Analytically weak solutions to SPDEs with unbounded time-dependent differential operators and an application

We analyze the concepts of analytically weak solutions of stochastic differential equations (SDEs) in Hilbert spaces with time-dependent unbounded operators and give conditions for existence and uniqueness of such solutions. Our studies are motivated by a stochastic partial differential equation (SPDE) arising in industrial mathematics

N-Dimensional Quasipolar Coordinates - Theory and Application

In this thesis, various generalizations to the n-dimension of the polar coordinates and spherical coordinates are introduced and compared with each other and the existent ones in the literature. The proof of the Jacobian of these coordinates is very often wrongfully claimed. Currently, prior to our proof, there are only two complete proofs of the Jacobian of these coordinates known to us. A friendlier definition of these coordinates is introduced and an original, direct, short, and elementary proof of the Jacobian of these coordinates is given. A method, which we call a perturbative (not perturbation) method, is introduced so that the approach in the general case is also valid in all special cases. After the proof, the definitions of the n-dimensional quasiballs (hyperballs for n ≥ 4) and the n-dimensional quasispheres (hyperspheres for n ≥ 4) are given. The Jacobian is used to calculate the n-dimensional quasivolume of the n-dimensional quasiball and the n-dimensional quasi-surface area of the n-dimensional quasisphere directly. The formulas obtained afterwards are free of any special functions and could be introduced without any advanced mathematical knowledge. Numerical results are provided in a table followed by interpretations of these results

Smart City, Citizen Engagement, and Information System Research

The paper highlights the importance of involvement of citizens in all the steps of smart city initiatives.Therefore, authors try to identify key factors and enablers for effective engagement and involvement of citizens and residents in any smart city project

Simulations of Flow in a Solar Roof Collector Driven by Natural Convection.

The solar roof collector is modelled as a two dimensional air gap with one heated wall. The Boussinesq approximation is used to model the density variation. Four different air gap heights were simulated, namely 0.07m, 0.014m, 0,21m and 0.28m for a 2m long solar roof collector. The tilt angle of the solar collector was also varied between 15° and 55�� from horizontal. Predictions of velocities and mass flow rates in the air-gap are presented together with streamlines showing air flow patterns. The simulations show that a 0.14m air gap height at higher inclination angles is optimal for ventilation

Education as a complex system: an investigation of students’ learning behaviours in programming education using complexity approaches.

As a result of the COVID19 pandemic, more higher-level education courses have moved to online channels, raising challenges among educators in monitoring students’ learning progress. Thanks to the development of learning technologies, learning behaviours can be recorded at a more fine-grain level of detail, which can then be further analysed. Inspired by the premise of approaching education as a complex system, this research aims to develop a novel approach to analyse students’ learning behavioural data in programming education, utilising complexity methods. First, essential learning behavioural features are extracted. Second, a novel method based on Random Matrix Theory is developed to remove the noise and trend effect in the data in order to better highlight the differences in students’ learning behaviours. Third, Community Detection is applied to cluster the students into groups with similar learning behavioural characteristics. In the thesis also, motivated by a need to determine likely outcomes of students, a range of machine learning classification techniques have also been applied to predict the student learning outcomes based on behavioural data which has been cleaned of the noise and trend. The proposed approaches have been applied to datasets collected from a bespoke online learning platform in an Irish University. The datasets contain information from 566 students in different programming-related modules over a range of years encompassing pre and during the COVID19 pandemic. This gives us a unique opportunity to test our methods for the effects of the pandemic on learning. Results indicate the similarities and deviation in learning behaviours between student cohorts. Overall, we found that students interacted similarly with all course resources during the semester. However, while higher-performing students seem to be more active in practical tasks (e.g. programming exercises on labs), lower-performing students have been found to focus overmuch on lecture notes and lose their focus at the later phase of the semester. Additionally, students’ learning behaviours in a conventional university setting tend to differ significantly to those students in a fully online setting during the pandemic. We have also attempted to reduce the noise component in the data and the experimental results further demonstrate the better prediction performance of models which are trained based on the cleaned dataset, in comparison with the original dataset. Recommendations for current educational practice are made, including the continuous analysis of learning behaviours by the proposed methods and suggestions for the prompt interventions to in order to max- imise student supports

From SMOTE to Mixup for Deep Imbalanced Classification

Given imbalanced data, it is hard to train a good classifier using deep learning because of the poor generalization of minority classes. Traditionally, the well-known synthetic minority oversampling technique (SMOTE) for data augmentation, a data mining approach for imbalanced learning, has been used to improve this generalization. However, it is unclear whether SMOTE also benefits deep learning. In this work, we study why the original SMOTE is insufficient for deep learning, and enhance SMOTE using soft labels. Connecting the resulting soft SMOTE with Mixup, a modern data augmentation technique, leads to a unified framework that puts traditional and modern data augmentation techniques under the same umbrella. A careful study within this framework shows that Mixup improves generalization by implicitly achieving uneven margins between majority and minority classes. We then propose a novel margin-aware Mixup technique that more explicitly achieves uneven margins. Extensive experimental results demonstrate that our proposed technique yields state-of-the-art performance on deep imbalanced classification while achieving superior performance on extremely imbalanced data. The code is open-sourced in our developed package https://github.com/ntucllab/imbalanced-DL to foster future research in this direction.Comment: 25 pages, 3 figures. The paper is accepted by TAAI 202