Some aspects of a two-pore translocation problem

We report Brownian dynamics (BD) simulation results for a coarse-grained (CG) model semi-flexible polymer threading through two nanopores. Particularly we study a “tug-of-war” situation where equal and opposite forces are applied on each pore to avoid folds for the polymer segment in between the pores. We calculate mean first passage times (MFPT) through the left and the right pores and show how the MFPT decays as a function of the off-set voltage between the pores. We present results for several bias voltages and chain stiffness. Our BD simulation results validate recent experimental results and offer avenues to further explore various aspects of multi-pore translocation problem using BD simulation strategies which we believe will provide insights to design new experiments.

Weighted trapping time of weighted directed treelike network

With the deepening of research on complex networks, many properties of complex networks are gradually studied, for example, the mean first-passage times, the average receive times and the trapping times. In this paper, we further study the average trapping time of the weighted directed treelike network constructed by an iterative way. Firstly, we introduce our model inspired by trade network, each edge [Formula: see text] in undirected network is replaced by two directed edges with weights [Formula: see text] and [Formula: see text]. Then, the trap located at central node, we calculate the weighted directed trapping time (WDTT) and the average weighted directed trapping time (AWDTT). Remarkably, the WDTT has different formulas for even generations and odd generations. Finally, we analyze different cases for weight factors of weighted directed treelike network.

Computing Kemeny's constant for a barbell graph

In a graph theory setting, Kemeny’s constant is a graph parameter which measures a weighted average of the mean first passage times in a random walk on the vertices of the graph. In one sense, Kemeny’s constant is a measure of how well the graph is ‘connected’. An explicit computation for this parameter is given for graphs of order n consisting of two large cliques joined by an arbitrary number of parallel paths of equal length, as well as for two cliques joined by two paths of different length. In each case, Kemeny’s constant is shown to be O(n3), which is the largest possible order of Kemeny’s constant for a graph on n vertices. The approach used is based on interesting techniques in spectral graph theory and includes a generalization of using twin subgraphs to find the spectrum of a graph.