task stringclasses 3
values | gt_id int64 0 655 ⌀ | gt_latex stringlengths 21 649 ⌀ | similarity float64 -1 0.98 | strict_similarity float64 -1 0.97 | semantic_similarity float64 -1 0.98 | structural_similarity float64 -1 1 | element_overlap float64 -1 1 | page stringclasses 70
values | bbox listlengths 4 4 | raw_ocr stringlengths 0 1.67k | paper_id stringclasses 170
values |
|---|---|---|---|---|---|---|---|---|---|---|---|
repair_no_gt | null | null | 0.481416 | 0.412698 | 0.489796 | 0.522727 | 0.571429 | page_4 | [
1088.1143798828125,
1185.2830810546875,
1488.9521484375,
1314.9154052734375
] | \mathrm{SMMA}_{n}=\frac{1}{n}\sum_{i=1}^{n}\mathrm{GloSe}_{i} | 2511.16657v1 |
repair_no_gt | null | null | 0.452715 | 0.384615 | 0.410959 | 0.42029 | 0.888889 | page_4 | [
829.18310546875,
1519.0767822265625,
1753.3846435546875,
1616.2474365234375
] | \mathrm{{EMA}}_{n}=\mathrm{{EMA}}_{n-1}+{\frac{2}{n+1}}\times(\mathrm{{Close}}_{n}-\mathrm{{EMA}}_{n-1}) | 2511.16657v1 |
repair_no_gt | null | null | 0.244533 | 0.199288 | 0.189526 | 0.244681 | 0.6 | page_4 | [
732.8687133789062,
1869.9207763671875,
1859.419677734375,
2286.003173828125
] | \begin{array}{l}{{\mathrm{Lorwer~band:~BBL}_{n,k}=\mathrm{SMA}_{n}(\mathrm{Close})-k\times\mathrm{StdDev}_{n}(\mathrm{Close})}}\\ {{\mathrm{Middute~band:~BBM}_{n,k}=\mathrm{SMA}_{n}(\mathrm{Close})}}\\ {{\mathrm{Band~width}:~\mathrm{BBD}_{n,k}=\mathrm{BBW}_{n,k}=\mathrm{BB}\mathrm{BBT}_{n,k}}}\\ {{\mathrm{BBT}_{n,k}=\m... | 2511.16657v1 |
repair_no_gt | null | null | 0.364871 | 0.353982 | 0.352941 | 0.4 | 0.375 | page_5 | [
1088.5531005859375,
700.5897216796875,
1490.662109375,
805.6161499023438
] | \mathrm{RSI}_{n}=100-{\frac{100}{1+\mathrm{RS}}} | 2511.16657v1 |
repair_no_gt | null | null | 0.334582 | 0.302158 | 0.32 | 0.32967 | 0.5 | page_5 | [
1084.2340087890625,
861.3573608398438,
1486.7899169921875,
972.755859375
] | \mathrm{RS}=\frac{\mathrm{Average\;Gain}_{n}}{\mathrm{Average\;Loss}_{n}}. | 2511.16657v1 |
repair_no_gt | null | null | 0.268256 | 0.208251 | 0.228228 | 0.294671 | 0.555556 | page_5 | [
844.1702880859375,
1187.4500732421875,
1736.75634765625,
1375.390869140625
] | \begin{array}{l}{{\mathrm{MACD}_{n,m}=\mathrm{EM}\mathrm{A}_{n}(\mathrm{Close})-\mathrm{EM}\mathrm{A}_{m}(\mathrm{Close})}}\\ {{\mathrm{MACD}\mathrm{B}_{n,m,p}=\mathrm{MAC}\mathrm{D}_{n,m}-\mathrm{EM}\mathrm{A}_{p}(\mathrm{MACD}_{n,m})}}\\ {{\mathrm{MACD}\mathrm{S}_{n,m,m}=\mathrm{EM}\mathrm{A}_{p}(\mathrm{MACD}_{n,m})... | 2511.16657v1 |
with_gt | 4 | \[ \text{ADX}_{t} = \frac{\text{ADX}_{t-1} \times (n-1) + \text{DX}_{t}}{n} \] | 0.573224 | 0.517073 | 0.608696 | 0.606452 | 0.533333 | page_5 | [
970.0152587890625,
1753.7607421875,
1608.4010009765625,
1859.8529052734375
] | \mathrm{\bfAD}{\bf X}_{t}\,=\,\frac{\mathrm{\bfAD}{\bf X}_{t-1}\,\times\,\bigl(\eta-1\bigr)\,+\,\mathrm{\bfD}{\bf X}_{t}}{\eta} | 2511.16657v1 |
repair_no_gt | null | null | 0.507322 | 0.530466 | 0.471698 | 0.497512 | 0.6 | page_5 | [
1095.8880615234375,
1965.560791015625,
1474.804931640625,
2093.052734375
] | \mathrm{DX}_{t}={\frac{\left|{\bf D_{t}^{\ +}}-{\bf D_{t}^{\lbrack-\rbrack}}\right|}{\left|{\bf D}\rbrack_{t}^{+}+{\bf D}\rbrack_{t}^{-}\right|}} | 2511.16657v1 |
repair_no_gt | null | null | 0.253234 | 0.24186 | 0.254958 | 0.282353 | 0.222222 | page_5 | [
1071.2098388671875,
2162.99267578125,
1503.3956298828125,
2299.131591796875
] | \begin{array}{l}{{\displaystyle{\int}\Pi_{t}^{+}\implies\Pi\mathrm{i}_{\Theta}\mathrm{l}_{t}\dots\Pi\mathrm{i}_{\Theta}\mathrm{l}_{t-1}}}\\ {{\mathrm{I})\Omega_{t}^{-}\begin{array}{l}{{\displaystyle{\int}\Omega_{t-1}}}\\ {{\displaystyle{\int}\Omega_{t}^{-}\implies\mathrm{I}.\Psi_{t}}}\end{array} | 2511.16657v1 |
