Levich Institute and Physics Department, City College of New York, New York, NY 10031, USA.
Proc Natl Acad Sci U S A. 2012 Feb 21;109(8):2825-30. doi: 10.1073/pnas.1106612109. Epub 2012 Feb 3.
The human brain is organized in functional modules. Such an organization presents a basic conundrum: Modules ought to be sufficiently independent to guarantee functional specialization and sufficiently connected to bind multiple processors for efficient information transfer. It is commonly accepted that small-world architecture of short paths and large local clustering may solve this problem. However, there is intrinsic tension between shortcuts generating small worlds and the persistence of modularity, a global property unrelated to local clustering. Here, we present a possible solution to this puzzle. We first show that a modified percolation theory can define a set of hierarchically organized modules made of strong links in functional brain networks. These modules are "large-world" self-similar structures and, therefore, are far from being small-world. However, incorporating weaker ties to the network converts it into a small world preserving an underlying backbone of well-defined modules. Remarkably, weak ties are precisely organized as predicted by theory maximizing information transfer with minimal wiring cost. This trade-off architecture is reminiscent of the "strength of weak ties" crucial concept of social networks. Such a design suggests a natural solution to the paradox of efficient information flow in the highly modular structure of the brain.
人类大脑组织在功能模块中。这种组织提出了一个基本的难题：模块应该足够独立，以保证功能专业化，并且足够连接多个处理器，以实现有效的信息传递。人们普遍认为，短路径的小世界结构和大的局部聚类可能会解决这个问题。然而，在生成小世界的捷径和模块性的持久性之间存在内在的紧张关系，模块性是一种与局部聚类无关的全局属性。在这里，我们提出了这个难题的一个可能的解决方案。我们首先表明，修改后的渗流理论可以定义一组由功能大脑网络中的强连接组成的层次化模块。这些模块是“大的世界”自相似结构，因此，远非小世界。然而，将较弱的联系纳入网络会将其转换为一个小世界，同时保留定义明确的模块的基本骨架。值得注意的是，弱联系的组织方式与理论上预测的以最小布线成本最大化信息传输的方式完全一致。这种权衡架构让人联想到社会网络中至关重要的“弱联系的力量”这一概念。这种设计为大脑高度模块化结构中的有效信息流提供了一个自然的解决方案。
