differential algebraic systems as differential equations on manifolds based on the theory of differential equations on manifolds existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications both the autonomous and nonautonomous case are considered moreover a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on certain lower dimensional manifolds this class includes systems for which the application of ode solvers is known to lead to difficulties finally some solution approach based on continuation techniques is outlined

likelihood ratio based confidence intervals in survival analysis abstract confidence intervals for the survival function and the cumulative hazard function are considered these confidence intervals are based on an inversion of the likelihood ratio statistic to do this two extensions of the likelihood each of which yields meaningful likelihood ratio hypothesis tests and subsequent confidence intervals are considered the choice of the best extension is difficult in the failure time setting the binomial extension is best in constructing confidence intervals concerning the survival function and the poisson extension is best in constructing confidence intervals concerning the cumulative hazard simulations indicate that these two methods perform as well as or better than competitors based on the asymptotic normality of the estimator

projecting low dimensional chaos from spatiotemporal dynamics in a model for plastic instability we investigate the possibility of projecting low dimensional chaos from spatiotemporal dynamics of a model for a kind of plastic instability observed under constant strain rate deformation conditions we first discuss the relationship between the spatiotemporal patterns of the model reflected in the nature of dislocation bands and the nature of stress serrations we show that at low applied strain rates there is a one to one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops we then show that the model equations are spatiotemporally chaotic by demonstrating the number of positive lyapunov exponents and lyapunov dimension scale with the system size at low and high strain rates using a modified algorithm for calculating correlation dimension density we show that the stress strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos this is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities which is known to be low dimensionally chaotic however the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands

minimizing separable convex functions subject to simple chain constraints minimizing a separable convex objective subject to an ordering restriction on its variables is a generalization of a class of problems in statistical estimation and inventory control it is shown that a pool adjacent violators pav algorithm can be used to compute an optimal solution of this problem as well as the minimal and maximal extended solutions which provide lower and upper bounds on all optimal solutions and solve certain subproblems these results unify and extend several previously known results in addition it is shown that a pav algorithm can be applied to solving the problem with integer constraints on the variables

inconsistency of the maximum likelihood estimator of a distribution having increasing failure rate average abstract marshall and proschan showed that the mle for a life distribution with increasing failure rate is strongly consistent ann math statist 1965 36 69 77 in this note the author shows that the mle for a life distribution with increasing failure rate average is not consistent in fact maximum likelihood estimation in the ifra case yields estimators of the average failure rate and of the distribution function which in general coverage a s to values other than the true values in the decreasing failure rate average case the mle fails to exist

nonparametric maximum likelihood estimation of survival functions with a general stochastic ordering and its dual summary this paper discusses estimation of survival functions under an arbitrary partial stochas tic ordering of the underlying populations this technique is especially useful when data are not easily acquired from one or more of the populations but data from the other populations are available estimation of the ordered survival functions entails use of a fenchel duality theorem that results in an algorithm to identify and resolve violations of the underlying ordering the algorithm produces estimates which converge to the maximum likelihood estimates of the survival functions given the underlying ordering the method is illustrated by an example in life testing of components and in clinical trials estimation of a survival function p t is often of prime interest if the functional form of the survival function is unknown nonparametric methods such as the product limit estimator kaplan meier 1958 are needed johansen 1978 showed that the product limit estimator is a maximum likelihood estimator in the class of all distributions under a generalized maximum likelihood framework kiefer wolfowitz 1956 since the generalized maximum likelihood esti mates for continuous survival functions place probability only on those time points at which observations occur suppose however that one desires to estimate a number of survival functions when a partial stochastic ordering exists among them and under censoring for example in a clinical trial of two treatments for a rare debilitating disease let pi p2 and p3 be the survival functions respectively for the disease free group and for the disease groups under the two treatments the well documented survival function p1 can be used to generate better estimates for p2 and p3 by using the order restrictions pi t p2 t and pi t p3 t brunk et al 1966 developed the maximum likelihood estimators for two stochastically ordered distributions for uncensored independent random samples dykstra

large sample behaviour of the product limit estimator on the whole line weak convergence results are proved for the product limit estimator on the whole line applications are given to confidence band construction estimation of mean lifetime and to the theory of q functions the results are obtained using stochastic calculus and in probability linear bounds for empirical processes

maximum likelihood estimation of the survival functions of stochastically ordered random variables abstract many times aspects of populations exist that must satisfy a stochastic ordering requirement nevertheless estimates may not bear out this stochastic ordering because of the inherent variability of the observations this article will consider the problem of finding maximum likelihood estimates of stochastically ordered survival functions for the cases a one survival function being fixed in advance and b estimating two survival functions when the data include censored observations a numerical example is discussed in detail to illustrate the solution to this problem

