ogaude/glyphfix-math-lora
Image-Text-to-Text • 4B • Updated • 9
Datasets:
id string | image image | latex string | target_text string | arxiv_id string | paper_version string | title string | authors list | license_spdx string | license_uri string | arxiv_url string | flags list | image_sha256 string | bitmap_sha256 string | width int32 | height int32 | group string | mining_class string | control_glyph string | tags list |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
00012d2ae7ebbf59 | 1 + \Psi_N(z) = \prod_{a\in A_{+,N}} \left(1+\frac{z}{a}\right), | ```latex
1 + \Psi_N(z) = \prod_{a\in A_{+,N}} \left(1+\frac{z}{a}\right),
``` | 2502.01109 | v2 | Geometric Gauss Sums and Gross-Koblitz Formula over Function Fields | [
"Ting-Wei Chang"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2502.01109v2 | [
"greek"
] | 3d5e5ac931de73b8894019b9e133c72a4eee3b3f2e9c179fb996d78481f34512 | 6e4084603e209c111d303b2d1b931655f4a476fc99fc54918da53b4c0dcf4cb9 | 637 | 146 | replay | null | null | [] | |
0011d5084cd2b0a6 | R_{\mathbf{A}} (\mathbf{x}) = \frac{\mathbf{x}^T\mathbf{A}\mathbf{x}}{\mathbf{x}^T \mathbf{x}}. | ```latex
R_{\mathbf{A}} (\mathbf{x}) = \frac{\mathbf{x}^T\mathbf{A}\mathbf{x}}{\mathbf{x}^T \mathbf{x}}.
``` | 2510.06653 | v2 | Mass-Lumped Virtual Element Method with Strong Stability-Preserving Runge-Kutta Time Stepping for Two-Dimensional Parabolic Problems | [
"Paulo Akira F. Enabe",
"Rodrigo Provasi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2510.06653v2 | [
"decoration"
] | 8bde201e83b0229a44b9cce7c03906606bdc580afa81c369607a26fcab32cd1a | 8a5602dbd7b3cca29a28eceb2cf31a29e36a16d323b4df7f14c218b582bb2654 | 370 | 129 | replay | null | null | [] | |
00135fe5d87a2d47 | \mathcal{R}_{p,s}(\Omega)\le C \tau_\Omega^{p-\frac{D}{s}}. | ```latex
\mathcal{R}_{p,s}(\Omega)\le C \tau_\Omega^{p-\frac{D}{s}}.
``` | 2607.08405 | v1 | A capacitary approach to Lyapunov-type inequalities for elliptic problems on weighted graphs | [
"Mohamed Jleli",
"Bessem Samet"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2607.08405v1 | [
"greek",
"decoration"
] | bf4ff891a7a5eba93e6736a3b3b8ba33116b42a37f1f49d25bedb67e224d60a1 | 478b9ba1ba22f4dd05fc0eb91278f398e8d2711febc88c3f9c0b38787478418c | 405 | 95 | replay | null | null | [] | |
00183339db9cc34d | \mu_{xy}^{(k)}(\mathcal M^+)-\mu_{xy}^{(k)}(\mathcal M^-) &= x^\top \left(\mathcal M_{\bullet,\bullet,k}^{+,(d)} -\mathcal M_{\bullet,\bullet,k}^{-,(d)}\right)y = (\gamma_{\max}-\gamma_{\min})x^\top x\, y^\top y = \gamma_{\max}-\gamma_{\min}. | ```latex
\mu_{xy}^{(k)}(\mathcal M^+)-\mu_{xy}^{(k)}(\mathcal M^-) &= x^\top \left(\mathcal M_{\bullet,\bullet,k}^{+,(d)} -\mathcal M_{\bullet,\bullet,k}^{-,(d)}\right)y = (\gamma_{\max}-\gamma_{\min})x^\top x\, y^\top y = \gamma_{\max}-\gamma_{\min}.
``` | 2607.06330 | v2 | Estimation of Linear Functionals in Multilayer Panels under Staggered Adoption | [
"Alberto Bordino",
"Thomas B. Berrett",
"Olga Klopp"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2607.06330v2 | [
"greek",
"decoration"
] | 60fb0f4af89ae8275e29401a1da09806c87e217b8f0fe13e6eb46bc2fdbf5864 | 710a979b3378cecaf05347611a59db7ab128e276ba6c44e5e0caa532e3d0a044 | 1,899 | 110 | replay | null | null | [] | |
002356381808df66 | |g^\top \Phi_{\mathrm{up}} \, y| & \le c_1 \frac{\sigma^2 \sqrt{T(r + \zeta_N)}}{\gamma_\mathrm{min} \, \rho_N^{1/2}} \, \|g\|_2 \, + c_1 \, \frac{\sigma \sqrt{r + \zeta_N}}{\gamma_\mathrm{min} \, \rho_N^{1/2}} \|W_{\mathrm{up}}^\top g\|_2 + c_1 \frac{\sigma^2 T}{\gamma_\mathrm{min}\, \rho_N^{1/2}} \, \|g\|_2 \, \|V^\t... | ```latex
|g^\top \Phi_{\mathrm{up}} \, y| & \le c_1 \frac{\sigma^2 \sqrt{T(r + \zeta_N)}}{\gamma_\mathrm{min} \, \rho_N^{1/2}} \, \|g\|_2 \, + c_1 \, \frac{\sigma \sqrt{r + \zeta_N}}{\gamma_\mathrm{min} \, \rho_N^{1/2}} \|W_{\mathrm{up}}^\top g\|_2 + c_1 \frac{\sigma^2 T}{\gamma_\mathrm{min}\, \rho_N^{1/2}} \, \|g\|_2 ... | 2607.06330 | v2 | Estimation of Linear Functionals in Multilayer Panels under Staggered Adoption | [
"Alberto Bordino",
"Thomas B. Berrett",
"Olga Klopp"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2607.06330v2 | [
"greek",
"decoration"
] | a60a779223d38bbe318237372fbe32ff32f48b0a016d73b6f179431817c29a6c | 6ecf5f6d7988297912d166ecbfdb0735c2aeb952204f29fe43aa940870c4b963 | 1,814 | 313 | error | decoration | null | [] | |
00283378bcd16f4f | O^{st}_x(f):=\sum_{x \sim_{st}x'/\sim}O_{x'}(f) | ```latex
O^{st}_x(f):=\sum_{x \sim_{st}x'/\sim}O_{x'}(f)
``` | 2510.07845 | v1 | A description of the depth-$r$ Bernstein center for rational depths | [
"Sarbartha Bhattacharya",
"Tsao-Hsien Chen"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2510.07845v1 | [
"prime"
] | 16f48e1dacd74e1bf55ea22aeb305c207e39389d106dc10598693a5eb1ba1a45 | d9efd3521070dffee0017f07677153629b93440e0d94b38a408b857920bc96da | 529 | 137 | replay | null | null | [] | |
003f1172525fd091 | \widetilde{f}: \widetilde{\mathcal{M}} \to \widetilde{\mathcal{T}}, | ```latex
\widetilde{f}: \widetilde{\mathcal{M}} \to \widetilde{\mathcal{T}},
``` | 2412.19052 | v3 | A Novel Double Periodic Conformal Flattening Algorithm for Genus-One Surfaces | [
"Zhong-Heng Tan",
"Tiexiang Li",
"Wen-Wei Lin",
"Lok Ming Lui"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2412.19052v3 | [
"decoration"
] | 4c9e1573ca19aac976657734e646bdc630120192eac3a4729c835ed3884ac384 | 53c4610629dafd3a18ae503691034f18e3ed410fc14aca671a7bb5426faf0032 | 276 | 81 | replay | null | null | [] | |
0041aac22cf71844 | b^d-a^d=(b-a)(b^{d-1}+b^{d-2}a+\dots+ba^{d-2}+a^{d-1}) | ```latex
b^d-a^d=(b-a)(b^{d-1}+b^{d-2}a+\dots+ba^{d-2}+a^{d-1})
``` | 2501.13780 | v2 | Matrix Completion in Group Testing: Bounds and Simulations | [
"Trung-Khang Tran",
"Thach V. Bui"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2501.13780v2 | [
"plain"
] | 5a4a500ae6ebfd73dfbd09cb3284abee2e558447811991e7cd37ee630b74e248 | d485847bab6c2b02ca1604c04d1d5b6f7696b3c7f44675c8175f244e91bc92cf | 1,109 | 77 | replay | null | null | [] | |
00447d1570e1e196 | \frac{d}{dt}(M_{1,0} + M_{0,1}) = 0. | ```latex
\frac{d}{dt}(M_{1,0} + M_{0,1}) = 0.
``` | 2604.07793 | v1 | Error Analysis of a Conforming FEM for Multidimensional Fragmentation Equations | [
"Arushi",
"Naresh Kumar"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2604.07793v1 | [
"plain"
] | 65cec31c97c4094d5d8696bb21d482e1990da04c823ffab40fd2316ed60eb4c4 | 6b4841b6d3aef9e4535b864d7690c566d77b0a4c6f3c5f08646a7622e5f674b7 | 455 | 124 | replay | null | null | [] | |
004a67ab97eeb799 | \partial_t\varphi(t_0,x_0,y_0) + \mathcal Q^\star[\varphi](t_0,x_0,y_0)>0 . | ```latex
\partial_t\varphi(t_0,x_0,y_0) + \mathcal Q^\star[\varphi](t_0,x_0,y_0)>0 .
``` | 2505.08989 | v5 | Agency Problems and Adversarial Bilevel Optimization under Uncertainty and Cyber Threats | [
"Thibaut Mastrolia",
"Haoze Yan"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2505.08989v5 | [
"greek",
"decoration"
] | 6f96641f00350d66a77858b74cbdaa200e6b2681b5d5840df28d08e63a76c87e | 4a7ea98bbac5524e95fc9246e1fd208202637fab129b8147271a0f6136c7f5bb | 791 | 71 | error | decoration | null | [] | |
004e8f86b197a332 | \Big(-\!\!\!\!\!\!\!\int_{B_{3r}(g_0)}|u|^{p_0}\Big)^{1/p_0}\leq c_0\,\inf_{B_{r}}u. | ```latex
\Big(-\!\!\!\!\!\!\!\int_{B_{3r}(g_0)}|u|^{p_0}\Big)^{1/p_0}\leq c_0\,\inf_{B_{r}}u.
``` | 2506.07521 | v1 | Critical singular problems in Carnot groups | [
"Stefano Biagi",
"Mattia Galeotti",
"Eugenio Vecchi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2506.07521v1 | [
"plain"
] | 59f0fb48d00469d3387b9975226fd13a9b376031b832cbe6ab54c4473260b335 | 60a60117a54beb98b7dbde45d5ddfd465dd14e0de7f5be645163bdc76880a52d | 626 | 143 | error | other | null | [] | |
005a66415788c202 | z_1>s+\frac{|z|^2-s^2}{2(R+s)}. | ```latex
z_1>s+\frac{|z|^2-s^2}{2(R+s)}.
``` | 2602.22027 | v2 | Range expansion by growth and congestion | [
"Henri Berestycki",
"Antoine Mellet"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2602.22027v2 | [
"plain"
] | 5189b2c397773840a399ce9e8c2cde5726275d2439a26d59aaf15a078ab50d45 | 0ff1c03dd864cf44bc4e773ad3a74705cc7f6ea393bcdfedc0769f23bf6fa6c2 | 412 | 142 | replay | null | null | [] | |
00604037f4953b0e | \sqrt{1+\beta(\widetilde \sigma_i)^2 \sigma_t^2} + \alpha(\widetilde \sigma_i) \sigma_t \le \sqrt{1+ \frac{\tau(b)^4}{64b^4} \frac{\sigma_t^2}{\widetilde\sigma_i^2}} + \tau(b)\frac{\sigma_t}{\widetilde\sigma_i} \le 1+\tau(b)\left(1 +\frac{\tau(b)}{8b^2} \right)\frac{\sigma_t}{\widetilde \sigma_i} | ```latex
\sqrt{1+\beta(\widetilde \sigma_i)^2 \sigma_t^2} + \alpha(\widetilde \sigma_i) \sigma_t \le \sqrt{1+ \frac{\tau(b)^4}{64b^4} \frac{\sigma_t^2}{\widetilde\sigma_i^2}} + \tau(b)\frac{\sigma_t}{\widetilde\sigma_i} \le 1+\tau(b)\left(1 +\frac{\tau(b)}{8b^2} \right)\frac{\sigma_t}{\widetilde \sigma_i}
``` | 2403.09170 | v3 | Analysis of singular subspaces under random perturbations | [
"Ke Wang"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2403.09170v3 | [
"greek",
"decoration"
] | f87c71857f8e40ebda96cbd7ab10f667b68c1243cea5ad8fa705d0f68da6f70f | e5eb52a7d319cfe6d8dfa45e551f1d3283ab9a73a1cf703668fcf1b3b290a289 | 1,669 | 170 | replay | null | null | [] | |
006aca23f24d4d52 | \sum \limits_i \tilde{d}_i = \sum \limits_{i \in S^C} \tilde{d}_i + \sum \limits_{i \in S} \tilde{d}_i = \sum \limits_{i \in S^C}d_i + \sum \limits_{i \in S}a. | ```latex
\sum \limits_i \tilde{d}_i = \sum \limits_{i \in S^C} \tilde{d}_i + \sum \limits_{i \in S} \tilde{d}_i = \sum \limits_{i \in S^C}d_i + \sum \limits_{i \in S}a.
