We deal with randomness-quantifiers and concentrate on their ability do discern the hallmark of chaos in time-series used in connection with pseudo random number generators (PRNG). Workers in the field are motivated to use chaotic maps for generating PRNGs because of the simplicity of their implementation. Although there exist very efficient general-purpose benchmarks for testing PRNGs, we feel that the analysis provided here sheds additional didactic light on the importance of the main statistical characteristics of a chaotic map, namely, i) its invariant measure and ii) the mixing constant. This is of help in answering two questions that arise in applications, that is, (1) which is the best PRNG among the available ones? and (2) If a given PRNG turns out not to be good enough and a randomization procedure must still be applied to it, which is the best applicable randomization procedure?. Our answer provides a comparative analysis of several quantifiers advanced in the extant literature.
Random Coupling of Chaotic Maps leads to Spatiotemporal Synchronisation
我们研究了耦合混沌映射网络的时空动力学，在耦合连接中具有不同程度的随机性。虽然严格的最近邻耦合永远不允许时空同步在我们的系统中，随机重新布线的一些连接稳定整个网络在$x^*$，其中$x^*$是强不稳定的不动点解的局部混沌映射。事实上，空间连接中最小程度的随机性为耦合参数空间中的同步不动点打开了一个稳定的窗口。此外，发生时空同步的起始处的耦合$ε_{bifr}$与重新布线的位点的分数p成比例，作为幂律，0.1 < p < 1。我们还表明，随机连接的正则化效果可以理解从系统的概率发展方程的稳定性分析，并获得近似的解析表达式的范围和$ε_{bifr}$。
Control transition in a temporally random classical spin chain
Rutgers University（罗格斯大学）；Flatiron Institute（平顿研究所）；International Centre for Theoretical Sciences (ICTS-TIFR), Tata Institute of Fundamental Research（国际理论科学中心（ICTS-TIFR），塔塔基础研究所）；Princeton University（普林斯顿大学）
