An O(n log n)-Time Algorithm for the Restricted Scaffold Assignment

The assignment problem takes as input two finite point sets S and T and establishes a correspondence between points in S and points in T, such that each point in S maps to exactly one point in T, and each point in T maps to at least one point in S. In this paper we show that this problem has an O(n log n)-time solution, provided that the points in S and T are restricted to lie on a line (linear time, if S and T are presorted).Comment: 13 pages, 8 figure

Deformations of minimal Lagrangian submanifolds with boundary

Let $L$ be a special Lagrangian submanifold of a compact, Calabi-Yau manifold $M$ with boundary lying on the symplectic, codimension 2 submanifold $W$. It is shown how deformations of $L$ which keep the boundary of $L$ confined to $W$ can be described by an elliptic boundary value problem, and two results about minimal Lagrangian submanifolds with boundary are derived using this fact. The first is that the space of minimal Lagrangian submanifolds near $L$ with boundary on $W$ is found to be finite dimensional and is parametrised over the space of harmonic 1-forms of $L$ satisfying Neumann boundary conditions. The second is that if $W'$ is a symplectic, codimension 2 submanifold sufficiently near $W$, then under suitable conditions, there exists a minimal Lagrangian submanifold $L'$ near $L$ with boundary on $W'$.Comment: Final version; to appear in Proceedings of the American Mathematical Society. The presentation is somewhat cleaner in places and the result is restated for a general Calabi-Yau settin

SLS Fabrication of Highly Porous Model Including Fine Flow Channel Network Aiming at Regeneration of Highly Metabolic Organs

Fabrication of very porous scaffold for regeneration of highly metabolic organs is reported. Polycaprolactone (PCL) powder was mixed with fine salt grains as filler and SLS processed to develop a model including fine flow channel network. The fabricated model was rinsed with water to dissolve the salt, and high porosity of 90% was successfully obtained. Additionally, residual powder in the channels was effectively removed by solution of the filler. Through micro-CT observation, it was confirmed that channels of which diameter was smaller than 1mm were successfully fabricated and repeating branching and merging. Result of culture test is also reported.Mechanical Engineerin