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\begin{tabular}{lll} \hline\noalign{\smallskip} recording filename & subject gender & subject age (years) \\ \noalign{\smallskip}\hline\noalign{\smallskip} chb01\_01.edf & female & 11 \\ chb02\_01.edf & male & 11 \\ chb03\_01.edf & female & 14 \\ chb04\_01.edf & male & 22 \\ chb05\_01.edf & female & 7 \\ chb06\_01.edf & female & 1.5 \\ chb07\_01.edf & female & 14.5 \\ chb08\_02.edf & male & 3.5 \\ chb09\_01.edf & female & 10 \\ chb10\_01.edf & male & 3 \\ chb11\_01.edf & female & 12 \\ chb12\_06.edf & female & 2 \\ chb13\_02.edf & female & 3 \\ chb14\_01.edf & female & 9 \\ chb15\_02.edf & male & 16 \\ chb16\_01.edf & female & 7 \\ chb17a\_03.edf & female & 12 \\ chb18\_02.edf & female & 18 \\ chb19\_02.edf & female & 19 \\ chb20\_01.edf & female & 6 \\ chb22\_01.edf & female & 9 \\ chb23\_06.edf & female & 6 \\ \noalign{\smallskip}\hline \end{tabular}
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\begin{tabular}{llll} \hline\noalign{\smallskip} FP1-F7 & F7-T7 & T7-P7 & P7-O1 \\ FP1-F3 & F3-C3 & C3-P3 & P3-O1 \\ FP2-F4 & F4-C4 & C4-P4 & P4-O2 \\ FZ-CZ & CZ-PZ & T7-FT9 & \\ FT9-FT10 & FT10-T8 & & \\ \noalign{\smallskip}\hline \end{tabular}
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\begin{tabular}{ll} \toprule Concepts/Abbreviations & Definition \\ \hline GADGMSS & General-Accumulation Discrete GM(1,1) model in Simplex Space \\ TGMI & Traditional GM(1,1) model with \emph{ilr}-transformation \\ IGADGM & Infused General-Accumulation Discrete GM(1,1) model \\ DE algorithm & Differential Evolution algorithm \\ Compositional data & A data type, characteristics of proportions and constant-sum constrict \\ Simplex Space & Mathematical space of compositional data \\ Aitchison geometry & Geometry in Simplex space \\ \emph{ilr} transformation & isometric logratio transforming compositional data from Simplex space to Euclidean space \\ Development coefficient & Overall change rate year-on-year for a complete system \\ \emph{DF} & Determination Factor for weighing the proportion of the results from the two models\\ \bottomrule \end{tabular}
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\begin{tabular}{ccccccccccc} \toprule Region&2010&2011&2012&2013&2014&2015&2016&2017&2018&2019\\ \midrule Arctic nations&10.23\%&12.06\%&13.63\%&12.81\%&13.38\%&15.15\%&16.67\%&19.12\%&19.77\%&18.29\%\\ Middle east &46.77\%&49.50\%&49.75\%&51.76\%&52.79\%&50.38\%&47.01\%&43.56\%&45.75\%&47.34\%\\ Africa&21.92\%&18.53\%&16.87\%&16.58\%&15.61\%&12.63\%&12.63\%&13.26\%&12.42\%&11.93\%\\ America&8.28\%&8.46\%&9.18\%&8.42\%&9.42\%&10.10\%&10.81\%&10.92\%&11.03\%&11.28\%\\ Southeast Asia&12.79\%&11.44\%&10.55\%&10.43\%&8.80\%&11.74\%&12.89\%&13.13\%&11.03\%&11.15\%\\ \bottomrule \end{tabular}
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\begin{tabular}{ccc} \toprule Name & Abbreviation & Formula \\ \hline Component Vector Percentage Error & CVPE & $\frac{\langle ilr(X_1),ilr(X_2) \rangle}{\langle ilr(X_1),ilr(X_1)\rangle}$ \\ Mean Component Percentage Error & MCPE & $\frac{1}{n}\sum_{i=1}^{n}\frac{\langle ilr(x_{1i}),ilr(x_{2i}) \rangle}{\langle ilr(x_{1i}),ilr(x_{1i})\rangle}$ \\ Mean Absolute Percentage Error & MAPE & $\frac{1}{nD}\sum_{i=1}^{n}|\frac{ilr(x_{1i})-ilr(x_{2i})}{ilr(x_{1i})}|$ \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccccccccc} \toprule Region&2010&2011&2012&2013&2014&2015&2016&2017&2018&2019\\ \midrule America&57.32\%&59.67\%&59.55\%&60.33\%&63.56\%&56.55\%&58.27\%&57.03\%&47.81\%&44.08\%\\ Europe&26.69\%&24.82\%&23.43\%&23.78\%&20.91\%&27.66\%&24.97\%&24.72\%&34.45\%&36.33\%\\ Asia&15.99\%&15.51\%&17.03\%&15.89\%&15.53\%&15.79\%&16.75\%&18.26\%&17.74\%&19.59\%\\ \bottomrule \end{tabular}
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\begin{tabular}{cccccccccc} \toprule & \multicolumn{3}{c|}{American} & \multicolumn{3}{c|}{Europe} & \multicolumn{3}{c}{Asia} \\ \cline{2-10} Times & TGMI & GADGMSS & \multicolumn{1}{c|}{IGADGM} & TGMI & GADGMSS & \multicolumn{1}{c|}{IGADGM} & TGMI & GADGMSS & IGADGM \\ \hline 2010 & 0.57 & 0.57 & 0.57 & 0.27 & 0.27 & 0.27 & 0.16 & 0.16 & 0.16 \\ 2011 & 0.61 & 0.59 & 0.60 & 0.24 & 0.24 & 0.24 & 0.16 & 0.17 & 0.16 \\ 2012 & 0.60 & 0.58 & 0.59 & 0.24 & 0.25 & 0.24 & 0.16 & 0.17 & 0.17 \\ 2013 & 0.60 & 0.59 & 0.59 & 0.24 & 0.25 & 0.25 & 0.16 & 0.16 & 0.16 \\ 2014 & 0.59 & 0.61 & 0.60 & 0.24 & 0.24 & 0.24 & 0.16 & 0.15 & 0.16 \\ 2015 & 0.59 & 0.56 & 0.58 & 0.25 & 0.26 & 0.26 & 0.17 & 0.17 & 0.17 \\ 2016 & 0.58 & 0.57 & 0.58 & 0.25 & 0.25 & 0.25 & 0.17 & 0.17 & 0.17 \\ 2017 & 0.58 & 0.56 & 0.57 & 0.25 & 0.26 & 0.26 & 0.17 & 0.18 & 0.18 \\ 2018 & 0.57 & 0.55 & 0.56 & 0.25 & 0.27 & 0.26 & 0.17 & 0.19 & 0.18 \\ 2019 & 0.57 & 0.56 & 0.56 & 0.25 & 0.26 & 0.26 & 0.18 & 0.18 & 0.18 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccccc} \toprule & \multicolumn{3}{c|}{Prediction Error} & \multicolumn{3}{c}{Fitting Error} \\ \cline{2-7} & CVPE & MCPE & MAPE & CVPE & MCPE & MAPE \\ \hline TGMI & 0.215 & 0.213 & 0.132 & 0.032 & 0.008 & 0.150 \\ GADGMSS & 0.307 & 0.283 & \textbf{0.087} & 0.025 & 0.007 & 0.163 \\ IGADGM & \textbf{0.204} & \textbf{0.204} & 0.125 & \textbf{0.024} & \textbf{0.006} & \textbf{0.148} \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccccccccc} \toprule Region&2010&2011&2012&2013&2014&2015&2016&2017&2018&2019\\ \midrule Middle East&58.20\%&61.28\%&60.64\%&59.96\%&57.30\%&54.13\%&55.91\%&55.05\%&57.04\%&54.29\%\\ Africa&19.26\%&16.79\%&15.52\%&14.50\%&15.64\%&17.67\%&15.52\%&14.36\%&13.56\%&14.85\%\\ America&8.57\%&8.03\%&12.64\%&15.02\%&14.71\%&12.09\%&11.00\%&12.07\%&13.14\%&14.23\%\\ Asia-Pacific&13.97\%&13.90\%&11.20\%&10.52\%&12.35\%&16.12\%&17.57\%&18.52\%&16.27\%&16.63\%\\ \bottomrule \end{tabular}
