On linear equations over split octonions

Autor: Lopatin, Artem, Zubkov, Alexandr N.

Over an algebraically closed field, affine varieties of solutions of the linear equations a(xb)=c and a(bx)=c over split octonions are described. The set of solutions of a general linear monomial equation over split octonions is considered. We also s

Externí odkaz: http://arxiv.org/abs/2411.08500

Magnetoconductivity of Dirac semimetals and chiral magnetic effect from Keldysh technique

Autor: Abramchuk, R. A., Zubkov, M. A.

Negative magnetoresistance in Dirac semimetals is typically considered as a manifestation of chiral magnetic effect (CME). The relation between these two phenomena has the status of a hypothesis and is based on sequence of assumptions. We rely on the

Externí odkaz: http://arxiv.org/abs/2409.14941

Gemini: A Family of Highly Capable Multimodal Models

Autor: Gemini Team, Anil, Rohan, Borgeaud, Sebastian, Alayrac, Jean-Baptiste, Yu, Jiahui, Soricut, Radu, Schalkwyk, Johan, Dai, Andrew M., Hauth, Anja, Millican, Katie, Silver, David, Johnson, Melvin, Antonoglou, Ioannis, Schrittwieser, Julian, Glaese, Amelia, Chen, Jilin, Pitler, Emily, Lillicrap, Timothy, Lazaridou, Angeliki, Firat, Orhan, Molloy, James, Isard, Michael, Barham, Paul R., Hennigan, Tom, Lee, Benjamin, Viola, Fabio, Reynolds, Malcolm, Xu, Yuanzhong, Doherty, Ryan, Collins, Eli, Meyer, Clemens, Rutherford, Eliza, Moreira, Erica, Ayoub, Kareem, Goel, Megha, Krawczyk, Jack, Du, Cosmo, Chi, Ed, Cheng, Heng-Tze, Ni, Eric, Shah, Purvi, Kane, Patrick, Chan, Betty, Faruqui, Manaal, Severyn, Aliaksei, Lin, Hanzhao, Li, YaGuang, Cheng, Yong, Ittycheriah, Abe, Mahdieh, Mahdis, Chen, Mia, Sun, Pei, Tran, Dustin, Bagri, Sumit, Lakshminarayanan, Balaji, Liu, Jeremiah, Orban, Andras, Güra, Fabian, Zhou, Hao, Song, Xinying, Boffy, Aurelien, Ganapathy, Harish, Zheng, Steven, Choe, HyunJeong, Weisz, Ágoston, Zhu, Tao, Lu, Yifeng, Gopal, Siddharth, Kahn, Jarrod, Kula, Maciej, Pitman, Jeff, Shah, Rushin, Taropa, Emanuel, Merey, Majd Al, Baeuml, Martin, Chen, Zhifeng, Shafey, Laurent El, Zhang, Yujing, Sercinoglu, Olcan, Tucker, George, Piqueras, Enrique, Krikun, Maxim, Barr, Iain, Savinov, Nikolay, Danihelka, Ivo, Roelofs, Becca, White, Anaïs, Andreassen, Anders, von Glehn, Tamara, Yagati, Lakshman, Kazemi, Mehran, Gonzalez, Lucas, Khalman, Misha, Sygnowski, Jakub, Frechette, Alexandre, Smith, Charlotte, Culp, Laura, Proleev, Lev, Luan, Yi, Chen, Xi, Lottes, James, Schucher, Nathan, Lebron, Federico, Rrustemi, Alban, Clay, Natalie, Crone, Phil, Kocisky, Tomas, Zhao, Jeffrey, Perz, Bartek, Yu, Dian, Howard, Heidi, Bloniarz, Adam, Rae, Jack