repair_no_gt | null | null | 0.406974 | 0.480769 | 0.366812 | 0.38009 | 0.4 | page_5 | [
918.3305053710938,
2509.54736328125,
1663.6865234375,
2623.80517578125
] | \mathrm{Williams~}\zeta_{0}\mathrm{R}_{n}=\frac{\mathrm{High}_{n}-\mathrm{Close}}{\mathrm{High}_{n}-\mathrm{Iow}_{n}}\times100\gamma_{0} | 2511.16657v1 |
repair_no_gt | null | null | 0.403242 | 0.373089 | 0.425703 | 0.451327 | 0.307692 | page_5 | [
633.5162963867188,
2902.94091796875,
1950.931640625,
3034.577880859375
] | \mathrm{ATR}_{n}=\frac{1}{n}\sum_{i=1}^{n}\operatorname*{max}(\mathrm{High}_{i}-\mathrm{Low}_{i},|\mathrm{High}_{i}-\mathrm{Close}_{i-1}|,|\mathrm{Low}_{i}-\mathrm{Close}_{i-1}|) | 2511.16657v1 |
repair_no_gt | null | null | 0.19783 | 0.17033 | 0.198813 | 0.216981 | 0.238095 | page_6 | [
939.6572265625,
430.7757263183594,
1641.141845703125,
666.8075561523438
] | \begin{array}{l}{{\nabla_{0}\mathrm{K}=\frac{\displaystyle{\nabla}\!{\mathrm{lose}}-{\mathrm{Min~Low}_{n}}}_{n}}}\\ {{\mathrm{~}\!\!\!\nabla_{\mathrm{dC}}\mathrm{In}\mathrm{s}\,\mathrm{High}_{n}-{\mathrm{Min~Low}_{n}}}}\\ {{\mathrm{~}\!\!\mathrm{~}\!\!\mathrm{~}\!\!\mathrm{~}\!\!\mathrm{~}\!\!\vphantom{~}\!\!\mathrm{~}... | 2511.16657v1 |
repair_no_gt | null | null | 0.393814 | 0.433735 | 0.370044 | 0.378378 | 0.4 | page_6 | [
878.1707153320312,
1010.1703491210938,
1698.8084716796875,
1125.40283203125
] | \mathrm{SQZ}_{n,m,p,q}=\frac{\mathrm{SM}\mathrm{IA}(\mathrm{Close}_{n})-\mathrm{SM}\mathrm{A}(\mathrm{Close}_{m})}{\mathrm{SMA}(\mathrm{Close}_{p})\times q} | 2511.16657v1 |
with_gt | 8 | \[
w_i = \{ P_t \mid t \in [20(i-1)+1, 20i] \}.
\] | 0.808059 | 0.598291 | 0.875 | 0.892857 | 1 | page_6 | [
973.2694091796875,
1943.4090576171875,
1604.5711669921875,
2005.1082763671875
] | w_{i}\,=\,\{P_{t}\,\mid\,t\,\in\,[20(i\,-\,1)\,+\,1,20i]\}. | 2511.16657v1 |
with_gt | 9 | \[
M_i = \{ \max(\text{High}_{w_i}), \max(\text{Close}_{w_i}) \}, \quad
m_i = \{ \min(\text{Low}_{w_i}), \min(\text{Close}_{w_i}) \}.
\] | 0.718748 | 0.662461 | 0.769912 | 0.77451 | 0.571429 | page_6 | [
613.574462890625,
2168.63916015625,
1964.8392333984375,
2227.96435546875
] | M_{i}=\{\mathrm{max}(\mathrm{High}_{w},),\mathrm{max}(\mathrm{Close}_{w_{i}})\},\quad m_{i}=\{\mathrm{min}(\mathrm{Low}_{w_{i}}),\mathrm{min}(\mathrm{Close}_{w_{i}})\}. | 2511.16657v1 |
with_gt | 10 | \[
L = \text{sort}\left( \bigcup_{i=1}^{10} (M_i \cup m_i) \right).
\] | 0.800568 | 0.748299 | 0.823529 | 0.844444 | 0.777778 | page_6 | [
1045.0712890625,
2332.823974609375,
1531.0760498046875,
2474.712890625
] | L\simeq\mathrm{sort}\left(\bigcup_{i=1}^{10}(M_{i}\cup m_{i})\right). | 2511.16657v1 |
repair_no_gt | null | null | 0.258387 | 0.261538 | 0.228571 | 0.306122 | 0.272727 | page_6 | [
1046.169921875,
2332.8408203125,
1531.345703125,
2474.806640625
] | L\simeq\mathrm{sort}\left(\bigcup_{i=1}^{10}(M_{i}\cup m_{i})\right). | 2511.16657v1 |
repair_no_gt | null | null | 0.511082 | 0.424242 | 0.542857 | 0.5 | 0.666667 | page_6 | [
1152.0052490234375,
2707.5146484375,
1432.9051513671875,
2760.5859375
] | \left|{\mathcal D}_{i+1}-{\mathcal A}_{i}\right|\,<\,\delta, | 2511.16657v1 |
with_gt | 12 | \[
\mathcal{G} = \{ G_1, G_2, \dots, G_k \},
\] | 0.576128 | 0.438095 | 0.666667 | 0.590164 | 0.6 | page_6 | [
1079.7393798828125,
2960.88525390625,
1495.3179931640625,
3024.648681640625
] | \displaystyle{\cal G}=\{G_{1},G_{2},\dots,G_{k}\}, | 2511.16657v1 |
with_gt | 14 | \[
\bar{x}_j = \frac{1}{|G_j|} \sum_{x_i \in G_j} x_i.
