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1,914 results on '"Liu, Zhiyu"'

1. Castelnuovo bound for curves in projective 3-folds

Author

Liu, Zhiyu

Subjects
Mathematics - Algebraic Geometry, High Energy Physics - Theory, Mathematical Physics, Mathematics - Symplectic Geometry
Abstract

The Castelnuovo bound conjecture, which is proposed by physicists, predicts an effective vanishing result for Gopakumar-Vafa invariants of Calabi-Yau 3-folds of Picard number one. Previously, it is only known for a few cases and all the proofs rely on the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda. In this paper, we prove the Castelnuovo bound conjecture for any Calabi-Yau 3-folds of Picard number one, up to a linear term and finitely many degree, without assuming the conjecture of Bayer-Macr\`i-Toda. Furthermore, we prove an effective vanishing theorem for surface-counting invariants of Calabi-Yau 4-folds of Picard number one. We also apply our techniques to study low-degree curves on some explicit Calabi-Yau 3-folds. Our approach is based on a general iterative method to obtain upper bounds for the genus of one-dimensional closed subschemes in a fixed 3-fold, which is a combination of classical techniques and the wall-crossing of weak stability conditions on derived categories, and works for any projective 3-fold with at worst isolated singularities over any algebraically closed field., Comment: 39 pages. Comments are very welcome!

Published
2024

2. Atomic sheaves on hyper-K\'ahler manifolds via Bridgeland moduli spaces

Author

Guo, Hanfei and Liu, Zhiyu

Subjects
Mathematics - Algebraic Geometry
Abstract

In this paper, we provide new examples of 1-obstructed and atomic sheaves on an infinite series of locally complete families of projective hyper-K\"ahler manifolds. More precisely, (1) we prove that the fixed loci of the natural anti-symplectic involutions on the moduli spaces of stable objects in the Kuznetsov component $\mathcal{K}u(X)$ of a Gushel--Mukai fourfold $X$ are 1-obstructed Lagrangian submanifolds, (2) we construct a family of immersed atomic Lagrangian submanifolds on each moduli space of stable objects in $\mathcal{K}u(X)$, and (3) we construct non-rigid projectively hyperholomorphic twisted bundles on any hyper-K\"ahler manifold of $\mathrm{K3^{[n]}}$-type for infinitely many $n$. Additionally, we discuss examples of atomic Lagrangian submanifolds satisfying $b_1=20$ in a family of hyper-K\"ahler manifolds of $\mathrm{K3^{[2]}}$-type, as well as atomic sheaves supported on non-atomic Lagrangians., Comment: 40 pages. Comments are very welcome! Ver2: results on projectively hyperholomorphic bundles are added

Published
2024

3. Lagrangian families of Bridgeland moduli spaces from Gushel-Mukai fourfolds and double EPW cubes

Author

Feyzbakhsh, Soheyla, Guo, Hanfei, Liu, Zhiyu, and Zhang, Shizhuo

Subjects
Mathematics - Algebraic Geometry, Primary 14F08, secondary 14J42, 14J45, 14D20, 14D23
Abstract

Let $X$ be a very general Gushel-Mukai (GM) variety of dimension $n\geq 4$, and let $Y$ be a smooth hyperplane section. There are natural pull-back and push-forward functors between the semi-orthogonal components (known as the Kuznetsov components) of the derived categories of $X$ and $Y$. In the first part of the paper, we prove that the Bridgeland stability of objects is preserved by both pull-back and push-forward functors. We then explore various applications of this result, such as constructing an 8-dimensional smooth family of Lagrangian subvarieties for each moduli space of stable objects in the Kuznetsov component of a general GM fourfold, and proving the projectivity of the moduli spaces of semistable objects of any class in the Kuznetsov component of a general GM threefold, as conjectured by Perry, Pertusi, and Zhao. In the second part, we study in detail the double EPW cube, a 6-dimensional hyperk\"ahler manifold associated with a very general GM fourfold $X$, through the Bridgeland moduli space, and show that it is the maximal rationally connected (MRC) quotient of the Hilbert scheme of twisted cubics on $X$. We also prove that it admits a covering by Lagrangian subvarieties, constructed from the Hilbert schemes of twisted cubics on GM threefolds., Comment: 62 pages. Comments are very welcome! Ver2: results are generalized to general cases

