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Abstract Bacteria utilize cell-cell signaling to coordinate gene expression in populations of cells. Bacterial signal exchange was originally interpreted as a mechanism bacteria use to regulate gene expression in response to changes in cell density, denoted as quorum sensing. Bacterial communication is now known to encompass the exchange of multiple chemical signals between different species of bacteria. Such signal crosstalk within communities of bacteria can have unexpected consequences. Some bacterial species even utilize more than one orthogonal signaling molecule, enabling such species to simultaneously communicate within distinct subsets of species. Such cells utilizing two sets of signals act as a bridge to link gene expression states within the community. Here, a mathematical model was implemented to investigate the consequences of multi-signal communication within heterogeneous bacterial communities. The model was inspired by simple neural networks, with nodes representing bacterial species and directed weights between nodes accounting for the impacts of inter-species signal exchange on gene expression. The activity state of such a network is defined as the gene expression state of each species within the community. Using the model, the stability of the activity states of such networks to changes in signal concentration and population size were quantified. Networks exchanging one set of signals were compared to network exchanging two orthogonal sets of signals. A multilayer neural network model was developed to analyze such networks exchanging orthogonal sets of signals. The model reveals that signal crosstalk increased the activity of the network. These networks were largely resilient to perturbation, however networks were more sensitive to perturbations of the largest population size. Bacterial species utilizing two orthogonal signals, within multilayer networks, had the potential to couple activity states of species that cannot directly communicate. These results give insight into strategies for manipulating signal exchange to predict and control gene expression within bacterial communities. 

Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the topological properties of the brain network. The development of group-level statistical inference procedures in brain graphs while accounting for the heterogeneity and randomness still remains a difficult task. In this study, we develop a robust statistical framework based on persistent homology using theorder statisticsfor analyzing brain networks. The use of order statistics greatly simplifies the computation of the persistent barcodes. We validate the proposed methods using comprehensive simulation studies and subsequently apply to the resting-state functional magnetic resonance images. We found a statistically significanttopologicaldifference between the male and female brain networks.