We show how to construct an O p n separator decomposition of a planar graph G in O n time Such a decomposition de nes a binary tree where each node corresponds to a subgraph of G and stores an O p n separator of that subgraph We also show how to construct an O n way decomposition tree in parallel in O log n time so that each node corresponds to a subgraph of G and stores an O n separator of tha...

The combined use of brush anodes and glass fiber (GF1) separators, and plastic mesh supporters were used here for the first time to create a scalable microbial fuel cell architecture. Separators prevented short circuiting of closely-spaced electrodes, and cathode supporters were used to avoid water gaps between the separator and cathode that can reduce power production. The maximum power densit...

Acoustic cell retention devices have provided a practical alternative for up to 50 L/day perfusion cultures but further scale-up has been limited. A novel temperature-controlled and larger-scale acoustic separator was evaluated at up to 400 L/day for a 10(7) CHO cell/mL perfusion culture using a 100-L bioreactor that produced up to 34 g/day recombinant protein. The increased active volume of th...

Plotkin, Rao, and Smith (SODA’97) showed that any graph with m edges and n vertices that excludes Kh as a depth O(l logn)-minor has a separator of size O(n/l + lh logn) and that such a separator can be found in O(mn/l) time. A time bound of O(m + n/l) for any constant ǫ > 0 was later given (W., FOCS’11) which is an improvement for non-sparse graphs. We give three new algorithms. The first has t...

A set of vertices S ⊆ V is called a safe separator for treewidth, if S is a separator of G, and the treewidth of G equals the maximum of the treewidth over all connected components W of G S of the graph, obtained by making S a clique in the subgraph of G, induced by W ∪ S. We show tha t such safe separators are a very powerful tool for preprocessing graphs when we want to compute their treewidt...

Given an n-vertex weighted planar graph G, a separator is a subset S of vertices such that each component of G S has at most two-thirds of the original weight. We give an algorithm nding a separator while balancing these two parameters of G[S]: the number of components, and the cost of a minimum spanning forest. In particular, given uniform edge costs and a positive integer k pn, we nd a separa...

We introduce the concept of multi-directional width-bounded geometric separators and obtain an improved separator for grid graphs. This yields an improved exact algorithm for the protein folding problem in the HP-model. For a grid graph G with n grid points P , there exists a separator A ⊆ P such that A has at most 1.02074 √ n points, and G−A has two disconnected subgraphs each with at most 2 3...

grammar ThreeFieldGrammar; structure { start: field1 & separator & field2 & separator & field3 & "\n"; separator: "-"; abstract field1; abstract field2; abstract field3; } An abstract grammar captures an incomplete specification. A non-terminal node must be declared abstract if it does not have a corresponding RHS. A grammar that has at least one abstract node must be declared abstract. A deriv...

Separation of chalcopyrite from molybdenite is currently mainly carried out by flotation, but this process costly because the extensive use inhibitors. This study briefly describes a 7.0T/100CGC low-temperature superconducting magnetic separator and discusses its separation principle as well effect induction on molybdenite. A molybdenum (Mo) concentrate assaying 6.00% copper (Cu) 19.01% Mo was ...

A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable (resp. a locally threshold testable) separator. In both cases, we design a decision procedure based on the occurrence of special patterns in automata accepting...