Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

The Moon is a unique natural laboratory for the study of the deep space plasma and energetic particles environment. During more than 3/4 of its orbit around the Earth it is exposed to the solar wind. Being an unmagnetized body and lacking a substantial atmosphere, solar wind and solar energetic particles bombard the Moon's surface, interacting with the lunar regolith and the tenuous lunar exosphere. Energetic particles arriving at the Moon's surface can be absorbed, or scattered, or can remove another particle from the lunar regolith by sputtering or desorption...

A new era of lunar exploration has begun with participation of all major space agencies. This activity brings opportunities for revolutionary science experiments and observatories on the Moon. The idea of a lunar gravitational-wave detector was already proposed during the Apollo programme. The key characteristic of the Moon is that it is seismically extremely quiet. It was also pointed out that the permanently shadowed regions at the lunar poles provide ideal conditions for gravitational-wave detection...

The proposed lunar telescope for optical and infrared astronomy aims at very large aperture, 600 m2 , at a fundable cost. It comprises an array of 18 separate telescopes, each of 6.5 m aperture. The 200 m diameter array will be located within 1/2° (15 km) of a lunar pole on approximately level ground, with a perimeter screen deployed to provide shade and cooling to cryogenic temperature. The 500 m diameter screen will allow unobscured access down to 8° elevation...

The hydrogen 21-cm signal is predicted to be the richest probe of the young Universe, including those eras known as the cosmic Dark Ages, the Cosmic Dawn (when the first star and black hole formed) and the Epoch of Reionization. This signal holds the key to deciphering processes that take place at the early stages of cosmic history. In this opinion piece, we discuss the potential scientific merit of lunar observations of the 21-cm signal and their advantages over more affordable terrestrial efforts. The Moon is a prime location for radio cosmology which will enable precision observations of the low-frequency radio sky...

No abstract text is available yet for this article.

The Moon presents unique opportunities for high-impact astronomy that could enhance our understanding of our solar system, the possibility of life beyond Earth, and the evolution of the universe. A handful of locations on the lunar surface are 'sites of extraordinary scientific importance' (SESIs) for such studies, presenting opportunities for astronomical research unmatched anywhere else. For instance, the farside of the Moon, the most radio-quiet location in the inner solar system, could allow for the emplacement of telescopes to study the cosmic Dark Ages in ways that are impossible elsewhere...

The era following the separation of CMB photons from matter, until the emergence of the first stars and galaxies, is known as the Cosmic Dark Ages. Studying the electromagnetic radiation emitted by neutral hydrogen having the 21 cm rest wavelength is the only way to explore this significant phase in the Universe's history, offering opportunities to investigate essential questions about dark matter physics, the standard cosmological model and inflation. Due to cosmological redshift, this signal is now only observable at frequencies inaccessible from the Earth's surface due to ionospheric absorption and reflection...

At redshifts beyond [Formula: see text], the 21 cm line from neutral hydrogen is expected to be essentially the only viable probe of the three-dimensional matter distribution. The lunar far-side is an extremely appealing site for future radio arrays that target this signal, as it is protected from terrestrial radio frequency interference, and has no ionosphere to attenuate and absorb radio emission at low frequencies (tens of MHz and below). We forecast the sensitivity of low-frequency lunar radio arrays to the bispectrum of the 21 cm brightness temperature field, which can in turn be used to probe primordial non-Gaussianity generated by particular early universe models...

At the Royal Society meeting in 2023, we have mainly presented our lunar orbit array concept called DSL, and also briefly introduced a concept of a lunar surface array, LARAF. As the DSL concept had been presented before, in this article, we introduce the LARAF. We propose to build an array in the far side of the Moon, with a master station which handles the data collection and processing, and 20 stations with maximum baseline of 10 km. Each station consists of 12 membrane antenna units, and the stations are connected to the master station by power line and optical fibre...

The Moon has no atmosphere, hence, it offers a unique opportunity to place telescopes on its surface for astronomical observations. It is phase-locked with Earth, and its far side remains free from ground-based interference, enabling the optimal use of radio telescopes. However, the surface of the Moon, as any other airless planetary object in the solar system, is continually bombarded by interplanetary dust particles that cause impact damage and generate secondary ejecta particles that continually overturn the top layer of the lunar regolith...

