Stroke affects millions each year. Poststroke brain edema predicts the severity of eventual stroke damage, yet our concept of how edema develops is incomplete and treatment options remain limited. In early stages, fluid accumulation occurs owing to a net gain of ions, widely thought to enter from the vascular compartment. Here, we used magnetic resonance imaging, radiolabeled tracers, and multiphoton imaging in rodents to show instead that cerebrospinal fluid surrounding the brain enters the tissue within minutes of an ischemic insult along perivascular flow channels. This process was initiated by ischemic spreading depolarizations along with subsequent vasoconstriction, which in turn enlarged the perivascular spaces and doubled glymphatic inflow speeds. Thus, our understanding of poststroke edema needs to be revised, and these findings could provide a conceptual basis for development of alternative treatment strategies.

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For a pure electron plasma in a sufficiently strong magnetic field, there is a many-electron adiabatic invariant which constrains the collisional dynamics. For the case of a uniform magnetic field, the adiabatic invariant is the total kinetic energy associated with the electron velocity components that are perpendicular to the magnetic field (i.e., ∑j mv2j⊥ /2). Were the adiabatic invariant an exact constant of the motion, no exchange of energy would be possible between the parallel and the perpendicular degrees of freedom, and the plasma could acquire and maintain two different temperatures, T∥ and T⊥. However, an adiabatic invariant is not strictly conserved. In the present case, each collision produces an exponentially small exchange of energy between the parallel and the perpendicular degrees of freedom, and these act cumulatively in such a way that T∥ and T⊥ relax to a common value. This paper provides a calculation of the equipartition rate.

We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative. The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type.

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