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1. Simultaneous Primitive Roots over Finite Rings

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11A07, Secondary 11N37
Abstract

This note investigates the average density of prime numbers $p\in[x,2x]$ with respect to a random simultaneous primitive root $g\leq p^{1/2+\varepsilon}$ over the finite rings $\mathbb{Z}/p\mathbb{Z}$ and $\mathbb{Z}/p^2\mathbb{Z}$ as $x \to \infty$., Comment: Twenty Pages. Keywords: Prime number; Primitive root; Simultaneous primitive root; Hensel lemma; Artin Primitive Root Conjecture

Published
2025

2. Density of Squarefree Totients $p-1$ and Primitive Roots

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11A07, Secondary 11N05
Abstract

This note determines an effective asymptotic formula for the number of squarefree totients $p-1$ with a fixed primitive root $u\ne \pm 1, v^2$., Comment: Twenty Pages. Keywords: Primitive root; Squarefree totient; Distribution of primes. arXiv admin note: text overlap with arXiv:2106.00544

Published
2024

3. Euclid preparation. Simulations and nonlinearities beyond $\Lambda$CDM. 2. Results from non-standard simulations

Author

Euclid Collaboration, Rácz, G., Breton, M. -A., Fiorini, B., Brun, A. M. C. Le, Winther, H. -A., Sakr, Z., Pizzuti, L., Ragagnin, A., Gayoux, T., Altamura, E., Carella, E., Pardede, K., Verza, G., Koyama, K., Baldi, M., Pourtsidou, A., Vernizzi, F., Adame, A. G., Adamek, J., Avila, S., Carbone, C., Despali, G., Giocoli, C., Hernández-Aguayo, C., Hassani, F., Kunz, M., Li, B., Rasera, Y., Yepes, G., Gonzalez-Perez, V., Corasaniti, P. -S., García-Bellido, J., Hamaus, N., Kiessling, A., Marinucci, M., Moretti, C., Mota, D. F., Piga, L., Pisani, A., Szapudi, I., Tallada-Crespí, P., Aghanim, N., Andreon, S., Baccigalupi, C., Bardelli, S., Bonino, D., Branchini, E., Brescia, M., Brinchmann, J., Camera, S., Capobianco, V., Cardone, V. F., Carretero, J., Casas, S., Castellano, M., Castignani, G., Cavuoti, S., Cimatti, A., Colodro-Conde, C., Congedo, G., Conselice, C. J., Conversi, L., Copin, Y., Courbin, F., Courtois, H. M., Da Silva, A., Degaudenzi, H., De Lucia, G., Douspis, M., Dubath, F., Duncan, C. A. J., Dupac, X., Dusini, S., Ealet, A., Farina, M., Farrens, S., Ferriol, S., Fosalba, P., Frailis, M., Franceschi, E., Fumana, M., Galeotta, S., Gillis, B., Gómez-Alvarez, P., Grazian, A., Grupp, F., Haugan, S. V. H., Holmes, W., Hormuth, F., Hornstrup, A., Ilić, S., Jahnke, K., Jhabvala, M., Joachimi, B., Keihänen, E., Kermiche, S., Kilbinger, M., Kitching, T., Kubik, B., Kurki-Suonio, H., Lilje, P. B., Lindholm, V., Lloro, I., Mainetti, G., Maiorano, E., Mansutti, O., Marggraf, O., Markovic, K., Martinelli, M., Martinet, N., Marulli, F., Massey, R., Medinaceli, E., Mei, S., Mellier, Y., Meneghetti, M., Meylan, G., Moresco, M., Moscardini, L., Niemi, S. -M., Padilla, C., Paltani, S., Pasian, F., Pedersen, K., Percival, W. J., Pettorino, V., Pires, S., Polenta, G., Poncet, M., Popa, L. A., Raison, F., Rebolo, R., Renzi, A., Rhodes, J., Riccio, G., Romelli, E., Roncarelli, M., Saglia, R., Salvignol, J. -C., Sánchez, A. G., Sapone, D., Sartoris, B., Schirmer, M., Schrabback, T., Secroun, A., Seidel, G., Serrano, S., Sirignano, C., Sirri, G., Stanco, L., Steinwagner, J., Taylor, A. N., Tereno, I., Toledo-Moreo, R., Torradeflot, F., Tutusaus, I., Valenziano, L., Vassallo, T., Kleijn, G. Verdoes, Wang, Y., Weller, J., Zucca, E., Biviano, A., Boucaud, A., Bozzo, E., Burigana, C., Calabrese, M., Di Ferdinando, D., Vigo, J. A. Escartin, Fabbian, G., Finelli, F., Gracia-Carpio, J., Matthew, S., Mauri, N., Pezzotta, A., Pöntinen, M., Porciani, C., Scottez, V., Tenti, M., Viel, M., Wiesmann, M., Akrami, Y., Allevato, V., Anselmi, S., Archidiacono, M., Atrio-Barandela, F., Balaguera-Antolinez, A., Ballardini, M., Bertacca, D., Blot, L., Borgani, S., Bruton, S., Cabanac, R., Calabro, A., Quevedo, B. Camacho, Cappi, A., Caro, F., Carvalho, C. S., Castro, T., Chambers, K. C., Contarini, S., Cooray, A. R., De Caro, B., de la Torre, S., Desprez, G., Díaz-Sánchez, A., Diaz, J. J., Di Domizio, S., Dole, H., Escoffier, S., Ferrari, A. G., Ferreira, P. G., Ferrero, I., Fontana, A., Fornari, F., Gabarra, L., Ganga, K., Gasparetto, T., Gaztanaga, E., Giacomini, F., Gianotti, F., Gozaliasl, G., Gutierrez, C. M., Hall, A., Hildebrandt, H., Hjorth, J., Muñoz, A. Jimenez, Kajava, J. J. E., Kansal, V., Karagiannis, D., Kirkpatrick, C. C., Lacasa, F., Graet, J. Le, Legrand, L., Lesgourgues, J., Liaudat, T. I., Loureiro, A., Macias-Perez, J., Maggio, G., Magliocchetti, M., Mannucci, F., Maoli, R., Martins, C. J. A. P., Maurin, L., Metcalf, R. B., Miluzio, M., Monaco, P., Montoro, A., Mora, A., Morgante, G., Nadathur, S., Walton, Nicholas A., Patrizii, L., Popa, V., Potter, D., Reimberg, P., Risso, I., Rocci, P. -F., Sahlén, M., Schneider, A., Sereno, M., Silvestri, A., Mancini, A. Spurio, Stadel, J., Tanidis, K., Tao, C., Tessore, N., Testera, G., Teyssier, R., Toft, S., Tosi, S., Troja, A., Tucci, M., Valieri, C., Valiviita, J., Vergani, D., and Vielzeuf, P.

Subjects
Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract

The Euclid mission will measure cosmological parameters with unprecedented precision. To distinguish between cosmological models, it is essential to generate realistic mock observables from cosmological simulations that were run in both the standard $\Lambda$-cold-dark-matter ($\Lambda$CDM) paradigm and in many non-standard models beyond $\Lambda$CDM. We present the scientific results from a suite of cosmological N-body simulations using non-standard models including dynamical dark energy, k-essence, interacting dark energy, modified gravity, massive neutrinos, and primordial non-Gaussianities. We investigate how these models affect the large-scale-structure formation and evolution in addition to providing synthetic observables that can be used to test and constrain these models with Euclid data. We developed a custom pipeline based on the Rockstar halo finder and the nbodykit large-scale structure toolkit to analyse the particle output of non-standard simulations and generate mock observables such as halo and void catalogues, mass density fields, and power spectra in a consistent way. We compare these observables with those from the standard $\Lambda$CDM model and quantify the deviations. We find that non-standard cosmological models can leave significant imprints on the synthetic observables that we have generated. Our results demonstrate that non-standard cosmological N-body simulations provide valuable insights into the physics of dark energy and dark matter, which is essential to maximising the scientific return of Euclid., Comment: 22 pages, 7 figures

Published
2024

4. Room-temperature optical spin polarization of an electron spin qudit in a vanadyl -- free base porphyrin dimer

Author

Privitera, Alberto, Chiesa, Alessandro, Santanni, Fabio, Carella, Angelo, Ranieri, Davide, Caneschi, Andrea, Krzyaniak, Matthew D., Young, Ryan M., Wasielewski, Michael R., Carretta, Stefano, and Sessoli, Roberta

Subjects
Quantum Physics, Physics - Chemical Physics
Abstract

Photoexcited organic chromophores appended to molecular qubits can serve as a source of spin initialization or multi-level qudit generation for quantum information applications. So far, this approach has been primarily investigated in chromophore/stable radical systems. Here, we extend this concept to a meso-meso linked oxovanadium(IV) porphyrin - free base porphyrin dimer. Femtosecond transient absorption experiments reveal that photoexcitation of the free base porphyrin leads to picosecond triplet state formation via enhanced intersystem crossing. Time-resolved electron paramagnetic resonance (TREPR) experiments carried out at both 85 K and room temperature reveal the formation of a long-lived spin-polarized quartet state through triplet-doublet spin mixing. Notably, a distinct hyperfine structure arising from the interaction between the electron spin quartet state and the vanadyl nucleus (51V, I=7/2) is evident, with the quartet state exhibiting long-lived spin polarization even at room temperature. Theoretical simulations of the TREPR spectra confirm the photogenerated quartet state and provide insights into the non-Boltzmann spin populations. Exploit-ing this phenomenon affords the possibility of using photoinduced triplet states in porphyrins for quantum information as a resource to polarize and magnetically couple molecular electronic or nuclear spin qubits and qudits.

