Resonant structures based on amorphous silicon sub-oxide doped with Er3+ with silicon nanoclusters for an efficient emission at 1550 nm

We present a resonant approach to enhance 1550nm emission efficiency of amorphous silicon sub-oxide doped with Er3+ (a-SiOx) layers with silicon nanoclusters (Si-NC). Two distinct techniques were combined to provide a structure that allowed increasing approximately 12x the 1550nm emission. First, layers of SiO2 were obtained by conventional wet oxidation and a-SiOx matrix was deposited by reactive RF co-sputtering. Secondly, an extra pump channel (4I15/2 to 4I9/2) of Er3+ was created due to Si-NC formation on the same a-SiOx matrix via a hard annealing at 1150 C. The SiO2 and the a-SiOx thicknesses were designed to support resonances near the pumping wavelength (~500nm), near the Si-NC emission (~800nm) and near the a-SiOx emission (~1550nm) enhancing the optical pumping process.Comment: 14 pages, 4 figures, in submissio

Bayesian parameter estimation in the second LISA Pathfinder Mock Data Challenge

A main scientific output of the LISA Pathfinder mission is to provide a noise model that can be extended to the future gravitational wave observatory, LISA. The success of the mission depends thus upon a deep understanding of the instrument, especially the ability to correctly determine the parameters of the underlying noise model. In this work we estimate the parameters of a simplified model of the LISA Technology Package (LTP) instrument. We describe the LTP by means of a closed-loop model that is used to generate the data, both injected signals and noise. Then, parameters are estimated using a Bayesian framework and it is shown that this method reaches the optimal attainable error, the Cramer-Rao bound. We also address an important issue for the mission: how to efficiently combine the results of different experiments to obtain a unique set of parameters describing the instrument.Comment: 14 pages, 4 figures, submitted to PR

Time domain maximum likelihood parameter estimation in LISA Pathfinder Data Analysis

LISA is the upcoming space-based Gravitational Wave telescope. LISA Pathfinder, to be launched in the coming years, will prove and verify the detection principle of the fundamental Doppler link of LISA on a flight hardware identical in design to that of LISA. LISA Pathfinder will collect a picture of all noise disturbances possibly affecting LISA, achieving the unprecedented pureness of geodesic motion necessary for the detection of gravitational waves. The first steps of both missions will crucially depend on a very precise calibration of the key system parameters. Moreover, robust parameters estimation is of fundamental importance in the correct assessment of the residual force noise, an essential part of the data processing for LISA. In this paper we present a maximum likelihood parameter estimation technique in time domain being devised for this calibration and show its proficiency on simulated data and validation through Monte Carlo realizations of independent noise runs. We discuss its robustness to non-standard scenarios possibly arising during the real-life mission, as well as its independence to the initial guess and non-gaussianities. Furthermore, we apply the same technique to data produced in mission-like fashion during operational exercises with a realistic simulator provided by ESA.Comment: 16 pages (two columns), 15 figures, 5 tables, submitted to Phys. Rev.

Local Isometric immersions of pseudo-spherical surfaces and evolution equations

The class of differential equations describing pseudo-spherical surfaces, first introduced by Chern and Tenenblat [3], is characterized by the property that to each solution of a differential equation, within the class, there corresponds a 2-dimensional Riemannian metric of curvature equal to $-1$. The class of differential equations describing pseudo-spherical surfaces carries close ties to the property of complete integrability, as manifested by the existence of infinite hierarchies of conservation laws and associated linear problems. As such, it contains many important known examples of integrable equations, like the sine-Gordon, Liouville and KdV equations. It also gives rise to many new families of integrable equations. The question we address in this paper concerns the local isometric immersion of pseudo-spherical surfaces in ${\bf E}^{3}$ from the perspective of the differential equations that give rise to the metrics. Indeed, a classical theorem in the differential geometry of surfaces states that any pseudo-spherical surface can be locally isometrically immersed in ${\bf E}^{3}$. In the case of the sine-Gordon equation, one can derive an expression for the second fundamental form of the immersion that depends only on a jet of finite order of the solution of the pde. A natural question is to know if this remarkable property extends to equations other than the sine-Gordon equation within the class of differential equations describing pseudo-spherical surfaces. In an earlier paper [11], we have shown that this property fails to hold for all other second order equations, except for those belonging to a very special class of evolution equations. In the present paper, we consider a class of evolution equations for $u(x,t)$ of order $k\geq 3$ describing pseudo-spherical surfaces. We show that whenever an isometric immersion in ${\bf E}^3$ exists, depending on a jet of finite order of $u$, then the coefficients of the second fundamental forms are functions of the independent variables $x$ and $t$ only.Comment: Fields Institute Communications, 2015, Hamiltonian PDEs and Applications, pp.N

Parameter estimation in LISA Pathfinder operational exercises

The LISA Pathfinder data analysis team has been developing in the last years the infrastructure and methods required to run the mission during flight operations. These are gathered in the LTPDA toolbox, an object oriented MATLAB toolbox that allows all the data analysis functionalities for the mission, while storing the history of all operations performed to the data, thus easing traceability and reproducibility of the analysis. The parameter estimation methods in the toolbox have been applied recently to data sets generated with the OSE (Off-line Simulations Environment), a detailed LISA Pathfinder non-linear simulator that will serve as a reference simulator during mission operations. These operational exercises aim at testing the on-orbit experiments in a realistic environment in terms of software and time constraints. These simulations, so called operational exercises, are the last verification step before translating these experiments into tele-command sequences for the spacecraft, producing therefore very relevant datasets to test our data analysis methods. In this contribution we report the results obtained with three different parameter estimation methods during one of these operational exercises.Comment: 10 pages, 3 figures, prepared for the Proceedings of the 9th Edoardo Amaldi Conference on Gravitational Waves, JPC

Nonlocal aspects of λ\lambda-symmetries and ODEs reduction

A reduction method of ODEs not possessing Lie point symmetries makes use of the so called $\lambda$-symmetries (C. Muriel and J. L. Romero, \emph{IMA J. Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE $\mathcal{Y}$ is used here to recover $\lambda$-symmetries of $\mathcal{Y}$ as nonlocal symmetries. In this framework, by embedding $\mathcal{Y}$ into a suitable system $\mathcal{Y}^{\prime}$ determined by the function $\lambda$, any $\lambda$-symmetry of $\mathcal{Y}$ can be recovered by a local symmetry of $\mathcal{Y}^{\prime}$. As a consequence, the reduction method of Muriel and Romero follows from the standard method of reduction by differential invariants applied to $\mathcal{Y}^{\prime}$.Comment: 13 page

From Uterus to Brain: An Update on Epidemiology, Clinical Features, and Treatment of Brain Metastases From Gestational Trophoblastic Neoplasia

In this review, we provide the state of the art about brain metastases (BMs) from gestational trophoblastic neoplasia (GTN), a rare condition. Data concerning the epidemiology, clinical presentation, innovations in therapeutic modalities, and outcomes of GTN BMs are comprehensively presented with particular attention to the role of radiotherapy, neurosurgery, and the most recent chemotherapy regimens. Good response rates have been achieved thanks to multi-agent chemotherapy, but brain involvement by GTNs entails significant risks for patients’ health since sudden and extensive intracranial hemorrhages are possible. Moreover, despite the evolution of treatment protocols, a small proportion of these patients ultimately develops a resistant disease. To tackle this unmet clinical need, immunotherapy has been recently proposed. The role of this novel option for this subset of patients as well as the achieved results so far are also discussed