About

Zixuan Cang is an Assistant Professor in the Department of Mathematics at North Carolina State University. His research interests focus on topological and geometric data analysis, optimal transport, data-driven modeling, and their applications to data-driven biology. He is actively seeking motivated graduate students and currently has a postdoctoral position available. Interested candidates are encouraged to contact him directly.

Research topics

• Computer Science
• Biology
• Computational biology
• Artificial Intelligence
• Machine Learning
• Data Mining
• Remote sensing
• Geography
• Endocrinology
• Genetics
• Algorithm
• Anatomy
• Ecology
• Cell biology
• Biochemistry
• Immunology
• Mathematics

Selected publications

• CellRefiner v1.0.0

  Zenodo (CERN European Organization for Nuclear Research) · 2026-01-15 · 1 citations

  otherOpen access

  CellRefiner is a physical model-based method that integrates a scRNA-seq dataset with a paired spatial transcriptomics (ST) dataset to generate single-cell resolution in the imputed ST data. CellRefiner models cells as particles connected by forces, and then optimizes cell locations with spatial proximity constraints, gene expression similarity, and ligand-receptor interactions between cells.This is the release accompanying the publication.

  PublisherDOI

• CellRefiner v1.0.0

  Zenodo (CERN European Organization for Nuclear Research) · 2026-01-15

  otherOpen access

  CellRefiner is a physical model-based method that integrates a scRNA-seq dataset with a paired spatial transcriptomics (ST) dataset to generate single-cell resolution in the imputed ST data. CellRefiner models cells as particles connected by forces, and then optimizes cell locations with spatial proximity constraints, gene expression similarity, and ligand-receptor interactions between cells.This is the release accompanying the publication.

  PublisherDOI

• Multiscale domain identification for spatial transcriptomics via persistent homology

  Cell Reports Methods · 2026-03-30 · 1 citations

  articleOpen accessSenior author

  Spatial transcriptomics (ST) measures gene expression at a set of spatial locations in a tissue. Communities of nearby cells that express similar genes form spatial domains. Specialized clustering algorithms have been developed to identify spatial domains. These methods often locate spatial domains at a single morphological scale, and interactions across multiple scales are often overlooked. For example, large domains often contain smaller substructures and heterogeneous regions may lie between homogeneous domains. Topological data analysis (TDA) is an emerging mathematical toolkit that studies the underlying features of data at various geometric scales, especially useful for analyzing biological datasets with multiscale characteristics. Using TDA, we develop persistent homology for domains at multiple scales (PHD-MS) to locate tissue structures that persist across morphological scales. We apply PHD-MS to highlight multiscale spatial domains across tissue types and ST technologies. We compare PHD-MS domains against expert-annotated ground truth, where PHD-MS outperforms traditional clustering approaches.

  PublisherDOI

• Reconstructing single-cell resolution from spatial transcriptomics with CellRefiner

  Nature Communications · 2026-02-27

  articleOpen access

  Single-cell RNA sequencing technologies profile the transcriptome of individual cells but lack the spatial context necessary for dissecting cellular interactions like cell-cell communications. On the other hand, most current spatial transcriptomic technologies lack cellular resolution, limiting their capability for realistic downstream analysis. Here we present CellRefiner, a physical model-based method that integrates a single-cell dataset with a paired spatial dataset to generate single-cell resolution in the imputed spatial data. CellRefiner models cells as particles connected by forces, and then optimizes cell locations with spatial proximity constraints, gene expression similarity, and ligand-receptor interactions between cells. We systematically benchmark CellRefiner over a variety of simulated and real datasets using Visium, MERFISH, seqFISH, Slide-seqV2, and STARmap datasets to demonstrate its accuracy, robustness, and ability to recover spatial patterns of cells. We also demonstrate its utility for improving spatially dependent analysis over the original spatial data for the contact-based cell-cell communication on mouse cortex and lymph node tissues. Our results show CellRefiner is capable of reconstructing single-cell resolution from non-single-cell resolution spatial data, allowing downstream analysis that requires individual-cell resolution and spatial information.