``` | 2510.06653 | v2 | Mass-Lumped Virtual Element Method with Strong Stability-Preserving Runge-Kutta Time Stepping for Two-Dimensional Parabolic Problems | [
"Paulo Akira F. Enabe",
"Rodrigo Provasi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2510.06653v2 | [
"decoration"
] | 2bf22e58a2b80d373ceccf5ecaf8da6b7b3ecec6a1cc0267136a064e558450cf | c1fdc647598a26bf4c096d1bb937a164e08679f42b61f741adb71e61a3d17259 | 889 | 132 | replay | null | null | [] | |
006b095ca7fa9b48 | T_{i,j}f(x) =x_i\frac{\partial f}{\partial x_j}-x_j\frac{\partial f}{\partial x_i}. | ```latex
T_{i,j}f(x) =x_i\frac{\partial f}{\partial x_j}-x_j\frac{\partial f}{\partial x_i}.
``` | 2604.26728 | v2 | $\mathcal H$-Harmonic Bergman-Besov Spaces on the Real Hyperbolic Ball | [
"A. Ersin Üreyen"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2604.26728v2 | [
"plain"
] | 9900954d2ef9f8357f684c23dfc74569dd221d9128a0b70314e88be50c7f89f2 | 274a980a66e4f47d6ecf2904f6d8976892b084a043161d0451c0a9ce8e789e39 | 572 | 138 | replay | null | null | [] | |
007baffda9bd2167 | \begin{gathered} \mathbb{E}\Biggl[F(X_1,\dots,X_n)\prod_{i=0}^{m}\biggl(\mathop{\diamond}_{j=1}^N Z_{Ni+j}\biggr)\Biggr]\\ \qquad{}=\mathbb{E}\Biggl[F(X_1,\dots,X_n)\mathop{\diamond}_{j=1}^N Z_{Nm+j}\prod_{i=0}^{m-1}\biggl(\mathop{\diamond}_{j=1}^N Z_{Ni+j}\biggr)\Biggr]. \end{gathered} | ```latex
\begin{gathered} \mathbb{E}\Biggl[F(X_1,\dots,X_n)\prod_{i=0}^{m}\biggl(\mathop{\diamond}_{j=1}^N Z_{Ni+j}\biggr)\Biggr]\\ \qquad{}=\mathbb{E}\Biggl[F(X_1,\dots,X_n)\mathop{\diamond}_{j=1}^N Z_{Nm+j}\prod_{i=0}^{m-1}\biggl(\mathop{\diamond}_{j=1}^N Z_{Ni+j}\biggr)\Biggr]. \end{gathered}
``` | 2507.23737 | v3 | Renormalisation of Singular SPDEs with Correlated Coefficients | [
"Nicolas Clozeau",
"Harprit Singh"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2507.23737v3 | [
"decoration"
] | 4e526fa9a1ebb9bbe9df189bee0b7f9f5015f6bed5281551fe4d86e728b09695 | 6b73deae3c8686694330131aa74d83eb7b2fa59525a3206e6cc6947b520e2c9b | 1,051 | 338 | error | other | null | [] | |
007fa825ff3e90bd | \begin{aligned} h(\ell)^2 |w_{\ell,\delta}|_{H^2(\Omega)}^2 &\lesssim h(\ell)^2 \left( |w_{\ell,\delta} - w_\delta|_{H^2(\Omega)}^2 + |w_\delta|_{H^2(\Omega)}^2 \right) \\ &\lesssim h(\ell)^2 \left( \left( \tilde \beta_\ell^{[3,2,2]} \right)^2 |w_\delta|_{H^3(\Omega)}^2 + \frac{1}{\delta^2} \right) \\ &\lesssim h(\ell)... | ```latex
\begin{aligned} h(\ell)^2 |w_{\ell,\delta}|_{H^2(\Omega)}^2 &\lesssim h(\ell)^2 \left( |w_{\ell,\delta} - w_\delta|_{H^2(\Omega)}^2 + |w_\delta|_{H^2(\Omega)}^2 \right) \\ &\lesssim h(\ell)^2 \left( \left( \tilde \beta_\ell^{[3,2,2]} \right)^2 |w_\delta|_{H^3(\Omega)}^2 + \frac{1}{\delta^2} \right) \\ &\lesssi... | 2507.03521 | v2 | PINN-DG: Residual neural network methods trained with Finite Elements | [
"Georgios Grekas",
"Charalambos G. Makridakis",
"Tristan Pryer"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2507.03521v2 | [
"greek",
"decoration"
] | 2f61799158625fc068f4d572f47341dc53206a7c053042112a17e97192d698e1 | bb0bdb312ffaaa1487707ee31ab0095e2acfec730117608679e1d06bd1a4a7b5 | 1,135 | 473 | replay | null | null | [] | |
008845d6cc5230fe | T_N = \{ t_n \mid t_n = T (n/N)^r, \; 0\le n \le N\} | ```latex
T_N = \{ t_n \mid t_n = T (n/N)^r, \; 0\le n \le N\}
``` | 2602.08325 | v1 | A numerical study for tempered time-fractional advection-dispersion equation on graded meshes | [
"Liangcai Huang",
"Lin Li",
"Shujuan Lü"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2602.08325v1 | [
"plain"
] | 124e9d209125714920abc3825e8bdb1a35d93caf3f78da260dc110d35ae67c10 | e106b9052ca6ea54f3625f0bd0f9c52f335fe2708bbb380e5a3997e9ac40d79c | 837 | 71 | error | other | null | [
"spacing_only"
] | |
008cb2114eaf1f0a | D_{kl}=\ell'_l(\xi_k), \quad 0\leqslant k,l \leqslant p, | ```latex
D_{kl}=\ell'_l(\xi_k), \quad 0\leqslant k,l \leqslant p,
``` | 2203.11184 | v2 | A discontinuous Galerkin spectral element method for a nonconservative compressible multicomponent flow model | [
"Rémi Abgrall",
"Pratik Rai",
"Florent Renac"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2203.11184v2 | [
"prime",
"greek"
] | 3c9e8bb9d255b22633ae2d76992950d1aca104fbb1bb948450f70e67c5779c91 | 68407ea765eef60ece107ab044a5eb193f5d17434d998c4387ba6fcff6c18b9f | 597 | 73 | error | dropped_prime | null | [] | |
009ad747e41db053 | \left\vert a_{n}\left( J_{0},J_{n}\right) \right\vert & \leq\sum _{\substack{J_{1}J_{2},...,J_{n-1}\in\mathcal{G}\\J_{k-1}\neq J_{k}for1\leq k\leq n}}\left\vert \left\langle h_{J_{0};\kappa}^{\eta},h_{J_{1};\kappa }^{\eta}\right\rangle \left\langle h_{J_{1};\kappa}^{\eta},h_{J_{2};\kappa }^{\eta}\right\rangle ...\left\... | ```latex
\left\vert a_{n}\left( J_{0},J_{n}\right) \right\vert & \leq\sum _{\substack{J_{1}J_{2},...,J_{n-1}\in\mathcal{G}\\J_{k-1}\neq J_{k}for1\leq k\leq n}}\left\vert \left\langle h_{J_{0};\kappa}^{\eta},h_{J_{1};\kappa }^{\eta}\right\rangle \left\langle h_{J_{1};\kappa}^{\eta},h_{J_{2};\kappa }^{\eta}\right\rangle ... | 2411.18457 | v8 | A comparison of trilinear testing conditions for the paraboloid Fourier extension and Kakeya conjectures in three dimensions | [
"Eric T. Sawyer"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2411.18457v8 | [
"greek",
"decoration",
"i_1"
] | 3daeb3e1e07b7dbf8a62e832b32e66fe5cc95341e677baa692ea907d87395130 | 0361bdfdab8cde674681ced9f7cd08e61cb6ec482c833893e34c6087c48aa706 | 1,627 | 387 | error | symbol_swap | null | [] | |
00ac07181660e411 | A(x) = |\{1\leq q \leq x \mid s_q \neq 0\}| \sim \frac{\alpha x}{\sqrt{\log x}}, | ```latex
A(x) = |\{1\leq q \leq x \mid s_q \neq 0\}| \sim \frac{\alpha x}{\sqrt{\log x}},
``` | 2506.07474 | v1 | Erdős-Kac type theorem for the number of scattering geodesics on modular surface | [
"Sudhir Pujahari",
"Punya Plaban Satpathy"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2506.07474v1 | [
"greek"
] | 17c93a2e3e512eeec9d8469c77d5c56f087566344d5ba02dc03a40ae79304955 | ff5886a5a5baf3e53de6ff592db716cb08e490d95c0662aee7a21b076d6df2e3 | 873 | 123 | replay | null | null | [] | |
00b142e10f4f4e8d | \hat{T}_{X,j,k} \equiv \max\{ -\hat{t}_X(j), \hat{t}_X(k) \} ,\quad \hat{T}_{Y,j,k} \equiv \max\{ \hat{t}_Y(j), -\hat{t}_Y(k) \} , | ```latex
\hat{T}_{X,j,k} \equiv \max\{ -\hat{t}_X(j), \hat{t}_X(k) \} ,\quad \hat{T}_{Y,j,k} \equiv \max\{ \hat{t}_Y(j), -\hat{t}_Y(k) \} ,
``` | 2501.05338 | v1 | Comparing latent inequality with ordinal data | [
"David M. Kaplan",
"Wei Zhao"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2501.05338v1 | [
"decoration"
] | 6fcdae6de67b4cb371c31cac3ac969f38cb0e36d8a47844ef5a5ca1db6351eb2 | b2bc308b764b94c18abfb316a2ed13bdea24771b56ebbc79220301a06dbcbe92 | 1,305 | 82 | replay | null | null | [] | |
00ba0a75ddb17f74 | \begin{array}{lcl} x & = & (i_1,j_1)\otimes (i_2,j_2)\otimes \ldots \otimes (i_p,j_p)\otimes S_B((r,s)) \\ y & = & (k_1,\ell_1)\otimes (k_2,\ell_2)\otimes \ldots \otimes (k_p,\ell_p)\otimes S_B((t,u)) \end{array} | ```latex
\begin{array}{lcl} x & = & (i_1,j_1)\otimes (i_2,j_2)\otimes \ldots \otimes (i_p,j_p)\otimes S_B((r,s)) \\ y & = & (k_1,\ell_1)\otimes (k_2,\ell_2)\otimes \ldots \otimes (k_p,\ell_p)\otimes S_B((t,u)) \end{array}
``` | 2110.06404 | v3 | The Sierpinski Carpet as a Final Coalgebra | [
"Victoria Noquez",
"Lawrence S. Moss"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2110.06404v3 | [
"plain"
] | 807a26705399c94f233d2165b045a64c75ee0934e270fe6a63816fe95eedf1dc | d4d7764b995a93b39fde2a699915858ba7d3e34b2402b960f9928194aa75eb02 | 1,104 | 133 | error | other | null | [] | |
00bae81080ea3a6b | \frac{d}{dt}\int_{\Omega}u|\mathbf{x}|^{2}\,dx = & -2\int_{\Omega}\nabla u\cdot\nabla x\,dx + 2\chi\int_{\Omega}x\cdot(u\chi(x)\nabla(K_{2}\ast u))\,dx \\ = & -2\int_{\partial\Omega}u(x\cdot\nu)\,dx + 4\int_{\Omega}u\,dx + 2\chi\int_{\Omega}x\cdot u\chi(x)\int_{\Omega}\frac{-1}{2\pi}\frac{x-y}{|x-y|^{2}}u\,dy\,dx \\ = ... | ```latex
\frac{d}{dt}\int_{\Omega}u|\mathbf{x}|^{2}\,dx = & -2\int_{\Omega}\nabla u\cdot\nabla x\,dx + 2\chi\int_{\Omega}x\cdot(u\chi(x)\nabla(K_{2}\ast u))\,dx \\ = & -2\int_{\partial\Omega}u(x\cdot\nu)\,dx + 4\int_{\Omega}u\,dx + 2\chi\int_{\Omega}x\cdot u\chi(x)\int_{\Omega}\frac{-1}{2\pi}\frac{x-y}{|x-y|^{2}}u\,dy\... | 2603.08070 | v1 | Chemotaxis with tomography | [
"Valeria Cuentas",
"Elio Espejo"
] | CC0-1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | https://arxiv.org/abs/2603.08070v1 | [
"greek",
"decoration",
"i_1"
] | dda5e8bdfafb59b524397c679accfea65f3f942d46cb9592c9b16e094ea71371 | eede5d10dcfb70a16b2e3518d226078d5ecb29f9052e4e28ccdbbe3a1e247ac6 | 1,837 | 371 | error | symbol_swap | null | [] | |
00bee7e4110111e9 | g_t(\theta) \triangleq \left(r_t + \gamma \langle \phi(s_{t+1}), \theta \rangle - \langle \phi(s_{t}), \theta \rangle\right) \phi(s_t), \forall \theta \in \mathbb{R}^K. | ```latex
g_t(\theta) \triangleq \left(r_t + \gamma \langle \phi(s_{t+1}), \theta \rangle - \langle \phi(s_{t}), \theta \rangle\right) \phi(s_t), \forall \theta \in \mathbb{R}^K.