W., Lu, Han, Sifre, Laurent, Maggioni, Marcello, Alcober, Fred, Garrette, Dan, Barnes, Megan, Thakoor, Shantanu, Austin, Jacob, Barth-Maron, Gabriel, Wong, William, Joshi, Rishabh, Chaabouni, Rahma, Fatiha, Deeni, Ahuja, Arun, Tomar, Gaurav Singh, Senter, Evan, Chadwick, Martin, Kornakov, Ilya, Attaluri, Nithya, Iturrate, Iñaki, Liu, Ruibo, Li, Yunxuan, Cogan, Sarah, Chen, Jeremy, Jia, Chao, Gu, Chenjie, Zhang, Qiao, Grimstad, Jordan, Hartman, Ale Jakse, Garcia, Xavier, Pillai, Thanumalayan Sankaranarayana, Devlin, Jacob, Laskin, Michael, Casas, Diego de Las, Valter, Dasha, Tao, Connie, Blanco, Lorenzo, Badia, Adrià Puigdomènech, Reitter, David, Chen, Mianna, Brennan, Jenny, Rivera, Clara, Brin, Sergey, Iqbal, Shariq, Surita, Gabriela, Labanowski, Jane, Rao, Abhi, Winkler, Stephanie, Parisotto, Emilio, Gu, Yiming, Olszewska, Kate, Addanki, Ravi, Miech, Antoine, Louis, Annie, Teplyashin, Denis, Brown, Geoff, Catt, Elliot, Balaguer, Jan, Xiang, Jackie, Wang, Pidong, Ashwood, Zoe, Briukhov, Anton, Webson, Albert, Ganapathy, Sanjay, Sanghavi, Smit, Kannan, Ajay, Chang, Ming-Wei, Stjerngren, Axel, Djolonga, Josip, Sun, Yuting, Bapna, Ankur, Aitchison, Matthew, Pejman, Pedram, Michalewski, Henryk, Yu, Tianhe, Wang, Cindy, Love, Juliette, Ahn, Junwhan, Bloxwich, Dawn, Han, Kehang, Humphreys, Peter, Sellam, Thibault, Bradbury, James, Godbole, Varun, Samangooei, Sina, Damoc, Bogdan, Kaskasoli, Alex, Arnold, Sébastien M. R., Vasudevan, Vijay, Agrawal, Shubham, Riesa, Jason, Lepikhin, Dmitry, Tanburn, Richard, Srinivasan, Srivatsan, Lim, Hyeontaek, Hodkinson, Sarah, Shyam, Pranav, Ferret, Johan, Hand, Steven, Garg, Ankush, Paine, Tom Le, Li, Jian, Li, Yujia, Giang, Minh, Neitz, Alexander, Abbas, Zaheer, York, Sarah, Reid, Machel, Cole, Elizabeth, Chowdhery, Aakanksha, Das, Dipanjan, Rogozińska, Dominika, Nikolaev, Vitaliy, Sprechmann, Pablo, Nado, Zachary, Zilka, Lukas, Prost, Flavien, He, Luheng, Monteiro, Marianne, Mishra, Gaurav, Welty, Chris, Newlan, Josh, Jia, Dawei, Allamanis, Miltiadis, Hu, Clara Huiyi, de Liedekerke, Raoul, Gilmer, Justin, Saroufim, Carl, Rijhwani, Shruti, Hou, Shaobo, Shrivastava, Disha, Baddepudi, Anirudh, Goldin, Alex, Ozturel, Adnan, Cassirer, Albin, Xu, Yunhan, Sohn, Daniel, Sachan, Devendra, Amplayo, Reinald Kim, Swanson, Craig, Petrova, Dessie, Narayan, Shashi, Guez, Arthur, Brahma, Siddhartha, Landon, Jessica, Patel, Miteyan, Zhao, Ruizhe, Villela, Kevin, Wang, Luyu, Jia, Wenhao, Rahtz, Matthew, Giménez, Mai, Yeung, Legg, Keeling, James, Georgiev, Petko, Mincu, Diana, Wu, Boxi, Haykal, Salem, Saputro, Rachel, Vodrahalli, Kiran, Qin, James, Cankara, Zeynep, Sharma, Abhanshu, Fernando, Nick, Hawkins, Will, Neyshabur, Behnam, Kim, Solomon, Hutter, Adrian, Agrawal, Priyanka, Castro-Ros, Alex, Driessche, George van