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Euclid preparation. Three-dimensional galaxy clustering in configuration space: Three-point correlation function estimation

यह शोध पत्र यूक्लिड मिशन के डेटा विश्लेषण पाइपलाइन के भीतर थ्री-पॉइंट कोरिलेशन फंक्शन का कुशलतापूर्वक अनुमान लगाने के लिए एक डायरेक्ट काउंटिंग विधि और एक स्फेरिकल हार्मोनिक डिकंपोजिशन दृष्टिकोण के साथ-साथ एक रैंडम स्प्लिट तकनीक को प्रस्तुत और मान्य करता है, जो यह प्रदर्शित करता है कि अंतिम सर्वेक्षण के पूर्ण थ्री-पॉइंट क्लस्टरिंग विश्लेषण को वैज्ञानिक आवश्यकताओं को पूरा करते हुए कम्प्यूटेशनल रूप से व्यवहार्य बनाना संभव है।

मूल लेखक: Euclid Collaboration, A. Veropalumbo (INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy, INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy, Dipartimento di Fisica
प्रकाशित 2026-05-06
📖 6 मिनट में पढ़ें🧠 गहराई से पढ़ें

मूल लेखक: Euclid Collaboration, A. Veropalumbo (INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy, INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy, Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy), M. Moresco (Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), F. Marulli (Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), E. Branchini (Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy, INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy, INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy), M. Guidi (Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), A. Farina (Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy, INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy, INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy), A. Pugno (Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany), E. Sefusatti (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy), D. Tavagnacco (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), F. Rizzo (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), E. Romelli (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), S. de la Torre (Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France), A. Eggemeier (Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany), E. Sihvola (Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland), M. Viel (IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy, INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy, ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy), N. Aghanim (Université Paris-Saclay, CNRS, Institut d'astrophysique spatiale, 91405, Orsay, France), B. Altieri (ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain), S. Andreon (INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy), N. Auricchio (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), C. Baccigalupi (IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy, INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy, SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy), M. Baldi (Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), S. Bardelli (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), P. Battaglia (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), A. Biviano (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy), M. Brescia (Department of Physics "E. Pancini", University Federico II, Via Cinthia 6, 80126, Napoli, Italy, INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy), S. Camera (Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy, INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy, INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese), G. Cañas-Herrera (Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK, Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands), V. Capobianco (INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese), C. Carbone (INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy), V. F. Cardone (INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy, INFN-Sezione di Roma, Piazzale Aldo Moro, 2 - c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy), J. Carretero (Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Port d'Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra), S. Casas (Institute for Theoretical Particle Physics and Cosmology, Deutsches Zentrum für Luft- und Raumfahrt e. V), M. Castellano (INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy), G. Castignani (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), S. Cavuoti (INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy, INFN section of Naples, Via Cinthia 6, 80126, Napoli, Italy), K. C. Chambers (Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA), A. Cimatti (Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), C. Colodro-Conde (Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain), G. Congedo (Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK), C. J. Conselice (Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK), L. Conversi (European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy, ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain), Y. Copin (Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France), F. Courbin (Institut de Ciències del Cosmos, Institució Catalana de Recerca i Estudis Avançats, Institut de Ciencies de l'Espai), H. M. Courtois (UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France), A. Da Silva (Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal, Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal), H. Degaudenzi (Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland), G. De Lucia (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), H. Dole (Université Paris-Saclay, CNRS, Institut d'astrophysique spatiale, 91405, Orsay, France), F. Dubath (Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland), X. Dupac (ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain), S. Dusini (INFN-Padova, Via Marzolo 8, 35131 Padova, Italy), S. Escoffier (Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France), M. Farina (INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy), R. Farinelli (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), F. Faustini (INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy, Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy), S. Ferriol (Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France), F. Finelli (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy), P. Fosalba (Institut d'Estudis Espacials de Catalunya, Institute of Space Sciences), S. Fotopoulou (School of Physics, HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK), M. Frailis (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), E. Franceschi (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), M. Fumana (INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy), S. Galeotta (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), K. George (University Observatory, LMU Faculty of Physics, Scheinerstr. 