Forward–Backward Stochastic Differential Equations (
            <scp>SDEs</scp>
            )

Zhang, Jianfeng

doi:10.1002/9780470061602.eqf02018

Cited by 3 publications

(3 citation statements)

References 39 publications

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“…"-would be immensely valuable in understanding the temporal dynamics and regulation of the behaviors of individual cells across biological conditions. [23] [42,37,6,11,51,50] [13] [14] Table 1: Methods for integrating and extrapolating single-cell time series data. OT = optimal transport; ODE = ordinary differential equations; AE = autoencoder.…”

Section: Introductionmentioning

confidence: 99%

“…For example, optimal transport-based methods, such as Waddington-OT [36], TrajectoryNet [42] and TIGON [37], operate on pairs of measurements in a time series, with the goal of aligning cells from two neighboring time points under the assumption that a single cell's profile changes minimally between time points. Alternatively, neural ordinary/stochastic differential equation (ODE/SDE) based methods, such as PRESCIENT [49], RNAForecaster [6], MIOFlow [11], FBSDE [51] and scNODE [50], assume that each cell develops autonomously, and the cell's future state is determined based on the cell's current expression profile. Autoencoder models either assume that time is an additive variable in the embedding space [23] or are coupled with optimal transport or ODE based methods to optimize non-linear cell projection and cross-time alignment [42,11,50].…”

Section: Introductionmentioning

confidence: 99%

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Multi-condition and multi-modal temporal profile inference during mouse embryonic development

Zhang,

Qiu,

Filippova

et al. 2024

Preprint

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The emergence of single-cell time-series datasets enables modeling of changes in various types of cellular profiles over time. However, due to the disruptive nature of single-cell measurements, it is impossible to capture the full temporal trajectory of a particular cell. Furthermore, single-cell profiles can be collected at mismatched time points across different conditions (e.g., sex, batch, disease) and data modalities (e.g., scRNA-seq, scATAC-seq), which makes modeling challenging. Here we propose a joint modeling framework, Sunbear, for integrating multi-condition and multi-modal single-cell profiles across time. Sunbear can be used to impute single-cell temporal profile changes, align multi-dataset and multi-modal profiles across time, and extrapolate single-cell profiles in a missing modality. We applied Sunbear to reveal sex-biased transcription during mouse embryonic development and predict dynamic relationships between epigenetic priming and transcription for cells in which multi-modal profiles are unavailable. Sunbear thus enables the projection of single-cell time-series snapshots to multi-modal and multi-condition views of cellular trajectories.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-condition and multi-modal temporal profile inference during mouse embryonic development

Zhang,

Qiu,

Filippova

et al. 2024

Preprint

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“…MIOFlow [17] follows the geometry by operating in the latent space of an geodesic autoencoder. FBSDE [40] integrates the forward and backward movements of two SDEs in time to capture the cell developmental dynamics. TIGON [32] uses dynamical unbalanced OT [7] to reconstructs dynamic trajectories and population growth simultaneously.…”

Section: Introductionmentioning

confidence: 99%

stVCR: Reconstructing spatio-temporal dynamics of cell development using optimal transport

Peng,

Zhou,

2024

Preprint

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Time-series spatial transcriptome data with single-cell resolution provide an opportunity to study cell differentiation, growth and migration in physical space over time. Due to the destructive nature of sequencing, simultaneous reconstruction of cell differentiation, growth and migration trajectories remains challenging, especially migration in physical space, as the coordinates obtained at different temporal snapshots are not in the same coordinate system. To realize this potential, we developed stVCR, which is an optimal transport algorithm with dynamical form, unbalanced setting and invariance to rigid body transformations. stVCR extends the previous algorithm, which only reconstructs differentiation trajectories and population growth, to end-to-end simultaneously reconstruct cell differentiation, growth, migration in physical space and align spatial coordinates of multiple snapshots. In addition, stVCR allows the study of the interaction between gene expression and spatial migration and the effect of gene expression and spatial migration on growth. We verified the effectiveness of stVCR on simulated data and axolotl brain regeneration data.

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