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AI and the nature of disagreement Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Anthony Niblett, Albert Yoon
Litigation is a creature of disagreement. Our essay explores the potential of artificial intelligence (AI) to help reduce legal disagreements. In any litigation, parties disagree over the facts, the law, or how the law applies to the facts. The source of the parties' disagreements matters. It may determine the extent to which AI can help resolve their disputes. AI is helpful in clarifying the parties’
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Towards human-centred standards for legal help AI Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Margaret Hagan
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
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Valence and interactions in judicial voting Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Edward D. Lee, George T. Cantwell
The collective statistics of voting on judicial courts present hints about their inner workings. Many approaches for studying these statistics, however, assume that judges’ decisions are conditionally independent: a judge reaches a decision based on the case at hand and his or her personal views. In reality, judges interact. We develop a minimal model that accounts for judge bias, depending on the
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A network model of legal relations Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Ted Sichelman, Henry E. Smith
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
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Judicial hierarchy and discursive influence Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Felix Herron, Keith Carlson, Daniel N. Rockmore, Michael A. Livermore
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
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The latent net effectiveness of institutional complexes: a heuristic model Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Ashok Vardhan Adipudi, Rakhyun E. Kim
International institutions strive to achieve their own objectives while operating within a complex network of interdependencies. These interdependencies create an extensive web of relationships that serve as potential pathways for broader institutional impacts. The actions taken by individual institutions, their mutual influences, and the pattern of connectivity collectively shape the overall performance
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GPT-4 passes the bar exam Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Daniel Martin Katz, Michael James Bommarito, Shang Gao, Pablo Arredondo
In this paper, we experimentally evaluate the zero-shot performance of GPT-4 against prior generations of GPT on the entire uniform bar examination (UBE), including not only the multiple-choice multistate bar examination (MBE), but also the open-ended multistate essay exam (MEE) and multistate performance test (MPT) components. On the MBE, GPT-4 significantly outperforms both human test-takers and
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Large language models as tax attorneys: a case study in legal capabilities emergence Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 John J. Nay, David Karamardian, Sarah B. Lawsky, Wenting Tao, Meghana Bhat, Raghav Jain, Aaron Travis Lee, Jonathan H. Choi, Jungo Kasai
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
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Words or code first? Is the legacy document or a code statement the better starting point for complexity-reducing legal automation? Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Oliver R. Goodenough, Preston J. Carlson
Law is a critical tool that humans have created to assist them in managing complex social interactions. Computational Law holds the potential to significantly enhance our capacity to express and manage legal complexity, and a number of advantages can result from restating public and private legal rules in computable form. Capturing that potential depends in part on the approaches taken to automation
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Empirical legal analysis simplified: reducing complexity through automatic identification and evaluation of legally relevant factors Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Morgan A. Gray, Jaromir Savelka, Wesley M. Oliver, Kevin D. Ashley
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
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Scaling laws: legal and social complexity in US localities Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Elliott Ash, Christoph Goessmann, Suresh Naidu
Law sets out the rules for society and the economy, particularly important for interactions between strangers. Legal code is a form of non-rival infrastructure, a public good important for investment and innovation. This paper investigates whether legal code complexity scales with population size in US localities. We analyse a corpus of municipal codes from 3259 cities and measure legal complexity
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Coalitions in international litigation: a network perspective Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 R. Mastrandrea, G. Antuofermo, M. Ovadek, T. Y.-C. Yeung, A. Dyevre, G. Caldarelli
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
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Discovering significant topics from legal decisions with selective inference Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Jerrold Soh Tsin Howe
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
