A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

Educational simulation in construction: the virtual construction simulator

Students in the architecture, engineering, and construction disciplines are often challenged with visualizing and understanding the complex spatial and temporal relationships involved in designing and constructing three-dimensional (3D) structures. An evolving body of research traces the use of educational computer simulations to enhance student learning experiences through testing real-world scenarios and the development of student decision-making skills. Ongoing research at Pennsylvania State University aims to improve engineering education in construction through interactive construction project learning applications in an immersive virtual reality environment. This paper describes the first- and second-generation development of the Virtual Construction Simulator (VCS), a tool that enables students to simultaneously create and review construction schedules through 3D model interaction. The educational value and utility of VCS was assessed through surveys, focus group interviews, and a student exercise conducted in a construction management class. Results revealed VCS is a valuable and effective four-dimensional (4D) model creation and schedule review application that fosters collaborative work and greater student task focus. This paper concludes with a discussion of the findings and the future development steps of the VCS educational simulation

Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0

The effectiveness of assessment learning objects produced using pair programming

Pair Programming is a technique from the software development method eXtreme Programming (XP) whereby two programmers work closely together to develop a piece of software. A similar approach has been used to develop a set of Assessment Learning Objects (ALO). Three members of academic staff have developed a set of ALOs for a total of three different modules (two with overlapping content). In each case a pair programming approach was taken to the development of the ALO. In addition to demonstrating the efficiency of this approach in terms of staff time spent developing the ALOs, a statistical analysis of the outcomes for students who made use of the ALOs is used to demonstrate the effectiveness of the ALOs produced via this method.

Student projects: plagiarism and assessment

Within the Information Technology degree programme of the University of Reading, the students undertake a major project in their final year. The module is both a hurdle to an honours degree and significant in terms of assessment weighting. The two year history so far has shown that bad citation and plagiarism are issues, and in one case called for the due referral of a project report. In the light of experience to date, we are focusing firstly on plagiarism prevention, giving generic advice on report writing and citation practice, and secondly on detection. In the longer term, I believe we need to reflect on what capabilities we should be creating in our undergraduates and therefore what and how we should be assessing them.

Linkage disequilibrium assessment via log-linear modeling of SNP haplotype frequencies

Analyses of high-density single-nucleotide polymorphism (SNP) data, such as genetic mapping and linkage disequilibrium (LD) studies, require phase-known haplotypes to allow for the correlation between tightly linked loci. However, current SNP genotyping technology cannot determine phase, which must be inferred statistically. In this paper, we present a new Bayesian Markov chain Monte Carlo (MCMC) algorithm for population haplotype frequency estimation, particulary in the context of LD assessment. The novel feature of the method is the incorporation of a log-linear prior model for population haplotype frequencies. We present simulations to suggest that 1) the log-linear prior model is more appropriate than the standard coalescent process in the presence of recombination (>0.02cM between adjacent loci), and 2) there is substantial inflation in measures of LD obtained by a "two-stage" approach to the analysis by treating the "best" haplotype configuration as correct, without regard to uncertainty in the recombination process. Genet Epidemiol 25:106-114, 2003. (C) 2003 Wiley-Liss, Inc.

Learning from risks: A tool for post-project risk assessment

Risk management (RM) comprises of risk identification, risk analysis, response planning, monitoring and action planning tasks that are carried out throughout the life cycle of a project in order to ensure that project objectives are met. Although the methodological aspects of RM are well-defined, the philosophical background is rather vague. In this paper, a learning-based approach is proposed. In order to implement this approach in practice, a tool has been developed to facilitate construction of a lessons learned database that contains risk-related information and risk assessment throughout the life cycle of a project. The tool is tested on a real construction project. The case study findings demonstrate that it can be used for storing as well as updating risk-related information and finally, carrying out a post-project appraisal. The major weaknesses of the tool are identified as, subjectivity of the risk rating process and unwillingness of people to enter information about reasons of failure.

Integrating constructive feedback in personalised e-learning

When using e-learning material some students progress readily, others have difficulties. In a traditional classroom the teacher would identify those with difficulties and direct them to additional resources. This support is not easily available within e-learning. A new approach to providing constructive feedback is developed that will enable an e-learning system to identify areas of weakness and provide guidance on further study. The approach is based on the tagging of learning material with appropriate keywords that indicate the contents. Thus if a student performs poorly on an assessment on topic X, there is a need to suggest further study of X and participation in activities related to X such as forums. As well as supporting the learner this type of constructive feedback can also inform other stakeholders. For example a tutor can monitor the progress of a cohort; an instructional designer can monitor the quality of learning objects in facilitating the appropriate knowledge across many learners.