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Individual undergraduate learners have heterogeneous knowledge backgrounds and undergo diverse learning experiences during their university studies. Consequently, designs of virtual learning environments should adjust to learners' needs and competencies, especially in the current pandemic crisis. This paper discusses pedagogical aspects of personalized and self-regulated learning and situates its focus on design, implementation, and scale of e-content and e-activities for individualized learning pathways (ILP). Characteristics of ILP such as shape, length, and turning points enabled through adaptive features of existing Learning Management Systems (LMS) have seldom been discussed in the literature. We tackle this issue from a didactical perspective of microlearning with regards to three adaptive learning strategies: 1) Feedback Adaptations, 2) Task Design, and 3) Task Sequence Design. Within a first phase of a complete initial Design Research (DR) cycle, we have collected and analysed data which enable us to generate, cluster and label queries and differentiated items for each of the three strategies. Further on, we offer a visualization of possible ILP illustrated with contextual examples of productive, technology-based task and feedback designs applicable and scalable in higher education settings.
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In the present investigation, new explicit approaches by the Milstein method and increment function of the Jacobian derivative of the drift coefficient are designed. Several numerical tests such as Cox–Ingersoll–Ross process, stochastic Brusselator, and Davis-Skodje system are presented to illustrate the accuracy and the efficiency of our schemes. Furthermore, we show that the strong convergence rate of our procedures is approximately one.
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This study presents a novel numerical method to solve PDEs with the fractional Caputo operator. In this method, we apply the Newton interpolation numerical scheme in Laplace space, and then, the solution is returned to real space through the inverse Laplace transform. The Newton polynomial provides good results as compared to the Lagrangian polynomial, which is used to construct the Adams–Bashforth method. This procedure is used to solve fractional Buckmaster and diffusion equations. Finally, a few numerical simulations are presented, ensuring that this strategy is highly stable and quickly converges to an exact solution.
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The application field of big data technology is very wide. In any industry, data and information can be analyzed through big data, and the results of these analysis are of high practical value. However, with the advent of the Internet era today, various fields are constantly developing, including the education circle. Using network education to carry out a series of teaching activities, can comprehensively improve the effectiveness of education. In the current COVID-19 epidemic, many schools and many industries have adopted computer technology and big data technologies, such as web conferencing, online classroom, remote conferencing, remote video and other teaching and production activities. This paper focuses on the role and value of computer data analysis in applied mathematics. The research shows that cloud data analysis has super high application value in applied mathematics. © 2022 SPIE
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The COVID-19 pandemic has led to the abrupt assumption in the university context, of the distance education to guarantee the continuity of the teaching-learning process (PEA), in which virtuality plays a decisive role. There is evidence of a growing introduction of this modality;however, shortcomings related to its use were revealed in the PEA of the Applied Mathematics curriculum on Health Information Systems career, at the University of Medical Sciences of Santiago de Cuba. In correspondence with ministerial methodological guidelines, the curriculum was virtualized, in the course-by-meeting mode, taking into account technological, organizational and pedagogical aspects;under the guidance of theoretical methods such as analysis and synthesis, historical-logical, and systemic-structural;and empirical methods such as scientific observation and documentary review. The space created in the Virtual Health University of Santiago de Cuba, allows the continuity of the PEA in the midst of the restrictive measures established. Greater independence, self-preparation and protagonism of the actors involved, and an adequate level of essentials are guaranteed, and the rational use of Information and Communication Technologies is encouraged.
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In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined;also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.
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We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.
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The purpose of this study is to introduce a new T-X family lifetime distribution known as exponentiated exponential-inverse Weibull, and we refer to this distribution as EE-IW. The new model’s basic mathematical characteristics are studied. The maximum likelihood (ML) estimator (MLE) approach is used to estimate the parameters. A Monte Carlo simulation is done to examine the behavior of the estimators. Finally, a real-world dataset is utilized to show the utility of the proposed model in many industries and to compare it to well-known distributions.
