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30 November 2021 | Story Leonie Bolleurs | Photo Supplied
Prof Johan Meyer, Senior Professor in the Department of Mathematics and Applied Mathematics, says he is looking forward to learning from others in the field during this collaboration.

What do trees, black holes, earthquakes, and time structures have in common? 

The answer to this question is that these, in one way or the other, form the focus of some of the abstracts delivered during the Annual Congress of the South African Mathematical Society. The society has as its main objective the advancement of mathematics in South Africa. 

The Department of Mathematics and Applied Mathematics at the University of the Free State (UFS), in conjunction with the South African Mathematical Society (SAMS 2021), is hosting the 64th Annual Congress of the society this week (29 November to 1 December 2021).

Prof Johan Meyer, Senior Professor in the department, says the congress, which is being conducted online, is focusing on all aspects of mathematics research, including history and teaching.

Learning from others in the field

The congress, which aims to share the latest research results in mathematics, will be attended by staff and students from universities across South Africa as well as abroad. “Anyone from the public is, of course, welcome to attend or even share their results if they are also involved in mathematics research,” adds Prof Meyer. 

He says that he is looking forward to learning from others in the field during this collaboration. 

The congress will include discussions on more than 120 abstracts, covering category theory, algebra, topology, logic; functional analysis and operator theory; finite groups and combinatorial structures; graph theory and combinatorics; lie symmetries and nonlinear differential equations; and applied and numerical mathematics.

Array of interesting topics presented

“It is important in many areas of science and engineering to predict and to simulate rare, random events, the occurrence of which may have negative or even catastrophic consequences. Examples include internet server overflows, mechanical breakdowns, floods, and financial crashes. Rare events can also have a positive effect, triggering for example chemical reactions or driving genetic evolution via random mutations.” Prof Hugo Touchette from Stellenbosch University will be shedding some light on this interesting topic in his presentation on Predicting and simulating rare events.

Prof Jeandrew Brink, Associate Professor in the Department of Mathematics and Applied Mathematics at the UFS, is presenting a plenary session on the topic Determining the geometry of strong field space-times in spite of tacitly assuming the answer during every measurement. In South Africa, state-of-the art pulsar timing data from the MeerKAT telescope will make a considerable contribution to conducting GR orbital tests. Prof Brink comments on how pulsar timing tests differ from tests using gravitational wave detectors, as well as what we can learn from the framework already employed to perform pulsar timing measurements.

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Mathematical methods used to detect and classify breast cancer masses
2016-08-10

Description: Breast lesions Tags: Breast lesions

Examples of Acho’s breast mass
segmentation identification

Breast cancer is the leading cause of female mortality in developing countries. According to the World Health Organization (WHO), the low survival rates in developing countries are mainly due to the lack of early detection and adequate diagnosis programs.

Seeing the picture more clearly

Susan Acho from the University of the Free State’s Department of Medical Physics, breast cancer research focuses on using mathematical methods to delineate and classify breast masses. Advancements in medical research have led to remarkable progress in breast cancer detection, however, according to Acho, the methods of diagnosis currently available commercially, lack a detailed finesse in accurately identifying the boundaries of breast mass lesions.

Inspiration drawn from pioneer

Drawing inspiration from the Mammography Computer Aided Diagnosis Development and Implementation (CAADI) project, which was the brainchild Prof William Rae, Head of the department of Medical Physics, Acho’s MMedSc thesis titled ‘Segmentation and Quantitative Characterisation of Breast Masses Imaged using Digital Mammography’ investigates classical segmentation algorithms, texture features and classification of breast masses in mammography. It is a rare research topic in South Africa.

 Characterisation of breast masses, involves delineating and analysing the breast mass region on a mammogram in order to determine its shape, margin and texture composition. Computer-aided diagnosis (CAD) program detects the outline of the mass lesion, and uses this information together with its texture features to determine the clinical traits of the mass. CAD programs mark suspicious areas for second look or areas on a mammogram that the radiologist might have overlooked. It can act as an independent double reader of a mammogram in institutions where there is a shortage of trained mammogram readers. 

Light at the end of the tunnel

Breast cancer is one of the most common malignancies among females in South Africa. “The challenge is being able to apply these mathematical methods in the medical field to help find solutions to specific medical problems, and that’s what I hope my research will do,” she says.

By using mathematics, physics and digital imaging to understand breast masses on mammograms, her research bridges the gap between these fields to provide algorithms which are applicable in medical image interpretation.

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