SydneySCIENCE Highlights

Cracking the code: mathematics and the art of organisation

Again, it is the patterns in the world around us that have caught the eye of Associate Professor Georg Gottwald. “We are surrounded by patterns, in the fur of animals, in chemical reactions. The natural world is humming with organisation.”

It is Gottwald’s mission to mathematically explain the essence of these patterns and the generic mechanisms that form them. “Once we understand the organisation of these systems we can tap into these patterns and use them to our advantage.”

One of the systems that Gottwald works on involves the electrical signals that generate coordinated muscle contraction in heart tissue. In hospitals across the country the relationship between contraction and relaxation of heart tissue is used as an indicator of health, with abnormalities outside a certain ratio understood as a sign of instability in heart rhythms.

Gottwald’s work shows that we need to change the way we interpret deviations from this ratio, with some startling ramifications for the medical world. “This diagnostic tool is conservative, over-prescribing the need for further care. I believe we can study the relationship of these rhythms to create a much more powerful diagnostic tool,” enthuses Gottwald.

Seeking to understand all systems, Gottwald has developed a test for chaos in any data set tracked across time, such as climate temperature plots and stock market data. This test can determine if a system is chaotic or regular, without knowing the real world context.

This test for chaos has provided theoretical backing for the long used power spectrum, a well-known measure used in physics. The power spectrum has been used for decades to roughly distinguish data as either regular or chaotic. Gottwald has proved, for the first time, the mathematical theory behind these classifications.

In general a chaotic state is often the better option for biological systems. “We tend to think that chaos is bad, but in most cases it’s the best state for a system. In chaotic systems the inherent variability allows the system to respond quickly and easily to external stimuli.”

Accounting for this variability can be difficult, each aspect of a system changes at its own pace. “The weather is a very complex system with processes running on multiple spatial and temporal scales. A vortex will move slowly over a number of days, but there are also smaller faster systems that change over minutes.”

“I want to find models that describe how the large scales move, without having to incorporate every small system. I want to reduce model complexity, use fewer variables.”

To do this Gottwald first needs to know what the slow motion is, and how to describe it dynamically. Then he needs to know how to incorporate all the fast systems.

“We can’t neglect the fast components, even though they change too rapidly to feel the changes of the slow systems. We have to work out a simple way to put all variability back in.”

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