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Suyoung Choi (Ajou University)
Topological Data Analysis for Non-Destructive Testing in Civil Engineering
We explore the potential applications of industrial mathematics in civil engineering, with a focus on non-destructive testing (NDT). In particular, we introduce topological data analysis (TDA) techniques that can enhance model performance when analyzing ground-penetrating radar (GPR) survey images.
RNA Landscape Analysis via Combinatorial Hodge Decomposition
Yusuke Imoto (Kyoto University)
Cell differentiation can be conceptualized as movement on Waddington’s epigenetic landscape, yet reconstructing this landscape from high-dimensional single-cell data remains challenging. Here, we propose landscape analysis, a novel framework for single-cell RNA-seq data that reconstructs an RNA landscape, which is Waddington’s landscape-like structure, and performs downstream dynamical analysis utilizing this landscape. Single-cell RNA-seq measures transcript levels for approximately 20,000 genes per cell, producing a high-dimensional expression matrix. By applying RNA velocity, we convert these static profiles into vectors that predict each cell’s future transcriptional trajectory. We then perform Hodge decomposition on this velocity field to extract the potential that forms the gradient component. The resulting potential surface defines the RNA landscape’s height. Finally, by geometrically or statistically analyzing the potential, we derive biologically meaningful insights such as single-cell trajectories, time-resolved differential expression dynamics, and gene functions in cell differentiation. We applied landscape analysis to time-series scRNA-seq data of the PGCLC induction system, identifying differentiation pathways and candidate genes driving induction.
Junwon You (POSTECH)
PHLP: Interpretable Link Prediction via Persistent Homology and Its Extension to Knowledge Graph Completion
We introduce PHLP, a novel and interpretable link prediction framework that utilizes persistent homology to extract topological features from local subgraphs. Unlike conventional GNN-based methods, PHLP offers a transparent feature extraction process that captures topological patterns underlying graph connectivity. PHLP achieves near–state-of-the-art performance across standard benchmarks without relying on GNNs. We also briefly present preliminary results on extending PHLP to knowledge graph completion, demonstrating its potential in capturing relational patterns through topological representations. This research conducted together with Eunwoo Heo and Jae-Hun Jung.
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