We establish the inexistence of countable bases for the family of definable cardinals associated with countable Borel equivalence relations which are not measure reducible to E0, thereby ruling out natural generalizations of the Glimm-Effros dichotomy. We also push the primary known results concerning the abstract structure of the Borel cardinal hierarchy nearly to its base, using arguments sub...

Plasmodium falciparum-infected erythrocytes adhere dichotomously to the host receptors CD36 and chondroitin sulfate A (CSA). This dichotomy is associated with parasite sequestration to microvasculature beds (CD36) or placenta (CSA), leading to site-specific pathogenesis. Both properties are mediated by members of the variant P. falciparum erythrocyte membrane protein 1 (PfEMP-1) family and resi...

In this paper, we present Dichotomy, a novel practical architecture that exploits channel diversity to improve wireless multi-hop network throughput with a single transceiver. Unlike previous link-layer multichannel work that requires complex coordination and is difficult to implement, Dichotomy operates without clock synchronization, and with greatly reduced switching overhead. The core idea i...

We consider C Hamiltonian functions on compact 4-dimensional symplectic manifolds to study elliptic dynamics of the Hamiltonian flow, namely the so-called Newhouse dichotomy. We show that for any open set U intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through U . Moreover, this implies that for far from Anosov regular energ...