1, 81679 Munich, Germany), W. Gillard (Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France), B. Gillis (Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK), C. Giocoli (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), P. Gómez-Alvarez (FRACTAL S.L.N.E., calle Tulipán 2, Portal 13 1A, 28231, Las Rozas de Madrid, Spain, ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain), J. Gracia-Carpio (Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany), A. Grazian (INAF-Osservatorio Astronomico di Padova, Via dell'Osservatorio 5, 35122 Padova, Italy), F. Grupp (Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany, Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, Germany), L. Guzzo (Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy, INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy, INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy), W. Holmes (Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA), F. Hormuth (Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany), A. Hornstrup (Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark, Cosmic Dawn Center), K. Jahnke (Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany), M. Jhabvala (NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA), B. Joachimi (Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK), S. Kermiche (Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France), A. Kiessling (Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA), B. Kubik (Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France), M. Kunz (Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland), H. Kurki-Suonio (Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland, Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland), A. M. C. Le Brun (Laboratoire d'etude de l'Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France), S. Ligori (INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese), P. B. Lilje (Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315 Oslo, Norway), V. Lindholm (Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland, Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland), I. Lloro (SKAO, Jodrell Bank, Lower Withington, Macclesfield SK11 9FT, UK), G. Mainetti (Centre de Calcul de l'IN2P3/CNRS, 21 avenue Pierre de Coubertin 69627 Villeurbanne Cedex, France), D. Maino (Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy, INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy, INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy), E. Maiorano (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), O. Mansutti (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), S. Marcin (University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science, 5210 Windisch, Switzerland), O. Marggraf (Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany), M. Martinelli (INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy, INFN-Sezione di Roma, Piazzale Aldo Moro, 2 - c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy), N. Martinet (Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France), R. J. Massey (Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham, DH1 3LE, UK), E. Medinaceli (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), S. Mei (Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France, CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007, CPB-IN2P3, Berkeley, USA), M. Melchior (University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland), Y. Mellier (Institut d'Astrophysique de Paris, 98bis Boulevard Arago, 75014, Paris, France, Institut d'Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France), M. Meneghetti (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), E. Merlin (INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy), G. Meylan (Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne), A. Mora (Telespazio UK S.L. for European Space Agency), L. Moscardini (Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), C. Neissner (Institut de Física d'Altes Energies, Port d'Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra), S. -M. Niemi (European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands), J. W. Nightingale (School of Mathematics, Statistics and Physics, Newcastle University, Herschel Building, Newcastle-upon-Tyne, NE1 7RU, UK), C. Padilla (Institut de Física d'Altes Energies), S. Paltani (Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland), F. Pasian (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), K. Pedersen (DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark), W. J. Percival (Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada), V. Pettorino (European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands), S. Pires (Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France), G. Polenta (Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy), M. Poncet (Centre National d'Etudes Spatiales -- Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France), L. A. Popa (Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov, 077125, Romania), L. Pozzetti (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), F. Raison (Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany), A. Renzi (Dipartimento di Fisica e Astronomia "G. Galilei", Università di Padova, Via Marzolo 8, 35131 Padova, Italy, INFN-Padova, Via Marzolo 8, 35131 Padova, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), J. Rhodes (Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA, 91109, USA), G. Riccio (INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy), M. Roncarelli (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), R. Saglia (Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, Germany, Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany), Z. Sakr (Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany, Institut de Recherche en Astrophysique et Planétologie, Université St Joseph, Faculty of Sciences, Beirut, Lebanon), D. Sapone (Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile), B. Sartoris (Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, Germany, INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), P. Schneider (Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany), T. Schrabback (Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria), A. Secroun (Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France), G. Seidel (Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany), S. Serrano (Institut d'Estudis Espacials de Catalunya, Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain, Institute of Space Sciences), P. Simon (Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany), C. Sirignano (Dipartimento di Fisica e Astronomia "G. Galilei", Università di Padova, Via Marzolo 8, 35131 Padova, Italy, INFN-Padova, Via Marzolo 8, 35131 Padova, Italy), G. Sirri (INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), L. Stanco (INFN-Padova, Via Marzolo 8, 35131 Padova, Italy), J. Steinwagner (Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany), P. Tallada-Crespí (Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Port d'Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra), A. N. Taylor (Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK), I. Tereno (Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016 Lisboa, Portugal, Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal), N. Tessore (Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK), S. Toft (Cosmic Dawn Center, Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark), R. Toledo-Moreo (Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain), F. Torradeflot (Port d'Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas), I. Tutusaus (Institute of Space Sciences, Institut d'Estudis Espacials de Catalunya, Institut de Recherche en Astrophysique et Planétologie), L. Valenziano (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy), J. Valiviita (Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland, Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland), T. Vassallo (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), G. Verdoes Kleijn (Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands), Y. Wang (Caltech/IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA), J. Weller (Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, Germany, Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany), G. Zamorani (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), F. M. Zerbi (INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy), E. Zucca (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), V. Allevato (INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy), M. Ballardini (Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy, Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), C. Benoist (Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice cedex 4, France), M. Bolzonella (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), E. Bozzo (Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland), C. Burigana (INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy, INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy), R. Cabanac (Institut de Recherche en Astrophysique et Planétologie), M. Calabrese (Astronomical Observatory of the Autonomous Region of the Aosta Valley, INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy), A. Cappi (Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice cedex 4, France, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), T. Castro (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy, IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy, ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy), J. A. Escartin Vigo (Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany), L. Gabarra (Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK), J. García-Bellido (Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain), V. Gautard (CEA Saclay, DFR/IRFU, Service d'Astrophysique, Bat. 709, 91191 Gif-sur-Yvette, France), J. Macias-Perez (Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000, Grenoble, France), R. Maoli (Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy, INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy), J. Martín-Fleitas (Aurora Technology for European Space Agency), N. Mauri (Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy, INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), R. B. Metcalf (Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), P. Monaco (Dipartimento di Fisica - Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy, INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy, IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy), A. Pezzotta (INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy), M. Pöntinen (Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland), I. Risso (INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy, INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy), V. Scottez (Institut d'Astrophysique de Paris, 98bis Boulevard Arago, 75014, Paris, France, ICL, Junia, Université Catholique de Lille, LITL, 59000 Lille, France), M. Sereno (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), M. Tenti (INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), M. Tucci (Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland), M. Wiesmann (Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, 0315 Oslo, Norway), Y. Akrami (Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain, CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA), G. Alguero (Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000, Grenoble, France), I. T. Andika (University Observatory, LMU Faculty of Physics, Scheinerstr. 1, 81679 Munich, Germany), G. Angora (INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy, Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy), S. Anselmi (INFN-Padova, Via Marzolo 8, 35131 Padova, Italy, Dipartimento di Fisica e Astronomia "G. Galilei", Università di Padova, Via Marzolo 8, 35131 Padova, Italy, Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France), M. Archidiacono (Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy, INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy), F. Atrio-Barandela (Departamento de Física Fundamental. Universidad de Salamanca. Plaza de la Merced s/n. 37008 Salamanca, Spain), E. Aubourg (Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France, IRFU, CEA, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France), L. Bazzanini (Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), J. Bel (Aix-Marseille Université, Université de Toulon, CNRS, CPT, Marseille, France), D. Bertacca (Dipartimento di Fisica e Astronomia "G. Galilei", Università di Padova, Via Marzolo 8, 35131 Padova, Italy, INAF-Osservatorio Astronomico di Padova, Via dell'Osservatorio 5, 35122 Padova, Italy, INFN-Padova, Via Marzolo 8, 35131 Padova, Italy), M. Bethermin (Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France), F. Beutler (Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK), A. Blanchard (Institut de Recherche en Astrophysique et Planétologie), L. Blot (Center for Data-Driven Discovery, Kavli IPMU, Laboratoire d'etude de l'Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France), H. Böhringer (Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany, University Observatory, LMU Faculty of Physics, Scheinerstr. 1, 81679 Munich, Germany, Max-Planck-Institut für Physik, Boltzmannstr. 8, 85748 Garching, Germany), M. Bonici (Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy), S. Borgani (Dipartimento di Fisica - Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy, IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy, INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy, ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy), M. L. Brown (Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK), S. Bruton (California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA), A. Calabro (INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy), B. Camacho Quevedo (IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy, SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy, INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), F. Caro (INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy), C. S. Carvalho (Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal), F. Cogato (Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), S. Conseil (Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, F-69100, France), A. R. Cooray (Department of Physics \& Astronomy, University of California Irvine, Irvine CA 92697, USA), O. Cucciati (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), S. Davini (INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy), G. Desprez (Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands), A. Díaz-Sánchez (Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain), S. Di Domizio (Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy, INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy), J. M. Diego (Instituto de Física de Cantabria, Edificio Juan Jordá, Avenida de los Castros, 39005 Santander, Spain), V. Duret (Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France), M. Y. Elkhashab (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy, Dipartimento di Fisica - Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy, IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy), A. Enia (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), Y. Fang (Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, Germany), A. G. Ferrari (INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), A. Finoguenov (Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland), F. Fontanot (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy), A. Franco (INFN, Sezione di Lecce, Via per Arnesano, CP-193, 73100, Lecce, Italy, Department of Mathematics and Physics E. De Giorgi, University of Salento, Via per Arnesano, CP-I93, 73100, Lecce, Italy, INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100, Lecce, Italy), K. Ganga (Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France), T. Gasparetto (INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy), E. Gaztanaga (Institute of Space Sciences, Institut d'Estudis Espacials de Catalunya, Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK), F. Giacomini (INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), F. Gianotti (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), G. Gozaliasl (Department of Computer Science, Aalto University, PO