3d Modularity

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures include: mock modular forms, $SL(2,\mathbb{Z})$ Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs.Comment: 119 pages, 10 figures and 20 table

A Comparison of Airport Risks: Unmanned Aircraft Systems (UAS) Sightings, Wildlife Strikes, and Runway Incursions

To provide a context for the potential threat of unmanned aircraft systems (UAS) sightings on airport operations, this paper compares the characteristics of UAS sightings with two common airport threats: wildlife strikes and runway incursions. This study analyzed over 60,000 events in a three-year period (September 2016 to August 2019), including 6,551 UAS sightings from the Federal Aviation Administration (FAA) UAS Sightings Report database, 47,574 wildlife strikes from the FAA Wildlife Strike database, and 6,041 runway incursions from the FAA Runway Safety database. The results suggest both similarities and differences among the airport threats. Both UAS sightings and wildlife strikes vary by time of year and time of day. UAS sightings and wildlife strikes farther from the airport occur at higher altitudes than sightings and strikes occurring close to the airport. However, UAS sightings are reported at higher altitudes than wildlife strikes, and the distance of UAS sightings from the airport is farther than that of wildlife strikes, in general. The severities of UAS sightings and runway incursions are similar. Pilots take evasive actions in three percent of UAS sightings, and runway incursions of severity A and B are also rare. Pilots of general aviation (GA) aircraft reported the most UAS sightings, and GA operations are also involved in more runway incursions. Considering the kind of airport affected, UAS sightings and wildlife strikes are more common at primary airports, notably large and medium hub airports, whereas runway incursions are more common at reliever airports. Generally, UAS have had a minimal impact on airport operations despite their growing prevalence, which reflects the overall success of integrating this new airspace user into the national airspace system

Synapse elimination and learning rules co-regulated by MHC class I H2-Db.

The formation of precise connections between retina and lateral geniculate nucleus (LGN) involves the activity-dependent elimination of some synapses, with strengthening and retention of others. Here we show that the major histocompatibility complex (MHC) class I molecule H2-D(b) is necessary and sufficient for synapse elimination in the retinogeniculate system. In mice lacking both H2-K(b) and H2-D(b) (K(b)D(b)(-/-)), despite intact retinal activity and basal synaptic transmission, the developmentally regulated decrease in functional convergence of retinal ganglion cell synaptic inputs to LGN neurons fails and eye-specific layers do not form. Neuronal expression of just H2-D(b) in K(b)D(b)(-/-) mice rescues both synapse elimination and eye-specific segregation despite a compromised immune system. When patterns of stimulation mimicking endogenous retinal waves are used to probe synaptic learning rules at retinogeniculate synapses, long-term potentiation (LTP) is intact but long-term depression (LTD) is impaired in K(b)D(b)(-/-) mice. This change is due to an increase in Ca(2+)-permeable AMPA (α-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid) receptors. Restoring H2-D(b) to K(b)D(b)(-/-) neurons renders AMPA receptors Ca(2+) impermeable and rescues LTD. These observations reveal an MHC-class-I-mediated link between developmental synapse pruning and balanced synaptic learning rules enabling both LTD and LTP, and demonstrate a direct requirement for H2-D(b) in functional and structural synapse pruning in CNS neurons