Motivated by efforts to return humanity to the Moon, three cases are reviewed for X-ray astronomy from the lunar surface: (i) facilitation of ambitious engineering designs including high-throughput telescopes, long focal length optics and X-ray interferometery; (ii) occultation studies and the gain they enable in astrometric precision; and (iii) multi-messenger time-domain coordinated observations. The potential benefits of, and challenges presented by, operating from the Moon are discussed. Some of these cases have relatively low mass budgets and could be conducted as early pathfinders, while others are more ambitious and will likely need to await improvements in technology or well-developed lunar bases...

We look at what astronomy from the Moon might be like over the next few decades. The Moon offers the possibility of installing large telescopes or interferometers with instruments larger than those on orbiting telescopes. We first present examples of ambitious science cases, in particular ideas that cannot be implemented from Earth. After a general review of observational approaches, from photometry to high contrast and high angular resolution imaging, we propose as a first step a 1-metre-class precursor and explore what science can be done with it...

In the first special issue on 'Astronomy from the Moon: the next decades', two projects for the infrared domain, considered as justifying a lunar implementation, were presented: a general purpose light collector for the 1-200 μm range, of diameter much larger than any ELT on Earth and a specialized instrument in the very far-infrared aiming at the detection of the weak CMB spectral distortions. Learning from the launch of JWST, to surpass it in spatial, spectral resolution, spectral coverage and sensitivity, the concept of a large infrared, lunar collector is revisited to be specified on a more realistic approach...

We propose and evaluate an automated pipeline for discovering significant topics from legal decision texts by passing features synthesized with topic models through penalized regressions and post-selection significance tests. The method identifies case topics significantly correlated with outcomes, topic-word distributions which can be manually interpreted to gain insights about significant topics, and case-topic weights which can be used to identify representative cases for each topic. We demonstrate the method on a new dataset of domain name disputes and a canonical dataset of European Court of Human Rights violation cases...

We apply network science principles to analyse the coalitions formed by European Union nations and institutions during litigation proceedings at the European Court of Justice. By constructing Friends and Foes networks, we explore their characteristics and dynamics through the application of cluster detection, motif analysis and duplex analysis. Our findings demonstrate that the Friends and Foes networks exhibit disassortative behaviour, highlighting the inclination of nodes to connect with dissimilar nodes...

As more groups consider how AI may be used in the legal sector, this paper envisions how companies and policymakers can prioritize the perspective of community members as they design AI and policies around it. It presents findings of structured interviews and design sessions with community members, in which they were asked about whether, how, and why they would use AI tools powered by large language models to respond to legal problems like receiving an eviction notice. The respondents reviewed options for simple versus complex interfaces for AI tools, and expressed how they would want to engage with an AI tool to resolve a legal problem...

Better understanding of Large Language Models' (LLMs) legal analysis abilities can contribute to improving the efficiency of legal services, governing artificial intelligence and leveraging LLMs to identify inconsistencies in law. This paper explores LLM capabilities in applying tax law. We choose this area of law because it has a structure that allows us to set up automated validation pipelines across thousands of examples, requires logical reasoning and maths skills, and enables us to test LLM capabilities in a manner relevant to real-world economic lives of citizens and companies...

From at least the early twentieth century, legal scholars have recognized that rights and other legal relations inhere between individual legal actors, forming a vast and complex social network. Yet, no legal scholar has used the mathematical machinery of network theory to formalize these relationships. Here, we propose the first such approach by modelling a rudimentary, static set of real property relations using network theory. Then, we apply our toy model to measure the level of modularity-essentially, the community structure-among aggregations of these real property relations and associated actors...

We apply a dynamic influence model to the opinions of the US federal courts to examine the role of the US Supreme Court in influencing the direction of legal discourse in the federal courts. We propose two mechanisms for how the Court affects innovation in legal language: a selection mechanism where the Court's influence primarily derives from its discretionary jurisdiction, and an authorship mechanism in which the Court's influence derives directly from its own innovations. To test these alternative hypotheses, we develop a novel influence measure based on a dynamic topic model that separates the Court's own language innovations from those of the lower courts...

This paper investigates the potential for reducing the complexity of AI and Law and empirical legal studies projects through a novel annotation methodology that relies on GPT Family Models to assist human annotators. Improving the speed, cost and quality of annotation could greatly benefit such projects. In modelling types of legal claims, researchers in the fields of empirical legal studies and AI and Law have long relied on manually annotating factors in case texts. To demonstrate our methodology, we employ cases and factors regarding whether a police officer has constitutional authority to detain a motorist on the basis of the officer's suspicion that the motorist is trafficking drugs...