Quantitative methods to determine the student workload: II. Statistical models for the microcurricular performance indicators.

Previously, we observed that the student workload follows an inverse relation with the learning rate (an application of the kinematic notion of speed contextualized to the learning process). Motivated by this finding, we propose a quantitative estimation of the learning rate using a different source of information: the historical records of final grades of a given course. According to empirical data analyzed in other similar studies, the distribution functions of final grades exhibit a regular pattern: a Gaussian behavior for the approval region and a homogeneous distribution for the failed one. This fact is combined with the incidence of student elimination-desertion rules for introducing two simple agent-based models. Our analysis is complemented by revisiting the performance indicators typically employed to characterize the student promotion and progression. We discuss some other performance indicators to characterize the learning advancement of students: the group learning rate and the learning curve. We compare the results of Monte Carlo simulations with empirical data, observing a good agreement in the behavior of performance indicators derived from these sources. This analysis suggests an adaptive method for the readjustment of the student workload (the number of academic credits) considering the group learning rates during a follow-up period, which resembles the readjustment of prices of goods (and services) in correspondence with the evolution of supply and demand.

Quantitative methods to determine the student workload. I. Empirical study based on digital platforms.

We present a quantitative study of an online course developed during COVID19 sanitary emergency in Chile. We reconstruct the teaching-learning process considering the activity logs on digital platforms in order to answer the question of How do our students study? The results from the analysis evidence the complex adaptive character of the academic environment, which exhibits regularities similar to those found in financial markets (e.g., distributions of the daily time devoted to learning activities follow patterns like Pareto's or Zipf's law). Our empirical results illustrate (i) the relevance of economic notions in the understanding of the teaching-learning processes and (ii) the reliability of quantitative methods based on digital platforms to conduct experimental studies in this framework. We introduce in the present work a series of indicators to characterize the performance of professors, students' follow-up of the course, and their learning progress by crossing information with the results of assessments. In this context, the learning rate appears as a key statistical descriptor for the allocation of the student workload.

Fluctuations in measured radioactive decay rates inside a modified Faraday cage: Correlations with space weather.

For several years, reports have been published about fluctuations in measured radioactive decay time-series and in some instances linked to astrophysical as well as classical environmental influences. Anomalous behaviors of radioactive decay measurement and measurement of capacitance inside and outside a modified Faraday cage were documented by our group in previous work. In the present report, we present an in-depth analysis of our measurement with regard to possible correlations with space weather, i.e. the geomagnetic activity (GMA) and cosmic-ray activity (CRA). Our analysis revealed that the decay and capacitance time-series are statistically significantly correlated with GMA and CRA when specific conditions are met. The conditions are explained in detail and an outlook is given on how to further investigate this important finding. Our discovery is relevant for all researchers investigating radioactive decay measurements since they point out that the space weather condition during the measurement is relevant for partially explaining the observed variability.

Extended canonical Monte Carlo methods: Improving accuracy of microcanonical calculations using a reweighting technique.

Velazquez and Curilef [J. Stat. Mech. (2010); J. Stat. Mech. (2010)] have proposed a methodology to extend Monte Carlo algorithms that are based on canonical ensemble. According to our previous study, their proposal allows us to overcome slow sampling problems in systems that undergo any type of temperature-driven phase transition. After a comprehensive review about ideas and connections of this framework, we discuss the application of a reweighting technique to improve the accuracy of microcanonical calculations, specifically, the well-known multihistograms method of Ferrenberg and Swendsen [Phys. Rev. Lett. 63, 1195 (1989)]. As an example of application, we reconsider the study of the four-state Potts model on the square lattice L×L with periodic boundary conditions. This analysis allows us to detect the existence of a very small latent heat per site qL during the occurrence of temperature-driven phase transition of this model, whose size dependence seems to follow a power law qL(L)∝(1/L)z with exponent z≃0.26±0.02. Discussed is the compatibility of these results with the continuous character of temperature-driven phase transition when L→+∞.

Improving the efficiency of Monte Carlo simulations of systems that undergo temperature-driven phase transitions.

Recently, Velazquez and Curilef proposed a methodology to extend Monte Carlo algorithms based on a canonical ensemble which aims to overcome slow sampling problems associated with temperature-driven discontinuous phase transitions. We show in this work that Monte Carlo algorithms extended with this methodology also exhibit a remarkable efficiency near a critical point. Our study is performed for the particular case of a two-dimensional four-state Potts model on a square lattice with periodic boundary conditions. This analysis reveals that the extended version of Metropolis importance sampling is more efficient than the usual Swendsen-Wang and Wolff cluster algorithms. These results demonstrate the effectiveness of this methodology to improve the efficiency of MC simulations of systems that undergo any type of temperature-driven phase transition.

Normal and hyperspherical mode analysis of NO-doped Kr crystals upon Rydberg excitation of the impurity.

Molecular dynamics simulations and both normal mode and hyperspherical mode analyses of NO-doped Kr solid are carried out in order to get insights into the structural relaxation of the medium upon electronic excitation of the NO molecule. A combined study is reported on the time evolution of the cage radius and on the density of vibrational states, according to the hyperspherical and normal mode analyses. For the hyperspherical modes, hyper-radial and grand angular contributions are considered. For the normal modes, radial and tangential contributions are examined. Results show that the first shell radius dynamics is driven by modes with frequencies at approximately 47 and approximately 15 cm-1. The first one is related to the ultrafast regime where a large part of the energy is transmitted to the lattice and the second one to relaxation and slow redistribution of the energy. The density of vibrational states gamma(omega) is characterized by a broad distribution of bands peaking around the frequencies of approximately 13, approximately 19, approximately 25, approximately 31, approximately 37, approximately 47, and approximately 103 cm-1 (very small band). The dominant modes in the relaxation process were at 14.89, 23.49, and 53.78 cm-1; they present the largest amplitudes and the greatest energy contributions. The mode at 14.89 cm-1 is present in both the fit of the first shell radius and in the hyper-radial kinetic energy spectrum and resulted the one with the largest amplitude, although could not be revealed by the total kinetic energy power spectrum.