``` | 2502.04662 | v1 | Adversarially-Robust TD Learning with Markovian Data: Finite-Time Rates and Fundamental Limits | [
"Sreejeet Maity",
"Aritra Mitra"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2502.04662v1 | [
"greek",
"decoration"
] | 708986b936158b671d45f2cb1811642364b159ae2d8efe117e7b09f8c00ec1cd | e363cf7a7673acf3613301e8b758dcd82f2d2a0981faf6cf551185e8d8f619e6 | 1,162 | 76 | replay | null | null | [] | |
00c031edbf330175 | K' = \{ c_{i_1}c_{i_2} \cdots c_{i_m} - \mathcal{N}( c_{i_1}c_{i_2} \cdots c_{i_m}) \,|\, m \le d_0, c_i \in J(\mathfrak{g}) \} | ```latex
K' = \{ c_{i_1}c_{i_2} \cdots c_{i_m} - \mathcal{N}( c_{i_1}c_{i_2} \cdots c_{i_m}) \,|\, m \le d_0, c_i \in J(\mathfrak{g}) \}
``` | 2402.00483 | v4 | Gelfand-Tsetlin modules for Lie algebras of rank $2$ | [
"Milica Anđelić",
"Carlos M. da Fonseca",
"Vyacheslav Futorny",
"Andrew Tsylke"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2402.00483v4 | [
"prime",
"decoration"
] | 1b34eb8f250da42a59d2669ff71c38fcd769f91042b277d1ebf2fd10fdf1f542 | 3eeb5a089de14a5532058d278646114a6fada459b845d174d81cc3fc68d1d73f | 1,219 | 72 | error | symbol_swap | null | [] | |
00ce00fbbc29a6b5 | f(P) = \sum_{i,j,r,s=1}^n a_{ijrs} p_{ij} p_{rs} + \sum_{i,j=1}^n b_{ij} p_{ij} + c. | ```latex
f(P) = \sum_{i,j,r,s=1}^n a_{ijrs} p_{ij} p_{rs} + \sum_{i,j=1}^n b_{ij} p_{ij} + c.
``` | 2406.19377 | v2 | Grassmannian optimization is NP-hard | [
"Zehua Lai",
"Lek-Heng Lim",
"Ke Ye"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2406.19377v2 | [
"plain"
] | c6c79156fa435221d966d5eb8944be16893d28797d606d8985e5a01ae7339e25 | b032ff3104270a65494f02368722975d9b5b67ecf1b078c88cf33a0ddc9d47f9 | 881 | 162 | control | null | 1 | [] | |
00d2941c87ec744c | \mathrm{II}_{\Sigma_T} \geq\frac{7}{8T\max_{\Sigma_T}N}\,h_T>0. | ```latex
\mathrm{II}_{\Sigma_T} \geq\frac{7}{8T\max_{\Sigma_T}N}\,h_T>0.
``` | 2609.10160 | v1 | Integral of Scalar Curvature under Volume Collapse | [
"Guoyi Xu"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2609.10160v1 | [
"greek",
"decoration"
] | 36b427aba23c0ebfafb2315f87915bdbeebbc0be834f8a7cfd899322792abe59 | 96773b3361b94ed3a610799a2e28212d59617b9220fa88b7e080ce35e0fb12ad | 611 | 135 | error | greek_latin | null | [] | |
00d479ccd5908dd5 | \displaystyle H''_{x\mu}(t)\tilde \mu(t)=\sum_{i=1}^{n_c}\nabla_x c_i(t)\tilde\mu_i(t), | ```latex
\displaystyle H''_{x\mu}(t)\tilde \mu(t)=\sum_{i=1}^{n_c}\nabla_x c_i(t)\tilde\mu_i(t),
``` | 2605.06991 | v1 | A Semi-smooth Newton Method for the Constrained Optimal Control of Continuous-Time Linear Systems | [
"Simon J. Jones",
"Dominic Liao-McPherson",
"Marco M. Nicotra"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2605.06991v1 | [
"prime",
"greek",
"decoration"
] | b17c34369c5f847d608514b658064176a454d35de54da0066d2d737bed6b5249 | f8263fb9c1eb4c66d12c54bffaf9c3538cd4a6a0e9fb8244bf1d834cfb20f796 | 651 | 156 | replay | null | null | [] | |
00d53492c9814c21 | z_{i+1} &= b_{i+1} (-1)^{i+2} \langle L w_{i+1}, z_{i+1} \rangle^{-1} w_{i+1} - b_{i+1} (-1)^{i+1} \langle L w_i, z_i \rangle^{-1} w_i \\ &= b_i (-1)^{i-1} \langle L w_{i-1}, z_i \rangle^{-1} w_{i-1} + c_i (-1)^{i+1} \langle L w_i, z_i \rangle^{-1} w_i. | ```latex
z_{i+1} &= b_{i+1} (-1)^{i+2} \langle L w_{i+1}, z_{i+1} \rangle^{-1} w_{i+1} - b_{i+1} (-1)^{i+1} \langle L w_i, z_i \rangle^{-1} w_i \\ &= b_i (-1)^{i-1} \langle L w_{i-1}, z_i \rangle^{-1} w_{i-1} + c_i (-1)^{i+1} \langle L w_i, z_i \rangle^{-1} w_i.
``` | 2412.01475 | v2 | Planar radial mean bodies are convex | [
"J. Haddad"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2412.01475v2 | [
"plain"
] | aa96e56ef3e5944c60f6d5c7cb6dfb2765b94f50d6555a9b58d1651fbcf79dd5 | de34c9d2a117c5456ae3b33951da5eda538ce20d55e185f4b681c0b145ea82ab | 1,390 | 154 | replay | null | null | [] | |
00e202da73666897 | I:=\big[-c_{e}\|u_{0}\|_{H^{4}({\mathbb R}^{d})}-c_{e}, \ c_{e}\|u_{0}\|_{H^{4}({\mathbb R}^{d})}+c_{e}\big], \quad 5\leq d\leq 7 | ```latex
I:=\big[-c_{e}\|u_{0}\|_{H^{4}({\mathbb R}^{d})}-c_{e}, \ c_{e}\|u_{0}\|_{H^{4}({\mathbb R}^{d})}+c_{e}\big], \quad 5\leq d\leq 7
``` | 2603.07804 | v1 | Solvability of a class of integro-differential equations with Laplace and bi-Laplace operators | [
"Vitali Vougalter",
"Vitaly Volpert"
] | CC0-1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | https://arxiv.org/abs/2603.07804v1 | [
"decoration",
"i_1"
] | 0ac0ea2b136e604d60bd175f7f96a49f376df8fd844fde67fafd5433dd88b5b6 | a4bc361b20b6c67eace7a350a77e5b977f873b8e5e5b5eaed1e545ab127acc9c | 1,254 | 81 | error | other | null | [] | |
00e7e91eee4b9c18 | \mathcal{C}_L := C_o \circ \text{bl}_L \circ \text{bl}_{L-1} \cdots \circ \text{bl}_1 \circ \sigma \circ C_i | ```latex
\mathcal{C}_L := C_o \circ \text{bl}_L \circ \text{bl}_{L-1} \cdots \circ \text{bl}_1 \circ \sigma \circ C_i
``` | 2507.03521 | v2 | PINN-DG: Residual neural network methods trained with Finite Elements | [
"Georgios Grekas",
"Charalambos G. Makridakis",
"Tristan Pryer"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2507.03521v2 | [
"greek",
"decoration"
] | 3b4327b4c3e2b39b4aa83cc1794fb1e9346d48dd924a32e7ba2c2be887cdf038 | e723f43ba4ba57b7b6b92ee878a8f980b05b3037e24cedf2838232fac8505eba | 822 | 65 | error | decoration | null | [] | |
00e7f897f408d2e4 | \hspace{0.1cm} & \frac{\vert \mathcal{S}_0 \vert}{n}\displaystyle\sum_{x^\ell \in \mathcal{D}^{\mathcal{P}}_1} \min(0,\beta^\top x^{\ell}) - \frac{\vert \mathcal{S}_1 \vert}{n}\displaystyle\sum_{x^\ell \in \mathcal{D}^{\mathcal{P}}_0} \min(0,\beta^\top x^{\ell}) \leq c \\ &\frac{\vert \mathcal{S}_0 \vert}{n}\displaysty... | ```latex
\hspace{0.1cm} & \frac{\vert \mathcal{S}_0 \vert}{n}\displaystyle\sum_{x^\ell \in \mathcal{D}^{\mathcal{P}}_1} \min(0,\beta^\top x^{\ell}) - \frac{\vert \mathcal{S}_1 \vert}{n}\displaystyle\sum_{x^\ell \in \mathcal{D}^{\mathcal{P}}_0} \min(0,\beta^\top x^{\ell}) \leq c \\ &\frac{\vert \mathcal{S}_0 \vert}{n}\d... | 2412.01585 | v3 | FairML: A Julia Package for Fair Classification | [
"Jan Pablo Burgard",
"João Vitor Pamplona"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2412.01585v3 | [
"greek",
"decoration"
] | c9b0fce6dda9e2aa6d35532abb4e0146eadcba74e5fedb25aa357c8993dc9b38 | aac9770e2f65800f46ff05de29920dfcf85417ec4451c3298221e6747309adfb | 1,175 | 334 | error | decoration | null | [] | |
00f3f9a92c90ca1b | x_{i+1}^j-x_{i}^j+w_l \leq w_{s}. | ```latex
x_{i+1}^j-x_{i}^j+w_l \leq w_{s}.
``` | 2502.04586 | v1 | Automatic Ply Partitioning for Laminar Composite Process Planning | [
"Eric Garner",
"Amir Mirzendehdel"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2502.04586v1 | [
"plain"
] | 4c0698089f95bda775a18c7c39e047eb34ec0e8319dc1b2e3bd08201a638f3e5 | f64fd4ff93b4a4738b7eeda4f08477b9b30c5726a9e965cfe826bc0b8c42a022 | 450 | 82 | replay | null | null | [] | |
01013f10dcf530fd | N^{\rm wor}_{p,q}(\mathcal{P}_{n})\asymp n^{d(1/p-1/q)_{+}}, | ```latex
N^{\rm wor}_{p,q}(\mathcal{P}_{n})\asymp n^{d(1/p-1/q)_{+}},
``` | 2507.06505 | v1 | Average Nikolskii factors for random diffusion polynomials on closed Riemannian manifolds | [
"Yun Ling",
"Heping Wang"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2507.06505v1 | [
"decoration"
] | 5e438f66e4673a6aaf2d5cad2c4361766f35a7246ef15c1a36ed5947a0d21f85 | 7569112385414844f13e388f287e5742c78f808265dbb85936b5c8442d848255 | 528 | 85 | replay | null | null | [] | |
010304b196f7ea95 | &(q-1)\sum_{j\in J}\int_{\Omega}\frac{(a(x)+u_{n}^{q})}{(1+u_{n})^{q}}\vert D_{j}u_{n}\vert^{p_{j}}\\&\qquad+\sum_{j\in J}\int_{\Omega}b(x)\frac{u_{n}\vert D_{j}u_{n}\vert^{p_{j}}}{\left(u_{n}+\frac{1}{n}\right)^{\theta+1}}\left[1-(1+u_{n})^{1-q}\right]\\ &\quad=\int_{\Omega} f_{n}\left[1-(1+u_{n})^{1-q}\right]. | ```latex
&(q-1)\sum_{j\in J}\int_{\Omega}\frac{(a(x)+u_{n}^{q})}{(1+u_{n})^{q}}\vert D_{j}u_{n}\vert^{p_{j}}\\&\qquad+\sum_{j\in J}\int_{\Omega}b(x)\frac{u_{n}\vert D_{j}u_{n}\vert^{p_{j}}}{\left(u_{n}+\frac{1}{n}\right)^{\theta+1}}\left[1-(1+u_{n})^{1-q}\right]\\ &\quad=\int_{\Omega} f_{n}\left[1-(1+u_{n})^{1-q}\right... | 2512.08391 | v1 | A Class of Non-linear Anisotropic Elliptic problems with Unbounded Coefficients and Singular Quadratic Lower Order Terms | [
"Fessel Achhoud",
"Hichem Khelifi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2512.08391v1 | [
"greek"
] | 791c70d7c42d1c0909f634fa588cf9fa02801bd1b1cd62fc7892f104865a1fbe | 3eb48f14d1fea9e0d1cf5c6b9b188c079c02b0e4ee35dac2882eb0023644f501 | 1,030 | 448 | error | symbol_swap | null | [] | |
0107bd486644b38f | \frac{(z,q^2/z,q^2;q^2)_\infty}{(z,q/z,q;q)_\infty}=\frac{1}{(zq,q/z,q;q^2)_\infty}~, | ```latex
\frac{(z,q^2/z,q^2;q^2)_\infty}{(z,q/z,q;q)_\infty}=\frac{1}{(zq,q/z,q;q^2)_\infty}~,
``` | 2507.06294 | v1 | Argyres-Douglas Theories, Macdonald Indices and Arc Space of Zhu Algebra | [
"George Andrews",
"Anindya Banerjee",
"Chinmaya Bhargava",
"Ranveer Kumar Singh",
"Runkai Tao"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2507.06294v1 | [
"plain"
] | 01def2e508985946809396c0d8d91cf0e02cf62cbc05668a88fdd93cc3e4872f | 3689ce8383f84c8643c210597c8b37a3bff79b499dcabd753131a4fc8b8d4eaf | 800 | 142 | error | other | null | [
"spacing_only"
] | |
010a900c95a12bf1 | {\cal H}'=U{\cal H}U^{-1}-i\hbar U\frac{ \partial U^{-1}}{\partial t}. | ```latex
{\cal H}'=U{\cal H}U^{-1}-i\hbar U\frac{ \partial U^{-1}}{\partial t}.