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Legal hypergraphs Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-26 Corinna Coupette, Dirk Hartung, Daniel Martin Katz
Complexity science provides a powerful framework for understanding physical, biological and social systems, and network analysis is one of its principal tools. Since many complex systems exhibit multilateral interactions that change over time, in recent years, network scientists have become increasingly interested in modelling and measuring dynamic networks featuring higher-order relations. At the
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Geodiversity for science and society Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Joseph Bailey, Richard Field, Derk van Ree, Franziska Schrodt
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Promoting diversity in geoheritage evaluation: creating an evaluation method for the scientific value of Quaternary sites in arid environments Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Kenta Sayama
A rigorous assessment is an essential part of geoconservation, and choosing an appropriate evaluation method is essential for this process. Globally, an increasing number of sites are being assessed for their geoheritage values, but the most popular methods have been created by researchers with experiences centred in Europe, without considerations of regional differences. To understand whether regional
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Towards a taxonomy of geodiversity Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Jan Hjort, Arie C. Seijmonsbergen, Julia Kemppinen, Helena Tukiainen, Tuija Maliniemi, John E. Gordon, Janne Alahuhta, Murray Gray
Geodiversity is a topical concept in earth and environmental sciences. Geodiversity information is needed to conserve nature, use ecosystem services and achieve sustainable development goals. Despite the increasing demand for geodiversity data, there exists no comprehensive system for categorizing geodiversity. Here, we present a hierarchically structured taxonomy that is potentially applicable in
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A framework for quantifying geodiversity at the local scale: a case study from the Rokua UNESCO Global Geopark Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Helena Tukiainen, Tuija Maliniemi, José Brilha, Janne Alahuhta, Jan Hjort
Geoconservation and related quantitative and qualitative geodiversity assessments are gaining increasing attention. However, methodologies for measuring geodiversity at local scale are currently rare. Here, we present a framework for assessing local-scale geodiversity of different landforms using field-based and digital elevation model (DEM-) derived data from the Rokua UNESCO Global Geopark in Finland
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Global geodiversity components are not equally represented in UNESCO Global Geoparks Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Emma M. N. Polman, Arie C. Seijmonsbergen, Hannes Versteegh, W. Daniel Kissling
The aim of UNESCO Global Geoparks (UGGs) is to protect globally significant geoheritage and geodiversity, but quantitative evidence on the global representativeness of geodiversity components (i.e. geology, soils, geomorphology and hydrology) in these geoparks is in short supply. Here, we provide a first assessment by deriving a global map of geodiversity to test whether the presence of geodiversity
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Quantitative measurement of geodiversity uniqueness: research implications and conservation applications Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Janne Alahuhta, Jorge García-Girón, Jan Hjort, Henriikka Salminen, Helena Tukiainen, Jani Heino
Quantitative approaches are needed to complement qualitative explorations to identify sites with unique geodiversity and thereby guide geoconservation and geoheritage programmes. Here, we introduce the concept and associated index of ‘geodiversity uniqueness’. This index is based on a numerical analysis of geofeatures and allows the identification of sites with unique geodiversity in a study area.
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Case studies associated with the 10 major geodiversity-related topics Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Murray Gray
This paper outlines the 10 major topics related to geodiversity that have emerged since the concept was first introduced in 1993, 30 years ago. After a short introduction, each of the 10 topics is then illustrated by a relevant case study. The 10 topics (italics) and their case studies (bold) are as follows: 1. Celebrating , International Geodiversity Day ; 2. Measurement/Assessment , Potential role
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Geodiversity data for Europe Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 M. Toivanen, T. Maliniemi, J. Hjort, H. Salminen, T. Ala-Hulkko, J. Kemppinen, O. Karjalainen, A. Poturalska, P. Kiilunen, H. Snåre, O. Leppiniemi, E. Makopoulou, J. Alahuhta, H. Tukiainen
Geodiversity is an essential part of nature's diversity. However, geodiversity is insufficiently understood in terms of its spatial distribution and its relationship to biodiversity over large spatial extents. Here, we present European geodiversity data at resolutions of 1 km and 10 km. We assess terrestrial geodiversity quantitatively as a richness variable (georichness) using a commonly employed
