An alternative look at the linear regression model

An alternative look at the linear regression model is taken by proposing an original treatment of a full column rank model (design) matrix. In such a situation, the Moore–Penrose inverse of the matrix can be obtained by utilizing a particular formula which is applicable solely when a matrix to be inverted can be columnwise partitioned into two matrices of disjoint ranges. It turns out that this approach, besides simplifying derivations, provides a novel insight into some of the notions involved in the model and reduces computational costs needed to obtain sought estimators. The paper contains also a numerical example based on astronomical observations of the localization of Polaris, demonstrating usefulness of the proposed approach.

Testing Algorithms for Identifying Source Confusion in the H i-MaNGA Survey

Astronomical observations of neutral atomic hydrogen (H i) are an important tracer of several key processes of galaxy evolution, but face significant difficulties with terrestrial telescopes. Among these is source confusion, or the inability to distinguish between emission from multiple nearby sources separated by distances smaller than the telescope’s spatial resolution. Confusion can compromise the data for the primary target if the flux from the secondary galaxy is sufficient. This paper presents an assessment of the confusion-flagging methods of the H i-MaNGA survey, using higher-resolution H i data from the Westorbork Synthesis Radio Telescope-Apertif survey. We find that removing potentially confused observations using a confusion probability metric—calculated from the relationship between galaxy color, surface brightness, and H i content—successfully eliminates all significantly confused observations in our sample, although roughly half of the eliminated observations are not significantly confused.

Pierre des Noyers, a scholar and scientific intermediary at the court of Louise-Marie Gonzaga

Pierre des Noyers, secretary of Queen of Poland Louise-Marie Gonzaga, is known for his role as a messenger, envoy, court journalist and sometimes propagandist. His work as an unofficial diplomat for the Queen and ambassador for France is less famous though no less interesting. Even though he was already quite involved in these time-consuming tasks, Pierre des Noyers also acted as a scientific intermediary for the quite curious Queen Louise-Marie of Poland. He maintained contacts with many scholars from France and Italy. He could nurture this network thanks to his position as an informal diplomat at the court of the Queen and his dedication to science in general. Even by discarding his most official and political letters, his known correspondence amounts to several hundred letters written in a period of around 50 years to various friends and scholars. Roberval, Gassendi, Boulliau, Hevelius or Pascal are among these contacts and he plays for most of them the role of a scientific intermediary sharing with them observations, books and anecdotes. His letters are filled with astronomical observations, prodigies and prophecies. Des Noyers was also a practitioner of science. Having possessed a rather large collection of scientific instruments he always sought the improved ones and his daily life was marked by scientific studies. He wrote meteorological bulletins for Academia del Cimento in Florence, studied the measurement of time, observed the sun and showed interest in the inner workings of the human body. This article will delve further into more scientific aspects of Pierre des Noyers’s life, both at the court of Louise-Marie and outside. The first part presents a rough overview of the secretary’s contacts in the scientific environment of 17th Century France and how they were used to connect scholars from Poland with this environment. The second part of this work presents Pierre des Noyers’s practice of science as a tool to understand the world and for which utmost diligence in measurement and practice is required. The last part focuses on des Noyers’s application of this scientific method in two, now pseudo-scientific fields: astrology and divination.