``` | 2408.01770 | v3 | Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian | [
"Alexander J. Silenko"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2408.01770v3 | [
"prime"
] | 2946cf7aa6940e2be58a3c3b7b1492161f1f74f4c5f59f49325d296c138cd3af | 945ba0e147327d2e1a62341e94f188ba43e9b819a9cdd31be1aaad44f3634f40 | 582 | 130 | replay | null | null | [] | |
010ab699e72247a4 | \min_x \quad \frac{1}{2}\| A x - b \|_2^2 + \lambda \| x \|_1, | ```latex
\min_x \quad \frac{1}{2}\| A x - b \|_2^2 + \lambda \| x \|_1,
``` | 2601.07628 | v3 | D-PDLP: Scaling PDLP to Distributed Multi-GPU Systems | [
"Hongpei Li",
"Yicheng Huang",
"Huikang Liu",
"Dongdong Ge",
"Yinyu Ye"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2601.07628v3 | [
"greek"
] | 8ce1b8ec9f2fd01625d71f9f935ea0a8514a80b1700bd7d120f6a2341dd30ee9 | 899e36af382738459c008ff8ff2d9c2c756ef656b2eb6eb97cc46a0ab201f7bd | 603 | 122 | replay | null | null | [] | |
010fce0e44d345f1 | G_{ij}(\mathbf r) = \delta_{ij}\Psi(r) - \partial_i\partial_j\Phi(r) + \varepsilon_{ij}\chi(r), | ```latex
G_{ij}(\mathbf r) = \delta_{ij}\Psi(r) - \partial_i\partial_j\Phi(r) + \varepsilon_{ij}\chi(r),
``` | 2603.07830 | v1 | Force Dipole Interactions in Membranes with Odd Viscosity | [
"Sneha Krishnan",
"Udaya Maurya",
"Rickmoy Samanta"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2603.07830v1 | [
"greek",
"decoration"
] | bae75350c54b298d17464bd0bbaf1a8cb88f7e0ab2fea5a0b3a6dc77d7f0a4f3 | 8405e7daf2ca9df54c8a7101c5c81f49c46c7dd4e8cdd4b7110dae53ab1aba31 | 821 | 73 | replay | null | null | [] | |
011f61b05172874d | s: \mathcal{O}_{\mathbb{P}(\mathcal{K}_d)}(-1) \otimes T_{\mathbb{P}^2} & \to \Omega_{\mathbb{P}^2}(d) \\ \lambda B_\ell \otimes v &\mapsto \lambda B_\ell(v,-) | ```latex
s: \mathcal{O}_{\mathbb{P}(\mathcal{K}_d)}(-1) \otimes T_{\mathbb{P}^2} & \to \Omega_{\mathbb{P}^2}(d) \\ \lambda B_\ell \otimes v &\mapsto \lambda B_\ell(v,-)
``` | 2405.11943 | v2 | Chow ring of the stack of plane nodal curves | [
"Alessio Cela",
"Ajith Urundolil Kumaran",
"Xiaohan Yan"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2405.11943v2 | [
"greek",
"decoration"
] | 4f1a2445cadbc9bb5b6a278a1c2461e58ce53a61fc7f447e1204e78ed1e7ad71 | 59d96fab78452791ccea6b80c89a3a1b5fef8b455a45acfafd77a70975d39e3d | 727 | 144 | control | null | \ell | [] | |
01240109c2aa7aa6 | p_t \le \frac{\mathrm{OPT}_{n,t}}{n\,\Delta_g(\gamma_t-\eta_t;D_t)}\,\delta_t + \frac{L_g\,\eta_t}{\Delta_g(\gamma_t-\eta_t;D_t)}. | ```latex
p_t \le \frac{\mathrm{OPT}_{n,t}}{n\,\Delta_g(\gamma_t-\eta_t;D_t)}\,\delta_t + \frac{L_g\,\eta_t}{\Delta_g(\gamma_t-\eta_t;D_t)}.
``` | 2604.07744 | v1 | The Condition-Number Principle for Prototype Clustering | [
"Romano Li",
"Jianfei Cao"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2604.07744v1 | [
"greek",
"decoration"
] | 4d175a10dbe1995a1774871da43c001f66dde38d72f36f427449a35ca3859743 | 0c5601707c5268eb76a49e93d65ab139f146a694691f6fba51d7e2cd18a7489a | 931 | 139 | error | decoration | null | [] | |
012db42e7f06f127 | x_{k + 1} \coloneqq x_k - \eta_k\nabla f(x_k), \qquad (\eta_k > 0: \text{step size}), | ```latex
x_{k + 1} \coloneqq x_k - \eta_k\nabla f(x_k), \qquad (\eta_k > 0: \text{step size}),
``` | 2602.08618 | v1 | Nesterov's accelerated gradient for unbounded convex functions finds the minimum-norm point in the dual space | [
"Keiya Sakabe"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2602.08618v1 | [
"greek"
] | b9d23bc3efcb77a3147ba75a5c0d4d33ee004e71946b7ba4f2e36530fbc8ecb6 | 84a9dc8f98de1b921c95a76b22a65319045d109f6dd6814ba82ee24b6fca8aa2 | 1,026 | 71 | error | symbol_swap | null | [] | |
0138fb4d9c0647d3 | H_n(S^1 \times B^3) \cong \begin{cases} \mathbb{Z} & n = 0,1 \\ 0 & \text{otherwise }\\ \end{cases} | ```latex
H_n(S^1 \times B^3) \cong \begin{cases} \mathbb{Z} & n = 0,1 \\ 0 & \text{otherwise }\\ \end{cases}
``` | 2306.14442 | v2 | Topology Estimation of Simulated 4D Image Data by Combining Downscaling and Convolutional Neural Networks | [
"Khalil Mathieu Hannouch",
"Stephan Chalup"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2306.14442v2 | [
"decoration"
] | 56ed5971760302633c9122f674053fc19caac7967932e8efa0d7186b3452b18a | bb8c620145f8d02e4130a0ff5954eaf82cc6dcfc69cb09cb90aba079590ec8ef | 681 | 170 | error | other | null | [] | |
01393751494e2fa1 | r^{-d/2-\beta}\cdot (2t_{\max})^2\cdot \bigg(\frac{Z \log(1/r)}{2t_{\max} - 2t_{\min}}\bigg)^2\cdot (r^{-d/2-\beta})^2 \bigg(\frac{Z \log(1/r)}{2t_{\max} - 2t_{\min}}\bigg)^2=o(1). | ```latex
r^{-d/2-\beta}\cdot (2t_{\max})^2\cdot \bigg(\frac{Z \log(1/r)}{2t_{\max} - 2t_{\min}}\bigg)^2\cdot (r^{-d/2-\beta})^2 \bigg(\frac{Z \log(1/r)}{2t_{\max} - 2t_{\min}}\bigg)^2=o(1).
``` | 2512.04191 | v2 | Sharp thresholds, hitting times and the power of choice for random geometric graphs | [
"Dawid Ignasiak",
"Lyuben Lichev"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2512.04191v2 | [
"greek"
] | d96c1c742e9cb458adf1fcf8eaf74c2a0f80060ba6b8373fb0b4ed22aca3f11d | e27c67915767d4055aa5a8fd31e68b10f97589eac97f6984f7b15b1c3a0e4c43 | 1,577 | 149 | error | other | null | [] | |
01485d8faf9a7228 | A(N) = \begin{pmatrix} 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 \\ 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\ 1... | ```latex
A(N) = \begin{pmatrix} 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 \\ 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0... | 2507.06927 | v1 | Walk Matrix-Based Upper Bounds on Generalized Cospectral Mates | [
"Muhammad Raza",
"Mudassir Shabbir",
"Waseem Abbas"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2507.06927v1 | [
"plain"
] | b115754ba2d286fd6ff508b1825f8e27fcc4a19adacf647e8fee439f039b5e5d | 5c390f7f754eda6abd0065b4abd56d453fcb6a551a67112fdd8c1c9d761f2a13 | 829 | 558 | replay | null | null | [] | |
015dbb9bba99b046 | \nabla^2G(\mathbf{x}) = \delta(\mathbf{x}), | ```latex
\nabla^2G(\mathbf{x}) = \delta(\mathbf{x}),
``` | 2512.08555 | v1 | A scalable high-order multigrid-FFT Poisson solver for unbounded domains on adaptive multiresolution grids | [
"Gilles Poncelet",
"Jonathan Lambrechts",
"Thomas Gillis",
"Philippe Chatelain"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2512.08555v1 | [
"greek",
"decoration"
] | 498a1559053e562c1f93b62f0b7e59dac0191e91c7064a8e3318fbebb679e029 | 8380f9dce189fe1ca33a5df5432e808f6ff5b09b5d61d9e0f6cca5f1cfadda12 | 351 | 76 | replay | null | null | [] | |
015e408413410b66 | \begin{aligned} & \min_{\theta \in \mathcal{D}} ~ \mathcal{S}_\mathcal{T}(\theta): l(\theta; u^*_{\theta})=\frac{1}{\mathcal{T}} \sum_{i=1}^\mathcal{T} \Vert \Tilde{u}^p(i) - u^*_{\theta} \Vert_2^2 \\ & ~s.t. ~~ u^*_{\theta} = \arg \min_{u} J(u;\theta). \end{aligned} | ```latex
\begin{aligned} & \min_{\theta \in \mathcal{D}} ~ \mathcal{S}_\mathcal{T}(\theta): l(\theta; u^*_{\theta})=\frac{1}{\mathcal{T}} \sum_{i=1}^\mathcal{T} \Vert \Tilde{u}^p(i) - u^*_{\theta} \Vert_2^2 \\ & ~s.t. ~~ u^*_{\theta} = \arg \min_{u} J(u;\theta). \end{aligned}
``` | 2409.10884 | v2 | 3DIOC: Direct Data-Driven Inverse Optimal Control for LTI Systems | [
"Chendi Qu",
"Jianping He",
"Xiaoming Duan"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2409.10884v2 | [
"greek",
"decoration"
] | f279dc226f5dac0ed8eadb70fdfe3a80c2b35e8355ee51ba3be61e4a2450b807 | 1354a00fba496c4e75ad2ca1fba5fd5cf29e16abccab5aa29cdbc5ba91b66aa0 | 916 | 258 | error | decoration | null | [] | |
015ede55c2b23487 | \frac{\partial}{\partial z}I_{x,\tilde{z}}\simeq\frac{I_{x,\tilde{z}+\Delta} - I_{x,\tilde{z}-\Delta}}{2\Delta}. | ```latex
\frac{\partial}{\partial z}I_{x,\tilde{z}}\simeq\frac{I_{x,\tilde{z}+\Delta} - I_{x,\tilde{z}-\Delta}}{2\Delta}.
``` | 2510.02989 | v3 | Transport of Event Equation: Phase Retrieval from Defocus Events | [
"Kaito Hori",
"Chihiro Tsutake",
"Keita Takahashi",
"Toshiaki Fujii"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2510.02989v3 | [
"greek",
"decoration",
"i_1"
] | 79a4d90c24b1cd316130c9df81272fccbce636cb98d4ed0e89d38535376addf4 | 7e1db35080bc6b3b777b8bdfa14e112394b4ae2337cb4e55dedc3c2c60627783 | 553 | 125 | replay | null | null | [] | |
0170992b0bff7cb9 | R = w_q \cdot Q_{ortho} + w_b \cdot B_{split} + R_{progress} - P_{penalty} | ```latex
R = w_q \cdot Q_{ortho} + w_b \cdot B_{split} + R_{progress} - P_{penalty}
``` | 2606.10601 | v1 | Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation | [
"Anirudh Kalyan",
"Cosmin Anitescu",
"Xiaoying Zhuang",
"Timon Rabczuk",
"Somdatta Goswami",
"Sundararajan Natarajan"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2606.10601v1 | [
"plain"
] | 334d15097ef6b9654ef9834edc05c5bc974bc35ce5245db02ca19520f70b32f1 | a2feb177303b21577dbe79af545d78b56bd71c3803cfd59acbf19daaddd3e8d6 | 1,036 | 71 | replay | null | null | [] | |
0174ff23d73cd71b | \begin{aligned} \mathcal{I}_{1} &= \int_{\mathbb{R}^{N}}\chi_{R}u\Delta k \, dx + \int_{\mathbb{R}^N}k u \Delta \chi_{R} \, dx + 2\int_{\mathbb{R}^{N}}u \langle \nabla k, \nabla \chi_{R}\rangle \, dx\\ &=:\mathcal{I}'_{1} + \mathcal{I}''_{1} + \mathcal{I}'''_{1}. \end{aligned} | ```latex
\begin{aligned} \mathcal{I}_{1} &= \int_{\mathbb{R}^{N}}\chi_{R}u\Delta k \, dx + \int_{\mathbb{R}^N}k u \Delta \chi_{R} \, dx + 2\int_{\mathbb{R}^{N}}u \langle \nabla k, \nabla \chi_{R}\rangle \, dx\\ &=:\mathcal{I}'_{1} + \mathcal{I}''_{1} + \mathcal{I}'''_{1}. \end{aligned}
``` | 2605.07911 | v1 | Blow-up of solutions to semilinear parabolic equations driven by mixed local-nonlocal operators with large initial data | [
"Stefano Biagi",
"Fabio Punzo",
"Eugenio Vecchi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2605.07911v1 | [
"prime",
"greek",
"decoration",
"i_1"
] | 6a048e9288c4e7f444048ef9c9d1569ff49f5ec967bfd1403e86ef01d41702e6 | 50bf211ccc9e574fde6ba252f7f0244cc1cb938b4d491feb8f69332a020d16de | 1,310 | 204 | replay | null | null | [] | |
017a666dabd7419d | \frac{\mathrm{ord}_x(a_{-u_s})-\mathrm{ord}_x(a_{-m_s})}{u_s-m_s}\geq\frac{\mathrm{ord}_x(a_{-m_s})-\mathrm{ord}_x(a_{-m_{s-1}})}{m_s-m_{s-1}}. | ```latex
\frac{\mathrm{ord}_x(a_{-u_s})-\mathrm{ord}_x(a_{-m_s})}{u_s-m_s}\geq\frac{\mathrm{ord}_x(a_{-m_s})-\mathrm{ord}_x(a_{-m_{s-1}})}{m_s-m_{s-1}}.