Published
2024

4. Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descent

Author

Liu, Zhiyu, Han, Zhi, Tang, Yandong, Zhao, Xi-Le, and Wang, Yao

Subjects
Computer Science - Machine Learning, Mathematics - Optimization and Control, Statistics - Machine Learning
Abstract

This paper considers the problem of recovering a tensor with an underlying low-tubal-rank structure from a small number of corrupted linear measurements. Traditional approaches tackling such a problem require the computation of tensor Singular Value Decomposition (t-SVD), that is a computationally intensive process, rendering them impractical for dealing with large-scale tensors. Aim to address this challenge, we propose an efficient and effective low-tubal-rank tensor recovery method based on a factorization procedure akin to the Burer-Monteiro (BM) method. Precisely, our fundamental approach involves decomposing a large tensor into two smaller factor tensors, followed by solving the problem through factorized gradient descent (FGD). This strategy eliminates the need for t-SVD computation, thereby reducing computational costs and storage requirements. We provide rigorous theoretical analysis to ensure the convergence of FGD under both noise-free and noisy situations. Additionally, it is worth noting that our method does not require the precise estimation of the tensor tubal-rank. Even in cases where the tubal-rank is slightly overestimated, our approach continues to demonstrate robust performance. A series of experiments have been carried out to demonstrate that, as compared to other popular ones, our approach exhibits superior performance in multiple scenarios, in terms of the faster computational speed and the smaller convergence error., Comment: 13 pages, 4 figures

Published
2024

5. Gemini: A Family of Highly Capable Multimodal Models

Author

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, Rahimtoroghi, Elahe, Georgaki, Maria, Raul, Amit, Ruder, Sebastian, Redshaw, Morgan, Lee, Jinhyuk, Zhou, Denny, Jalan, Komal, Li, Dinghua, Hechtman, Blake, Schuh, Parker, Nasr, Milad, Milan, Kieran, Mikulik, Vladimir, Franco, Juliana, Green, Tim, Nguyen, Nam, Kelley, Joe, Mahendru, Aroma, Hu, Andrea, Howland, Joshua, Vargas, Ben, Hui, Jeffrey, Bansal, Kshitij, Rao, Vikram, Ghiya, Rakesh, Wang, Emma, Ye, Ke, Sarr, Jean Michel, Preston, Melanie Moranski, Elish, Madeleine, Li, Steve, Kaku, Aakash, Gupta, Jigar, Pasupat, Ice, Juan, Da-Cheng, Someswar, Milan, M., Tejvi, Chen, Xinyun, Amini, Aida, Fabrikant, Alex, Chu, Eric, Dong, Xuanyi, Muthal, Amruta, Buthpitiya, Senaka, Jauhari, Sarthak, Khandelwal, Urvashi, Hitron, Ayal, Ren, Jie, Rinaldi, Larissa, Drath, Shahar, Dabush, Avigail, Jiang, Nan-Jiang, Godhia, Harshal, Sachs, Uli, Chen, Anthony, Fan, Yicheng, Taitelbaum, Hagai, Noga, Hila, Dai, Zhuyun, Wang, James, Hamer, Jenny, Ferng, Chun-Sung, Elkind, Chenel, Atias, Aviel, Lee, Paulina, 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, and Vinyals, Oriol

Subjects
Computer Science - Computation and Language, Computer Science - Artificial Intelligence, Computer Science - Computer Vision and Pattern Recognition
Abstract

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 from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI.

Published
2023

6. Stability manifolds of Kuznetsov components of prime Fano threefolds

Author

Fan, Changping, Liu, Zhiyu, and Ma, Songtao Kenneth

Subjects
Mathematics - Algebraic Geometry
Abstract

Let $X$ be a cubic threefold, quartic double solid or Gushel--Mukai threefold, and $\mathcal{K}u(X)\subset \mathrm{D}^b(X)$ be its Kuznetsov component. We show that a stability condition $\sigma$ on $\mathcal{K}u(X)$ is Serre-invariant if and only if its homological dimension is at most $2$. As a corollary, we prove that all Serre-invariant stability conditions on $\mathcal{K}u(X)$ form a contractible connected component of the stability manifold., Comment: 19 pages, comments are very welcome!

