Matrix-F5 algorithms and tropical Gr\"obner bases computation

Let $K$ be a field equipped with a valuation. Tropical varieties over $K$ can be defined with a theory of Gr\"obner bases taking into account the valuation of $K$. Because of the use of the valuation, this theory is promising for stable computations over polynomial rings over a $p$-adic fields.We design a strategy to compute such tropical Gr\"obner bases by adapting the Matrix-F5 algorithm. Two variants of the Matrix-F5 algorithm, depending on how the Macaulay matrices are built, are available to tropical computation with respective modifications. The former is more numerically stable while the latter is faster.Our study is performed both over any exact field with valuation and some inexact fields like $\mathbb{Q}\_p$ or $\mathbb{F}\_q \llbracket t \rrbracket.$ In the latter case, we track the loss in precision, and show that the numerical stability can compare very favorably to the case of classical Gr\"obner bases when the valuation is non-trivial. Numerical examples are provided

Quantitative exponential bounds for the renewal theorem with spread-out distributions

We establish explicit exponential convergence estimates for the renewal theorem, in terms of a uniform component of the inter arrival distribution, of its Laplace transform which is assumed finite on a positive interval, and of the Laplace transform of some related random variable. Our proof is based on a coupling construction relying on discrete-time Markovian structures that underly the renewal processes and on Lyapunov-Doeblin type arguments.Comment: Accepted for publication in Markov Processes and Related Field

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

Northridge Earthquake — Van Norman Complex Ground Movement

The January 17, 1994, Northridge Earthquake severely shook the Van Norman Complex, in the northern San Fernando Valley. Located in the nearfield, over the vicinity of the ruptured fault, the Van Norman Complex was subjected to many types of ground movements, including strong ground motions, tectonic displacements, ground deformation of natural soil deposits, and deformation of embankments and other engineered fills. The complex provides a well-documented case of how these various types of ground movements interact and their effects on engineered facilities. Throughout the complex, sand boils, liquefaction induced lateral spreading, and ground cracks were observed. Eleven water retaining embankments, including the Los Angeles Reservoir, underwent measurable movement. One small dike failed at the San Fernando Tailrace Channel at the northern end of the site. A great number of large diameter pipes and channels broke throughout the complex

A Tylosaurine Mosasauridae (Squamata) from the Late Cretaceous of the Basque-Cantabrian Region

An isolated mosasaurid tooth from the Campanian of Alava (Basque Country), previously referred to as cf. Mosasaurus sp., is here reattributed to a tylosaurine. It may belong to Tylosaurus, a nearly cosmopolitan genus known from the Santonian-Maastrichtian. This is the first occurrence of a tylosaurine mosasaurid in the Iberian Peninsula. Moreover, it corresponds to the southernmost occurrence of this clade in the northern margin of the Mediterranean Tethys. ylosaurinae fossils are known from North America, Europe, New Zealand, Antarctica, Africa and Asia, but remain unknown from the southern Mediterranean Tethyan margin and from tropical palaeolatitudes.Un diente aislado de mosasaurio procedente del Campaniense de Álava (País Vasco), previamente asignado a cf. Mosasaurus sp., se atribuye en este trabajo a un tilosaurino. Podría pertenecer a Tylosaurus, un género cuasi cosmopolita del Santoniense-Maastrichtiense. Es la primera cita de un mosasáurido tilosaurino en la Península Ibérica. Además, se trata del registro más meridional de este clado en el margen norte del Tetis mediterráneo. Los Tylosaurinae están representados por fósiles en Norteamérica, Europa, Nueva Zelanda, Antártida, África y Asia, pero carecen de registro en el margen sur del Tetis mediterráneo y en paleolatitudes tropicales

Effect of enthalpy-entropy compensation during sorption of water vapour in tropical woods: the case of Bubinga (Guibourtia Tessmanii J. Léonard ; G. Pellegriniana J.L.)

International audienceThe study of sorption of water vapour by a tropical wood (Bubinga) at 20°C, 38°C, 50°C and 60°C has permitted to obtain adsorption and desorption isotherms. Sigmoids have been obtained and they all show hysteresis phenomenon. From these isotherms, we were able to determine Gibbs energy, enthalpy and entropy variations. These variations were analysed and shown to be all negative for adsorption and all positive for desorption, with a great dependence to the moisture content during adsorption and desorption. Temperature had no significant effect on these parameters. Such dependence is mentioned in the scientific literature for softwood and is surely related to the availability of sorption sites. A linear relationship between enthalpy and entropy was shown to exist and the effect of enthalpy–entropy was studied for adsorption and desorption of water vapour by wood. In fact, the isokinetic temperature was determined and compared to the harmonic mean of temperatures

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