``` | 2511.18809 | v2 | Comparison between formal slopes and p-adic slopes | [
"Yezheng Gao"
] | CC0-1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | https://arxiv.org/abs/2511.18809v2 | [
"decoration"
] | 90b391c10e080d30b7c83c34e370e6f5a05a2254684d98b752fefab5a822a46a | 37f54f7441d3a05a5872a723575371fee917574082ab5beb8d1e0ccbaf7b0838 | 1,196 | 135 | replay | null | null | [] | |
018264182c823f0d | K_m(A, r_0) = \text{span} \{v_1, v_2, \dots, v_m\}, | ```latex
K_m(A, r_0) = \text{span} \{v_1, v_2, \dots, v_m\},
``` | 2508.05793 | v1 | On the Choice of Subspace for the Quasi-minimal Residual Method for Linear Inverse Problems | [
"Moshen Hu",
"Lucas Onisk"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2508.05793v1 | [
"plain"
] | df7119e901e6b8d7ed12a6190142f9b933cbfd18e8a7b3756a2e5182e40fa094 | 88194dad9c7d69d57c15472036da481219ec9bc46d5d9ced8bed0abdce106c3d | 729 | 71 | replay | null | null | [] | |
01928a537ea10bd2 | |x(t)| \leq C_T|x(s)| \quad \mbox{ for } \quad e_{\ast}\leq s\leq t. | ```latex
|x(t)| \leq C_T|x(s)| \quad \mbox{ for } \quad e_{\ast}\leq s\leq t.
``` | 2411.05765 | v1 | Uniform $h$-dichotomies: noncritical uniformity and expansivity | [
"Heli Elorreaga",
"Juan Peña",
"Gonzalo Robledo"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2411.05765v1 | [
"plain"
] | c0bff9b2d199c6efa8e07a1e8c766027f9efcfd3f2ed5ac8a3abd2c476ea5448 | d518c0b1b78a7891cc0d09286aa49a5f6726f86e1b38128ba2d5be24334a5d87 | 785 | 71 | error | symbol_swap | null | [] | |
01a9640162102125 | J_{k-1}(y) \ll_{k} y^{k-1} \hspace{10pt} \text{ for } \hspace{10pt} y > 0. | ```latex
J_{k-1}(y) \ll_{k} y^{k-1} \hspace{10pt} \text{ for } \hspace{10pt} y > 0.
``` | 2410.16921 | v2 | Trace formula and functional equation | [
"Chung-Hang Kwan",
"Wing Hong Leung"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2410.16921v2 | [
"plain"
] | 9400cce21ea9b7d05ceedfb29ef240b2039c1b85b874ec1cb9ea30cc46eb8604 | 736dd1731dddcc13b508a9ec18ac12d9ec17d79b117dcfc721b2dcc1fc457f17 | 663 | 76 | error | other | null | [] | |
01ae61a56f71a936 | I,\quad ST^i\,(0\leq i<N),\quad ST^nST^i\,(n\in\mathscr{N},\,0\leq i<N/(N,n^2)). | ```latex
I,\quad ST^i\,(0\leq i<N),\quad ST^nST^i\,(n\in\mathscr{N},\,0\leq i<N/(N,n^2)).
``` | 2506.16823 | v2 | Correspondence among congruence families for generalized Frobenius partitions via modular permutations | [
"Rong Chen",
"Xiao-Jie Zhu"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2506.16823v2 | [
"decoration",
"i_1"
] | f6776c899895a36df56a94ed772077567d2c6d21025b8ada1496b146ef20a1e9 | 86aeff60bcb55791b2b60de55e7a0cb5df012ed5812872b3c7e039c8ddc338e4 | 1,331 | 76 | error | decoration | null | [] | |
01c743ecb6f7844b | \frac{\partial\mathcal{L}}{\partial\nabla_j\varphi^i} = \frac{\partial}{\partial\nabla_j\varphi^i} \left(-\rho_o W(\rho_o,J)\right) = \left(-\rho_o\frac{\partial W}{\partial J}\right) \left(\frac{\partial J}{\partial\nabla_j\varphi^i}\right). | ```latex
\frac{\partial\mathcal{L}}{\partial\nabla_j\varphi^i} = \frac{\partial}{\partial\nabla_j\varphi^i} \left(-\rho_o W(\rho_o,J)\right) = \left(-\rho_o\frac{\partial W}{\partial J}\right) \left(\frac{\partial J}{\partial\nabla_j\varphi^i}\right).
``` | 2512.08841 | v1 | Space-time discretization for barotropic flow stemming from a multisymplectic variational formulation | [
"Mukthesh Mahadev",
"Marc Gerritsma"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2512.08841v1 | [
"greek",
"decoration"
] | a0a3a2de1568495c57830d1c93f46fcf7b0b9982ddaad898926aa7257505e420 | 7c009eac57f6b7038f38e6ef47ff0eedc7d4b5cca30407bc67f0a542e99ae7d4 | 1,244 | 141 | replay | null | null | [] | |
01cc3b7ee7ff3b02 | k_i^{(m)} = k_j^{(m)} \,\,\,\forall m, \,\forall i,j \in C_a. | ```latex
k_i^{(m)} = k_j^{(m)} \,\,\,\forall m, \,\forall i,j \in C_a.
``` | 2510.11207 | v2 | Fibration Symmetries and Cluster Synchronization in Multi-Body Systems | [
"Margherita Bertè",
"Tommaso Gili"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2510.11207v2 | [
"plain"
] | 86e513e1e459c5087d3c1462192b1f2bd19d8bd7a12b3889c9f88b2e7a373ebe | cc08ba44b5b51775fd15991aa53c2e76173aa122b03ba07b87ee28203e3cc09e | 600 | 90 | error | other | null | [
"spacing_only"
] | |
01ce52364c0fb254 | M^{\lambda} / G^{\lambda,\max} \cong S^{\lambda} , | ```latex
M^{\lambda} / G^{\lambda,\max} \cong S^{\lambda} ,
``` | 2307.00587 | v3 | A new presentation for Specht modules with distinct parts | [
"Tamar Friedmann",
"Phil Hanlon",
"Michelle L. Wachs"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2307.00587v3 | [
"greek"
] | dfb3a13baa7a6255796949ca5bbec294d1e3694a24a9961ca88d5076e55e08ee | 44536b92216027a1732b17c3471b851d6bfe8b0f630bc9a35c0b13eab6f6d221 | 386 | 77 | replay | null | null | [] | |
01d4744d9b416d8b | \min_{x\in \mathbb{R}^{n}}\max_{y\in \mathbb{R}^{m}} f(x,y) , | ```latex
\min_{x\in \mathbb{R}^{n}}\max_{y\in \mathbb{R}^{m}} f(x,y) ,
``` | 2506.07290 | v1 | Stochastic Moving Anchor Algorithms and a Popov's Scheme with Moving Anchor | [
"James Alcala",
"Yat Tin Chow",
"Mahesh Sunkula"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2506.07290v1 | [
"decoration"
] | 59c6bb352601f4a6cf177e277a855c4aa37d420c74178c9d9c51993273ac5335 | 494068e8288b86dc50aa0f90ba14f59048b7011aea51acd33af8a781a04d9bcf | 372 | 96 | replay | null | null | [] | |
01d717a99699d8c5 | \text{error}(i) = \frac{\|\hat{y}_i - y_i\|}{\|y_i\|}. | ```latex
\text{error}(i) = \frac{\|\hat{y}_i - y_i\|}{\|y_i\|}.
``` | 2410.16377 | v2 | A Simple Model of Inference Scaling Laws | [
"Noam Levi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2410.16377v2 | [
"decoration"
] | 90a2e05936cd8745f9341f450eeed81dd1e206abfb61a2c8cbd24507a9d2762f | 7cb8eb4b0c95a094896267b50373c6d7260b80747014e52934361bda34585169 | 449 | 138 | replay | null | null | [] | |
01dacc0ebe1c36c8 | \rho(x)\rho(y)=m(x,y)\rho(x+y), \forall x,y\in G. | ```latex
\rho(x)\rho(y)=m(x,y)\rho(x+y), \forall x,y\in G.
``` | 2509.14676 | v2 | Spectral Barron spaces arising from quantum harmonic analysis | [
"Yaogan Mensah"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2509.14676v2 | [
"greek"
] | 9ef945e54606ce588b6579cef7b6cd3a1ce90345f8997991bbd8f31260122b63 | 4152e9122e4bf1928ce8609a6577c4a32129039172557e5ab47e5cae1fcc76a9 | 830 | 71 | replay | null | null | [] | |
01df9291a81f9863 | (-z)^\alpha \mathbf{F}^I_{-\alpha,\beta,-\mu}(z) &= (-z)^\alpha (1-z)^\frac{-1+\alpha-\beta-\mu}{2}\mathbf{F}^I_{-\alpha,\mu,-\beta}(\frac{z}{z-1}). \\ &=(-z)^\alpha (1-z)^\frac{-1+\alpha-\beta+\mu}{2}\mathbf{F}^I_{-\alpha,-\mu,\beta}(\frac{z}{z-1}) \\ &= (-z)^\alpha (1-z)^{-\beta} \mathbf{F}^I_{-\alpha,-\beta,\mu}(z). | ```latex
(-z)^\alpha \mathbf{F}^I_{-\alpha,\beta,-\mu}(z) &= (-z)^\alpha (1-z)^\frac{-1+\alpha-\beta-\mu}{2}\mathbf{F}^I_{-\alpha,\mu,-\beta}(\frac{z}{z-1}). \\ &=(-z)^\alpha (1-z)^\frac{-1+\alpha-\beta+\mu}{2}\mathbf{F}^I_{-\alpha,-\mu,\beta}(\frac{z}{z-1}) \\ &= (-z)^\alpha (1-z)^{-\beta} \mathbf{F}^I_{-\alpha,-\beta... | 2509.03235 | v2 | Exactly solvable Schrödinger operators related to the hypergeometric equation | [
"Jan Dereziński",
"Pedram Karimi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2509.03235v2 | [
"greek",
"decoration",
"i_1"
] | 9076210bcc7251213969b554916754cb3549e8b825a59aaf74009bc82093d160 | 80540462a436756403144b6b92b9c5a5c7d122558c52b2bd53a4c8e159056494 | 1,247 | 304 | error | other | null | [] | |
01e3ee784025753e | r_2 \geq y_1\sqrt{1+M^2N} \geq \sqrt{\frac{1+M^2N}{1+N}}r_1 | ```latex
r_2 \geq y_1\sqrt{1+M^2N} \geq \sqrt{\frac{1+M^2N}{1+N}}r_1
``` | 2606.11055 | v1 | Exponential mixing and enhanced dissipation on the unit sphere with Rossby-Haurwitz flows | [
"Augusto Del Zotto",
"Marc Nualart"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2606.11055v1 | [
"plain"
] | b63a97bdcdee31a2d25063ad66173b685f332d105edef391c997b950339db328 | f0e09b92fbc6fb02806e0b379848f36a91fa92c302ab8bdfe9123a79fa02565e | 777 | 140 | replay | null | null | [] | |
01ee5a0438383705 | \left\| (1-\Pi_k)(P-z)^{-1}(1-\Pi_k) \right\|_{L^p(M)\to L^{p'}(M)} \lesssim k^{2\sigma(q)+1-m}. | ```latex
\left\| (1-\Pi_k)(P-z)^{-1}(1-\Pi_k) \right\|_{L^p(M)\to L^{p'}(M)} \lesssim k^{2\sigma(q)+1-m}.
``` | 2609.10127 | v1 | Resolvent bounds and eigenvalue estimates of generalized Schrödinger operators with complex potentials on compact manifolds | [
"Eduard Stefanescu"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2609.10127v1 | [
"prime",
"greek"
] | 1bb23c73686eb2650ab7101e7a461e1f20021f9194971654f92d541e2a33d4a6 | 76e38ea584f17ef4471702400f34757a64b89c9108f67a9d454e4cc5671d62ec | 1,195 | 94 | control | null | ' | [] | |
01ee6f92a10fd012 | (\mathbb{C} \varepsilon(u), \varepsilon(v))_{L^2(\Omega)} = \langle f, v\rangle_{V^* \times V} + \langle g, v\rangle_{\widetilde{H}^{-1/2}(\Gamma_{\mathrm{N}}) \times \widetilde{H}^{1/2}(\Gamma_{\mathrm{N}})}. | ```latex
(\mathbb{C} \varepsilon(u), \varepsilon(v))_{L^2(\Omega)} = \langle f, v\rangle_{V^* \times V} + \langle g, v\rangle_{\widetilde{H}^{-1/2}(\Gamma_{\mathrm{N}}) \times \widetilde{H}^{1/2}(\Gamma_{\mathrm{N}})}.
