Wens Vincent
Laboratoire de Cartographie fonctionnelle du Cerveau, UNI-ULB Neurosciences Institute, Université libre de Bruxelles (ULB), Brussels, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):012823. doi: 10.1103/PhysRevE.91.012823. Epub 2015 Jan 28.
Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated connectivity estimation may be affected by spatial leakage, an artifact of inverse modeling that limits the interpretability of network analysis. This paper investigates general analytical aspects pertaining to this issue. First, the existence of spatial leakage is derived from the topological structure of inverse operators. Then the geometry of spatial leakage is modeled and used to define a geometric correction scheme, which limits spatial leakage effects in connectivity estimation. Finally, this new approach for network analysis is compared analytically to existing methods based on linear regressions, which are shown to yield biased coupling estimates.
网络理论和逆建模是应用物理学的两种标准工具，在通过间接测量研究空间分布式系统的动态组织时，需要将二者结合使用。然而，相关的连通性估计可能会受到空间泄漏的影响，空间泄漏是逆建模中的一种伪迹，它限制了网络分析的可解释性。本文研究了与该问题相关的一般分析方面。首先，从逆算子的拓扑结构推导出空间泄漏的存在性。然后对空间泄漏的几何形状进行建模，并用于定义一种几何校正方案，该方案可限制连通性估计中的空间泄漏效应。最后，将这种新的网络分析方法与基于线性回归的现有方法进行了分析比较，结果表明现有方法会产生有偏差的耦合估计。