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\begin{tabular}{ccccccccccccc} \toprule & \multicolumn{3}{c|}{Middle East} & \multicolumn{3}{c|}{Africa} & \multicolumn{3}{c|}{America} & \multicolumn{3}{c}{Asia\&Pacific} \\ \cline{1-13} Times & TGMI & GADGMSS & \multicolumn{1}{c|}{IGADGM} & TGMI & GADGMSS & \multicolumn{1}{c|}{IGADGM} & TGMI & GADGMSS & \multicolumn{1}{c|}{IGADGM} & TGMI & GADGMSS & IGADGM \\ \cline{2-13} 2010 & 0.58 & 0.58 & 0.58 & 0.19 & 0.19 & 0.19 & 0.09 & 0.09 & 0.09 & 0.14 & 0.14 & 0.14 \\ 2011 & 0.62 & 0.62 & 0.62 & 0.16 & 0.16 & 0.16 & 0.11 & 0.09 & 0.10 & 0.11 & 0.12 & 0.12 \\ 2012 & 0.61 & 0.57 & 0.58 & 0.16 & 0.18 & 0.17 & 0.11 & 0.11 & 0.11 & 0.12 & 0.15 & 0.14 \\ 2013 & 0.59 & 0.58 & 0.59 & 0.16 & 0.16 & 0.16 & 0.12 & 0.15 & 0.14 & 0.13 & 0.12 & 0.12 \\ 2014 & 0.58 & 0.56 & 0.57 & 0.16 & 0.16 & 0.16 & 0.12 & 0.16 & 0.14 & 0.14 & 0.12 & 0.13 \\ 2015 & 0.56 & 0.54 & 0.55 & 0.16 & 0.18 & 0.17 & 0.13 & 0.13 & 0.13 & 0.15 & 0.15 & 0.15 \\ 2016 & 0.55 & 0.55 & 0.55 & 0.16 & 0.18 & 0.17 & 0.13 & 0.12 & 0.12 & 0.16 & 0.16 & 0.16 \\ 2017 & 0.53 & 0.56 & 0.55 & 0.16 & 0.17 & 0.16 & 0.14 & 0.12 & 0.13 & 0.17 & 0.16 & 0.16 \\ 2018 & 0.52 & 0.55 & 0.54 & 0.16 & 0.18 & 0.17 & 0.14 & 0.13 & 0.13 & 0.18 & 0.15 & 0.16 \\ 2019 & 0.50 & 0.55 & 0.53 & 0.16 & 0.18 & 0.17 & 0.15 & 0.13 & 0.14 & 0.19 & 0.14 & 0.16 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccccc} \toprule & \multicolumn{3}{c|}{Prediction Error} & \multicolumn{3}{c}{Fitting Error} \\ \cline{2-7} & \multicolumn{1}{c}{CVPE} & \multicolumn{1}{c}{MCPE} & \multicolumn{1}{c}{MAPE} & \multicolumn{1}{c}{CVPE} & \multicolumn{1}{c}{MCPE} & \multicolumn{1}{c}{MAPE} \\ \hline TGMI & 0.032 & 0.032 & \textbf{0.018} & 0.075 & 0.032 & 0.245 \\ GADGMSS & 0.053 & 0.053 & 0.025 & \textbf{0.038} & \textbf{0.017} & \textbf{0.168} \\ IGADGM & \textbf{0.031} & \textbf{0.031} & 0.019 & 0.041 & 0.018 & 0.182 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccccccc} \toprule & \multicolumn{3}{c|}{Prediction Error} & \multicolumn{3}{c}{Fitting Error} \\ \cline{2-7} Models & CVPE & MCPE & MAPE & CVPE & MCPE & MAPE \\ \hline ARIMA & 0.091 & 0.091 & 0.180 & 0.046 & 0.031 & 0.137 \\ IGADGM & \textbf{0.031} & \textbf{0.031} & \textbf{0.082} & 0.010 & 0.007 & 0.054 \\ LR & 0.059 & 0.059 & 0.152 & 0.013 & 0.009 & 0.076 \\ SVM & 0.145 & 0.144 & 0.221 & 0.017 & 0.011 & 0.091 \\ GaussianNB & 0.133 & 0.133 & 0.212 & \textbf{0.000} & \textbf{0.000} & \textbf{0.008} \\ \bottomrule \end{tabular}
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\begin{tabular}{cccccc} \toprule Years & Arctic field & Middle East & Africa & Americas & Southeast Asia \\ \hline 2020 & 0.195 & 0.454 & 0.117 & 0.116 & 0.118 \\ 2021 & 0.196 & 0.442 & 0.121 & 0.118 & 0.123 \\ 2022 & 0.202 & 0.436 & 0.117 & 0.121 & 0.124 \\ 2023 & 0.210 & 0.430 & 0.113 & 0.123 & 0.124 \\ 2024 & 0.217 & 0.424 & 0.109 & 0.125 & 0.125 \\ 2025 & 0.225 & 0.418 & 0.105 & 0.127 & 0.125 \\ \bottomrule \end{tabular}
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\begin{tabular}{ccc} \toprule Name&Route&Voyage(sea mile)\\ \midrule Middle East route 1& Kuwait port-strait of Hormuz-Singapore-Lianyungang&6371\\ Middle East route 2&Suez-Mander strait-Singapore-Lianyungang&7362\\ West Africa&Lagos-Cape Town-Singapore-Lianyungang&10588\\ The South America&the port of Maracaibo-panama canal-Paific-Lianyungang&9527\\ The Arctic passage 1&Murmansk NSR-Bering strait-Lianyungang&7355.4\\ The Arctic passage 2&NSR Rotterdam-Bering strait-Lianyungang&8992\\ \bottomrule \end{tabular}
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\begin{tabular}{lll} \hline Parameter & Description & Prior\\ \hline\hline $\xi_{r}$ & Fraction of recycled NS in low-mass Gaussian & $U(0,1)$ \\ \hline $\mu_{r1}$ & Mean of low-mass Gaussian in $m_r$ distribution & $U(1.1M_{\odot},1.5M_{\odot}$) \\ \hline $\sigma_{r1}$ & Standard deviation of low-mass Gaussian in $m_r$ distribution & $U(0.005M_{\odot},0.5M_{\odot}$) \\ \hline $\mu_{r2}$ & Mean of high-mass Gaussian in $m_r$ distribution & $U(\mu_{r1},2.0M_{\odot}$) \\ \hline $\sigma_{r2}$ & Standard deviation of high-mass Gaussian in $m_r$ distribution & $U(0.005M_{\odot},0.5M_{\odot}$) \\ \hline $\xi_{s}$ & Fraction of slow NS in low-mass Gaussian & $U(0,1)$ \\ \hline $\mu_{s1}$ & Mean of low-mass Gaussian in $m_s$ distribution & $U(1.1M_{\odot},1.5M_{\odot}$) \\ \hline $\sigma_{s1}$ & Standard deviation of low-mass Gaussian in $m_s$ distribution & $U(0.005M_{\odot},0.5M_{\odot}$) \\ \hline $\mu_{s2}$ & Mean of high-mass Gaussian in $m_s$ distribution & $U(\mu_{s1},2.0M_{\odot}$) \\ \hline $\sigma_{s2}$ & Standard deviation of high-mass Gaussian in $m_s$ distribution & $U(0.005M_{\odot},0.5M_{\odot}$) \\ \hline $m_\text{min}$ & Minimum possible NS mass & $1M_{\odot}$ \\ \hline $m_\text{max}$ & Maximum possible NS mass & $3M_{\odot}$ \\ \hline $t_{*}$ & characteristic delay time & $U(5~\mathrm{Myr},500~\mathrm{Myr}$)\\ \hline \end{tabular}