``` | 2404.02768 | v2 | Locking-free hybrid high-order method for linear elasticity | [
"Carsten Carstensen",
"Ngoc Tien Tran"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2404.02768v2 | [
"greek",
"decoration"
] | 30d0aa3b2940939c3807f28aaccbee4e50068fffcc9a1c005c34414c9d6dd8f6 | bd039e0d751094639772347e74d057da40da0c7b35d2c28eac8de509c38b63c5 | 1,208 | 82 | error | decoration | null | [] | |
0201ce8197aded93 | p=\tilde p=(A^*\cdot \tilde u)\tilde{}=u\cdot A =\check A(u)\in L^2(G). | ```latex
p=\tilde p=(A^*\cdot \tilde u)\tilde{}=u\cdot A =\check A(u)\in L^2(G).
``` | 2412.06584 | v1 | On the structure of Spectral Sets | [
"Jean Ludwig",
"Lyudmila Turowska"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2412.06584v1 | [
"decoration"
] | 0f3e5d874a84f0ac4c82c513f283c2ed8539e5a0e43f2c3dd41a6f1af1c9338b | fb9f098450d18d967887af7a2285ad8605e9dddf81953a5e658a15f4ff6b975a | 894 | 77 | error | decoration | null | [] | |
0204150cc9c0d400 | \begin{aligned} 2^{i_0-1}\leq\sqrt{1+\frac{P_x}{d(\bm{X})}}\leq2^{i_0}. \end{aligned} | ```latex
\begin{aligned} 2^{i_0-1}\leq\sqrt{1+\frac{P_x}{d(\bm{X})}}\leq2^{i_0}. \end{aligned}
``` | 2407.21698 | v1 | Long-Term Energy Management for Microgrid with Hybrid Hydrogen-Battery Energy Storage: A Prediction-Free Coordinated Optimization Framework | [
"Ning Qi",
"Kaidi Huang",
"Zhiyuan Fan",
"Bolun Xu"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2407.21698v1 | [
"decoration"
] | ba38cef856828bc2e7857d38a9e8d2d5dc794273492f39c8f479787dc01f30a0 | 7e8f8ef71dca2d18cf549974f4e711add1f159bc52094d98f7b81c3eb9a8af03 | 576 | 170 | error | decoration | null | [] | |
020af512540a50ba | (m-1)(\beta'\cdot (-K_S)-2) \le g. | ```latex
(m-1)(\beta'\cdot (-K_S)-2) \le g.
``` | 2503.18905 | v2 | A Brill-Noether Theorem for (toric) surfaces | [
"Alessio Cela",
"Carl Lian"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2503.18905v2 | [
"prime",
"greek"
] | 258c0874df3db7afa0a0b0179fb704944c9814c80a97cc8ed62aadaf06f3cb95 | f9fa632d91fc6ed6e036c1df5b65734d5b5ea2e714637452d8b4159ccbd152f7 | 628 | 72 | control | null | ' | [] | |
020bfe4981200072 | R(T)= \tilde{O}\big( K^{\frac{1}{2}} T^{ \frac{1}{2} + \frac{3c(1-b)}{2}} \big). | ```latex
R(T)= \tilde{O}\big( K^{\frac{1}{2}} T^{ \frac{1}{2} + \frac{3c(1-b)}{2}} \big).
``` | 2510.08435 | v1 | Navigating Sparsities in High-Dimensional Linear Contextual Bandits | [
"Rui Zhao",
"Zihan Chen",
"Zemin Zheng"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2510.08435v1 | [
"decoration"
] | da6d848bead8741b7698c4a8ca8e411247cda7e72bbd4045cc7cc262424fa630 | 7286b706c411dc6e07748402ce3ac0c84ec876e5c9d4870377f31ed426281497 | 567 | 94 | error | other | null | [] | |
020c52acd5810b2b | \mathsf{A}_1^{(0)} = \left( \mathsf{M}^{(0)}_{1,\eta} \right)^{\eta_1} \cdots \left( \mathsf{M}^{(0)}_{5,\eta} \right)^{\eta_5} | ```latex
\mathsf{A}_1^{(0)} = \left( \mathsf{M}^{(0)}_{1,\eta} \right)^{\eta_1} \cdots \left( \mathsf{M}^{(0)}_{5,\eta} \right)^{\eta_5}
``` | 2604.07444 | v1 | Resurgence of high-energy string amplitudes | [
"Xavier Kervyn",
"Stephan Stieberger"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2604.07444v1 | [
"greek",
"decoration"
] | b54549e440b8a21a8f5cdb06f38e1f7ce5059f62e2bb48dc50927896eee58a8a | 337731d5768222c8a6096f0f647963536f87d506816153207e3ef1bd2f68fd64 | 608 | 112 | error | decoration | null | [] | |
020eb2a88760ce30 | R_A^{\star}=2R_B^{\mathrm{full}}-R_B^{\dagger}, | ```latex
R_A^{\star}=2R_B^{\mathrm{full}}-R_B^{\dagger},
``` | 2603.04199 | v2 | Bayesian Adversarial Privacy | [
"Cameron Bell",
"Timothy Johnston",
"Antoine Luciano",
"Christian P Robert"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2603.04199v2 | [
"decoration"
] | 2dc4de924d0ed086e9ce0a54dd2ece4084f70ddb66ca8a16c5a3001e1117f4f3 | b4ce2428651572b1a26daf028e81f17c2bdbbade60298eb6298831b0d137aaea | 402 | 81 | replay | null | null | [] | |
0211a14ad5a58c11 | &|\Delta(\alpha,\beta,M,N,Q,a)|\\ &\ll ||\alpha||\left(MQ^{-1}\mathcal E^*(\beta,N,Q)+(\log X)^\kappa N^2Q+(\log X)^\kappa N^2D^{-\frac 12}M+D^CX^\epsilon\left(Q^{\frac{15}{8}}N^{\frac{11}{4}}+M^\frac{3}{20}Q^{\frac{33}{20}}N^{\frac{51}{20}}\right) \right)^\frac 12. | ```latex
&|\Delta(\alpha,\beta,M,N,Q,a)|\\ &\ll ||\alpha||\left(MQ^{-1}\mathcal E^*(\beta,N,Q)+(\log X)^\kappa N^2Q+(\log X)^\kappa N^2D^{-\frac 12}M+D^CX^\epsilon\left(Q^{\frac{15}{8}}N^{\frac{11}{4}}+M^\frac{3}{20}Q^{\frac{33}{20}}N^{\frac{51}{20}}\right) \right)^\frac 12.
``` | 2604.25177 | v2 | Trilinear Kloosterman fractions I: partially fixed moduli and unbalanced convolutions | [
"Thomas Wright"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2604.25177v2 | [
"greek",
"decoration"
] | 76779874a153ad4792edd68b620492c69c754d4e789584fcea2fb4930ef7399c | 39c46b221f1d9e0b6f24e4e6920b22133f3b406af1d213f220dedd8874f43111 | 2,212 | 199 | error | symbol_swap | null | [] | |
021879dd18985b6c | f_m(t) := \begin{cases} \frac{1}{m-1} t^m & m \neq 1 \\ t \log t & m = 1 \end{cases} | ```latex
f_m(t) := \begin{cases} \frac{1}{m-1} t^m & m \neq 1 \\ t \log t & m = 1 \end{cases}
``` | 2604.04169 | v2 | An Aronson-Bénilan / Li-Yau estimate in the JKO scheme in small dimension | [
"Fanch Coudreuse"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2604.04169v2 | [
"plain"
] | c81572c4a4e2501e437f830ff7417eb4e98e931eb9bf0e35af878e6a37e3a9c5 | ab3a0ea517a5b3c5e22a98c77c10b6abf41526afee0b2c8f785d4f5451de88e6 | 565 | 170 | replay | null | null | [] | |
022560b784886d1f | \begin{array}{rcl} c(t)&=&A(t)b\\ C(t)&=& \dot A(t)A(t)^{-1}+A(t)BA(t)^{-1}\\ q_j(t,x)&=& A(t)f_j(A(t)^{-1}x) \end{array} | ```latex
\begin{array}{rcl} c(t)&=&A(t)b\\ C(t)&=& \dot A(t)A(t)^{-1}+A(t)BA(t)^{-1}\\ q_j(t,x)&=& A(t)f_j(A(t)^{-1}x) \end{array}
``` | 2506.07189 | v2 | On gauge transforms of autonomous ordinary differential equations | [
"Giuseppe Gaeta",
"Sebastian Walcher"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2506.07189v2 | [
"decoration"
] | ffac2547a712b0ad3d6e58b894d25c6b719f123b5cc54bafb6c5f7f25fed52e9 | 427887e8b9d7bef64a7fb38d0faa382cdd9c2395aeea1261548191446fb80700 | 842 | 197 | error | other | null | [] | |
02269693040e28f4 | \frac{d\sigma_{zy}^{res}(\eta)}{d\eta}=\frac{d\sigma_{zy}^{0}(\eta)}{d\eta}+ k \int_{0}^{1} \sigma_{zy}^{res}(t) \left( -\frac{2\eta}{\gamma_1 \pi^{2} (t^{2} - \eta^{2})} \sqrt{\frac{t^{2} - 1}{\eta^{2} - 1}}\right) dt, | ```latex
\frac{d\sigma_{zy}^{res}(\eta)}{d\eta}=\frac{d\sigma_{zy}^{0}(\eta)}{d\eta}+ k \int_{0}^{1} \sigma_{zy}^{res}(t) \left( -\frac{2\eta}{\gamma_1 \pi^{2} (t^{2} - \eta^{2})} \sqrt{\frac{t^{2} - 1}{\eta^{2} - 1}}\right) dt,
``` | 2606.12007 | v1 | Residual stress gradient in a thin film within the dislocation pile-up theory | [
"A. V. Druzhinin",
"C. Cancellieri"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2606.12007v1 | [
"greek"
] | 7c20b7f6db0ce24a99a59345108462ba694f5567a7a43ee45badc7b336ef2eb2 | f12f40465521cdc99ad1a4e1ecfedc54c0a1f602d9b2d71a4605c7e94aeb1962 | 1,400 | 175 | replay | null | null | [] | |
022c432730896314 | a^{A_{l-1}}_{1,r}(k) = \#\left\{ s\in\{0,1,\dots,k\} \mid k-2s\equiv r\pmod l \right\}. | ```latex
a^{A_{l-1}}_{1,r}(k) = \#\left\{ s\in\{0,1,\dots,k\} \mid k-2s\equiv r\pmod l \right\}.
``` | 2608.06451 | v1 | New symplectic singularities from $SU(2)$ gauge theories | [
"Amihay Hanany",
"Guhesh Kumaran",
"Deshuo Liu",
"Travis Schedler"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2608.06451v1 | [
"plain"
] | 61f50c919b4534c4ca8175001680b93667c06f320449a80b137f394c16cf40c1 | 0b0caeccd03c067bf412fb5ae57a754dfd29d286a6313e54abfa96c3b5050001 | 1,191 | 89 | replay | null | null | [] | |
022e221c432fde23 | |u|^{(\alpha,\frac{\alpha}{2})}_{\Omega_{T}}=|u|^{(0)}_{\Omega_{T}}+ \max_{(\boldsymbol{x},t)\in\Omega_{T},\,|h|<\infty} \frac{|u(\boldsymbol{x}+h,t+\frac{h}{2})-u(\boldsymbol{x},t)|}{|h|^{\alpha}}<\infty. | ```latex
|u|^{(\alpha,\frac{\alpha}{2})}_{\Omega_{T}}=|u|^{(0)}_{\Omega_{T}}+ \max_{(\boldsymbol{x},t)\in\Omega_{T},\,|h|<\infty} \frac{|u(\boldsymbol{x}+h,t+\frac{h}{2})-u(\boldsymbol{x},t)|}{|h|^{\alpha}}<\infty.
``` | 2510.19502 | v6 | Correct mathematical models of joint filtration of two immiscible viscous liquids | [
"Anvarbek Meirmanov",
"Akbota Senkebayeva"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2510.19502v6 | [
"greek",
"decoration"
] | 81564465204d7060a9cc8f24336609306804cb757e9e6e6f99a6594a71667af0 | 003e443f3ef06c20aa2c43e90e0c27a13f1ab94350f1f0e1fdca5929af8d7f55 | 1,347 | 147 | error | decoration | null | [] | |
022ecc48e75d9ab8 | U = Q_k \cdot O_l \cdot Q_{k-1} \cdot O_{l-1} \cdot \ldots \cdot Q_1 \cdot O_1. | ```latex
U = Q_k \cdot O_l \cdot Q_{k-1} \cdot O_{l-1} \cdot \ldots \cdot Q_1 \cdot O_1.
``` | 2412.06145 | v1 | Optimizing Qubit Mapping with Quasi-Orthogonal Space-Time Block Codes and Quaternion Orthogonal Designs | [
"Valentine Nyirahafashimana",
"Nurisya Mohd Shah",
"Umair Abdul Halim",
"Mohamed Othman",
"Sharifah Kartini Said Husain"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2412.06145v1 | [
"plain"
] | 7ad5bfa769445c9bb40fcd6b349596c246ebc7e26d82a2ddc2e7df0203801714 | d58650c32abc776f8b9d16ddf4a1e9897ba26b794fa040f3e03cdfc5d58026b1 | 830 | 66 | replay | null | null | [] | |
02341a06e3617aed | f\circ\Gamma_{H_{1}}=\Gamma_{B_{1}}\circ(f\otimes f) | ```latex
f\circ\Gamma_{H_{1}}=\Gamma_{B_{1}}\circ(f\otimes f)
``` | 2605.07497 | v1 | Opposite brace triples, Hopf braces and matched pairs of Hopf algebras | [
"Ramón González Rodríguez",
"Brais Ramos Pérez"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2605.07497v1 | [
"greek"
] | b58a320edad0eb0a2fd5037dbf9075efc9457e1520cc0d726ccf8c455ccdf93e | 54ba1771f7b4d4d79c0b0660d936a00d63975eec6447e15383d1e55a19eb1d7b | 515 | 71 | replay | null | null | [] | |
0234a2b46161686d | M^* = \sum_{j\in \mathcal J^*} M_j^*. | ```latex
M^* = \sum_{j\in \mathcal J^*} M_j^*.
