Pretentiously detecting power cancellation

Granville and Soundararajan have recently introduced the notion of pretentiousness in the study of multiplicative functions of modulus bounded by 1, essentially the idea that two functions which are similar in a precise sense should exhibit similar behavior. It turns out, somewhat surprisingly, that this does not directly extend to detecting power cancellation - there are multiplicative functions which exhibit as much cancellation as possible in their partial sums that, modified slightly, give rise to functions which exhibit almost as little as possible. We develop two new notions of pretentiousness under which power cancellation can be detected, one of which applies to a much broader class of multiplicative functions

When Winning is the Only Thing: Pure Strategy Nash Equilibria in a Three-Candidate Spatial Voting Model

It is well-known that there are no pure strategy Nash equilibria (PSNE) in the standard three-candidate spatial voting model when candidates maximize their share of the vote. When all that matters to the candidates is winning the election, however, we show that PSNE do exist. We provide a complete characterization of such equilibria and then extend our results to elections with an arbitrary number of candidates. Finally, when two candidates face the potential entrant of a third, we show that PSNE no longer exist, however, they do exist when the number of existing candidates is at least three.Voting, spatial equilibrium, location models, entry.

Studies on cultured Schwann cells: the induction of myelin synthesis, and the control of their proliferation by a new growth factor

We have recently described the use of immunological methods to identify and purify rat Schwann cells. In dissociated cultures of neonatal sciatic nerve, all of the cells can be identified by antigenic criteria as either Schwann cells or fibroblasts. The fibroblasts may be removed by treatment with antiserum to the Thy-1 antigen and complement. The purified Schwann cells have been used to study the regulation of the expression of myelin components, and the stimulation of Schwann cell division by a soluble growth factor. Among the components of myelin, we have concentrated on the peripheral myelin glycoprotein P_0, which constitutes 50–60% of the protein in peripheral myelin. We have studied the distribution of P_0 in vitro and in vivo by immunofluorescence, immuno-autoradiography on SDS gels, and solid-phase radioimmunoassay. Our results support the hypothesis that P_0 is induced specifically as a consequence of the interaction between the Schwann cell and the myelinated type of axon. The level of P_0 in the myelin membrane is at least 1000-fold higher than in the Schwann cell membrane. Purified Schwann cells divide very slowly in a conventional tissue culture medium. This has allowed us to purify a new growth factor from extracts of brain and pituitary, tentatively named Glial Growth Factor (GGF). The activity resides in a basic protein with a native molecular weight of 6 × 10^4 daltons and a subunit molecular weight of 3 × 10^4 daltons, which is active at levels comparable to those of epidermal growth factor. GGF is mitogenic for Schwann cells, astrocytes and muscle fibroblasts