Published
2024

5. International multicenter validation of AI-driven ultrasound detection of ovarian cancer

Author

Christiansen, Filip, Konuk, Emir, Ganeshan, Adithya Raju, Welch, Robert, Palés Huix, Joana, Czekierdowski, Artur, Leone, Francesco Paolo Giuseppe, Haak, Lucia Anna, Fruscio, Robert, Gaurilcikas, Adrius, Franchi, Dorella, Fischerova, Daniela, Mor, Elisa, Savelli, Luca, Pascual, Maria Àngela, Kudla, Marek Jerzy, Guerriero, Stefano, Buonomo, Francesca, Liuba, Karina, Montik, Nina, Alcázar, Juan Luis, Domali, Ekaterini, Pangilinan, Nelinda Catherine P., Carella, Chiara, Munaretto, Maria, Saskova, Petra, Verri, Debora, Visenzi, Chiara, Herman, Pawel, Smith, Kevin, and Epstein, Elisabeth

Published
2025
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6. Nutritional assessment and medical dietary therapy for management of obesity in patients with non-dialysis chronic kidney disease: a practical guide for endocrinologist, nutritionists and nephrologists. A consensus statement from the Italian society of endocrinology (SIE), working group of the club nutrition–hormones and metabolism; the Italian society of nutraceuticals (SINut), club ketodiets and nutraceuticals “KetoNut-SINut”; and the Italian society of nephrology (SIN)

Author

Annunziata, G., Caprio, M., Verde, L., Carella, A. M., Camajani, E., Benvenuto, A., Paolini, B., De Nicola, L., Aucella, F., Bellizzi, V., Barberi, S., Grassi, D., Fogacci, F., Colao, A., Cicero, A. F. G., Prodam, F., Aimaretti, G., Muscogiuri, G., and Barrea, L.

Published
2024
Full Text
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8. Euclid. I. Overview of the Euclid mission