Published
2023

7. New perspectives on categorical Torelli theorems for del Pezzo threefolds

Author

Feyzbakhsh, Soheyla, Liu, Zhiyu, and Zhang, Shizhuo

Subjects
Mathematics - Algebraic Geometry, Primary 14F05, secondary 14J45, 14D20, 14D23
Abstract

Let $Y_d$ be a del Pezzo threefold of Picard rank one and degree $d\geq 2$. In this paper, we apply two different viewpoints to study $Y_d$ via a particular admissible subcategory of its bounded derived category, called the Kuznetsov component: (i) Brill-Noether reconstruction. We show that $Y_d$ can be uniquely recovered as a Brill-Noether locus of Bridgeland stable objects in its Kuznetsov component. (ii) Exact equivalences. We prove that, up to composing with an explicit auto-equivalence, any Fourier-Mukai type equivalence of Kuznetsov components of two del Pezzo threefolds of degree $2\leq d\leq 4$ can be lifted to an equivalence of their bounded derived categories. As a result, we obtain a complete description of the group of Fourier-Mukai type auto-equivalences of the Kuznetsov component of $Y_d$. We also describe the group of Fourier-Mukai type auto-equivalences of Kuznetsov components of index one prime Fano threefolds $X_{2g-2}$ of genus $g=6$ and $8$. As an application, first we identify the group of automorphisms of $X_{14}$ and its associated $Y_3$. Then we give a new disproof of Kuznetsov's Fano threefold conjecture by assuming Gushel-Mukai threefolds are general. In an appendix, we classify instanton sheaves on quartic double solids, generalizing a result of Druel., Comment: 35 pages, added results on index one prime Fano threefolds and the application to Kuznetsov's Fano threefold conjecture. Comments are very welcome!

Published
2023

8. Analysis and Improvement Measures for a 66 kV Shunt Capacitor Fault

Author

He, Jianying, Tian, Qingyang, Liu, Zhiyu, Angrisani, Leopoldo, Series Editor, Arteaga, Marco, Series Editor, Chakraborty, Samarjit, Series Editor, Chen, Jiming, Series Editor, Chen, Shanben, Series Editor, Chen, Tan Kay, Series Editor, Dillmann, Rüdiger, Series Editor, Duan, Haibin, Series Editor, Ferrari, Gianluigi, Series Editor, Ferre, Manuel, Series Editor, Jabbari, Faryar, Series Editor, Jia, Limin, Series Editor, Kacprzyk, Janusz, Series Editor, Khamis, Alaa, Series Editor, Kroeger, Torsten, Series Editor, Li, Yong, Series Editor, Liang, Qilian, Series Editor, Martín, Ferran, Series Editor, Ming, Tan Cher, Series Editor, Minker, Wolfgang, Series Editor, Misra, Pradeep, Series Editor, Mukhopadhyay, Subhas, Series Editor, Ning, Cun-Zheng, Series Editor, Nishida, Toyoaki, Series Editor, Oneto, Luca, Series Editor, Panigrahi, Bijaya Ketan, Series Editor, Pascucci, Federica, Series Editor, Qin, Yong, Series Editor, Seng, Gan Woon, Series Editor, Speidel, Joachim, Series Editor, Veiga, Germano, Series Editor, Wu, Haitao, Series Editor, Zamboni, Walter, Series Editor, Tan, Kay Chen, Series Editor, Yang, Qingxin, editor, Li, Zewen, editor, and Luo, An, editor

Published
2024
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9. Research on Distributed Network Data Storage Security based on block chain

Author

Li, Qiuxiang, Liu, Zhiyu, Chen, Yanru, Zheng, Zheng, Editor-in-Chief, Xi, Zhiyu, Associate Editor, Gong, Siqian, Series Editor, Hong, Wei-Chiang, Series Editor, Mellal, Mohamed Arezki, Series Editor, Narayanan, Ramadas, Series Editor, Nguyen, Quang Ngoc, Series Editor, Ong, Hwai Chyuan, Series Editor, Sun, Zaicheng, Series Editor, Ullah, Sharif, Series Editor, Wu, Junwei, Series Editor, Zhang, Baochang, Series Editor, Zhang, Wei, Series Editor, Zhu, Quanxin, Series Editor, Zheng, Wei, Series Editor, Rauf, Abdul, editor, Zakuan, Norhayati, editor, Sohail, Muhammad Tayyab, editor, and Azmi, Ruzita, editor