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The status and future of essential geodiversity variables Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Franziska Schrodt, Grant Vernham, Joseph Bailey, Richard Field, John E. Gordon, Murray Gray, Jan Hjort, Carina Hoorn, Malcom L. Hunter Jr., Jonathan Larwood, Angela Lausch, Manu Monge-Ganuzas, Stephanie Miller, Derk van Ree, Arie Christoffel Seijmonsbergen, Phoebe L. Zarnetske, W. Daniel Kissling
Rapid environmental change, natural resource overconsumption and increasing concerns about ecological sustainability have led to the development of ‘Essential Variables' (EVs). EVs are harmonized data products to inform policy and to enable effective management of natural resources by monitoring global changes. Recent years have seen the instigation of new EVs beyond those established for climate,
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Linking geodiversity and geosystem services to human well-being for the sustainable utilization of the subsurface and the urban environment Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 D. van Ree, P. J. H. van Beukering, M. W. Hofkes
Because the functions of the subsurface are hidden from view, its important role in society is often ignored or taken for granted. The subsurface is, however, an essential part of the global ecosystem with important contributions to human well-being. Geodiversity is an important characteristic in this respect. Material supply is the more obvious role of the subsurface with projections of a doubling
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The influence of scale-dependent geodiversity on species distribution models in a biodiversity hotspot Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Beth E. Gerstner, Mary E. Blair, Patrick Bills, Cristian A. Cruz-Rodriguez, Phoebe L. Zarnetske
Improving models of species' distributions is essential for conservation, especially in light of global change. Species distribution models (SDMs) often rely on mean environmental conditions, yet species distributions are also a function of environmental heterogeneity and filtering acting at multiple spatial scales. Geodiversity, which we define as the variation of abiotic features and processes of
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Monitoring vegetation- and geodiversity with remote sensing and traits Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Angela Lausch, Peter Selsam, Marion Pause, Jan Bumberger
Geodiversity has shaped and structured the Earth's surface at all spatio-temporal scales, not only through long-term processes but also through medium- and short-term processes. Geodiversity is, therefore, a key control and regulating variable in the overall development of landscapes and biodiversity. However, climate change and land use intensity are leading to major changes and disturbances in bio-
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A test of Conserving Nature's Stage: protecting a diversity of geophysical traits can also support a diversity of species at a landscape scale Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Stephanie N. Miller, Paul Beier, Fabio Suzart de Albuquerque
Conserving Nature's Stage (CNS) is a concept from conservation planning that promotes the protection of areas encompassing a broad range of enduring geophysical traits to provide long-term habitat for diverse species. The efficacy of using enduring geophysical characteristics as surrogates for biodiversity, independent of non-geophysical features and when considering finer resolution area selections
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Geoconservation at the International Union for Conservation of Nature (IUCN) Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Manu Monge-Ganuzas, Francisco Guillén-Mondéjar, Enrique Díaz-Martínez, Nadia Herrero, José Brilha
This work describes the achievements made towards geoconservation within the International Union for Conservation of Nature (IUCN) from the 1990s onwards. The key milestones in the recognition of geoconservation within the IUCN are presented. Initially, the IUCN's geoconservation efforts were focused on refining the criteria for World Heritage (WH) designation. Subsequently, the actions focused on
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Geodiversity in the Amazon drainage basin Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 Cécile M. E. Alsbach, Arie C. Seijmonsbergen, Carina Hoorn
The Amazon is the largest drainage basin on Earth and contains a wide variety of abiotic landscape features. In spite of this, the geodiversity in this basin has not yet been objectively evaluated. We address this knowledge gap by combining a meta-analysis of an existing global geodiversity map and its components with a systematic literature review, to identify the key characteristics of geodiversity
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The dilemma of valuing geodiversity: geoconservation versus geotourism Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-02-12 S. Anougmar, A. Meesters, D. van Ree, T. Compernolle
Geodiversity and geosystem services are confronting global threats. However, the majority of conservation strategies tend to overlook the geological component within ecosystems. The existing literature centres on biodiversity, ecosystem services and their economic valuation. In this paper, we conduct a systematic literature review to identify the gap in the assessment of geological diversity, pinpointing
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The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Lucas E. A. Porto, Rafael Rabelo, Marcelo Terra Cunha, Adán Cabello
