Browsing by Author "Miranda, Pablo"

Now showing 1 - 5 of 5
  • Thumbnail Image
    Item
    Discrete spectrum of quantum Hall effect Hamiltonians I. Monotone edge potentials
    (EUROPEAN MATHEMATICAL SOC, 2011) Bruneau, Vincent; Miranda, Pablo; Raikov, Georgi
    We consider the unperturbed operator H-0 = (-i del - A)(2) + W, self-adjoint in L-2(R-2). Here A is a magnetic potential which generates a constant magnetic field b > 0, and the edge potential W is a non-decreasing non-constant bounded function depending only on the first coordinate x is an element of R of (x, y) is an element of R-2. Then the spectrum of H-0 has a band structure and is absolutely continuous; moreover, the assumption lim(x ->infinity)(W(x) - W(-x)) < 2b implies the existence of infinitely many spectral gaps for H-0. We consider the perturbed operators H-+/- = H-0 +/- V where the electric potential V is an element of L-infinity(R-2) is non-negative and decays at infinity. We investigate the asymptotic distribution of the discrete spectrum of H-+/- in the spectral gaps of H-0. We introduce an effective Hamiltonian which governs the main asymptotic term; this Hamiltonian involves a pseudo-differential operator with generalized anti-Wick symbol equal to V. Further, we restrict our attention on perturbations V of compact support and constant sign. We establish a geometric condition on the support of V which guarantees the finiteness of the number of the eigenvalues of H-+/- in any spectral gap of H-0. In the case where this condition is violated, we show that, generically, the convergence of the infinite series of eigenvalues of H+ (resp. H-) to the lower (resp. upper) edge of a given spectral gap, is Gaussian.
  • Thumbnail Image
    Item
    Discrete spectrum of quantum Hall effect Hamiltonians II: Periodic edge potentials
    (IOS PRESS, 2012) Miranda, Pablo; Raikov, Georgi
    We consider the unperturbed operator H-0 := (-i del-A)(2) + W, self-adjoint in L-2(R-2). Here A is a magnetic potential which generates a constant magnetic field b > 0, and the edge potential W = (W) over bar is a T-periodic non-constant bounded function depending only on the first coordinate x is an element of R of (x, y) is an element of R-2. Then the spectrum sigma(H-0) of H-0 has a band structure, the band functions are bT-periodic, and generically there are infinitely many open gaps in sigma(H-0). We establish explicit sufficient conditions which guarantee that a given band of sigma(H-0) has a positive length, and all the extremal points of the corresponding band function are non-degenerate. Under these assumptions we consider the perturbed operators H-+/- = H-0 +/- V where the electric potential V is an element of L-infinity(R-2) is non-negative and decays at infinity. We investigate the asymptotic distribution of the discrete spectrum of H-+/- in the spectral gaps of H-0. We introduce an effective Hamiltonian which governs the main asymptotic term; this Hamiltonian could be interpreted as a 1D Schrodinger operator with infinite-matrix-valued potential. Further, we restrict our attention on perturbations V of compact support. We find that there are infinitely many discrete eigenvalues in any open gap in the spectrum sigma(H-0), and the convergence of these eigenvalues to the corresponding spectral edge is asymptotically Gaussian.
