Constructions by transfinitely many workers

Constructions of Plane Curves with Many Points

In this paper we investigate some plane curves with many points over Q, finite fields and cyclotomic fields. In a previous paper [4] the first two authors constructed a sequence of absolutely irreducible polynomials Pd(x, y) ∈ Z[x, y] of degree d having low height and many integral solutions to Pd(x, y) = 0. (The definition of these polynomials will be recalled in §4.) Here we construct further...

Efficient constructions for one sharing of many secrets

Scoring Workers in Crowdsourcing: How Many Control Questions are Enough?

We study the problem of estimating continuous quantities, such as prices, probabilities, and point spreads, using a crowdsourcing approach. A challenging aspect of combining the crowd’s answers is that workers’ reliabilities and biases are usually unknown and highly diverse. Control items with known answers can be used to evaluate workers’ performance, and hence improve the combined results on ...

Logical constructions suggested by vision

I thank Jaap van der Does for numerous helpful conversations.

Diagrams Indexed by Grothendieck Constructions

Let I be a small indexing category, G : I → Cat be a functor and BG ∈ Cat denote the Grothendieck construction on G. We define and study Quillen pairs between the category of diagrams of simplicial sets (resp. categories) indexed on BG and the category of I-diagrams over N(G) (resp. G). As an application we obtain a Quillen equivalence between the categories of presheaves of simplicial sets (re...