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A number of recent publications regarding important issues in mathematics are summarized. Topics include how culture influences reasoning ability, research into prime numbers, the of teaching mathematics at Cambridge University in the 19th century, and awards in mathematics offered by the Clay Mathematics Institute of Cambridge, Mass; and named publications include 'Union News,' 'Science News,' 'Quantum,' and 'Historia Mathematica.'

Statistical phylogenetic analysis currently relies on complex, dedicated software packages, making it difficult for evolutionary biologists to explore new models and inference strategies. Recent years have seen more generic solutions based on probabilistic graphical models, but this formalism can only partly express phylogenetic problems. Here, we show that universal probabilistic programming languages (PPLs) solve the expressivity problem, while still supporting automated generation of efficient inference algorithms. To prove the latter point, we develop automated generation of sequential Monte Carlo (SMC) algorithms for PPL descriptions of arbitrary biological diversification (birth-death) models. SMC is a new inference strategy for these problems, supporting both parameter inference and efficient estimation of Bayes factors that are used in model testing. We take advantage of this in automatically generating SMC algorithms for several recent diversification models that have been difficult or impossible to tackle previously. Finally, applying these algorithms to 40 bird phylogenies, we show that models with slowing diversification, constant turnover and many small shifts generally explain the data best. Our work opens up several related problem domains to PPL approaches, and shows that few hurdles remain before these techniques can be effectively applied to the full range of phylogenetic models.

Background: The biodiversity domain, and in particular biological taxonomy, is moving in the direction of semantization of its research outputs. The present work introduces OpenBiodiv-O, the ontology that serves as the basis of the OpenBiodiv Knowledge Management System. Our intent is to provide an ontology that fills the gaps between ontologies for biodiversity resources, such as DarwinCore-based ontologies, and semantic publishing ontologies, such as the SPAR Ontologies. We bridge this gap by providing an ontology focusing on biological taxonomy., Results: OpenBiodiv-O introduces classes, properties, and axioms in the domains of scholarly biodiversity publishing and biological taxonomy and aligns them with several important domain ontologies (FaBiO, DoCO, DwC, Darwin-SW, NOMEN, ENVO). By doing so, it bridges the ontological gap across scholarly biodiversity publishing and biological taxonomy and allows for the creation of a Linked Open Dataset (LOD) of biodiversity information (a biodiversity knowledge graph) and enables the creation of the OpenBiodiv Knowledge Management System. A key feature of the ontology is that it is an ontology of the scientific process of biological taxonomy and not of any particular state of knowledge. This feature allows it to express a multiplicity of scientific opinions. The resulting OpenBiodiv knowledge system may gain a high level of trust in the scientific community as it does not force a scientific opinion on its users (e.g. practicing taxonomists, library researchers, etc.), but rather provides the tools for experts to encode different views as science progresses., Conclusions: OpenBiodiv-O provides a conceptual model of the structure of a biodiversity publication and the development of related taxonomic concepts. It also serves as the basis for the OpenBiodiv Knowledge Management System.

Background: Interpreting large-scale studies from microarrays or next-generation sequencing for further experimental testing remains one of the major challenges in quantitative biology. Combining expression with physical or genetic interaction data has already been successfully applied to enhance knowledge from all types of high-throughput studies. Yet, toolboxes for navigating and understanding even small gene or protein networks are poorly developed., Results: We introduce two Cytoscape plug-ins, which support the generation and interpretation of experiment-based interaction networks. The virtual pathway explorer viPEr creates so-called focus networks by joining a list of experimentally determined genes with the interactome of a specific organism. viPEr calculates all paths between two or more user-selected nodes, or explores the neighborhood of a single selected node. Numerical values from expression studies assigned to the nodes serve to score identified paths. The pathway enrichment analysis tool PEANuT annotates networks with pathway information from various sources and calculates enriched pathways between a focus and a background network. Using time series expression data of atorvastatin treated primary hepatocytes from six patients, we demonstrate the handling and applicability of viPEr and PEANuT. Based on our investigations using viPEr and PEANuT, we suggest a role of the FoxA1/A2/A3 transcriptional network in the cellular response to atorvastatin treatment. Moreover, we find an enrichment of metabolic and cancer pathways in the Fox transcriptional network and demonstrate a patient-specific reaction to the drug., Conclusions: The Cytoscape plug-in viPEr integrates -omics data with interactome data. It supports the interpretation and navigation of large-scale datasets by creating focus networks, facilitating mechanistic predictions from -omics studies. PEANuT provides an up-front method to identify underlying biological principles by calculating enriched pathways in focus networks.