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\begin{tabular}{ccc} \hline $k$ ($\unit[]{km\, s^{-1} M_\odot^{-1}}$)& $f_\text{radio}$ & $f_\text{GW}$ \\ \hline\hline 100 & 0.084 & 0.083\\ 200 & 0.084 & 0.083 \\ 300 & 0.082 & 0.083 \\ 400 & 0.059 & 0.083 \\ 500 & 0.042 & 0.083 \\ 600 & 0.02 & 0.081 \\ 700 & 0.004 & 0.06 \\ 800 & 0 & 0.034 \\ \hline \end{tabular}
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\begin{tabular}{lcc} \toprule & $\phi$ explicitly known & $\phi$ relation to \textit{data fidelity} \\ \cline{1-3} Colorization & \ding{55} & Luminance and edge related \\ Inpainting & \ding{51} & Binary mask based \\ Denoising & \ding{55} & Noise-level adaptive \\\bottomrule \\ \end{tabular}
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\begin{tabular}{|c|ccc|l} \cline{1-4} i & & Bob & & \\ \cline{1-4} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & \ \ \ \ 0 \ \ \ \ & \\ \cline{2-4} Alice & \multicolumn{1}{c|}{ \ \ 0 \ \ } & \multicolumn{1}{c|}{0} & 0 & \\ \cline{2-4} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & 1 & \\ \cline{1-4} \end{tabular}\!\!\!\!, \ \ \begin{tabular}{|c|ccc|l} \cline{1-4} ii & & Bob & & \\ \cline{1-4} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & \ \ \ \ 0 \ \ \ \ & \\ \cline{2-4} Alice & \multicolumn{1}{c|}{ \ \ 0 \ \ } & \multicolumn{1}{c|}{1} & 1 & \\ \cline{2-4} & \multicolumn{1}{c|}{} & \multicolumn{1}{c|}{} & 0 & \\ \cline{1-4} \end{tabular}
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\begin{tabular}{lll} \hline Datasets & Entity type & Number of annotations \\ \hline NCBI Disease & Disease & 6881 \\ BC5CDR & Disease & 12694 \\ BC5CDR & Drug/Chem. & 15411 \\ BC4CHEMD & Drug/Chem. & 79824 \\ BC2GM & Gene/Protein & 20703 \\ JNLPBA & Gene/Protein & 35460 \\ LINNAEUS & Species & 4077 \\ Species-800 & Species & 3708 \\ \hline \end{tabular}
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\begin{tabular}{||c|ccccc||} \hline Name & $a$ (au) & $e$ & $i$ (deg) & $q$ (au) & $Q$ (au) \\ [0.5ex] \hline\hline 29P/Schwassmann-Wachmann 1 & 5.99 & 0.045 & 9.391 & 5.72 & 6.26 \\ \hline 39P/Oterma & 7.251 & 0.246 & 1.943 & 5.471 & 9.032 \\ \hline 2000 GM137 & 7.862 & 0.121 & 15.865 & 6.907 & 8.816 \\ \hline 2004 VP112 & 8.7 & 0.047 & 6.851 & 8.288 & 9.112 \\ \hline P/2005 S2 (Skiff) & 7.965 & 0.197 & 3.141 & 6.398 & 9.531 \\ \hline P/2005 T3 (Read) & 7.509 & 0.174 & 6.261 & 6.202 & 8.816 \\ \hline 2007 TB434 & 8.704 & 0.026 & 9.768 & 8.477 & 8.931 \\ \hline P/2008 CL94 (Lemmon) & 6.171 & 0.119 & 8.348 & 5.434 & 6.907 \\ \hline P/2010 C1 (Scotti) & 7.066 & 0.259 & 9.142 & 5.235 & 8.896 \\ \hline P/2010 H5 (Scotti) & 7.144 & 0.156 & 14.087 & 6.026 & 8.261 \\ \hline P/2011 C2 (Gibbs) & 7.366 & 0.268 & 10.911 & 5.389 & 9.344 \\ \hline 2011 FS53 & 6.763 & 0.144 & 7.645 & 5.789 & 7.737 \\ \hline 2014 HY195 & 7.158 & 0.104 & 22.896 & 6.412 & 7.903 \\ \hline P/2015 M2 (PANSTARRS) & 7.203 & 0.179 & 3.974 & 5.913 & 8.492 \\ \hline 494219 & 5.751 & 0.047 & 43.422 & 5.481 & 6.022 \\ \hline \end{tabular}
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\begin{tabular}{||c|cccccc||} \hline Population & Reservoir & \multicolumn{2}{c}{Total Number} & \multicolumn{2}{c}{Time in Region (kyr)} & Near Centaur Limit \\ [0.5ex] & & OJFCs & NCs & OJFCs & NCs & \\ \hline\hline Classical & 4800 & 62 & 102 & 24.3$\pm$6.3 & 10.9$\pm$1.7 & 261$\pm$90 \\ \hline Resonant & 4800 & 84 & 133 & 26.7$\pm$5.2 & 13.3$\pm$2.0 & 279$\pm$79 \\ \hline Scattering & 4900 & 14 & 19 & 37.0$\pm$18.7 & 14.4$\pm$4.2 & 187$\pm$127 \\ \hline Combined & 14500 & 160 & 254 & 26.6$\pm$4.0 & 12.4$\pm$1.3 & 262$\pm$55 \\ \hline \end{tabular}
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\begin{tabular}{|c|rr|rr|rr|rr|} \hline \multirow{3}{*}{Models} & \multicolumn{2}{c|}{\multirow{2}{*}{ Full}} & \multicolumn{6}{c|}{Bilinear projection (BP)} \\ \cline{4-9} & & & \multicolumn{2}{c|}{$\alpha=1$} & \multicolumn{2}{c|}{$\alpha=2$} & \multicolumn{2}{c|}{$\alpha=3$} \\ \cline{2-9} & \multicolumn{1}{c}{EXC} & \multicolumn{1}{c|}{INC} & \multicolumn{1}{c}{EXC} & \multicolumn{1}{c|}{INC} & \multicolumn{1}{c}{EXC} & \multicolumn{1}{c|}{INC} & \multicolumn{1}{c}{EXC} & \multicolumn{1}{c|}{INC} \\ \hline S-VGG & 2,578,944 & 2,589,194 & 8,548 & 18,798 & 29,928 & 50,418 & 57,996 & 88,726 \\ \hline ResNet-56 & 1,660,768 & 1,663,338 & 32,128 & 34,698 & 128,416 & 138,666 & 299,456 & 309,706 \\ \hline SqueezeNet & 467,370 & 469,380 & 10,080 & 15,210 & 40,128 & 60,618 & 89,196 & 135,286 \\ \hline MobileNet v2 & 2,223,872 & 2,236,682 & 112,432 & 125,242 & 654,056 & 705,266 & 3,065,346 & 3,180,556 \\ \hline Image captioner & 7,712,160 & 15,976,416 & 26,468 & 8,290,724 & 50,224 & 16,570,480 & 70,848 & 24,847,104 \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|} \hline \multirow{2}{*}{Models} & \multirow{2}{*}{Full} & \multicolumn{3}{c|}{BP} \\ \cline{3-5} & & $\alpha=1$ & $\alpha=2$ & $\alpha=3$\\ \hline Top-1 error & 28.5 & 36.7 & 32.2 & 28.9 \\ Top-5 error & 9.4 & 14.3 & 11.9 & 10.2 \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|} \hline \multirow{2}{*}{Models} & \multirow{2}{*}{Full} & \multicolumn{3}{c|}{BP} &\multirow{2}{*}{CP} &\multirow{2}{*}{LR} \\ \cline{3-5} & & $\alpha=1$ & $\alpha=2$ & $\alpha=3$ & &\\ \hline S-VGG & 82.9 & 