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

Mechanisms for photon sorting based on slit-groove arrays

Mechanisms for one-dimensional photon sorting are theoretically studied in the framework of a couple mode method. The considered system is a nanopatterned structure composed of two different pixels drilled on the surface of a thin gold layer. Each pixel consists of a slit-groove array designed to squeeze a large fraction of the incident light into the central slit. The Double-Pixel is optimized to resolve two different frequencies in the near infrared. This system shows a high transmission efficiency and a small crosstalk. Its response is found to strongly depend on the effective area shared by overlapping pixels. Three different regimes for the process of photon sorting are identified and the main physical trends underneath in such regimes are unveiled. Optimal efficiencies for the photon sorting are obtained for a moderate number of grooves that overlap with grooves of the neighbor pixel. Results could be applied to optical and infrared detectors.Comment: 12 pages, 4 figure

Transmittance of a subwavelength aperture flanked by a finite groove array \\ placed near the focus of a conventional lens

One-dimensional light harvesting structures illuminated by a conventional lens are studied in this paper. Our theoretical study shows that high transmission efficiencies are obtained when the structure is placed near the focal plane of the lens. The considered structure is a finite slit-groove array (SGA) with a given number of grooves that are symmetrically distributed with respect to a central slit. The SGA is nano-patterned on an opaque metallic film. It is found that a total transmittance of 80% is achieved even for a single slit when (i) Fabry-Perot like modes are excited inside the slit and (ii) the effective cross section of the aperture becomes of the order of the full width at half maximum of the incident beam. A further enhancement of 8% is produced by the groove array. The optimal geometry for the groove array consists of a moderate number of grooves ($\geq 4$) at either side of the slit, separated by a distance of half the incident wavelength $\lambda$. Grooves should be deeper (with depth $\geq \lambda/4$) than those typically reported for plane wave illumination in order to increase their individual scattering cross section.Comment: 7 pages, 6 figure

Geometric aspects of nonholonomic field theories

A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations for the constrained system can be recovered by a suitable projection of the equations for the underlying free (i.e. unconstrained) Lagrangian system.Comment: 29 pages; typos remove

Interpreting the Hours-Technology time-varying relationship

We investigate the time varying relation between hours and technology shocks using a structural business cycle model. We propose an RBC model with a Constant Elasticity of Substitution (CES) production function that allows for capital- and labor-augmenting technology shocks. We estimate the model with Bayesian techniques. In the full sample, we find (i) evidence in favor of a less than unitary elasticity of substitution (rejecting Cobb-Douglas) and (ii) a sizable role for capital augmenting shock for business cycles fluctuations. In rolling sub-samples, we document that the transmission of technology shocks to hours worked has been varying over time. We argue that this change is due to the increase of the elasticity of factor substitution. That is, labor and capital became less complementary throughout the sample inducing a change in the sign and size of the response of hours. We conjecture that this change may have been induced by a change in the skill composition of the labor input.Hours Worked and Business Cycles, Bayesian Methods.

COINTEGRATION VECTOR ESTIMATION BY DOLS FOR A THREE-DIMENSIONAL PANEL

This paper extends the asymptotic results of the dynamic ordinary least squares (DOLS) cointegration vector estimator of Mark and Sul (2003) to a three-dimensional panel. We use a balanced panel of N and M lengths observed over T time periods. The cointegration vector is homogenous across individuals but we allow for individual heterogeneity using different short-run dynamics, individual-specific fixed effects and individual-specific time trends. Both individual effects are considered for the first two dimensions. This paper was motivated by the three-dimensional panel cointegration analysis used to estimate the total factor productivity for Colombian regions and sectors during 1975-2000 by Iregui, Melo and Ramírez (2007). They used the methodology proposed by Marrocu, Paci and Pala (2000); however, hypothesis testing is not valid under this technique. The methodology we are currently proposing allows us to estimate the long-run relationship and to construct asymptotically valid test statistics in the 3D-panel context.Cointegration, Dynamic OLS estimation, panel data in three dimensions. Classification JEL: C13; C33.

Translatio Studiorum: Traslado de los libros y diálogo de las civilizaciones en la Edad Media

El propósito de este breve ensayo es trazar un esbozo del viaje cultural y filosófico, del traslado de los libros y del conocimiento, que cubrió muchas áreas y muchas historias en la edad media, que se conoce como translatio studiorum. Este viaje recorrió largas distancias, invirtió tiempo en diferentes lugares y estableció una compleja trama de relaciones entre pueblos, culturas y civilizaciones a lo largo de las orillas del Mare Nostrum. La historia de las ideas intenta reestablecer el conocimiento del legado olvidado de las tradiciones árabe, bizantina y judía para la cultura occidental.The purpose of this paper is to sketch the cultural and philosophical travel, the translation of the books and the knowledge, that covered many areas and many histories in the Middle Ages, that is called translatio studiorum. This travel covered long distances, spent time in diferent places and stablished a complex netwok of relations between peoples, cultures and civilizations all along the shores of the Mare Nostrum. The history of ideas claims to re-establish the acknowledge of the forgotten legacy from Arabian, Byzantin and Jewis traditions for the modern Western culture

An Approach to Publish Spatial Data on the Web: The GeoLinked Data Case

In this paper we report on an ongoing process aimed at publishing hydrographical data on the Web with a Spanish GeoLinked Data Use Case. Moreover, we discuss the process we followed, and propose methodological guidelines for all the activities involved within the process

Optimal light harvesting structures at optical and infrared frequencies

One-dimensional light harvesting structures with a realistic geometry nano-patterned on an opaque metallic film are optimized to render high transmission efficiencies at optical and infrared frequencies. Simple design rules are developed for the particular case of a slit-groove array with a given number of grooves that are symmetrically distributed with respect to a central slit. These rules take advantage of the hybridization of Fabry-Perot modes in the slit and surface modes of the corrugated metal surface. Same design rules apply for optical and infrared frequencies. The parameter space of the groove array is also examined with a conjugate gradient optimization algorithm that used as a seed the geometries optimized following physical intuition. Both uniform and nonuniform groove arrays are considered. The largest transmission enhancement, with respect to a uniform array, is obtained for a chirped groove profile. Such enhancement is a function of the wavelength. It decreases from 39% in the optical part of the spectrum to 15% at the long wavelength infrared.Comment: 13 pages, 5 figure