Tozzi Arturo, Peters James F
Center for Nonlinear Science, Department of Physics, University of North Texas, 1155 Union Circle, #311427, Denton, TX 76203-5017 USA.
Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor's Circle, Winnipeg, MB R3T 5V6 Canada.
Cogn Neurodyn. 2017 Jun;11(3):283-292. doi: 10.1007/s11571-017-9431-7. Epub 2017 Mar 14.
Recent approaches to brain phase spaces reinforce the foremost role of symmetries and energy requirements in the assessment of nervous activity. Changes in thermodynamic parameters and dimensions occur in the brain during symmetry breakings and transitions from one functional state to another. Based on topological results and string-like trajectories into nervous energy landscapes, we provide a novel method for the evaluation of energetic features and constraints in different brain functional activities. We show how abstract approaches, namely the Borsuk-Ulam theorem and its variants, may display real, energetic physical counterparts. When topology meets the physics of the brain, we arrive at a general model of neuronal activity, in terms of multidimensional manifolds and computational geometry, that has the potential to be operationalized.
近期对脑相空间的研究方法强化了对称性和能量需求在神经活动评估中的首要作用。在对称性破缺以及从一种功能状态转变为另一种功能状态的过程中，大脑的热力学参数和维度会发生变化。基于拓扑学结果以及神经能量景观中的类弦轨迹，我们提供了一种评估不同脑功能活动中能量特征和约束的新方法。我们展示了抽象方法，即博苏克 - 乌拉姆定理及其变体，如何能呈现出真实的、具有能量的物理对应物。当拓扑学与大脑物理学相结合时，我们得出了一个关于神经元活动的通用模型，该模型基于多维流形和计算几何，具有可操作化的潜力。
