nonlinear differential equations abstract recently obtained results on superposition principles for systems of ordinary nonlinear equations are reviewed in particular the general solution of the matrix riccati equation is expressed in terms of five particular solutions the study of superposition laws is related to the problem of backlund transformations for nonlinear partial differential equations to the problem of transforming nonlinear equations into linear ones and to the classification of primitive filtered lie algebras