A necessary condition for the probabilities of a set of events to exhibit Bell non-locality or Kochen–Specker contextuality is that the graph of exclusivity of the events contains induced odd cycles with five or more vertices, called odd holes, or their complements, called odd antiholes. From this perspective, events whose graph of exclusivity are odd holes or antiholes are the building blocks of contextuality
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Observer effect, quasi-probabilities and generalized Specker’s boxes Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 K. Onggadinata, D. Kaszlikowski, P. Kurzyński
Quantum non-locality and contextuality can be simulated with quasi-probabilities, i.e. probabilities that take negative values. Here, we show that another quantum phenomenon, the observer effect, admits a quasi-probabilistic description too. We also investigate post-quantum observer effects based on the Specker’s triangle scenario. This scenario comprises three observables, with the possibility of
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Hidden variables, free choice, context-independence and all that Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Ehtibar N. Dzhafarov
This paper provides a systematic account of the hidden variable models (HVMs) formulated to describe systems of random variables with mutually exclusive contexts. Any such system can be described either by a model with free choice but generally context-dependent mapping of the hidden variables into observable ones, or by a model with context-independent mapping but generally compromised free choice
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On geometrical aspects of the graph approach to contextuality Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Barbara Amaral, Marcelo Terra Cunha
The connection between contextuality and graph theory has paved the way for numerous advancements in the field. One notable development is the realization that sets of probability distributions in many contextuality scenarios can be effectively described using well-established convex sets from graph theory. This geometric approach allows for a beautiful characterization of these sets. The application
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Comparing the cost of violating causal assumptions in Bell experiments: locality, free choice and arrow-of-time Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Pawel Blasiak, Christoph Gallus
The causal modelling of Bell experiments relies on three fundamental assumptions: locality, freedom of choice and arrow-of-time. It turns out that nature violates Bell inequalities, which implies the failure of at least one of those assumptions. Since rejecting any of them, even partially, is sufficient to explain the observed correlations, it is natural to inquire about the cost in each case. This
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Causality and signalling of garden-path sentences Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Daphne Wang, Mehrnoosh Sadrzadeh
Sheaves are mathematical objects that describe the globally compatible data associated with open sets of a topological space. Original examples of sheaves were continuous functions; later they also became powerful tools in algebraic geometry, as well as logic and set theory. More recently, sheaves have been applied to the theory of contextuality in quantum mechanics. Whenever the local data are not
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Agreement and disagreement in a non-classical world Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Adam Brandenburger, Patricia Contreras-Tejada, Pierfrancesco La Mura, Giannicola Scarpa, Kai Steverson
The Agreement Theorem Aumann (1976 Ann. Stat. 4 , 1236–1239. ( doi:10.1214/aos/1176343654 )) states that if two Bayesian agents start with a common prior, then they cannot have common knowledge that they hold different posterior probabilities of some underlying event of interest. In short, the two agents cannot ‘agree to disagree’. This result applies in the classical domain where classical probability
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Combining contextuality and causality: a game semantics approach Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Samson Abramsky, Rui Soares Barbosa, Amy Searle
We develop an approach to combining contextuality with causality, which is general enough to cover causal background structure, adaptive measurement-based quantum computation and causal networks. The key idea is to view contextuality as arising from a game played between Experimenter and Nature, allowing for causal dependencies in the actions of both the Experimenter (choice of measurements) and Nature
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Measures of contextuality in cyclic systems and the negative probabilities measure CNT 3 Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Giulio Camillo, Víctor H. Cervantes
Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistently connected systems). One such measure is based on quasi-couplings using negative probabilities (here denoted by CNT 3 , Dzhafarov & Kujala, 2016 Quantum interaction ). Dzhafarov & Kujala (Dzhafarov & Kujala 2019 Phil. Trans. R. Soc. A 377 , 20190149. ( doi:10.1098/rsta.2019.0149
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A proof of Specker’s principle Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Guido Bacciagaluppi
Specker’s principle, the condition that pairwise orthogonal propositions must be jointly orthogonal (or rather, the ‘exclusivity principle’ that follows from it), has been much investigated recently within the programme of finding physical principles to characterize quantum mechanics. Specker’s principle, however, largely appears to lack a physical justification. In this paper, I present a proof of
