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Abstract We study collections of subrings of$$H^*({\overline {\mathcal {M}}}_{g,n})$$that are closed under the tautological operations that map cohomology classes on moduli spaces of smaller dimension to those on moduli spaces of larger dimension and contain the tautological subrings. Such extensions of tautological rings are well-suited for inductive arguments and flexible enough for a wide range of applications. In particular, we confirm predictions of Chenevier and Lannes for the$$\ell $$-adic Galois representations and Hodge structures that appear in$$H^k({\overline {\mathcal {M}}}_{g,n})$$for$$k = 13$$,$$14$$and$$15$$. We also show that$$H^4({\overline {\mathcal {M}}}_{g,n})$$is generated by tautological classes for allgandn, confirming a prediction of Arbarello and Cornalba from the 1990s. In order to establish the final base cases needed for the inductive proofs of our main results, we use Mukai’s construction of canonically embedded pentagonal curves of genus 7 as linear sections of an orthogonal Grassmannian and a decomposition of the diagonal to show that the pure weight cohomology of$${\mathcal {M}}_{7,n}$$is generated by algebraic cycle classes, for$$n \leq 3$$. 

Abstract We prove that the rational cohomology group$$H^{11}(\overline {\mathcal {M}}_{g,n})$$vanishes unless$$g = 1$$and$$n \geq 11$$. We show furthermore that$$H^k(\overline {\mathcal {M}}_{g,n})$$is pure Hodge–Tate for all even$$k \leq 12$$and deduce that$$\# \overline {\mathcal {M}}_{g,n}(\mathbb {F}_q)$$is surprisingly well approximated by a polynomial inq. In addition, we use$$H^{11}(\overline {\mathcal {M}}_{1,11})$$and its image under Gysin push-forward for tautological maps to produce many new examples of moduli spaces of stable curves with nonvanishing odd cohomology and nontautological algebraic cycle classes in Chow cohomology. 

Biological systems are typically dependent on transportation networks for the efficient distribution of resources and information. Revealing the decentralized mechanisms underlying the generative process of these networks is key in our global understanding of their functions and is of interest to design, manage and improve human transport systems. Ants are a particularly interesting taxon to address these issues because some species build multi-sink multi-source transport networks analogous to human ones. Here, by combining empirical field data and modelling at several scales of description, we show that pre-existing mechanisms of recruitment with positive feedback involved in foraging can account for the structure of complex ant transport networks. Specifically, we find that emergent group-level properties of these empirical networks, such as robustness, efficiency and cost, can arise from models built on simple individual-level behaviour addressing a quality-distance trade-off by the means of pheromone trails. Our work represents a first step in developing a theory for the generation of effective multi-source multi-sink transport networks based on combining exploration and positive reinforcement of best sources.