Rotbart Tal, Reuveni Shlomi, Urbakh Michael
School of Chemistry, Tel-Aviv University, Tel-Aviv 69978, Israel.
Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, Massachusetts 02115, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):060101. doi: 10.1103/PhysRevE.92.060101. Epub 2015 Dec 14.
We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of Michaelis and Menten. Stopping a process in its midst-only to start it all over again-may prolong, leave unchanged, or even shorten the time taken for its completion. Here we are interested in the optimal restart problem, i.e., in finding a restart rate which brings the mean completion time of a process to a minimum. We derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest. We then continue to discover regimes at which solutions to the problem take on universal, details independent forms which further give rise to optimal scaling laws. The formalism we develop, and the results obtained, can be utilized when optimizing stochastic search processes and randomized computer algorithms. An immediate connection with kinetic proofreading is also noted and discussed.
我们研究了重新启动和重试对一般过程平均完成时间的影响。在科学的各个分支中都产生了这样做的需求，并且我们表明，利用米氏（Michaelis）和门滕（Menten）的经典反应方案可以自然地解决这一问题。在过程进行中停止它——只是为了再次从头开始——可能会延长、保持不变，甚至缩短其完成所需的时间。在此，我们关注最优重新启动问题，即找到一个能使过程的平均完成时间达到最小的重新启动速率。我们推导了该问题的控制方程，并表明在某些特殊情况下它是完全可解的。然后，我们继续探索该问题的解呈现出通用的、与细节无关的形式的区域，这些形式进而产生了最优标度律。我们所发展的形式体系以及所获得的结果，可用于优化随机搜索过程和随机计算机算法。还指出并讨论了与动力学校对的直接联系。
