How Fast Is the Bandit?

Abstract

In this article we investigate the rate of convergence of the so-called two-armed bandit algorithm. The behavior of the algorithm turns out to be highly non standard: no central limit theorem, possible occurrence of two different rates of convergence with positive probability.     

考虑行车状态的一维元胞自动机交通流模型

在Nagel Schrekenberg单车道元胞自动机交通流模型（简称NS模型）的基础上，考虑车辆之间的相对运动薛郁等提出了一种改进的单车道元胞自动机交通流模型（简称改进的NS模型）.通过两种情况列出了改进的NS模型存在不尽周严的地方，随之在新模型中引入了行车状态 变量和反馈规则，从而控制车辆出现倒车和刹车过急等现象.通过计算机对新模型进行模拟 ，发现减速概率和车流密度对车流状态的演化影响很大，当减速概率高（如道路条件差）时 ，即使车流密度低，车流也会出现局部堵塞状态；而当减速概率一定时，随着车流密度增加 ，车流的运动相与堵塞相发生了全局性的交替出现，此时类似于波的波峰和波谷的传播.与 改进的NS模型相比较，新模型模拟的车流量较高，说明新模型减少了车流的总体停滞状态. 关键词： 交通流 元胞自动机 行车状态 反馈规则     

The unstable behavior of cellular premixed flames induced by intrinsic instability

The unstable behavior of cellular premixed flames induced by intrinsic instability is studied by two-dimensional unsteady calculations of reactive flows. In the present numerical simulation, the compressible Navier–Stokes equation including a one-step irreversible chemical reaction is employed. We consider two basic types of phenomena to account for the intrinsic instability of premixed flames, i.e., hydrodynamic and diffusive-thermal effects. The hydrodynamic effect is caused by the thermal expansion through the flame front; the diffusive-thermal effect is caused by the preferential diffusion of mass versus heat. A disturbance with several wavelength components is superimposed on a planar flame, and the formation of a cellular flame induced by hydrodynamic and diffusive-thermal effects is numerically simulated. After the cellular-flame formation, the combination and division of cells are observed. The behavior of cellular-flame fronts becomes more unstable when the Lewis number is lower than unity, since the diffusive-thermal effect has a great influence on the unstable behavior. The cell size changes with time, and its average is greater than the critical wavelength and becomes smaller by decreasing the Lewis number. The flame velocity of cellular flames depends strongly on the length of computational domain in the direction tangential to the flame front. As the length of computational domain increases, the flame velocity becomes larger. This is because the long-wavelength components of disturbances play an important role in the shape of cellular flames, i.e., in the flame-surface area.     

The finite-size scaling study of the specific heat and the Binder parameter for the six-dimensional Ising model

The six-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L=4,6,8,10. The temperature variations and the finite-size scaling plots of the specific heat and Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice T_C=10.838(1), T_C=10.836(20) and T_C=10.835(1) are obtained from the intersection points of specific heat curves, Binder parameter curves and the straight line fit of specific heat maxima, respectively. These results are in agreement with the more precise value of T_C=10.835(5). The value obtained for the critical exponent of the specific heat, i.e., =0.012(2) is also in agreement with =0 predicted by the theory.     

人工脑的三维模型及应用

将二维人工脑模型推广到三维，并给出了一个实际应用算例，还将二、三维模型的计算结果进行了对比，发现三维模型的计算效果明显优于二维模型。     

The dynamics of defect ensembles in one-dimensional cellular automata

We investigate the dynamics of ensembles of diffusive defects in one-dimensional deterministic cellular automata. The work builds on earlier results on individual random walks in cellular automata. Here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects. Simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied. Their equilibrium behavior is also characterized. The design principles of cellular automata with desired diffusive interaction properties become transparent from this analysis.     

Rotators,periodicity, and absence of diffusion in cyclic cellular automata

Cyclic cellular automata are two-dimensional cellular automata which generalize lattice versions of the Lorentz gas and certain biochemistry models of artificial life. We show that rotators and time reversibility play a special role in the creation of closed orbits in cyclic cellular automata. We also prove that almost every orbit is closed (periodic) and the absence of diffusion for the flipping rotator model (also known as the ant).     

Dimension-Splitting for Simplifying Diffusion in Lattice-Gas Models

We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to each dimension, and with all dimensions treated identically. We show that the model resulting from this technique is equivalent to the macroscopic diffusion equation in the appropriate limit. This technique saves computational resources and reduces the complexity of model design, programming, debugging, simulation and analysis. For example, a reaction-diffusion simulation can be designed and tested as a one-dimensional system, and then directly extended to two or more dimensions. We illustrate the use of this approach in constructing a microscopically reversible model of diffusion-limited aggregation as well as in a model of growth of biological films.     

Computation of critical exponents for two-dimensional ising model on a cellular automaton

Static critical exponents for the two-dimensional Ising model are computed on a cellular automaton. The analysis of the data within the framework of the finite-size scaling theory reproduces their well-established values.