den, Wang, Tao, Yang, Fan, Chang, Shuo-yiin, Komarek, Paul, McIlroy, Ross, Lučić, Mario, Zhang, Guodong, Farhan, Wael, Sharman, Michael, Natsev, Paul, Michel, Paul, Bansal, Yamini, Qiao, Siyuan, Cao, Kris, Shakeri, Siamak, Butterfield, Christina, Chung, Justin, Rubenstein, Paul Kishan, Agrawal, Shivani, Mensch, Arthur, Soparkar, Kedar, Lenc, Karel, Chung, Timothy, Pope, Aedan, Maggiore, Loren, Kay, Jackie, Jhakra, Priya, Wang, Shibo, Maynez, Joshua, Phuong, Mary, Tobin, Taylor, Tacchetti, Andrea, Trebacz, Maja, Robinson, Kevin, Katariya, Yash, Riedel, Sebastian, Bailey, Paige, Xiao, Kefan, Ghelani, Nimesh, Aroyo, Lora, Slone, Ambrose, Houlsby, Neil, Xiong, Xuehan, Yang, Zhen, Gribovskaya, Elena, Adler, Jonas, Wirth, Mateo, Lee, Lisa, Li, Music, Kagohara, Thais, Pavagadhi, Jay, Bridgers, Sophie, Bortsova, Anna, Ghemawat, Sanjay, Ahmed, Zafarali, Liu, Tianqi, Powell, Richard, Bolina, Vijay, Iinuma, Mariko, Zablotskaia, Polina, Besley, James, Chung, Da-Woon, Dozat, Timothy, Comanescu, Ramona, Si, Xiance, Greer, Jeremy, Su, Guolong, Polacek, Martin, Kaufman, Raphaël Lopez, Tokumine, Simon, Hu, Hexiang, Buchatskaya, Elena, Miao, Yingjie, Elhawaty, Mohamed, Siddhant, Aditya, Tomasev, Nenad, Xing, Jinwei, Greer, Christina, Miller, Helen, Ashraf, Shereen, Roy, Aurko, Zhang, Zizhao, Ma, Ada, Filos, Angelos, Besta, Milos, Blevins, Rory, Klimenko, Ted, Yeh, Chih-Kuan, Changpinyo, Soravit, Mu, Jiaqi, Chang, Oscar, Pajarskas, Mantas, Muir, Carrie, Cohen, Vered, Lan, Charline Le, Haridasan, Krishna, Marathe, Amit, Hansen, Steven, Douglas, Sholto, Samuel, Rajkumar, Wang, Mingqiu, Austin, Sophia, Lan, Chang, Jiang, Jiepu, Chiu, Justin, Lorenzo, Jaime Alonso, Sjösund, Lars Lowe, Cevey, Sébastien, Gleicher, Zach, Avrahami, Thi, Boral, Anudhyan, Srinivasan, Hansa, Selo, Vittorio, May, Rhys, Aisopos, Konstantinos, Hussenot, Léonard, Soares, Livio Baldini, Baumli, Kate, Chang, Michael B., Recasens, Adrià, Caine, Ben, Pritzel, Alexander, Pavetic, Filip, Pardo, Fabio, Gergely, Anita, Frye, Justin, Ramasesh, Vinay, Horgan, Dan, Badola, Kartikeya, Kassner, Nora, Roy, Subhrajit, Dyer, Ethan, Campos, Víctor Campos, Tomala, Alex, Tang, Yunhao, Badawy, Dalia El, White, Elspeth, Mustafa, Basil, Lang, Oran, Jindal, Abhishek, Vikram, Sharad, Gong, Zhitao, Caelles, Sergi, Hemsley, Ross, Thornton, Gregory, Feng, Fangxiaoyu, Stokowiec, Wojciech, Zheng, Ce, Thacker, Phoebe, Ünlü, Çağlar, Zhang, Zhishuai, Saleh, Mohammad, Svensson, James, Bileschi, Max, Patil, Piyush, Anand, Ankesh, Ring, Roman, Tsihlas, Katerina, Vezer, Arpi, Selvi, Marco, Shevlane, Toby, Rodriguez, Mikel, Kwiatkowski, Tom, Daruki, Samira, Rong, Keran, Dafoe, 