Abstract. The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are C 1,1 curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.
Nursing has reciprocal benefits for both mother and infant, helping to promote maternal behavior and bonding. To test the "rewarding" nature of nursing, functional magnetic resonance imaging was used to map brain activity in lactating dams exposed to their suckling pups versus cocaine. Suckling stimulation in lactating dams and cocaine exposure in virgin females activated the dopamine reward system. In contrast, lactating dams exposed to cocaine instead of pups showed a suppression of brain activity in the reward system. These data support the notion that pup stimulation is more reinforcing than cocaine, underscoring the importance of pup seeking over other rewarding stimuli during lactation.
We minimize a discrete version of the squared mean curvature integral for polyhedral surfaces in three-space, using Brakke's Surface Evolver [Brakke 1992]. Our experimental results support the conjecture that the smooth minimizers exist for each genus and are stereographic projections of certain minimal surfaces in the three-sphere.
We show it is possible to tile three-dimensional space using only tetrahedra
with acute dihedral angles. We present several constructions to achieve this,
including one in which all dihedral angles are less than $77.08^\circ$, and
another which tiles a slab in space.Comment: 20 pages; 17 figures; 1 table; see also
http://www.cs.duke.edu/~ungor/abstracts/acute_tiling.htm
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