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Even though vaccines for coronavirus are increasingly available, it will be many months before sufficient herd immunity is achieved. Thus, testing remains a key tool for those managing health care and making policy decisions. Test errors, both false positive tests and false negative tests, mean that the surface positivity (the observed fraction of tests that are positive) does not accurately represent the incidence rate (the unobserved fraction of individuals infected with coronavirus). In this report, directed to individuals tasked with providing analytical advice to policymakers, we describe a method for translating from the surface positivity to a point estimate for the incidence rate, then to an appropriate range of values for the incidence rate, and finally to the risk (defined as the probability of including one infected individual) associated with groups of different sizes. The method is summarized in four equations that can be implemented in a spreadsheet or using a handheld calculator. We discuss limitations of the method and provide an appendix describing the underlying mathematical models.
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In a pandemic, healthcare decisionmakers face the challenge of allocating critical, but scarce healthcare resources in a dynamic, uncertain environment. Their decisions will not only affect the patients coming to the hospital for treatment, but also the Military Treatment Facility's personnel responsible. The decisionmaker must decide how to allocate these resources to achieve multiple, conflicting objectives under multiple constraints. In response, we propose a methodology for the implementation of both Portfolio Decision Analysis and Goal Programming. The steps of this methodology provide a framework with which the decisionmaker can develop optimal allocation of resources. This framework was then applied to a notional case study using both a linear value function and a piecewise value function to show the effect of non-linear value functions on each method. Complementary analysis was conducted to illustrate insights into the model and the problem itself. This application showed the merits of both models. Both, using the framework provided, allow for as much fidelity as required by the situation. Each model can be updated to account for the dynamic environment or based on analysis performed. The flexibility and adaptability of these models is especially useful in our problem.
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As the COVID-19 pandemic continues, mathematical epidemiologists share their views on what models reveal about how the disease has spread, the current state of play and what work still needs to be done.
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Foundation of Applied Mathematics is one of the mathematics servicing courses for Diploma of Applied Science programme in Universiti Teknologi MARA (UiTM), Malaysia. This course was previously taught in a physical classroom using direct confrontation. A few negative factors were found to contribute to the course's failure rate: i) inadequate exercises, ii) poor study habit and iii) reluctance to consult the lecturer oropting to study with peers only. Due to the ongoing COVID-19outbreak, the students are forced to do independent learning at home. Ascribable to this issue, the lecturers were inspired to investigate their students' motivation and participation in this course, which associate to their self-regulated learning (SRL). This paperpresents the implementation of open and distance learning (ODL) in teaching the subject of Foundation ofApplied Mathematics. The ODL was intended to promote SRL for student, thereby increasing their motivationand participation in learning activities. At present, no literature has been found study on SRL in current ODLmethod, mainly for this course. Online questionnaires were collected at the end of March - July 2020 academic semester to investigate students' perceptions on ODL and its effects to Self-Regulated Learning (SRL). Descriptive analysis was used to analyze the data. The findings indicated that the level of agreement for ODL has positive contributions to the students' SRL.
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We present a collection of selected materials from the All-Russian Conference "Scientific Services & Internet (SSI-2021), which took place on September 20-23, 2021 at Keldysh Institute of Applied Mathematics in Moscow, Russia. However, because of the worldwide COVID-19 crisis, SSI-2021 had to take place online. The issues discussed at the conference include: digital libraries, information systems, knowledge representation, national bibliographic systems, ontology engineering, parallel computing, Semantic Web, situational modeling. © 2021 Copyright for this paper by its authors.
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BACKGROUND: To understand the impact and volume of coronavirus (COVID-19) crisis, univariate analysis is tedious for describing the datasets reported daily. However, to capture the full picture and be able to compare situations and consequences for different countries, multivariate analytical models are suggested in order to visualize and compare the situation of different countries more accurately and precisely. AIMS: We aimed to utilize data analysis tools that display the relative positions of data points in fewer dimensions while keeping the variation of the original data set as much as possible, and cluster countries according to their scores on the formed dimensions. METHODS: Principal component analysis (PCA) and Partitioning around medoids (PAM) clustering algorithms were used to analyze data of 56 countries, 82 countries and 91 countries with COVID-19 at three time points, eligible countries included in the analysis are those with total cases of 500 or more with no missing data. RESULTS: After performing PCA, we generated two scores: Disease Magnitude score that represents total cases, total deaths, total actives cases, and critically ill cases, and Mortality Recovery Ratio score that represents the ratio between total deaths to total recoveries in any given country. CONCLUSION: Accurate multivariate analyses can be of great value as they can simplify difficult concepts, explore and communicate findings from health datasets, and support the decision-making process.