Cut the fat

Robust water/fat separation in the presence of large field inhomogeneities using a graph cut algorithm.

Water/fat separation is a classical problem for in vivo proton MRI. Although many methods have been proposed to address this problem, robust water/fat separation remains a challenge, especially in the presence of large amplitude of static field inhomogeneities. This problem is challenging because of the nonuniqueness of the solution for an isolated voxel. This paper tackles the problem using a ...

Microscopic fat cell size measurements on frozen-cut adipose tissue in comparison with automatic determinations of osmium-fixed fat cells.

Diameters of fat cells in adipose tissue slices, floating in an isoosmolar solution, were measured under a microscope. The slices were obtained from percutaneous biopsies by freeze-cutting after brief formaldehyde fixation. All cells in a given part of the slice were measured, thus avoiding selection. A normal distribution of fat cell diameters could be demonstrated with this method, as has bee...

The Taming of the Cut. Classical Refutations with Analytic Cut

Logical s-t Min-Cut Problem: An Extension to the Classic s-t Min-Cut Problem

Let $G$ be a weighted digraph, $s$ and $t$ be two vertices of $G$, and $t$ is reachable from $s$. The logical $s$-$t$ min-cut (LSTMC) problem states how $t$ can be made unreachable from $s$ by removal of some edges of $G$ where (a) the sum of weights of the removed edges is minimum and (b) all outgoing edges of any vertex of $G$ cannot be removed together. If we ignore the second constraint, ca...

Maximum Cut Problem, MAX-CUT

The MAXIMUM CUT problem (MAX-CUT) is one of the simplest graph partitioning problems to conceptualize, and yet it is one of the most difficult combinatorial optimization problems to solve. The objective of MAX-CUT is to partition the set of vertices of a graph into two subsets, such that the sum of the weights of the edges having one endpoint in each of the subsets is maximum. This problem is k...