Extreme statistics of non-intersecting Brownian paths

We consider finite collections of $N$ non-intersecting Brownian paths on the line and on the half-line with both absorbing and reflecting boundary conditions (corresponding to Brownian excursions and reflected Brownian motions) and compute in each case the joint distribution of the maximal height of the top path and the location at which this maximum is attained. The resulting formulas are analogous to the ones obtained in [MFQR13] for the joint distribution of $\mathcal{M}={\rm max}_{x\in\mathbb{R}}\{\mathcal{A}_2(x)-x^2\}$ and $\mathcal{T}={\rm argmax}_{x\in\mathbb{R}}\{\mathcal{A}_2(x)-x^2\}$, where $\mathcal{A}_2$ is the Airy$_2$ process, and we use them to show that in the three cases the joint distribution converges, as $N\to\infty$, to the joint distribution of $\mathcal{M}$ and $\mathcal{T}$. In the case of non-intersecting Brownian bridges on the line, we also establish small deviation inequalities for the argmax which match the tail behavior of $\mathcal{T}$. Our proofs are based on the method introduced in [CQR13,BCR15] for obtaining formulas for the probability that the top line of these line ensembles stays below a given curve, which are given in terms of the Fredholm determinant of certain "path-integral" kernels.Comment: Minor corrections, improved exposition. To appear in Electron. J. Proba

Efectos dinámicos debidos al tráfico de ferrocarril sobre la infraestructura de vía y las estructuras

La vía tradicional sobre balasto sigue siendo una selección para las líneas de alta velocidad a pesar de los problemas técnicos y la prestación del funcionamiento. El problema de la vía sobre balasto es el proceso continuo del deterioro de éste debido a las cargas asociadas al tráfico ferroviario. En consecuencia es imprescindible un mantenimiento continuado para mantener un alineamiento adecuado de la vía. Por eso se surge la necesidad de comprender mejor el mecanismo involucrado en el deterioro de la vía y los factores claves que rigen su progresión a lo largo de ciclos de carga con el fin de reducir los costos del mantenimiento de la vía y mejorar el diseño de las nuevas vías. La presente tesis intenta por un lado desarrollar los modelos más adecuados y eficientes del vehículo y de la vía para los cálculos de los efectos dinámicos debido al tráfico de ferrocarril sobre la infraestructura de la vía sobre balasto, y por otro evaluar estos efectos dinámicos sobre el deterioro de la vía sobre balasto a largo plazo, empleando un adecuado modelo de predicción del deterioro de la misma. Se incluye en el trabajo una recopilación del estado del arte en lo referente a la dinámica de la vía, a la modelización del vehículo, de la vía y de la interacción entre ambos. También se hace un repaso al deterioro de la vía y los factores que influyen en su proceso. Para la primera línea de investigación de esta tesis, se han desarrollado los diferentes modelos del vehículo y de la vía y la modelización de la interacción entre ambos para los cálculos dinámicos en dos y tres dimensiones. En la interacción vehículo-vía, se ha empleado la formulación de contacto nodo-superficie para establecer la identificación de las superficies en contacto y el método de los multiplicadores de Lagrange para imponer las restricciones de contacto. El modelo de interacción se ha contrastado con los casos reportados en la literatura. Teniendo en cuenta el contacto no lineal entre rueda-carril y los perfiles de irregularidades distribuidas de la vía, se han evaluado y comparado los efectos dinámicos sobre el sistema vehículo-vía en la interacción de ambos, para distintas velocidades de circulación del vehículo, en los aspectos como la vibración del vehículo, fuerza de contacto, fuerza transmitida en los railpads, la vibración del carril. También se hace un estudio de la influencia de las propiedades de los componentes de la vía en la respuesta dinámica del sistema vehículo-vía. Se ha desarrollado el modelo del asiento de la vía que consiste en la implementación del modelo de acumulación de Bochum y del modelo de hipoplasticidad en la subrutina del usuario \UMAT" del programa ABAQUS. La implementación numérica ha sido comprobado al comparar los resultados de las simulaciones numéricas con los reportados en la literatura. Se ha evaluado la calidad geométrica de la vía sobre balasto de los tramos de estudio con datos reales de la auscultación proporcionados por ADIF (2012). Se ha propuesto una metodología de simulación, empleando el modelo de asiento, para reproducir el deterioro de la geometría de la vía. Se usan los perfiles de la nivelación longitudinal de la auscultación como perfiles de irregularidades iniciales de la vía en las simulaciones numéricas. También se evalúa la influencia de la velocidad de circulación sobre el deterioro de la vía. The traditional ballast track structures are still being used in high speed railways lines with success, however technical problems or performance features have led to ballast track solution in some cases. The considerable maintenance work is needed for ballasted tracks due to the track deterioration. Therefore it is very important to understand the mechanism of track deterioration and to predict the track settlement or track irregularity growth rate in order to reduce track maintenance costs and enable new track structures to be designed. This thesis attempts to develop the most adequate and efficient models for calculation of dynamic track load effects on railways track infrastructure, and to evaluate these dynamic effects on the track settlement, using a track settlement prediction model, which consists of the vehicle/track dynamic model previously selected and a track settlement law. A revision of the state of the knowledge regarding the track dynamics, the modelling of the vehicle, the track and the interaction between them is included. An overview related to the track deterioration and the factors influencing the track settlement is also done. For the first research of this thesis, the different models of vehicle, track and the modelling of the interaction between both have been developed. In the vehicle-track interaction, the node-surface contact formulation to establish the identification of the surfaces in contact and the Lagrange multipliers method to enforce contact constraint are used. The interaction model has been verified by contrast with some benchmarks reported in the literature. Considering the nonlinear contact between wheel-rail and the track irregularities, the dynamic effects on the vehicle-track system have been evaluated and compared, for different speeds of the vehicle, in aspects as vehicle vibration, contact force, force transmitted in railpads, rail vibration. A study of the influence of the properties of the track components on the the dynamic response of the vehicle-track system has been done. The track settlement model is developed that consist of the Bochum accumulation model and the hipoplasticity model in the user subroutine \UMAT" of the program ABAQUS. The numerical implementation has been verified by comparing the numerical results with those reported in the literature. The geometric quality of the ballast track has been evaluated with real data of auscultation provided by ADIF (2012). The simulation methodology has been proposed, using the settlement model for the ballast material, to reproduce the deterioration of the track geometry. The profiles of the longitudinal level of the auscultation is used as initial profiles of the track irregularities in the numerical simulation. The influence of the running speed on the track deterioration is also investigated

