Cannibal Animal Games: A new variant of Tic-Tac-Toe

This paper presents a new partial two-player game, called the cannibal animal game, which is a variant of Tic-Tac-Toe. The game is played on the infinite grid, where in each round a player chooses and occupies free cells. The first player Alice can occupy a cell in each turn and wins if she occupies a set of cells, the union of a subset of which is a translated, reflected and/or rotated copy of a previously agreed upon polyomino P (called an animal). The objective of the second player Bob is to prevent Alice from creating her animal by occupying in each round a translated, reflected and/or rotated copy of P. An animal is a cannibal if Bob has a winning strategy, and a non-cannibal otherwise. This paper presents some new tools, such as the bounding strategy and the punching lemma, to classify animals into cannibals or non-cannibals. We also show that the pairing strategy works for this problem.

CB1 cannabinoid receptor deficiency promotes cardiac remodeling induced by pressure overload in mice

Background: The endocannabinoid system is known to play a role in regulating myocardial contractility, but the influence of cannabinoid receptor 1 (CB1) deficiency on chronic heart failure (CHF) remains unclear. In this study we attempted to investigate the effect of CB1 deficiency on CHF induced by pressure overload and the possible mechanisms involved. Methods and results: A CHF model was created by transverse aortic constriction (TAC) in both CB1 knockout mice and wild-type mice. CB1 knockout mice showed a marked increase of mortality due to CHF from 4 to 8 weeks after TAC (p = 0.021). Five weeks after TAC, in contrast to wild-type mice, CB1 knockout mice had a higher left ventricular (LV) end-diastolic pressure, lower rate of LV pressure change (± dp/dt max), lower LV contractility index, and a larger heart weight to body weight ratio and lung weight to body weight ratio compared with wild-type mice (all p < 0.05-0.001). Phosphorylation of the epidermal growth factor receptor (EGFR) and mitogen-activated protein kinases (P38 and ERK) was higher in CB1 knockout mice than that in wild-type mice. In cultured neonatal rat cardiomyocytes, a CB1 agonist reduced cAMP production stimulated by isoproterenol or forskolin, and suppressed phosphorylation of the EGFR, P38, and ERK, while the inhibitory effect of a CB1 agonist on EGFR phosphorylation was abrogated by CB1 knockdown. Conclusion: These findings indicate that cannabinoid receptor 1 inactivation promotes cardiac remodeling by enhancing the activity of the epidermal growth factor receptor and mitogen-activated protein kinases. © 2012 Elsevier Ireland Ltd.