  PublisherDOI

• Synchronization of Unbalanced Dynamical Optimal Transport across Multiple Spaces

  ArXiv.org · 2026-02-21

  articleOpen access1st authorCorresponding

  Many biological systems are observed through heterogeneous modalities, requiring transport models that couple dynamics across spaces while allowing mass variation. To address this challenge, we introduce Unbalanced Synchronized Optimal Transport (UnSyncOT), a novel dynamical framework that synchronizes transport-reaction flows between spaces via either geometric embeddings (Monge type) or Markov kernels (Kantorovich type). For both cases we prove that UnSyncOT can be reduced to a single-space problem: the Monge model becomes a Benamou-Brenier problem with a metric-modified kinetic energy, and the Kantorovich model yields a nonlocal action induced by the synchronization operator, both of which fit within a dissipation-distance formulation. We also analyze the pure transport (Wasserstein) and pure reaction (Fisher-Rao) limits and derive structural properties. For the Kantorovich case we propose an approximate UnSyncOT by introducing a Hellinger-Kantorovich based trapezoidal time discretization of the secondary action for efficient computation. Finally we present staggered-grid discretizations and primal-dual solvers, validate the convergence, stability, and efficiency, and demonstrate coherent dynamics reconstructions across spaces.

  PublisherOA PDF

• Synchronization of Unbalanced Dynamical Optimal Transport across Multiple Spaces

  Open MIND · 2026-02-21

  preprint1st authorCorresponding

  Many biological systems are observed through heterogeneous modalities, requiring transport models that couple dynamics across spaces while allowing mass variation. To address this challenge, we introduce Unbalanced Synchronized Optimal Transport (UnSyncOT), a novel dynamical framework that synchronizes transport-reaction flows between spaces via either geometric embeddings (Monge type) or Markov kernels (Kantorovich type). For both cases we prove that UnSyncOT can be reduced to a single-space problem: the Monge model becomes a Benamou-Brenier problem with a metric-modified kinetic energy, and the Kantorovich model yields a nonlocal action induced by the synchronization operator, both of which fit within a dissipation-distance formulation. We also analyze the pure transport (Wasserstein) and pure reaction (Fisher-Rao) limits and derive structural properties. For the Kantorovich case we propose an approximate UnSyncOT by introducing a Hellinger-Kantorovich based trapezoidal time discretization of the secondary action for efficient computation. Finally we present staggered-grid discretizations and primal-dual solvers, validate the convergence, stability, and efficiency, and demonstrate coherent dynamics reconstructions across spaces.

  DOI

• RAFT-UP: Robust Alignment for Spatial Transcriptomics with Explicit Control of Spatial Distortion

  arXiv (Cornell University) · 2026-03-18

  preprintOpen accessSenior author

  Spatial transcriptomics (ST) profiles gene expression across a tissue section while preserving the spatial coordinates. Because current ST technologies typically profile two-dimensional tissue slices, integrating and aligning slices from different regions of the same three-dimensional tissue or from samples under different conditions enables analyses that reveal 3D organization and condition-associated spatial patterns. Two major challenges remain. First, interpretable and flexible control over spatial distortion is needed because rigid transformations can be overly restrictive, whereas highly deformable mappings may arbitrarily distort spatial proximity. Second, biologically plausible matching is also needed, especially when the slices overlap partially. Here, we introduce RAFT-UP, a tool for robust ST alignment that provides explicit control over spatial distance preservation through a fused supervised Gromov-Wasserstein (FsGW) optimal transport framework. FsGW combines expression and spatial information, incorporates spot-wise constraints to discourage biologically implausible matches, and enforces a pairwise distance-consistency constraint that prevents mapping two pairs of spots when their spatial distances differ beyond a specified tolerance. We demonstrate that RAFT-UP accurately aligns slices from different regions of the same tissue and slices from different samples. Benchmarking shows that RAFT-UP improves spatial distance preservation while achieving spot label matching accuracy comparable to state-of-the-art methods. Finally, we demonstrate RAFT-UP on two spatially constrained downstream applications, including spatiotemporal mapping of developing mouse midbrain and comparative cross-slice analysis of cell-cell communication. RAFT-UP is available as open-source software.

  PublisherDOI

• RAFT-UP: Robust Alignment for Spatial Transcriptomics with Explicit Control of Spatial Distortion

