The ODE/IM correspondence is a relation between the spectral analysis of ordinary differential equations (ODE) and quantum integrable models (IM). We briefly review some essential ideas of the correspondence and its application to the exact WKB analysis. In particular, we discuss the relation between the exact WKB periods and the Y-functions in two-dimensional integrable field theories, where the thermodynamic Bethe ansatz equations and their wall-crossing phenomena play an important role.
Low-frequency radio observations of the redshifted 21 cm line of neutral hydrogen have the potential to open up a new window on the high-redshift Universe, in particular the cosmic dark ages. In this article, we review the properties of the 21 cm line as the only known way to probe the cosmic dark ages. The 21 cm line is the spectral line that is created by a change in the energy state of neutral hydrogen atoms. By mapping the intensity of redshifted 21 cm line, the low-frequency radio observations can provide a very precise picture of the underlying matter distributions in the period after recombination. The projects to measure the 21 cm line during the dark ages from the far side of the Moon are also introduced.
Schooling fish exhibit giant vortices such as balls, tori, rings and cylinders, among other collective patterns. After reviewing previous studies, we introduce a new agent-based model that incorporates the topological nature of interactions and the escape response characteristic to fish. The model indicates that giant vortices are formed by limiting the number of interacting neighbors. It also reproduces a power-law dependence of the projected area of the cluster on the number of agents.
We briefly introduce recent experimental studies of quantized vortices and quantum hydrodynamics. In particular, experimental studies with optical methods are reviewed. Various optical methods developed for room-temperature experiments could be adapted for the investigation of the superfluid helium properties. Some typical examples including laser ablation and optical tweezers are described.