No abstract

Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3D structure of a molecule from several noisy 2D projections images taken at unknown viewing angles. Most reconstruction algorithms require a low-resolution initialization for the 3D structure, which is the goal of ab initio modeling. Suggested by Zvi Kam in 1980, the method of moments (MoM) offers one approach, wherein loworder statistics of the 2D images are computed and a 3D structure is estimated by solving a system of polynomial equations. Unfortunately, Kam's method suffers from restrictive assumptions, most notably that viewing angles should be distributed uniformly. Often unrealistic, uniformity entails the computation of higher-order correlations, as in this case first and second moments fail to determine the 3D structure. In the present paper, we remove this hypothesis, by permitting an unknown, non-uniform distribution of viewing angles in MoM. Perhaps surprisingly, we show that this case is statistically easier than the uniform case, as now first and second moments generically suffice to determine

Acetylcholine (ACh) is associated with the modulation of brain activity linked to arousal, attention, and emotional valence. We performed dual-color mesoscopic imaging of ACh and calcium across the neocortex of awake mice to investigate the spatiotemporal dynamics of cholinergic signaling and their relationship to cortical output. We find distinct movement-defined behavioral states are represented in spatially heterogeneous cholinergic networks that are differentially coupled to fluctuations in local circuit activity.