The notion of (k,m)-agreeable society was introduced by Deborah Berg et al.:a family of convex subsets of R is called (k,m)-agreeable if any subfamily of size m contains at least one non-empty k-fold intersection. In that paper, the (k,m)-agreeability of a convex family was shown to imply the existence of a subfamily of size βn with non-empty intersection, where n is the size of the original fa...

In approval voting, individuals vote for all platforms that they find acceptable. In this situation it is natural to ask: When is agreement possible? What conditions guarantee that some fraction of the voters agree on even a single platform? Berg et. al. found such conditions when voters are asked to make a decision on a single issue that can be represented on a linear spectrum. In particular, ...

The FindStat project provides an online platform for mathematicians, particularly for combinatorialists, to gather information about combinatorial statistics and their relations. As of January 2014, the FindStat database contains 173 statistics on 17 combinatorial collections. The project was initiated by Chris Berg and Christian Stump in 2011 at the Laboratoire de combinatoire et d’informatiqu...

Current guidelines in the three water-related areas (drinking water, wastewater and recreational water) assess quality, in microbiological terms, by measuring indicator organisms. This chapter looks at the history and examines some of the methods used to assess the microbiological quality of water, highlighting the current limitations and also possible future developments. Traditionally, indica...

We consider the following problem: Preprocess a set S of n axis-parallel boxes in R so that given a query of an axis-parallel box in R, the pairs of boxes of S whose intersection intersects the query box can be reported efficiently. For the case that d = 2, we present a data structure of size O(n log n) supporting O(log n+ k) query time, where k is the size of the output. This improves the prev...