The hydrodynamic flow of an incompressible and isotropic Casson fluid through a yawed cylinder is investigated by employing continuity, momentum, and energy equations satisfying suitable boundary conditions. The density variation is governed by Boussinesq approximation. The model equations consisting of coupled partial differential equations (PDEs) are transformed by applying non-similar transformation relations. The set of transformed PDEs is solved using the analytical technique of homotopy analysis method (HAM). The impacts of varying yaw angle, and mixed convection and Casson parameters over fluid velocity (chordwise and spanwise components), its temperature, Nusselt number, and skin friction coefficients are investigated and explained through various graphs. It is found that the enhancing yaw angle, Casson parameter, and convection parameter augment the fluid velocity, heat transfer rate, and skin friction and reduce the fluid temperature. The agreement of present and published results justifies the application of HAM in modeling the mixed convective Casson fluid flow past a yawed cylinder.
In this research study, we propose an Explainable Artificial Intelligence (XAI) model that provides the earliest possible global and local interpretation of students' performance at various stages of course length. Global and local interpretation is provided in such a way that the prediction accuracy of a single local observation is close to the model's overall prediction accuracy. For the earliest possible understanding of student performance, local and global interpretation is provided at 20%, 40%, 60%, 80%, and 100% of course length. Machine Learning (ML) and Deep Learning (DL) which are subfields of Artificial Intelligence (AI) have recently emerged to assist all educational institution's in predicting the performance, engagement, and dropout rate of online students. Unfortunately, traditional ML and DL techniques lack in providing data analysis results in an understandable human way. Explainable AI (XAI), a new branch of AI, can be used in educational settings, specifically in VLEs, to provide the instructor with the study performance results of thousands or even millions of online students in a humanunderstandable way. Thus, unlike black box approaches such as traditional ML and DL techniques, XAI can help instructors to interpret the strengths and weaknesses of an individual student, providing them with timely personalized feedback and guidance. Various traditional and various ensemble ML algorithms were trained on demographic, clickstream, and assessment features to determine which algorithm gives the best performance result. The best-performing ML algorithm was ultimately selected and provided to the XAI model as an input for local and global interpretation of students' study behavior at various percentages of course length. We have used various XAI tools to give students' performance reports to instructors, in an explicable human way, at different stages of course length. The intermediate data analysis and performance reports will help instructors and all key stakeholders in decision-making and optimally facilitate online students.
Several distinct entrainment patterns can occur in the FitzHugh–Nagumo (FHN) model under external periodic forcing. Investigating the FHN model under different types of periodic forcing reveals the existence of multiple disconnected 1:1 entrainment segments for constant, low enough values of the input amplitude when the unforced system is in the vicinity of a Hopf bifurcation. This entrainment structure is termed polyglot to distinguish it from the single 1:1 entrainment region ( monoglot) structure typically observed in Arnold tongue diagrams. The emergence of polyglot entrainment is then explained using phase-plane analysis and other dynamical system tools. Entrainment results are investigated for other slow-fast systems of neuronal, circadian, and glycolytic oscillations. Exploring these models, we found that polyglot entrainment structure (multiple 1:1 regions) is observed when the unforced system is in the vicinity of a Hopf bifurcation and the Hopf point is located near a knee of a cubic-like nullcline.
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