Unified formalism for higher-order non-autonomous dynamical systems

This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher-order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.Comment: 43 pp. We have corrected and clarified the statement of Propositions 2 and 3. A remark is added after Proposition

A retrospective segmentation analysis of placental volume by magnetic resonance imaging from first trimester to term gestation

Background Abnormalities of the placenta affect 5–7% of pregnancies. Because disturbances in fetal growth are often preceded by dysfunction of the placenta or attenuation of its normal expansion, placental health warrants careful surveillance. There are limited normative data available for placental volume by MRI. Objective To determine normative ranges of placental volume by MRI throughout gestation. Materials and methods In this cross-sectional retrospective analysis, we reviewed MRI examinations of pregnant females obtained between 2002 and 2017 at a single institution. We performed semi-automated segmentation of the placenta in images obtained in patients with no radiologic evidence of maternal or fetal pathology, using the Philips Intellispace Tumor Tracking Tool. Results Placental segmentation was performed in 112 women and had a high degree of interrater reliability (single-measure intraclass correlation coefficient =0.978 with 95% confidence interval [CI] 0.956, 0.989; P<0.001). Normative data on placental volume by MRI increased nonlinearly from 6 weeks to 39 weeks of gestation, with wider variability of placental volume at higher gestational age (GA). We fit placental volumetric data to a polynomial curve of third order described as placental volume = –0.02*GA3 + 1.6*GA2 – 13.3*GA + 8.3. Placental volume showed positive correlation with estimated fetal weight (P=0.03) and birth weight (P=0.05). Conclusion This study provides normative placental volume by MRI from early first trimester to term gestation. Deviations in placental volume from normal might prove to be an imaging biomarker of adverse fetal health and neonatal outcome, and further studies are needed to more fully understand this metric. Assessment of placental volume should be considered in all routine fetal MRI examinations

Non-local fractional derivatives. Discrete and continuous

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When the functions are good enough, these approximation procedures give a measure of the order of approximation. These results also allows us to prove the coincidence, for good enough functions, of the Marchaud and Gr\"unwald-Letnikov derivatives in every point and the speed of convergence to the Gr\"unwald-Letnikov derivative. The fractional discrete derivative will be also described as a Neumann-Dirichlet operator defined by a semi-discrete extension problem. Some operators related to the Harmonic Analysis associated to the discrete derivative will be also considered, in particular their behavior in the Lebesgue spaces $\ell^p(\mathbb{Z}).

Photoluminiscence of a quantum dot hybridized with a continuum

We calculate the intensity of photon emission from a trion in a single quantum dot, as a function of energy and gate voltage, using the impurity Anderson model and variational wave functions. Assuming a flat density of conduction states and constant hybridization energy, the results agree with the main features observed in recent experiments: non-monotonic dependence of the energy on gate voltage, non-Lorentzian line shapes, and a line width that increases near the regions of instability of the single electron final state to occupations zero or two.Comment: 4 pages, 3 figures, Journal-ref adde

Design of a phonetic corpus for speech recognition in catalan

In this paper, we present the design of a corpus for speech recognition to be used for the recording of a speech database in Catalan. A previous database in Spanish was the reference in setting the specifications about the characteristics of the sentences and in the minimum number of units required. An analysis of unit frequencies were carried out in order to know which units were relevant for training and to compare the results with the figures from the designed corpus. Three different sub-corpora were generated, one for training, ...Peer ReviewedPostprint (published version

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