October 25, 1842

Arbiter, October 25

Lecture 18: October 25 18.1 Martingales

As a motivation, consider a fair game (i.e., the expected win/loss from each play of the game is zero). Suppose a gambler plays the game multiple times; neither his stakes, nor the outcome of the games need be independent, but each play is fair. Let Zi denote the outcome of the i game and Xi the gambler’s capital after game i. Fairness ensures that the expected capital after a game is the same ...

Erratum, Vol. 9, October 25 Release

Metamaterials: Shrinking Circuit Elements and Nano-optics (October 25, 2006)

Metamaterials are engineered composite media with unconventional electromagnetic and optical properties. They can be formed by embedding sub-wavelength inclusions as "artificial molecules" in host media in order to exhibit specific desired response functions that are not readily available in nature, but physically realizable. These metamaterials have exciting characteristics in manipulating and...

Paul H. Patterson (October 22, 1943 - June 25, 2014).

Eminent Caltech neuroscientist, Paul H. Patterson, died on June 25, 2014 as a result of glioblastoma multiforme. He is survived by wife, Carolyn, and son, Paul Claire, both great sources of joy for him. Paul’s numerous personal and scientific contributions will long outlast his tenure in life. Being both an amazing scientist and human being, Paul influenced and inspired countless friends, colla...