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Corrected Bell and non-contextuality inequalities for realistic experiments Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Kim Vallée, Pierre-Emmanuel Emeriau, Boris Bourdoncle, Adel Sohbi, Shane Mansfield, Damian Markham
Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a non-classical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden variables, for which it forces a contradiction with the assumptions of parameter-independence and determinism. The former can be justified by the empirical property
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Quantum contextuality, causality and freedom of choice Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-29 Samson Abramsky, Adán Cabello, Ehtibar N. Dzhafarov, Paweł Kurzyński
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Cosmologies with positive λ: hierarchies of future behaviour Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Helmut Friedrich
Smooth Cauchy data on S 3 for the Einstein- λ -vacuum field equations with cosmological constant λ > 0 that are sufficiently close to de Sitter data develop into a solution that admits a smooth conformal boundary J + in its future. The conformal Einstein equations determine a smooth conformal extension across J + that defines on ‘the other side’ again a λ -vacuum solution. In this article, we discuss
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At the interface of asymptotics, conformal methods and analysis in general relativity Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 G. Taujanskas, J. A. Valiente Kroon
This is an introductory article for the proceedings associated with the Royal Society Hooke discussion meeting of the same title which took place in London in May 2023. We review the history of Penrose’s conformal compactification, null infinity and a number of related fundamental developments in mathematical general relativity from the last 60 years. This article is part of a discussion meeting issue
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Guest-editing under the spotlight Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 John Dainton, Richard A. Dixon
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The case against smooth null infinity IV: Linearized gravity around Schwarzschild—an overview Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Leonhard Kehrberger
This paper is the fourth in a series dedicated to the mathematically rigorous asymptotic analysis of gravitational radiation under astrophysically realistic set-ups. It provides an overview of the physical ideas involved in setting up the mathematical problem, the mathematical challenges that need to be overcome once the problem is posed, as well as the main new results we will obtain in upcoming work
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Analytic and conformal scattering in general relativity Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Jean-Philippe Nicolas
This paper is about two important trends of scattering theory in general relativity: time-dependent spectral analytic scattering and conformal scattering. The former was initiated by Jonathan Dimock and Bernard Kay in the mid-1980s and is based on spectral and functional analysis. The latter was proposed by Roger Penrose in 1965 and then constructed for the first time by Gerard Friedlander in 1980
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Asymptotically de Sitter metrics from scattering data in all dimensions Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Peter Hintz
In space–time dimensions n + 1 ≥ 4 , we show the existence of solutions of the Einstein vacuum equations which describe asymptotically de Sitter space–times with prescribed smooth data at the conformal boundary. This provides a short alternative proof of a special case of a result by Shlapentokh-Rothman and Rodnianski, and generalizes earlier results of Friedrich and Anderson to all dimensions. This
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Calculation of asymptotic charges at the critical sets of null infinity Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Mariem Magdy Ali Mohamed
The asymptotic structure of null and spatial infinities of asymptotically flat spacetimes plays an essential role in discussing gravitational radiation, gravitational memory effect, and conserved quantities in General Relativity (GR). Bondi, Metzner and Sachs (BMS) established that the asymptotic symmetry group for asymptotically simple spacetimes is the infinite-dimensional BMS group. Given that null
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From conformal infinity to equations of motion: conserved quantities in general relativity Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Roger Penrose
This paper describes conservation laws in general relativity (GR) dating back to the mass-energy conservation of Bondi and Sachs in the early 1960s but using 2-spinor techniques. The notion of conformal infinity is employed, and the highly original ideas of E. T. Newman are discussed in relation to twistor theory. The controversial NP constants are introduced, and their meaning is considered in a new
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Characterizations of Kerr-de Sitter in arbitrary dimension from null infinity Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 M. Mars, C. Peón-Nieto
