Extending the double ramification cycle by resolving the Abel-Jacobi map

Over the moduli space of smooth curves, the double ramification cycle can be defined by pulling back the unit section of the universal jacobian along the Abel-Jacobi map. This breaks down over the boundary since the Abel-Jacobi map fails to extend. We construct a `universal' resolution of the Abel-Jacobi map, and thereby extend the double ramification cycle to the whole of the moduli of stable curves. In the non-twisted case, we show that our extension coincides with the cycle constructed by Li, Graber, Vakil via a virtual fundamental class on a space of rubber maps.Comment: 35 pages, 1 figure. v2:Exposition heavily revised (and hopefully improved). Main results unchanged. There was a gap in the proof of lemma 3.14; it is replaced by the construction in lemma 6.1. v3: Extended to include the `k-twisted' case, where one allows powers of the relative dualising sheaf. v4. Final version, to appear in J. Inst. Math. Jussieu. Comments still very welcom

GENDER AND GRADUATE ECONOMICS EDUCATION IN THE US

This paper reports on the ?ndings of a survey of top economics graduate schools as they relate to women and men. The results provide strong evidence that at these top graduate schools, women graduate students are less integrated in their economic disciplines than are male graduate students. In the second part of the paper, this paper relates those ?ndings to alternative theories as to why this is the case. This paper concludes by suggesting that the emphasis on theoretical studies in the current core of the graduate economics program can be seen as a type of hazing process that seems to have a signi?cant cost since many women (and men) with great creative promise are discouraged from continuing in economics and do not bene?t nearly as much as they would have from more policy-driven core courses.

Batch-Incremental Learning for Mining Data Streams

The data stream model for data mining places harsh restrictions on a learning algorithm. First, a model must be induced incrementally. Second, processing time for instances must keep up with their speed of arrival. Third, a model may only use a constant amount of memory, and must be ready for prediction at any point in time. We attempt to overcome these restrictions by presenting a data stream classification algorithm where the data is split into a stream of disjoint batches. Single batches of data can be processed one after the other by any standard non-incremental learning algorithm. Our approach uses ensembles of decision trees. These tree ensembles are iteratively merged into a single interpretable model of constant maximal size. Using benchmark datasets the algorithm is evaluated for accuracy against state-of-the-art algorithms that make use of the entire dataset

The Brauer-Manin obstruction on Kummer varieties and ranks of twists of abelian varieties

Let r > 0 be an integer. We present a sufficient condition for an abelian variety A over a number field k to have infinitely many quadratic twists of rank at least r, in terms of density properties of rational points on the Kummer variety Km(A^r) of the r-fold product of A with itself. One consequence of our results is the following. Fix an abelian variety A over k, and suppose that for some r > 0 the Brauer-Manin obstruction to weak approximation on the Kummer variety Km(A^r) is the only one. Then A has a quadratic twist of rank at least r. Hence if the Brauer-Manin obstruction is the only one to weak approximation on all Kummer varieties, then ranks of twists of any positive-dimensional abelian variety are unbounded. This relates two significant open questions.Comment: 12 pages; final versio