初级视皮层风车结构的不确定原理
An uncertainty principle underlying the pinwheel structure in the primary visual cortex
摘要：
V1中的视觉信息由称为方向偏好列的模块阵列处理。在包括人类在内的某些物种中，方向柱围绕像车轮辐条一样的奇异点呈放射状排列，称为风车。风车结构已被观察到第一次与光学成像技术，最近在体内双光子成像证明其组织与单细胞精度。在这项研究中，我们提供的证据表明，风车是事实上的最佳分布编码在最佳的角位置和动量。在过去的几年里，许多作者已经认识到，V1的功能结构是局部不变的旋转和平移的对称群SE（2）。在本研究中，我们表明，用于构建风车的方向皮层地图可以建模为相干态，即最好的配置本地化的角位置和角动量。我们采用的理论是基于众所周知的不确定原理，介绍了海森堡在量子力学，后来扩展到许多其他群体的不变性。在这里，我们陈述了一个相应的原则，在皮质几何与SE（2）对称性，并通过计算其极小值，我们得到了一个模型的定向活动地图的皮质。众所周知，风车结构是直接从这些活动图构建的，我们将能够从视觉皮层功能结构的组对称性开始正式再现它们的结构。初级视皮层被建模为一个完整的系统，其中简单细胞的集合实现SE（2）群，水平连接实现其李代数和风车实现其最小不确定性状态。
英文摘要：
The visual information in V1 is processed by an array of modules called orientation preference columns. In some species including humans, orientation columns are radially arranged around singular points like the spokes of a wheel, that are called pinwheels. The pinwheel structure has been observed first with optical imaging techniques and more recently by in vivo two-photon imaging proving their organization with single cell precision. In this research we provide evidence that pinwheels are de facto optimal distributions for coding at the best angular position and momentum. In the last years many authors have recognized that the functional architecture of V1 is locally invariant with respect to the symmetry group of rotations and translations SE(2). In the present study we show that the orientation cortical maps used to construct pinwheels can be modeled as coherent states, i.e. the configurations best localized both in angular position and angular momentum. The theory we adopt is based on the well known uncertainty principle, introduced by Heisenberg in quantum mechanics and later extended to many other groups of invariance. Here we state a corresponding principle in the cortical geometry with SE(2) symmetry, and by computing its minimizers we obtain a model of orientation activity maps in the cortex. As it is well known the pinwheels configuration is directly constructed from these activity maps, and we will be able to formally reproduce their structure starting from the group symmetries of the functional architecture of the visual cortex. The primary visual cortex is then modeled as an integrated system in which the set of simple cells implements the SE(2) group, the horizontal connectivity implements its Lie algebra and the pinwheels implement its minimal uncertainty states.
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