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Bacon, Geoff, Greene, David, Mirylenka, Daniil, Zhou, Chen, Sarvana, Obaid, Goyal, Abhimanyu, Andermatt, Samuel, Siegler, Patrick, Horn, Ben, Israel, Assaf, Pongetti, Francesco, Chen, Chih-Wei "Louis", Selvatici, Marco, Silva, Pedro, Wang, Kathie, Tolins, Jackson, Guu, Kelvin, Yogev, Roey, Cai, Xiaochen, Agostini, Alessandro, Shah, Maulik, Nguyen, Hung, Donnaile, Noah Ó, Pereira, Sébastien, Friso, Linda, Stambler, Adam, Kuang, Chenkai, Romanikhin, Yan, Geller, Mark, Yan, ZJ, Jang, Kane, Lee, Cheng-Chun, Fica, Wojciech, Malmi, Eric, Tan, Qijun, Banica, Dan, Balle, Daniel, Pham, Ryan, Huang, Yanping, Avram, Diana, Shi, Hongzhi, Singh, Jasjot, Hidey, Chris, Ahuja, Niharika, Saxena, Pranab, Dooley, Dan, Potharaju, Srividya Pranavi, O'Neill, Eileen, Gokulchandran, Anand, Foley, Ryan, Zhao, Kai, Dusenberry, Mike, Liu, Yuan, Mehta, Pulkit, Kotikalapudi, Ragha, Safranek-Shrader, Chalence, Goodman, Andrew, Kessinger, Joshua, Globen, Eran, Kolhar, Prateek, Gorgolewski, Chris, Ibrahim, Ali, Song, Yang, Eichenbaum, Ali, Brovelli, Thomas, Potluri, Sahitya, Lahoti, Preethi, Baetu, Cip, Ghorbani, Ali, Chen, Charles, Crawford, Andy, Pal, Shalini, Sridhar, Mukund, Gurita, Petru, Mujika, Asier, Petrovski, Igor, Cedoz, Pierre-Louis, Li, Chenmei, Chen, Shiyuan, Santo, Niccolò Dal, Goyal, Siddharth, Punjabi, Jitesh, Kappaganthu, Karthik, Kwak, Chester, LV, Pallavi, Velury, Sarmishta, Choudhury, Himadri, Hall, Jamie, Shah, Premal, Figueira, Ricardo, Thomas, Matt, Lu, Minjie, Zhou, Ting, Kumar, Chintu, Jurdi, Thomas, Chikkerur, Sharat, Ma, Yenai, Yu, Adams, Kwak, Soo, Ähdel, Victor, Rajayogam, Sujeevan, Choma, Travis, Liu, Fei, Barua, Aditya, Ji, Colin, Park, Ji Ho, Hellendoorn, Vincent, Bailey, Alex, Bilal, Taylan, Zhou, Huanjie, Khatir, Mehrdad, Sutton, Charles, Rzadkowski, Wojciech, Macintosh, Fiona, Shagin, Konstantin, Medina, Paul, Liang, Chen, Zhou, Jinjing, Shah, Pararth, Bi, Yingying, Dankovics, Attila, Banga, Shipra, Lehmann, Sabine, Bredesen, Marissa, Lin, Zifan, Hoffmann, John Eric, Lai, Jonathan, Chung, Raynald, Yang, Kai, Balani, Nihal, Bražinskas, Arthur, Sozanschi, Andrei, Hayes, Matthew, Alcalde, Héctor Fernández, Makarov, Peter, Chen, Will, Stella, Antonio, Snijders, Liselotte, Mandl, Michael, Kärrman, Ante, Nowak, Paweł, Wu, Xinyi, Dyck, Alex, Vaidyanathan, Krishnan, R, Raghavender, Mallet, Jessica, Rudominer, Mitch, Johnston, Eric, Mittal, Sushil, Udathu, Akhil, Christensen, Janara, Verma, Vishal, Irving, Zach, Santucci, Andreas, Elsayed, Gamaleldin, Davoodi, Elnaz, Georgiev, Marin, Tenney, Ian, Hua, Nan, Cideron, Geoffrey, Leurent, Edouard, Alnahlawi, Mahmoud, Georgescu, Ionut, Wei, Nan, Zheng, Ivy, Scandinaro, Dylan, Jiang, Heinrich, Snoek, Jasper, Sundararajan, Mukund, Wang, Xuezhi, Ontiveros, Zack, Karo, Itay, Cole, Jeremy, Rajashekhar, Vinu, Tumeh, Lara, Ben-David, Eyal, Jain, Rishub, Uesato, Jonathan, Datta, Romina, Bunyan, Oskar, Wu, Shimu, Zhang, John, Stanczyk, Piotr, Zhang, Ye, Steiner, David, Naskar, Subhajit, Azzam, Michael, Johnson, Matthew, Paszke, Adam, Chiu, Chung-Cheng, Elias, Jaume