ALBERT

Description: The movement of atmospheric air masses can be seen as a continuous flow of gases and particles hovering over our planet, and it can be locally simplified by means of three-dimensional trajectories. These trajectories can hence be seen as a way of connecting distant areas of the globe during a given period of time. In this paper we present a mathematical formalism to construct spatial and spatiotemporal networks where the nodes represent the subsets of a partition of a geographical area and the links between them are inferred from sampled trajectories of air masses passing over and across them. We propose different estimators of the intensity of the links, relying on different bio-physical hypotheses and covering adjustable time periods. This construction leads to a new definition of spatiotemporal networks characterized by adjacency matrices giving, e.g., the probability of connection between distant areas during a chosen period of time. We applied our methodology to characterize tropospheric connectivity in two real geographical contexts: the watersheds of the French region Provence-Alpes-Côte d’Azur and the coastline of the Mediterranean Sea. The analysis of the constructed networks allowed identifying a marked seasonal pattern in air mass movements in the two study areas. If our methodology is applied to samples of air-mass trajectories, with potential implications in aerobiology and plant epidemiology, it could be applied to other types of trajectories, such as animal trajectories, to characterize connectivity between different components of the landscape hosting the animals.

Description: Copula functions can be utilized in financial applications to determine the dependence structure of the financial asset returns in the portfolio. Empirical evidence has proved the inadequacy of the multi-normal distribution, traditionally adopted to model the financial asset returns distribution. Copula functions can be employed in a flexible way for building efficient algorithms and to simulate a more adequate distribution of the financial assets. This paper aims to describe some simple statistical procedures currently employed to calibrate the copula functions to the financial market data. Furthermore, we present some useful methods for choosing which copula function better fits the real financial data. Also, some algorithms to simulate random variates from certain types of copula functions are illustrated. Finally, for illustration purposes, the previous procedures described are applied to two Italian equities. In particular, we show how to generate efficient Monte Carlo scenarios of equity log-returns in the bivariate case using different types of copula functions.

Description: The dynamics of collaboration networks of firms follow a life cycle of growth and decline. That does not imply they also become less resilient. Instead, declining collaboration networks may still have the ability to mitigate shocks from firms leaving and to recover from these losses by adapting to new partners. To demonstrate this, we analyze 21.500 R&D collaborations of 14.500 firms in six different industrial sectors over 25 years. We calculate time-dependent probabilities of firms leaving the network and simulate drop-out cascades to determine the expected dynamics of decline. We then show that deviations from these expectations result from the adaptivity of the network, which mitigates the decline. These deviations can be used as a measure of network resilience.

Description: This article explores the ongoing COVID-19 pandemic, asking how long it might last. Focusing on Bahrain, which has a finite population of 1.7M, it aimed to predict the size and duration of the pandemic, which is key information for administering public health policy. We compare the predictions made by numerical solutions of variations of the Kermack-McKendrick SIR epidemic model and Tsallis-Tirnakli model with the curve-fitting solution of the Bass model of product adoption. The results reiterate the complex and difficult nature of estimating parameters, and how this can lead to initial predictions that are far from reality. The Tsallis-Tirnakli and Bass models yield more realistic results using data-driven approaches but greatly differ in their predictions. The study discusses possible sources for predictive inaccuracies, as identified during our predictions for Bahrain, the United States, and the world. We conclude that additional factors such as variations in social network structure, public health policy, and differences in population and population density are major sources of inaccuracies in estimating size and duration.

Description: Mathematics is the engine, vehicle, driver, and language of today’s initiatives, innovations, and human endeavors. In this mathematical-driven world, the ability to perform mathematical tasks and logical reasoning is also essential in solving quotidian tasks and problems. Therefore, mathematical competency and problem-solving skills are kept as an integral component in almost every educational curriculum around the globe. However, there are numerous stumbling blocks along the way to successful teaching, conducive learning environment, and good student performances in almost all disciplines, but more prevalent and visible in mathematics. The major concerns of educators responsible for teaching mathematics and mathematics-related courses are to find effective and innovative ways to deliver mathematical content, to extend the concepts and theories beyond the classrooms, to integrate mathematics with important concepts such as gamification, data mining, learning analytics, deep learning, and effective tools such as mobile devices, learning management systems, and digital technology, and to maintain a good record of students’ performance. In online deliveries, these concerns are further escalated due to no or limited one-to-one interactions and lack of face time, to mention a few. This article investigates the efficacy and effectiveness of traditional and innovative pedagogical practices used in online mathematic courses at the University of the South Pacific (USP). It examines the interdependence of embedded activities and students’ achievement. The results indicate that these online mathematics courses were highly dominated by conventional approaches and were less interactive and engaging, resulting in lower success rates when compared to the courses from other disciplines. To recommend possible ways to enhance the quality of learning and teaching in online mathematics courses, selected online courses from the information system discipline were explored. The reasons for the high online presence in the course were investigated and activities that could lead to collaborative and active learning beyond the passive materials were data mined. The evidence drawn from the statistical analysis highlights the importance of including selected interactive and engaging activities in online learning space of mathematics courses to promote student engagement and help create a sense of community among geographically dispersed students. Overall, based on the observations and theoretical foundation from literature, it can be said that including regular and frequent active assessment strategies, such as weekly quizzes and discussion forums, could extend and promote interactive and engaging learning in online learning space.

