Equidistribution of Heegner Points and Ternary Quadratic Forms

We prove new equidistribution results for Galois orbits of Heegner points with respect to reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize one of the equidistribution theorems established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system

Orochi: Investigating Requirements and Expectations for Multipurpose Daily Used Supernumerary Robotic Limbs

Supernumerary robotic limbs (SRLs) present many opportunities for daily use. However, their obtrusiveness and limitations in interaction genericity hinder their daily use. To address challenges of daily use, we extracted three design considerations from previous literature and embodied them in a wearable we call Orochi. The considerations include the following: 1) multipurpose use, 2) wearability by context, and 3) unobtrusiveness in public. We implemented Orochi as a snake-shaped robot with 25 DoFs and two end effectors, and demonstrated several novel interactions enabled by its limber design. Using Orochi, we conducted hands-on focus groups to explore how multipurpose SRLs are used daily and we conducted a survey to explore how they are perceived when used in public. Participants approved Orochi's design and proposed different use cases and postures in which it could be worn. Orochi's unobtrusive design was generally well received, yet novel interactions raise several challenges for social acceptance. We discuss the significance of our results by highlighting future research opportunities based on the design, implementation, and evaluation of Orochi

Word reading strategies: A replication and follow up intervention

The first stage of this study involved a replication of the cluster analysts procedures used by Freebody and Byrne (1988) to classify Year 2 readers according to their word reading strategies based on lists of irregular and pseudowords. A four-cluster-solution produced three groups similar to those reported by Freebody and Byrne (1988), and a fourth group which could not be classified using their criteria. A three-cluster-solution produced a more parsimonious interpretation, with these groups meeting the criteria for LB (low on both Irregular and pseudowords), HB (high on both), and Phoenician readers (average or above on pseudoword, low on irregular words). There was no evidence of a discrete group of Chinese readers (low on pseudowords, average or above average on irregular words). These results were interpreted in the context of stage models of reading development. A replication was carried out of Freebody and Byrnes (1988) examination of differences in the phonemic awareness abilities of the subjects grouped on the basis of the four-cluster-solution. Subjects were tested using the initial-consonant-elision and the final-consonant-matching tasks. Three additional phonemic awareness tasks were also used: telescoping, segmenting and rhyming. Results showed unacceptable reliability of the telescoping, segmenting and final consonant-matching tasks, coupled with ceiling effects for telescoping and segmenting. Consequently, only the results from the combined initial-consonant-elision and final-consonant matching tasks, and the rhyming tasks were used. Consistent with the findings of Freebody and Byrne (1988), the LB group showed significantly lower phonemic awareness than the other groups combined, the HB group showed the reverse outcome. This finding is consistent with previous research that has shown a relationship between phonemic awareness and reading achievement. There was a significant difference for the remaining two groups, but only on the rhyming task in favour of the Phoenician readers, reflecting their ability to recognise sound patterns within words. The second stage of the study consisted of a single subject design investigation in which baseline data was collected for six (LB) subjects. As the requirement of stable and level baselines was not met for five of the six subjects, the decision was made to implement a changing criterion design with the other subject. He was given explicit Instruction In which he was taught to discriminate between the letters he previously confused, and the strategy of sounding out regular word types without stopping between sounds. His daily data showed that by the end of the Intervention phase, consisting of 16 half-hour teaching sessions, he had reached criteria in reading mixed regular word types. In addition, his post-test score on the pseudoword list indicated that he would now qualify as a Phoenician reader. Further research is required to investigate the extent to which changes In word reading strategy can be brought about by Instruction

Computations in non-commutative Iwasawa theory

We study special values of L-functions of elliptic curves over Q twisted by Artin representations that factor through a false Tate curve extension $Q(\mu_p^\infty,\sqrt[p^\infty]{m})/Q$. In this setting, we explain how to compute L-functions and the corresponding Iwasawa-theoretic invariants of non-abelian twists of elliptic curves. Our results provide both theoretical and computational evidence for the main conjecture of non-commutative Iwasawa theory.Comment: 60 pages; with appendix by John Coates and Ramdorai Sujath

Astrobites as a Community-led Model for Education, Science Communication, and Accessibility in Astrophysics

Support for early career astronomers who are just beginning to explore astronomy research is imperative to increase retention of diverse practitioners in the field. Since 2010, Astrobites has played an instrumental role in engaging members of the community -- particularly undergraduate and graduate students -- in research. In this white paper, the Astrobites collaboration outlines our multi-faceted online education platform that both eases the transition into astronomy research and promotes inclusive professional development opportunities. We additionally offer recommendations for how the astronomy community can reduce barriers to entry to astronomy research in the coming decade

Probing reflection from aerosols with the near-infrared dayside spectrum of WASP-80b

The presence of aerosols is intimately linked to the global energy budget and the composition of a planet's atmospheres. Their ability to reflect incoming light prevents energy from being deposited into the atmosphere, and they shape spectra of exoplanets. We observed five near-infrared secondary eclipses of WASP-80b with the Wide Field Camera 3 (WFC3) aboard the \textit{Hubble Space Telescope} to provide constraints on the presence and properties of atmospheric aerosols. We detect a broadband eclipse depth of $34\pm10$\,ppm for WASP-80b. We detect a higher planetary flux than expected from thermal emission alone at $1.6\sigma$, which hints toward the presence of reflecting aerosols on this planet's dayside, indicating a geometric albedo of $A_g<0.33$ at 3$\sigma$. We paired the WFC3 data with Spitzer data and explored multiple atmospheric models with and without aerosols to interpret this spectrum. Albeit consistent with a clear dayside atmosphere, we found a slight preference for near-solar metallicities and for dayside clouds over hazes. We exclude soot haze formation rates higher than $10^{-10.7}$ g cm$^{-2}$s$^{-1}$ and tholin formation rates higher than $10^{-12.0}$ g cm$^{-2}$s$^{-1}$ at $3\sigma$. We applied the same atmospheric models to a previously published WFC3/Spitzer transmission spectrum for this planet and found weak haze formation. A single soot haze formation rate best fits both the dayside and the transmission spectra simultaneously. However, we emphasize that no models provide satisfactory fits in terms of the chi-square of both spectra simultaneously, indicating longitudinal dissimilarity in the atmosphere's aerosol composition.Comment: Published in ApJ Letters (20 Oct 2023