Abstract Introduction Emerging data from our group found longitudinal sleep variability within the Seattle Longitudinal Study was significantly associated with cognitive impairment and predicted 10-years downstream. While this supports a link between instability, aging, decline, mechanism linking these processes is unknown. MRI-visible perivascular space (PVS) burden putative marker of glymphat...

I describe the entry process in a spatial market over an in...nite time horizon. I show that, as long as the strategy space at the location stage is unbounded, the results derived from the single-period Stackelberg model of entry coincide with those obtained in the in...nite horizon model. On the contrary, if the strategy space is bounded, then the later the follower enters, the closer to the c...

(1) For all sets X1, X2 and for all sets a1, a2 holds [:X1 7−→ a1, X2 7−→ a2 :] = [:X1, X2 :] 7−→ 〈a1, a2〉. Let I be a set. One can check that 0I is function yielding. Next we state two propositions: (2) For all functions f , g holds x(g · f ) = g ·x f . (3) For all functions f , g, h holds x( f · [:g, h :]) = x f · [:h, g :]. Let f be a function yielding function. Observe that x f is function ...