Carlson J M, Doyle J
Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Aug;60(2 Pt A):1412-27. doi: 10.1103/physreve.60.1412.
We introduce a mechanism for generating power law distributions, referred to as highly optimized tolerance (HOT), which is motivated by biological organisms and advanced engineering technologies. Our focus is on systems which are optimized, either through natural selection or engineering design, to provide robust performance despite uncertain environments. We suggest that power laws in these systems are due to tradeoffs between yield, cost of resources, and tolerance to risks. These tradeoffs lead to highly optimized designs that allow for occasional large events. We investigate the mechanism in the context of percolation and sand pile models in order to emphasize the sharp contrasts between HOT and self-organized criticality (SOC), which has been widely suggested as the origin for power laws in complex systems. Like SOC, HOT produces power laws. However, compared to SOC, HOT states exist for densities which are higher than the critical density, and the power laws are not restricted to special values of the density. The characteristic features of HOT systems include: (1) high efficiency, performance, and robustness to designed-for uncertainties; (2) hypersensitivity to design flaws and unanticipated perturbations; (3) nongeneric, specialized, structured configurations; and (4) power laws. The first three of these are in contrast to the traditional hallmarks of criticality, and are obtained by simply adding the element of design to percolation and sand pile models, which completely changes their characteristics.
我们引入了一种生成幂律分布的机制，称为高度优化容限（HOT），其灵感来源于生物有机体和先进工程技术。我们关注的是那些通过自然选择或工程设计进行了优化的系统，以便在不确定的环境中仍能提供稳健的性能。我们认为，这些系统中的幂律是由于产量、资源成本和风险容忍度之间的权衡所致。这些权衡导致了高度优化的设计，允许偶尔出现大事件。我们在渗流和沙堆模型的背景下研究这种机制，以强调HOT与自组织临界性（SOC）之间的鲜明对比，SOC已被广泛认为是复杂系统中幂律的起源。与SOC一样，HOT也会产生幂律。然而，与SOC相比，HOT状态存在于高于临界密度的密度下，并且幂律不限于密度的特殊值。HOT系统的特征包括：（1）对针对设计的不确定性具有高效率、高性能和稳健性；（2）对设计缺陷和意外扰动高度敏感；（3）非通用、专门化、结构化的配置；（4）幂律。其中前三个与传统的临界性特征形成对比，并且是通过简单地将设计元素添加到渗流和沙堆模型中获得的，这完全改变了它们的特性。
