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Research Frontiers in Manifold Learning and Non-linear Dimensionality Reduction

Develops algorithms for discovering and analyzing low-dimensional manifold structures embedded in high-dimensional spaces using topological principles.

Geodesic Preservation in High-Dimensional Biological Networks

Intrinsic Dimensionality as Phenotypic Complexity Signature

Manifold Curvature and Disease State Transitions

Non-linear Topology in Single-Cell Trajectory Inference

Persistent Homology Across Molecular Interaction Landscapes

Latent Manifold Instability in Developmental Systems

Metric Distortion in Multi-omics Data Integration

Topological Data Analysis of Protein Conformational Ensembles

Local Intrinsic Dimension in Cellular Heterogeneity Detection

Manifold Alignment for Cross-species Genomic Comparison

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