\] | 0.810917 | 0.666667 | 0.841121 | 0.87234 | 1 | page_7 | [
1114.11181640625,
431.8594665527344,
1461.8114013671875,
559.9429931640625
] | \bar{x}_{j}=\left.\frac{1}{\left|G_{j}\right|}\sum_{x_{i}\in G_{j}}x_{i}. | 2511.16657v1 |
repair_no_gt | null | null | 0.488773 | 0.472222 | 0.544 | 0.504673 | 0.285714 | page_7 | [
1102.4364013671875,
681.8671875,
1477.4854736328125,
741.0512084960938
] | S\,=\,\{\overline{{{x}}}_{1},\overline{{{x}}}_{2},\ast\cdot,\overline{{{x}}}_{k}\} | 2511.16657v1 |
with_gt | 16 | \[
\text{Support}_1 = \max\{ \bar{x}_j \in S \mid \bar{x}_j < P_t \}, \quad
\text{Support}_2 = \max\{ \bar{x}_j \in S \mid \bar{x}_j < \text{Support}_1 \},
\] | 0.605672 | 0.603261 | 0.649007 | 0.625455 | 0.4 | page_7 | [
549.1729736328125,
976.7181396484375,
2025.124755859375,
1038.21826171875
] | {\mathrm{Support}}_{1}=\operatorname*{max}\{{\vec{x}}_{j}\in S\mid{\vec{x}}_{j}<P_{t}\},\quad{\mathrm{Support}}_{2}=\operatorname*{max}\{{\vec{x}}_{j}\in S\mid{\vec{x}}_{j}<{\mathrm{Support}}_{1}\}, | 2511.16657v1 |
with_gt | 17 | \[
\text{Resistance}_1 = \min\{ \bar{x}_j \in S \mid \bar{x}_j > P_t \}, \quad
\text{Resistance}_2 = \min\{ \bar{x}_j \in S \mid \bar{x}_j > \text{Resistance}_1 \}.
\] | 0.602043 | 0.601036 | 0.64375 | 0.62116 | 0.4 | page_7 | [
505.9270935058594,
1158.494873046875,
2085.3837890625,
1218.644287109375
] | {\mathrm{Resistance}}_{1}=\operatorname*{min}\{{\vec{x}}_{i}\in S\mid{\vec{x}}_{i}>P_{t}\},\quad{\mathrm{Resistance}}_{2}=\operatorname*{min}\{{\vec{x}}_{i}\in S\mid{\vec{x}}_{i}>{\mathrm{Resistance}}_{1}\}. | 2511.16657v1 |
repair_no_gt | null | null | 0.515867 | 0.109091 | 0.72 | 0.70903 | 0.533333 | page_8 | [
408.7941589355469,
2300.36181640625,
2075.035400390625,
2417.005859375
] | D(n,h)=\frac{1}{2}\left(\operatorname*{max}_{i\in\left[n+1,n+h\right]}P(i)-P(n)\right)+\frac{1}{2}\left(\operatorname*{min}_{i\in\left[n+1,n+h\right]}P(i)-P(n)\right)+\frac{1}{2}\left(P(n+h)-P(n)\right) | 2511.16657v1 |
repair_no_gt | null | null | 0.175327 | 0.210526 | 0.185185 | 0.190476 | 0 | page_8 | [
2012.922119140625,
2411.056884765625,
2066.2041015625,
2456.4501953125
] | ({\mathbf{1}}) | 2511.16657v1 |
repair_no_gt | null | null | 0.466182 | 0.392453 | 0.484018 | 0.44086 | 0.666667 | page_8 | [
987.9466552734375,
2922.436279296875,
1496.0771484375,
3054.287109375
] | Y(n)=\left\{\begin{array}{l l}{{1}}&{{\mathrm{if~}D(n,h)>0}}\\ {{0}}&{{\mathrm{if~}D(n,h)\leq0}}\end{array}\right. | 2511.16657v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_8 | [
2012.2508544921875,
2964.544189453125,
2066.090576171875,
3012.71435546875
] | (2) | 2511.16657v1 |
repair_no_gt | null | null | 0.37635 | 0.305195 | 0.295964 | 0.474886 | 0.714286 | page_9 | [
929.9833374023438,
1214.66259765625,
1550.6265869140625,
1269.40185546875
] | \begin{array}{l l l}{{\mathrm{AUC}_{\mathrm{diff}}}}&{{=}}&{{\mathrm{AUC}_{\mathrm{train}}-\mathrm{AUC}_{\mathrm{test}}}}\end{array} | 2511.16657v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_9 | [
2012.806396484375,
1216.6064453125,
2065.69140625,
1266.7677001953125
] | (3) | 2511.16657v1 |
repair_no_gt | null | null | 0.270217 | 0.336683 | 0.25 | 0.312727 | 0.066667 | page_9 | [
930.9403686523438,
1279.346923828125,
1549.3377685546875,
1334.0821533203125
] | \Delta(\mathrm{\boldmath{~x~}})_{\mathrm{diff}}\;\;\;\;\longrightarrow\;\;\;\;\Delta(\mathrm{\boldmath{~x~}}_{\mathrm{train}}\;\longrightarrow\;\Lambda\mathrm{\<_{y}~}_{\mathrm{\boldmath{~x~}}\to}^{\mathrm{\boldmath{~v~}}} | 2511.16657v1 |
repair_no_gt | null | null | 0.204973 | 0.181818 | 0.222222 | 0.307692 | 0 | page_9 | [
2012.901611328125,
1283.531982421875,
2065.595458984375,
1331.931640625
] | \mathbf{\tau}(4) | 2511.16657v1 |
repair_no_gt | null | null | 0.26114 | 0.338624 | 0.3 | 0.16835 | 0.058824 | page_10 | [
912.7753295898438,
