Gaia Early Data Release 3: The celestial reference frame (Gaia-CRF3)

Context. Gaia-CRF3 is the celestial reference frame for positions and proper motions in the third release of data from the Gaia mission, Gaia DR3 (and for the early third release, Gaia EDR3, which contains identical astrometric results). The reference frame is defined by the positions and proper motions at epoch 2016.0 for a specific set of extragalactic sources in the (E)DR3 catalogue. Aims. We describe the construction of Gaia-CRF3 and its properties in terms of the distributions in magnitude, colour, and astrometric quality. Methods. Compact extragalactic sources in Gaia DR3 were identified by positional cross-matching with 17 external catalogues of quasi-stellar objects (QSO) and active galactic nuclei (AGN), followed by astrometric filtering designed to remove stellar contaminants. Selecting a clean sample was favoured over including a higher number of extragalactic sources. For the final sample, the random and systematic errors in the proper motions are analysed, as well as the radio-optical offsets in position for sources in the third realisation of the International Celestial Reference Frame (ICRF3). Results. Gaia-CRF3 comprises about 1.6 million QSO-like sources, of which 1.2 million have five-parameter astrometric solutions in Gaia DR3 and 0.4 million have six-parameter solutions. The sources span the magnitude range G = 13-21 with a peak density at 20.6 mag, at which the typical positional uncertainty is about 1 mas. The proper motions show systematic errors on the level of 12 μas yr-1 on angular scales greater than 15 deg. For the 3142 optical counterparts of ICRF3 sources in the S/X frequency bands, the median offset from the radio positions is about 0.5 mas, but it exceeds 4 mas in either coordinate for 127 sources. We outline the future of Gaia-CRF in the next Gaia data releases. Appendices give further details on the external catalogues used, how to extract information about the Gaia-CRF3 sources, potential (Galactic) confusion sources, and the estimation of the spin and orientation of an astrometric solution

Gaia Data Release 3: the extragalactic content

Galaxie

Smoothing imprecise 1-dimensional terrains

We study optimization problems for polyhedral terrains in the presence of data imprecision. An imprecise terrain is given by a triangulated point set where the height component of the vertices is speci¯ed by an interval of possible values. We restrict ourselves to terrains with a one-dimensional projection, usually referred to as 1.5-dimensional terrains, where an imprecise terrain is given by an x-monotone polyline, and the y-coordinate of each vertex is not ¯xed but only constrained to a given interval. Motivated mainly by applications in terrain analysis, in this paper we study ¯ve di®erent optimization measures related to obtaining smooth terrains, for the 1.5-dimensional case. In particular, we present exact algorithms to minimize and maximize the average turning angle, as well as to minimize the maximum slope change. Furthermore, we also give approximation algorithms to minimize the largest turning angle and to maximize the smallest turning angle

Smoothing imprecise 1-dimensional terrains

We study optimization problems for polyhedral terrains in the presence of data imprecision. An imprecise terrain is given by a triangulated point set where the height component of the vertices is speci¯ed by an interval of possible values. We restrict ourselves to terrains with a one-dimensional projection, usually referred to as 1.5-dimensional terrains, where an imprecise terrain is given by an x-monotone polyline, and the y-coordinate of each vertex is not ¯xed but only constrained to a given interval. Motivated mainly by applications in terrain analysis, in this paper we study ¯ve di®erent optimization measures related to obtaining smooth terrains, for the 1.5-dimensional case. In particular, we present exact algorithms to minimize and maximize the average turning angle, as well as to minimize the maximum slope change. Furthermore, we also give approximation algorithms to minimize the largest turning angle and to maximize the smallest turning angle

Searching for Meiji-Tokyo: Heterogeneous Visual Media and the Turn to Global Urban History, Digitalization, and Deep Learning

History & Complexit

Smoothing imprecise 1.5D terrains

We study optimization problems in an imprecision model for polyhedral terrains. An imprecise terrain is given by a triangulated point set where the height component of the vertices is specified by an interval of possible values. We restrict ourselves to 1.5-dimensional terrains: an imprecise terrain is given by an x-monotone polyline, and the y-coordinate of each vertex is not fixed but constrained to a given interval. Motivated by applications in terrain analysis, in this paper we present two linear-time approximation algorithms, for minimizing the largest turning angle and for maximizing the smallest one. In addition, we also provide linear time exact algorithms for minimizing and maximizing the sum of the turning angles

Mixing Methods: Practical Insights from the Humanities in the Digital Age

Digitality is a cause and a consequence of different data cultures. It applies to the 10 research projects that are included in this volume. They are rooted in various humanities disciplines such as art history, philosophy, musicology, religious studies, architectural history, media studies, and literature studies. As diverse as the disciplines are the objects and their formats, which are the subject of this book. The cultural data of the projects include recordings of music and spoken word, photographs and other types of images, handwriting, typoscripts and maps. The oldest material dates back to 500 BCE, followed by medieval times, the 18th and 19th centuries, early 20th century and the present. All projects share that they study their material with digital methods, although digitality comes into play at different moments and layers in each of the projects. Hardly readable manuscripts from the 18th century have to be treated with specialized OCR-methods while Plato’s texts are already available in digital form, and therefore open up other affordances for analysis. Special analysis possibilities had to be developed for certain image sources. For all projects, however, it is equally true that only the digitization of the objects makes them accessible to the methods that are the subject of this book.History, Form & Aesthetic