68.5 & 74.3 & {\bf 83.1} & 81.7 & 81.8 \\ ResNet-56 & 92.7 & 83.4 & 89.9 & {\bf 93.0} & 91.3 & 90.5 \\ SqueezeNet & 81.6 & 66.3 & 72.5 & {\bf 81.9} & - & - \\ MobileNet v2 & {\bf 80.3} & 70.4 & 74.0 & 78.7 & - & - \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|} \hline \multirow{2}{*}{Models} & \multirow{2}{*}{Full} & \multicolumn{3}{c|}{BP} &\multirow{2}{*}{CP} &\multirow{2}{*}{LR} \\ \cline{3-5} & & $\alpha=1$ & $\alpha=2$ & $\alpha=3$ & &\\ \hline S-VGG & 93.6 & 87.3 & 89.1 & {\bf 93.7} & 92.3 & 92.2 \\ ResNet-56 & 97.3 & 93.7 & 95.4 & {\bf 97.3} & 96.4 & 96.1 \\ SqueezeNet & {\bf 92.1} & 87.4 & 90.5 & 92.0 & - & - \\ MobileNet v2 & {\bf 94.6} & 88.6 & 92.3 & 94.4 & - & - \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline Model & $\alpha=1$ & $\alpha=2$ & $\alpha=3$ \\ \hline S-VGG & 34K & 91K & 159K \\ \hline ResNet-56 & 153K & 612K & 1.4M \\ \hline SqueezeNet & 313K & 1.2M & 2.7M \\ \hline MobileNet v2 & 353K & 4.7M & 23.0M \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|} \hline Model & $\alpha=1$ & $\alpha=2$ & $\alpha=3$ \\ \hline S-VGG & 0.02G & 0.06G & 0.14G \\ \hline ResNet-56 & 0.52G &2.09G & 4.71G \\ \hline SqueezeNet & 0.03G & 0.01G & 0.32G \\ \hline MobileNet v2 & 0.06G &0.96G & 0.48G \\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c} \toprule \multicolumn{6}{c|}{CASIA-B} & \multicolumn{6}{c}{OUMVLP} \\ \hline Layer Name & In\_C & Out\_C & Kernel & Global & N-part & Layer Name & In\_C & Out\_C & Kernel & Global & N-part \\ \midrule \multirow{2}[2]{*}{Conv3d} & \multirow{2}[2]{*}{\checkmark} & \multirow{2}[2]{*}{32} & \multirow{2}[2]{*}{(3, 3, 3)} & \multirow{2}[2]{*}{\checkmark} & \multirow{2}[2]{*}{$\times$} & Conv3d & 1 & 32 & (3, 3, 3) & \checkmark & $\times$ \\ \cline{7-12} & & & & & & Conv3d & 32 & 32 & (3, 3, 3) & \checkmark & $\times$ \\ \hline LTA & 32 & 32 & (3, 1, 1) & $-$ & $-$ & LTA & 32 & 32 & (3, 1, 1) & $-$ & $-$ \\ \hline \multirow{2}[2]{*}{GLConvA} & \multirow{2}[2]{*}{32} & \multirow{2}[2]{*}{32} & \multirow{2}[2]{*}{(3, 3, 3)} & \multirow{2}[2]{*}{\checkmark} & \multirow{2}[2]{*}{8} & GLConvA & 32 & 64 & (3, 3, 3) & \checkmark & 8 \\ \cline{7-12} & & & & & & GLConvA & 64 & 64 & (3, 3, 3) & \checkmark & 8 \\ \hline Max Pooling & $-$ & $-$ & (1, 2, 2) & $-$ & $-$ & Max Pooling & $-$ & $-$ & (1, 2, 2) & $-$ & $-$ \\ \hline \multirow{2}[2]{*}{GLConvA} & \multirow{2}[2]{*}{64} & \multirow{2}[2]{*}{128} & \multirow{2}[2]{*}{(3, 3, 3)} & \multirow{2}[2]{*}{\checkmark} & \multirow{2}[2]{*}{8} & GLConvA & 64 & 128 & (3, 3, 3) & \checkmark & 8 \\ \cline{7-12} & & & & & & GLConvA & 128 & 128 & (3, 3, 3) & \checkmark & 8 \\ \hline \multirow{2}[2]{*}{GLConvB} & \multirow{2}[2]{*}{128} & \multirow{2}[2]{*}{128} & \multirow{2}[2]{*}{(3, 3, 3)} & \multirow{2}[2]{*}{\checkmark} & \multirow{2}[2]{*}{8} & GLConvA & 128 & 256 & (3, 3, 3) & \checkmark & 8 \\ \cline{7-12} & & & & & & GLConvB & 256 & 256 & (3, 3, 3) & \checkmark & 8 \\ \bottomrule \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c} \toprule \multirow{2}[2]{*}{\textbf{Method}} & \multicolumn{14}{c|}{\textbf{Probe View}} & \multicolumn{1}{c}{\multirow{2}[2]{*}{\textbf{Mean}}} \\ \cline{2-15} \multicolumn{1}{c|}{} & $0^{\circ}$ & $15^{\circ}$ & $30^{\circ}$ & $45^{\circ}$ & $60^{\circ}$ & $75^{\circ}$ & $90^{\circ}$ & $180^{\circ}$ & $195^{\circ}$ & $210^{\circ}$ & $225^{\circ}$ & $240^{\circ}$ & $255^{\circ}$ & $270^{\circ}$ & \\ \midrule GEINet & 23.2 & 38.1 & 48.0 & 51.8 & 47.5 & 48.1 & 43.8 & 27.3 & 37.9 & 46.8 & 49.9 & 45.9 & 45.7 & 41.0 & 42.5 \\ \hline GaitSet & 79.3 & 87.9 & 90.0 & 90.1 & 88.0 & 88.7 & 87.7 & 81.8 & 86.5 & 89.0 & 89.2 & 87.2 & 87.6 & 86.2 & 87.1 \\ \hline GaitPart & 82.6 & 88.9 & 90.8 & 91.0 & 89.7 & 89.9 & 89.5 & 85.2 & 88.1 & 90.0 & 90.1 & 89.0 & 89.1 & 88.2 & 88.7 \\ \hline GLN & 83.8 & 90.0 & 91.0 & 91.2 & 90.3 & 90.0 & 89.4 & 85.3 & \textbf{89.1} & \textbf{90.5} & \textbf{90.6} & 89.6 & 89.3 & 88.5 & 89.2 \\ \hline Ours & \textbf{84.9} & \textbf{90.2} & \textbf{91.1} & \textbf{91.5} & \textbf{91.1} & \textbf{90.8} & \textbf{90.3} & \textbf{88.5} & 88.6 & 90.3 & 90.4 & \textbf{89.6} & \textbf{89.5} & \textbf{88.8} & \textbf{89.7} \\ \bottomrule \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c|c|c} \toprule \multicolumn{2}{c|}{GLConvA-1} & \multicolumn{2}{c|}{GLConvA-2} & \multicolumn{2}{c|}{GLConvB} & \multirow{2}[2]{*}{NM} & \multirow{2}[2]{*}{BG} & \multirow{2}[2]{*}{CL} \\ \cline{1-6} Global & N-parts & Global & N-parts & Global & N-parts & & & \\ \midrule \checkmark & $\times$ & \checkmark & $\times$ & \checkmark & $\times$ & 97.1 & 93.7 & 81.9 \\ \hline $\times$ & 8 & $\times$ & 8 & $\times$ & 8 & 96.2 & 92.5 & 80.4 \\ \hline \checkmark & 2 & \checkmark & 2 & \checkmark & 2 & 97.3 & 94.3 & 82.9 \\ \hline \checkmark & 4 & \checkmark & 4 & \checkmark & 4 & 97.4 & 94.5 & 83.0 \\ \hline \checkmark & 8 & \checkmark & 8 & \checkmark & 8 & \textbf{97.4} & \textbf{94.5} & \textbf{83.6} \\ \bottomrule \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c} \toprule \multicolumn{3}{c|}{\textbf{Spatial Feature Mapping}} & \multirow{2}[2]{*}{NM} & \multirow{2}[2]{*}{BG} & \multirow{2}[2]{*}{CL} & \multirow{2}[2]{*}{Mean} \\ \cline{1-3} $F_{Max}^{1\times1\times W_{2}}$ & $F_{Avg}^{1\times1\times W_{2}}$ & $GeM$ & & & & \\ \midrule \checkmark & & & 97.3 & 94.0 & 82.5 & 91.3 \\ \hline & \checkmark & & 96.3 & 92.1 & 77.2 & 88.5 \\ \hline \checkmark & \checkmark & & 97.2 & 94.0 & 82.8 & 91.3 \\ \hline & & \checkmark & \textbf{97.4} & \textbf{94.5} & \textbf{83.6} & \textbf{91.8} \\ \bottomrule \end{tabular}
