Exponential localization of singular vectors in spatiotemporal chaos

In a dynamical system the singular vector (SV) indicates which perturbation will exhibit maximal growth after a time interval $\tau$. We show that in systems with spatiotemporal chaos the SV exponentially localizes in space. Under a suitable transformation, the SV can be described in terms of the Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us to deduce a universal power law $\tau^{-\gamma}$ for the localization of the SV. Moreover the same exponent $\gamma$ characterizes the finite-$\tau$ deviation of the Lyapunov exponent in excellent agreement with simulations. Our results may help improving existing forecasting techniques.Comment: 5 page

Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator

Kim and Pollard (Annals of Statistics, 18 (1990) 191?219) showed that a general class of M-estimators converge at rate n1/3 rather than at the standard rate n1/2. Many times, this situation arises when the objective function is non-smooth. The limiting distribution is the (almost surely unique) random vector that maximizes a certain Gaussian process and is difficult to analyze analytically. In this paper, we propose the use of the subsampling method for inferential purposes. The general method is then applied to Manski?s maximum score estimator and its small sample performance is highlighted via a simulation study.Publicad

Logarithmic bred vectors in spatiotemporal chaos: structure and growth

Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth- rates of logarithmic bred vectors (which are constructed by using a given norm). We find that, after a suitable transformation, logarithmic bred vectors are roughly piecewise copies of the leading Lyapunov vector. This fact allows us to deduce a scaling law for the bred vector growth rate as a function of their amplitude. In addition, we relate growth rates with the spectrum of Lyapunov exponents corresponding to the most expanding directions. We illustrate our results with simulations of the Lorenz '96 model.Comment: 8 pages, 8 figure

Using weibull mixture distributions to model heterogeneous survival data

In this article we use Bayesian methods to fit a Weibull mixture model with an unknown number of components to possibly right censored survival data. This is done using the recently developed, birth-death MCMC algorithm. We also show how to estimate the survivor function and the expected hazard rate from the MCMA output

Optimal Operation of Pipeline Transportation Systems

11th Triennial World Congress. Tallinn. Estonia. USSR. 1990This paper presents a simulator of an oil pipeline for scheduling purposes. The simulator includes an algorithm for optimizing the energy operating costs. The optimization algorithm works in two steps. The first one consists of the computation of a function that measures the estimated mininltun cost to the goal node. This computation involves the use of Bellman's optimality principle and of some heuristic rules in order to avoid the combinatorial explosion. During the second step the optinltmum trajectory is obtained with the help of the function mentioned above and using an accurate simulation of the transportation system. The simulation considers those aspects which are relevant t.o the optimization problem and takes into account the following factors: topology and topography of the network. non-linear characteristics of pumps and pipelines, variable demands of consumers, time changing prices of electrical energy and hydraulic equations throughout the system. The simulator is being used by CAMPSA (the major oil distribution company in Spain) Some results obtained with an oil pipeline system in Northern Spain are presented in the paper