Author

Euclid Collaboration, Mellier, Y., Abdurro'uf, Barroso, J. A. Acevedo, Achúcarro, A., Adamek, J., Adam, R., Addison, G. E., Aghanim, N., Aguena, M., Ajani, V., Akrami, Y., Al-Bahlawan, A., Alavi, A., Albuquerque, I. S., Alestas, G., Alguero, G., Allaoui, A., Allen, S. W., Allevato, V., Alonso-Tetilla, A. V., Altieri, B., Alvarez-Candal, A., Alvi, S., Amara, A., Amendola, L., Amiaux, J., Andika, I. T., Andreon, S., Andrews, A., Angora, G., Angulo, R. E., Annibali, F., Anselmi, A., Anselmi, S., Arcari, S., Archidiacono, M., Aricò, G., Arnaud, M., Arnouts, S., Asgari, M., Asorey, J., Atayde, L., Atek, H., Atrio-Barandela, F., Aubert, M., Aubourg, E., Auphan, T., Auricchio, N., Aussel, B., Aussel, H., Avelino, P. P., Avgoustidis, A., Avila, S., Awan, S., Azzollini, R., Baccigalupi, C., Bachelet, E., Bacon, D., Baes, M., Bagley, M. B., Bahr-Kalus, B., Balaguera-Antolinez, A., Balbinot, E., Balcells, M., Baldi, M., Baldry, I., Balestra, A., Ballardini, M., Ballester, O., Balogh, M., Bañados, E., Barbier, R., Bardelli, S., Baron, M., Barreiro, T., Barrena, R., Barriere, J. -C., Barros, B. J., Barthelemy, A., Bartolo, N., Basset, A., Battaglia, P., Battisti, A. J., Baugh, C. M., Baumont, L., Bazzanini, L., Beaulieu, J. -P., Beckmann, V., Belikov, A. N., Bel, J., Bellagamba, F., Bella, M., Bellini, E., Benabed, K., Bender, R., Benevento, G., Bennett, C. L., Benson, K., Bergamini, P., Bermejo-Climent, J. R., Bernardeau, F., Bertacca, D., Berthe, M., Berthier, J., Bethermin, M., Beutler, F., Bevillon, C., Bhargava, S., Bhatawdekar, R., Bianchi, D., Bisigello, L., Biviano, A., Blake, R. P., Blanchard, A., Blazek, J., Blot, L., Bosco, A., Bodendorf, C., Boenke, T., Böhringer, H., Boldrini, P., Bolzonella, M., Bonchi, A., Bonici, M., Bonino, D., Bonino, L., Bonvin, C., Bon, W., Booth, J. T., Borgani, S., Borlaff, A. S., Borsato, E., Bose, B., Botticella, M. T., Boucaud, A., Bouche, F., Boucher, J. S., Boutigny, D., Bouvard, T., Bouwens, R., Bouy, H., Bowler, R. A. A., Bozza, V., Bozzo, E., Branchini, E., Brando, G., Brau-Nogue, S., Brekke, P., Bremer, M. N., Brescia, M., Breton, M. -A., Brinchmann, J., Brinckmann, T., Brockley-Blatt, C., Brodwin, M., Brouard, L., Brown, M. L., Bruton, S., Bucko, J., Buddelmeijer, H., Buenadicha, G., Buitrago, F., Burger, P., Burigana, C., Busillo, V., Busonero, D., Cabanac, R., Cabayol-Garcia, L., Cagliari, M. S., Caillat, A., Caillat, L., Calabrese, M., Calabro, A., Calderone, G., Calura, F., Quevedo, B. Camacho, Camera, S., Campos, L., Canas-Herrera, G., Candini, G. P., Cantiello, M., Capobianco, V., Cappellaro, E., Cappelluti, N., Cappi, A., Caputi, K. I., Cara, C., Carbone, C., Cardone, V. F., Carella, E., Carlberg, R. G., Carle, M., Carminati, L., Caro, F., Carrasco, J. M., Carretero, J., Carrilho, P., Duque, J. Carron, Carry, B., Carvalho, A., Carvalho, C. S., Casas, R., Casas, S., Casenove, P., Casey, C. M., Cassata, P., Castander, F. J., Castelao, D., Castellano, M., Castiblanco, L., Castignani, G., Castro, T., Cavet, C., Cavuoti, S., Chabaud, P. -Y., Chambers, K. C., Charles, Y., Charlot, S., Chartab, N., Chary, R., Chaumeil, F., Cho, H., Chon, G., Ciancetta, E., Ciliegi, P., Cimatti, A., Cimino, M., Cioni, M. -R. L., Claydon, R., Cleland, C., Clément, B., Clements, D. L., Clerc, N., Clesse, S., Codis, S., Cogato, F., Colbert, J., Cole, R. E., Coles, P., Collett, T. E., Collins, R. S., Colodro-Conde, C., Colombo, C., Combes, F., Conforti, V., Congedo, G., Conseil, S., Conselice, C. J., Contarini, S., Contini, T., Conversi, L., Cooray, A. R., Copin, Y., Corasaniti, P. -S., Corcho-Caballero, P., Corcione, L., Cordes, O., Corpace, O., Correnti, M., Costanzi, M., Costille, A., Courbin, F., Mifsud, L. Courcoult, Courtois, H. M., Cousinou, M. -C., Covone, G., Cowell, T., Cragg, C., Cresci, G., Cristiani, S., Crocce, M., Cropper, M., Crouzet, P. E, Csizi, B., Cuby, J. -G., Cucchetti, E., Cucciati, O., Cuillandre, J. -C., Cunha, P. A. C., Cuozzo, V., Daddi, E., D'Addona, M., Dafonte, C., Dagoneau, N., Dalessandro, E., Dalton, G. B., D'Amico, G., Dannerbauer, H., Danto, P., Das, I., Da Silva, A., da Silva, R., Doumerg, W. d'Assignies, Daste, G., Davies, J. E., Davini, S., Dayal, P., de Boer, T., Decarli, R., De Caro, B., Degaudenzi, H., Degni, G., de Jong, J. T. A., de la Bella, L. F., de la Torre, S., Delhaise, F., Delley, D., Delucchi, G., De Lucia, G., Denniston, J., De Paolis, F., De Petris, M., Derosa, A., Desai, S., Desjacques, V., Despali, G., Desprez, G., De Vicente-Albendea, J., Deville, Y., Dias, J. D. F., Díaz-Sánchez, A., Diaz, J. J., Di Domizio, S., Diego, J. M., Di Ferdinando, D., Di Giorgio, A. M., Dimauro, P., Dinis, J., Dolag, K., Dolding, C., Dole, H., Sánchez, H. Domínguez, Doré, O., Dournac, F., Douspis, M., Dreihahn, H., Droge, B., Dryer, B., Dubath, F., Duc, P. -A., Ducret, F., Duffy, C., Dufresne, F., Duncan, C. A. J., Dupac, X., Duret, V., Durrer, R., Durret, F., Dusini, S., Ealet, A., Eggemeier, A., Eisenhardt, P. R. M., Elbaz, D., Elkhashab, M. Y., Ellien, A., Endicott, J., Enia, A., Erben, T., Vigo, J. A. Escartin, Escoffier, S., Sanz, I. Escudero, Essert, J., Ettori, S., Ezziati, M., Fabbian, G., Fabricius, M., Fang, Y., Farina, A., Farina, M., Farinelli, R., Farrens, S., Faustini, F., Feltre, A., Ferguson, A. M. N., Ferrando, P., Ferrari, A. G., Ferré-Mateu, A., Ferreira, P. G., Ferreras, I., Ferrero, I., Ferriol, S., Ferruit, P., Filleul, D., Finelli, F., Finkelstein, S. L., Finoguenov, A., Fiorini, B., Flentge, F., Focardi, P., Fonseca, J., Fontana, A., Fontanot, F., Fornari, F., Fosalba, P., Fossati, M., Fotopoulou, S., Fouchez, D., Fourmanoit, N., Frailis, M., Fraix-Burnet, D., Franceschi, E., Franco, A., Franzetti, P., Freihoefer, J., Frenk, C. . S., Frittoli, G., Frugier, P. -A., Frusciante, N., Fumagalli, A., Fumagalli, M., Fumana, M., Fu, Y., Gabarra, L., Galeotta, S., Galluccio, L., Ganga, K., Gao, H., García-Bellido, J., Garcia, K., Gardner, J. P., Garilli, B., Gaspar-Venancio, L. -M., Gasparetto, T., Gautard, V., Gavazzi, R., Gaztanaga, E., Genolet, L., Santos, R. Genova, Gentile, F., George, K., Gerbino, M., Ghaffari, Z., Giacomini, F., Gianotti, F., Gibb, G. P. S., Gillard, W., Gillis, B., Ginolfi, M., Giocoli, C., Girardi, M., Giri, S. K., Goh, L. W. K., Gómez-Alvarez, P., Gonzalez-Perez, V., Gonzalez, A. H., Gonzalez, E. J., Gonzalez, J. C., Beauchamps, S. Gouyou, Gozaliasl, G., Gracia-Carpio, J., Grandis, S., Granett, B. R., Granvik, M., Grazian, A., Gregorio, A., Grenet, C., Grillo, C., Grupp, F., Gruppioni, C., Gruppuso, A., Guerbuez, C., Guerrini, S., Guidi, M., Guillard, P., Gutierrez, C. M., Guttridge, P., Guzzo, L., Gwyn, S., Haapala, J., Haase, J., Haddow, C. R., Hailey, M., Hall, A., Hall, D., Hamaus, N., Haridasu, B. S., Harnois-Déraps, J., Harper, C., Hartley, W. G., Hasinger, G., Hassani, F., Hatch, N. A., Haugan, S. V. H., Häußler, B., Heavens, A., Heisenberg, L., Helmi, A., Helou, G., Hemmati, S., Henares, K., Herent, O., Hernández-Monteagudo, C., Heuberger, T., Hewett, P. C., Heydenreich, S., Hildebrandt, H., Hirschmann, M., Hjorth, J., Hoar, J., Hoekstra, H., Holland, A. D., Holliman, M. S., Holmes, W., Hook, I., Horeau, B., Hormuth, F., Hornstrup, A., Hosseini, S., Hu, D., Hudelot, P., Hudson, M. J., Huertas-Company, M., Huff, E. M., Hughes, A. C. N., Humphrey, A., Hunt, L. K., Huynh, D. D., Ibata, R., Ichikawa, K., Iglesias-Groth, S., Ilbert, O., Ilić, S., Ingoglia, L., Iodice, E., Israel, H., Israelsson, U. E., Izzo, L., Jablonka, P., Jackson, N., Jacobson, J., Jafariyazani, M., Jahnke, K., Jain, B., Jansen, H., Jarvis, M. J., Jasche, J., Jauzac, M., Jeffrey, N., Jhabvala, M., Jimenez-Teja, Y., Muñoz, A. Jimenez, Joachimi, B., Johansson, P. H., Joudaki, S., Jullo, E., Kajava, J. J. E., Kang, Y., Kannawadi, A., Kansal, V., Karagiannis, D., Kärcher, M., Kashlinsky, A., Kazandjian, M. V., Keck, F., Keihänen, E., Kerins, E., Kermiche, S., Khalil, A., Kiessling, A., Kiiveri, K., Kilbinger, M., Kim, J., King, R., Kirkpatrick, C. C., Kitching, T., Kluge, M., Knabenhans, M., Knapen, J. H., Knebe, A., Kneib, J. -P., Kohley, R., Koopmans, L. V. E., Koskinen, H., Koulouridis, E., Kou, R., Kovács, A., Kovačić, I., Kowalczyk, A., Koyama, K., Kraljic, K., Krause, O., Kruk, S., Kubik, B., Kuchner, U., Kuijken, K., Kümmel, M., Kunz, M., Kurki-Suonio, H., Lacasa, F., Lacey, C. G., La