How many meanings does a word have?

How Many Rational Points Does a Random Curve Have?

A large part of modern arithmetic geometry is dedicated to or motivated by the study of rational points on varieties. For an elliptic curve over Q, the set of rational points forms a finitely generated abelian group. The ranks of these groups, when ranging over all elliptic curves, are conjectured to be evenly distributed between rank 0 and rank 1, with higher ranks being negligible. We will de...

Learning Word Meanings from Context : How Broadly Generalizable ?

This study investigated incidental learning of word meanings from context during normal reading. A total of 352 students in third, fifth, and seventh grades read either expository or narrative passages selected from grade-level textbooks, and after six days were tested on their knowledge of difficult words from the passages. Small but reliable gains in knowledge of words from the passages read ...

How many species have mass M?

Within large taxonomic assemblages, the number of species with adult body mass M is characterized by a broad but asymmetric distribution, with the largest mass being orders of magnitude larger than the typical mass. This canonical shape can be explained by cladogenetic diffusion that is bounded below by a hard limit on viable species mass and above by extinction risks that increase weakly with ...

Perspective. How many women have osteoporosis?

Osteoporosis is widely viewed as a major public health concern, but the exact magnitude of the problem is uncertain and likely to depend on how the condition is defined. Noninvasive bone mineral measurements can be used to define a state of heightened fracture risk (osteopenia), or the ultimate clinical manifestation of fracture can be assessed (established osteoporosis). If bone mineral measur...

How many doctors should Sri Lanka have?