Box 15400, Espoo, FI-00 076, Finland, Department of Physics, P.O. Box 64, University of Helsinki, 00014 Helsinki, Finland), A. Gruppuso (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), C. M. Gutierrez (Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain, Universidad de La Laguna, Dpto. Astrofí sica, E-38206 La Laguna, Tenerife, Spain), A. Hall (Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK), H. Hildebrandt (Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute), J. Hjorth (DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark), S. Joudaki (Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK), J. J. E. Kajava (Department of Physics and Astronomy, Vesilinnantie 5, University of Turku, 20014 Turku, Finland, Finnish Centre for Astronomy with ESO, Serco for European Space Agency), Y. Kang (Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland), V. Kansal (ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia, Centre for Astrophysics \& Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia), D. Karagiannis (Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy, Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town, 7535, South Africa), K. Kiiveri (Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland), J. Kim (Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK), C. C. Kirkpatrick (Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland), S. Kruk (ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain), M. Lattanzi (Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy), L. Legrand (DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK, Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK), M. Lembo (Institut d'Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France), F. Lepori (Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland), G. Leroy (Department of Physics, Centre for Extragalactic Astronomy, Durham University, South Road, Durham, DH1 3LE, UK, Department of Physics, Institute for Computational Cosmology, Durham University, South Road, Durham, DH1 3LE, UK), G. F. Lesci (Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), J. Lesgourgues (Institute for Theoretical Particle Physics and Cosmology), T. I. Liaudat (IRFU, CEA, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France), S. J. Liu (INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy), A. Loureiro (Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm, SE-106 91, Sweden, Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK), M. Magliocchetti (INAF-Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy), F. Mannucci (INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125, Firenze, Italy), C. J. A. P. Martins (Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal, Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal), L. Maurin (Université Paris-Saclay, CNRS, Institut d'astrophysique spatiale, 91405, Orsay, France), M. Migliaccio (Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma, Italy, INFN, Sezione di Roma 2, Via della Ricerca Scientifica 1, Roma, Italy), M. Miluzio (ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain, HE Space for European Space Agency), C. Moretti (INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy, IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy), G. Morgante (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), S. Nadathur (Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK), K. Naidoo (Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK, Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany), P. Natoli (Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy, Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy), A. Navarro-Alsina (Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany), S. Nesseris (Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain), L. Pagano (Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy, Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy), D. Paoletti (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy, INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy), F. Passalacqua (Dipartimento di Fisica e Astronomia "G. Galilei", Università di Padova, Via Marzolo 8, 35131 Padova, Italy, INFN-Padova, Via Marzolo 8, 35131 Padova, Italy), K. Paterson (Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany), L. Patrizii (INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy), R. Paviot (Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France), A. Pisani (Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France), D. Potter (Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland), G. W. Pratt (Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France), S. Quai (Dipartimento di Fisica e Astronomia "Augusto Righi" - Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy, INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), M. Radovich (INAF-Osservatorio Astronomico di Padova, Via dell'Osservatorio 5, 35122 Padova, Italy), K. Rojas (University of Applied Sciences and Arts of Northwestern Switzerland, School of Computer Science, 5210 Windisch, Switzerland), W. Roster (Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany), S. Sacquegna (INAF - Osservatorio Astronomico d'Abruzzo, Via Maggini, 64100, Teramo, Italy), M. Sahlén (Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, 751 37 Uppsala, Sweden), D. B. Sanders (Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA), E. Sarpa (SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy, ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy, INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy), A. Schneider (Department of Astrophysics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland), D. Sciotti (INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy, INFN-Sezione di Roma, Piazzale Aldo Moro, 2 - c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy), E. Sellentin (Mathematical Institute, University of Leiden, Einsteinweg 55, 2333 CA Leiden, The Netherlands, Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands), L. C. Smith (Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK), J. G. Sorce (Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, 59000 Lille, France, Université Paris-Saclay, CNRS, Institut d'astrophysique spatiale, 91405, Orsay, France), K. Tanidis (Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK), C. Tao (Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France), F. Tarsitano (Institute for Particle Physics and Astrophysics, Dept. of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland, Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland), G. Testera (INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy), R. Teyssier (Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA), S. Tosi (Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy, INFN-Sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy, INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy), A. Troja (Dipartimento di Fisica e Astronomia "G. Galilei", Università di Padova, Via Marzolo 8, 35131 Padova, Italy, INFN-Padova, Via Marzolo 8, 35131 Padova, Italy), A. Venhola (Space physics and astronomy research unit, University of Oulu, Pentti Kaiteran katu 1, FI-90014 Oulu, Finland), D. Vergani (INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy), F. Vernizzi (Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France), G. Verza (International Centre for Theoretical Physics, Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, 10010, New York, NY, USA), P. Vielzeuf (Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France), S. Vinciguerra (Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France), N. A. Walton (Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK), A. H. Wright (Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute)