Franca, F., Lagarde, N., Lahav, O., Laigle, C., La Marca, A., La Marle, O., Lamine, B., Lam, M. C., Lançon, A., Landt, H., Langer, M., Lapi, A., Larcheveque, C., Larsen, S. S., Lattanzi, M., Laudisio, F., Laugier, D., Laureijs, R., Laurent, V., Lavaux, G., Lawrenson, A., Lazanu, A., Lazeyras, T., Boulc'h, Q. Le, Brun, A. M. C. Le, Brun, V. Le, Leclercq, F., Lee, S., Graet, J. Le, Legrand, L., Leirvik, K. N., Jeune, M. Le, Lembo, M., Mignant, D. Le, Lepinzan, M. D., Lepori, F., Reun, A. Le, Leroy, G., Lesci, G. F., Lesgourgues, J., Leuzzi, L., Levi, M. E., Liaudat, T. I., Libet, G., Liebing, P., Ligori, S., Lilje, P. B., Lin, C. -C., Linde, D., Linder, E., Lindholm, V., Linke, L., Li, S. -S., Liu, S. J., Lloro, I., Lobo, F. S. N., Lodieu, N., Lombardi, M., Lombriser, L., Lonare, P., Longo, G., López-Caniego, M., Lopez, X. Lopez, Alvarez, J. Lorenzo, Loureiro, A., Loveday, J., Lusso, E., Macias-Perez, J., Maciaszek, T., Maggio, G., Magliocchetti, M., Magnard, F., Magnier, E. A., Magro, A., Mahler, G., Mainetti, G., Maino, D., Maiorano, E., Malavasi, N., Mamon, G. A., Mancini, C., Mandelbaum, R., Manera, M., Manjón-García, A., Mannucci, F., Mansutti, O., Outeiro, M. Manteiga, Maoli, R., Maraston, C., Marcin, S., Marcos-Arenal, P., Margalef-Bentabol, B., Marggraf, O., Marinucci, D., Marinucci, M., Markovic, K., Marleau, F. R., Marpaud, J., Martignac, J., Martín-Fleitas, J., Martin-Moruno, P., Martin, E. L., Martinelli, M., Martinet, N., Martin, H., Martins, C. J. A. P., Marulli, F., Massari, D., Massey, R., Masters, D. C., Matarrese, S., Matsuoka, Y., Matthew, S., Maughan, B. J., Mauri, N., Maurin, L., Maurogordato, S., McCarthy, K., McConnachie, A. W., McCracken, H. J., McDonald, I., McEwen, J. D., McPartland, C. J. R., Medinaceli, E., Mehta, V., Mei, S., Melchior, M., Melin, J. -B., Ménard, B., Mendes, J., Mendez-Abreu, J., Meneghetti, M., Mercurio, A., Merlin, E., Metcalf, R. B., Meylan, G., Migliaccio, M., Mignoli, M., Miller, L., Miluzio, M., Milvang-Jensen, B., Mimoso, J. P., Miquel, R., Miyatake, H., Mobasher, B., Mohr, J. J., Monaco, P., Monguió, M., Montoro, A., Mora, A., Dizgah, A. Moradinezhad, Moresco, M., Moretti, C., Morgante, G., Morisset, N., Moriya, T. J., Morris, P. W., Mortlock, D. J., Moscardini, L., Mota, D. F., Mottet, S., Moustakas, L. A., Moutard, T., Müller, T., Munari, E., Murphree, G., Murray, C., Murray, N., Musi, P., Nadathur, S., Nagam, B. C., Nagao, T., Naidoo, K., Nakajima, R., Nally, C., Natoli, P., Navarro-Alsina, A., Girones, D. Navarro, Neissner, C., Nersesian, A., Nesseris, S., Nguyen-Kim, H. N., Nicastro, L., Nichol, R. C., Nielbock, M., Niemi, S. -M., Nieto, S., Nilsson, K., Noller, J., Norberg, P., Nouri-Zonoz, A., Ntelis, P., Nucita, A. A., Nugent, P., Nunes, N. J., Nutma, T., Ocampo, I., Odier, J., Oesch, P. A., Oguri, M., Oliveira, D. Magalhaes, Onoue, M., Oosterbroek, T., Oppizzi, F., Ordenovic, C., Osato, K., Pacaud, F., Pace, F., Padilla, C., Paech, K., Pagano, L., Page, M. J., Palazzi, E., Paltani, S., Pamuk, S., Pandolfi, S., Paoletti, D., Paolillo, M., Papaderos, P., Pardede, K., Parimbelli, G., Parmar, A., Partmann, C., Pasian, F., Passalacqua, F., Paterson, K., Patrizii, L., Pattison, C., Paulino-Afonso, A., Paviot, R., Peacock, J. A., Pearce, F. R., Pedersen, K., Peel, A., Peletier, R. F., Ibanez, M. Pellejero, Pello, R., Penny, M. T., Percival, W. J., Perez-Garrido, A., Perotto, L., Pettorino, V., Pezzotta, A., Pezzuto, S., Philippon, A., Pierre, M., Piersanti, O., Pietroni, M., Piga, L., Pilo, L., Pires, S., Pisani, A., Pizzella, A., Pizzuti, L., Plana, C., Polenta, G., Pollack, J. E., Poncet, M., Pöntinen, M., Pool, P., Popa, L. A., Popa, V., Popp, J., Porciani, C., Porth, L., Potter, D., Poulain, M., Pourtsidou, A., Pozzetti, L., Prandoni, I., Pratt, G. W., Prezelus, S., Prieto, E., Pugno, A., Quai, S., Quilley, L., Racca, G. D., Raccanelli, A., Rácz, G., Radinović, S., Radovich, M., Ragagnin, A., Ragnit, U., Raison, F., Ramos-Chernenko, N., Ranc, C., Rasera, Y., Raylet, N., Rebolo, R., Refregier, A., Reimberg, P., Reiprich, T. H., Renk, F., Renzi, A., Retre, J., Revaz, Y., Reylé, C., Reynolds, L., Rhodes, J., Ricci, F., Ricci, M., Riccio, G., Ricken, S. O., Rissanen, S., Risso, I., Rix, H. -W., Robin, A. C., Rocca-Volmerange, B., Rocci, P. -F., Rodenhuis, M., Rodighiero, G., Monroy, M. Rodriguez, Rollins, R. P., Romanello, M., Roman, J., Romelli, E., Romero-Gomez, M., Roncarelli, M., Rosati, P., Rosset, C., Rossetti, E., Roster, W., Rottgering, H. J. A., Rozas-Fernández, A., Ruane, K., Rubino-Martin, J. A., Rudolph, A., Ruppin, F., Rusholme, B., Sacquegna, S., Sáez-Casares, I., Saga, S., Saglia, R., Sahlén, M., Saifollahi, T., Sakr, Z., Salvalaggio, J., Salvaterra, R., Salvati, L., Salvato, M., Salvignol, J. -C., Sánchez, A. G., Sanchez, E., Sanders, D. B., Sapone, D., Saponara, M., Sarpa, E., Sarron, F., Sartori, S., Sartoris, B., Sassolas, B., Sauniere, L., Sauvage, M., Sawicki, M., Scaramella, R., Scarlata, C., Scharré, L., Schaye, J., Schewtschenko, J. A., Schindler, J. -T., Schinnerer, E., Schirmer, M., Schmidt, F., Schmidt, M., Schneider, A., Schneider, M., Schneider, P., Schöneberg, N., Schrabback, T., Schultheis, M., Schulz, S., Schuster, N., Schwartz, J., Sciotti, D., Scodeggio, M., Scognamiglio, D., Scott, D., Scottez, V., Secroun, A., Sefusatti, E., Seidel, G., Seiffert, M., Sellentin, E., Selwood, M., Semboloni, E., Sereno, M., Serjeant, S., Serrano, S., Setnikar, G., Shankar, F., Sharples, R. M., Short, A., Shulevski, A., Shuntov, M., Sias, M., Sikkema, G., Silvestri, A., Simon, P., Sirignano, C., Sirri, G., Skottfelt, J., Slezak, E., Sluse, D., Smith, G. P., Smith, L. C., Smith, R. E., Smit, S. J. A., Soldano, F., Solheim, B. G. B., Sorce, J. G., Sorrenti, F., Soubrie, E., Spinoglio, L., Mancini, A. Spurio, Stadel, J., Stagnaro, L., Stanco, L., Stanford, S. A., Starck, J. -L., Stassi, P., Steinwagner, J., Stern, D., Stone, C., Strada, P., Strafella, F., Stramaccioni, D., Surace, C., Sureau, F., Suyu, S. H., Swindells, I., Szafraniec, M., Szapudi, I., Taamoli, S., Talia, M., Tallada-Crespí, P., Tanidis, K., Tao, C., Tarrío, P., Tavagnacco, D., Taylor, A. N., Taylor, J. E., Taylor, P. L., Teixeira, E. M., Tenti, M., Idiago, P. Teodoro, Teplitz, H. I., Tereno, I., Tessore, N., Testa, V., Testera, G., Tewes, M., Teyssier, R., Theret, N., Thizy, C., Thomas, P. D., Toba, Y., Toft, S., Toledo-Moreo, R., Tolstoy, E., Tommasi, E., Torbaniuk, O., Torradeflot, F., Tortora, C., Tosi, S., Tosti, S., Trifoglio, M., Troja, A., Trombetti, T., Tronconi, A., Tsedrik, M., Tsyganov, A., Tucci, M., Tutusaus, I., Uhlemann, C., Ulivi, L., Urbano, M., Vacher, L., Vaillon, L., Valageas, P., Valdes, I., Valentijn, E. A., Valenziano, L., Valieri, C., Valiviita, J., Broeck, M. Van den, Vassallo, T., Vavrek, R., Vega-Ferrero, J., Venemans, B., Venhola, A., Ventura, S., Kleijn, G. Verdoes, Vergani, D., Verma, A., Vernizzi, F., Veropalumbo, A., Verza, G., Vescovi, C., Vibert, D., Viel, M., Vielzeuf, P., Viglione, C., Viitanen, A., Villaescusa-Navarro, F., Vinciguerra, S., Visticot, F., Voggel, K., von Wietersheim-Kramsta, M., Vriend, W. J., Wachter, S., Walmsley, M., Walth, G., Walton, D. M., Walton, N. A., Wander, M., Wang, L., Wang, Y., Weaver, J. R., Weller, J., Wetzstein, M., Whalen, D. J., Whittam, I. H., Widmer, A., Wiesmann, M., Wilde, J., Williams, O. R., Winther, H. -A., Wittje, A., Wong, J. H. W., Wright, A. H., Yankelevich, V., Yeung, H. W., Yoon, M., Youles, S., Yung, L. Y. A., Zacchei, A., Zalesky, L., Zamorani, G., Vitorelli, A. Zamorano, Marc, M. Zanoni, Zennaro, M., Zerbi, F. M., Zinchenko, I. A., Zoubian, J., Zucca, E., and Zumalacarregui, M.

