In real physical systems the underlying spatial components might not have crisp boundaries and their interactions might not be instantaneous. To this end, we propose δ-MAPS; a method that identifies spatially contiguous and possibly overlapping components referred to as domains, and identifies the lagged functional relationships between them. Informally, a domain is a spatially contiguous region that somehow participates in the same dynamic effect or function. The latter will result in highly correlated temporal activity between grid cells of the same domain. δ-MAPS first identifies the epicenters of activity of a domain. Next, it identifies a domain as the maximum possible set of spatially contiguous grid cells that include the detected epicenters and satisfy a homogeneity constraint. After identifying the domains, δ-MAPS infers a functional network between them. The proposed network inference method examines the statistical significance of each lagged correlation between two domains, applies a multiple-testing process to control the rate of false positives, infers a range of potential lag values for each edge, and assigns a weight to each edge reflecting the magnitude of interaction between two domains. δ-MAPS is related to clustering, multivariate statistical techniques and network community detection. However, as we discuss and also show with synthetic data, it is also significantly different, avoiding many of the known limitations of these methods.We illustrate the application of δ-MAPS on data from two domains: climate science and neuroscience. First, the sea-surface temperature climate network identifies some well-known teleconnections (such as the lagged connection between the El Nin\(\tilde {o}\) Southern Oscillation and the Indian Ocean). Second, the analysis of resting state fMRI cortical data confirms the presence of known functional resting state networks (default mode, occipital, motor/somatosensory and auditory), and shows that the cortical network includes a backbone of relatively few regions that are densely interconnected.

中文翻译：

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δ-MAPS：从时空数据到功能域之间的加权和滞后网络。

在实际的物理系统中，潜在的空间成分可能没有清晰的边界，并且它们的相互作用可能不是瞬时的。为此，我们提出了δ- MAPS。一种方法，该方法标识在空间上连续且可能重叠的组件（称为“域”），并标识它们之间的滞后功能关系。非正式地，域是某种程度上参与相同动态效果或功能的空间连续区域。后者将导致同一域的网格单元之间高度相关的时间活动。δ-MAPS首先确定域活动的震中。接下来，它将一个域标识为包括检测到的震中并满足同质性约束的最大空间连续网格单元集。识别域后，δ- MAPS会推断它们之间的功能网络。拟议的网络推理方法检查两个域之间每个滞后相关性的统计显着性，应用多重测试过程来控制误报率，推断每个边缘的潜在滞后值范围，并为每个边缘分配权重两个领域之间的互动程度。δ-MAPS与聚类，多元统计技术和网络社区检测有关。但是，正如我们讨论并用合成数据显示的那样，它也有很大的不同，避免了这些方法的许多已知局限。我们说明了δ- MAPS在来自气候科学和神经科学两个领域的数据上的应用。首先，海面温度气候网络确定了一些众所周知的远程连接（例如El Nin \（\ tilde {o} \）之间的滞后连接南方涛动和印度洋）。其次，对静息状态功能磁共振成像皮质数据的分析证实了已知的功能性静息状态网络（默认模式，枕骨，运动/体感和听觉）的存在，并表明皮质网络包括密集互连的相对较少区域的骨干。