A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter

By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations

The Liquefaction Sand Boils in the San Francisco Marina District During the 1989 Loma Prieta Earthquake

The paper presents and analyzes the observations of the sand boils that emerged in the Marina District after the Loma Prieta Earthquake of October 17, 1989. The sand boils left behind by liquefaction revealed an old lagoon, the periphery of which had experienced severe damage in the 1906 San Francisco earthquake. The buildings in the Marina District were damaged primarily as the liquefied ground spread laterally along the shoreline of the 1906 lagoon that was filled to host the 1915 Panama-Pacific International Exposition in San Francisco. The present work infers that the sand boils are not random phenomena but instrumental sensors to understand the ground failure induced by liquefaction

In-flight measurements of energetic radiation from lightning and thunderclouds

In the certification procedure aircraft builders carry out so-called icing tests flights, where the zero degree Celsius altitude is deliberately sought and crossed in or under thunderstorms. Airbus also used these flights to test ILDAS, a system aimed to determine lightning severity and attachment points during flight from high speed data on the electric and magnetic field at the aircraft surface. We used this unique opportunity to enhance the ILDAS systems with two x-ray detectors coupled to high speed data recorders in an attempt to determine the x-rays produced by lightning in-situ, with synchronous determination of the lightning current distribution and electric field at the aircraft. Such data are of interest in a study of lightning physics. In addition, the data may provide clues to the x-ray dose for personnel and equipment during flights. The icing campaign ran in April 2014; in six flights we collected data of 61 lightning strikes on an Airbus test aircraft. In this communication we briefly describe ILDAS and present selected results on three strikes, two aircraft initiated and one intercepted. Most of the x-rays have been observed synchronous with initiating negative leader steps, and as bursts immediately preceding the current of the recoil process. Those processes include the return stroke. The bursts last one to four micro-second and attain x-ray energies up to 10 MeV. Intensity and spectral distribution of the x-rays and the association with the current distribution are discussed. ILDAS also continuously records x-rays at low resolution in time and amplitude.Comment: 28 pages, 9 figure

Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble

A time series delta(n), the fluctuation of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of NxN random matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble as a function of beta (zero or positive) by Monte Carlo simulations. The fluctuation of delta(n) and the autocorrelation function vary logarithmically with n for any beta>0 (1<<n<<N). The simple logarithmic behavior reported for the higher-order moments of delta(n) for the GOE (beta=1) and the GUE (beta=2) is valid for any positive beta and is accounted for by Gaussian distributions whose variances depend linearly on ln(n). The 1/f noise previously demonstrated for delta(n) series of the three Gaussian ensembles, is characterized by wavelet analysis both as a function of beta and of N. When beta decreases from 1 to 0, for a given and large enough N, the evolution from a 1/f noise at beta=1 to a 1/f^2 noise at beta=0 is heterogeneous with a ~1/f^2 noise at the finest scales and a ~1/f noise at the coarsest ones. The range of scales in which a ~1/f^2 noise predominates grows progressively when beta decreases. Asymptotically, a 1/f^2 noise is found for beta=0 while a 1/f noise is the rule for beta positive.Comment: 35 pages, 10 figures, corresponding author: G. Le Cae

A Markov Chain based method for generating long-range dependence

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov Modulated Process based upon an infinite Markov chain is described. The work described is motivated by applications in telecommunications where LRD is a known property of time-series measured on the internet. The process can generate a time series exhibiting LRD with known parameters and is particularly suitable for modelling internet traffic since the time series is in terms of ones and zeros which can be interpreted as data packets and inter-packet gaps. The method is extremely simple computationally and analytically and could prove more tractable than other methods described in the literatureComment: 8 pages, 2 figure

New ophthalmosaurid ichthyosaurs from the European lower cretaceous demonstrate extensive ichthyosaur survival across the Jurassic–Cretaceous boundary

Background Ichthyosauria is a diverse clade of marine amniotes that spanned most of the Mesozoic. Until recently, most authors interpreted the fossil record as showing that three major extinction events affected this group during its history: one during the latest Triassic, one at the Jurassic–Cretaceous boundary (JCB), and one (resulting in total extinction) at the Cenomanian-Turonian boundary. The JCB was believed to eradicate most of the peculiar morphotypes found in the Late Jurassic, in favor of apparently less specialized forms in the Cretaceous. However, the record of ichthyosaurs from the Berriasian–Barremian interval is extremely limited, and the effects of the end-Jurassic extinction event on ichthyosaurs remains poorly understood. Methodology/Principal Findings Based on new material from the Hauterivian of England and Germany and on abundant material from the Cambridge Greensand Formation, we name a new ophthalmosaurid, Acamptonectes densus gen. et sp. nov. This taxon shares numerous features with Ophthalmosaurus, a genus now restricted to the Callovian–Berriasian interval. Our phylogenetic analysis indicates that Ophthalmosauridae diverged early in its history into two markedly distinct clades, Ophthalmosaurinae and Platypterygiinae, both of which cross the JCB and persist to the late Albian at least. To evaluate the effect of the JCB extinction event on ichthyosaurs, we calculated cladogenesis, extinction, and survival rates for each stage of the Oxfordian–Barremian interval, under different scenarios. The extinction rate during the JCB never surpasses the background extinction rate for the Oxfordian–Barremian interval and the JCB records one of the highest survival rates of the interval. Conclusions/Significance There is currently no evidence that ichthyosaurs were affected by the JCB extinction event, in contrast to many other marine groups. Ophthalmosaurid ichthyosaurs remained diverse from their rapid radiation in the Middle Jurassic to their total extinction at the beginning of the Late Cretaceous

New data on the ichthyosaur Platypterygius hercynicus and its implications for the validity of the genus

The description of a nearly complete skull from the late Albian of northwestern France reveals previously unknown anatomical features of Platypterygius hercynicus (Kuhn 1946), and of European Cretaceous ichthyosaurs in general. These include a wide frontal forming the anteromedial border of the supratemporal fenestra, a parietal excluded from the parietal foramen, and the likely presence of a squamosal, inferred from a very large and deep facet on the quadratojugal. The absence of a squamosal has been considered as an autapomorphy of the genus Platypterygius for more than ten years and has been applied to all known species by default, but the described specimen casts doubt on this putative autapomorphy. Actually, it is shown that all characters that have been proposed previously as autapomorphic for the genus Platypterygius are either not found in all the species currently referred to this genus, or are also present in other Ophthalmosauridae. Consequently, the genus Platypterygius must be completely revised.Peer reviewe

Regional frequency analysis of extreme storm surges along the French coast

A good knowledge of extreme storm surges is necessary to ensure protection against flood. In this paper we introduce a methodology to determine time series of skew surges in France as well as a statistical approach for estimating extreme storm surges. With the aim to cope with the outlier issue in surge series, a regional frequency analysis has been carried out for the surges along the Atlantic coast and the Channel coast. This methodology is not the current approach used to estimate extreme surges in France. First results showed that the extreme events identified as outliers in at-site analyses do not appear to be outliers any more in the regional empirical distribution. Indeed the regional distribution presents a curve to the top with these extreme events that a mixed exponential distribution seems to recreate. Thus, the regional approach appears to be more reliable for some sites than at-site analyses. A fast comparison at a given site showed surge estimates with the regional approach and a mixed exponential distribution are higher than surge estimates with an at-site fitting. In the case of Brest, the 1000-yr return surge is 167 cm in height with the regional approach instead of 126 cm with an at-site analysis