Subjects
Astrophysics - Cosmology and Nongalactic Astrophysics, Astrophysics - Astrophysics of Galaxies, Astrophysics - Instrumentation and Methods for Astrophysics
Abstract

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

Published
2024

9. Small Prime $k$th Power Residues and Nonresidues in Arithmetic Progressions

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11A15, Secondary 11L40, 11E25, 11R29
Abstract

Let $p$ be a large odd prime, let $x=(\log p)^{1+\varepsilon}$ and let $q\ll\log\log p$ be an integer, where $\varepsilon>0$ is a small number. This note proves the existence of small prime quadratic residues and prime quadratic nonresidues in the arithmetic progression $a+qm\ll x$, with relatively prime $1\leq a

Published
2024

10. Legendre Conjecture over Arithmetic Progressions

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11N05, Secondary 11N32
Abstract

Let $1\leq a1$ be a large number. This note discusses the existence of a short sequence of primes $p\equiv a\bmod q$ between two squares $x^2$ and $(x+1)^2$., Comment: Seven Pages. Keywords: Prime in short interval; Prime in arithmetic progression; Distribution of prime; Legendre conjecture

Published
2024

11. Correction: Inflammation scores based on C‑reactive protein and albumin predict mortality in hospitalized older patients independent of the admission diagnosis

Author

Di Rosa, Mirko, Sabbatinelli, Jacopo, Giuliani, Angelica, Carella, Miriam, Magro, Daniele, Biscetti, Leonardo, Soraci, Luca, Spannella, Francesco, Fedecostante, Massimiliano, Lenci, Federica, Tortato, Elena, Pimpini, Lorenzo, Burattini, Maurizio, Cecchini, Sara, Cherubini, Antonio, Bonfigli, Anna Rita, Capalbo, Maria, Procopio, Antonio Domenico, Balistreri, Carmela Rita, and Olivieri, Fabiola

Published
2024
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12. Inflammation scores based on C-reactive protein and albumin predict mortality in hospitalized older patients independent of the admission diagnosis

Author

Di Rosa, Mirko, Sabbatinelli, Jacopo, Giuliani, Angelica, Carella, Miriam, Magro, Daniele, Biscetti, Leonardo, Soraci, Luca, Spannella, Francesco, Fedecostante, Massimiliano, Lenci, Federica, Tortato, Elena, Pimpini, Lorenzo, Burattini, Maurizio, Cecchini, Sara, Cherubini, Antonio, Bonfigli, Anna Rita, Capalbo, Maria, Procopio, Antonio Domenico, Balistreri, Carmela Rita, and Olivieri, Fabiola

Published
2024
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13. Busulfan-fludarabine versus busulfan-cyclophosphamide for allogeneic transplant in acute myeloid leukemia: long term analysis of GITMO AML-R2 trial

Author

Cavallaro, Gianluca, Grassi, Anna, Pavoni, Chiara, Micò, Maria Caterina, Busca, Alessandro, Cavattoni, Irene Maria, Santarone, Stella, Borghero, Carlo, Olivieri, Attilio, Milone, Giuseppe, Chiusolo, Patrizia, Musto, Pellegrino, Saccardi, Riccardo, Patriarca, Francesca, Pane, Fabrizio, Saporiti, Giorgia, Rivela, Paolo, Terruzzi, Elisabetta, Cerretti, Raffaella, Marotta, Giuseppe, Carella, Angelo Michele, Nagler, Arnon, Russo, Domenico, Corradini, Paolo, Bernasconi, Paolo, Iori, Anna Paola, Castagna, Luca, Mordini, Nicola, Oldani, Elena, Di Grazia, Carmen, Bacigalupo, Andrea, and Rambaldi, Alessandro

Published
2024
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14. Stem cell collection and hematological recovery in the Fondazione Italiana Linfomi (FIL) MCL0208 clinical trial

Author

Clerico, Michele, Ferrero, Simone, Alessandria, Beatrice, Zaccaria, Gian Maria, Genuardi, Elisa, Ragaini, Simone, Tavarozzi, Rita, Cavallo, Federica, Hohaus, Stefan, Musuraca, Gerardo, Carella, Angelo Michele, Stelitano, Caterina, Tani, Monica, Gaidano, Gianluca, Olivieri, Jacopo, Usai, Sara Veronica, Galimberti, Sara, Re, Francesca, Mian, Michael, Castellino, Claudia, Pavone, Vincenzo, Evangelista, Andrea, Bruno, Benedetto, Cortelazzo, Sergio, Passera, Roberto, and Ladetto, Marco

Published
2024
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16. Human leukocyte antigen variants associate with BNT162b2 mRNA vaccine response

Author

Esposito, Martina, Minnai, Francesca, Copetti, Massimiliano, Miscio, Giuseppe, Perna, Rita, Piepoli, Ada, De Vincentis, Gabriella, Benvenuto, Mario, D’Addetta, Paola, Croci, Susanna, Baldassarri, Margherita, Bruttini, Mirella, Fallerini, Chiara, Brugnoni, Raffaella, Cavalcante, Paola, Baggi, Fulvio, Corsini, Elena Maria Grazia, Ciusani, Emilio, Andreetta, Francesca, Dragani, Tommaso A., Fratelli, Maddalena, Carella, Massimo, Mantegazza, Renato E., Renieri, Alessandra, and Colombo, Francesca

Published
2024
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17. Inflammation and acute cardiotoxicity in adult hematological patients treated with CAR-T cells: results from a pilot proof-of-concept study

Author

Camilli, Massimiliano, Viscovo, Marcello, Felici, Tamara, Maggio, Luca, Ballacci, Federico, Carella, Giacomo, Bonanni, Alice, Lamendola, Priscilla, Tinti, Lorenzo, Di Renzo, Antonio, Coarelli, Giulia, Galli, Eugenio, Liuzzo, Giovanna, Burzotta, Francesco, Montone, Rocco Antonio, Sorà, Federica, Sica, Simona, Hohaus, Stefan, Lanza, Gaetano Antonio, Crea, Filippo, Lombardo, Antonella, and Minotti, Giorgio

Published
2024
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19. Euclid preparation. Modelling spectroscopic clustering on mildly nonlinear scales in beyond-$\Lambda$CDM models