Published
2024
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10. Forecasting Analysis of Guangzhou's Gross Domestic Product Based on ARIMA Model

Author

Peng, Minjing, Liu, Zhiyu, Zheng, Zheng, Editor-in-Chief, Xi, Zhiyu, Associate Editor, Gong, Siqian, Series Editor, Hong, Wei-Chiang, Series Editor, Mellal, Mohamed Arezki, Series Editor, Narayanan, Ramadas, Series Editor, Nguyen, Quang Ngoc, Series Editor, Ong, Hwai Chyuan, Series Editor, Sun, Zaicheng, Series Editor, Ullah, Sharif, Series Editor, Wu, Junwei, Series Editor, Zhang, Baochang, Series Editor, Zhang, Wei, Series Editor, Zhu, Quanxin, Series Editor, Zheng, Wei, Series Editor, Rauf, Abdul, editor, Zakuan, Norhayati, editor, Sohail, Muhammad Tayyab, editor, and Azmi, Ruzita, editor

Published
2024
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18. Flexoelectricity-stabilized ferroelectric phase with enhanced reliability in ultrathin La:HfO2 films

Author

Jiao, Peijie, Cheng, Hao, Li, Jiayi, Chen, Hongying, Liu, Zhiyu, Xi, Zhongnan, Ding, Wenjuan, Ma, Xingyue, Wang, Jian, Zheng, Ningchong, Nie, Yuefeng, Deng, Yu, Bellaiche, Laurent, Yang, Yurong, and Wu, Di

Subjects
Condensed Matter - Materials Science
Abstract

Doped HfO2 thin films exhibit robust ferroelectric properties even for nanometric thicknesses, are compatible with current Si technology and thus have great potential for the revival of integrated ferroelectrics. Phase control and reliability are core issues for their applications. Here we show that, in (111)-oriented 5%La:HfO2 (HLO) epitaxial thin films deposited on (La0.3Sr0.7)(Al0.65Ta0.35)O3 substrates, the flexoelectric effect, arising from the strain gradient along the films normal, induces a rhombohedral distortion in the otherwise Pca21 orthorhombic structure. Density functional calculations reveal that the distorted structure is indeed more stable than the pure Pca21 structure, when applying an electric field mimicking the flexoelectric field. This rhombohedral distortion greatly improves the fatigue endurance of HLO thin films by further stabilizing the metastable ferroelectric phase against the transition to the thermodynamically stable non-polar monoclinic phase during repetitive cycling. Our results demonstrate that the flexoelectric effect, though negligibly weak in bulk, is crucial to optimize the structure and properties of doped HfO2 thin films with nanometric thicknesses for integrated ferroelectric applications.

Published
2023
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19. Castelnuovo bound and higher genus Gromov-Witten invariants of quintic 3-folds

Author

Liu, Zhiyu and Ruan, Yongbin

Subjects
Mathematics - Algebraic Geometry, High Energy Physics - Theory, Mathematics - Symplectic Geometry, 14N35 (Primary), 14J33, 14H50, 14F08 (Secondary)
Abstract

We prove a conjectural vanishing result for Gopakumar--Vafa invariants of quintic 3-folds, referred to as Castelnuovo bound in the literature. Furthermore, we calculate Gopakumar--Vafa invariants at Castelnuovo bound $g=\frac{d^2+5d+10}{10}$. As physicists showed, these two properties allow us to compute all Gromov--Witten invariants of quintic 3-folds up to genus $53$, provided that the conifold gap condition holds. We also give a bound for the genus of any one-dimensional closed subscheme in a smooth hypersurface of degree $\leq 5$, which may be of independent interest., Comment: 31 pages. v2: minor changes, added more references and fixed some typos