Presolar Grains

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Planetary Science. Please check back later for the full article. Presolar grains are dust produced by stars that died before the formation of the Earth’s solar system. Stardust grains condense out of cooling gas lost via stellar winds from the surface of low-mass stars and stellar explosions and become a constituent of interstellar medium (ISM). About 4.6 Ga, a molecular cloud in the ISM collapsed to form the solar system, during which some primordial stardust grains from the ISM survived and were incorporated into small bodies formed in the early solar system. Some of these small solar system bodies, including asteroids and comets, escaped planet formation and have remained minimally altered, thus preserving their initially incorporated presolar grains. Fragments of asteroids and comets are collected on Earth as interplanetary dust particles (IDPs) and meteorites. Presolar grains have been found in primitive IDPs and chondrites—stony meteorites that have not been modified by either melting or differentiation of their parent bodies. Presolar grains, typically less than a few μm, are identified in primitive extraterrestrial materials by their unique isotopic signatures, revealing the effects of galactic chemical evolution (GCE), stellar nucleosynthesis, and cosmic ray exposure. Comparisons of presolar grain isotope data with stellar observations and nucleosynthesis model calculations suggest that presolar grains were dominantly sourced from asymptotic giant branch stars and core-collapse supernovae, although there are still ambiguities in assigning the type of star to some groups of grains. So far, various presolar phases have been identified such as corundum, olivine, and silicon carbide, reflecting diverse condensation environments in different types of stars. The abundances of different presolar phases in primitive extraterrestrial materials vary widely, ranging from a few percent for presolar silicates to a few parts per million for presolar oxides. Presolar grain studies rely on the synergy between astronomy, astrophysics, nuclear physics, and cosmochemistry. To understand the stellar sources of presolar grains, it is important to compare isotope data of presolar grains to astronomical observations for different types of stellar objects. When such astronomical observations are unavailable, stellar nucleosynthesis models must be relied upon, which require inputs of (a) initial stellar composition estimated based on solar system nuclide abundances, (b) stellar evolution models, and (c) nuclear reaction rates determined by theories and laboratory experiments. Once the stellar source of a group of presolar grains is ascertained, isotope information extracted from the grains can then be used to constrain stellar mixing processes, nuclear reaction rates, GCE, and the ISM residence times of the grains. In addition, crystal structures and chemical compositions of presolar grains can provide information to infer dust condensation conditions in their parent stars, while abundances of presolar grains in primitive chondrites can help constrain secondary processing experienced by the parent asteroids of their host chondrites. Since the discovery of presolar grains in meteorites in 1980s, a diverse array of information about stars and GCE has been gleaned by studying them. Technological advances will likely allow for the discovery of additional types of presolar grains and analysis of smaller, more typical presolar grains in the future.

Geodetic foundations of cartography in Europe in 19th century

Geodetic surveying comprises the determination of locations on and the dimensions of the earth’s surface at a various scales. In the 19th century, its technologies are those of direct measurement of the earth’s surface combined with astronomical observations. Its social context encompasses all those individuals and institutions involved in the creation, preservation, use, and arrangement of knowledge of the earth. In the introductory part of the paper the author mentions several important events in the history of the 19th century geodesy. Geodetic work on determining the size of the Earth by measuring the lengths of the meridian arcs continues in this century. An international surveying organization was established and the international meter convention adopted. Basing on a detailed research of geodetic surveying in Central, Eastern and Southeastern Europe in the 19th century, a part of these surveys is presented that relates to Switzerland, Austro-Hungarian Monarchy, Austria, Hungary, Slovenia and Croatia. Common to all these geodetic surveys is that they were necessary for the development of cartography and were carried out by military institutions. The developed geodetic networks are characterized by the use of different ellipsoids, different prime meridians, different coordinate systems and their origin. In the area under consideration in the 19th century, there were five different ellipsoids in use suggested by Bessel, Bonenberger, Schmidt, Valbeck and Zach. Prime meridians were

THE COMPLEX OF ANCIENT OBSERVATORIES ON THE TABLE MOUNTAIN IN INGUSHETIA

The proximity of the three ancient sanctuaries to each other on the flat top of the Table Mountain against the background of the sacred peaks of Kazbek and Tsey-Loam, the opportunity to observe the sunrises and sunsets in the highlands of the Caucasus, cosmogonic myths, all this gave an assumption about the astronomical functions of these sanctuaries. The purpose of the study was to prove that these ancient sanctuaries were used by the priests to determine the key moments in the annual cycle of the Sun and were a calendar. This is proved by using special computer programs and calculators that determine the azimuth and altitude of the Sun; instrumental observations and measurements on the ground. It is established that the shrines of Myat-Seli and Myater-Dyal on Table Mountain in Ingushetia are a complex of medieval solar near-horizon observatories. And it is hypothesized that these sanctuaries were built on the site from which solar cycles were observed from about the beginning of the 1st millennium BC. This work also provides prerequisites for determining various astronomical observations from sanctuaries and the presence of other ancient observatories in the Caucasus. A method has been developed for searching for prehistoric solar, lunar and stellar near-horizon observatories.

