Shape is foundational to biology. Observing and documenting shape has fueled biological understanding as the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. To comprehensively quantify the vast morphological diversity in biology, we focus thus on Topological Data Analysis (TDA). TDA is an emerging mathematical discipline that uses principles from algebraic topology to comprehensively measure shape in a broad scope of different datasets. As a proof of concept, we explore a series of applications of TDA in plant biology with a variety of data inputs.
With the Euler Characteristic Transform and X-ray CT scans of a wide array of barley varieties, we can predict genomic markers based solely on shape characteristics of their seeds alone. With persistent homology and Molecular Cartography technology, we can model patterns of mRNA spatial localization for different genes, cell types, and organs of the soybean root and nodule. With mapper and RNAseq data, we can uncover novel lung cancer subtypes. With adjacency complex filtrations, we can describe the intricate patterns made by pavement cells in arabidopsis leaves.
The vision of TDA, that data is shape and shape is data, will be relevant as biology transitions into a data-driven era where meaningful interpretation of large datasets is a limiting factor.
I am an Assistant Professor for Data Science at the
Division of Plant Science and Technology (DPST) of the University of Missouri—Columbia (MU). I also have an adjunct appointment at MU's
Department of Mathematics. I am mainly interested in understanding and modeling plant morphology using topological data analysis (TDA). I am also interested in morphometrics, developmental plant biology, basic image processing, educational research, and data science for social justice. I go by he/él pronouns.
I got my PhD from the Department of
Computational Mathematics, Science and Engineering (CMSE) at Michigan State University. I went there for the math and I stayed for the plants. My dissertation consisted of applying tools from algebraic topology to plant shape data. Before that, I got my math degree from the
Universidad de Guanajuato with extensive support from the
Mathematics Research Center (CIMAT). During my undegraduate degree, I tried to quantify the morphology of pre-Columbian masks with TDA, and how this might reveal their culture of origin.
