Stability estimate for the Lane-Emden inequality

Autor: Carlen, Eric, Lewin, Mathieu, Lieb, Elliott H., Seiringer, Robert

The Lane-Emden inequality controls $\iint_{\mathbb{R}^{2d}}\rho(x)\rho(y)|x-y|^{-\lambda}\,dx\,dy$ in terms of the $L^1$ and $L^p$ norms of $\rho$. We provide a remainder estimate for this inequality in terms of a suitable distance of $\rho$ to the m

Externí odkaz: http://arxiv.org/abs/2410.20113

On an inequality of Lin, Kim and Hsieh and Strong Subadditivity

Autor: Carlen, Eric A., Loss, Michael P.

We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the non Neumann entropy.
Comment: This version corrects several typos, includes a short discussion of cases of equality, and corrects a small

Externí odkaz: http://arxiv.org/abs/2402.15920

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, Allan, FitzGerald, Nicholas, Gu-Lemberg, Keren, Khan, Mina, Hendricks, Lisa Anne, Pellat, Marie, Feinberg, Vladimir, Cobon-Kerr, James, Sainath, Tara, Rauh, Maribeth, Hashemi, Sayed Hadi, Ives, Richard, Hasson, Yana, Noland, Eric, Cao, Yuan, Byrd, Nathan, Hou, Le, Wang, Qingze, Sottiaux, Thibault, Paganini, Michela, Lespiau, Jean-Baptiste, Moufarek, Alexandre, Hassan, Samer, Shivakumar, Kaushik, van Amersfoort, Joost, Mandhane, Amol, Joshi, Pratik, Goyal, Anirudh, Tung, Matthew, Brock, Andrew, Sheahan, Hannah, Misra, Vedant, Li, Cheng, Rakićević, Nemanja, Dehghani, Mostafa, Liu, Fangyu, Mittal, Sid, Oh, Junhyuk, Noury, Seb, Sezener, Eren, Huot, Fantine, Lamm, Matthew, De Cao, Nicola, Chen, Charlie, Mudgal, Sidharth, Stella, Romina, Brooks, Kevin, Vasudevan, Gautam, Liu, Chenxi, Chain, Mainak, Melinkeri, Nivedita, Cohen, Aaron, Wang, Venus, Seymore, Kristie, Zubkov, Sergey, Goel, Rahul, Yue, Summer, Krishnakumaran, Sai, Albert, Brian, Hurley, Nate, Sano, Motoki, Mohananey, Anhad, Joughin, Jonah, Filonov, Egor, Kępa, Tomasz, Eldawy, Yomna, Lim, Jiawern, Rishi, Rahul, Badiezadegan, Shirin, Bos, Taylor, Chang, Jerry, Jain, Sanil, Padmanabhan, Sri Gayatri Sundara, Puttagunta, Subha, Krishna, Kalpesh, Baker, Leslie, Kalb, Norbert, Bedapudi, Vamsi, Kurzrok, Adam, Lei, Shuntong, Yu, Anthony, Litvin, Oren, Zhou, Xiang, Wu, Zhichun, Sobell, Sam, Siciliano, Andrea, Papir, Alan, Neale, Robby, Bragagnolo, Jonas, Toor, Tej, Chen, Tina, Anklin, Valentin, Wang, Feiran, Feng, Richie, Gholami, Milad, Ling, Kevin, Liu, Lijuan, Walter, Jules, Moghaddam, Hamid, Kishore, Arun, Adamek, Jakub, Mercado, Tyler, Mallinson, Jonathan, Wandekar, Siddhinita, Cagle, Stephen, Ofek, Eran, Garrido, Guillermo, Lombriser, Clemens, Mukha, Maksim, Sun, Botu, Mohammad, Hafeezul Rahman, Matak, Josip, Qian, Yadi, Peswani, Vikas, Janus, Pawel, Yuan, Quan, Schelin, Leif, David, Oana, Garg, Ankur, He, Yifan, Duzhyi, Oleksii, Älgmyr, Anton, Lottaz, Timothée, Li, Qi, Yadav, Vikas, Xu, Luyao, Chinien, Alex, Shivanna, Rakesh, Chuklin, Aleksandr, Li, Josie, Spadine, Carrie, Wolfe, Travis, Mohamed, Kareem, Das, Subhabrata, Dai, Zihang, He, Kyle, von Dincklage, Daniel, Upadhyay, Shyam, Maurya, Akanksha, Chi, Luyan, Krause, Sebastian, Salama, Khalid, Rabinovitch, Pam G, M, Pavan Kumar Reddy, Selvan, Aarush, Dektiarev, Mikhail, Ghiasi, Golnaz, Guven, Erdem, Gupta, Himanshu, Liu, Boyi, Sharma, Deepak, Shtacher, Idan Heimlich, Paul, Shachi, Akerlund, Oscar, Aubet, François-Xavier, Huang, Terry, Zhu, Chen, Zhu, Eric, Teixeira, Elico, Fritze, Matthew, Bertolini, Francesco, Marinescu, Liana-Eleonora, Bölle, Martin, Paulus, Dominik, Gupta, Khyatti, Latkar, Tejasi, Chang, Max, Sanders, Jason, Wilson, Roopa, Wu, Xuewei, Tan, Yi-Xuan, Thiet, Lam Nguyen, Doshi, Tulsee, Lall, Sid, Mishra, Swaroop, Chen, Wanming, Luong, Thang, Benjamin, Seth, Lee, Jasmine, Andrejczuk, Ewa, Rabiej, Dominik, Ranjan, Vipul, Styrc, Krzysztof, Yin, Pengcheng, Simon, Jon, Harriott, Malcolm Rose, Bansal, Mudit, Robsky, Alexei, 