Description: Background: Educationally designed videos have the advantage of explaining difficult concepts via graphic diagrams and dynamic illustrations. The benefits of videos will be enhanced if videos are well-designed, concise, explore scientifically correct content, and have a clear presentation.Aims: Video as an open educational resource (OER) is the cornerstone for online learning. YouTube has been widely used as a distribution platform for OER. The aim of this study was to evaluate the engagement of hand surgery videos on a dedicated education channel on YouTube.Methods: The senior author has been utilizing a YouTube channel dedicated to the education of clinicians in Hand Surgery, surgical education, and management since 2008. The degree of engagement was evaluated using YouTube Analytics, providing up-to-date metrics and reports.Results: Since 2008, there have been 6521 subscribers with 1,360,680 views, a total view time of 35,033 h and an average view time of 1.72 min. The channel views averaged 1000 views per day. There were 4,324,724 impressions with a 7.32% click-through rate, with the United States of America accounting for 23.5% of the audience. YouTube search accounted for 33.3% of the traffic source and suggested videos by others were 19.4%, and external links were 19%. Playback location was through mobile devices in 76.7%, while 16% was through the computer. The two popular playlists were “flaps in hand surgery” (50.2%) and “basic hand surgery workshop” (21.9%). Sharing by WhatsApp was most popular (27.9%) in embedded websites and apps. Overall there were 488 comments on the channel.Conclusion: This paper confirms the phenomenon of micro-learning by online learners. It is recommended that educational videos as OER should be confined to 2 min, made compatible for the mobile device, and be optimized for sharing on social media. These can be used as resources for blended learning, allowing better utilization of time for deliberate practice in surgical training.

Description: The mechanical contraction of the pumping heart is driven by electrical excitation waves running across the heart muscle due to the excitable electrophysiology of heart cells. With cardiac arrhythmias these waves turn into stable or chaotic spiral waves (also called rotors) whose observation in the heart is very challenging. While mechanical motion can be measured in 3D using ultrasound, electrical activity can (so far) not be measured directly within the muscle and with limited resolution on the heart surface, only. To bridge the gap between measurable and not measurable quantities we use two approaches from machine learning, echo state networks and convolutional autoencoders, to solve two relevant data modelling tasks in cardiac dynamics: Recovering excitation patterns from noisy, blurred or undersampled observations and reconstructing complex electrical excitation waves from mechanical deformation. For the synthetic data sets used to evaluate both methods we obtained satisfying solutions with echo state networks and good results with convolutional autoencoders, both clearly indicating that the data reconstruction tasks can in principle be solved by means of machine learning.

Description: An outer-independent double Roman dominating function (OIDRDF) of a graph G is a function h:V(G)→{0,1,2,3} such that i) every vertex v with f(v)=0 is adjacent to at least one vertex with label 3 or to at least two vertices with label 2, ii) every vertex v with f(v)=1 is adjacent to at least one vertex with label greater than 1, and iii) all vertices labeled by 0 are an independent set. The weight of an OIDRDF is the sum of its function values over all vertices. The outer-independent double Roman domination number γoidR (G) is the minimum weight of an OIDRDF on G. It has been shown that for any tree T of order n ≥ 3, γoidR (T) ≤ 5n/4 and the problem of characterizing those trees attaining equality was raised. In this article, we solve this problem and we give additional bounds on the outer-independent double Roman domination number. In particular, we show that, for any connected graph G of order n with minimum degree at least two in which the set of vertices with degree at least three is independent, γoidR (T) ≤ 4n/3.

Description: A copula-based approach is used to estimate the dependence among three lumber strength properties: modulus of elasticity (MOE), modulus of rupture (MOR), and ultimate tensile strength (UTS). MOR and UTS are destructive measurements so they cannot be obtained simultaneously for lumber specimens. The dependence modeling is possible under an appropriate experimental design with i) a shoulder group for rupture, ii) a shoulder group for tension, and iii) other groups proof loaded in either the rupture or tension mode with survivors tested to failure in the mode that was not initially tested. With a fitted copula model based on an assumption of no damage due to the proof loading procedure, we conclude that there is a strong dependence between MOR and UTS conditioning on MOE. To assess the “no damage assumption,” a graphical method with simulated data from the fitted copula model is used. It suggests that there may be some damage to the lumber specimens due to proof loading, especially for weaker lumber specimens. Information from the dependence model can potentially help reduce monitoring costs in the lumber industry.

Description: Data assimilation in models representing spatio-temporal phenomena poses a challenge, particularly if the spatial histogram of the variable appears with multiple modes. The traditional Kalman model is based on a Gaussian initial distribution and Gauss-linear forward and observation models. This model is contained in the class of Gaussian distribution and is therefore analytically tractable. It is however unsuitable for representing multimodality. We define the selection Kalman model that is based on a selection-Gaussian initial distribution and Gauss-linear forward and observation models. The selection-Gaussian distribution can be seen as a generalization of the Gaussian distribution and may represent multimodality, skewness and peakedness. This selection Kalman model is contained in the class of selection-Gaussian distributions and therefore it is analytically tractable. An efficient recursive algorithm for assessing the selection Kalman model is specified. The synthetic case study of spatio-temporal inversion of an initial state, inspired by pollution monitoring, suggests that the use of the selection Kalman model offers significant improvements compared to the traditional Kalman model when reconstructing discontinuous initial states.