Stochastic Biasing and Galaxy-Mass Density Relation in the Weakly Non-linear Regime

It is believed that the biasing of the galaxies plays an important role for understanding the large-scale structure of the universe. In general, the biasing of galaxy formation could be stochastic. Furthermore, the future galaxy survey might allow us to explore the time evolution of the galaxy distribution. In this paper, the analytic study of the galaxy-mass density relation and its time evolution is presented within the framework of the stochastic biasing. In the weakly non-linear regime, we derive a general formula for the galaxy-mass density relation as a conditional mean using the Edgeworth expansion. The resulting expression contains the joint moments of the total mass and galaxy distributions. Using the perturbation theory, we investigate the time evolution of the joint moments and examine the influence of the initial stochasticity on the galaxy-mass density relation. The analysis shows that the galaxy-mass density relation could be well-approximated by the linear relation. Compared with the skewness of the galaxy distribution, we find that the estimation of the higher order moments using the conditional mean could be affected by the stochasticity. Therefore, the galaxy-mass density relation as a conditional mean should be used with a caution as a tool for estimating the skewness and the kurtosis.Comment: 22 pages, 7 Encapusulated Postscript Figures, aastex, The title and the structure of the paper has been changed, Results and conclusions unchanged, Accepted for publication in Ap

An Iterative Abstraction Algorithm for Reactive Correct-by-Construction Controller Synthesis

In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a Finite Transition System (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are under- and over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the efficiency of the new abstraction algorithm is illustrated by numerical examples.Comment: A shorter version has been accepted for publication in the 54th IEEE Conference on Decision and Control (held Tuesday through Friday, December 15-18, 2015 at the Osaka International Convention Center, Osaka, Japan

Synthesis of Distributed Longitudinal Control Protocols for a Platoon of Autonomous Vehicles

We develop a framework for control protocol synthesis for a platoon of autonomous vehicles subject to temporal logic specifications. We describe the desired behavior of the platoon in a set of linear temporal logic formulas, such as collision avoidance, close spacing or comfortability. The problem of decomposing a global specification for the platoon into distributed specification for each pair of adjacent vehicles is hard to solve. We use the invariant specifications to tackle this problem and the decomposition is proved to be scalable.. Based on the specifications in Assumption/Guarantee form, we can construct a two-player game (between the vehicle and its closest leader) locally to automatically synthesize a controller protocol for each vehicle. Simulation example for a distributed vehicles control problem is also shown

A Comparative Efficiency Analysis of Wheat Farms using Parametric and Nonparametric Methods

Efficiency Analysis, Deterministic Nonparametric Method, Parametric, Stochastic Frontier., Production Economics, Q12,

Circulating and persistent currents induced by a current magnification and Aharonov-Casher phase

We considered the circulating current induced by the current magnification and the persistent current induced by Aharonov-Casher flux. The persistent currents have directional dependence on the direct current flow, but the circulating currents have no directional dependence. Hence in the equilibrium, only the persistent current can survives on the ring. For the charge current, the persistent charge current cancelled between spin up and down states, because of the time reversal symmetry of the Hamiltonian on the ring. So there are only circulating charge currents on the ring for electrons with unpolarized spin in the nonequilibrium. However, only the persistent spin currents contributes to the spin currents for electrons with unpolarized spin.Comment: 9 pages and 4 ps figure