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, Carpenter, John, Papamakarios, George, Kemp, Rupert, Kafle, Sushant, Grunina, Tanya, Sinha, Rishika, Talbert, Alice, Wu, Diane, Owusu-Afriyie, Denese, Thornton, Chloe, Pont-Tuset, Jordi, Narayana, Pradyumna, Li, Jing, Fatehi, Saaber, Wieting, John, Ajmeri, Omar, Uria, Benigno, Ko, Yeongil, Knight, Laura, Héliou, Amélie, Niu, Ning, Gu, Shane, Pang, Chenxi, Li, Yeqing, Levine, Nir, Stolovich, Ariel, Santamaria-Fernandez, Rebeca, Goenka, Sonam, Yustalim, Wenny, Strudel, Robin, Elqursh, Ali, Deck, Charlie, Lee, Hyo, Li, Zonglin, Levin, Kyle, Hoffmann, Raphael, Holtmann-Rice, Dan, Bachem, Olivier, Arora, Sho, Koh, Christy, Yeganeh, Soheil Hassas, Põder, Siim, Tariq, Mukarram, Sun, Yanhua, Ionita, Lucian, Seyedhosseini, Mojtaba, Tafti, Pouya, Liu, Zhiyu, Gulati, Anmol, Liu, Jasmine, Ye, Xinyu, Chrzaszcz, Bart, Wang, Lily, Sethi, Nikhil, Li, Tianrun, Brown, Ben, Singh, Shreya, Fan, Wei, Parisi, Aaron, Stanton, Joe, Koverkathu, Vinod, Choquette-Choo, Christopher A., Li, Yunjie, Lu, TJ, Shroff, 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, Tekur, Chetan, Kale, Mihir Sanjay, Wei, Jinliang, Sang, Ruoxin, Saeta, Brennan, Liechty, Tyler, Sun, Yi, Zhao, Yao, Lee, Stephan, Nayak, Pandu, Fritz, Doug, Vuyyuru, Manish Reddy, Aslanides, John, Vyas, Nidhi, Wicke, Martin, Ma, Xiao, Eltyshev, Evgenii, Martin, Nina, Cate, Hardie, Manyika, James, Amiri, Keyvan, Kim, Yelin, Xiong, Xi, Kang, Kai, Luisier, Florian, Tripuraneni, Nilesh, Madras, David, Guo, Mandy, Waters, Austin, Wang, Oliver, Ainslie, Joshua, Baldridge, Jason, Zhang, Han, Pruthi, Garima, Bauer, Jakob, Yang, Feng, Mansour, Riham, Gelman, Jason, Xu, Yang, Polovets, George, Liu, Ji, Cai, Honglong, Chen, Warren, Sheng, XiangHai, Xue, Emily, Ozair, Sherjil, Angermueller, Christof, Li, Xiaowei, Sinha, Anoop, Wang, Weiren, Wiesinger, Julia, Koukoumidis, Emmanouil, Tian, Yuan, Iyer, Anand, Gurumurthy, Madhu, Goldenson, Mark, Shah, Parashar, Blake, MK, Yu, Hongkun, Urbanowicz, Anthony, Palomaki, Jennimaria, Fernando, Chrisantha, Durden, Ken, Mehta, Harsh, Momchev, Nikola, 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Listík, Vít, Carlen, Mathias, van de Kerkhof, Jan, Pikus, Marcin, Zaher, Krunoslav, Müller, Paul, Zykova, Sasha, Stefanec, Richard, Gatsko, Vitaly, Hirnschall, Christoph, Sethi, Ashwin, Xu, Xingyu Federico, Ahuja, Chetan, Tsai, Beth, Stefanoiu, Anca, Feng, Bo, Dhandhania, Keshav, Katyal, Manish, Gupta, Akshay, Parulekar, Atharva, Pitta, Divya, Zhao, Jing, Bhatia, Vivaan, Bhavnani, Yashodha, Alhadlaq, Omar, Li, Xiaolin, Danenberg, Peter, Tu, Dennis, Pine, Alex, Filippova, Vera, Ghosh, Abhipso, Limonchik, Ben, Urala, Bhargava, Lanka, Chaitanya Krishna, Clive, Derik, Li, Edward, Wu, Hao, Hongtongsak, Kevin, Li, Ianna, Thakkar, Kalind, Omarov, Kuanysh, Majmundar, Kushal, Alverson, Michael, Kucharski, Michael, Patel, Mohak, Jain, Mudit, Zabelin, Maksim, Pelagatti, Paolo, Kohli, Rohan, Kumar, Saurabh, Kim, Joseph, Sankar, Swetha, Shah, Vineet, Ramachandruni, Lakshmi, Zeng, Xiangkai, Bariach, Ben, Weidinger, Laura, Vu, Tu, Andreev, Alek, He, Antoine, Hui, Kevin, Kashem, Sheleem, Subramanya, 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

Dynamics and Quantum Optimal Transport: Three lectures on quantum entropy and quantum Markov semigroups

Autor: Carlen, Eric

This document presents the contents of three lectures delivered by the author at the Erd\H{o}s Center School ``Optimal Transport on Quantum Structures'', Septemer 19-23, 2022 in Budapest, Hungary. It presents a fairly self contained account of an act

Externí odkaz: http://arxiv.org/abs/2306.10903

Spectrum for some Quantum Markov semigroups describing $N$-particle systems evolving under a binary collision mechanism

Autor: Carlen, Eric A., Loss, Michael P.

We compute the spectrum for a class of quantum Markov semigroups describing systems of $N$ particle interacting through a binary collision mechanism. These quantum Markov semgroups are associated to a novel kind of quantum random walk on graphs, with

Externí odkaz: http://arxiv.org/abs/2204.07860