On the second moment of the number of crossings by a stationary Gaussian process

Cram\'{e}r and Leadbetter introduced in 1967 the sufficient condition $$\frac{r''(s)-r''(0)}{s}\in L^1([0,\delta],dx),\qquad \delta>0,$$ to have a finite variance of the number of zeros of a centered stationary Gaussian process with twice differentiable covariance function $r$. This condition is known as the Geman condition, since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean. This paper shows that the Geman condition is still sufficient and necessary to have a finite variance of the number of any fixed level crossings. For the generalization to the number of a curve crossings, a condition on the curve has to be added to the Geman condition.Comment: Published at http://dx.doi.org/10.1214/009117906000000142 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rice formulae and Gaussian waves

We use Rice formulae in order to compute the moments of some level functionals which are linked to problems in oceanography and optics: the number of specular points in one and two dimensions, the distribution of the normal angle of level curves and the number of dislocations in random wavefronts. We compute expectations and, in some cases, also second moments of such functionals. Moments of order greater than one are more involved, but one needs them whenever one wants to perform statistical inference on some parameters in the model or to test the model itself. In some cases, we are able to use these computations to obtain a central limit theorem.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ265 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Estimation in models driven by fractional Brownian motion

Let $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type $$X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^t\mu\bigl(X(u)\bigr)\mathrm {d}u.$$ In different particular models where $\sigma(x)=\sigma$ or $\sigma(x)=\sigma x$ and $\mu(x)=\mu$ or $\mu(x)=\mu x$, we propose a central limit theorem for estimators of $H$ and of $\sigma$ based on regression methods. Then we give tests of the hypothesis on $\sigma$ for these models. We also consider functional estimation on $\sigma(\cdot)$ in the above more general models based in the asymptotic behavior of functionals of the 2nd-order increments of the fBm.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP105 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estimation for Stochastic Damping Hamiltonian Systems under Partial Observation. II Drift term

International audienceThis paper is the second part of our study started with \citet*{CLP}. For some ergodic hamiltonian systems we obtained a central limit theorem for a non-parametric estimator of the invariant density, under partial observation (only the positions are observed). Here we obtain similarly a central limit theorem for a non-parametric estimator of the drift term. This theorem lies on the previous result for the invariant density

1D Convolutional Neural Network for Detecting Ventricular Heartbeats

This paper shows a novel approach for detecting ventricular heartbeats using a 1D Convolutional Neural Network (1D-CNN). The algorithm input is the raw ECG signal, i.e., no signal pre-processing nor feature extraction are involved. The output of the 1D-CNN is filtered using a combination of linear and nonlinear filters to produce the final output. The MIT-BIH arrhythmia database was used for both algorithm training/tuning and evaluation. The assessment methodology followed the interpatient paradigm, where the algorithm was trained and evaluated using independent subsets. The performance of the proposed method was evaluated for two tasks; QRS detection, and heartbeat classification. QRS detection resulted in a sensitivity of 99.0% and a positive predictivity of 96.5%. The performance assessment of the ventricular ectopic beat detection resulted in a sensitivity of 85.8% and a positive predictivity of 64.5%. Although there is still room for improvement, the results suggest that convolutional neural networks are a promising approach for building heartbeat classifiers

Draft Genome Sequence of the Moderately Halophilic Bacterium Pseudoalteromonas ruthenica Strain CP76

Pseudoalteromonas ruthenica strain CP76, isolated from a saltern in Spain, is a moderately halophilic bacterium belonging to the Gammaproteobacteria. Here we report the draft genome sequence, which consists of a 4.0-Mb chromosome, of this strain, which is able to produce the extracellular enzyme haloprotease CPI

La prótesis de cadera con recubrimiento de vidrio Primeros resultados con 2 años de evolución

El presente trabajo analiza los primeros resultados clínicos y radiográficos de un estudio con la prótesis de cadera no cementada con recubrimiento «de vidrio» a nivel metafísario (prótesis CRM). La casuística comprende 80 artroplastias totales implantadas desde 1991 a 1994 con un seguimiento mínimo de 2 años. La evolución clínica, valorada según el sistema de Harris modificado, ha sido satisfactoria en el 90% de los enfermos. La observación radiográfica ha mostrado buena fijación y orientación de los componentes femorales en 72 casos. La conclusión de este análisis preliminar permite apreciar que el recubrimiento protésico con cerámica de vidrio supone un mecanismo de seguridad en la fijación primaria y secundaria de la prótesis de cadera.This work analizes the first clinical and radiological results of a cementless hip prosthesis with glass coating at metaphyseal level (CRM prosthesis). A total of 80 arthroplasties implanted since may 1991 to 1994 were studied with a two year follow-up. The clinical assesment was done by the modified Harris score, being satisfactory in 90% of the patients. The radiological study demonstrated good fixation and orientation of the prosthetic compounds in 72 cases. The prosthetic model studied provides a security mechanism both for primary and secondary fixation of the femoral stem and acetabular cup