Products of Nearly Holomorphic Eigenforms

We prove that the product of two nearly holomorphic Hecke eigenforms is again a Hecke eigenform for only finitely many choices of factors.Comment: 8 page

Trust in Science: CRISPR-Cas9 and the Ban on Human Germline Editing

This is the final version of the article. Available from Springer Verlag via the DOI in this record.In 2015 scientists called for a partial ban on genome editing in human germline cells. This call was a response to the rapid development of the CRISPR-Cas9 system, a molecular tool that allows researchers to modify genomic DNA in living organisms with high precision and ease of use. Importantly, the ban was meant to be a trust-building exercise that promises a 'prudent' way forward. The goal of this paper is to analyse whether the ban can deliver on this promise. To do so the focus will be put on the precedent on which the current ban is modelled, namely the Asilomar ban on recombinant DNA technology. The analysis of this case will show (a) that the Asilomar ban was successful because of a specific two-step containment strategy it employed and (b) that this two-step approach is also key to making the current ban work. It will be argued, however, that the Asilomar strategy cannot be transferred to human genome editing and that the current ban therefore fails to deliver on its promise. The paper will close with a reflection on the reasons for this failure and on what can be learned from it about the regulation of novel molecular tools.The research leading to this paper has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 324186

EXPANSION PROPERTIES OF LEVI GRAPHS

ABSTRACT. The Levi graph of a balanced incomplete block design is the bipartite graph whose vertices are the points and blocks of the design, with each block adjacent to those points it contains. We derive upper and lower bounds on the isoperimetric numbers of such graphs, with particular attention to the special cases of finite projective planes and Hadamard designs. 1