On Certainty, Change, and “Mathematical Hinges”

Isaac Newton on Mathematical Certainty and Method

On Certainty

Certainty is an epistemic quality or, as philosophers are used to say, an epistemic modality. It is not easily accounted for as such; but things get even more complicated due to the fact that certainty is often confused with other epistemic modalities. Since I cannot discuss here the quite sophisticated technical treatments of certainty, I focus on disentangling certainty from and relating it t...

Opening the pore hinges on proline.

absence of Hh ligand, Ptc restrains Smo activity ; binding of Hh to Ptc releases Smo, which then transmits the intracellular signal. The regulation of Smo activity therefore occupies a pivotal position in the cellular response to Hh. Previous work had identified small molecules that inhibit or activate Hh signaling by interacting with Smo 6–8. These include the antagonist cyclopamine as well as...

Flexible antibodies with nonprotein hinges

There is a significant need for antibodies that can bind targets with greater affinity. Here we describe a novel strategy employing chemical semisynthesis to produce symmetroadhesins: antibody-like molecules having nonprotein hinge regions that are more flexible and extendible and are capable of two-handed binding. Native chemical ligation was carried out under mild, non-denaturing conditions t...

on semihypergroups and hypergroups

in this thesis, first the notion of weak mutual associativity (w.m.a.) and the necessary and sufficient condition for a $(l,gamma)$-associated hypersemigroup $(h, ast)$ derived from some family of $lesssim$-preordered semigroups to be a hypergroup, are given. second, by proving the fact that the concrete categories, semihypergroups and hypergroups have not free objects we will introduce t...