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\begin{tabular}{c|c|c|c|c} \toprule \multicolumn{2}{c|}{Downsampling} & \multirow{2}[2]{*}{NM} & \multirow{2}[2]{*}{BG} & \multirow{2}[2]{*}{CL} \\ \cline{1-2} 1st pooling layer & 2nd pooling layer & & & \\ \midrule SP & SP & 96.3 & 90.9 & 77.7 \\ \hline SP & LTA & 97.0 & 93.9 & 82.2 \\ \hline LTA & SP & \textbf{97.4} & \textbf{94.5} & \textbf{83.6} \\ \hline LTA & LTA & 94.4 & 89.2 & 74.7 \\ \bottomrule \end{tabular}
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\begin{tabular}{lllll} \toprule \multicolumn{1}{r}{} & \multicolumn{2}{c}{Validation Accuracy} & \multicolumn{2}{c}{Test Accuracy} \\ \cmidrule(r){2-5} Model Name & 1-img prediction & 4-rot prediction & 1-img prediction & 4-rot prediction \\ \midrule Baseline & 63.20 & \ & 63.04 & \ \\ Reg with loss & 69.34 & 71.18 & 67.61 & \textbf{69.49} \\ Reg with loss and conf & \textbf{69.56} & \textbf{71.44} & \textbf{67.93} & 69.32 \\ Sep with loss & 60.04 & 60.38 & 57.92 & 58.32 \\ Sep with loss and conf & 64.56 & 65.02 & 62.59 & 63.12 \\ \bottomrule \end{tabular}
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\begin{tabular}{|c||cc|cc|} \hline \multirow{2}{*}{Parameter settings} & \multicolumn{2}{c|}{COVID-19} & \multicolumn{2}{c|}{Robotic Instrument} \\ \cline{2-5} & Loss & IoU &Loss & mIoU \\ \hline $\tau=1,\upsilon=10$ & 0.034 & 72.8 & 0.086 & 71.2 \\ $\tau=1,\upsilon=1$ & 0.033 & 73.4 & 0.086 & 71.5 \\ $\tau=10,\upsilon=1$ & 0.031 & 73.1 & 0.093 & 72.7 \\ $\tau=10,\upsilon=0.1$ & 0.031 & 72.8 & 0.086 & 72.1 \\ $\tau=10,\upsilon=0.01$ & 0.033 & 72.7 & 0.090 & 71.8 \\ \hline \end{tabular}
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\begin{tabular}{|c||cc|cc|} \hline \multirow{2}{*}{Method} & \multicolumn{2}{c|}{Part 1} & \multicolumn{2}{c|}{Part 2} \\ \cline{2-5} & Pixel Acc. & IoU & Pixel Acc. & IoU \\ \hline Cross-entropy & 81.1 & 69.6 & 86.6 & 76.8 \\ Dice loss & 80.7 & 70.0 & 85.5 & 76.1 \\ Tversky loss & 80.7 & 68.1 & {\bf 89.1} & 76.0 \\ Focal loss & 80.0 & 68.5 & 87.3 & 76.9 \\ lov{\'a}sz-softmax & 79.6 & 70.0 & 88.2 & 77.7 \\ Ours & {\bf 83.8} & {\bf 71.3} & 88.3 & {\bf 78.1} \\ \hline \end{tabular}
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\begin{tabular}{|c||cc|cc|} \hline \multirow{2}{*}{Method} & \multicolumn{2}{c|}{Binary} & \multicolumn{2}{c|}{Multi-class} \\ \cline{2-5} & Pixel Acc. & IoU & Pixel Acc. & mIoU \\ \hline Cross-entropy & 94.6 & 86.0 & 81.1 & 66.2 \\ Dice loss & {\bf 97.7} & 84.7 & 78.5 & 67.6 \\ Tversky loss & 96.4 & 85.9 & 79.7 & 68.6 \\ Focal loss & 94.8 & 86.2 & 80.0 & 69.5 \\ lov{\'a}sz-softmax & 96.3 & 86.0 & 80.1 & 68.9 \\ Ours & 95.8 & {\bf 87.4} & {\bf 81.5} & {\bf 72.5} \\ \hline \end{tabular}
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\begin{tabular}{|c||cccc|} \hline Method & Shaft & Wrist & Claspers & Probe \\ \hline Cross-entropy & 81.1 & 55.3 & 55.5 & 72.9 \\ Dice loss & 83.8 & 61.8 & 54.2 & 70.5 \\ Tversky loss & 84.9 & 64.8 & 55.4 & 69.3 \\ Focal loss & 86.5 & 62.9 & 56.5 & 72.0 \\ lov{\'a}sz-softmax & 86.3 & 64.4 & 55.5 & 69.3 \\ Ours & {\bf 88.2} & {\bf 67.1} & {\bf 61.1} & {\bf 73.4} \\ \hline \end{tabular}
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\begin{tabular}{|c||cc|cc|} \hline \multirow{2}{*}{Method} & \multicolumn{2}{c|}{COVID-19} & \multicolumn{2}{c|}{Robotic Instrument} \\ \cline{2-5} & Part 1 & Part 2 & Binary & Multi-class \\ \hline Ours + Tversky loss & 71.6 & 78.5 & 87.7 & 73.1 \\ Ours + Dice loss & 71.5 & 78.0 & 87.8 & 73.2 \\ \hline \end{tabular}
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\begin{tabular}{ll} \hline Parameter & Description \\ \hline \hline $\beta (t)$ & Rate at which susceptible individuals become infected due to \\ & contacts with infectious individuals at time $t$; $\beta(t)$ is a function \\ & of the mobility variables $\mathbf{m}(t)$ at time $t$ \\ $\gamma_A$ & Weight representing lower risk of infection when infectious \\ & individuals are asymptomatic \\ $\rho_{EI}$ & Rate at which exposed individuals become symptomatic\\ $\rho_{EA}$ & Rate at which exposed individuals become asymptomatic \\ $\rho_{IR}$ & Rate at which symptomatic individuals recover on their own \\ $\rho_{IH}$ & Rate at which symptomatic individuals develop severe symptoms\\ & and become hospitalized\\ $\rho_{AR}$ & Rate at which asymptomatic individuals recover on their own \\ $\rho_{HR}$ & Rate at which hospitalized individuals recover \\ $\alpha_D$ &Proportion of hospitalized individuals that die, relative to those \\ & that recover \\ \hline \hline \end{tabular}
