My research aims to develop advanced techniques to uncover hidden patterns, particularly in the fields of biomedicine and complex systems.
Mathematical methods developed
– Clustering Algorithms: Developed stable hierarchical clustering based on persistent homology. These algorithms are designed to outperform standard methods when dealing with multiclustering phenomena and meaningful outliers. sc26
– Topological Data Analysis (TDA): Applying persistent homology to analyze gene expression databases
and experimental images of malignant cell invasion of healthy tissue. springer22 plos20 bioarxiv19
– Parameter identification with uncertainty quantification: Utilizing Bayesian inference within data-driven frameworks to identify model parameters with quantified uncertainty in epidemiological models and to devise pattern based diagnosis tools. rip22 maid22 jmi22
– Biofilm Modeling: Using stochastic behavior rules and hybrid models to process experimental data on bacterial spreading patterns, which enables the prediction of complex biofilm dynamics and their responses to antibiotics cnsns18
Primary Methodologies
– Persistent Homology: Used to track how the «shape» of data changes across different scales. sc26 springer22 plos20 bioarxiv19
– Wasserstein Distances: Optimal transport metrics used to compare pattern in images, profiles, and persistence diagrams. sc26
– Fermat Distance: A metric applied to gene expression data to enhance the separation of data clusters. bioarxiv19
– Hybrid Modeling: Combining discrete data points with continuum descriptions to simulate biological growth cnsns18
– Bayesian formulations: including Plackett-Luce approaches for discrete set-ups jmi22 rip22
