Effects of Langmuir Kinetics of Two-Lane Totally Asymmetric Exclusion Processes in Protein Traffic

In this paper, we study a two-lane totally asymmetric simple exclusion process (TASEP) coupled with random attachment and detachment of particles (Langmuir kinetics) in both lanes under open boundary conditions. Our model can describe the directed motion of molecular motors, attachment and detachment of motors, and free inter-lane transition of motors between filaments. In this paper, we focus on some finite-size effects of the system because normally the sizes of most real systems are finite and small (e.g., size $\leq 10,000$). A special finite-size effect of the two-lane system has been observed, which is that the density wall moves left first and then move towards the right with the increase of the lane-changing rate. We called it the jumping effect. We find that increasing attachment and detachment rates will weaken the jumping effect. We also confirmed that when the size of the two-lane system is large enough, the jumping effect disappears, and the two-lane system has a similar density profile to a single-lane TASEP coupled with Langmuir kinetics. Increasing lane-changing rates has little effect on density and current after the density reaches maximum. Also, lane-changing rate has no effect on density profiles of a two-lane TASEP coupled with Langmuir kinetics at a large attachment/detachment rate and/or a large system size. Mean-field approximation is presented and it agrees with our Monte Carlo simulations.Comment: 15 pages, 8 figures. To be published in IJMP

Iterative estimating equations: Linear convergence and asymptotic properties

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.Comment: Published in at http://dx.doi.org/10.1214/009053607000000208 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Agent-Based Load Balancing on Homogeneous Minigrids: Macroscopic Modeling and Characterization

Abstract—In this paper, we present a macroscopic characterization of agent-based load balancing in homogeneous minigrid environments. The agent-based load balancing is regarded as agent distribution from a macroscopic point of view. We study two quantities on minigrids: the number and size of teams where agents (tasks) queue. In macroscopic modeling, the load balancing mechanism is characterized using differential equations. We show that the load balancing we concern always converges to a steady state. Furthermore, we show that load balancing with different initial distributions converges to the same steady state gradually. Also, we prove that the steady state becomes an even distribution if and only if agents have complete knowledge about agent teams on minigrids. Utility gains and efficiency are introduced to measure the quality of load balancing. Through numerical simulations, we discuss the utility gains and efficiency of load balancing in different cases and give a series of analysis. In order to maximize the utility gain and the efficiency, we theoretically discuss the optimization of agents ’ strategies. Finally, in order to validate our proposed agentbased load balancing mechanism, we develop a computing platform, called Simulation System for Grid Task Distribution (SSGTD). Through experimentation, we note that our experimental results in general confirm our theoretical proofs and numerical simulation results on the proposed equation system. In addition, we find a very interesting phenomenon, that is, our agent-based load balancing mechanism is topology-independent