K{o}nigsberg Sightseeing: Eulerian Walks in Temporal Graphs

An Eulerian walk (or Eulerian trail) is a walk (resp. trail) that visits every edge of a graph $G$ at least (resp. exactly) once. This notion was first discussed by Leonhard Euler while solving the famous Seven Bridges of K{o}nigsberg problem in 1736. What if Euler had to take a bus? In a temporal graph $(G,lambda)$, with $lambda: E(G)to 2^{[tau]}$, an edge $ein E(G)$ is available only at the times specified by $lambda(e)subseteq [tau]$, in the same way the connections of the public transportation network of a city or of sightseeing tours are available only at scheduled times. In this scenario, even though several translations of Eulerian trails and walks are possible in temporal terms, only a very particular variation has been exploited in the literature, specifically for infinite dynamic networks (Orlin, 1984). In this paper, we deal with temporal walks, local trails, and trails, respectively referring to edge traversal with no constraints, constrained to not repeating the same edge in a single timestamp, and constrained to never repeating the same edge throughout the entire traversal. We show that, if the edges are always available, then deciding whether $(G,lambda)$ has a temporal walk or trail is polynomial, while deciding whether it has a local trail is NP-complete even if it has lifetime~2. In contrast, in the general case, solving any of these problems is NP-complete, even under very strict hypothesis.

Topological states between inversion symmetric atomic insulators

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary correspondence has been well-tested for strong topological invariants, and forms the basis for all proposed technological applications of topology. Here, we report that a group of weak topological invariants, which depend only on the symmetries of the atomic lattice, also induces a particular type of bulk-boundary correspondence. It predicts the presence or absence of states localised at the interface between two inversion-symmetric band insulators with trivial values for their strong invariants, based on the space group representation of the bands on either side of the junction. We show that this corresponds with symmetry-based classifications of topological materials. The interface modes are protected by the combination of band topology and symmetry of the interface, and may be used for topological transport and signal manipulation in heterojunction-based devices.

A collective insight into the cultural and academic journeys of Native Hawaiians while pursuing careers in physics and astronomy

In the field of astronomy, Maunakea is known as a prestigious site for observing and science. In Native Hawaiian culture, Maunakea is revered as the connection between past, present, and future generations and their ancestral lands of Hawaii. We have reached a juncture at which it is necessary to allow and enable Native Hawaiians to pursue careers in astronomy, especially on Maunakea. This paper serves to tell the accounts of four Kanaka astronomers and raise awareness of the barriers they have faced while pursuing astronomy careers. The authors identify issues that the community faces due to the disconnect between astronomy and Hawaii communities and propose resolutions to lead the way forward.

Detecting Magnetic Fields in Exoplanets with Spectropolarimetry of the Helium Line at 1083 nm

The magnetic fields of the solar system planets provide valuable insights into the planets interiors and can have dramatic consequences for the evolution of their atmospheres and interaction with the solar wind. However, we have little direct knowledge of magnetic fields in exoplanets. Here we present a method for detecting magnetic fields in the atmospheres of close-in exoplanets based on spectropolarimetric transit observations at the wavelength of the helium line at 1083 nm. This methodology has been successfully applied before for exploring magnetic fields in solar coronal filaments. Strong absorption signatures (transit depths on the order of a few percent) in the 1083 nm line have recently been observed for several close-in exoplanets. We show that in the conditions in these escaping atmospheres, metastable helium atoms should be optically pumped by the starlight and, for field strengths more than a few $times 10^{-4}$ G, should align with the magnetic field. This results in linearly polarized absorption at 1083 nm that traces the field direction (the Hanle effect), which we explore by both analytic computation and with the Hazel numerical code. The linear polarization $sqrt{Q^2+U^2}/I$ ranges from $sim 10^{-3}$ in optimistic cases down to a few $times 10^{-5}$ for particularly unfavorable cases, with very weak dependence on field strength. The line-of-sight component of the field results in a slight circular polarization (the Zeeman effect), also reaching $V/Isim {rm few}times 10^{-5}(B_parallel/10,{rm G})$. We discuss the detectability of these signals with current (SPIRou) and future (extremely large telescope) high-resolution infrared spectropolarimeters, and we briefly comment on possible sources of astrophysical contamination.

A method to identify and characterise binary candidates - a study of CoRoT data

The analysis of the CoRoT space mission data was performed aiming to test a method that selects, among the several light curves observed, the transiting systems that likely host a low-mass star orbiting the main target. The method identifies stellar companions by fitting a model to the observed transits. Applying this model, that uses equations like Keplers third law and an empirical mass-radius relation, it is possible to estimate the mass and radius of the primary and secondary objects as well as the semimajor axis and inclination angle of the orbit. We focus on how the method can be used in the characterisation of transiting systems having a low-mass stellar companion with no need to be monitored with radial-velocity measurements or ground-based photometric observations. The model, which provides a good estimate of the system parameters, is also useful as a complementary approach to select possible planetary candidates. A list of confirmed binaries together with our estimate of their parameters are presented. The characterisation of the first twelve detected CoRoT exoplanetary systems was also performed and agrees very well with the results of their respective announcement papers. The comparison with confirmed systems validates our method, specially when the radius of the secondary companion is smaller than 1.5 Rjup, in the case of planets, or larger than 2 Rjup, in the case of low-mass stars. Intermediate situations are not conclusive.