Explanipedia

Convergence Rate of the Solution of Multi-marginal Schrodinger Bridge Problem with Marginal Constraints from SDEs Open

Rentian Yao, Yeo-Reum Kim, Geoffrey Schiebinger · 2025

In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE) with a constant diffusion coefficient, and with time depend…

Gradient-flow SDEs have unique transient population dynamics Open

Nicolas Lanzetti, Antonio Terpin, Geoffrey Schiebinger · 2025

Identifying the drift and diffusion of an SDE from its population dynamics is a notoriously challenging task. Researchers in machine learning and single cell biology have only been able to prove a partial identifiability result: for potent…

Principal Curves In Metric Spaces And The Space Of Probability Measures Open

Andrew Warren, Anton Afanassiev, Fuminori Kobayashi, Young‐Heon Kim, Geoffrey Schiebinger · 2025

We introduce principal curves in Wasserstein space, and in general compact metric spaces. Our motivation for the Wasserstein case comes from optimal-transport-based trajectory inference, where a developing population of cells traces out a …

Single-Cell Transcriptomics Reveals Evolutionary Reconfiguration of Embryonic Cell Fate Specification in the Sea Urchin Heliocidaris erythrogramma Open

Abdull J. Massri, Alejandro Berrío, Anton Afanassiev, Laura Greenstreet, Krista Pipho , et al. · 2024

Altered regulatory interactions during development likely underlie a large fraction of phenotypic diversity within and between species, yet identifying specific evolutionary changes remains challenging. Analysis of single-cell developmenta…

Spatial Transcriptomics Brings New Challenges and Opportunities for Trajectory Inference Open

Matthieu Heitz, Yuxuan Ma, Sharvaj Kubal, Geoffrey Schiebinger · 2024

Spatial transcriptomics (ST) brings new dimensions to the analysis of single-cell data. While some methods for data analysis can be ported over without major modifications, they are the exception rather than the rule. Trajectory inference …

Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots Open

Vincent Guan, Joseph Janssen, H. Rahmani, Andrew Warren, Stephen X. Zhang , et al. · 2024

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SD…

Neuropeptide signalling orchestrates T cell differentiation Open

Yu Hou, Lin-Yu Sun, Martin W. LaFleur, Linglin Huang, Conner Lambden , et al. · 2024

Optimal sequencing depth for single-cell RNA-sequencing in Wasserstein space Open

J. Kim, Sharvaj Kubal, Geoffrey Schiebinger · 2024

How many samples should one collect for an empirical distribution to be as close as possible to the true population? This question is not trivial in the context of single-cell RNA-sequencing. With limited sequencing depth, profiling more c…

Cellular proliferation biases clonal lineage tracing and trajectory inference Open

Becca Bonham-Carter, Geoffrey Schiebinger · 2024

Motivation Lineage tracing and trajectory inference from single-cell RNA-sequencing data hold tremendous potential for uncovering the genetic programs driving development and disease. Single cell datasets are thought to provide an unbiased…

Single-cell transcriptomics reveals evolutionary reconfiguration of embryonic cell fate specification in the sea urchinHeliocidaris erythrogramma Open

Abdull J. Massri, Alejandro Berrío, Anton Afanassiev, Laura Greenstreet, Krista Pipho , et al. · 2024

Altered regulatory interactions during development likely underlie a large fraction of phenotypic diversity within and between species, yet identifying specific evolutionary changes remains challenging. Analysis of single-cell developmenta…

Time- and lineage-resolved transcriptional profiling uncovers gene expression programs and clonal relationships that underlie human T lineage specification Open

Yale S. Michaels, Matthew C. Major, Becca Bonham-Carter, Jing-Qi Zhang, Tiam Heydari , et al. · 2023

T cells develop from multi-potent hematopoietic progenitors in the thymus and provide adaptive protection against pathogens and cancer. However, the emergence of human T cell-competent blood progenitors, and their subsequent specification …

Reconstruction of single cell lineage trajectories and identification of diversity in fates during the epithelial-to-mesenchymal transition Open

Yu-Chen Cheng, Yun Zhang, Shubham Tripathi, BV Harshavardhan, Mohit Kumar Jolly , et al. · 2023

Exploring the complexity of the epithelial-to-mesenchymal transition (EMT) unveils a diversity of potential cell fates; however, the exact timing and intricate mechanisms by which early cell states diverge into distinct EMT trajectories re…

Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm Open

Nabarun Deb, Young‐Heon Kim, Soumik Pal, Geoffrey Schiebinger · 2023

We prove that the sequence of marginals obtained from the iterations of the Sinkhorn algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges to an absolutely continuous curve on the $2$-Wasserstein sp…

Cellular proliferation biases clonal lineage tracing and trajectory inference Open

Becca Bonham-Carter, Geoffrey Schiebinger · 2023

We identify a fundamental statistical phenomenon in single-cell time courses with clone-based lineage tracing. Through simple probabilistic arguments, we show how the relative growth rates of cells influence the probability that they will …

Manifold Learning with Sparse Regularised Optimal Transport Open

Stephen X. Zhang, Gilles Mordant, Tetsuya Matsumoto, Geoffrey Schiebinger · 2023

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom …

Trajectory inference for a branching SDE model of cell differentiation Open

Elias Ventre, Aden Forrow, Nitya Gadhiwala, Parijat Chakraborty, Omer Angel , et al. · 2023