Published
2022

20. Cutting sequence and Sturmian sequence in billiard

Author

Liu, Zhiyu

Subjects
Mathematics - Dynamical Systems
Abstract

The winning rule of billiards is to drive the billiard ball on the table into the designated holes. We try to study the trajectory of the billiard ball, so that we can predict the direction of the ball. For rational slopes, we got cutting sequence by setting up the square torus. We simplified cutting sequence using shearing and flipping and we obtain the transformation between trajectory slope and cutting sequence. For irrational slopes, we look at some properties of Sturmian sequence, which help us distinguish between cutting sequence and Sturmian sequence. In conclusion, in the case of different slopes, we use different sequences to do research., Comment: 29 pages,11 figures. arXiv admin note: text overlap with arXiv:1507.02571 by other authors

Published
2022

21. Brill--Noether theory for Kuznetsov components and refined categorical Torelli theorems for index one Fano threefolds

Author

Jacovskis, Augustinas, Liu, Zhiyu, and Zhang, Shizhuo

Subjects
Mathematics - Algebraic Geometry, 14F05, 14J45, 14D20, 14D23
Abstract

We show by a uniform argument that every index one prime Fano threefold $X$ of genus $g\geq 6$ can be reconstructed as a Brill--Noether locus inside a Bridgeland moduli space of stable objects in the Kuznetsov component $\mathcal{K}u(X)$. As an application, we prove refined categorical Torelli theorems for $X$ and compute the fiber of the period map for each Fano threefold of genus $g\geq 7$ in terms of a certain gluing object associated with the subcategory $\langle \mathcal{O}_X \rangle^{\perp}$. This unifies results of Mukai, Brambilla-Faenzi, Debarre-Iliev-Manivel, Faenzi-Verra, Iliev-Markushevich-Tikhomirov and Kuznetsov., Comment: 45 pages. Comments are very welcome!

Published
2022

22. Editorial – Ocean Dynamics in 2023: overview and thank you to reviewers

Author

Ezer, Tal, Bonaduce, Antonio, Carniel, Sandro, Amin, Chabchoub, de Camargo, Ricardo, Estrada-Allis, Sheila N., Fringer, Oliver B., Gangopadhyay, Avijit, Gao, Guoping, Greatbatch, Richard J., Lermusiaux, Pierre F. J., Liu, Zhiyu, Miyazawa, Yasumasa, Forster, Alejandro Orfila, Pinones, Andrea, Stanev, Emil, Sun, Chaojiao, Volker, Christoph, Wang, Jia, Xu, Fanghua, and Young, Emma

Published
2024
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23. Influencing factors and establishment of a prediction model for the tumor regression after neoadjuvant chemoradiotherapy in locally advanced rectal cancer

Author

LIU Zhiyu, XU Dong, CHEN Xihao, LI Jipeng

Subjects
rectal cancer, local advanced, neoadjuvant chemoradiotherapy, tumor regression prediction, Neoplasms. Tumors. Oncology. Including cancer and carcinogens, RC254-282
Abstract

Background and purpose: The standard therapy for locally advanced rectal cancer (LARC) is neoadjuvant chemoradiotherapy (nCRT) followed by surgery. NCRT can make the tumor regress and downstage, and increase the R0 resection rate. However, individual differences in rectal cancer are large, and some patients respond poorly to nCRT and cannot benefit from nCRT. Therefore, it is necessary to establish effective screening measures to identify patients with poor response to nCRT. This study aimed to analyze the influencing factors of nCRT for LARC and construct the tumor regression prediction model. Methods: Data of 158 LARC patients who underwent total mesenteric resection after receiving nCRT at the First Hospital Affiliated to Air Force Medical University from January 2016 to December 2020 were collected. Baseline clinical indicators before nCRT were collected, including laboratory examination, tumor markers and magnetic resonance imaging (MRI). According to the tumor size reported by MRI before and after nCRT, Response Evaluation Criteria in Solid Tumors (RECIST) was used to evaluate the extent of tumor regression after nCRT. After receiver operating characteristic (ROC) curve was used to standardize the clinical baseline indicators, logistic regression analysis was carried out to screen the factors affecting the tumor regression. The tumor regression prediction model was constructed by logistic regression, and the performance of the model was evaluated based on decision curve analysis (DCA) and the calibration curve. The accuracy of the model was tested by 10-fold cross-validation. Results: This retrospective cohort study enrolled 158 patients, in which, 98 patients achieved complete response (CR) or partial response (PR). The objective response rate was 62%. Sixty patients had poor response to nCRT, either stable disease (SD) or progressive disease (PD). Multivariate logistic regression analysis showed that tumor diameter before treatment (P