``` | 2606.10916 | v1 | Range Penalization: Theoretical Insights with Applications in Federated Learning | [
"Yiyuan She",
"Zhaojun Hu",
"Yifan Sun"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2606.10916v1 | [
"decoration"
] | bcf0feee652c6f4f895138d4e617c214bc9d8764bedd413f2d6730b137be8c7d | a3cf00024083f486edc7f7657b980ad5221eae2400a720288ba0aae7da9be05a | 334 | 133 | replay | null | null | [] | |
024513a39c2e8e62 | \begin{aligned} \sum_{u\in T}d_{G-S}(u)\leq kt-ks-2+q. \end{aligned} | ```latex
\begin{aligned} \sum_{u\in T}d_{G-S}(u)\leq kt-ks-2+q. \end{aligned}
``` | 2508.05678 | v1 | Spectral conditions for graphs to contain $k$-factors | [
"Xinying Tang",
"Wenqian Zhang"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2508.05678v1 | [
"plain"
] | f5a39ecc0b4489d0ea3b8143dae1c5f804d6812411ae5cb5510215d72b3f6edc | d530faf35a18f5bc4d2076337b2525ad129290dc558ea0beb5259a2e12e6a408 | 670 | 129 | control | null | l | [] | |
024a2a9fcd2828fa | \lim\limits_{t\rightarrow\infty}\mathcal{L}^{(0)}_{*}\ge\frac{1}{2}\frac{\min_{k\in[n]}\|x_k\|_2^2}{\max_{k\in[n]}\|x_k\|_2^2}\sigma^2\frac{1+\mu^2}{2} | ```latex
\lim\limits_{t\rightarrow\infty}\mathcal{L}^{(0)}_{*}\ge\frac{1}{2}\frac{\min_{k\in[n]}\|x_k\|_2^2}{\max_{k\in[n]}\|x_k\|_2^2}\sigma^2\frac{1+\mu^2}{2}
``` | 2402.18905 | v2 | Characterizing the Training Dynamics of Private Fine-tuning with Langevin diffusion | [
"Shuqi Ke",
"Charlie Hou",
"Sewoong Oh",
"Giulia Fanti"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2402.18905v2 | [
"greek",
"decoration"
] | b524145eaca5645aa7493f21d739cb2a34a9132d5bd5487e4a3c24d8ae77db6d | 192371f9d3cb1b231591b944c8c3488d0ca787c68c7f22ae7738951ada39c8ff | 796 | 147 | replay | null | null | [] | |
024f49bb362c0487 | \left\vert \left\langle \mathsf{M}_{u}^{s}\bigtriangleup_{I}^{\varphi }f,h_{J;\kappa}^{\eta}\right\rangle \right\vert \leq2^{D-\kappa \operatorname*{dtree}\left( J,\mathcal{G}_{2s}\left[ I\right] \right) },\ \ \ \ \ \text{for }I,J\in\mathcal{G}, | ```latex
\left\vert \left\langle \mathsf{M}_{u}^{s}\bigtriangleup_{I}^{\varphi }f,h_{J;\kappa}^{\eta}\right\rangle \right\vert \leq2^{D-\kappa \operatorname*{dtree}\left( J,\mathcal{G}_{2s}\left[ I\right] \right) },\ \ \ \ \ \text{for }I,J\in\mathcal{G},
``` | 2411.18457 | v8 | A comparison of trilinear testing conditions for the paraboloid Fourier extension and Kakeya conjectures in three dimensions | [
"Eric T. Sawyer"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2411.18457v8 | [
"greek",
"decoration",
"i_1"
] | 3f1ca9518552cd30cc3c00acbd838edc2a48682301d3230af48d8c7a5fd92c48 | ec2769e65ad2bfaed2c20f6403715e5147a1c81c84549520581c5ccc9fac8a1b | 1,142 | 86 | error | decoration | null | [] | |
025900011683e36f | U_0^{(1)}(\mathfrak{g}) \subset U_0^{(2)}(\mathfrak{g}) \subset \cdots \subset U_0^{(i)}(\mathfrak{g}) \subset \cdots, | ```latex
U_0^{(1)}(\mathfrak{g}) \subset U_0^{(2)}(\mathfrak{g}) \subset \cdots \subset U_0^{(i)}(\mathfrak{g}) \subset \cdots,
``` | 2402.00483 | v4 | Gelfand-Tsetlin modules for Lie algebras of rank $2$ | [
"Milica Anđelić",
"Carlos M. da Fonseca",
"Vyacheslav Futorny",
"Andrew Tsylke"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2402.00483v4 | [
"decoration"
] | 2f0d59f2a1572be85229efb8d8839d1ff0d569d92ca6a16fcd471cc7bda78ba5 | b86ece31b17a0aed3800d7c1890cdbce827a1a8290f86b32ddf082ec9baaf31d | 866 | 83 | error | other | null | [] | |
025c8a01eab53113 | |11\rangle = \binom{0}{1} \otimes \binom{0}{1} = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix}. | ```latex
|11\rangle = \binom{0}{1} \otimes \binom{0}{1} = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \end{pmatrix}.
``` | 2412.05595 | v1 | Quantum Annealing and Tensor Networks: a Powerful Combination to Solve Optimization Problems | [
"Miquel Albertí Binimelis"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2412.05595v1 | [
"i_1"
] | 63c9cd82a686b69be90eb7f9b862e710ee0e73a797b5434ab52b816b66dc1cf4 | 39cfcacedd374dfcce26d30abc2686b96d688700f9c659ea0e8549acb243d9e3 | 614 | 259 | error | other | null | [] | |
025d7aface508037 | h_{\alpha,\theta; \alpha}(t \vert z , 1-\theta,\gamma) &= \frac{1}{\pi t}\, {\rm Im} \sum_{k=0}^\infty \frac{\Gamma(\gamma+\theta/\alpha+k)}{k! \, \Gamma(\gamma+\theta/\alpha)} (-z e^{-i\pi\alpha} t^{-\alpha})^k \\ &= \frac{1}{\pi t}\, {\rm Im} \, \frac{1}{(1+z e^{-i\pi\alpha}t^{-\alpha})^{\gamma+\theta/\alpha}} \\ &= ... | ```latex
h_{\alpha,\theta; \alpha}(t \vert z , 1-\theta,\gamma) &= \frac{1}{\pi t}\, {\rm Im} \sum_{k=0}^\infty \frac{\Gamma(\gamma+\theta/\alpha+k)}{k! \, \Gamma(\gamma+\theta/\alpha)} (-z e^{-i\pi\alpha} t^{-\alpha})^k \\ &= \frac{1}{\pi t}\, {\rm Im} \, \frac{1}{(1+z e^{-i\pi\alpha}t^{-\alpha})^{\gamma+\theta/\alpha... | 2507.06665 | v1 | Distributions based on Stable Mixtures and Gamma-Stable Convolutions | [
"Nomvelo Karabo Sibisi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2507.06665v1 | [
"greek",
"i_1"
] | 3468248380d8a5f6d2ab974dbcd752d14c55f7470125090a4cd089aef2b29985 | f5711400afe410e90d69ca10ab6a65da808c9a8e5ef5eec83f0067734dd7d612 | 1,315 | 429 | replay | null | null | [] | |
026b3366e7d655aa | d(d^2-1) a^3 - 3(d+2)(d^2-1)a^2 + 3(d^2-4)(d-1)a - (d-2)^2(d+1)= 0. | ```latex
d(d^2-1) a^3 - 3(d+2)(d^2-1)a^2 + 3(d^2-4)(d-1)a - (d-2)^2(d+1)= 0.
``` | 2505.05894 | v1 | Comment and correction for "On Explicit Construction of Simplex $t$-designs" by M. S. Baladram | [
"Jakub Czartowski"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2505.05894v1 | [
"plain"
] | 5e259358b80d31008fd27ca3a14547f46f0683a38be7ba9a4452ac6ca3feee82 | ee68c0f9150e4e0f24e62c5dc22e8ba50f9dfcf887041bdedd8f415d13391700 | 1,607 | 76 | replay | null | null | [] | |
027f5fc5fa18b0a0 | A_t(z) = \left(\frac{z_1+ t}{1+ tz_1}, \sqrt{1-t^2} \frac{z'}{1 + tz_1}\right), | ```latex
A_t(z) = \left(\frac{z_1+ t}{1+ tz_1}, \sqrt{1-t^2} \frac{z'}{1 + tz_1}\right),
``` | 2311.10705 | v2 | Holomorphic maps acting as Kobayashi isometries on a family of geodesics | [
"Filippo Bracci",
"Łukasz Kosiński",
"Włodzimierz Zwonek"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2311.10705v2 | [
"prime"
] | 0a958bce56100446fe291e63954753cf581b248e0086957f9fa86fd5a0e89ce6 | 581718cb2fbce2c857d64c08b9330683079f49683e2360391425d27908c8e816 | 785 | 140 | control | null | ' | [] | |
028ddb8f1a635e5c | \forall j\in \mathbb{N}_M,\;\displaystyle{\frac{LA}{M}}\leq \displaystyle{\sum_{l\in \mathbb{N}_L}\vert z_Mg_l(j,.)\vert^2}\leq \displaystyle{\frac{LB}{M}}\; \; \text{ a.e. on }[0,1[. | ```latex
\forall j\in \mathbb{N}_M,\;\displaystyle{\frac{LA}{M}}\leq \displaystyle{\sum_{l\in \mathbb{N}_L}\vert z_Mg_l(j,.)\vert^2}\leq \displaystyle{\frac{LB}{M}}\; \; \text{ a.e. on }[0,1[.
``` | 2407.05495 | v3 | Multi-window Gabor systems on discrete periodic sets | [
"Najib Khachiaa"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2407.05495v3 | [
"decoration"
] | dc251d4e24774764921583181a9cf90f1b8d2b6786efe8a20f32db7dbf2b77ab | 577e4b8ff94f05880bf8dec8e51ab33612f88620bf462670f05ae6cc9a7507ee | 1,181 | 154 | error | symbol_swap | null | [] | |
029637574ab803e2 | \mathcal{L}_\varepsilon := \left\{ \pmb{\sigma} \in \mathcal{Q}_N \ | \ U_p(\pmb{\sigma}) < - \varepsilon N \right\} , | ```latex
\mathcal{L}_\varepsilon := \left\{ \pmb{\sigma} \in \mathcal{Q}_N \ | \ U_p(\pmb{\sigma}) < - \varepsilon N \right\} ,
``` | 2505.02458 | v2 | The Quantum Random Energy Model is the Limit of Quantum $ p $-Spin Glasses | [
"Anouar Kouraich",
"Chokri Manai",
"Simone Warzel"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2505.02458v2 | [
"greek",
"decoration"
] | 94e7deae5bbabeb95986d0e9c88fbde6047b2fccab084b2974ca527c1f911f9e | 8396b2c3e7bb3dd48b14fe563f9a856ee5b364d022d2934898fd8447ca151eff | 722 | 73 | error | symbol_swap | null | [] | |
0298d3a5da98fcba | \int E_x\,\lambda_M(dx)=I_{\mathcal K_n} | ```latex
\int E_x\,\lambda_M(dx)=I_{\mathcal K_n}
``` | 2609.10072 | v1 | Haar-Bayesian Pure-State Prediction under Relative-Entropy Loss: Arbitrary-Effect Reduction and Global Optimality | [
"Masahito Hayashi",
"Ayanava Dasgupta",
"Naqueeb Ahmad Warsi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2609.10072v1 | [
"greek",
"decoration",
"i_1"
] | f739c51df2ea1d5d6d46ad9b098bac21404be35efb877d05887210c26f945b40 | 354536900d17ecc3d8f32f66b80149c97f076323f4f9751b42913e8b5c221af0 | 434 | 131 | replay | null | null | [] | |
02a7e83a69e99229 | V_a := \ker\left(L - \Lambda_a\right)\neq\{0\}. | ```latex
V_a := \ker\left(L - \Lambda_a\right)\neq\{0\}.
``` | 2601.05422 | v1 | Variations on two Cabrelli's works | [
"Elona Agora",
"Jorge Antezana",
"Diana Carbajal"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2601.05422v1 | [
"greek"
] | 261f6c0974dea269a5aa0fd2515c19fd874c1e98e2172bf3d1e706ca0a6ef018 | 37f855277b0c9c1a9eb10907882d722dfb579fd94d9051eed21019c81e56721c | 556 | 71 | error | other | null | [] | |
02ac8b044a8d351e | \phi = \begin{pmatrix} 1 & 0 & 0 \\ -\alpha _{2} & 1 & 0 \\ \alpha _{1} & 0 & 1 \end{pmatrix} . | ```latex
\phi = \begin{pmatrix} 1 & 0 & 0 \\ -\alpha _{2} & 1 & 0 \\ \alpha _{1} & 0 & 1 \end{pmatrix} .
