Emergence of density dynamics by surface interpolation in elementary cellular automata

A classic problem in elementary cellular automata (ECAs) is the specification of numerical tools to represent and study their dynamical behaviour. Mean field theory and basins of attraction have been commonly used; however, although the first case gives the long term estimation of density, frequently it does not show an adequate approximation for the step-by-step temporal behaviour; mainly for non-trivial behaviour. In the second case, basins of attraction display a complete representation of the evolution of an ECA, but they are limited up to configurations of 32 cells; and for the same ECA, one can obtain tens of basins to analyse. This paper is devoted to represent the dynamics of density in ECAs for hundreds of cells using only two surfaces calculated by the nearest-neighbour interpolation. A diversity of surfaces emerges in this analysis. Consequently, we propose a surface and histogram based classification for periodic, chaotic and complex ECA.     

有超车规则的交通流的元胞自动机模型

分析和评论了2014年美国大学生数学建模竞赛（MCM）A题,以及获得outstanding winner奖的6篇论文。首先对试题进行分析,并结合已有文献指出A题的主要解题思路;然后,通过评述获奖论文,指出学生论文的优点及存在的问题;最后,对今年赛题的某些问题进行讨论。     

Lattice games without rational strategies

We show that the lattice games of Guo and Miller support universal computation, disproving their conjecture that all lattice games have rational strategies. We also state an explicit counterexample to that conjecture: a three dimensional lattice game whose set of winning positions does not have a rational generating function.     

Three-dimensional cellular automaton simulation of tumour growth in inhomogeneous oxygen environment

Cellular automaton theory has previously been used to study cell growth. In this study, we present a three-dimensional cellular automaton model performing the growth simulation of normal and cancerous cells. The necessary nutrient supply is provided by an artificial arterial tree which is generated by constrained constructive optimization. Spatial oxygen diffusion is approximated again by a cellular automaton model. All results could be illustrated dynamically by three-dimensional volume visualization. Because of the chosen modelling approach, an extension of the model to simulate angiogenic processes is possible.     

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     

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。