Published
2024
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24. Efficient textual explanations for complex road and traffic scenarios based on semantic segmentation

Author

Zhao, Yiyue, Yun, Xinyu, Chai, Chen, Liu, Zhiyu, Fan, Wenxuan, and Luo, Xiao

Subjects
Computer Science - Computer Vision and Pattern Recognition
Abstract

The complex driving environment brings great challenges to the visual perception of autonomous vehicles. It's essential to extract clear and explainable information from the complex road and traffic scenarios and offer clues to decision and control. However, the previous scene explanation had been implemented as a separate model. The black box model makes it difficult to interpret the driving environment. It cannot detect comprehensive textual information and requires a high computational load and time consumption. Thus, this study proposed a comprehensive and efficient textual explanation model. From 336k video frames of the driving environment, critical images of complex road and traffic scenarios were selected into a dataset. Through transfer learning, this study established an accurate and efficient segmentation model to obtain the critical traffic elements in the environment. Based on the XGBoost algorithm, a comprehensive model was developed. The model provided textual information about states of traffic elements, the motion of conflict objects, and scenario complexity. The approach was verified on the real-world road. It improved the perception accuracy of critical traffic elements to 78.8%. The time consumption reached 13 minutes for each epoch, which was 11.5 times more efficient than the pre-trained network. The textual information analyzed from the model was also accordant with reality. The findings offer clear and explainable information about the complex driving environment, which lays a foundation for subsequent decision and control. It can improve the visual perception ability and enrich the prior knowledge and judgments of complex traffic situations.

Published
2022

27. A moduli theoretic approach to Lagrangian subvarieties of hyperk\'ahler varieties: Examples

Author

Guo, Hanfei, Liu, Zhiyu, and Zhang, Shizhuo

Subjects
Mathematics - Algebraic Geometry, Primary 14F05, secondary 14J45, 14D20, 14D23
Abstract

We propose two conjectures on a moduli theoretic approach to constructing Lagrangian subvarieties of hyperk\"ahler varieties arising from the Kuznetsov components of cubic fourfolds or Gushel--Mukai fourfolds. Then we verify the conjectures in several cases, recovering classical examples. As a corollary, we confirm a conjecture of O'Grady in several instances on the existence of Lagrangian covering families for hyperk\"ahler varieties., Comment: 20 pages. Comments are welcome!

Published
2022

28. Infinitesimal categorical Torelli theorems for Fano threefolds

Author

Jacovskis, Augustinas, Lin, Xun, Liu, Zhiyu, and Zhang, Shizhuo

Subjects
Mathematics - Algebraic Geometry, Primary 14F05, secondary 14J45, 14D20, 14D23
Abstract

Let $X$ be a smooth Fano variety and $\mathcal{K}u(X)$ the Kuznetsov component. Torelli theorems for $\mathcal{K}u(X)$ says that it is uniquely determined by a polarized abelian variety attached to it. An infinitesimal Torelli theorem for $X$ says that the differential of the period map is injective. A categorical variant of infinitesimal Torelli theorem for $X$ says that the morphism $H^1(X,T_X)\xrightarrow{\eta} HH^2(\mathcal{K}u(X))$ is injective. In the present article, we use the machinery of Hochschild (co)homology to relate the three Torelli-type theorems for smooth Fano varieties via a commutative diagram. As an application, we first prove infinitesimal categorical Torelli theorem for a class of prime Fano threefolds. Then we prove a restatement of the Debarre-Iliev-Manivel conjecture infinitesimally., Comment: Correct typos, final version, to appear in Journal of Pure and Applied algebra. arXiv admin note: substantial text overlap with arXiv:2108.02946

Published
2022

29. Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces

Author

Guo, Hanfei, Liu, Zhiyu, and Zhang, Shizhuo

Subjects
Mathematics - Algebraic Geometry, Primary 14F05, secondary 14J45, 14D20, 14D23
Abstract

