Making sense of complex processes: Uncovering hidden structure in sequential data
Alexander van Werde created methods to reveal hidden barriers and simplify complex data, helping improve understanding of dynamic systems across science and technology.
From the movements of animals and molecules to the flow of traffic or financial trends, sequential data, meaning data where the order of events matters, is present in many areas. For his PhD research, Alexander van Werde developed new mathematical tools to understand the hidden structure behind such processes. His work sheds new light on how to detect barriers that influence movement and how to simplify complex data by revealing underlying patterns.
Given the originality of his research, Alexander van Werde was awarded his PhD cum laude, an award given to only the top five percent of doctoral graduates at 果冻传媒.
Discovering invisible barriers in movement
In many scientific fields, researchers study the movements of animals, molecules, or other entities over time. However, these movements can be influenced by unseen factors, such as rivers or roads that animals avoid or hidden structures inside cells.
In the first part of his PhD thesis, Alexander van Werde explored how to detect such barriers, which partially restrict movement. Using mathematical models based on Brownian motion, he showed how different data collection strategies, such as longer observation periods or more frequent measurements, affect our ability to detect these unseen influences.
His findings revealed three distinct situations. In the first situation, barrier recovery is gradual but reliable. In the second, frequent observations allow for the much faster recovery. Finally, short observation periods only provide partial insights into the barriers encountered.
These results are useful for fields such as ecology and microbiology, where movement patterns often reveal hidden structures in natural systems.
Simplifying complex data using spectral methods
The second part of Van Werde鈥檚 thesis addresses another major challenge: how to make sense of complex datasets where a system can be in many different states at the same time. This type of data is hard to interpret unless it is simplified.
To make this easier, Van Werde focused on spectral methods. These rely on mathematical properties of matrices to uncover structure in the data, such as groups or repeating patterns.
Many existing approaches assume observations are independent, but this does not hold for data collected from ongoing processes where past events influence future ones.
Van Werde developed new theoretical tools to analyze matrices built from such dependent data. This required new ways of reasoning since the data points are no longer independent.
His results provide new understanding for areas such as clustering states in time-based models and studying the structure of networks.
A broader research environment
Van Werde carried out his research within the (Statistics, Probability, and Operations Research) at 果冻传媒. This cluster is closely connected to , a well-known institute that helps make Eindhoven an internationally recognized center for research in stochastics.
The project was financially supported by the Dutch Research Council (NWO) as part of the research programme , within the Open Competition Domain Science 鈥� M.
PhD researcher Alexander van Werde
Understanding complex systems through simpler models
By combining rigorous mathematics with real world motivation, Van Werde鈥檚 thesis provides valuable tools for analyzing systems that change over time, ranging from biological and ecological systems to complex digital environments.
With this research, Alexander van Werde contributes to the growing field of sequential data analysis. His work enables scientists and engineers to extract meaningful structure from data that is otherwise difficult to interpret.
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Supervisors
Jaron Sanders, Sem Borst
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