Sanchez, Mohiuddin, Afroz, Muhammad, Faizan, Miao, Jin, Lee, Andrew, Vieillard, Nino, Park, Jane, Zhang, Jiageng, Stanway, Jeff, Garmon, Drew, Karmarkar, Abhijit, Dong, Zhe, Lee, Jong, Kumar, Aviral, Zhou, Luowei, Evens, Jonathan, Isaac, William, Irving, Geoffrey, Loper, Edward, Fink, Michael, Arkatkar, Isha, Chen, Nanxin, Shafran, Izhak, Petrychenko, Ivan, Chen, Zhe, Jia, Johnson, Levskaya, Anselm, Zhu, Zhenkai, Grabowski, Peter, Mao, Yu, Magni, Alberto, Yao, Kaisheng, Snaider, Javier, Casagrande, Norman, Palmer, Evan, Suganthan, Paul, Castaño, Alfonso, Giannoumis, Irene, Kim, Wooyeol, Rybiński, Mikołaj, Sreevatsa, Ashwin, Prendki, Jennifer, Soergel, David, Goedeckemeyer, Adrian, Gierke, Willi, Jafari, Mohsen, Gaba, Meenu, Wiesner, Jeremy, Wright, Diana Gage, Wei, Yawen, Vashisht, Harsha, Kulizhskaya, Yana, Hoover, Jay, Le, Maigo, Li, Lu, Iwuanyanwu, Chimezie, Liu, Lu, Ramirez, Kevin, Khorlin, Andrey, Cui, Albert, LIN, Tian, Wu, Marcus, Aguilar, Ricardo, Pallo, Keith, Chakladar, Abhishek, Perng, Ginger, Abellan, Elena Allica, Zhang, Mingyang, Dasgupta, Ishita, Kushman, Nate, Penchev, Ivo, Repina, Alena, Wu, Xihui, van der Weide, Tom, Ponnapalli, Priya, Kaplan, Caroline, Simsa, Jiri, Li, Shuangfeng, Dousse, Olivier, Piper, Jeff, Ie, Nathan, Pasumarthi, Rama, Lintz, Nathan, Vijayakumar, Anitha, Andor, Daniel, Valenzuela, Pedro, Lui, Minnie, Paduraru, Cosmin, Peng, Daiyi, Lee, Katherine, Zhang, Shuyuan, Greene, Somer, Nguyen, Duc Dung, Kurylowicz, Paula, Hardin, Cassidy, Dixon, Lucas, Janzer, Lili, Choo, Kiam, Feng, Ziqiang, Zhang, Biao, Singhal, Achintya, Du, Dayou, McKinnon, Dan, Antropova, Natasha, Bolukbasi, Tolga, Keller, Orgad, Reid, David, Finchelstein, Daniel, Raad, Maria Abi, Crocker, Remi, Hawkins, Peter, Dadashi, Robert, Gaffney, Colin, Franko, Ken, Bulanova, Anna, Leblond, Rémi, Chung, Shirley, Askham, Harry, Cobo, Luis C., Xu, Kelvin, Fischer, Felix, Xu, Jun, Sorokin, Christina, Alberti, Chris, Lin, Chu-Cheng, Evans, Colin, Dimitriev, Alek, Forbes, Hannah, Banarse, Dylan, Tung, Zora, Omernick, Mark, Bishop, Colton, Sterneck, Rachel, Jain, Rohan, Xia, Jiawei, Amid, Ehsan, Piccinno, Francesco, Wang, Xingyu, Banzal, Praseem, Mankowitz, Daniel J., Polozov, Alex, Krakovna, Victoria, Brown, Sasha, Bateni, MohammadHossein, Duan, Dennis, Firoiu, Vlad, Thotakuri, Meghana, Natan, Tom, Geist, Matthieu, Girgin, Ser