Jinwon Park | Searcharxiv

arXiv2026

Effects of Divalent Cations on Diffusion Dynamics of Biological Water Confined between Lipid Membranes

Biological water is an ionic solution containing both monovalent and divalent ions. However, the effects of divalent ions on the dynamics of biological water remain largely unknown. Here, we investigate how the transport dynamics of water molecules nanoconfined between lipid membranes depends on the concentration of calcium (Ca2+) and magnesium (Mg2+) ions by using molecular dynamics simulations and the generalized transport equation for biological water. We find that the diffusion coefficient of biological water monotonically increases with Ca2+ ion concentration but exhibits a largely opposite, non-monotonic dependence on Mg2+ concentration. The deviation of the water molecules' displacement distribution from the Gaussian also shows distinct dependence on the concentrations of Mg2+ and Ca2+. These contrasting behaviors originate from the different hydration radii of these divalent ions and their distinct effects on the interfacial structure and dynamics of biological water. The relaxation of the lateral displacement distribution of water molecules toward a Gaussian is determined by the time-correlation function of diffusion coefficient fluctuations, whose relaxation time increases with salt concentrations. The primary source of the lateral diffusion coefficient fluctuation is thermal motion of water molecules in the longitudinal direction, along which microscopic environments surrounding a water molecule, including the functional groups of lipid membrane and ion concentrations, drastically change.

cond-mat.soft↗

arXiv2026

Fair Model-based Clustering

The goal of fair clustering is to find clusters such that the proportion of sensitive attributes (e.g., gender, race, etc.) in each cluster is similar to that of the entire dataset. Various fair clustering algorithms have been proposed that modify standard K-means clustering to satisfy a given fairness constraint. A critical limitation of several existing fair clustering algorithms is that the number of parameters to be learned is proportional to the sample size because the cluster assignment of each datum should be optimized simultaneously with the cluster center, and thus scaling up the algorithms is difficult. In this paper, we propose a new fair clustering algorithm based on a finite mixture model, called Fair Model-based Clustering (FMC). A main advantage of FMC is that the number of learnable parameters is independent of the sample size and thus can be scaled up easily. In particular, mini-batch learning is possible to obtain clusters that are approximately fair. Moreover, FMC can be applied to non-metric data (e.g., categorical data) as long as the likelihood is well-defined. Theoretical and empirical justifications for the superiority of the proposed algorithm are provided.

stat.ML↗