A core challenge for modern biology is how to infer the trajectories of individual cells from population-level time courses of high-dimensional gene expression data. Birth and death of cells present a particular difficulty: existing trajec…

Cellular population dynamics shape the route to human pluripotency Open

Francesco Panariello, Onelia Gagliano, Camilla Luni, Antonio Grimaldi, Silvia Angiolillo , et al. · 2023

Brassinosteroid gene regulatory networks at cellular resolution in the Arabidopsis root Open

Trevor M. Nolan, Nemanja Vukašinović, Che‐Wei Hsu, Jingyuan Zhang, Isabelle Vanhoutte , et al. · 2023

Brassinosteroids are plant steroid hormones that regulate diverse processes, such as cell division and cell elongation, through gene regulatory networks that vary in space and time. By using time series single-cell RNA sequencing to profil…

Reconstruction of Single Cell Lineage Trajectories and Identification of Diversity in Fates During the Epithelial-to-Mesenchymal Transition Open

Yu-Chen Cheng, Yun Zhang, Shubham Tripathi, Harshavardhan BV, Mohit Kumar Jolly , et al. · 2023

Cellular population dynamics shape the route to human pluripotency Open

Nicola Elvassore, Onelia Gagliano, Francesco Panariello, Camilla Luni, Antonio Grimaldi , et al. · 2022

Human cellular reprogramming to induced pluripotency is still an inefficient process and this has long hindered the study of the role of critical intermediate stages. We take advantage of high efficiency reprogramming in microfluidics and …

Brassinosteroid gene regulatory networks at cellular resolution Open

Trevor M. Nolan, Nemanja Vukašinović, Che‐Wei Hsu, Jingyuan Zhang, Isabelle Vanhoutte , et al. · 2022

Brassinosteroids (BRs) are plant steroid hormones that regulate diverse processes such as cell division and cell elongation. BRs control thousands of genes through gene regulatory networks that vary in space and time. By using time-series …

CRISPR screens reveal neuropeptide signaling orchestrates T helper cell differentiation Open

Vijay K. Kuchroo, Yu Hou, Martin W. LaFleur, Linglin Huang, Conner Lambden , et al. · 2022

The balance between T helper type 1 (Th1) cells and other Th cells is critical for antiviral and anti-tumor responses, but how this fine balance is achieved remains poorly understood. Here, we dissected the dynamic regulation of Th1 cell d…

Beyond kNN: Adaptive, Sparse Neighborhood Graphs via Optimal Transport Open

Tetsuya Matsumoto, Stephen X. Zhang, Geoffrey Schiebinger · 2022

Nearest neighbour graphs are widely used to capture the geometry or topology of a dataset. One of the most common strategies to construct such a graph is based on selecting a fixed number k of nearest neighbours (kNN) for each point. Howev…

Trajectory Inference via Mean-field Langevin in Path Space Open

Stephen X. Zhang, Lénaïc Chizat, Matthieu Heitz, Geoffrey Schiebinger · 2022

Trajectory inference aims at recovering the dynamics of a population from snapshots of its temporal marginals. To solve this task, a min-entropy estimator relative to the Wiener measure in path space was introduced by Lavenant et al. arXiv…

The DNA-based global positioning system—a theoretical framework for large-scale spatial genomics Open

Laura Greenstreet, Anton Afanassiev, Yusuke Kijima, Matthieu Heitz, Soh Ishiguro , et al. · 2022

We present GPS-seq, a theoretical framework that enables massively scalable, optics-free spatial transcriptomics. GPS-seq combines data from high-throughput sequencing with manifold learning to obtain the spatial transcriptomic landscape o…

A single-cell Arabidopsis root atlas reveals developmental trajectories in wild-type and cell identity mutants Open

Rachel Shahan, Che‐Wei Hsu, Trevor M. Nolan, Benjamin Cole, Isaiah Taylor , et al. · 2022

Optimal transport analysis reveals trajectories in steady-state systems Open

Stephen Zhang, Anton Afanassiev, Laura Greenstreet, Tetsuya Matsumoto, Geoffrey Schiebinger · 2021

Understanding how cells change their identity and behaviour in living systems is an important question in many fields of biology. The problem of inferring cell trajectories from single-cell measurements has been a major topic in the single…

Hematopoiesis at single cell resolution spanning human development and maturation Open

Hojun Li, Jideofor Ezike, Anton Afanassiev, Laura Greenstreet, Stephen X. Zhang , et al. · 2021

Hematopoiesis is a process of constitutive regeneration whereby hematopoietic stem and progenitor cells (HSPCs) replenish mature blood cells. During maturation and aging, HSPCs shift their output to support the demands of prenatal developm…

LineageOT is a unified framework for lineage tracing and trajectory inference Open

Aden Forrow, Geoffrey Schiebinger · 2021

Optimal transport analysis reveals trajectories in steady-state systems Open

Stephen X. Zhang, Anton Afanassiev, Laura Greenstreet, Tetsuya Matsumoto, Geoffrey Schiebinger · 2021

Understanding how cells change their identity and behaviour in living systems is an important question in many fields of biology. The problem of inferring cell trajectories from single-cell measurements has been a major topic in the single…

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