The Kerr and Kerr-de Sitter metrics share remarkable local geometric properties in four dimensions. Gibbons et al. found a generalization of the Kerr-de Sitter metric to higher dimensions, to which the local characterization above cannot be applied. One viable approach to characterize this family is to understand the behaviour of these metrics at future null infinity. We review Friedrich’s and Fefferman-Graham
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Polyhomogeneous spin-0 fields in Minkowski space–time Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Edgar Gasperín
The asymptotic behaviour of massless spin-0 fields close to spatial and null infinity in Minkowski space–time is studied by means of Friedrich’s cylinder at spatial infinity. The results are applied to a system of equations called the good–bad–ugly which serves as a model for the Einstein field equations in generalized harmonic gauge. The relation between the logarithmic terms (polyhomogeneity) appearing
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Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Rodrigo Panosso Macedo
This work offers a didactical introduction to the calculations and geometrical properties of a static, spherically symmetric spacetime foliated by hyperboloidal time surfaces. We discuss the various degrees of freedom involved, namely the height function, responsible for introducing the hyperboloidal time coordinate, and a radial compactification function. A central outcome is the expression of the
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Conformal methods in mathematical cosmology Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Paul Tod
When he first introduced the notion of a conformal boundary into the study of asymptotically empty space–times, Penrose noted that the boundary would be null, space-like or time-like according as the cosmological constant Λ was zero, positive or negative. While most applications of the idea of a conformal boundary have been to the zero- Λ , asymptotically Minkowskian case, there also has been work
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Conformal geodesics and the evolution of spacetimes with positive Cosmological constant Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Marica Minucci
This article provides a discussion on the construction of conformal Gaussian gauge systems to study the evolution of solutions to the Einstein field equations with positive Cosmological constant. This is done by means of a gauge based on the properties of conformal geodesics. The use of this gauge, combined with the extended conformal Einstein field equations, yields evolution equations in the form
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Asymptotic symmetries of projectively compact order one Einstein manifolds Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2024-01-15 Jack Borthwick, Yannick Herfray
We show that the boundary of a projectively compact Einstein manifold of dimension n can be extended by a line bundle naturally constructed from the projective compactification. This extended boundary is such that its automorphisms can be identified with asymptotic symmetries of the compactification. The construction is motivated by the investigation of a new curved orbit decomposition for a n + 1
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The role of gravity in naturalness versus consistency: strong- CP and dark energy Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2023-12-18 Gia Dvali
There is an ongoing debate on how seriously one should take the naturalness puzzles as the guidelines to new physics. In this debate gravity is often put aside, as an insignificant spectator force. However, this attitude misses the entire essence of the story. Through its S -matrix formulation, gravity promotes certain puzzles, such as the cosmological constant and strong- C P problems, into the consistency
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After the Higgs boson discovery: a turning point in particle physics Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2023-12-18 Stefan Pokorski
The discovery of the Higgs particle has completed the Standard Model of elementary interactions which is stunningly successful in describing most of the elementary processes observed so far in the laboratories. Nevertheless, it is not the Theory of Everything. Its structure faces some theoretical puzzles and, even more importantly, it leaves unexplained neutrino masses and several fundamental astrophysical
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Flavour physics as a window to new physics searches Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2023-12-18 Peter Križan
Flavour physics is one of the essential elements of the Standard Model (SM). Experimental studies of weak decays of B and D mesons at B factories have, together with the discovery of the Higgs boson at LHC, provided the final confirmation of the validity of the SM. The present generation of precision flavour physics experiments is looking for departures from the SM. We discuss studies of anomalies
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Experimental perspectives on the matter–antimatter asymmetry puzzle: developments in electron EDM and H¯ experiments Philos. Trans. Royal Soc. A: Math. Phys. Eng. Sci. (IF 5.0) Pub Date : 2023-12-18 D. Comparat, C. Malbrunot, S. Malbrunot-Ettenauer, E. Widmann, P. Yzombard
In the search for clues to the matter–antimatter puzzle, experiments with atoms or molecules play a particular role. These systems allow measurements with very high precision, as demonstrated by the unprecedented limits down to 10 − 30 e cm on electron EDM using molecular ions, and relative measurements at the level of 10 − 12 in spectroscopy of antihydrogen atoms. Building on these impressive measurements