Avoiding matrix exponentials for large transition rate matrices.

Exact methods for the exponentiation of matrices of dimension N can be computationally expensive in terms of execution time (N3) and memory requirements (N2), not to mention numerical precision issues. A matrix often exponentiated in the natural sciences is the rate matrix. Here, we explore five methods to exponentiate rate matrices, some of which apply more broadly to other matrix types.

An accurate probabilistic step finder for time-series analysis.

Noisy time-series data-from various experiments, including Förster resonance energy transfer, patch clamp, and force spectroscopy, among others-are commonly analyzed with either hidden Markov models or step-finding algorithms, both of which detect discrete transitions. Hidden Markov models, including their extensions to infinite state spaces, inherently assume exponential-or technically geometric-holding time distributions, biasing step locations toward steps with geometric holding times, especially in sparse and/or noisy data. In contrast, existing step-finding algorithms, while free of this restraint, often rely on ad hoc metrics to penalize steps recovered in time traces (by using various information criteria) and otherwise rely on approximate greedy algorithms to identify putative global optima.

Gene expression model inference from snapshot RNA data using Bayesian non-parametrics.

Gene expression models, which are key towards understanding cellular regulatory response, underlie observations of single-cell transcriptional dynamics. Although RNA expression data encode information on gene expression models, existing computational frameworks do not perform simultaneous Bayesian inference of gene expression models and parameters from such data. Rather, gene expression models-composed of gene states, their connectivities and associated parameters-are currently deduced by pre-specifying gene state numbers and connectivity before learning associated rate parameters.

Monte Carlo samplers for efficient network inference.

Accessing information on an underlying network driving a biological process often involves interrupting the process and collecting snapshot data. When snapshot data are stochastic, the data's structure necessitates a probabilistic description to infer underlying reaction networks. As an example, we may imagine wanting to learn gene state networks from the type of data collected in single molecule RNA fluorescence in situ hybridization (RNA-FISH).