मूल पेपर CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/) के तहत लाइसेंस किया गया है। नीचे दिए गए पेपर की यह व्याख्या AI से तैयार की गई है। इसे लेखकों ने न तो लिखा है, न इसका समर्थन किया है। तकनीकी सटीकता के लिए मूल पेपर देखें। पूरा डिस्क्लेमर पढ़ें

कल्पना कीजिए कि ब्रह्मांड एक विशाल, तीन-आयामी (3D) पार्टी है। इस पार्टी में आकाशगंगाएँ (galaxies) मेहमान हैं। लंबे समय से, खगोलशास्त्री इस पार्टी का अध्ययन यह देखकर कर रहे हैं कि मेहमान आपस में कैसे जोड़े बनाते हैं (two-point statistics)। वे पूछते हैं: "यदि मैं यहाँ खड़ा हूँ, तो मेरे बगल में दूसरे मेहमान के खड़े होने की कितनी संभावना है?" यह बहुत सफल रहा है, लेकिन यह एक जटिल बातचीत को केवल जोड़ों में फुसफुसाते लोगों को सुनकर समझने जैसा है।

यह शोध पत्र इस बात पर केंद्रित है कि सुनने वाले उपकरणों को पूरी समूह चर्चा सुनने के लिए कैसे अपग्रेड किया जाए। विशेष रूप से, यह इस पर ध्यान केंद्रित करता है कि तीन आकाशगंगाएँ मिलकर एक त्रिभुज (triangle) कैसे बनाती हैं। इसे थ्री-पॉइंट कोरिलेशन फंक्शन (3PCF) कहा जाता है।

यहाँ टीम द्वारा किए गए कार्यों का रोजमर्रा के उपमाओं (analogies) का उपयोग करते हुए एक सरल विवरण दिया गया है:

1. समस्या: त्रिभुजों को गिनना कठिन है

ब्रह्मांड के आकार को समझने के लिए, टीम को एक विशाल डेटासेट (यूक्लिड सर्वे, जो लाखों आकाशगंगाओं का मानचित्र बनाएगा) में तीन आकाशगंगाओं द्वारा बनाए गए हर संभावित त्रिभुज को गिनने की आवश्यकता है।

  • चुनौती: यदि आपके पास 10 लाख मेहमान हैं, तो तीन मेहमानों के हर संभावित समूह को गिनना एक मानक कंप्यूटर के लिए गणितीय रूप से असंभव कार्य है। यह एक स्टेडियम में 1,00,000 प्रशंसकों के बीच तीन लोगों के हर संभावित समूह को हाथ से गिनने जैसा है। इसमें लगने वाला समय बहुत तेजी से (क्यूबिक रूप से) बढ़ता है, जिससे इसे पूरा करने में वर्षों या सदियाँ लग सकती हैं।

2. समाधान: दो अलग-अलग गिनती रणनीतियाँ

टीम ने एक सॉफ्टवेयर पाइपलाइन (कंप्यूटरों के लिए निर्देशों का एक सेट) विकसित की है जिसमें इस गिनती की समस्या को हल करने के दो अलग-अलग तरीके हैं:

  • विधि A: "ब्रूट फोर्स" गणना (प्रत्यक्ष गणना - Direct Counting)

    • यह कैसे काम करती है: यह प्रत्येक आकाशगंगा की जाँच करती है, उसके पड़ोसियों को ढूंढती है, और फिर तीन के हर संभावित संयोजन की जाँच करती है।
    • उपमा: यह एक जासूस की तरह है जो कमरे में आए हर व्यक्ति के पास जाता है और पूछता है, "आपके दो सबसे अच्छे दोस्त कौन हैं?" और फिर उसे लिख लेता है। यह 100% सटीक और वास्तविक है, लेकिन यह अविश्वसनीय रूप से धीमी है।
    • निर्णय: शोध पत्र कहता है कि यह विधि अंतिम, विशाल यूक्लिड सर्वे के लिए बहुत धीमी है। इसे केवल एक "गोल्ड स्टैंडर्ड" के रूप में रखा गया है ताकि यह जांचा जा सके कि दूसरा तरीका सही ढंग से काम कर रहा है या नहीं।
  • विधि B: "हारमोनिक" शॉर्टकट (स्फेरिक हार्मोनिक डिकंपोजिशन - Spherical Harmonic Decomposition)

    • यह कैसे काम करती है: आकाशगंगाओं के पैटर्न को गिनने के बजाय, यह पद्धति आकाशगंगाओं के पैटर्न को "तरंगों" या "परतों" (जैसे एक जटिल ध्वनि को संगीत के नोट्स में तोड़ना) में विभाजित करती है। यह इन परतों में पैटर्न को गिनती है और फिर उन पर से त्रिभुज की गणना को पुनर्गठित करती है।
    • उपमा: हर विशिष्ट तीन लोगों के समूह को गिनने के बजाय, आप भीड़ के सामान्य "वाइब" (vibe) को देखते हैं। आप देखते हैं कि लोग कुछ निश्चित आकृतियों में क्लस्टर (समूह बनाना) बनाते हैं। आप इन आकृतियों का विश्लेषण करके त्रिभुजों की संख्या को पुनर्गठित कर सकते हैं।
    • निर्णय: यह बहुत, बहुत तेज़ है (क्यूबिक के बजाय क्वाड्रेटिक रूप से स्केल होता है)। शोध पत्र यह सिद्ध करता है कि भले ही यह एक अनुमान (approximation) है (यह हर सूक्ष्म विवरण को नहीं पकड़ता), यह मिशन के वैज्ञानिक लक्ष्यों के लिए पर्याप्त सटीक है।

3. "स्प्लिट" ट्रिक: कार्यभार को कम करना

तेज़ "हारमोनिक" विधि के साथ भी, रैंडम बैकग्राउंड नॉइज़ (डेटा को कैलिब्रेट करने के लिए उपयोग किया जाता है) को गिनना अभी भी बहुत भारी काम था।

