A Resampling-Based Framework for Network Structure Learning in High-Dimensional Data

RSNet is an open-source R package that provides a resampling-based framework for robust and interpretable network inference, designed to address the limited-sample-size challenges common in high-dimensional data. It supports both the estimation of partial correlation networks modeled as Gaussian networks and conditional Gaussian Bayesian networks for mixed data types that combine continuous and discrete variables. The framework incorporates multiple resampling strategies, including bootstrap, subsampling, and cluster-based approaches, to accommodate both independent and correlated observations. To enhance interpretability, RSNet integrates graphlet-based topology analysis that captures higher-order connectivity and edge sign information, enabling single-node and subnetwork-level insights. Notably, RSNet is the first R package to efficiently construct signed graphlet degree vector matrices (GDVMs) in near-constant time for sparse networks, providing scalable analysis of higher-order network structure. Collectively, RSNet offers a versatile tool for statistically reliable and interpretable network inference in high-dimensional data.

A Data-facilitated Numerical Method for Richards Equation to Model Water Flow Dynamics in Soil

Root-zone soil moisture monitoring is essential for precision agriculture, smart irrigation, and drought prevention. Modeling the spatiotemporal water flow dynamics in soil is typically achieved by solving a hydrological model, such as the Richards equation which is a highly nonlinear partial differential equation (PDE). In this paper, we present a novel data-facilitated numerical method for solving the mixed-form Richards equation. This numerical method, which we call the D-GRW (Data-facilitated global Random Walk) method, synergistically integrates adaptive linearization scheme, neural networks, and global random walk in a finite volume discretization framework to produce accurate numerical solutions of the Richards equation with guaranteed convergence under reasonable assumptions. Through three illustrative examples, we demonstrate and discuss the superior accuracy and mass conservation performance of our D-GRW method and compare it with benchmark numerical methods and commercial solver.