tan, Li, Hui, Ye, Jiayu, Roval, Ofir, Tojo, Reiko, Kwong, Michael, Lee-Thorp, James, Yew, Christopher, Sinopalnikov, Danila, Ramos, Sabela, Mellor, John, Sharma, Abhishek, Wu, Kathy, Miller, David, Sonnerat, Nicolas, Vnukov, Denis, Greig, Rory, Beattie, Jennifer, Caveness, Emily, Bai, Libin, Eisenschlos, Julian, Korchemniy, Alex, Tsai, Tomy, Jasarevic, Mimi, Kong, Weize, Dao, Phuong, Zheng, Zeyu, Liu, Frederick, Zhu, Rui, Teh, Tian Huey, Sanmiya, Jason, Gladchenko, Evgeny, Trdin, Nejc, Toyama, Daniel, Rosen, Evan, Tavakkol, Sasan, Xue, Linting, Elkind, Chen, Woodman, Oliver, 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Prakash, Varadarajan, Mani, Bahargam, Sanaz, Willoughby, Rob, Gaddy, David, Desjardins, Guillaume, Cornero, Marco, Robenek, Brona, Mittal, Bhavishya, Albrecht, Ben, Shenoy, Ashish, Moiseev, Fedor, Jacobsson, Henrik, Ghaffarkhah, Alireza, Rivière, Morgane, Walton, Alanna, Crepy, Clément, Parrish, Alicia, Zhou, Zongwei, Farabet, Clement, Radebaugh, Carey, Srinivasan, Praveen, van der Salm, Claudia, Fidjeland, Andreas, Scellato, Salvatore, Latorre-Chimoto, Eri, Klimczak-Plucińska, Hanna, Bridson, David, de Cesare, Dario, Hudson, Tom, Mendolicchio, Piermaria, Walker, Lexi, Morris, Alex, Mauger, Matthew, Guseynov, Alexey, Reid, Alison, Odoom, Seth, Loher, Lucia, Cotruta, Victor, Yenugula, Madhavi, Grewe, Dominik, Petrushkina, Anastasia, Duerig, Tom, Sanchez, Antonio, Yadlowsky, Steve, Shen, Amy, Globerson, Amir, Webb, Lynette, Dua, Sahil, Li, Dong, Bhupatiraju, Surya, Hurt, Dan, Qureshi, Haroon, Agarwal, Ananth, Shani, Tomer, Eyal, Matan, Khare, Anuj, Belle, Shreyas Rammohan, Wang, Lei, 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Amar, Hsiao, Sissie, Hassabis, Demis, Kavukcuoglu, Koray, Sadovsky, Adam, Le, Quoc, Strohman, Trevor, Wu, Yonghui, Petrov, Slav, Dean, Jeffrey, Vinyals, Oriol

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging fro

Externí odkaz: http://arxiv.org/abs/2312.11805

Linkage for periplectic supergroups in positive characteristic

Autor: Marko, Frantisek, Zubkov, Alexandr N.

We consider the periplectic supergroup ${\bf P} (n)$ over a ground field $\Bbbk$ of characteristic $p>2$. We show that there are four blocks of ${\bf P} (n)$ of simple supermodules $L^{\epsilon}(\lambda)$ corresponding to dominant weights $\lambda$ o

Externí odkaz: http://arxiv.org/abs/2311.02136

Effective lagrangian for the macroscopic motion of fermionic matter

Autor: Selch, M., Abramchuk, R. A., Zubkov, M. A.

We consider macroscopic motion of quantum field systems. Zubarev statistical operator allows to describe several types of motion of such systems in thermal equilibrium. We formulate the corresponding effective theory on the language of functional int

Externí odkaz: http://arxiv.org/abs/2310.02098