  • नवाचार: टीम ने एक "रैंडम स्प्लिट" तकनीक पेश की।
  • उपमा: कल्पना कीजिए कि आपको अपने पत्ता गिनने वाली मशीन को कैलिब्रेट करने के लिए 50,000 पेड़ों के पत्तों की संख्या गिननी है। एक साथ 50,000 पेड़ों पर चढ़ने के बजाय, आप काम को विभाजित करते हैं। आप 25 अलग-अलग टीमें भेजते हैं, जिनमें से प्रत्येक 2,000 पेड़ों पर चढ़ती है, और फिर आप उनके परिणामों का औसत निकालते हैं।
  • परिणाम: इस ट्रिक ने बिना सटीकता खोए, कंप्यूटिंग समय को 10 गुना कम कर दिया। यह एक सुपरकंप्यूटर को मेनफ्रेम का काम करने के लिए कहने जैसा है।

4. "त्रिभुज के आकार" का मुद्दा

लेखकों ने पाया कि "हारमोनिक" शॉर्टकट अधिकांश त्रिभुज आकारों (जैसे एक लंबा, पतला त्रिभुज) के लिए पूरी तरह से काम करता है। हालांकि, इसे आइसोसेलेस त्रिभुजों (जहाँ दो भुजाएँ बिल्कुल समान लंबाई की होती हैं) के साथ थोड़ा संघर्ष करना पड़ता है।

  • उपमा: इस शॉर्टकट को एक ऐसे अनुवादक के रूप में सोचें जो लंबे, बहते हुए वाक्यों का अनुवाद करने में बहुत अच्छा है लेकिन कभी-कभी बहुत छोटे, दोहराव वाले वाक्यांशों पर लड़खड़ा जाता है।
  • समाधान: शोध पत्र नोट करता है कि इन विशिष्ट "लड़खड़ाने वाले" आकारों के लिए, टीम अभी भी धीमी "ब्रूट फोर्स" विधि का उपयोग कर सकती है क्योंकि वे दुर्लभ हैं। अधिकांश त्रिभुजों के लिए, तेज़ विधि एकदम सही है।

5. अंतिम परीक्षण: क्या यह काम कर गया?

टीम ने नकली आकाशगंगा डेटा (सिमुलेशन) का उपयोग करके हजारों परीक्षण किए, जहाँ उन्हें उत्तर पहले से पता था।

  • "नल टेस्ट" (Null Test): उन्होंने एक नकली ब्रह्मांड बनाया जहाँ आकाशगंगाओं को यादृच्छिक (random) रूप से रखा गया था (जैसे टीवी स्क्रीन पर स्टैटिक शोर)। इस ब्रह्मांड में, शून्य त्रिभुज होने चाहिए। उनके कोड ने सही ढंग से शून्य त्रिभुज पाए, जिससे यह सिद्ध हुआ कि यह कोड नकली पैटर्न नहीं बनाता है।
  • गति परीक्षण (Speed Test): उन्होंने गणना की कि अंतिम यूक्लिड डेटा को प्रोसेस करने में कितना समय लगेगा।
    • पुराना तरीका (ब्रूट फोर्स): वर्षों लग जाते।
    • नया तरीका (हारमोनिक + स्प्लिट): इसे लगभग एक दिन में किया जा सकता है।

निष्कर्ष

यह शोध पत्र अनिवार्य रूप से एक नए, सुपर-फास्ट कैलकुलेटर के लिए एक "यूजर मैनुअल" और "क्वालिटी कंट्रोल रिपोर्ट" है, जिसे यूक्लिड स्पेस टेलीस्कोप के लिए डिज़ाइन किया गया है। यह सिद्ध करता है कि अब हम ब्रह्मांड के जटिल 3D आकारों (आकाशगंगाओं के त्रिभुजों) को तेज़ी से और सटीकता से माप सकते हैं। यह हमें डार्क एनर्जी और ब्रह्मांड के विकास को समझने की वर्तमान सीमाओं को तोड़ने की अनुमति देता है, वह भी बिना कंप्यूटर के गणित पूरा होने के लिए सदियों तक प्रतीक्षा किए।

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