780.35986328125,
1567.1976318359375,
837.3226928710938
] | \Delta\lbrack\mathrm{{{\cal{O}_{m i n}}}}\implies\mathrm{{\cal{I}_{\ell}}}\Lambda\S\Lambda\lbrack\mathrm{{\cal{C}_{t r a i n}}},\Lambda\rbrack\Lambda\lbrack\ast\rbrack\mathrm{{\cal{C}_{t e s t}}}\rbrace | 2511.16657v1 |
repair_no_gt | null | null | 0.196581 | 0.179487 | 0.222222 | 0.269231 | 0 | page_10 | [
2012.973876953125,
784.6788940429688,
2066.295166015625,
834.5150146484375
] | ({\mathfrak{I}}) | 2511.16657v1 |
with_gt | 3 | \begin{equation}
\mathrm{Prob}_{\text{weighted}} = \frac{{\mathrm{Prob} - \mathrm{Prob}_{\text{min}}}}{{\mathrm{Prob}_{\text{max}} - \mathrm{Prob}_{\text{min}}}}
\end{equation} | 0.728253 | 0.763636 | 0.734513 | 0.741071 | 0.571429 | page_11 | [
918.5040283203125,
2561.101318359375,
1559.192626953125,
2672.685791015625
] | {\mathrm{Prob}}_{\mathrm{weighted}}={\frac{{\mathrm{Prob}}-{\mathrm{Prob}}_{\mathrm{min}}}{{\mathrm{Prob}}_{\mathrm{max}}-{\mathrm{Prob}}_{\mathrm{min}}}} | 2511.16657v1 |
repair_no_gt | null | null | 0.204973 | 0.181818 | 0.222222 | 0.307692 | 0 | page_11 | [
2013.0509033203125,
2594.22216796875,
2065.526611328125,
2642.97607421875
] | \mathbf{\tau}(6) | 2511.16657v1 |
with_gt | 0 | \begin{equation} \label{eq:acousitcHelm}
-\Delta p - \omega^{2}\kappa^2\left(1-\frac{\gamma}{\omega}\im\right)p = q
\end{equation} | 0.658771 | 0.682692 | 0.662921 | 0.662722 | 0.5625 | page_1 | [
813.31591796875,
1499.24658203125,
1327.2105712890625,
1589.7100830078125
] | -\Delta p-\omega^{2}\kappa^{2}\left(1-\frac{\gamma}{\omega}\nu\right)p\equiv q | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_1 | [
299.4112854003906,
1516.3756103515625,
387.2133483886719,
1568.0081787109375
] | (1.1) | 2511.16808v1 |
repair_no_gt | null | null | 0.219903 | 0.181818 | 0.19708 | 0.182628 | 0.5 | page_3 | [
536.5584716796875,
1373.981201171875,
1595.64892578125,
1579.3143310546875
] | H=\frac{1}{h^{2}}\left[-\frac{\frac{1}{6}}{-\frac{2}{3}}\begin{array}{c c c}{{-\frac{2}{3}}}&{{-\frac{1}{6}}}\\ {{-\frac{2}{3}}}&{{\frac{10}{3}}}&{{-\frac{2}{3}}}\\ {{-\frac{1}{6}}}&{{-\frac{2}{3}}}&{{-\frac{1}{6}}}\end{array}\right]\left[\frac{1}{12}\begin{array}{c c c}{{\frac{1}{2}}}&{{\frac{1}{12}}}&{{\frac{1}{12}}}... | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_3 | [
298.25201416015625,
1450.20263671875,
387.6949462890625,
1502.51318359375
] | (2.1) | 2511.16808v1 |
with_gt | 2 | \begin{equation}\label{eq:disc4thCompact3D}
H = L - \kappa^2 \omega^2 \left(1-\frac{\gamma}{\omega} \im\right) M
\end{equation} | 0.597358 | 0.60733 | 0.583851 | 0.586667 | 0.642857 | page_3 | [
816.974853515625,
1732.7340087890625,
1317.5357666015625,
1824.945556640625
] | H=L-\kappa^{2}\omega^{2}\left(1-\frac{\gamma}{\omega}\nu\right)M | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_3 | [
298.2362976074219,
1751.7244873046875,
389.2129821777344,
1803.2335205078125
] | (2.2) | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_3 | [
298.2623596191406,
1751.7745361328125,
388.74200439453125,
1803.038818359375
] | (2.2) | 2511.16808v1 |
repair_no_gt | null | null | 0.313792 | 0.277778 | 0.321429 | 0.309434 | 0.4 | page_3 | [
603.4992065429688,
1914.2413330078125,
1528.12109375,
2092.0830078125
] | {\cal L}=-\frac{1}{6h^{2}}\left[\left[1\begin{array}{c c c}{{1}}&{{1}}&{{\mp}}\\ {{1}}&{{2}}&{{1}}\\ {{1}}&{{1}}&{{1}}\end{array}\right]\left[1\begin{array}{c c c}{{\ 2}}&{{1}}\\ {{\ 2}}&{{2}}&{{1}}\\ {{1}}&{{1}}&{{\mp}}\end{array}\right]\right] | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_3 | [
298.0514221191406,
1976.43994140625,
388.0951843261719,
2027.9371337890625
] | (2.4) | 2511.16808v1 |
repair_no_gt | null | null | 0.315175 | 0.28496 | 0.294479 | 0.273764 | 0.571429 | page_3 | [
681.6275634765625,
2175.45849609375,
1451.159912109375,
2353.080078125
