Qing Nie

Christopher Rackauckas, Qing Nie

Stochastic differential equations (SDE) often exhibit large random transitions. This property, which we denote as pathwise stiffness, causes transient bursts of stiffness which limit the allowed step size for common fixed time step explicit and drift-implicit integrators. We present four separate methods to efficiently handle this stiffness. First, we utilize a computational technique to derive stability-optimized adaptive methods of strong order 1.5 for SDEs. The resulting explicit methods are shown to exhibit substantially enlarged stability regions which allows for them to solve pathwise stiff biological models orders of magnitude more efficiently than previous methods like SRIW1 and Euler-Maruyama. Secondly, these integrators include a stiffness estimator which allows for automatically switching between implicit and explicit schemes based on the current stiffness. In addition, adaptive L-stable strong order 1.5 implicit integrators for SDEs and stochastic differential algebraic equations (SDAEs) in mass-matrix form with additive noise are derived and are demonstrated as more efficient than the explicit methods on stiff chemical reaction networks by nearly 8x. Lastly, we developed an adaptive implicit-explicit (IMEX) integration method based off of a common method for diffusion-reaction-convection PDEs and show numerically that it can achieve strong order 1.5. These methods are benchmarked on a range of problems varying from non-stiff to extreme pathwise stiff and demonstrate speedups between 5x-6000x while showing computationally infeasibility of fixed time step integrators on many of these test equations.

Kathryn Dover, Zixuan Cang, Anna Ma et al.

High-dimensional multimodal data arises in many scientific fields. The integration of multimodal data becomes challenging when there is no known correspondence between the samples and the features of different datasets. To tackle this challenge, we introduce AVIDA, a framework for simultaneously performing data alignment and dimension reduction. In the numerical experiments, Gromov-Wasserstein optimal transport and t-distributed stochastic neighbor embedding are used as the alignment and dimension reduction modules respectively. We show that AVIDA correctly aligns high-dimensional datasets without common features with four synthesized datasets and two real multimodal single-cell datasets. Compared to several existing methods, we demonstrate that AVIDA better preserves structures of individual datasets, especially distinct local structures in the joint low-dimensional visualization, while achieving comparable alignment performance. Such a property is important in multimodal single-cell data analysis as some biological processes are uniquely captured by one of the datasets. In general applications, other methods can be used for the alignment and dimension reduction modules.

Xiangzheng Cheng, Haili Huang, Ye Su et al.

In multicellular organisms, cells coordinate their activities through cell-cell communication (CCC), which are crucial for development, tissue homeostasis, and disease progression. Recent advances in single-cell and spatial omics technologies provide unprecedented opportunities to systematically infer and analyze CCC from these omics data, either by integrating prior knowledge of ligand-receptor interactions (LRIs) or through de novo approaches. A variety of computational methods have been developed, focusing on methodological innovations, accurate modeling of complex signaling mechanisms, and investigation of broader biological questions. These advances have greatly enhanced our ability to analyze CCC and generate biological hypotheses. Here, we introduce the biological mechanisms and modeling strategies of CCC, and provide a focused overview of more than 140 computational methods for inferring CCC from single-cell and spatial transcriptomic data, emphasizing the diversity in methodological frameworks and biological questions. Finally, we discuss the current challenges and future opportunities in this rapidly evolving field.

Christopher Rackauckas, Qing Nie

Performant numerical solving of differential equations is required for large-scale scientific modeling. In this manuscript we focus on two questions: (1) how can researchers empirically verify theoretical advances and consistently compare methods in production software settings and (2) how can users (scientific domain experts) keep up with the state-of-the-art methods to select those which are most appropriate? Here we describe how the confederated modular API of DifferentialEquations.jl addresses these concerns. We detail the package-free API which allows numerical methods researchers to readily utilize and benchmark any compatible method directly in full-scale scientific applications. In addition, we describe how the complexity of the method choices is abstracted via a polyalgorithm. We show how scientific tooling built on top of DifferentialEquations.jl, such as packages for dynamical systems quantification and quantum optics simulation, both benefit from this structure and provide themselves as convenient benchmarking tools.