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\begin{tabular}{|l|l|l|} \hline & \multicolumn{1}{c|}{\textbf{Number of Scenarios}} & \multicolumn{1}{c|}{\textbf{How are they used}} \\ \hline \textbf{\begin{tabular}[c]{@{}l@{}}Virtual \\ Testing\end{tabular}} & \begin{tabular}[c]{@{}l@{}}High. Any number of \\test scenarios can be \\ generated in the given \\logical scenario \\ parameter space\end{tabular} & \begin{tabular}[c]{@{}l@{}}\\ Embedded in all aspects of \\ system development, conduct \\ massive scene tests to verify \\ the boundaries of autonomous \\ driving functions \\\\ \end{tabular} \\ \hline \textbf{\begin{tabular}[c]{@{}l@{}}Close\\ Field \\ Testing\end{tabular}} & \begin{tabular}[c]{@{}l@{}}Low. Due to the \\ limitation of the test \\ field.\end{tabular} & \begin{tabular}[c]{@{}l@{}}\\ Validate key scenes, and \\ build new scene types that are \\ not encountered or have low \\ probability \\\\ \end{tabular} \\ \hline \textbf{\begin{tabular}[c]{@{}l@{}}Open\\ Road \\ Testing\end{tabular}} & \begin{tabular}[c]{@{}l@{}}High. Can encounter \\as many required test \\ scenarios as possible\end{tabular} & \begin{tabular}[c]{@{}l@{}}\\ Clarify the statistical property \\ of related events, verify the \\ system boundaries in actual \\ situations, detect the interaction \\ between autonomous vehicles \\ and traditional vehicles, and \\ discover new scenarios \\ that have not been considered \\\\ \end{tabular} \\ \hline \end{tabular}
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\begin{tabular}{lll} \textbf{Layer} & \textbf{Output Shape} & \textbf{\# Parameters} \\ \hline conv1(3,3) & (224, 224, 32) & 896 \\ batch normalization & (224, 224, 32) & 896 \\ max pooling(2,2) & ( 112, 112, 32) & 0 \\ conv2(3,3) & ( 112, 112, 64) & 18496 \\ batch normalization & (112, 112, 64) & 448 \\ max pooling(2,2) & (56, 56, 64) & 0 \\ conv3(3,3) & (56, 56, 128) & 73856 \\ batch normalization & (56, 56, 128) & 224 \\ max pooling(2,2) & (28, 28, 128) & 0 \\ flatten & (100352) & 0 \\ dense & (200) & 20070600 \\ dense & (1) & 201 \\ \hline \textbf{Total} & 20,164,833 & \\ \hline \end{tabular}
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\begin{tabular}{|clcccc|} \hline No.& Name & Objectives & Variables & Constraints & Best known $f(x,y)$ \\ \hline 1 & Cassini1 & 1 & 6 & 4 & 4.9307 \\ 2 & Cassini2 & 1 & 22 & 0 & 8.3830 \\ 3 & Messenger (reduced) & 1 & 18 & 0 & 8.6299 \\ 4 & Messenger (full) & 1 & 26 & 0 & 1.9579 \\ 5 & GTOC1 & 1 & 8 & 6 & -1581950.0 \\ 6 & Rosetta & 1 & 22 & 0 & 1.3434 \\ 7 & Sagas & 1 & 12 & 2 & 18.1877 \\ 8 & Cassini1-MINLP & 1 & 10 & 4 & 3.5007 \\ 9 & Cassini1-MO & 2 & 6 & 5 & na \\ 10 & Cassini1-MO-MINLP & 2 & 10 & 5 & na \\ \hline \end{tabular}
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\begin{tabular}{lcl} C/C++ &~~~:~~~& gtopx( benchmark, f, g, x ); \\ Python &~~~:~~~& [ f, g ] = gtopx( benchmark, x, o,n,m ) \\ Matlab &~~~:~~~& [ f, g ] = gtopxmex( benchmark, x ) \\ \end{tabular}
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\begin{tabular}{cc} \hline ~~~Value~~~ & ~~~~~~Planet~~~~~~ \\ \hline 1 & Mercury \\ 2 & Venus \\ 3 & Earth \\ 4 & Mars \\ 5 & Jupiter \\ 6 & Saturn \\ 7 & Uranus \\ 8 & Neptune \\ 9 & Pluto \\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline $\frac{\sigma_t}{t}$ & 1.5 & 1.4 & 1.3 & 1.2 & 1.1 & 1.0 & 0.9 & 0.8 & 0.7 & 0.6 & 0.5 & 0.4 & 0.3 \\ \hline $\frac{\sigma_q}{q}$ & any & 0.6 & 0.8 & 1.01 & 1.3 & 1.65 & 2.13 & 3.25 & 5.5 & 8.0 & 20.0 & 70.0 & 1000.0 \\ \hline $\delta(\mathcal{T})$ & 0.50 & 0.48 & 0.44 & 0.40 & 0.36 & 0.32 & 0.27 & 0.21 & 0.15 & 0.10 & 0.05 & 0.01& 0.00 \\ \hline $\delta(\hat{Q})$ & any & 0.1 & 0.21 & 0.32 & 0.44 & 0.54 & 0.64 & 0.76 & 0.86 & 0.90 & 0.96 & 0.99 & 1.00\\ \hline \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline $\frac{\sigma_t}{t}$ & 1.5 & 1.4 & 1.3 & 1.2 & 1.1 & 1.0 & 0.9 & 0.8 & 0.7 & 0.6 & 0.5 & 0.4 & 0.3 \\ \hline $\frac{\sigma_q}{q}$ & any & 0.39 & 0.6 & 0.85 & 1.2 & 1.54 & 2.1 & 3.2 & 5.9 & 8.0 & 20.0 & 80.0 & 1000.0 \\ \hline $\delta(\mathcal{T})$ & 0.50 & 0.48 & 0.44 & 0.40 & 0.36 & 0.32 & 0.27 & 0.21 & 0.15 & 0.10 & 0.05 & 0.01& 0.00 \\ \hline $\delta(\hat{Q})$ & any & 0.1 & 0.21 & 0.32 & 0.44 & 0.54 & 0.64 & 0.76 & 0.86 & 0.90 & 0.96 & 0.99 & 1.00\\ \hline \end{tabular}
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\begin{tabular}{|c|ccc|}\hline & \multicolumn{3}{c|}{Estimated order of convergence} \\ & $r$ & $p$ & $x$ \\\hline Optimally compatible & 1.0067 & 1.0076 & 1.0021 \\ Compatible & 1.0066 & 1.0055 & 0.5351 \\\hline \end{tabular}
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\begin{tabular}{c|c|c} \hline Calibrations (Distance) & $f_x$ (pixel) & $f_y$ (pixel) \\ \hline Reference (0km/0mi) & 1810.4 & 1840.1 \\ \hline Stop1 (2.63km/1.63mi) & 1870.1 & 1906.3 \\ \hline Stop2 (1.85km/1.15mi) & 1918.7 & 1939.0 \\ \hline Stop3 (7.54km/4.69mi) & 1935.2 & 1965.8 \\ \hline Relative Variation & 6.6256\% & 6.5715\% \\ \hline \end{tabular}
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\begin{tabular}{l|c|c} & Symmetrized & {\bf Rebalanced}\\\hline Inverted W & $(85 \pm 6)$\% & {\bf $\mathbf{(66 \pm 5)}$\%} \\ Grover & $(78 \pm 5)$\% & {\bf $\mathbf{(58 \pm 5)}$\%} \\ Gaussian $(\mu = -0.11)$ & $(98 \pm 6)$\% & {\bf $\mathbf{(56 \pm 5)}$\%} \\ Gaussian $(\mu = 0.78)$ & $(80 \pm 6)$\% & {\bf $\mathbf{(41 \pm 4)}$\%} \end{tabular}
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\begin{tabular}{|c|c|c|c|c|} \hline & \multicolumn{2}{c|}{Test Accuracy ($\%$): $f{=}5$} & \multicolumn{2}{c|}{Test Accuracy ($\%$): $f{=}17$} \\ \hline & OracleSGD & DiverseFL & OracleSGD & DiverseFL \\ \hline Gaussian & 81.0 & 80.8 & 28.5 & 28.5 \\ \hline \end{tabular}
