Center for Polymer Studies, Boston University, Boston, MA 02215;
Department of Physics, Boston University, Boston, MA 02215.
Proc Natl Acad Sci U S A. 2017 Nov 7;114(45):11826-11831. doi: 10.1073/pnas.1705704114. Epub 2017 Oct 24.
Scientists strive to understand how functionalities, such as conservation laws, emerge in complex systems. Living complex systems in particular create high-ordered functionalities by pairing up low-ordered complementary processes, e.g., one process to build and the other to correct. We propose a network mechanism that demonstrates how collective statistical laws can emerge at a macro (i.e., whole-network) level even when they do not exist at a unit (i.e., network-node) level. Drawing inspiration from neuroscience, we model a highly stylized dynamical neuronal network in which neurons fire either randomly or in response to the firing of neighboring neurons. A synapse connecting two neighboring neurons strengthens when both of these neurons are excited and weakens otherwise. We demonstrate that during this interplay between the synaptic and neuronal dynamics, when the network is near a critical point, both recurrent spontaneous and stimulated phase transitions enable the phase-dependent processes to replace each other and spontaneously generate a statistical conservation law-the conservation of synaptic strength. This conservation law is an emerging functionality selected by evolution and is thus a form of biological self-organized criticality in which the key dynamical modes are collective.
科学家们努力理解功能（例如守恒定律）如何在复杂系统中出现。特别是，生命复杂系统通过将低阶互补过程配对来创造高阶有序功能，例如一个过程用于构建，另一个过程用于纠错。我们提出了一种网络机制，展示了即使在单元（即网络节点）级别不存在时，集体统计定律如何在宏观（即整个网络）级别上出现。受神经科学的启发，我们构建了一个高度风格化的动力神经元网络模型，其中神经元要么随机放电，要么响应相邻神经元的放电而放电。连接两个相邻神经元的突触在这两个神经元都被激发时增强，否则减弱。我们证明，在突触和神经元动力学的相互作用过程中，当网络接近临界点时，无论是自发的还是受刺激的循环相变都会使相依的过程相互替换，并自发地产生统计守恒定律——突触强度的守恒。这种守恒定律是进化选择的一种涌现功能，因此是一种生物自组织临界性形式，其中关键的动力学模式是集体的。
