Studies of ecological networks (the web of interactions between species in a community) demonstrate an intricate link between a community's structure and its long-term viability. It remains unclear, however, how much a community's persistence depends on the identities of the species present, or how much the role played by each species varies as a function of the community in which it is found. We measured species' roles by studying how species are embedded within the overall network and the subsequent dynamic implications. Using data from 32 empirical food webs, we find that species' roles and dynamic importance are inherent species attributes and can be extrapolated across communities on the basis of taxonomic classification alone. Our results illustrate the variability of roles across species and communities and the relative importance of distinct species groups when attempting to conserve ecological communities.

Studying the interaction between a system's components and the temporal evolution of the system are two common ways to uncover and characterize its internal workings. Recently, several maps from a time series to a network have been proposed with the intent of using network metrics to characterize time series. Although these maps demonstrate that different time series result in networks with distinct topological properties, it remains unclear how these topological properties relate to the original time series. Here, we propose a map from a time series to a network with an approximate inverse operation, making it possible to use network statistics to characterize time series and time series statistics to characterize networks. As a proof of concept, we generate an ensemble of time series ranging from periodic to random and confirm that application of the proposed map retains much of the information encoded in the original time series (or networks) after application of the map (or its inverse). Our results suggest that network analysis can be used to distinguish different dynamic regimes in time series and, perhaps more importantly, time series analysis can provide a powerful set of tools that augment the traditional network analysis toolkit to quantify networks in new and useful ways.

Much of human knowledge sits in large databases of unstructured text. Leveraging this knowledge requires algorithms that extract and record metadata on unstructured text documents. Assigning topics to documents will enable intelligent searching, statistical characterization, and meaningful classification. Latent Dirichlet allocation (LDA) is the state of the art in topic modeling. Here, we perform a systematic theoretical and numerical analysis that demonstrates that current optimization techniques for LDA often yield results that are not accurate in inferring the most suitable model parameters. Adapting approaches from community detection in networks, we propose a new algorithm that displays high reproducibility and high accuracy and also has high computational efficiency. We apply it to a large set of documents in the English Wikipedia and reveal its hierarchical structure.

Although the mapping of codon to amino acid is conserved across nearly all species, the frequency at which synonymous codons are used varies both between organisms and between genes from the same organism. This variation affects diverse cellular processes including protein expression, regulation, and folding. Here, we mathematically model an additional layer of complexity and show that individual codon usage biases follow a position-dependent exponential decay model with unique parameter fits for each codon. We use this methodology to perform an in-depth analysis on codon usage bias in the model organism Escherichia coli. Our methodology shows that lowly and highly expressed genes are more similar in their codon usage patterns in the 5′-gene regions, but that these preferences diverge at distal sites resulting in greater positional dependency (pD, which we mathematically define later) for highly expressed genes. We show that position-dependent codon usage bias is partially explained by the structural requirements of mRNAs that results in increased usage of A/T rich codons shortly after the gene start. However, we also show that the pD of 4- and 6-fold degenerate codons is partially related to the gene copy number of cognate-tRNAs supporting existing hypotheses that posit benefits to a region of slow translation in the beginning of coding sequences. Lastly, we demonstrate that viewing codon usage bias through a position-dependent framework has practical utility by improving accuracy of gene expression prediction when incorporating positional dependencies into the Codon Adaptation Index model.

Existing research highlights that families face geographic, social, and psychological constraints that may limit the extent to which competition can take hold in school choice programs. In this paper, we address the implications of such findings by creating a network of student flows from 11 cohorts of eighth‐grade students in the Chicago Public Schools (CPS). We applied a custom algorithm to group together schools with similar sending and receiving patterns, and calculated the difference in mean achievement between a student's attended and assigned high schools. For all identified school groupings, we found that the students were on average moving to higher achieving schools. We also found that the movement toward higher achieving schools of the top achievement quartile of students was over twice as large as that of the bottom quartile, but that the flows of both the highest and lowest achieving student quartiles were toward higher achieving destinations. Our results suggest that student movements in CPS between the years of 2001 to 2005 were consistent with creating market pressure for improvement as well as increasing segregation by achievement. However, further research into how schools responded to those movements is required to make inferences about the level or consequences of competition generated by choice‐related reforms during that time.