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\begin{tabular}{||c|c|c|c|c||} \hline Index & Parameter & Description & Nominal Value & Units \\ [0.5ex] \hline\hline $1$ & $a$ & Number of resting microglia & $1000$ & cells\\ \hline $2$ & $k_{M1}$ & Activation rate of microglia to $M1$ & $0.44$ & $\frac{1}{\text{hours}}$ \\ \hline $3$ & $k_{M2}$ & Activation rate of microglia to $M2$ & $0.65$ & $\frac{1}{\text{hours}}$ \\ \hline $4$ & $k_{P}$ & Production rate of $P$ & $0.01$ & $\frac{pg/ml}{\text{hours} \cdot\text{cells}}$ \\ \hline $5$ & $k_{A}$ & Production rate of $A$ & $0.006$& $\frac{pg/ml}{\text{hours} \cdot \text{cells}}$ \\ \hline $6$ & $n_{P}$ & Hill coefficient for $P$ in $H(P)$ & $0.5$ & unitless \\ \hline $7$ & $K_{P}$ & Half-maximal concentration of $P$ & $10$ & $\frac{pg}{ml}$ \\ \hline $8$ & $n_{A}$ & Hill coefficient for $A$ in $H(A)$ & $0.5$ & unitless \\ \hline $9$ & $K_{A}$ & Half-maximal concentration of $A$ & $10$ & $\frac{pg}{ml}$ \\ \hline $10$ & $s_{M1 \rightarrow M2}$ & Rate of $M1 \rightarrow M2$ switch & $0.2$ & $\frac{1}{\text{hours}}$ \\ \hline $11$ & $s_{M2 \rightarrow M1}$ & Rate of $M2 \rightarrow M1$ switch & $0.2$ & $\frac{1}{\text{hours}}$ \\ \hline $12$ & $\mu_{M1}$ & Mortality rate of $M1$ & $0.1$ & $\frac{1}{\text{hours}}$ \\ \hline $13$ & $\mu_{M2}$ & Mortality rate of $M2$ & $0.1$ & $\frac{1}{\text{hours}}$ \\ \hline $14$ & $\mu_{A}$ & Natural decay rate of $A$ & $0.1$ & $\frac{1}{\text{hours}}$ \\ \hline $15$ & $\mu_{P}$ & Natural decay rate of $P$ & $0.1$ & $\frac{1}{\text{hours}}$ \\ \hline $16$ & $N_{A}$ & Hill coefficient for $A$ in $\hat{H}(A)$ & $0.5$ & unitless \\ \hline $17$ & $N_{P}$ & Hill coefficient for $P$ in $\hat{H}(P)$ & $0.5$ & unitless \\ \hline \end{tabular}
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\begin{tabular}{||c|c|c|c|c||} \hline Index & Parameter & Description & Nominal Value & Units \\ [0.5ex] \hline\hline $18$ & $b$ & Minimum value of $N_1$ & $0.3$ & unitless \\ \hline $19$ & $\tau_1$ & Steepness of $N_1$ & $1$ & unitless \\ \hline $20$ & $\tau_2$ & Steepness of $N_2$ & $1$ & unitless \\ \hline $21$ & $L$ & Maximum value of $N_2$ & $0.8$ & unitless \\ \hline $22$ & $t_0$ & Time at which treatment is applied & $0-15$ & hours\\ \hline \end{tabular}
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\begin{tabular}{ccccc} \toprule Dataset & Nodes & Edges & Classes & Features\\ \midrule Cora& 2,708 & 5,429 & 7 & 1,433\\ PubMed& 19,711 & 44,338 & 3 & 500\\ \midrule Flickr & 89,250 & 899,756 & 7 & 500\\ Reddit & 232,965 & 11,606,919 & 41 & 602\\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccc|cccc} \toprule \multirow{2}{*}{Networks} & \multicolumn{4}{c|}{Cora} & \multicolumn{4}{c}{PubMed}\\ \cline{2-9} & Accuracy & M.S. & D.S. & C.O. & Accuracy & M.S. & D.S. & C.O.\\ \midrule GCN & \textbf{81.4 ± 0.4} & 360K & 14.8M & 2.50e8 & 79.0 ± 0.3 & 125.75K & 37.6M & 6.38e8\\ Bi-GCN(binarize features only)& 81.1 ± 0.4 & 360K & \textbf{0.47M} & 2.50e8 & \textbf{79.4 ± 1.0} & 125.75K & \textbf{1.25M} & 6.38e8\\ Bi-GCN(binarize weights only)& 78.3 ± 1.5 & \textbf{11.53K} & 14.8M & 2.50e8 & 75.5 ± 1.4 & \textbf{4.19K}& 37.6M & 6.38e8\\ Bi-GCN & 81.2 ± 0.8 & \textbf{11.53K} & \textbf{0.47M} & \textbf{4.67e6} & 78.2 ± 1.0 & \textbf{4.19K}& \textbf{1.25M} & \textbf{1.55e7}\\ \midrule GAT & 83.0 ± 0.7 & 360.55K & 14.8M & 2.51e8 & 79.0 ± 0.3 & 126.27K & 37.6M & 6.44e8\\ FastGCN & 79.8 ± 0.3 & 360K & 14.8M & 2.50e8 & 79.1 ± 0.2 & 125.75K & 37.6M & 6.38e8\\ SGC & 81.0 ± 0.0 & 39.18K & 14.8M & 2.72e7 & 78.9 ± 0.0 & 5.86K & 37.6M & 2.98e7\\ \bottomrule \end{tabular}
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\begin{tabular}{c|cccc|cccc} \toprule \multirow{2}{*}{Networks} & \multicolumn{4}{c|}{Reddit} & \multicolumn{4}{c}{Flickr}\\ \cline{2-9} & F1-micro & M.S. & D.S. & C.O. & F1-micro & M.S. & D.S. & C.O.\\ \midrule inductiveGCN & \textbf{93.8 ± 0.1} &643.00K& 534.99M & 4.18e10 &\textbf{50.9 ± 0.3} &507.00K&170.23M & 1.18e10\\ Bi-inductiveGCN & 93.1 ± 0.2 & \textbf{21.25K} & \textbf{17.61M} & \textbf{4.18e9}& 50.2 ± 0.4&\textbf{16.87K}&\textbf{5.66M}&\textbf{4.65e8} \\ \midrule GraphSAGE& 95.2 ± 0.1 & 1286.00K & 534.99M & 8.01e10 & \textbf{50.9 ± 1.0}&1014.00K &170.23M& 2.34e10 \\ Bi-GraphSAGE & \textbf{95.3 ± 0.1} & \textbf{42.51K} & \textbf{17.61M} & \textbf{4.92e9} & 50.2 ± 0.4&\textbf{33.74K}& \textbf{5.66M}& \textbf{6.93e8}\\ \midrule GraphSAINT& \textbf{95.9 ± 0.1} & 1798.00K& 534.99M & 1.13e11&\textbf{52.1 ± 0.1}&1526.00K&170.23M&3.53e10\\ Bi-GraphSAINT& 95.7 ± 0.1 & \textbf{139.62K} &\textbf{17.61M} & \textbf{1.04e10} & 50.8 ± 0.2&\textbf{65.25K}&\textbf{5.66M}&\textbf{1.28e9}\\ \bottomrule \end{tabular}
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\begin{tabular}{|l|l|l|l|l|} \hline Characteristic & Early/No disease & Moderate disease & Advanced disease & Overall \\ \hline \# SDOCT-SAP pairs & 27216 & 5387 & 5831 & 38434 \\ \hline \# SDOCT & 26860 & 5289 & 5752 & 37901 \\ \hline \# SAP & 24055 & 4603 & 4920 & 33578 \\ \hline \# Eyes & 16856 & 3638 & 3885 & 23171 \\ \hline \# Patients & 10440 & 3123 & 3062 & 13284 \\ \hline Mean Age (SD) & 54.9 (20.4) & 59.1 (21.2) & 59.7 (20.7) & 56.2 (20.7) \\ \hline \# Female (\%) & 6039 (57.8\%) & 1805 (57.8\%) & 1585 (51.8\%) & 9429 (56.7\%) \\ \hline \# Race (\%) & & & & \\ Black & 2831 (27.1\%) & 959 (30.7\%) & 1156 (37.8\%) & 4946 (29.8\%) \\ White & 6407 (61.4\%) & 1826 (58.5\%) & 1540 (50.3\%) & 9773 (58.8\%) \\ Other & 1202 (11.5\%) & 338 (10.8\%) & 366 (12.0\%) & 1888 (11.4\%) \\ \hline Mean RNFL Thickness & & & & \\ in $\mu$m (SD) & 87.5 (17.5) & 73.6 (20.9) & 64.2 (23.4) & 82.0 (21.0) \\ \hline Median MD in dB (IQR) & -1.6 (-3.1, -0.3) & -8.2 (-9.8, -6.9) & -18.8 (-25.1, -14.9) & -2.7 (-6.9, -0.8) \\ \hline Median PSD in dB (IQR) & 1.9 (1.5, 2.6) & 7.0 (4.6, 9.5) & 9.7 (7.4, 11.9)& 2.3 (1.6, 5.7) \\ \hline \multicolumn{2}{l}{\scriptsize SD: Standard Deviation} & \multicolumn{3}{r}{\scriptsize IQR: Inter-Quartile Range} \\ \end{tabular}