] | M={\frac{1}{12}}\left[\left[\begin{array}{c c c}{{}}&{{1}}&{{\mp}}\\ {{}}&{{1}}&{{}}\\ {{}}&{{}}&{{}}\\ {{}}&{{}}&{{1}}\end{array}\right]\left[\begin{array}{c c}{{}}&{{1}}\\ {{}}&{{}}\\ {{}}&{{}}\\ {{}}&{{}}\end{array}\right]\ . | 2511.16808v1 |
repair_no_gt | null | null | 0.079237 | 0.075758 | 0.074766 | 0.042105 | 0.181818 | page_3 | [
298.379638671875,
2237.184814453125,
388.18109130859375,
2288.757568359375
] | (\ 2.4) | 2511.16808v1 |
repair_no_gt | null | null | 0.2078 | 0.188976 | 0.212389 | 0.247423 | 0.166667 | page_4 | [
298.87158203125,
488.48919677734375,
387.8479919433594,
540.3455810546875
] | (2.{\mathfrak{f}}) | 2511.16808v1 |
repair_no_gt | null | null | 0.230563 | 0.22695 | 0.240741 | 0.24 | 0.181818 | page_4 | [
985.8971557617188,
490.5947265625,
1156.6787109375,
542.512451171875
] | \mathbf{\}A_{h}\mathbf{u}=\mathbf{\partial}\mathbf{q} | 2511.16808v1 |
repair_no_gt | null | null | 0.255768 | 0.263804 | 0.28 | 0.29682 | 0.052632 | page_4 | [
793.3056640625,
915.827392578125,
1346.1561279296875,
977.95361328125
] | \mathcal{A}_{H}\otimes_{H}\longrightarrow\mathrm{\small{~\tilde{~}~\tilde{~}~\longrightarrow~}}_{H}\longrightarrow\sum_{\Delta_{\Delta_{\Delta_{\Delta}}}}^{\Delta_{\Delta_{\Delta}}}\Pi | 2511.16808v1 |
repair_no_gt | null | null | 0.252297 | 0.25 | 0.243243 | 0.257143 | 0.285714 | page_4 | [
975.4103393554688,
1155.9127197265625,
1156.8306884765625,
1207.51806640625
] | \mathbf{e}=P\mathbf{e}_{H}. | 2511.16808v1 |
repair_no_gt | null | null | 0.297777 | 0.279279 | 0.295567 | 0.322581 | 0.3125 | page_4 | [
792.0021362304688,
1367.6326904296875,
1335.7452392578125,
1429.9700927734375
] | T\mathrm{G}_{4}=\mathbb{\varepsilon}^{2}-\delta^{2}\hat{\varepsilon}^{2}+\mu_{3}\alpha\hat{\nu}^{2}+\mu_{3}\hat{\nu}^{2}\hat{\nu}_{4}, | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_4 | [
298.8861083984375,
1373.046630859375,
387.4305725097656,
1424.289794921875
] | (2.6) | 2511.16808v1 |
repair_no_gt | null | null | 0.456971 | 0.448276 | 0.45045 | 0.461538 | 0.5 | page_5 | [
896.820556640625,
692.0440063476562,
1241.6939697265625,
750.093505859375
] | H_{s}={\cal H}-\imath\alpha\omega^{2}M, | 2511.16808v1 |
repair_no_gt | null | null | 0.079237 | 0.075758 | 0.074766 | 0.042105 | 0.181818 | page_5 | [
298.23944091796875,
696.4129028320312,
388.26068115234375,
747.8347778320312
] | (\ 2.7) | 2511.16808v1 |
repair_no_gt | null | null | 0.45258 | 0.413043 | 0.454545 | 0.452991 | 0.5625 | page_5 | [
856.5474853515625,
2069.58935546875,
1275.406982421875,
2164.490478515625
] | \mathcal{H}_{l o c}:\underline{{{\mp\Gamma}}}\begin{array}{l}{{\mathrm{SUp}}}\\ {{\theta\in T^{h}i\,g h}}\end{array}\mathcal{P}(\widetilde{S}(\theta)). | 2511.16808v1 |
repair_no_gt | null | null | 0.478046 | 0.458333 | 0.509259 | 0.526316 | 0.315789 | page_5 | [
849.0430297851562,
2611.3037109375,
1286.042236328125,
2709.246337890625
] | \rho_{l o c}:=\mathrm{~{\frac{\mathrm{Sup}}{\theta{\in}T^{l o w}}}}\,\rho(\overline{{{T{G}}}}\langle\theta)\rangle. | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_5 | [
298.47930908203125,
2622.34130859375,
389.1498107910156,
2674.7158203125
] | (2.8) | 2511.16808v1 |
repair_no_gt | null | null | 0.364838 | 0.402985 | 0.343612 | 0.378641 | 0.307692 | page_6 | [
829.4612426757812,
689.34375,
1308.8636474609375,
748.22216796875
] | E(\theta)=\,s p a n\left\{\theta,\theta^{\prime},\theta^{\prime\prime},\theta^{\prime\prime\prime}\right\} | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_6 | [
298.1045837402344,
692.5729370117188,
390.1686706542969,
744.2731323242188
] | (2.9) | 2511.16808v1 |
with_gt | 9 | \begin{equation} \label{eq:symbolTG}
\widetilde{TG}(\theta) = \widetilde{\mathbf{S}}(\theta)^{\nu_2} (I-\widetilde{P}(\theta) \widetilde{H}_c^{-1}(\theta) \widetilde{R}(\theta) \widetilde{H}(\theta)) \widetilde{\mathbf{S}}(\theta)^{\nu_1}.
