In a geometry, a maximal cap is a collection of points of largest size no three of which are collinear. In AG(4, 3), maximal caps contain 20 points; the 81 points of AG(4, 3) can be partitioned into 4 mutually disjoint maximal caps together with a single point P , where every pair of points that makes a line with P lies entirely inside one of those caps. The caps in a partition can be paired up...

Imposing caps on managers’ pay has been a popular way to discipline managers of companies or banks that got into trouble during the recent financial crisis. Using a small extension of the standard principal-agent model, we argue that pay caps may serve the opposite purpose because the agent can be better off with a pay cap. Specifically, we show that, given a fixed effort level to be implemente...

Headley DB, DeLucca MV, Haufler D, Paré D. Incorporating 3D-printing technology in the design of head-caps and electrode drives for recording neurons in multiple brain regions. J Neurophysiol 113: 2721–2732, 2015. First published February 4, 2015; doi:10.1152/jn.00955.2014.—Recent advances in recording and computing hardware have enabled laboratories to record the electrical activity of multipl...

Introduction: The martian polar caps are in majority composed of CO2 ice [1-3]. Early modeling of the polar caps suggested that they were in equilibrium with the ~6 mbar CO2 atmosphere [2], and various observations have shown a ciclicity of growth and retreat, following martian seasons [4]. However, other studies show that CO2 ice constitutes only a thin veneer on the surface of a probably much...

In the central auditory system, cartwheel cells (CWCs) are a group of interneurons in the dorsal cochlear nucleus (DCN). While other DCN neurons respond to stimuli with a simple discharge pattern of single action potentials (SAPs), CWCs respond with complex action potentials (CAPs), consisting of SAPs superimposed on a slow depolarization. The CAPs in CWCs may participate in various auditory or...

CONTEXT The majority of Medicare drug benefits in managed care (Medicare + Choice) have annual dollar limits or caps and many beneficiaries face temporary but potentially significant gaps in coverage after exceeding caps before the end of the year. In the new national Medicare drug benefit, beneficiaries with high medication expenditures will also face a period without drug coverage when their ...

The range of scales is immense. At the high end we are looking at changes in the ice caps near the North and South poles, at the global ocean and atmospheric circulation patterns and, on a shorter time scale, at the motion of weather patterns around the globe. The length scale in each of these cases is in the thousand kilometre range, and this is not the subject of the present article, though w...

This paper models settlement arrangements between international telecommunication carriers. The FCC in the U.S. claims these arrangements cost U.S. consumers billions of dollars annually, largely to subsidize foreign carriers in low-income countries. A model is given which makes sense of this claim, as well as the role of costs, competition, and income disparities in settlement rate determinati...

A line in (Z/nZ)2 is any translate of a cyclic subgroup of order n. A subset X ⊂ (Z/nZ)2 is a cap if no three of its points are collinear, and X is complete if it is not properly contained in another cap. We determine bounds on Φ(n), the minimum size of a complete cap in (Z/nZ)2. The other natural extremal question of determining the maximum size of a cap in (Z/nZ)2 is considered in [8]. These ...

Drop N random caps all of the same angular radius θ = c √ 1 N logN on a unit sphere. Let U denote the part of the surface covered by these caps. We prove that if c > √ 2, then the probability that U is connected tends to 1 as N → ∞, while if c < 1, then the probability that U is connected tends to 0 as N → ∞.