Author

Euclid Collaboration, Bose, B., Carrilho, P., Marinucci, M., Moretti, C., Pietroni, M., Carella, E., Piga, L., Wright, B. S., Vernizzi, F., Carbone, C., Casas, S., D'Amico, G., Frusciante, N., Koyama, K., Pace, F., Pourtsidou, A., Baldi, M., de la Bella, L. F., Fiorini, B., Giocoli, C., Lombriser, L., Aghanim, N., Amara, A., Andreon, S., Auricchio, N., Bardelli, S., Bodendorf, C., Bonino, D., Branchini, E., Brescia, M., Brinchmann, J., Camera, S., Capobianco, V., Cardone, V. F., Carretero, J., Castellano, M., Cavuoti, S., Cimatti, A., Congedo, G., Conselice, C. J., Conversi, L., Copin, Y., Costille, A., Courbin, F., Courtois, H. M., Da Silva, A., Degaudenzi, H., Di Giorgio, A. M., Dubath, F., Duncan, C. A. J., Dupac, X., Dusini, S., Farina, M., Farrens, S., Ferriol, S., Fosalba, P., Frailis, M., Franceschi, E., Galeotta, S., Garilli, B., Gillis, B., Grazian, A., Grupp, F., Guzzo, L., Haugan, S. V. H., Hormuth, F., Hornstrup, A., Jahnke, K., Joachimi, B., Keihänen, E., Kermiche, S., Kiessling, A., Kilbinger, M., Kitching, T., Kunz, M., Kurki-Suonio, H., Ligori, S., Lilje, P. B., Lindholm, V., Lloro, I., Maino, D., Maiorano, E., Mansutti, O., Marggraf, O., Markovic, K., Martinet, N., Marulli, F., Massey, R., Medinaceli, E., Meneghetti, M., Meylan, G., Moresco, M., Moscardini, L., Munari, E., Niemi, S. -M., Padilla, C., Paltani, S., Pasian, F., Pedersen, K., Percival, W. J., Pettorino, V., Pires, S., Polenta, G., Poncet, M., Popa, L. A., Pozzetti, L., Raison, F., Renzi, A., Rhodes, J., Riccio, G., Romelli, E., Roncarelli, M., Saglia, R., Sapone, D., Sartoris, B., Schneider, P., Secroun, A., Seidel, G., Seiffert, M., Serrano, S., Sirignano, C., Sirri, G., Stanco, L., Starck, J. -L., Tallada-Crespí, P., Taylor, A. N., Tereno, I., Toledo-Moreo, R., Torradeflot, F., Tutusaus, I., Valentijn, E. A., Valenziano, L., Vassallo, T., Veropalumbo, A., Wang, Y., Weller, J., Zamorani, G., Zoubian, J., Zucca, E., Biviano, A., Bozzo, E., Burigana, C., Colodro-Conde, C., Di Ferdinando, D., Graciá-Carpio, J., Mauri, N., Neissner, C., Sakr, Z., Scottez, V., Tenti, M., Viel, M., Wiesmann, M., Akrami, Y., Allevato, V., Anselmi, S., Ballardini, M., Bernardeau, F., Borgani, S., Bruton, S., Cabanac, R., Cappi, A., Carvalho, C. S., Castignani, G., Castro, T., Cañas-Herrera, G., Chambers, K. C., Cooray, A. R., Coupon, J., Davini, S., de la Torre, S., De Lucia, G., Desprez, G., Di Domizio, S., Dole, H., Díaz-Sánchez, A., Vigo, J. A. Escartin, Escoffier, S., Ferreira, P. G., Ferrero, I., Finelli, F., Gabarra, L., Ganga, K., García-Bellido, J., Giacomini, F., Gozaliasl, G., Guinet, D., Hall, A., Joudaki, S., Kajava, J. J. E., Kansal, V., Karagiannis, D., Kirkpatrick, C. C., Legrand, L., Loureiro, A., Macias-Perez, J., Magliocchetti, M., Maoli, R., Martinelli, M., Martins, C. J. A. P., Matthew, S., Maturi, M., Maurin, L., Metcalf, R. B., Migliaccio, M., Monaco, P., Morgante, G., Nadathur, S., Walton, Nicholas A., Patrizii, L., Pezzotta, A., Popa, V., Porciani, C., Potter, D., Pöntinen, M., Reimberg, P., Rocci, P. -F., Sánchez, A. G., Schneider, A., Sefusatti, E., Sereno, M., Silvestri, A., Mancini, A. Spurio, Steinwagner, J., Testera, G., Teyssier, R., Toft, S., Tosi, S., Troja, A., Tucci, M., Valiviita, J., and Vergani, D.

Subjects
Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract

We investigate the approximations needed to efficiently predict the large-scale clustering of matter and dark matter halos in beyond-$\Lambda$CDM scenarios. We examine the normal branch of the Dvali-Gabadadze-Porrati model, the Hu-Sawicki $f(R)$ model, a slowly evolving dark energy, an interacting dark energy model and massive neutrinos. For each, we test approximations for the perturbative kernel calculations, including the omission of screening terms and the use of perturbative kernels based on the Einstein-de Sitter universe; we explore different infrared-resummation schemes, tracer bias models and a linear treatment of massive neutrinos; we employ two models for redshift space distortions, the Taruya-Nishimishi-Saito prescription and the Effective Field Theory of Large-Scale Structure. This work further provides a preliminary validation of the codes being considered by Euclid for the spectroscopic clustering probe in beyond-$\Lambda$CDM scenarios. We calculate and compare the $\chi^2$ statistic to assess the different modelling choices. This is done by fitting the spectroscopic clustering predictions to measurements from numerical simulations and perturbation theory-based mock data. We compare the behaviour of this statistic in the beyond-$\Lambda$CDM cases, as a function of the maximum scale included in the fit, to the baseline $\Lambda$CDM case. We find that the Einstein-de Sitter approximation without screening is surprisingly accurate for all cases when comparing to the halo clustering monopole and quadrupole obtained from simulations. Our results suggest that the inclusion of multiple redshift bins, higher-order multipoles, higher-order clustering statistics (such as the bispectrum) and photometric probes such as weak lensing, will be essential to extract information on massive neutrinos, modified gravity and dark energy., Comment: 29 pages, 10 figures, 4 tables, 3 appendices. Journal accepted version

Published
2023
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20. Squarefree Values Of Polynomials

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11N32, Secondary 11N25, 11N37
Abstract

This note presents new results for the squarefree value sets of quartic polynomials over the integers., Comment: Twenty-Eight Pages. Keywords: Squarefree integer, Irreducible polynomial

Published
2023

21. Largest Prime Factors of Polynomials

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11N05, Secondary 11N32
Abstract

LLet $x>1$ be a large number. This note shows that the largest prime factor of the quadratic product $\prod_{x\leq n\leq 2x}\left(n^2+1 \right)$ satisfies the relation $p \geq x^{3/2}$ as $x$ tends to infinity. This improves the current estimate $p \geq x^{1.279}$. In addition, it is shown that $n^2+1 $ has a large prime divisor in the interval $ p\in [x^{2-o(1)},x^2] $ for some $ n\geq x^{1-o(1)}$., Comment: Twenty Eight Pages. Keywords: Prime number; Distribution of prime; Polynomial prime value

Published
2023

22. DEMNUni: cross-correlating the nonlinear ISWRS effect with CMB-lensing and galaxies in the presence of massive neutrinos

Author

Cuozzo, Viviana, Carbone, Carmelita, Calabrese, Matteo, Carella, Elisabetta, and Migliaccio, Marina

Subjects
Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract

We present an analytical modelling of the angular cross-correlations between the Integrated Sachs Wolfe-Rees Sciama (ISWRS) effect and large-scale structure tracers in the presence of massive neutrinos. Our method has been validated against large N-body simulations with a massive neutrino particle component, namely the DEMNUni suite. We investigate the impact of different neutrino masses on the cross-correlations between the ISWRS effect and both the galaxy clustering and the lensing of the Cosmic Microwave Background (CMB). We also test the ability of current nonlinear matter power spectrum modellings to reproduce neutrino effects in such cross-correlations. We show that the multipole position of a characteristic sign inversion in the cross-spectra, due to nonlinear effects, is strongly related to the total neutrino mass $M_\nu$ and depends almost linearly on it. While these nonlinear cross-correlation signals may not be able alone to constrain the neutrino mass, our approach paves the way to the detection of such cross-spectra on small scales for their exploitation in combination with main probes from future galaxy surveys and CMB experiments., Comment: 30 pages, 13 figures (new version of several figures), this version matches the accepted version in JCAP

Published
2023
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23. Note on the Distribution of the Traces of Frobenius

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11K06, 11M50, Secondary 11G20, 14G10. and 14K15
Abstract

Let $E$ be a nonsingular elliptic curve over the rational numbers, and let $\tau^n=p^n+1-\#E(\mathbb{F}_{p^n})$. A result in the current literature claims that the normalized traces of Frobenius $\alpha_n=(\tau^n+\overline{\tau}^n)/2p^{n/2}$ are equidistributed on the interval $[-1,1]$ as $n\to \infty$. This short note has two goals: 1. Proposes a correction to this result on the distribution of the traces of Frobenius. 2. Provides a simple elementary proof of this result. More precisely, it is shown that the sequence $\{\alpha_n:n\geq1\}$ is dense but not equidistributed on the interval $[-1,1]$., Comment: Eleven Pages. Keywords: Algebraic curve; Traces of Frobenius; Sato-Tate distribution

Published
2023

24. A Result for Germain Primes

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11N05, Secondary 11N32
Abstract

This article determines a lower bound for the number Germain primes $p$ and $2p+1$ up to a large number $x$., Comment: Seventeen Pages. Keywords: Distribution of Primes; Germain Primes Conjecture; dePolignac Conjecture, Artin conjecture

Published
2023

27. Equidistributions of Sign Patterns of the Liouville Function and Normal Numbers

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11K16
Abstract

The equidistribution of the double sign patterns of the Liouville function $\lambda$ is proved unconditionally. As application, it is shown that the computable real number $$\sum_{n \geq 1} \frac{1+\lambda(n)}{2^{n}}$$ is a simply normal number in base 4., Comment: Eighteen Pages. Keywords: Sign pattern; Liouille function; Normal number

Published
2022

28. Note on the Chowla Conjecture and the Discrete Fourier Transform

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11N37, Secondary 11L03, 11K31
Abstract

Let $x\geq 1$ be a large integer, and let $a_00$ is an arbitrary constant., Comment: Thirty Four Pages. Keywords: Arithmetic function; Mobius function; Liouville function; Autocorrelation function; Correlation function; Chowla conjecture; Discrete Fourier transform

Published
2022

29. DEMNUni: comparing nonlinear power spectra prescriptions in the presence of massive neutrinos and dynamical dark energy

Author

Parimbelli, G., Carbone, C., Bel, J., Bose, B., Calabrese, M., Carella, E., and Zennaro, M.

