Distinct dynamic phases observed in bacterial microcosms

Progress on network modeling and analysis of gut microecology: a review

The gut microecological network is a complex microbial community within the human body that plays a key role in linking dietary nutrition and host physiology. To understand the complex relationships among microbes and their functions within this community, network analysis has emerged as a powerful tool. By representing the interactions between microbes and their associated omics data as a network, we can gain a comprehensive understanding of the ecological mechanisms that drive the human gut microbiota. In addition, the network-based approach provides a more intuitive analysis of the gut microbiota, simplifying the study of its complex dynamics and interdependencies. This review provides a comprehensive overview of the methods used to construct and analyze networks in the context of gut microecological background. We discuss various types of network modeling approaches, including co-occurrence networks, causal networks, dynamic networks, and multi-omics networks, and describe the analytical techniques used to identify important network properties. We also highlight the challenges and limitations of network modeling in this area, such as data scarcity and heterogeneity, and provide future research directions to overcome these limitations. By exploring these network-based methods, researchers can gain valuable insights into the intricate relationships and functional roles of microbial communities within the gut, ultimately advancing our understanding of the gut microbiota's impact on human health.

On inverse problems for several coupled PDE systems arising in mathematical biology

In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems, we mainly consider the non-negative solutions of the coupled equations, which are consistent with realistic settings in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction of the measurement/observation data due to averaging effects, the nonlinear coupling of multiple equations, and the non-negative constraints on the solutions, which pose significant challenges to the inverse problems. We develop a new and effective scheme to tackle the inverse problems and achieve unique identifiability results by properly controlling the injection of different source terms to obtain multiple sets of mean flux data. The approach relies on certain monotonicity properties which are related to the intrinsic structures of the coupled PDE system. We also connect our study to biological applications of practical interest.