Gravitational “Doppler Boosting / De-boosting” Effect within the Framework of General Relativity

The “Doppler boosting / de-boosting” relativistic effect increases / decreases the apparent luminosity of approaching / receding sources of radiation. This effect was analyzed in detail within the Special Relativity framework and was confirmed in many astronomical observations. It is however not clear if “Doppler boosting / de-boosting” exists in the framework of General Relativity as well, and if it exists, which equations describe it. The “Einstein’s elevator” and Einstein’s “Equivalence principle” allow to obtain the formula for “Doppler boosting / de-boosting” for a uniform gravitational field within the vicinity of the emitter/receiver. Under these simplified conditions, the ratio ℳ between apparent (L) and intrinsic (Lo) luminosity can be conveniently represented using source’s spectral index α and gravitational redshift z as ℳ(z, α) ≡ L/Lo=(z+1)^(α-3). This is the first step towards the complete set of equations that describe the gravitational "Doppler boosting / de-boosting" effect within the General Relativity framework including radial gravitational field and arbitrary values of distance h between emitter and receiver.

Collider Searches for Dark Matter through the Higgs Lens

Despite the fact that dark matter constitutes one of the cornerstones of the standard cosmological paradigm, its existence has so far only been inferred from astronomical observations, and its microscopic nature remains elusive. Theoretical arguments suggest that dark matter might be connected to the symmetry-breaking mechanism of the electroweak interactions or of other symmetries extending the Standard Model of particle physics. The resulting Higgs bosons, including the 125 GeV spin-0 particle discovered recently at the Large Hadron Collider, therefore represent a unique tool to search for dark matter candidates at collider experiments. This article reviews some of the relevant theoretical models as well as the results from the searches for dark matter in signatures that involve a Higgs-like particle at the Large Hadron Collider.

THE IMPACT OF COLOURFUL AND DYNAMIC LED MEDIA FACADE AND BILLBOARDS ON ASTRONOMICAL OBSERVATIONS

More and more LED media façades and LED billboards are being installed on architecture and buildings in order to decorate city skylines or to deliver advertisements. The shopping malls in the busiest streets in city centers make extensive use of LEDs to attract tourists and to promote the nighttime economy and business. In order to achieve the desired graphic and the display needed, these LED media façades and LED billboards utilize RGB LEDs or RBG white LEDs and a control system which emits a wide spectrum of light, including blue, green and red light. Although each of these colors contributes to skyglow via Rayleigh scattering, bluer colors of light are more efficiently scattered, and are of particular concern. The shift of the usage of conventional light sources like incandescent lamp, low pressure sodium and high pressure sodium light sources to this new type of colorful and dynamic LED media façade and billboards has brought new challenges to astronomers. This paper describes how the light emission from LED media façades and LED billboards increases the artificial skyglow in the atmosphere and more importantly how this brightening skyglow affects astronomical observations.

Energy Spectra of Atmospheric Turbulence for Calculating Cn2 Parameter. I. Maidanak and Suffa Observatories in Uzbekistan

Knowledge of the turbulence spectra is of interest for describing atmospheric conditions as applied to astronomical observations. This article discusses the deformations of the turbulence spectra with heights in a wide range of scales at the sites of the Maidanak and Suffa observatories. It is shown that the energy of baroclinic instability is high at the sites of these observatories and should be taken into account in the calculations of the refractive index structure constant Cn2.