Subjects
Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract

We provide an accurate comparison, against large cosmological $N$-body simulations, of different prescriptions for modelling nonlinear matter power spectra in the presence of massive neutrinos and dynamical dark energy. We test the current most widely used approaches: fitting functions (HALOFIT and HMcode), the halo-model reaction (ReACT) and emulators (baccoemu and EuclidEmulator2). Focussing on redshifts $z\leq2$ and scales $k\lesssim 1 \ h/$Mpc (where the simulation mass resolution provides $\sim 1\%$ accuracy), we find that HMcode and ReACT considerably improve over the HALOFIT prescriptions of Smith and Takahashi (both combined with the Bird correction), with an overall agreement of 2\% for all the cosmological scenarios considered. Concerning emulators, we find that, especially at low redshifts, EuclidEmulator2 remarkably agrees with the simulated spectra at $\lesssim 1\%$ level in scenarios with dynamical dark energy and massless neutrinos, reaching a maximum difference of $\sim 2\%$ at $z=2$. baccoemu has a similar behaviour as EuclidEmulator2, except for a couple of dark energy models. In cosmologies with massive neutrinos, at $z=0$ all the nonlinear prescriptions improve their agreement with respect to the massless neutrino case, except for the Bird and TakaBird models which, however, are not tailored to $w_0$--$w_a$ models. At $z>0$ we do not find a similar improvement when including massive neutrinos, probably due to the lower impact of neutrino free-streaming at higher redshifts; rather at $z=2$ EuclidEmulator2 exceeds $2\%$ agreement for some dark energy equation of state. When considering ratios between the matter power spectrum computed in a given cosmological model and its $\Lambda$CDM counterpart, all the tested prescriptions agree with simulated data, at sub-percent or percent level, depending on $z$. [ABRIDGED]

Published
2022
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30. Result on the Mobius Function over Shifted Primes

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11N37, Secondary 11L20
Abstract

This article provides new asymptotic results for the summatory Mobius function $\sum_{p \leq x} \mu(p+a) =O \left (x(\log x)^{-c} \right )$ and the summatory Liouville function $\sum_{p \leq x} \lambda(p+a) =O \left (x(\log x)^{-c} \right )$ over the shifted primes, where $a\ne0$ is a fixed parameter, and $c>1$ is an arbitrary constant. These results improve the current estimates $\sum_{p \leq x} \mu(p+a)=(1-\delta)\pi(x)$, and $\sum_{p \leq x} \lambda(p+a)=(1-\delta)\pi(x)$ for $\delta>0$, respectively. Furthermore, a conditional proof for the autocorrelation function $\sum_{p \leq x} \mu(p+a)\mu(p+b) =O \left (x(\log x)^{-c} \right )$, and an unconditional proof for the autocorrelation function $\sum_{p \leq x} \lambda(p+a)\lambda(p+b) =O \left (x(\log x)^{-c} \right )$ over the shifted primes, where $a\ne b$, are also included., Comment: Fifty Three Pages. Keywords: Shifted prime; Arithmetic function; Mobius function; Liouville function; vonMangoldt function; Correlation; Autocorrelation; Chowla conjecture; Sarnak conjecture

Published
2022

31. Simultaneous Primitive Root Values Of Polynomials

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11A07, 11N13, Secondary 11N05, 11N37
Abstract

Let $z\ne \pm1,w^2$ be a fixed integer, and let $f(t)\ne g(t)^2$ be a fixed polynomial over the integers. It is shown that the subset of primes $p\geq 2$ such that $z$ and $f(z)$ is a pair of simultaneous primitive roots modulo $p$ has nonzero density in the set of primes. The same analysis generalizes to \textit{admissible} $k$-tuple of polynomials $z$, $f_1(z)$, $f_2(z), \ldots$, $f_k(z)$, such that $f_i(z)\ne g_i(z)^2$, and $k\ll \log p$ is a small integer., Comment: Seventeen Pages. Keywords: Distribution of primes; Primitive root; Simultaneous primitive roots

Published
2022

33. Space weather-related activities and projects on-going at INAF-Turin Observatory

Author

Bemporad, Alessandro, Fineschi, Silvano, Abbo, Lucia, Benna, Carlo, Biondo, Ruggero, Capobianco, Gerardo, Carella, Francesco, Cora, Alberto, Frassati, Federica, Giordano, Silvio, Haudemand, Hervé, Landini, Federico, Loreggia, Davide, Mancuso, Salvatore, Mignone, Andrea, Nicolini, Gianalfredo, Pancrazzi, Maurizio, Salvati, Francesco, Susino, Roberto, Telloni, Daniele, and Zangrilli, Luca

Published
2023
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35. Note On The Catalan Constant And Prime Triples

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11J82, Secondary 11J72, 11Y60
Abstract

The existence of infinitely many consecutive prime triples $p_n$, $ p_{n+1}$, and $p_{n+2}$ as $n \to \infty$, is sufficient to prove that the Catalan constant $\beta(2)=0.9159655941\ldots $ is an irrational number. This note provides the detailed analysis. Moreover, the numerical data suggests that the irrationality measure is $\mu(\beta(2))=2$, the same as almost every irrational real numbers., Comment: Ten Pages. Keywords: Irrational number; Catalan constant; Irrationality measure; Prime triple

Published
2022

36. Autocorrelation of the Mobius Function

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11N37, Secondary 11P32
Abstract

Let $x\geq 1$ be a large integer, and let $\mu:\mathbb{N}\longrightarrow\{-1,0,1\}$ be the Mobius function. This article proposes an effective asymptotic result for the autocorrelation function $\sum_{n \leq x} \mu(n) \mu(n+t) =O\left( e^{-c\sqrt{\log x}}\right) $, where $t\ne 0$ be a small fixed integer, and $c>0$ is a constant., Comment: Eight Pages. Keywords: Autocorrelation; Correlation; Arithmetic function; Mobius function; Liouville function; Chola conjecture

Published
2022

37. Irrationality Measure Of $\pi^2$

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11J82, Secondary 11J72, 11Y60
Abstract

The note provides a simple proof of the irrationality measure $\mu(\pi^2)=2$ of the real number $\pi^2$. The current estimate gives the upper bound $\mu(\pi^2)\leq 5.0954 \ldots$., Comment: Five Pages. Keywords: Irrational number; Irrationality measure; Pi; Pi Square

Published
2021

38. A low-cost wave-solar powered Unmanned Surface Vehicle

Author

Elkolali, Moustafa, Al-Tawil, Ahmed, Much, Lennard, Schrader, Ryan, Masset, Olivier, Sayols, Marina, Jenkins, Andrew, Alonso, Sara, Carella, Alfredo, and Alcocer, Alex

Subjects
Computer Science - Robotics
Abstract

This paper presents a prototype of a low-cost Unmanned Surface Vehicle (USV) that is operated by wave and solar energy which can be used to minimize the cost of ocean data collection. The current prototype is a compact USV, with a length of 1.2m that can be deployed and recovered by two persons. The design includes an electrically operated winch that can be used to retract and lower the underwater unit. Several elements of the design make use of additive manufacturing and inexpensive materials. The vehicle can be controlled using radio frequency (RF) and a satellite communication, through a custom developed web application. Both the surface and underwater units were optimized with regard to drag, lift, weight, and price by using recommendation of previous research work and advanced materials. The USV could be used in water condition monitoring by measuring several parameters, such as dissolved oxygen, salinity, temperature, and pH.

