Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces

Identifying spatial and temporal organization in the circadian clock (Commentary on Pauls et al.)

To organize circadian (~24 h) rhythms in physiology and behavior, the brain’s master circadian clock in the suprachiasmatic nuclei (SCN) must, like a proficient goalkeeper or sculptor, coordinate and connect its signals in both time and space. Individual SCN neurons contain the intracellular molecular clockworks, but these several thousand cell autonomous oscillators require intercellular commu...

Hypersurfaces of the Heisenberg Group Are N-rectifiable

Definition 1. Let N ′ be a Carnot group and N be a subgroup of N ′ with Hausdorff dimension k. A subset E of another Carnot Group (M,dM ) is said to be N -rectifiable if there exists U , a positive measure subset of N , and a Lipschitz map f : U → M such that H k M (E \ f(U)) = 0. We say E is countably N -rectifiable if there exist a countable number of pairs of subsets Ui and Lipschitz maps fi...

Reply to Pauls et al.: p21 is a master regulator of HIV replication in macrophages through dNTP synthesis block.

Smooth Divisors of Projective Hypersurfaces

Star points on smooth hypersurfaces

— A point P on a smooth hypersurface X of degree d in PN is called a star point if and only if the intersection of X with the embedded tangent space TP (X) is a cone with vertex P . This notion is a generalization of total inflection points on plane curves and Eckardt points on smooth cubic surfaces in P3. We generalize results on the configuration space of total inflection points on plane curv...