[1] G. Faltings, Diophantine approximation on abelian varieties, Ann. of Math., 133 (1991), 549-576. [2] M. Hindry, Autour d'une conjecture de Serge Lang, Invent. math., 94 (1988), 575-603. [3] B. Poonen, Mordell-Lang plus Bogomolov, Invent. math., 137 (1999), 413-425. [4] M. McQuillan, Divison points on semi-abelian varieties, Invent. math., 120 (1995), 143-159. [5] A. Moriwaki, Arithmetic hei...

Link-INVENT enables design of PROTACs, fragment linking, and scaffold hopping while satisfying multiple optimization criteria.

Where product innovation requires several complementary patents, fragmented property rights can limit firms’ willingness to invest in R&D. We consider the research intensity in multiple simultaneous R&D contests and how it depends on whether firms already hold relevant patents as well as the availability of an option to invent around. A measure of technological uncertainty is also analysed. The...

The ability to reason beyond established knowledge allows organic chemists to solve synthetic problems and invent novel transformations. Herein, we propose a model that mimics chemical reasoning, and formalises reaction prediction as finding missing links in a knowledge graph. We have constructed a knowledge graph containing 14.4 million molecules and 8.2 million binary reactions, which represe...