Graph Quilting - Functional connectivity graph estimation from nonsimultaneous calcium imaging recordings
Neuronal functional connectivity is the statistical dependence of neurons’ activities. Functional connectivity is typically inferred from data of in vivo simultaneously recorded neurons in the framework of conditional dependence graphical models, where neurons are represented by nodes, and an edge connects two nodes if the two neurons' activities share covariability conditionally on all other sources of variability in the network. Studying functional connectivity helps us understand how neurons interact with one another while they process information under different stimuli and other experimental conditions, and ultimately it enables us to understand the functions of neuronal circuits and the causes of their dysfunction characterizing various brain disorders. New ambitious neuroscience projects (NeuroNex, NSF) involve the recording of the activities of tens-to-hundreds of thousands of neurons in 3-dimensional portions of brain via calcium imaging technology. A fundamental trade-off between temporal and spatial resolution characterizes this technology: the more neurons we aim to record from simultaneously, the coarser the time resolution is. Since important neuronal activity patterns happen on very short time scales, it is often preferred to record the activities of a subset of neurons at once with a fine temporal resolution rather than recording the activities of the entire neuronal population simultaneously with a coarse time resolution. Yet, if these subsets are recorded nonsimultaneously, only a subset O (colored sets in figure) of all neuronal pairs may have joint observations, while the rest OC remain unobserved, generating the graph quilting problem. Vinci et al. (2019) presents a thorough theoretical investigation of the problem and a first application to the analysis of nonsimultaneous calcium imaging recordings.
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