Orienting to pedagogical innovation: A case study of Vietnamese teachers' beliefs and practices regarding Task-based Language Teaching

Although research into language teacher cognition has become a well-established domain of inquiry for applied linguists over the past few decades, few in-depth studies have explored language teachers’ beliefs regarding task-based language teaching (TBLT). Furthermore, in the context of Vietnam, where TBLT is claimed to be adopted in the current national English curriculum and textbooks, no studies have been carried out to investigate the extent of orientation of the teachers toward TBLT. This qualitative case study aims to occupy such a research space. Following an extensive review of the literature relating to TBLT principles, task characteristics and teachers’ beliefs, an analysis of the mandated textbook was carried out to consider the extent to which it followed the principles and characteristics recommended by TBLT proponents. The study employed a multi-method approach to data collection. Specifically, it has investigated the beliefs and practices of a group of eleven English language teachers in two provincial Vietnamese upper secondary schools. Ten collaborative lesson planning sessions, twenty-two observations of skills lessons, twenty-two stimulated recall sessions of the observed lessons, and two focus group sessions were carried out to collect the data. The data, together with insights of the context, were subject to a procedure of grounded analysis, through which the data from various sources were compared and contrasted to identify significant themes. The data showed that the teachers’ patterns of practices were not related to current TBLT principles and favourable task characteristics. For example, the teachers tended to employ activities that were forms-focused, and conducted classroom activities in a non-communicative fashion. Their beliefs were found to incline to a structure-based approach, where language items were pre-taught before activities could be performed. A wide range of hindering factors were identified as constraining the implementation of TBLT in the context, such as the teachers’ current state of knowledge and beliefs about language teaching, their perceptions of the significant others, and the role of examinations. In light of a sociocultural perspective, the teachers’ beliefs in the present study were situated, shaped by their experiences as language learners and language teachers, and their interactions with the contexts in which they worked. Their beliefs were also found to be resistant to change. Teachers’ beliefs and practices in this study were also viewed through the lens of the Theory of Planned Behaviour through which core beliefs were identified to have close relationships to teachers’ behaviours in the classroom. The findings of the present investigation, being a case study, cannot be generalised beyond the context in which the data were collected. Nevertheless, they make an original contribution to academic understanding of teachers’ beliefs and their practices in the context of Vietnam, and in relatable contexts. Drawing on the findings, implications for theory, research, teacher professional development and language teaching policies are offered

Design for energy-efficient and reliable fog-assisted healthcare IoT systems

Cardiovascular disease and diabetes are two of the most dangerous diseases as they are the leading causes of death in all ages. Unfortunately, they cannot be completely cured with the current knowledge and existing technologies. However, they can be effectively managed by applying methods of continuous health monitoring. Nonetheless, it is difficult to achieve a high quality of healthcare with the current health monitoring systems which often have several limitations such as non-mobility support, energy inefficiency, and an insufficiency of advanced services. Therefore, this thesis presents a Fog computing approach focusing on four main tracks, and proposes it as a solution to the existing limitations. In the first track, the main goal is to introduce Fog computing and Fog services into remote health monitoring systems in order to enhance the quality of healthcare. In the second track, a Fog approach providing mobility support in a real-time health monitoring IoT system is proposed. The handover mechanism run by Fog-assisted smart gateways helps to maintain the connection between sensor nodes and the gateways with a minimized latency. Results show that the handover latency of the proposed Fog approach is 10%-50% less than other state-of-the-art mobility support approaches. In the third track, the designs of four energy-efficient health monitoring IoT systems are discussed and developed. Each energy-efficient system and its sensor nodes are designed to serve a specific purpose such as glucose monitoring, ECG monitoring, or fall detection; with the exception of the fourth system which is an advanced and combined system for simultaneously monitoring many diseases such as diabetes and cardiovascular disease. Results show that these sensor nodes can continuously work, depending on the application, up to 70-155 hours when using a 1000 mAh lithium battery. The fourth track mentioned above, provides a Fog-assisted remote health monitoring IoT system for diabetic patients with cardiovascular disease. Via several proposed algorithms such as QT interval extraction, activity status categorization, and fall detection algorithms, the system can process data and detect abnormalities in real-time. Results show that the proposed system using Fog services is a promising approach for improving the treatment of diabetic patients with cardiovascular disease

Fibonacci and Lucas series with elliptic functions

Ope