The Study Group

Organisation of the Study Group
The Study Group runs from Monday to Friday. On Monday the representatives from industry describe their projects of industrial origin and outline what they think needs to be done. Mathematicians then work collaboratively with industry representatives on the problems from Tuesday to Thursday in separate project groups. MISGSA participants join groups and work on which ever project suits their interest and expertise. On Friday there is summing up and report back to industry on the results obtained by each group.

Local participants
All delegates at MISGSA are expected to participate to a high degree in the modelling and problem solving small group sessions.

Moderator
Each project will be managed by a Moderator whose role will be to coordinate preliminary work including literature searches, outline any preliminary thoughts which need to be worked on, elicit contributions from all present, provide summaries throughout the workshop and assist in the preparation of a final technical report for the industrial participants. Moderators will be the leading authors in resulting publications. The travel expenses of Moderators will be paid by MISGSA.

Moderators are not expected to be experts in the field. Potential moderators should be aware that everyone will help and that we are all somewhat out of our depth to start with. The invited guests will contribute to all the problems within their area of expertise. The initial contribution of a moderator is to put together some useful information before the start of MISGSA.

Sometimes it is useful for someone on the second day, Tuesday, to briefly fill in theoretical background and this need not necessarily be the moderator. Participants interested in doing this should contact the moderator.

Student Moderator
As well as a Moderator, who is normally a member of staff, each project will have a Student Moderator. This will be an opportunity for a graduate student to learn leadership skills by working closely with the Moderator and contributing to the organisation of the Study Group. A duty of the Student Moderator will be to make the 10-15 minute progress report on Wednesday afternoon.

Lynx Geosystems Student prizes
Two prizes sponsored by Lynx Geosystems will be awarded to students for outstanding performance at MISGSA. The prizes are open to honours students, MSc and PhD students.

Prize for outstanding performance in a problem on control theory or optimization R500
Prize for outstanding performance in a problem on mathematical modelling or continuum mechanics R500

Graduate Student Workshop
A Graduate Student Workshop will be organised by Neville Fowkes from the University of Western Australia, Perth, Australia, on Saturday 26 January 2008. The aim of the workshop is to prepare graduate students who have had little or no experience at working on problems of industrial origin for the MISG which starts the following Monday.

Financial support
The following persons will be eligible for financial support for local travel and accommodation provided funds are available.:

• Moderators of problems
• Student Moderators
• Members of the Scientific Committee
• Honours students, higher degree students
• Post-doctoral Fellows

Participants may apply for financial support on the registration form.

Invited participants from overseas
Invited guests with considerable experience with Mathematics in Industry Study Groups will participate in the workshop. The invited guests are expected to maintain interest in the problems after the meeting and contribute to the writing of the reports for the Proceedings.

Invited talks
There will be several invited talks on the contribution of mathematics and mathematical modelling to solving problems in industry.

1. Compression of Hyperspectral Image Data
   Professor Steve Damelin, Unit for Advances in Mathematics and its Applications, Georgia Southern University and Professor Michael Sears, School of Computer Science, University of the Witwatersrand
   Abstract: Hyperspectral image data is obtained from airborne, spaceborne and terrestrial systems where the reflectance from each image point is sampled at a high number of spectral values (typically over a hundred) ranging across the visible and infrared regions of the electromagnetic spectrum. The information obtained allows the identification of, for example, vegetation types and mineral species, and the clustering of other image components.
   
   The processing, interpretation, and storage of this data is complicated by the huge volumes of high dimensional data obtained from even relatively small images. For example, the high spatial and spectral resolution core imaging system (Hyperspectral Core Imager) owned by AngloGold Ashanti and developed by SpecTerra Systems in Australia, which obtains hyperspectral image data from drill core for mineral identification and spatial distribution, acquires a gigabyte of data from just three metres of scanned core!
   
   Our problem concerns the compression of the massive amount of image data which are acquired by such systems. Can the data be compressed in such a way that essentially no information is lost, by exploiting the overlapping (multi-modular) spatial, and high redundancy of the spectral information?
   
   In the presentation, we shall first explain the problem of compression of Hyperspectral Core Imager data, why this is important, how the data s acquired, and why the data is multi-modular. For example we will explain how one typically finds double redundancy in core data with respect to both spatial and spectral pixels. Indeed, overlapping arises both from physical sampling and from the detectors themselves. Thus there is both sampling and data redundancy to deal with in trying to understand the nature of both the sample taken and the performance of the imaging instrument.
   
   Multi-modality may also arise because of different sources measuring different aspects of the data at the same time. For example, core data presents us with a combination of qualitative and categorical variants. In the case of double redundancy occurring naturally in overlapping data samples, say hyperspectral data from core images, we will suggest compressive sampling and wavelet techniques to remove the redundancy which is necessary for storage and transmission of images. Finally we will describe the challenge of developing methods to extract, cluster and predict patterns in an exploratory manner. In this case, we are expected to build graphs on the data by way of kernels which are adaptive, for example signature and prim-like kernels.
   
   

2. Interdisciplinary Mathematics at Georgia Southern University
   Professor Steve Damelin, Unit for Advances in Mathematics and its Applications, Georgia Southern University http://math.georgiasouthern.edu/damelin/applcenter.html
   Abstract: This talk will give an overview of our interdisciplinary mathematics centre at Georgia Southern University, The idea behind the talk is to form links with Universities in South Africa, industry in the form of student/postdoc and research collaborations.
   
   

3. Hybrid Finite Element Formulations
   J.A. Teixeira de Freitas, Departament of Civil Engineering and Architecture, Instituto Superior T?ico, Technical University of Lisbon
   Abstract: Three alternative sets of hybrid finite element formulations are presented. They are termed hybrid-mixed, hybrid and hybrid-Trefftz and differ essentially on the field conditions that the approximation functions are constrained to satisfy locally. Two models, namely the displacement and the stress models, are obtained for each formulation depending on whether inter-element continuity is enforced in terms of forces or displacements. Because they are derived from a strict hybrid approach released from the conventional node conformity concepts, these formulations allow different fields to be independently approximated, within certain consistency criteria, and enhance the use of a wide range of approximation functions, from digital functions to formal solutions of the governing systems of differential equations. The fundamental properties of the alternative formulations and models are identified and their relative merits and limitations are illustrated with numerical applications.