This paper describes two new types of winning sets in \(\mathbb{R}^n\), defined using variants of Schmidt’s game. These strong and absolute winning sets include many Diophantine sets of measure zero and first category, and ...

We define the symplectic rational blow-up operation, for a family of rational homology balls \(B_n\), which appeared in Fintushel and Stern's rational blow-down construction. We do this by exhibiting a symplectic structure ...

This paper gives an account of the unitary representations of the braid group that arise via the Hodge theory of cyclic branched coverings of \(\mathbb{P}^1\) , highlighting their connections with ergodic theory, complex ...

We constructed a corpus of digitized texts containing about 4% of all books ever printed. Analysis of this corpus enables us to investigate cultural trends quantitatively. We survey the vast terrain of ‘culturomics,’ ...

Despite the high inhibition of viral replication achieved by current anti-HIV drugs, many patients fail treatment, often with emergence of drug-resistant virus. Clinical observations show that the relationship between ...

Biologists have devoted much attention to assortative mating or homogamy, the tendency for sexual species to mate with similar others. In contrast, there has been little theoretical work on the broader phenomenon of ...

Traditionally microorganisms were considered to be autonomous organisms that could be studied in isolation. However, over the last decades cell-to-cell communication has been found to be ubiquitous. By secreting molecular ...

Tumor growth is caused by the acquisition of driver mutations, which enhance the net reproductive rate of cells. Driver mutations may increase cell division, reduce cell death, or allow cells to overcome density-limiting ...