Published
2021
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39. Prescribed Primitive Roots And The Least Primes

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11A07, 11N13, Secondary 11N05, 11N37
Abstract

Let $q\ne \pm1,v^2$ be a fixed integer, and let $x\geq 1$ be a large number. The least prime number $p \geq3 $ such that $q$ is a primitive root modulo $p$ is conjectured to be $p\ll (\log q)(\log \log q)^3),$ where $\gcd(p,q)=1$. This note proves the existence of small primes $p\ll(\log x)^c$, where $c>0$ is a constant, a close approximation to the conjectured upper bound., Comment: Eight Pages. Keywords: Primitive root, Least prime number, Artin primitive root conjecture

Published
2021

40. Equidistribution Mod $1$ And Normal Numbers

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, 11K16 (Primary), 11J72 (Secondary)
Abstract

Let $\alpha=0.a_1a_2a_3\ldots$ be an irrational number in base $b>1$, where $0\leq a_i

Published
2021

41. Sum of Divisors Function And The Largest Integer Function Over The Shifted Primes

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11N37, Secondary 11N05
Abstract

Let $ x\geq 1 $ be a large number, let $ [x]=x-\{x\} $ be the largest integer function, and let $ \sigma(n)$ be the sum of divisors function. This note presents the first proof of the asymptotic formula for the average order $ \sum_{p\leq x}\sigma([x/p])=c_0x\log \log x+O(x) $ over the primes, where $c_0>0$ is a constant. More generally, $ \sum_{p\leq x}\sigma([x/(p+a)])=c_0x\log \log x+O(x) $ for any fixed integer $a$., Comment: Nine Pages. Keywords: Arithmetic function; Sum of divisors function; Largest integer function; Average orders; Shifted primes. arXiv admin note: substantial text overlap with arXiv:2105.00790

Published
2021

42. Upper Bound of the Least Quadratic Nonresidues

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, 2020: Primary 11A15, Secondary 11L40
Abstract

Let $p\geq3$ be a large prime and let $n(p)\geq2$ denotes the least quadratic nonresidue modulo $p$. This note sharpens the standard upper bound of the least quadratic nonresidue from the unconditional upper bound $n(p)\ll p^{1/4\sqrt{e}+\varepsilon}$ to the conjectured upper bound $n(p)\ll (\log p)^{1+\varepsilon}$, where $\varepsilon>0$ is a small number, unconditionally. This improvement breaks the exponential upper bound barrier., Comment: Twenty Pages. Keywords: Least quadratic nonresidue; Square root mod $p$; Deterministic algorithm

Published
2021

43. Euler Totient Function And The Largest Integer Function Over The Shifted Primes

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, 2020: Primary 11N37, Secondary 11N05
Abstract

Let $ x\geq 1 $ be a large number, let $ [x]=x-\{x\} $ be the largest integer function, and let $ \varphi(n)$ be the Euler totient function. The asymptotic formula for the new finite sum over the primes $ \sum_{p\leq x}\varphi([x/p])=(6/\pi^2)x\log \log x+c_0x+O\left (x(\log x)^{-1}\right) $, where $c_0$ is a constant, is evaluated in this note., Comment: Nine Pages. Keywords: Shifted prime; Multiplicative function; Euler phi function; Average orders; Largest integer function

Published
2021

44. Approximate Atkin-Serre Conjecture

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, 2020: Primary 11F35, Secondary 11D45
Abstract

Let $\lambda(m)$ be the $m$th coefficient of a modular form $f(z)=\sum_{m\geq 1} \lambda(m)q^m$ of weight $k\geq 4$, let $p^n$ be a prime power, and let $\varepsilon>0$ be a small number. An approximate of the Atkin-Serre conjecture on the lower bound of the form $\left |\lambda\left (p^n\right )\right | \geq p^{(k-1)n/2-2k+2\varepsilon}$ is presented in this note., Comment: Twelve Pages. Keywords: Tau Function; Modular Function; Atkin-Serre Conjecture

Published
2021

45. Simultaneous Elements Of Prescribed Multiplicative Orders

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, Primary 11A07, Secondary 11N13
Abstract

Let $u\ne \pm 1$, and $v\ne \pm 1$ be a pair of fixed relatively prime squarefree integers, and let $d\geq 1$, and $e \geq1$ be a pair of fixed integers. It is shown that there are infinitely many primes $p\geq 2$ such that $u$ and $v$ have simultaneous prescribed multiplicative orders $\text{ord}_pu=(p-1)/d$ and $\text{ord}_pv=(p-1)/e$ respectively, unconditionally. In particular, a squarefree odd integer $u>2$ and $v=2$ are simultaneous primitive roots and quadratic residues (or quadratic nonresidues) modulo $p$ for infinitely many primes $p$, unconditionally., Comment: Twenty Pages. Keywords: Distribution of primes; Primes in arithmetic progressions; Simultaneous primitive roots; Simultaneous prescribed orders; Schinzel-Wojcik problem

Published
2021

46. SWELTO -- Space WEather Laboratory in Turin Observatory

Author

Bemporad, A., Abbo, L., Barghini, D., Benna, C., Biondo, R., Bonino, D., Capobianco, G., Carella, F., Cora, A., Fineschi, S., Frassati, F., Gardiol, D., Giordano, S., Liberatore, A., Mancuso, S., Mignone, A., Rasetti, S., Reale, F., Riva, A., Salvati, F., Susino, R., Volpicelli, A., and Zangrilli, L.

Subjects
Astrophysics - Solar and Stellar Astrophysics, Astrophysics - Instrumentation and Methods for Astrophysics, Physics - Space Physics
Abstract

SWELTO -- Space WEather Laboratory in Turin Observatory is a conceptual framework where new ideas for the analysis of space-based and ground-based data are developed and tested. The input data are (but not limited to) remote sensing observations (EUV images of the solar disk, Visible Light coronagraphic images, radio dynamic spectra, etc...), in situ plasma measurements (interplanetary plasma density, velocity, magnetic field, etc...), as well as measurements acquired by local sensors and detectors (radio antenna, fluxgate magnetometer, full-sky cameras, located in OATo). The output products are automatic identification, tracking, and monitoring of solar stationary and dynamic features near the Sun (coronal holes, active regions, coronal mass ejections, etc...), and in the interplanetary medium (shocks, plasmoids, corotating interaction regions, etc...), as well as reconstructions of the interplanetary medium where solar disturbances may propagate from the Sun to the Earth and beyond. These are based both on empirical models and numerical MHD simulations. The aim of SWELTO is not only to test new data analysis methods for future application for Space Weather monitoring and prediction purposes, but also to procure, test and deploy new ground-based instrumentation to monitor the ionospheric and geomagnetic responses to solar activity. Moreover, people involved in SWELTO are active in outreach to disseminate the topics related with Space Weather to students and the general public.

Published
2021

47. Average Orders of the Euler Phi Function, The Dedekind Psi Function, The Sum of Divisors Function, And The Largest Integer Function

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, 2020: Primary 11N37, Secondary 11N05
Abstract

Let $ x\geq 1 $ be a large number, let $ [x]=x-\{x\} $ be the largest integer function, and let $ \varphi(n)$ be the Euler totient function. The result $ \sum_{n\leq x}\varphi([x/n])=(6/\pi^2)x\log x+O\left ( x(\log x)^{2/3}(\log\log x)^{1/3}\right ) $ was proved very recently. This note presents a short elementary proof, and sharpen the error term to $ \sum_{n\leq x}\varphi([x/n])=(6/\pi^2)x\log x+O(x) $. In addition, the first proofs of the asymptotics formulas for the finite sums $ \sum_{n\leq x}\psi([x/n])=(15/\pi^2)x\log x+O(x\log \log x) $, and $ \sum_{n\leq x}\sigma([x/n])=(\pi^2/6)x\log x+O(x \log \log x) $ are also evaluated here., Comment: Thirteen Pages. Keywords: Multiplicative function; Average orders; Euler phi function; Dedekind psi function, Sum of divisors function; Largest integer function

Published
2021

50. Consecutive Quadratic Residues And Quadratic Nonresidue Modulo $p$

Author

Carella, N. A.

Subjects
Mathematics - General Mathematics, 2020: Primary 11A15, Secondary 11L40
Abstract

Let $p$ be a large prime, and let $k\ll \log p$. A new proof of the existence of any pattern of $k$ consecutive quadratic residues and quadratic nonresidues is introduced in this note. Further, an application to the least quadratic nonresidues $n_p$ modulo $p$ shows that $n_p\ll (\log p)(\log \log p)$., Comment: Twenty Pages. Keywords: Least quadratic nonresidue, Consecutive quadratic residues

Published
2020

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