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07 September 2018 Photo Stephen Collett
Mathematician makes popular contribution to science Prof Atangana
Prof Atangana is the first African under 40 years of age to be selected as African Academic of Science affiliated in Mathematics. He recently delivered his inaugural lecture and is pictured with Eelco Lukas, Director of the Institute for GroundwaterStudies at the UFS (middle) and Prof Hendri Kroukamp, Acting Vice-Rector: Academic

Prof Abdon Atangana, researcher in the Institute for Groundwater Studies at the University of the Free State (UFS), recently delivered his inaugural lecture on the topic: Understanding God’s Nature with Non-Local Operators.

His research interests are methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling. Prof Atangana is the founder of the fractional calculus with non-local and non-singular kernels popular in applied mathematics today. He has introduced more than 12 mathematical operators, most of which bear his name (such as the Atangana-Baleanu fractional integral).

He stated: “We will not stop until we change the classical view of doing mathematics. Mathematics is not a subject but a tool given to mankind by God to understand nature. One single mathematical operator cannot portray God’s nature accurately. Therefore the Atangana Baleanu was suggested.”

New weapons

Most physical problems can be expressed in terms of mathematical formulations called differential equations. According to him the differential equation’s aim is to analyse, understand, and predict the future of a physical problem. Prof Atangana introduced the Atangana-Baleanu fractional integral. This brought new weapons into applied mathematics to model complex real-world problems more accurately.

Prof Atangana explained: “The Atangana-Baleanu fractional derivative is able to describe real-world problems with different scales, or problems that change their properties during time and space for instance, the spread of cancer, the flow of water within heterogeneous aquifers, movement of pollution within fractured aquifers, and many others. This crossover behaviour is observed in many empirical systems.”

Sudden change

The Atangana-Baleanu fractional derivative is also able to describe physical or biological phenomena, such as a heart attack, the physiological progression from life to death, structural failure in an aeroplane, and many other physical occurrences with sudden change with no steady state.

The new differential and integral operators are nowadays in fashion and are being applied with great success in many fields to model complex natural phenomena. It is believed that the future of modelling complex real-world problems relies on these non-local operators.

News Archive

Eye tracker device a first in Africa
2013-07-31

 

 31 July 2013

Keeping an eye on empowerment

"If we can see what you see, we can think what you think."

Eye-tracking used to be one of those fabulous science-fiction inventions, along with Superman-like bionic ability. Could you really use the movement of your eyes to read people's minds? Or drive your car? Or transfix your enemy with a laser-beam?

Well, actually, yes, you can (apart, perhaps, from the laser beam… ). An eye tracker is not something from science fiction; it actually exists, and is widely used around the world for a number of purposes.

Simply put, an eye tracker is a device for measuring eye positions and eye movement. Its most obvious use is in marketing, to find out what people are looking at (when they see an advertisement, for instance, or when they are wandering along a supermarket aisle). The eye tracker measures where people look first, what attracts their attention, and what they look at the longest. It is used extensively in developed countries to predict consumer behaviour, based on what – literally – catches the eye.

On a more serious level, psychologists, therapists and educators can also use this device for a number of applications, such as analysis and education. And – most excitingly – eye tracking can be used by disabled people to use a computer and thereby operate a number of devices and machines. Impaired or disabled people can use eye tracking to get a whole new lease on life.

In South Africa and other developing countries, however, eye tracking is not widely used. Even though off-the-shelf webcams and open-source software can be obtained extremely cheaply, they are complex to use and the quality cannot be guaranteed. Specialist high-quality eye-tracking devices have to be imported, and they are extremely expensive – or rather – they used to be. Not anymore.

The Department of Computer Science and Informatics (CSI) at the University of the Free State has succeeded in developing a high-quality eye tracker at a fraction of the cost of the imported devices. Along with the hardware, the department has also developed specialised software for a number of applications. These would be useful for graphic designers, marketers, analysts, cognitive psychologists, language specialists, ophthalmologists, radiographers, occupational and speech therapists, and people with disabilities. In the not-too-distant future, even fleet owners and drivers would be able to use this technology.

"The research team at CSI has many years of eye-tracking experience," says team leader Prof Pieter Blignaut, "both with the technical aspect as well as the practical aspect. We also provide a multi-dimensional service to clients that includes the equipment, training and support. We even provide feedback to users.

"We have a basic desktop model available that can be used for research, and can be adapted so that people can interact with a computer. It will be possible in future to design a device that would be able to operate a wheelchair. We are working on a model incorporated into a pair of glasses which will provide gaze analysis for people in their natural surroundings, for instance when driving a vehicle.

"Up till now, the imported models have been too expensive," he continues. "But with our system, the technology is now within reach for anyone who needs it. This could lead to economic expansion and job creation."

The University of the Free State is the first manufacturer of eye-tracking devices in Africa, and Blignaut hopes that the project will contribute to nation-building and empowerment.

"The biggest advantage is that we now have a local manufacturer providing a quality product with local training and support."

In an eye-tracking device, a tiny infra-red light shines on the eye and causes a reflection which is picked up by a high-resolution camera. Every eye movement causes a change in the reflection, which is then mapped. Infra-red light is not harmful to the eye and is not even noticed. Eye movement is then completely natural.

Based on eye movements, a researcher can study cognitive patterns, driver behaviour, attention spans, even thinking patterns. A disabled person could use their eye-movements to interact with a computer, with future technology (still in development) that would enable that computer to control a wheelchair or operate machinery.

The UFS recently initiated the foundation of an eye-tracking interest group for South Africa (ETSA) and sponsor a biennial-eye tracking conference. Their website can be found at www.eyetrackingsa.co.za.

“Eye tracking is an amazing tool for empowerment and development in Africa, “ says Blignaut, “but it is not used as much as it should be, because it is seen as too expensive. We are trying to bring this technology within the reach of anyone and everyone who needs it.”

Issued by: Lacea Loader
Director: Strategic Communication

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