\end{equation} | 0.732504 | 0.635135 | 0.797136 | 0.794118 | 0.642857 | page_6 | [
603.7705688476562,
895.3079833984375,
1526.1475830078125,
963.6588134765625
] | \widehat{T G}(\theta)=\widetilde{\bf S}(\theta)^{\nu_{2}}(I-\widetilde{P}(\theta)\widetilde{H}_{c}^{-1}(\theta)\widetilde{R}(\theta)\widetilde{H}(\theta))\widetilde{\bf S}(\theta)^{\nu_{1}}. | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_6 | [
298.8012390136719,
906.548828125,
409.5874328613281,
958.564697265625
] | (2.10) | 2511.16808v1 |
repair_no_gt | null | null | 0.454184 | 0.390244 | 0.444444 | 0.38 | 0.833333 | page_6 | [
854.8790283203125,
2398.7392578125,
1276.21533203125,
2565.802001953125
] | R_{b i l i n}={\frac{1}{16}}\left[{\frac{1}{2}}\begin{array}{l l l}{{2}}&{{1}}\\ {{4}}&{{4}}&{{2}}\\ {{1}}&{{2}}&{{1}}\end{array}\right] | 2511.16808v1 |
repair_no_gt | null | null | 0.120084 | 0.21875 | 0.063158 | 0.045977 | 0.2 | page_6 | [
298.3182678222656,
2455.099609375,
388.06085205078125,
2507.182861328125
] | \left(3.1\right) | 2511.16808v1 |
repair_no_gt | null | null | 0.408943 | 0.153132 | 0.524862 | 0.348624 | 0.833333 | page_6 | [
738.1574096679688,
2647.4990234375,
1393.344482421875,
2913.9072265625
] | R_{b i c u b}={\frac{1}{256}}\left[{\frac{1}{4}}{\begin{array}{l l l l l}{4}&{4}&{6}&{4}&{1}\\ {4}&{16}&{24}&{16}&{4}\\ {6}&{24}&{36}&{24}&{6}\\ {4}&{16}&{24}&{16}&{4}\\ {4}&{4}&{6}&{4}\end{array}}\right]. | 2511.16808v1 |
repair_no_gt | null | null | 0.106975 | 0.203125 | 0.042105 | 0.045977 | 0.2 | page_6 | [
297.64764404296875,
2751.278564453125,
387.93426513671875,
2804.0029296875
] | \left(3.2\right) | 2511.16808v1 |
repair_no_gt | null | null | 0.196096 | 0.205556 | 0.234234 | 0.170347 | 0.066667 | page_7 | [
775.3008422851562,
591.9102172851562,
1362.3583984375,
650.7713012695312
] | P_{\Omega1\longrightarrow2}\stackrel{\longrightarrow}{\longrightarrow}\Phi_{\b\o{i c u b}},\qquad P_{2\longrightarrow1}\stackrel{\textstyle}{\longrightarrow}\stackrel{\textstyle{\cal P}_{3}}{\longrightarrow}\stackrel{\textstyle{\cal P}_{3}}{\i c v u b} | 2511.16808v1 |
repair_no_gt | null | null | 0.295217 | 0.348837 | 0.336207 | 0.230415 | 0.1 | page_7 | [
775.5849609375,
591.9531860351562,
1363.17138671875,
650.74462890625
] | P_{\Omega1\longrightarrow2}\implies{P_{b i c u b},\qquad P_{2}}_{\longrightarrow1}\underline{{{P_{2}}}}_{\longrightarrow}\underline{{{P_{b i c a u}}}} | 2511.16808v1 |
repair_no_gt | null | null | 0.290884 | 0.367347 | 0.262295 | 0.301887 | 0.153846 | page_7 | [
297.9279479980469,
593.5247802734375,
388.21026611328125,
643.9705200195312
] | \left({{\bar{3}}\cdot{\bar{3}}}\right) | 2511.16808v1 |
repair_no_gt | null | null | 0.13818 | 0.230769 | 0.082474 | 0.088889 | 0.181818 | page_7 | [
298.44964599609375,
771.7753295898438,
389.7696838378906,
824.5966796875
] | \left(\Im.4\right) | 2511.16808v1 |
repair_no_gt | null | null | 0.332434 | 0.360656 | 0.3379 | 0.320388 | 0.25 | page_7 | [
724.8262329101562,
772.0444946289062,
1411.286376953125,
831.51708984375
] | R_{k\to k+1}\underline{{{1}}}{}_{\mu}i\i n,\quad\Pi_{k+1\to k}\underline{{{-}}}\underline{{{-}}}\underline{{{P}}}_{b i c u b}. | 2511.16808v1 |
repair_no_gt | null | null | 0.373364 | 0.168889 | 0.432584 | 0.498316 | 0.5 | page_7 | [
629.4073486328125,
1643.93115234375,
1509.006591796875,
1737.4566650390625
] | R_{t r i l i n}=\frac{1}{4^{3}}\left[1\mathrm{\boldmath~\nabla~}\ 2\mathrm{\boldmath~\1~}\otimes\left[1\mathrm{\boldmath~\nabla~}\ 2\mathrm{\boldmath~\1~}\right]\otimes\left[1\mathrm{\boldmath~\nabla~}\ 2\mathrm{\boldmath~\nabla~}\right] | 2511.16808v1 |
repair_no_gt | null | null | 0.196853 | 0.335664 | 0.115385 | 0.159091 | 0.181818 | page_7 | [
298.65643310546875,
1665.5244140625,
387.38824462890625,
