Probabilidades y simulaciones asociadas a un juego de Blackjack

En este documento se presenta un estudio de cada una de las opciones que podemos encontrar en un juego de blackjack, las diferentes permutaciones que se asocian a cada uno de los puntajes y las probabilidades asociadas a cada una de las manos que se pueden obtener. Se muestra adicionalmente un estudio de las probabilidades asociadas al procedimiento en cada uno de los estados (dos, tres, cuatro o cinco cartas) y la dependencia estadística que se asocia a la necesidad de solicitar más cartas al dealer en cada una de las posibles combinaciones de cartas que tengamos. Finalmente se presenta una simulación del juego en un archivo de Microsoft Excel R, generando diez mil juegos bajo el uso de simulación Montecarlo. En este archivo podemos utilizar el análisis básico que utiliza el programa para el análisis de todos los juegos.This document shows a study of all the options that we can find on a blackjack game, all different permutations that we can associate to each of the scores and the probabilities associated to each card’s hand that we can obtain. Also is shown a study of the probabilities associated to the procedure at each state (two, three, four or five cards) and the statistical dependance associated to the need of request another cards to the dealer in every possible combinations of cards that we have. Finally is shown a game simulation in a Microsoft Excel’s file, generating ten thousand games using Montecarlo’s simulation. We can use the basic statistical analysis of the software in this file to analyze all the games

Un enfoque de la solucion de problemas en la enseñanza de la Programacion funcional

Este documento presenta una visión de cómo enseñar a los estudiantes a programar (programación funcional) siguiendo el ciclo de Polya. Se presentan cuatro pasos de un ciclo que enseña como programarlo y los pasos tomados son una muestra del que enseña Polya al plantear y resolver problemas. El lenguaje propuesto aquí es el llamado Hanskell y el cual será presentado mediante ejemplos

Un enfoque de la solucion de problemas en la enseñanza de la Programacion funcional

Este documento presenta una visión de cómo enseñar a los estudiantes a programar (programación funcional) siguiendo el ciclo de Polya. Se presentan cuatro pasos de un ciclo que enseña como programarlo y los pasos tomados son una muestra del que enseña Polya al plantear y resolver problemas. El lenguaje propuesto aquí es el llamado Hanskell y el cual será presentado mediante ejemplos

Survival analysis of time to SARS-CoV-2 PCR negativisation to optimise PCR prescription in health workers: the Henares COVID-19 healthcare workers cohort study.

Objectives Reverse transcriptase PCR (RT-PCR) is considered the gold standard in diagnosing COVID-19. Infected healthcare workers do not go back to work until RT-PCR has demonstrated that the virus is no longer present in the upper respiratory tract. The aim of this study is to determine the most efficient time to perform RT-PCR prior to healthcare workers’ reincorporation. Materials and methods This is a cohort study of healthcare workers with RT-PCR-confirmed COVID-19. Data were collected using the medical charts of healthcare workers and completed with a telephone interview. Kaplan-Meier curves were used to determine the influence of several variables on the time to RT-PCR negativisation. The impact of the variables on survival was assessed using the Breslow test. A Cox regression model was developed including the associated variables. Results 159 subjects with a positive RT-PCR out of 374 workers with suspected COVID-19 were included. The median time to negativisation was 25 days from symptom onset (IQR 20–35 days). Presence of IgG, dyspnoea, cough and throat pain were associated with significant longer time to negativisation. Cox logistic regression was used to adjust for confounding variables. Only dyspnoea and cough remained in the model as significant determinants of prolonged negativisation time. Adjusted HRs were 0.68 (0.48–096) for dyspnoea and 0.61 (0.42–0.88) for dry cough. Conclusions RT-PCR during the first 3 weeks leads to a high percentage of positive results. In the presence of respiratory symptoms, negativisation took nearly 1 week more. Those who developed antibodies needed longer time to negativisate.pre-print396 K

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file