We identify the double dual EPW sextic $\widetilde{Y}_{A^{\perp}}$ and the double EPW sextic $\widetilde{Y}_A$, associated with a very general Gushel-Mukai fourfold $X$, with the Bridgeland moduli spaces of stable objects of character $\Lambda_1$ and $\Lambda_2$ in the Kuznetsov component $\mathcal{K}u(X)$. This provides an affirmative answer to a question of Perry-Pertusi-Zhao. As an application, we prove a conjecture of Kuznetsov-Perry for very general Gushel-Mukai fourfolds., Comment: 27 pages, made changes according to referee's suggestions. To appear in Math. Res. Lett. Comments are welcome!

Published
2022

36. Effect of Ultrasonic-Assisted Treatment on the Flavor and Quality of Fermented Mackerel Enzymatic Hydrolysate

Author

GUO Zhengchang, LIU Zhiyu, FANG Xubo, CHEN Xiao’e, ZHOU Xiaomin, LI Zhen, MA Yuqiao, CHEN Bei, GAO Xiaonan, YANG Huicheng

Subjects
mackerel, ultrasound-assisted treatment, enzymatic hydrolysate, fermentation, flavor quality, Food processing and manufacture, TP368-456
Abstract

In order to investigate the effect of ultrasound-assisted fermentation on its flavor and quality, mackerel enzymatic hydrolysate was, fermented with Saccharomyces longosporus to enhance the flavor, and flavor and quality changes during different fermentation stages were monitored by measurement of total bacterial count and amino acid nitrogent content, sensory evaluation, and principal component analysis (PCA) of electronic nose data. Meanwhile, nutritional evaluation of the fermented product was carried out by analysis of free and essential amino acid composition, and the composition of flavor compounds was analyzed by gas chromatography-ion mobility spectrometry (GC-IMS). It was found that PCA effectively distinguished the flavor differences between the ultrasound and control groups during the fermentation process. The total bacterial count, amino acid nitrogen content and sensory score of the ultrasound group were higher than those of the control group during the whole fermentation process. On day 12 of fermentation, the ultrasound group had the best flavor quality with a total bacterial count of 8.90 (lg(CFU/mL)) and an amino acid nitrogen content of 0.78 g/100 g, and the fermented product had a rich umami taste and a fruity aroma. Moreover, the content of total free amino acids in the fermented product was 6.373 g/100 g, and the essential amino acid index (EAAI) value was 82.90, indicating a high nutritional value. GC-IMS results showed that the contents of off-flavor compounds such as, saturated straight-chain aldehydes gradually decreased, or even disappeared after 12 days of fermentation. In contrast, the contents of unsaturated alcohols and aroma-active substances (ketones and esters) significantly increased in the ultrasonic group compared with the control group. Thus, ultrasound-assisted treatment could improve the flavor quality of fermented mackerel enzymatic hydrolysate. This study may provide a theoretical basis for the application of ultrasonic technology in the development of seafood seasoning.

Published
2023
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45. Categorical Torelli theorems for Gushel-Mukai threefolds

Author

Jacovskis, Augustinas, Lin, Xun, Liu, Zhiyu, and Zhang, Shizhuo

Subjects
Mathematics - Algebraic Geometry, Primary 14F08, secondary 14J45, 14D20, 14D22
Abstract

We show that a general ordinary Gushel-Mukai(GM) threefold $X$ is reconstructed from the Kuznetsov component $\mathcal{K}u(X)$ together with an extra data coming from tautological sub-bundle of Grassmannian $\mathrm{Gr}(2,5)$. We also prove that $\mathcal{K}u(X)$ determines birational isomorphism class of $X$, while $\mathcal{K}u(X')$ determines the isomorphism class of a general special GM threefold $X'$. As an application, we prove a conjecture of Kuznetsov-Perry in dimension three under a mild assumption. Finally, we use $\mathcal{K}u(X)$ to restate a conjecture of Debarre-Iliev-Manivel regarding fibers of the period map for ordinary GM threefolds., Comment: 39 pages, final version, to appear in Journal of the London Mathematical Society

Published
2021
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