Omics-based approaches have become increasingly influential in identifying disease
mechanisms and drug responses. Considering that diseases and drug responses are co …

The Fokker--Planck (FP) equation governing the evolution of the probability density function
(PDF) is applicable to many disciplines, but it requires specification of the coefficients for …

With the rapid increase of valuable observational, experimental and simulating data for
complex systems, much effort is being devoted to discovering governing laws underlying the …

Many complex real world phenomena exhibit abrupt, intermittent, or jumping behaviors,
which are more suitable to be described by stochastic differential equations under non …

The emergence of transition phenomena between metastable states induced by noise plays
a fundamental role in a broad range of nonlinear systems. The computation of the most …

In this work, we propose a method to learn multivariate probability distributions using sample
path data from stochastic differential equations. Specifically, we consider temporally …

The concept of quasi-potential plays a central role in understanding the mechanisms of rare
events and characterizing the statistics of transition behaviors in stochastic dynamics …

Critical transitions are usually accompanied by a decline in ecosystem services and
potentially have negative impacts on human economies. Although some early warning …

It is a challenging issue to analyze complex dynamics from observed and simulated data. An
advantage of extracting dynamic behaviors from data is that this approach enables the …

Breast cancer cells exhibit three distinct phenotypes: basal, stem-like, and luminal states.
These phenotypes are closely associated with the invasion and spread of breast cancer. As …