We provide further explanation of the significance of an example in a recent paper of Wolf in the context of the problem of finding large subspaces in sumsets. Throughout these notes G will denote the group F2 , that is the n-dimensional vector space over F2, and PG will denote the normalized counting measure on G. The convolution of two functions f, g ∈ L(PG) is defined to be f ∗ g(x) := ∫

Agricultural biotechnology, especially genetic engineering or genetic modification (GM), is a topic of considerable controversy worldwide. The public debate is fraught with polarized views and opinions, some are held with religious zeal. Unfortunately, it is also marked with much ignorance and misinformation. Here we explore some popular misconceptions encountered in the public debate.

In an instance G = (A∪B,E) of the stable marriage problem with strict and possibly incomplete preference lists, a matchingM is popular if there is no matchingM ′ where the vertices that prefer M ′ to M outnumber those that prefer M to M ′. All stable matchings are popular and there is a simple linear time algorithm to compute a maximum-size popular matching. More generally, what we seek is a mi...

For a set A of n applicants and a set I of m items, let us consider the problem of matching applicants to items, where each applicant x ∈ A provides its preference list defined on items. We say that an applicant x prefers an item p than an item q if p is located at higher position than q in its preference list. For any matchingsM andM′ of the matching problem, we say that an applicant x prefers...

One of the most fundamental and ubiquitous problems in microeconomics and operations research is how to assign objects to agents based on their individual preferences. An assignment is called popular if there is no other assignment that is preferred by a majority of the agents. Popular assignments need not exist, but the minimax theorem implies the existence of a popular random assignment. In t...

For a set A of n people and a set B ofm items, with each person having a preference list that ranks all items from most wanted to least wanted, we consider the problem of matching every person with a unique item. A matchingM is called -popular if for any other matching M ′, the number of people who prefer M ′ to M is at most n plus the number of those who prefer M to M ′. In 2006, Mahdian showe...

It is good to see that London has produced an atlas well worthy to replace the German atlases which hitherto have flooded the country. The present atlas has twenty-four pages of illustrated letterpress and a fine plate illustrating the anatomy and physiology of the female body. The plates are extremely good, the muscles and chief organs being very distinct. We can strongly recommend this atlas ...