``` | 2407.05429 | v2 | The algebraic and geometric classification of noncommutative Jordan algebras | [
"Hani Abdelwahab",
"Kobiljon Abdurasulov",
"Ivan Kaygorodov"
] | CC0-1.0 | http://creativecommons.org/publicdomain/zero/1.0/ | https://arxiv.org/abs/2407.05429v2 | [
"greek"
] | 5dff1d8719bccfc1c45ef06e346ff8aa4cf0c79859a14f11c0d3d4dae1d562da | badcb35344b1dad3175bb2bb148fa58bb7dd733fbe59fd840ed7c3bcb1e75134 | 439 | 199 | control | null | 1 | [] | |
02ad39cbeb201750 | \mathcal{L}_{\rm{exp}}(\theta):=\mathbb{E}_{\mathbf y\sim\mu(\mathbb{B}(\mathbb{R}^n))}(\Vert P_n(\mathcal{N}_\theta(\mathbf y)-\mathbf x)\Vert^2_2). | ```latex
\mathcal{L}_{\rm{exp}}(\theta):=\mathbb{E}_{\mathbf y\sim\mu(\mathbb{B}(\mathbb{R}^n))}(\Vert P_n(\mathcal{N}_\theta(\mathbf y)-\mathbf x)\Vert^2_2).
``` | 2605.07365 | v1 | Solving Convolution-type Integral Equations using Preconditioned Neural Operators | [
"Raymond Chan",
"Lingfeng Li"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2605.07365v1 | [
"greek",
"decoration"
] | 34b498df623c172c400bfc0ee4eb74016470e5c4447a4f77de1bdde60dff9631 | f3eac9bc192ff59393b8e7ba132fabe1c3ec5573d29b29869589418d3aa7087d | 908 | 80 | error | other | null | [] | |
02b62eca871a8dab | (\mathcal{H}_{k}F)(a) \ll_{k} a^{\frac{k-1}{2}}, | ```latex
(\mathcal{H}_{k}F)(a) \ll_{k} a^{\frac{k-1}{2}},
``` | 2410.16921 | v2 | Trace formula and functional equation | [
"Chung-Hang Kwan",
"Wing Hong Leung"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2410.16921v2 | [
"decoration"
] | 41d7a545f12932bbe4eb8ab8fef678fcdfba7a75771c70a3c182983ac5121657 | 2fb9a913089ef27034906728bd6b4739b9e1eea632e7cc9565ccba33666b663f | 422 | 85 | error | other | null | [] | |
02b8e40e66dffa3b | \mathfrak{D}^{p}_{\varepsilon}(P\|Q) \coloneqq \inf_{R\in\mathcal{P}(X)} \left\{W_p^p(P,R) + \varepsilon \mathfrak{D}(R\|Q) \right\}. | ```latex
\mathfrak{D}^{p}_{\varepsilon}(P\|Q) \coloneqq \inf_{R\in\mathcal{P}(X)} \left\{W_p^p(P,R) + \varepsilon \mathfrak{D}(R\|Q) \right\}.
``` | 2505.12097 | v2 | Proximal optimal transport divergences | [
"Ricardo Baptista",
"Panagiota Birmpa",
"Markos A. Katsoulakis",
"Luc Rey-Bellet",
"Benjamin J. Zhang"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2505.12097v2 | [
"greek",
"decoration"
] | 33df32e1ed7ce7b9ac029f7ddb069f9f24a6aed5d0e7badd476224c8d27aa568 | 782808d1a05c4f3d6713b3f4aebbfee7eee64c80eeb337ecffc3c2cf1f14093a | 984 | 104 | error | symbol_swap | null | [] | |
02bd60b78de003d8 | k_t = k_0\mathcal{E}(\beta_1W_{1,t})=\frac{c_t}{B}>0,\quad t\ge 0. | ```latex
k_t = k_0\mathcal{E}(\beta_1W_{1,t})=\frac{c_t}{B}>0,\quad t\ge 0.
``` | 2502.05081 | v1 | Stochastic internal habit formation and optimality | [
"Michele Aleandri",
"Alessandro Bondi",
"Fausto Gozzi"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2502.05081v1 | [
"greek",
"decoration"
] | d58e61ae53810a97cd4d1bfa7cb852c347be1bc30e34001e212544d8510fc98d | f4cdf1e63b883cffdcdfdf612c71a2f13bc0b7f7c50c0ebbf857d94cb3d98d25 | 767 | 110 | replay | null | null | [] | |
02d0f99dcddfb9c1 | q\left(\frac{3\ell(n-a)}{3n}, \frac{\ell(4n-a)}{4n}\right) = \left(\frac{-1}{\ell} \right) q \left(\frac{a\ell}{4n}, \frac{3a\ell}{3n} \right) = \left(\frac{-1}{\ell} \right) q \left(\frac{a\ell}{4n}, \frac{4a\ell}{4n} \right) | ```latex
q\left(\frac{3\ell(n-a)}{3n}, \frac{\ell(4n-a)}{4n}\right) = \left(\frac{-1}{\ell} \right) q \left(\frac{a\ell}{4n}, \frac{3a\ell}{3n} \right) = \left(\frac{-1}{\ell} \right) q \left(\frac{a\ell}{4n}, \frac{4a\ell}{4n} \right)
``` | 2602.07693 | v1 | Ekedahl-Oort Types and Newton Polygons of Abelian Covers of $\mathbf{P}^1$ Branched at Three Points | [
"Darren Schmidt"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2602.07693v1 | [
"plain"
] | a78f1d93aeda4edb99d2e023bceddc461d2d142bec90e2ab14604c9d06e15bf7 | 7d7f3f6a631008e784bcab9ef719c861cf4b1751b5bc38b1d0f64623b607d3c3 | 1,535 | 140 | control | null | \ell | [] | |
02d6f0cd4a2b372d | N_{i,p}(u) = \frac{u-u_i}{u_{i+p}-u_i}\,N_{i,p-1}(u) + \frac{u_{i+p+1}-u}{u_{i+p+1}-u_{i+1}}\,N_{i+1,p-1}(u), | ```latex
N_{i,p}(u) = \frac{u-u_i}{u_{i+p}-u_i}\,N_{i,p-1}(u) + \frac{u_{i+p+1}-u}{u_{i+p+1}-u_{i+1}}\,N_{i+1,p-1}(u),
``` | 2606.10335 | v1 | A Physics-Informed B-Spline Framework for Continuous Approximation of Flow Data | [
"Junoh Jung",
"David Lenz",
"Emil Constantinescu",
"Tom Peterka"
] | CC-BY-4.0 | http://creativecommons.org/licenses/by/4.0/ | https://arxiv.org/abs/2606.10335v1 | [
"plain"
] | 91e5aad16e84f8dcf1ceaf9ab4b921efafad863f22cad1dea4917460707d0f8a | 61790ee0045c611f3fb435424991181594c66507d243f64721e63a10f2df95da | 1,235 | 125 | error | other | null | [
"spacing_only"
] |
End of preview. Expand in Data Studio
glyphfix-math-equations
Images of display equations from open-access mathematics papers, paired with the canonicalized LaTeX that produced them. The images are rendered by us from the papers' own LaTeX source, so each label should match the rendered glyphs, though we have not checked every row by hand. The set was put together with glyph-level notation errors of OCR models in mind: primes, Greek letters read as Latin ones, bold, bar and underline decorations, and the letter I read as the digit 1. It does not yet contain enough examples of those classes to measure them (see the status below).
This dataset is an independent project. It is not affiliated with, endorsed by, or sponsored by LightOn.
Why this dataset exists
Mathematical formulas are the part of a PDF where OCR mistakes cost the most. One wrong glyph, a prime read as the letter l, a Greek letter read as a Latin one, a lost bold or bar, an I read as 1, can change which mathematical object is meant, and a reader may not notice. We want OCR of formulas in PDFs to be as close to correct as we can get it.
This release is a first step. We work on images of single display equations because they are easy to measure, and we score them by whether the output typesets to the same bitmap as the paper's LaTeX. We checked full pages only on 50 pages, and on full pages we have not shown an improvement yet (see the model card).
Status: an initial release
This is our first release and we want to be honest about it. The train split is what the first LoRA was trained on, and the benchmark is the frozen set it was scored on. They were not built class by class: on this benchmark the base model made few errors on a prime read as l, Greek read as Latin or I read as 1 (and the dropped-prime flags are probably partly a scorer artifact), so those classes have too few examples to measure anything, and about half of the drop in failures was in layout, spacing and alignment wrapper rows. The model card has the per-class table and a breakdown of the remaining errors.
We want to build on it, with no date yet. The plan, which may change as we learn more:
- a training set built around each error class (primes, Greek letters, decorations, I against 1), so that these classes have enough events to measure
- possibly more training on the largest remaining buckets (layout / sizing, spacing, alignment wrappers, content),
after we have read the
contentbucket more closely - a new, separate benchmark, because the current one is frozen and its counts for the named classes are too small; any claim about the new training would need it
- a look at why the "same text, render differs" bucket grew
- more evidence on full pages, since that is the real target: a larger and separate set of pages, and a look at the
unbalanced
$$fences that cost this model equations on two test pages
New rows would come as a new version of this dataset. The current benchmark stays frozen so that results on it remain comparable.
Splits
| Split | Rows | Papers | CC0-1.0 rows |
|---|---|---|---|
| train | 8000 | 767 | 440 |
| benchmark | 2688 | 150 | 211 |
The splits are disjoint by paper. The benchmark split is an evaluation set: it is held out by paper and was frozen
before any mining or training. Do not train on it; a model trained on it can no longer be compared on this benchmark.
The leak scan that enforces this lives in the code repository (python -m glyphfix_math.leakscan).
The train split is the training set of the released LoRA and nothing else: other crops that were mined or considered during development are not released. The mining labels in the code repository cover 13958 mined train crops, which is more than the train split holds.
Fields
| Field | Meaning |
|---|---|
| id | stable crop identifier |
| image | PNG crop of the rendered equation |
| latex | canonicalized LaTeX of the equation |
| target_text | train only: the training target, the LaTeX in a fenced block |
| arxiv_id, paper_version | source paper and the pinned version the license was checked on |
| title, authors | title and full author list of the source paper |
| license_spdx, license_uri | license of the source paper (CC-BY-4.0, CC-BY-3.0 or CC0-1.0) |
| arxiv_url | versioned link to the source paper |
| flags | notation classes found in the equation |
| image_sha256, bitmap_sha256 | hash of the PNG file and of the rendered bitmap |
| width, height | image size in pixels |
| group, mining_class, control_glyph, tags | train only: how the row was selected |
| render_image_digest, preamble_sha256, canon_version, builder_version, env | benchmark only: render provenance |
Download and use
Download everything with the Hugging Face CLI (pip install -U huggingface_hub):
hf download ogaude/glyphfix-math-equations --repo-type dataset --local-dir glyphfix-math-equations
Or load a split with the datasets library:
from datasets import load_dataset
train = load_dataset("ogaude/glyphfix-math-equations", split="train")
benchmark = load_dataset("ogaude/glyphfix-math-equations", split="benchmark")
print(train[0]["latex"])
Keep the ATTRIBUTION.md file with any rows you reuse.
Intended use and limitations
Intended for training and evaluating OCR models on display equations, in particular on glyph-level notation. All
equations come from arXiv mathematics papers typeset in LaTeX and rendered with one pinned preamble, so the images
are clean renderings: no handwriting, scans, noise or page context. Papers are limited to CC BY 3.0, CC BY 4.0 and
CC0 versions, which is a small and self-selected part of arXiv. The latex label is canonicalized, so a model can
be correct and still differ from it as a string; the released benchmark scores by rendering, not by string match.
If you slice the benchmark by the flags field, expect small counts for primes, Greek letters and I against 1: a
class with few rows cannot support a claim about a model, so check the counts before you compare.
License
The dataset repository is licensed CC BY 4.0. Every record carries the license of its source paper in
license_spdx and license_uri; we included only papers that our checks found under CC BY 3.0, CC BY 4.0 or CC0, with the version pinned because the license is per paper version. Please check the license of a paper yourself before you rely on it. 440 train rows
and 211 benchmark rows come from CC0-1.0 papers. Our added labels and annotations are CC BY 4.0, Copyright 2026 Olivier Gaude.
Versions: this is project release v1.0.0, dataset tag dataset-v1.0.0, benchmark benchmark-v1 (see VERSIONING.md in the code repository).
Attribution
ATTRIBUTION.md and ATTRIBUTION.jsonl list every source paper with title, full author list, version, license, link,
split and row count. If you reuse rows, keep the attribution of their papers.
How it was built
Equations were extracted from each paper's LaTeX source, canonicalized, and re-rendered to images with pdflatex in a
pinned TeX Live image. The latex column is the canonicalized LaTeX, not the author's original source, which is an
indication of modification under CC BY 4.0 section 3(a)(1)(B). The page images used for page-level checks are not part
of this dataset. The raw equation body and its source file position are not shipped.
Citation
@misc{glyphfix-math-equations,
title = {glyphfix-math-equations: equation crops for glyph-level math OCR},
author = {Olivier Gaude},
year = {2026},
url = {https://huggingface.co/datasets/ogaude/glyphfix-math-equations}
}
Please also cite the source papers listed in ATTRIBUTION.md for any rows you reuse. If you use the benchmark or the scorer, also cite the model (https://huggingface.co/ogaude/glyphfix-math-lora) and the code repository (https://github.com/ogaude/glyphfix-math, which has a CITATION.cff).
Links and contact
- Model: https://huggingface.co/ogaude/glyphfix-math-lora
- Code: https://github.com/ogaude/glyphfix-math
To ask for a record to be removed, open an issue on the GitHub repository or write to ogaude.code+td@proton.me. Records are removed on request.
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