Granular approach to adaptivity in problem-based learning

Constructivist approach to learning has been around for quite some time. The constructivist theory has resulted in the development of a wide variety of learning environments, however the problem-based learning (PBL) environment is one of the most ideal and most popular area that implements the constructivism theory. PBL is an attractive approach to foster learner's critical problem solving and self-directed learning skills. However, it is difficult to implement effective PBL environments. A majority of existing PBL environments suffers from the fact that the students easily get inundated by the fine granularity of the problems and loose focus of overall aims of the learning process. This project has introduced student adaptivity technology into PBL environments to improve the effectiveness and efficiency of the learning process. To demonstrate the idea of PBL with student adaptivity, a web-based prototype is implemented in Process Costing, within the field of Accounting. Based on the architecture of the web-based intelligent educational systems, the problem base module is introduced. The basic architecture of the system is a typical three-tier, client-server structure. The client tier has the presentation interfaces that are implemented as HTML frames and run in a web browser. The application programs for performing adaptation, which were developed using PHP, reside in the middle layer, and communicate directly with the backend database: problem base, knowledge base that is the third tier. The web server as the communication channel also resides in the middle tier. With the system, students work on the real world costing calculation problems, and the system evaluates students' performance results on the problems to provide adaptation to the students. In summary, this project has successfully introduced the student adaptivity into the PBL environment. The strategies used in this thesis can be applied into the pure PBL educational systems to improve their adaptation capability

A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems

Extreme mass ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical modelling of these binary systems is extremely challenging because the scales involved expand over several orders of magnitude. One needs to handle large wavelength scales comparable to the size of the massive black hole and, at the same time, to resolve the scales in the vicinity of the small companion where radiation reaction effects play a crucial role. Adaptive finite element methods, in which quantitative control of errors is achieved automatically by finite element mesh adaptivity based on posteriori error estimation, are a natural choice that has great potential for achieving the high level of adaptivity required in these simulations. To demonstrate this, we present the results of simulations of a toy model, consisting of a point-like source orbiting a black hole under the action of a scalar gravitational field.Comment: 29 pages, 37 figures. RevTeX 4.0. Minor changes to match the published versio

About Adaptive Coding on Countable Alphabets: Max-Stable Envelope Classes

In this paper, we study the problem of lossless universal source coding for stationary memoryless sources on countably infinite alphabets. This task is generally not achievable without restricting the class of sources over which universality is desired. Building on our prior work, we propose natural families of sources characterized by a common dominating envelope. We particularly emphasize the notion of adaptivity, which is the ability to perform as well as an oracle knowing the envelope, without actually knowing it. This is closely related to the notion of hierarchical universal source coding, but with the important difference that families of envelope classes are not discretely indexed and not necessarily nested. Our contribution is to extend the classes of envelopes over which adaptive universal source coding is possible, namely by including max-stable (heavy-tailed) envelopes which are excellent models in many applications, such as natural language modeling. We derive a minimax lower bound on the redundancy of any code on such envelope classes, including an oracle that knows the envelope. We then propose a constructive code that does not use knowledge of the envelope. The code is computationally efficient and is structured to use an {E}xpanding {T}hreshold for {A}uto-{C}ensoring, and we therefore dub it the \textsc{ETAC}-code. We prove that the \textsc{ETAC}-code achieves the lower bound on the minimax redundancy within a factor logarithmic in the sequence length, and can be therefore qualified as a near-adaptive code over families of heavy-tailed envelopes. For finite and light-tailed envelopes the penalty is even less, and the same code follows closely previous results that explicitly made the light-tailed assumption. Our technical results are founded on methods from regular variation theory and concentration of measure

Adaptive Wireless Networking

This paper presents the Adaptive Wireless Networking (AWGN) project. The project aims to develop methods and technologies that can be used to design efficient adaptable and reconfigurable mobile terminals for future wireless communication systems. An overview of the activities in the project is given. Furthermore our vision on adaptivity in wireless communications and suggestions for future activities are presented