Words-to-Letters Valuations for Language Kleene Algebras with Variable Complements

We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language equivalence (under the standard language valuation) for Kleene algebra terms, this coincidence is broken if we extend the terms with complements. In this paper, we prove the decidability of some fragments of the equational theory: the universality problem is coNP-complete, and the inequational theory t <= s is coNP-complete when t does not contain Kleene-star. To this end, we introduce words-to-letters valuations; they are sufficient valuations for the equational theory and ease us in investigating the equational theory w.r.t. languages. Additionally, we prove that for words with variable complements, the equational theory coincides with the word equivalence.Comment: In Proceedings AFL 2023, arXiv:2309.0112

On Average-Case Hardness of Higher-Order Model Checking

We study a mixture between the average case and worst case complexities of higher-order model checking, the problem of deciding whether the tree generated by a given ? Y-term (or equivalently, a higher-order recursion scheme) satisfies the property expressed by a given tree automaton. Higher-order model checking has recently been studied extensively in the context of higher-order program verification. Although the worst-case complexity of the problem is k-EXPTIME complete for order-k terms, various higher-order model checkers have been developed that run efficiently for typical inputs, and program verification tools have been constructed on top of them. One may, therefore, hope that higher-order model checking can be solved efficiently in the average case, despite the worst-case complexity. We provide a negative result, by showing that, under certain assumptions, for almost every term, the higher-order model checking problem specialized for the term is k-EXPTIME hard with respect to the size of automata. The proof is based on a novel intersection type system that characterizes terms that do not contain any useless subterms

First Data Release of the Hyper Suprime-Cam Subaru Strategic Program

The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) is a three-layered imaging survey aimed at addressing some of the most outstanding questions in astronomy today, including the nature of dark matter and dark energy. The survey has been awarded 300 nights of observing time at the Subaru Telescope and it started in March 2014. This paper presents the first public data release of HSC-SSP. This release includes data taken in the first 1.7 years of observations (61.5 nights) and each of the Wide, Deep, and UltraDeep layers covers about 108, 26, and 4 square degrees down to depths of i~26.4, ~26.5, and ~27.0 mag, respectively (5sigma for point sources). All the layers are observed in five broad bands (grizy), and the Deep and UltraDeep layers are observed in narrow bands as well. We achieve an impressive image quality of 0.6 arcsec in the i-band in the Wide layer. We show that we achieve 1-2 per cent PSF photometry (rms) both internally and externally (against Pan-STARRS1), and ~10 mas and 40 mas internal and external astrometric accuracy, respectively. Both the calibrated images and catalogs are made available to the community through dedicated user interfaces and database servers. In addition to the pipeline products, we also provide value-added products such as photometric redshifts and a collection of public spectroscopic redshifts. Detailed descriptions of all the data can be found online. The data release website is https://hsc-release.mtk.nao.ac.jp/.Comment: 34 pages, 20 figures, 7 tables, moderate revision, accepted for publication in PAS

The Hyper Suprime-Cam SSP survey: Overview and survey design

Hyper Suprime-Cam (HSC) is a wide-field imaging camera on the prime focus of the 8.2-m Subaru telescope on the summit of Mauna Kea in Hawaii. A team of scientists from Japan, Taiwan, and Princeton University is using HSC to carry out a 300-night multi-band imaging survey of the high-latitude sky. The survey includes three layers: the Wide layer will cover 1400 deg2 in five broad bands (grizy), with a 5 σ point-source depth of r ≈ 26. The Deep layer covers a total of 26 deg2 in four fields, going roughly a magnitude fainter, while the UltraDeep layer goes almost a magnitude fainter still in two pointings of HSC (a total of 3.5 deg2). Here we describe the instrument, the science goals of the survey, and the survey strategy and data processing. This paper serves as an introduction to a special issue of the Publications of the Astronomical Society of Japan, which includes a large number of technical and scientific papers describing results from the early phases of this survey

Assessment of Office-Based Probing with Dacryoendoscopy for Treatment of Congenital Nasolacrimal Duct Obstruction: A Retrospective Study

We aimed to evaluate the safety and efficacy of office-based probing with dacryoendoscopy under local anesthesia for congenital nasolacrimal duct obstruction (CNLDO). This single-institution study retrospectively reviewed data on 72 eyes of 64 consecutive children (38 boys, 43 eyes; 26 girls, 29 eyes), aged between 6 and 17 (mean age: 10.0 ± 2.7) months with suspected CNLDO, from July 2016 to February 2022. These patients underwent probing with dacryoendoscopy under local anesthesia. CNLDO was diagnosed clinically based on the presence of epiphora and sticky eyes due to mucous discharge commencing within the first 3 months of life, increased tear meniscus height, and fluorescein dye disappearance test results. A total of 63 of the 72 eyes had narrowly defined CNLDO, and 9 eyes had other types of obstructions. The intervention success rate was 100% (63/63 eyes) for patients with typical CNLDO and 97.2% (70/72 eyes) for the entire study cohort. Moreover, CNLDO was classified into five types based on the features of the distal end of the nasolacrimal duct. Probing with dacryoendoscopy is safe and yields a high success rate in pediatric patients with CNLDO. This is the first study to assess the safety and efficacy of probing with dacryoendoscopy under local anesthesia in pediatric patients with CNLDO

Second Data Release of the Hyper Suprime-Cam Subaru Strategic Program

International audienceThis paper presents the second data release of the Hyper Suprime-Cam Subaru Strategic Program, a wide-field optical imaging survey using the 8.2 m Subaru Telescope. The release includes data from 174 nights of observation through 2018 January. The Wide layer data cover about 300 deg|$^2$| in all five broad-band filters (⁠|$grizy$|⁠) to the nominal survey exposure (10 min in |$gr$| and 20 min in |$izy$|⁠). Partially observed areas are also included in the release; about 1100 deg|$^2$| is observed in at least one filter and one exposure. The median seeing in the i-band is |${0_{.}^{\prime \prime }6}$|⁠, demonstrating the superb image quality of the survey. The Deep (26 deg|$^2$|⁠) and UltraDeep (4 deg|$^2$|⁠) data are jointly processed and the UltraDeep-COSMOS field reaches an unprecedented depth of |$i\sim 28$| at |$5 \, \sigma$| for point sources. In addition to the broad-band data, narrow-band data are also available in the Deep and UltraDeep fields. This release includes a major update to the processing pipeline, including improved sky subtraction, PSF modeling, object detection, and artifact rejection. The overall data quality has been improved, but this release is not without problems; there is a persistent deblender problem as well as new issues with masks around bright stars. The user is encouraged to review the issue list before utilizing the data for scientific explorations. All the image products as well as catalog products are available for download. The catalogs are also loaded into a database, which provides an easy interface for users to retrieve data for objects of interest. In addition to these main data products, detailed galaxy shape measurements withheld from Public Data Release 1 (PDR1) are now available to the community. The shape catalog is drawn from the S16A internal release, which has a larger area than PDR1 (160 deg|$^2$|⁠). All products are available at the data release site, https://hsc-release.mtk.nao.ac.jp/