spatial recurrence plots we propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time we introduce spatial recurrence plots srps as a graphical representation of the pointwise correlation matrix in terms of a two dimensional spatial return plot this technique is applied to the study of complex patterns generated by coupled map lattices which are characterized by measures of complexity based on srps we show that the complexity measures we propose for srps provide a systematic way of investigating the distribution of spatially coherent structures such as synchronization domains in lattice profiles this approach has potential for many more applications e g in surface roughness analyzes

stochastic reduction of loss in estimating normal means by isotonic regression cf barlow bartholomew bremner and brunk 1972 page 19 the estimator fi has been compared to the unrestricted estimator y and several results point to the superiority of the isotonic regression estimator when the order restriction holds it has been shown cf robertson wright and dykstra 1988 that the total error of the estimator is reduced through isotonic regression on any order restriction in the sense that

spatiotemporal nonlinearity in resting state fmri of the human brain in this work the spatiotemporal nonlinearity in resting state fmri data of the human brain was detected by nonlinear dynamics methods nine human subjects during resting state were imaged using single shot gradient echo planar imaging on a 1 5t scanner eigenvalue spectra for the covariance matrix correlation dimensions and spatiotemporal lyapunov exponents were calculated to detect the spatiotemporal nonlinearity in resting state fmri data by simulating adjusting and comparing the eigenvalue spectra of pure correlated noise with the corresponding real fmri data the intrinsic dimensionality was estimated the intrinsic dimensionality was used to extract the first few principal components from the real fmri data using principal component analysis which will preserve the correct phase dynamics while reducing both computational load and noise level of the data then the phase space was reconstructed using the time delay embedding method for their principal components and the correlation dimension was estimated by the grassberger procaccia algorithm of multiple variable series the spatiotemporal lyapunov exponents were calculated by using the method based on coupled map lattices through nonlinearity testing there are significant differences of correlation dimensions and spatiotemporal lyapunov exponents between fmri data and their surrogate data the fractal dimension and the positive spatiotemporal lyapunov exponents characterize the spatiotemporal nonlinear dynamics property of resting state fmri data therefore the results suggest that fluctuations presented in resting state may be an inherent model of basal neural activation of human brain cannot be fully attributed to noise

pointwise nonparametric maximum likelihood estimator of stochastically ordered survivor functions in this paper we consider estimation of survivor functions from groups of observations with right censored data when the groups are subject to a stochastic ordering constraint many methods and algorithms have been proposed to estimate distribution functions under such restrictions but none have completely satisfactory properties when the observations are censored we propose a pointwise constrained nonparametric maximum likelihood estimator which is defined at each time t by the estimates of the survivor functions subject to constraints applied at time t only we also propose an efficient method to obtain the estimator the estimator of each constrained survivor function is shown to be nonincreasing in t and its consistency and asymptotic distribution are established a simulation study suggests better small and large sample properties than for alternative estimators an example using prostate cancer data illustrates the method

nonstandard singular perturbation systems and higher index differential algebraic systems in order to obtain trajectory approximation results for a given singular perturbation system sps two systems are derived from it the slow and the fast one tikhonov s theorem gives sufficient conditions on them to ensure a good approximation for a standard sps i e its corresponding slow system is a differential algebraic system das of index 1 in this paper it is shown that a nonstandard sps with the parameter set to zero can be seen as a das of higher index this connection allows us to obtain a tikhonov s theorem when this das is of index 2

estimation of large scale dimension densities we propose a technique to calculate large scale dimension densities in both higher dimensional spatio temporal systems and low dimensional systems from only a few data points where known methods usually have an unsatisfactory scaling behavior this is mainly due to boundary and finite size effects with our rather simple method we normalize boundary effects and get a significant correction of the dimension estimate this straightforward approach is based on rather general assumptions so even weak coherent structures obtained from small spatial couplings can be detected with this method which is impossible by using the lyapunov dimension density we demonstrate the efficiency of our technique for coupled logistic maps coupled tent maps the lorenz attractor and the roessler attractor

on the connection between nonlinear differential algebraic equations and singularly perturbed control systems in nonstandard form considers a class of control systems represented by nonlinear differential equations depending on a small parameter the systems are not in the standard singularly perturbed form and therefore one of the challenges is to show that the control systems do represent singularly perturbed two time scale systems assumptions are introduced which guarantee that an equivalent representation for the systems can be obtained in the standard singularly perturbed form thereby justifying the two time scale property the equations for the slow dynamics are characterized by a set of differential algebraic equations which have been studied previosly in the literature the fast dynamics are characterized by differential equations both the slow and the fast dynamics are easily derived and are defined in terms of variables that define the original control system control design for the class of systems being considered is studied using the composite control approach

