A "Miserable Piece of Patchwork"

Miserable and strongly miserable impartial games

An impartial game is called (strongly) miserable if its normal and misère versions differ just slightly; more precisely, if some (all) zeros and ones of the Sprague-Grundy (SG) functions swap, while all larger values remain the same. We obtain necessary and sufficient conditions for (strong) miserability and show that NIM, Wythoff’s NIM, and game Euclid are miserable but not strongly miserable,...

On tame, pet, miserable, and strongly miserable impartial games

We consider tame impartial games and develop the Sprague-Grundy theory for misère playing the sum of such games that looks simpler than the classical theory suggested by Conway in 1976, which is based on the concept of genus. An impartial game is called pet if the sets of P-positions of its normal and misère versions are disjoint. We provide several equivalent characterizations and show that th...

Graphene patchwork.

Graphene oxide (GO) holds tremendous potential for large-area electronics, high strength and conducting fillers in composites, and high-surface-area electrodes for energy storage. Graphene oxide for such applications will require manufacturing methods that are industrially compatible but also preserve its unique properties. Recent work by Korkut et al. describes a promising new scheme for conti...

The Dark Side of a Patchwork Universe ∗

While observational cosmology has recently progressed fast, it revealed a serious dilemma called dark energy: an unknown source of exotic energy with negative pressure driving a current accelerating phase of the universe. All attempts so far to find a convincing theoretical explanation have failed, so that one of the last hopes is the yet to be developed quantum theory of gravity. In this artic...

Science fraud: from patchwork mouse to patchwork data.