Polya
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A Finite Certificate for the Positive $n=9$ Vasc Inequality
arXiv:2606.06136v1 Announce Type: new Abstract: We prove the positive-real $n=9$ case of the Vasc cyclic inequality. The proof was obtained with human-guided assistance from the AI agent MechMath Agent Team: the human-readable part reduces the rational inequality to a homogeneous polynomial inequality, fixes a cyclic maximum, and parametrizes each sorted fixed-maximum cone by cumulative gaps; the finite part is a certificate covering all $8!=40320$ sorted cones. MechMath Agent Team generated...
An Integrating Sphere Based Method for Quantifying RNA Encapsulation Efficiency in Lipid Nanoparticles without Lysis
Encapsulation efficiency (EE) is a critical quality attribute of lipid nanoparticle (LNP)-RNA formulations, determining the fraction of active RNA payload available for delivery and influencing therapeutic potency, dose accuracy, and product consistency. Conventional fluorescence-based EE assays, such as RiboGreen (RG), require detergent-mediated LNP lysis, which can introduce systematic bias arising from incomplete particle disruption and additional sample handling steps. Here, we report a...
Whole-genome duplication shaped cell-type evolution in the vertebrate brain
Abstract The complex brains of vertebrates have more cell types than those of their closest relatives. Whole-genome duplications (WGDs) occurred during early vertebrate evolution1, but it is unclear whether the duplicated genes (ohnologues) facilitated cell-type evolution. Here using brain single-cell transcriptomes from five chordates—human2, mouse3, lizard4, lamprey5 and amphioxus—we report that many cell-type families with conserved core transcription factors in vertebrates do not show...