1717.176513671875
] | \left(\mathbf{3},\mathbf{f}\right) | 2511.16808v1 |
repair_no_gt | null | null | 0.284432 | 0.1133 | 0.291971 | 0.355769 | 0.625 | page_7 | [
461.9779357910156,
1844.194580078125,
1758.4383544921875,
1938.627197265625
] | R_{t r i c u b}=\frac{1}{16^{3}}\left[1\quad4\quad6\quad4\quad1\right]\otimes\left[1\quad4\quad6\quad4\quad1\right]\otimes\left[1\quad4\quad6\quad4\quad4\quad1\right]. | 2511.16808v1 |
repair_no_gt | null | null | 0.106975 | 0.203125 | 0.042105 | 0.045977 | 0.2 | page_7 | [
299.0321350097656,
1865.6292724609375,
387.00775146484375,
1917.57177734375
] | \left(3.6\right) | 2511.16808v1 |
repair_no_gt | null | null | 0.454631 | 0.45098 | 0.442105 | 0.443243 | 0.538462 | page_7 | [
921.6295166015625,
2599.343994140625,
1215.4503173828125,
2715.015869140625
] | \frac{\sum_{H=1}^{m}(\mathrm{nn}z\bigl(H_{c}^{l}\bigr)\bigr)}{\mathrm{nn}z\bigl(H\bigr)} | 2511.16808v1 |
repair_no_gt | null | null | 0.207967 | 0.26087 | 0.211765 | 0.225 | 0 | page_7 | [
299.10028076171875,
2634.27880859375,
388.83538818359375,
2686.967529296875
] | ({\mathbf{3}}.{\overline{{T}}}) | 2511.16808v1 |
repair_no_gt | null | null | 0.194264 | 0.158273 | 0.188034 | 0.27451 | 0.166667 | page_7 | [
298.7181701660156,
2634.4287109375,
388.0821533203125,
2686.340576171875
] | ({\mathfrak{I}}.{\mathcal{T}}) | 2511.16808v1 |
repair_no_gt | null | null | 0.417136 | 0.394366 | 0.393939 | 0.40625 | 0.6 | page_8 | [
944.3551025390625,
2421.3935546875,
1191.3470458984375,
2484.16796875
] | H_{i}=V_{i}H V_{i}^{T} | 2511.16808v1 |
repair_no_gt | null | null | 0.247107 | 0.331126 | 0.174603 | 0.306306 | 0.166667 | page_8 | [
299.1658630371094,
2428.761962890625,
387.6405334472656,
2479.709228515625
] | \left({\mathfrak{I}}.{\mathfrak{G}}\right) | 2511.16808v1 |
with_gt | 18 | \begin{equation}
H_i\bfe_i = V_i\left(\bfq - H\bfu^{(k)}\right)
\qquad \text{and} \qquad
\bfu^{(k+1)} = \bfu^{(k)} + W_i \bfe_i
\end{equation} | 0.69061 | 0.671533 | 0.683417 | 0.694301 | 0.769231 | page_8 | [
541.8753662109375,
2686.0087890625,
1595.8973388671875,
2769.727783203125
] | H_{i}{\bf e}_{i}=V_{i}\left({\bf q-}\,H\,{\bf u}^{(k)}\right)\qquad\mathrm{and}\qquad{\bf u}^{(k+1)}={\bf u}^{(k)}+W_{i}{\bf e}_{i} | 2511.16808v1 |
repair_no_gt | null | null | 0.106975 | 0.203125 | 0.042105 | 0.045977 | 0.2 | page_8 | [
298.85552978515625,
2702.697998046875,
387.8091735839844,
2755.641357421875
] | \left(3.9\right) | 2511.16808v1 |
with_gt | 19 | \begin{equation}\label{eq:smoother}
S = I - w \left(\sum_{i=1}^m V_i^T W_i H_i^{-1} V_i \right) H
\end{equation} | 0.574138 | 0.574713 | 0.553191 | 0.552239 | 0.7 | page_9 | [
760.9052734375,
1658.055908203125,
1376.0931396484375,
1797.980224609375
] | S=I-w\left(\sum_{i=1}^{m}V_{i}^{T}W_{i}H_{i}^{-1}V_{i}\right)H | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_9 | [
298.4886169433594,
1701.3280029296875,
409.6883239746094,
1753.0306396484375
] | (3.10) | 2511.16808v1 |
with_gt | 20 | \begin{equation}\label{eq:smoother_symbol}
\widetilde{S}(\theta) = 1 - w \left( V^T W \Phi(\theta)^H H_i^{-1} \Phi(\theta) V \right) \widetilde{H}(\theta)
\end{equation} | 0.638363 | 0.623377 | 0.634686 | 0.641221 | 0.692308 | page_11 | [
661.575927734375,
743.0997314453125,
1473.51611328125,
809.8226928710938
] | \widetilde{S}(\theta)=1-w\left(V^{T}W^{\ }\Phi(\theta)^{H}H_{i}^{-1}\Phi(\theta)^{H}+\widetilde{H}(\theta)^{\ }\right)\widetilde{H}(\theta) | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_11 | [
298.33837890625,
751.8760375976562,
390.20965576171875,
805.988525390625
] | (4.1) | 2511.16808v1 |
with_gt | 21 | \begin{equation}\label{eq:Hsymbol}
\widetilde{H} = a + 2b \cos(\theta_1) + 2b \cos(\theta_2) + 4c \cos(\theta_1)\cos(\theta_2).
