Efficient Estimation of Copula-based Semiparametric Markov Models

This paper considers efficient estimation of copula-based semiparametric strictly stationary Markov models. These models are characterized by nonparametric invariant (one-dimensional marginal) distributions and parametric bivariate copula functions; where the copulas capture temporal dependence and tail dependence of the processes. The Markov processes generated via tail dependent copulas may look highly persistent and are useful for financial and economic applications. We first show that Markov processes generated via Clayton, Gumbel and Student's $t$ copulas and their survival copulas are all geometrically ergodic. We then propose a sieve maximum likelihood estimation (MLE) for the copula parameter, the invariant distribution and the conditional quantiles. We show that the sieve MLEs of any smooth functionals are root-$n$ consistent, asymptotically normal and efficient; and that their sieve likelihood ratio statistics are asymptotically chi-square distributed. We present Monte Carlo studies to compare the finite sample performance of the sieve MLE, the two-step estimator of Chen and Fan (2006), the correctly specified parametric MLE and the incorrectly specified parametric MLE. The simulation results indicate that our sieve MLEs perform very well; having much smaller biases and smaller variances than the two-step estimator for Markov models generated via Clayton, Gumbel and other tail dependent copulas.Copula, Tail dependence, Nonlinear Markov models, Geometric ergodicity, Sieve MLE, Semiparametric efficiency, Sieve likelihood ratio statistics, Value-at-Risk

Controllable terahertz radiation from a linear-dipole-array formed by a two-color laser filament in air

We have demonstrated the effective control on carrier-envelope phase, angular distribution as well as peak intensity of a nearly single-cycle terahertz pulse emitted from a laser filament formed by two-color, the fundamental and the corresponding second harmonics, femtosecond laser pulses propagating in air. Experimentally, such control has been performed by varying the filament length and the initial phase difference between the two-color laser components. A linear-dipole-array model, including the descriptions of the both generation (via laser field ionization) and propagation of the emitted terahertz pulse, is proposed to present a quantitative interpretation of the observations. Our results contribute to the understanding of terahertz generation in a femtosecond laser filament and suggest a practical way to control the electric field of terahertz pulse for potential applications

Analysis on relationship between extreme pathways and correlated reaction sets

Background: Constraint-based modeling of reconstructed genome-scale metabolic networks has been successfully applied on several microorganisms. In constraint-based modeling, in order to characterize all allowable phenotypes, network-based pathways, such as extreme pathways and elementary flux modes, are defined. However, as the scale of metabolic network rises, the number of extreme pathways and elementary flux modes increases exponentially. Uniform random sampling solves this problem to some extent to study the contents of the available phenotypes. After uniform random sampling, correlated reaction sets can be identified by the dependencies between reactions derived from sample phenotypes. In this paper, we study the relationship between extreme pathways and correlated reaction sets.Results: Correlated reaction sets are identified for E. coli core, red blood cell and Saccharomyces cerevisiae metabolic networks respectively. All extreme pathways are enumerated for the former two metabolic networks. As for Saccharomyces cerevisiae metabolic network, because of the large scale, we get a set of extreme pathways by sampling the whole extreme pathway space. In most cases, an extreme pathway covers a correlated reaction set in an \u27all or none\u27 manner, which means either all reactions in a correlated reaction set or none is used by some extreme pathway. In rare cases, besides the \u27all or none\u27 manner, a correlated reaction set may be fully covered by combination of a few extreme pathways with related function, which may bring redundancy and flexibility to improve the survivability of a cell. In a word, extreme pathways show strong complementary relationship on usage of reactions in the same correlated reaction set.Conclusion: Both extreme pathways and correlated reaction sets are derived from the topology information of metabolic networks. The strong relationship between correlated reaction sets and extreme pathways suggests a possible mechanism: as a controllable unit, an extreme pathway is regulated by its corresponding correlated reaction sets, and a correlated reaction set is further regulated by the organism\u27s regulatory network.<br /