ABC systems: structural and functional variations on a common theme

Geometry, Statistics, Probability: Variations on a Common Theme

ion Mathematicians like to talk about how things behave, rather than what they are. Nonmathematicians often prefer the reverse. "Anything that behaves this way is a vector (because I said so)" is not a natural way of talking to the nonmathematician. Mathematicians ought to be more sensitive to this than they typically are. Repeating examples in different words, emphasizing the equivalence of th...

Sex determination in insects: variations on a common theme.

Recent studies in a representative selection of holometabolous insects suggest that, despite diversity at the instructive level, the signal-relaying part of the sex-determining pathway is remarkably well conserved. In principle, it is composed of the transformer gene (tra), which acts as a common binary switch that transduces the selected sexual fate, female when ON, male when OFF, to the downs...

Variations on a theme.

A ring satisfying x = x is necessarily commutative. We consider a variety of weaker forms of this condition and show that many but not all of them imply commutativity. We also present a variety of elementary proofs of the fact that x = x implies commutativity.

Variations on a Theme

Variations on a Montagovian theme

What are the objects of knowledge, belief, probability, apriority or analyticity? For at least some of these properties, it seems plausible that the objects are sentences, or sentence-like entities. However, results from mathematical logic indicate that sentential properties are subject to severe formal limitations. After surveying these results, I argue that they are more problematic than ofte...