\end{equation} | 0.689175 | 0.678414 | 0.712963 | 0.71066 | 0.583333 | page_11 | [
599.437744140625,
1270.3809814453125,
1533.3297119140625,
1329.8128662109375
] | \tilde{H}=a+2b\cos(\theta_{1})+2b\cos(\theta_{2})+4c\cos(\theta_{1})\cos(\theta_{2}). | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_11 | [
298.2567443847656,
1274.5023193359375,
389.525634765625,
1326.878173828125
] | (4.2) | 2511.16808v1 |
repair_no_gt | null | null | 0.369157 | 0.244576 | 0.318408 | 0.508772 | 0.666667 | page_11 | [
506.1001892089844,
1424.236572265625,
1624.8677978515625,
1640.19482421875
] | \Phi=d i a g\left[1,e^{\l_{\L}\theta_{1}},e^{\l_{\L}\theta_{2}},e^{\l(\theta_{1}+\theta_{2})}\right]\quad\mathrm{and}\quad H_{\L\L}=\left[\begin{array}{l l l}{{a}}&{{b}}&{{b}}&{{c}}\\ {{b}}&{{a}}&{{b}}\\ {{c}}&{{b}}&{{b}}&{{a}}\end{array}\right]. | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_11 | [
298.1316833496094,
1506.1661376953125,
389.0720520019531,
1559.3939208984375
] | (4.4) | 2511.16808v1 |
repair_no_gt | null | null | 0.402082 | 0.344398 | 0.402948 | 0.402204 | 0.571429 | page_11 | [
495.0959167480469,
1730.8486328125,
1720.5435791015625,
1997.518310546875
] | \Phi=d i a g\left[e^{-u\theta_{2}},e^{-\imath\theta_{1}},1,e^{\imath\theta_{1}},e^{\imath\theta_{2}}\right]\quad\mathrm{and}\quad H_{i}=\left[\begin{array}{l l l l}{{e}}&{{c}}&{{b}}&{{c}}\\ {{c}}&{{a}}&{{b}}&{{b}}\\ {{b}}&{{b}}&{{a}}&{{c}}\\ {{c}}&{{b}}&{{c}}&{{a}}\end{array}\right]\ , | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_11 | [
297.3470458984375,
1836.695556640625,
389.5015563964844,
1889.4110107421875
] | (4.4) | 2511.16808v1 |
with_gt | 24 | \begin{equation}\label{eq:skew5lfa}
\Phi = diag\left[e^{-\im(\theta_1 + \theta_2)}, e^{-\im(\theta_2-\theta_1)},1, e^{\im(\theta_2 - \theta_1)}, e^{\im(\theta_1 + \theta_2)} \right]
\end{equation} | 0.736925 | 0.738889 | 0.755418 | 0.744027 | 0.642857 | page_11 | [
588.853515625,
2087.76318359375,
1544.5477294921875,
2176.0859375
] | \Phi=d i a g\left[e^{-\imath(\theta_{1}+\theta_{2})},e^{-\imath(\theta_{2}-\theta_{1})},1,e^{\imath(\theta_{2}-\theta_{1})},e^{\imath(\theta_{1}+\theta_{2})}\right] | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_11 | [
298.1009216308594,
2106.619140625,
388.1571350097656,
2159.448486328125
] | (4.5) | 2511.16808v1 |
repair_no_gt | null | null | 0.355471 | 0.252011 | 0.347541 | 0.204255 | 1 | page_11 | [
835.7207641601562,
2258.0673828125,
1298.61962890625,
2523.219970703125
] | H_{i}=\left[\begin{array}{c c c c}{{a}}&{{c}}&{{}}&{{}}\\ {{}}&{{a}}&{{c}}&{{}}\\ {{c}}&{{c}}&{{a}}&{{c}}&{{}}\\ {{}}&{{c}}&{{a}}&{{}}\\ {{}}&{{c}}&{{}}&{{a}}&{{}}\\ {{}}&{{c}}&{{}}&{{}}&{{a}}\end{array}\right]. | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_11 | [
297.73065185546875,
2364.612548828125,
387.8220520019531,
2416.55517578125
] | (4.6) | 2511.16808v1 |
with_gt | 26 | \begin{equation}
\widetilde{R}(\theta) = \frac{1}{4}\left(1+\cos(\theta_1)\right)\left(1+\cos(\theta_2)\right)
\end{equation} | 0.597854 | 0.638783 | 0.59 | 0.601093 | 0.5 | page_12 | [
739.6994018554688,
695.3617553710938,
1397.4256591796875,
790.9442749023438
] | \widetilde{\cal{M}}(\theta)\ --\frac{1}{4}\left(1\ +\mathrm{{\bf{COS}}}(\theta_{1})\right)\left(1\ +\mathrm{{\bf{COS}}}(\theta_{2})\right) | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_12 | [
298.10455322265625,
716.8741455078125,
389.753173828125,
770.8369140625
] | (4.7) | 2511.16808v1 |
with_gt | 27 | \begin{equation}
\widetilde{R}(\theta) = \frac{1}{64}\left(3+4\cos(\theta_1)+\cos(2\theta_1)\right)\left(3+4\cos(\theta_2)+\cos(2\theta_2)\right).
\end{equation} | 0.802066 | 0.819444 | 0.821138 | 0.805556 | 0.666667 | page_12 | [
501.1246337890625,
913.8964233398438,
1636.0086669921875,
1006.865478515625
] | \tilde{R}(\theta)=\frac{1}{64}\left(3+4\cos(\theta_{1})+\cos(2\theta_{1})\right)(3+4\cos(\theta_{2})+\cos(2\theta_{2})\right). | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_12 | [
298.75860595703125,
934.0109252929688,
388.9785461425781,
988.0309448242188
] | (4.8) | 2511.16808v1 |
noise | null | null | -1 | -1 | -1 | -1 | -1 | page_12 | [
298.3057861328125,
934.2164306640625,
388.3071594238281,
988.0075073242188
] | (4.8) | 2511.16808v1 |
End of preview. Expand in Data Studio
No dataset card yet
- Downloads last month
- 14