  • Thumbnail Image
    Item
    Portafolio electrónico en residencia de subespecialidad en anestesia regional y analgesia perioperatoria
    (2015) Miranda, Pablo; Fuente, René de la; Cuadra Fontaine, Juan Carlos de la ; Corvetto, Marcia; Altermatt Couratier, Fernando René
    Introducción: La Educación Médica Basada en Competencias es ahora el paradigma dominante para el diseño e implementación de los programas de formación. El desarrollo de portafolios electrónicos resulta útil para registrar las actividades asistenciales y académicas permitiendo un mayor compromiso con su proceso de aprendizaje. Las competencias requeridas por un sub-especialista en anestesia regional han sido explicitadas recientemente, sin embargo, datos sobre la cantidad de actividades necesarias para adquirirlas es un tema aún sin resolver. Objetivos: Presentar la implementación de un portafolio electrónico en el Programa de formación de Anestesia Regional y Analgesia Perioperatoria de la Pontificia Universidad Católica de Chile. Materiales y métodos: A contar del año 2013, se generó un portafolio electrónico acorde a las necesidades del programa. Dentro de las actividades se encuentran procedimientos de anestesia regional, manejo del dolor y actividades no asistenciales (presentaciones, proyectos de investigación, disecciones anatómicas, análisis crítico de literatura médica y supervisión de residentes de anestesiología). Se realizó una consulta a la base de datos obteniendo la información de las actividades realizadas y supervisadas por el residente del programa los primeros 6 meses, los datos obtenidos se analizaron con estadística descriptiva. Resultados: Se extrajeron un total de 321 registros, de los cuales 285 fueron procedimientos de anestesia regional y 36 actividades no clínicas, dentro de los que destacan 20 sesiones de disecciones anatómicas. Existen 23 actividades diferentes susceptibles de ser registradas, 19 procedimientos y 4 actividades no clínicas. Los procedimientos más realizados de extremidad inferior están el bloqueo ciático a nivel poplíteo y el femoral. En extremidad superior, los bloqueos más realizados son los de plexo braquial con un abordaje interescalénico y el supraclavicular. Al analizar los supervisores de las diferentes actividades nos encontramos que solo 4 docentes dan cuenta del 80% de las actividades clínicas y del 100% de las actividades académicas no clínicas. Se extrajeron 187 registros donde el residente de anestesia regional aparece como supervisor. Un 29% de esos procedimientos que dicen relación con anestesia regional, lo que habla del rol docente durante el desarrollo de la subespecialidad. Discusión y conclusiones: Al analizar los datos, se hacen evidentes distintas áreas de desarrollo durante la subespecialidad, hay una actividad asistencial y docente importante; sin embargo, hay un área no clínica muy fuerte, en donde están incluidos los proyectos de investigación, disecciones anatómicas, presentaciones, etc. Esto se contradice con lo señalado en la última guía de entrenamiento en anestesia regional y dolor agudo. El portafolio electrónico permite un registro de actividades sistemático, un análisis del proceso de formación y enfocar el aprendizaje a las áreas en donde la exposición sea considerada insuficiente. Un elemento importante de implementar en el futuro es una herramienta que permita evaluar las diferentes actividades registradas, ya que la sola exposición no garantiza un aprendizaje satisfactorio. Además, un sistema de evaluación contenido en el portafolio, permite hacer una curva de aprendizaje donde se pueden reflejar los progresos, enfatizando los avances obtenidos por el residente.
  • No Thumbnail Available
    Item
    Simulated-based training for ultrasound-guided popliteal block: determining the learning curve and transference to real patient
    (2024) Miranda, Pablo; Araneda, Andrea; Molina, Natalia; Miranda, Felipe; Morrison Corrales, Christopher Joseph; Corvetto Aqueveque, Marcia Antonia; Altermatt Couratier, Fernando René
    Background and Aims: This study aimed to determine the learning curve for an ultrasound-guided popliteal block and the transference of this training to a real patient situation. Methods: After approval by the ethics committee, ten first-year anesthesia residents were recruited to participate in a simulated-based training program to perform a single shot in plane popliteal block. (NCT06081790) Training consisted of 10 individual sessions, with direct feedback from the instructor, with a specific Laerdal® sciatic popliteal block phantom, lasting one hour and distributed weekly. At the end of each session, the resident’s performance was assessed. Residents were videotaped while performing the block, which was to be evaluated using a validated global rating scale (GRS). Additionally, a tracking motion device (ICSAD) attached to the operator’s hands recorded the total distance traveled by both hands (Total Path Length=TPL) and total procedure time (TPT). One week later, the same assessment was done on a real patient. Results: Ten residents completed the training and the assessments. Median values of GRS scores significantly improved from 14 to 28 through the training (p=0.02) (figure 1). Regarding ICSAD scores, TPT improved from 126 to 59.5 seconds (p=0.004), and TPL improved from 11.06 to 9.3 meters (p=0.432). We found no significant differences between the last simulated session and the subsequent measurement in an actual patient.
  • No Thumbnail Available
    Item
    Spectral asymptotics at thresholds for a Dirac-type operator on Z2
    (2023) Miranda, Pablo; Parra, Daniel; Raikov, Georgi
    In this article, we provide the spectral analysis of a Dirac-type operator on Z(2) by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We prove that it remains bounded outside a single threshold and obtain its main asymptotic term in the unbounded case. Interestingly, we show that the constant in the main asymptotic term encodes the interaction between a flat band and whole non-constant bands. The strategy used is the reduction of the spectral shift function to the eigenvalue counting function of some compact operator which can be studied as a toroidal pseudo-differential operator. (c) 2022 Elsevier Inc. All rights reserved.