Chapter 3 once more

Once more unto the breach, dear friends, once more.

The first issue of the World Journal of Critical Care Medicine (WJCCM), whose preparatory work was initiated on December 16, 2010, will be published on February 4, 2012. The WJCCM Editorial Board has now been established and consists of 105 distinguished experts from 27 countries. Our purpose of launching the WJCCM is to publish peer-reviewed, high-quality articles via an open-access online pub...

Divided Once More

Once More With Feeling

Chapter 1 Metrics for more than two points at once David H . Wolpert

The conventional definition of a topological metric over a space specifies properties of any measure of “how separated” two points in that space are. Here it is shown how to extend that definition, and in particular the triangle inequality, to concern arbitrary numbers of points. Such a measure of how separated the points within a collection are can be bootstrapped, to measure “how separated” f...

Limit complexities revisited [once more]

The main goal of this article is to put some known results in a common perspective and to simplify their proofs. We start with a simple proof of a result of Vereshchagin [13] saying that limsupnC(x|n) (here C(x|n) is conditional (plain) Kolmogorov complexity of x when n is known) equals C0 ′ (x), the plain Kolmogorov complexity with 0′-oracle. Then we use the same argument to prove similar resu...