‘Twixt Cup and lip…’

Havannah and TwixT are PSPACE-complete

Numerous popular abstract strategy games ranging from hex and havannah to lines of action belong to the class of connection games. Still, very few complexity results on such games have been obtained since hex was proved pspace-complete in the early eighties. We study the complexity of two connection games among the most widely played. Namely, we prove that havannah and twixt are pspacecomplete....

Between the Cup and the Lip on Post Keynesian Interest Rate Rules and Long-term Interest Rates Management

The paper states that, although Post Keynesian interest rules may be feasible and sustainable in favourable circumstances, there is a shared difficulty as for the setting of long-term interest rates in a context of strong uncertainty and shifting liquidity preference. According to Keynes theory of the interest rate, the variation in the long-term interest rate that authorities are seeking for m...

The expression of Wnt2b in the optic cup lip requires a border between the pigmented and nonpigmented epithelium

PURPOSE Wnt2b is normally expressed at the optic cup lip and is implicated in ciliary body induction. The lens has often been considered an organizer for the anterior eye, but recent studies demonstrate that the anterior cell fates are correctly specified in the absence of the lens. This study uses Wnt2b as a marker to reveal the mechanism behind the specification of the anterior domain of the ...

Many a Slip between the Cup and the Lip: Universal Access to Safe Abortion Services in India

Cup product and intersection

This is a handout for my algebraic topology course. The goal is to explain a geometric interpretation of the cup product. Namely, if X is a closed oriented smooth manifold, if A and B are oriented submanifolds of X, and if A and B intersect transversely, then the Poincaré dual of A∩B is the cup product of the Poincaré duals of A and B. As an application, we prove the Lefschetz fixed point formu...