  ArXiv.org · 2026-03-18

  articleOpen accessSenior author

  Spatial transcriptomics (ST) profiles gene expression across a tissue section while preserving the spatial coordinates. Because current ST technologies typically profile two-dimensional tissue slices, integrating and aligning slices from different regions of the same three-dimensional tissue or from samples under different conditions enables analyses that reveal 3D organization and condition-associated spatial patterns. Two major challenges remain. First, interpretable and flexible control over spatial distortion is needed because rigid transformations can be overly restrictive, whereas highly deformable mappings may arbitrarily distort spatial proximity. Second, biologically plausible matching is also needed, especially when the slices overlap partially. Here, we introduce RAFT-UP, a tool for robust ST alignment that provides explicit control over spatial distance preservation through a fused supervised Gromov-Wasserstein (FsGW) optimal transport framework. FsGW combines expression and spatial information, incorporates spot-wise constraints to discourage biologically implausible matches, and enforces a pairwise distance-consistency constraint that prevents mapping two pairs of spots when their spatial distances differ beyond a specified tolerance. We demonstrate that RAFT-UP accurately aligns slices from different regions of the same tissue and slices from different samples. Benchmarking shows that RAFT-UP improves spatial distance preservation while achieving spot label matching accuracy comparable to state-of-the-art methods. Finally, we demonstrate RAFT-UP on two spatially constrained downstream applications, including spatiotemporal mapping of developing mouse midbrain and comparative cross-slice analysis of cell-cell communication. RAFT-UP is available as open-source software.

  PublisherOA PDF

• OTMol: Robust Molecular Structure Comparison via Optimal Transport

  Journal of Chemical Information and Modeling · 2025-10-08

  articleOpen accessSenior authorCorresponding

  Root-mean-square deviation (RMSD) is widely used to assess structural similarity in systems ranging from flexible ligand conformers to complex molecular cluster configurations. Despite its wide utility, RMSD calculation is often challenged by inconsistent atom ordering, indistinguishable configurations in molecular clusters, and potential chirality inversion during alignment. These issues highlight the necessity of accurate atom-to-atom correspondence as a prerequisite for meaningful alignment. Traditional approaches often rely on heuristic cost matrices combined with the Hungarian algorithm, yet these methods underutilize the rich intra-molecular structural information and may fail to generalize across chemically diverse systems. In this work, we introduce OTMol, a method that formulates the molecular alignment task as a fused supervised Gromov-Wasserstein (fsGW) optimal transport problem. By leveraging the intrinsic geometric and topological relationships within each molecule, OTMol eliminates the need for manually defined cost functions and enables a principled, data-driven matching strategy. Importantly, OTMol preserves key chemical features such as molecular chirality and bond connectivity consistency. We evaluate OTMol across a wide range of molecular systems, including Adenosine triphosphate, Imatinib, lipids, small peptides, and water clusters, and demonstrate that it consistently achieves low RMSD values while preserving computational efficiency. Importantly, OTMol maintains molecular integrity by enforcing one-to-one mappings between entire molecules, thereby avoiding erroneous many-to-one alignments that often arise in comparing molecular clusters. Our results underscore the utility of optimal transport theory for molecular alignment and offer a generalizable framework applicable to structural comparison tasks in cheminformatics, molecular modeling, and related disciplines.

  PublisherOA PDFDOI

• Synchronized Optimal Transport for Joint Modeling of Dynamics Across Multiple Spaces

  SIAM Journal on Applied Mathematics · 2025-02-11 · 1 citations

  articleOpen access1st authorCorresponding

  Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain coherence in the dynamics across these diverse spaces. To address this challenge, we introduce synchronized optimal transport (SyncOT), a novel approach to jointly model dynamics that represent the same system through multiple spaces. Given the correspondence between the spaces, SyncOT minimizes the aggregated cost of the dynamics induced across all considered spaces. The problem is discretized into a finite-dimensional convex problem using a staggered grid. Primal-dual algorithm-based approaches are then developed to solve the discretized problem. Various numerical experiments demonstrate the capabilities and properties of SyncOT and validate the effectiveness of the proposed algorithms.

  PublisherOA PDFDOI

Recent grants

• Topological and Geometric Modeling and Computation of Structures and Functions in Single-Cell Omics Data

  NSF · $374k · 2022–2026

Frequent coauthors

• Qing Nie

  19 shared

• Guo‐Wei Wei

  Michigan State University

  18 shared

• Enrico Gratton

  University of California, Irvine

  6 shared

• Rachel Cinco

  University of California, Irvine

  6 shared

• Guo‐Wei Wei

  Michigan State University

  6 shared

• Kedi Wu

  4 shared

• Yanxiang Zhao

  George Washington University

  4 shared

• Suoqin Jin

  Wuhan University

  4 shared

Labs

• Mathematical BiologyPI

Education

• Ph.D., Mathematics

  University of North Carolina at Chapel Hill

  2015

• M.S., Mathematics

  University of North Carolina at Chapel Hill

  2011

• B.S., Mathematics

  University of Science and Technology of China

  2009