on the exponential stability of singularly perturbed systems this paper establishes some results and properties related to the exponential stability of general dynamical systems and in particular singularly perturbed systems for singularly perturbed systems it is shown that if both the reduced order system and the boundary layer system are exponentially stable then provided that some further regularity conditions are satisfied the full order system is exponentially stable for sufficiently small values of the perturbation parameter mu and its rate of convergence approaches that of the reduced order system mu 0 as mu approaches zero exponentially decaying norm bounds are given for the slow and fast components of the full order system trajectories to achieve this result a new converse lyapunov result for exponentially stable systems is presented

nonparametric estimation of a distribution subject to a stochastic precedence constraint for any two random variables x and y with distributions f and g defined on 0 x is said to stochastically precede y if p x y 1 2 for independent x and y stochastic precedence denoted by x spy is equivalent to e g x 1 2 the applicability of stochastic precedence in various statistical contexts including reliability modeling tests for distributional equality versus various alternatives and the relative performance of comparable tolerance bounds is discussed the problem of estimating the underlying distribution s of experimental data under the assumption that they obey a stochastic precedence sp constraint is treated in detail two estimation approaches one based on data shrinkage and the other involving data translation are used to construct estimators that conform to the sp constraint and each is shown to lead to a root n consistent estimator of the underlying distribution the asymptotic behavior of each of the estimators is fully characterized conditions are given under which

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

non standard singularly perturbed control systems and differential algebraic equations we consider a class of linear control systems represented by equations depending on a small parameter but which are not in the standard singularly perturbed form one of the challenging system theoretic problem is to obtain an equivalent representation for the control system which if possible is in the standard singularly perturbed form assumptions are introduced which guarantee that an equivalent representation can be obtained which is in the standard singularly perturbed form thereby justifying the two time scale property the equations for the slow dynamics are characterized by a set of differential algebraic equations which are easily derived from the original equations by setting the parameter to zero the original assumptions guarantee the existence of solutions of the obtained differential algebraic equations the fast dynamics are characterized by different equations in terms of matrices that define the original control system control design for the system being considered is studied using th

confidence interval estimation subject to order restrictions this article deals with the construction of confidence intervals when the components of the location parameter mu of the random variable mathbf x which is elliptically symmetrically distributed are subject to order restrictions several domination results are proved by studying the derivative of the coverage probability of the confidence intervals centered at the improved point estimators consequently we strengthen the previously known results regarding the simple ordering and obtain several new results for other general forms of order restrictions including the simple tree ordering the umbrella ordering the simple and the double loop ordering and some combination of these these domination results are obtained under the assumption that sigma is a diagonal matrix when sigma is nondiagonal some new intervals are introduced which dominate the standard intervals centered at the unrestricted maximum likelihood estimator for various types of order restrictions similar results are obtained for scale parameters as well contrary to the location problems in case of the scale parameters satisfying the simple ordering we find that the restricted maximum likelihood estimator of the largest parameter fails to universally dominate the unrestricted maximum likelihood estimator a similar negative result is noted for simple tree order restriction

statistical inference for uniform stochastic ordering in several populations tion for k population problems under uniform stochastic ordering restrictions we derive closed form estimates even with right censored data by a reparameterization which reduces the problem to a well known isotonic regression problem we also derive the asymptotic distribution of the likelihood ratio statistic for testing equality of the k populations against the uniform stochastic ordering restriction this asymptotic distribution is of the chi bar square type as discussed by robertson wright and dykstra these distributional results are obtained by appealing to elegant results from empirical process theory and showing that the proposed test is asymptotically distribution free recurrence formulas are derived for the weights of the chi bar square distribution for particular cases the theory developed in this paper is illustrated by an example involving data for survival times for carcinoma of the oropharynx

inferences under a stochastic ordering constraint the k sample case if x1 and x2 are random variables with distribution functions f1 and f2 then x1 is said to be stochastically larger than x2 if f1 f2 statistical inferences under stochastic ordering for the two sample case has a long and rich history in this article we consider the k sample case that is we have k populations with distribution functions f1 f2 fk k 2 and we assume that f1 f2 fk for k 2 the nonparametric maximum likelihood estimators of f1 and f2 under this order restriction have been known for a long time their asymptotic distributions have been derived only recently these results have very complicated forms and are hard to deal with when making statistical inferences we provide simple estimators when k 2 these are strongly uniformly consistent and their asymptotic distributions have simple forms if and are the empirical and our restricted estimators of fi then we show that asymptotically for all x and all u 0 with strict inequality in some cases this clearly show

lorenz like systems and classical dynamical equations with memory forcing an alternate point of view for singling out the origin of chaos an alternate view for the emergence of chaos in lorenz like systems is presented in this paper for such purpose the lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one dimensional motion of a particle in a two well potential with a forcing term depending on the memory of the particle past motion the dynamics of the original lorenz system in the proposed particle phase space can then be rewritten in terms of a one dimensional first exit time problem the emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall the whole problem is tackled analytically deriving a piecewise linearized lorenz like system that preserves all the essential properties of the original model