It has been widely acknowledged that the Goldman-Hodgkin-Katz (GHK) equation fully explains membrane potential behavior. The fundamental facet of the GHK equation lies in its consideration of permeability of membrane to ions, when the membrane serves as a separator for separating two electrolytic solutions. The GHK equation describes that: variation of membrane permeability to ion in accordance...

The notion of staircase separator, introduced in 2], greatly facilitates the design of divide-and-conquer algorithms for problems on rectangles. We generalize the concept of staircase separator to k-perfect staircase separator, namely a set of staircase separators which partitions a set S of n axis-parallel, disjoint rectangles into k subsets of (almost) equal size. We derive an optimal O(log n...

(1) p(x) = ∏ C ΨC(xC) ∏ S ΦS(xS) where ΨC(xC ) is the potential for a clique C , and ΦS(xS) is the potential for a separator S. After Junction Tree algorithm, the clique potential ΨC(xC) becomes the marginal probability for clique C . Thus, we are able to achieve a representation that is a product of marginals, and yet is also a representation of the joint probability. After we initialize maxim...

For a graph G with n vertices and m edges, we give a randomized Las Vegas algorithm that approximates a small balanced vertex separator of G in almost linear time. More precisely, we show the following, for any 2 3 ≤ α < 1 and any 0 < ε < 1 − α: If G contains an α-separator of size K, then our algorithm finds an (α + ε)-separator of size O(ε−1K2 log n) in time O(ε−1K3m log n) w.h.p. In particul...

Good flow and pressure control is essential for successful Underbalanced Drilling (UBD) operations. This work evaluates the use of Model Predictive Control (MPC) for integrated control of well conditions and the topside separation system during UBD. The downhole well pressure, separator liquid levels, and the separator pressure are controlled by manipulation of the rig pump, the choke, and the ...

We present I/O-efficient algorithms for computing optimal separator partitions of planar graphs. Our main result shows that, given a planar graph G with N vertices and an integer r > 0, a vertex separator of size O (N/√r) that partitions G into O(N/r) subgraphs of size at most r and boundary size O (√r) can be computed in O(sort(N)) I/Os, provided that M ≥ 56r log B. Together with the planar em...

Lithium-sulfur (Li-S) batteries have become promising candidates for electrical energy storage systems due to their high theoretical specific energy density, low cost and environmental friendliness. However, there are some technical obstacles of lithium-sulfur batteries to be addressed, such as the shuttle effect of polysulfides. Here, we introduced organically modified carbon nanotubes (CNTs) ...

We propose a class of graphs that would occur naturally in finite-element and finitedifference problems and we prove a bound on separators for this class of graphs. Graphs in this class are embedded in d-dimensional space in a certain manner. For d-dimensional graphs our separator bound is O(n(d−1)/d), which is the best possible bound. We also propose a simple randomized algorithm to find this ...

We introduce the notion of the width bounded geometric separator and develop the techniques for the existence of the width bounded separator in any d-dimensional Euclidean space. The separator is applied in obtaining 2 √ n) time exact algorithms for a class of NPcomplete geometric problems, whose previous algorithms take n √ n) time [2,5,1]. One of those problems is the well known disk covering...