Mathematical Tools That Can Save Lives

Computers and artificial intelligence can today effectively process and review vast amounts of data. However, a basic premise behind such advanced tools is that mathematical models must be continuously developed for data to be analyzed at all.

"Mathematics can play a very important role in uncovering patterns and structures in data from various measurements and studies. With mathematics, the external world can in many cases be seen in a new light, where causal chains become much clearer", explains Cordian Riener, professor at UiT and member of the advisory panel in AlToGeLis.

The AlToGeLiS consortium:

École Polytechnique Fédérale de Lausanne (Switzerland)
Kungliga Tekniska högskolan (Sweden)
Max Planck Institute of Molecular Cell Biology and Genetics (Germany)
Massachusetts Institute of Technology (USA)
UiT The Arctic University of Norway
University of Oxford (UK)

AlToGeLis is now building an international network for researchers who develop and promote mathematical techniques for data analysis through algebra, topology, and geometry.

For the consortium, analyses of data from research in life sciences is a new and important area of focus. It includes data that can provide new knowledge about the structure, composition, and function of living organisms and biological processes.

This was really a "wow" moment for me, to understand that sophisticated mathematical tools, developed on a purely theoretical level, can contribute to saving lives.

From theory to life-saving

In such a context, mathematics forms a fundamental basis for creating tools for data analysis, especially when it comes to statistics. In recent years, a new technique called topological data analysis has created room for new approaches in the interpretation of high-dimensional data.

In the researcher network AlToGeLis, topological tools have been used, among other things, to reveal multidimensional geometric structures and spaces in the brain. In Norway, researchers Edvard Ingjald Moser and May-Britt Moser are known for having made significant advances in this field.

"I remember the first time I heard about this field of study", says Riener.

"I was at a topology conference and talking to the person next to me. I was more than surprised when she told me that she, as a cancer researcher, had developed methods for topological data analysis that help us understand which cells are more likely to develop into cancer cells", Riener explains.

"This was really a "wow" moment for me, to understand that sophisticated mathematical tools, developed on a purely theoretical level, can contribute to saving lives", he adds.

Signatures and patterns

"Topology gives us tools to understand quantitative differences between shapes and complex structures and patterns in data. For many, topology might at first glance appear as a purely theoretical endeavor, without an obvious practical value. But in research conducted over the last 150 years, there are several examples where topological analyses can provide extremely valuable insights", emphasizes Riener.

He points out that topology can be used to quantify structural properties of cells. Cell data is often collected through 3D imaging technology that is converted into point clouds representing cell formations. By using topological tools, one can identify and quantify topological signatures, such as holes and clusters, that are characteristic of cancer cells.

Diagnostic tools can in such a context be developed using machine learning that automatically recognizes cancer cells based on their unique topological properties. Then, patterns in data that are often not visible initially in a measured point cloud can be discovered.

"With these tools and mathematical structures, a bridge can be built from theory to practice. We can identify biomarkers, develop new diagnostic tools, and understand the progression of disease in a more fundamental way", says Riener.

With these tools and mathematical structures, a bridge can be built from theory to practice. We can identify biomarkers, develop new diagnostic tools, and understand the progression of disease in a more fundamental way.

Provides new impulses

"That UiT and the Lie-Størmer Center have become part of the AlToGeLis network will give new impulses to our research", says Riener.

At the Lie-Størmer Center, there is the start of an MSCA postdoc this fall, dedicated to research on geometric analyses of data. There will also be a special subject day in 2025 where the research of the AlToGeLis network will be showcased. Riener hopes such initiatives will create a breeding ground for interdisciplinary collaboration.

"I hope that colleagues within the life sciences at UiT will become more interested in participating and collaborating with our colleagues in AlToGeLis. We also want the public to gain a greater understanding of the significance that topological methods can have for neuroscience in the near future", concludes Riener.

Kortnytt fra International Cooperation Section, Faculty of Science and Technology, Faculty of Health Sciences

Bredesen, Kim kim.bredesen@uit.no Rådgiver