A super-analogue of Kontsevich's theorem on graph homology

In this paper we will prove a super-analogue of a well-known result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology of an infinite-dimensional Lie algebra of symplectic vector fields.Comment: 15 page

Hierarchy and Feedback in the Evolution of the E. coli Transcription Network

The E.coli transcription network has an essentially feedforward structure, with, however, abundant feedback at the level of self-regulations. Here, we investigate how these properties emerged during evolution. An assessment of the role of gene duplication based on protein domain architecture shows that (i) transcriptional autoregulators have mostly arisen through duplication, while (ii) the expected feedback loops stemming from their initial cross-regulation are strongly selected against. This requires a divergent coevolution of the transcription factor DNA-binding sites and their respective DNA cis-regulatory regions. Moreover, we find that the network tends to grow by expansion of the existing hierarchical layers of computation, rather than by addition of new layers. We also argue that rewiring of regulatory links due to mutation/selection of novel transcription factor/DNA binding interactions appears not to significantly affect the network global hierarchy, and that horizontally transferred genes are mainly added at the bottom, as new target nodes. These findings highlight the important evolutionary roles of both duplication and selective deletion of crosstalks between autoregulators in the emergence of the hierarchical transcription network of E.coli.Comment: to appear in PNA

Challenges of open innovation: the paradox of firm investment in open-source software

Open innovation is a powerful framework encompassing the generation, capture, and employment of intellectual property at the firm level. We identify three fundamental challenges for firms in applying the concept of open innovation: finding creative ways to exploit internal innovation, incorporating external innovation into internal development, and motivating outsiders to supply an ongoing stream of external innovations. This latter challenge involves a paradox, why would firms spend money on R&D efforts if the results of these efforts are available to rival firms? To explore these challenges, we examine the activity of firms in opensource software to support their innovation strategies. Firms involved in open-source software often make investments that will be shared with real and potential rivals. We identify four strategies firms employ – pooled R&D/product development, spinouts, selling complements and attracting donated complements – and discuss how they address the three key challenges of open innovation. We conclude with suggestions for how similar strategies may apply in other industries and offer some possible avenues for future research on open innovation

Natural climate solutions

Our thanks for inputs by L. Almond, A. Baccini, A. Bowman, S. CookPatton, J. Evans, K. Holl, R. Lalasz, A. Nassikas, M. Spalding, M. Wolosin, and expert elicitation respondents. Our thanks for datasets developed by the Hansen lab and the NESCent grasslands working group (C. Lehmann, D. Griffith, T. M. Anderson, D. J. Beerling, W. Bond, E. Denton, E. Edwards, E. Forrestel, D. Fox, W. Hoffmann, R. Hyde, T. Kluyver, L. Mucina, B. Passey, S. Pau, J. Ratnam, N. Salamin, B. Santini, K. Simpson, M. Smith, B. Spriggs, C. Still, C. Strömberg, and C. P. Osborne). This study was made possible by funding from the Doris Duke Charitable Foundation. Woodbury was supported in part by USDA-NIFA Project 2011-67003-30205 Data deposition: A global spatial dataset of reforestation opportunities has been deposited on Zenodo (https://zenodo.org/record/883444). This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1710465114/-/DCSupplemental.Peer reviewedPublisher PD