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\begin{tabular}{|l|l|l|l|l|} \hline Method & Early/No disease & Moderate disease & Advanced disease & Overall \\ \hline Linear Regression & $4.11 \; (0.01)$ & $6.36 \; (0.03)$ & $13.34 \; (0.04)$ & $5.54 \; (0.01)$\\ \hline Fully connected model & $3.38 \; (0.01)$ & $6.47 \; (0.03)$ & $12.65 \; (0.04)$ & $5.00 \; (0.01)$\\ \hline Convolutional model & $3.32 \; (0.01)$ & $6.68 \; (0.03)$ & $11.97 \; (0.04)$ & $4.90 \; (0.01)$\\ \hline RetiNerveNet & $3.31 \; (0.01)$ & $\mathbf{6.34} \; (0.03)$ & $11.26 \; (0.04)$ & $4.70 \; (0.01)$\\ \hline RetiNN Ensemble & $\mathbf{3.29} \; (0.01)$ & $6.43 \; (0.03)$ & $\mathbf{11.10} \; (0.04)$ & $\mathbf{4.67} \; (0.01)$\\ \hline \multicolumn{5}{r}{\scriptsize Best results in \textbf{boldface}.} \\ \end{tabular}
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\begin{tabular}{|l|l|l|l|l|l|l|l|} \hline Method & Central & Temporal & Inferior & Inferior & Superior & Superior & MD \\ & & & & Nasal & & Nasal & \\ \hline Linear Regression & $4.99 \; (0.01)$ & $5.46 \; (0.01)$ & $5.67 \; (0.01)$ & $5.29 \; (0.01)$ & $5.87 \; (0.01)$ & $5.59 \; (0.01)$ & $4.31 \; (0.01)$ \\ \hline Fully conn. model & $4.42 \; (0.01)$ & $5.06 \; (0.01)$ & $5.39 \; (0.01)$ & $4.95 \; (0.01)$ & $5.33 \; (0.01)$ & $4.72 \; (0.01)$ & $3.75 \; (0.01)$ \\ \hline Convolutional model & $4.41 \; (0.01)$ & $5.28 \; (0.01)$ & $5.06 \; (0.01)$ & $4.49 \; (0.01)$ & $5.47 \; (0.01)$ & $4.80 \; (0.01)$ & $3.63 \; (0.01)$ \\ \hline RetiNerveNet & $4.40 \; (0.01)$ & $4.98 \; (0.01)$ & $4.87 \; (0.01)$ & $4.30 \; (0.01)$ & $\mathbf{5.26} \; (0.01)$ & $\mathbf{4.57} \; (0.01)$ & $3.51 \; (0.01)$ \\ \hline RetiNN Ensemble & $\mathbf{4.37} \; (0.01)$ & $\mathbf{4.97} \; (0.01)$ & $\mathbf{4.83} \; (0.01)$ & $\mathbf{4.27} \; (0.01)$ & $5.27 \; (0.01)$ & $\mathbf{4.57} \; (0.01)$ & $\mathbf{3.49} \; (0.01)$ \\ \hline \multicolumn{8}{r}{\scriptsize Best results in \textbf{boldface}.} \\ \end{tabular}
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\begin{tabular}{cccccccccc} \hline \multirow{2}{*}{Case} &\multicolumn{4}{c}{inflated state}& &\multicolumn{4}{c}{deflated state} \\ \cline{2-5} \cline{7-10} & $V_{u}$ [cc] & $V_{l}$ [cc] & $N_{j}$ & $N_{e}$ & & $V_{u}$ [cc] & $V_{l}$ [cc] & $N_{j}$ & $N_{e}$ \\ \hline \hline 1 & 173.5 & 242.9 & 58 & 62 & & 82.7 & 96.9 & 44 & 48 \\ 2 & 167.1 & 508.3 & 63 & 64 & & 69.9 & 116.4 & 62 & 63 \\ 3 & 231.7 & 357.6 & 66 & 67 & & 111.4 & 145.3 & 40 & 48 \\ 4 & 184.7 & 258.2 & 73 & 75 & & 71.4 & 100.4 & 36 & 40 \\ 5 & 246.1 & 353.3 & 62 & 67 & & 78.9 & 92.8 & 49 & 57 \\ 6 & 188.4 & 373.2 & 77 & 83 & & 65.8 & 104.1 & 30 & 37 \\ 7 & 131.9 & 257.9 & 97 & 98 & & 55.8 & 110.7 & 31 & 32 \\ 8 & 164.3 & 342.1 & 69 & 75 & & 102.3 & 196.7 & 39 & 42 \\ 9 & 198.8 & 375.4 & 58 & 67 & & 84.9 & 111.8 & 43 & 51 \\ 10 & 232.5 & 355.7 & 90 & 98 & & 113.5 & 186.4 & 60 & 64 \\ 11 & 163.7 & 212.1 & $-$ & $-$ & & 160.2 & 236.6 & $-$ & $-$ \\ \hline mean$\pm$SD & 189.3$\pm$35.1 & 330.6$\pm$83.4 & 71.3$\pm$13.3 & 75.6$\pm$13.3 & & 90.6$\pm$29.7 & 136.2$\pm$48.7 & 43.4$\pm$10.9 & 48.2$\pm$10.8 \\ \hline \end{tabular}
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\begin{tabular}{cccccc} \hline Error metric & Rigid & AF & PWA & LSM & Proposed \\ \hline \hline MD [mm] & 10.09 $\pm$ 2.14 & 4.13 $\pm$ 1.22 & 1.49 $\pm$ 0.20 & 0.24 $\pm$ 0.05 & 0.24 $\pm$ 0.06 \\ HD [mm] & 29.65 $\pm$ 5.72 & 15.97 $\pm$ 4.84 & 6.35 $\pm$ 1.85 & 0.74 $\pm$ 0.18 & 0.78 $\pm$ 0.17 \\ CD (mean) [mm] & 4.08 $\pm$ 1.15 & 3.83 $\pm$ 1.80 & 3.88 $\pm$ 1.68 & 3.86 $\pm$ 1.70 & 1.51 $\pm$ 0.58* \\ CD (maximum) [mm] & 11.48 $\pm$ 4.71 & 12.78 $\pm$ 6.61 & 12.07 $\pm$ 6.04 & 12.40 $\pm$ 6.14 & 7.53 $\pm$ 2.47* \\ TRE (surface) [mm] & 22.91 $\pm$ 8.81 & 10.65 $\pm$ 5.46 & 6.11 $\pm$ 3.69 & 4.57 $\pm$ 4.13 & 4.55 $\pm$ 2.82 \\ TRE (bronchus) [mm] & 7.59 $\pm$ 4.77 & 5.63 $\pm$ 3.60 & 6.10 $\pm$ 3.54 & 6.14 $\pm$ 3.51 & 3.97 $\pm$ 2.75* \\ \hline & & & & & \multicolumn{1}{r}{*: $p<$0.01}\\ \end{tabular}
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\begin{tabular}{ccc} \hline Case & Bronchus & Parenchyma\\ \hline \hline 1 & 0.315 $\pm$ 0.064 & 0.286 $\pm$ 0.194 \\ 2 & 0.372 $\pm$ 0.176 & 0.616 $\pm$ 0.506 \\ 3 & 0.320 $\pm$ 0.209 & 0.329 $\pm$ 0.162 \\ 4 & 0.275 $\pm$ 0.099 & 0.430 $\pm$ 0.398 \\ 5 & 0.247 $\pm$ 0.138 & 0.499 $\pm$ 0.330 \\ 6 & 0.230 $\pm$ 0.109 & 0.463 $\pm$ 0.239 \\ 7 & 0.250 $\pm$ 0.131 & 0.303 $\pm$ 0.138 \\ 8 & 0.295 $\pm$ 0.102 & 0.209 $\pm$ 0.159 \\ 9 & 0.350 $\pm$ 0.128 & 0.580 $\pm$ 0.640 \\ 10 & 0.255 $\pm$ 0.121 & 0.272 $\pm$ 0.118 \\ \hline Mean $\pm$ SD & 0.292 $\pm$ 0.141 & 0.395 $\pm$ 0.296* \\ \hline \hline & & \multicolumn{1}{r}{*: $p<$0.05}\\ \end{tabular}
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\begin{tabular}{cccccc} \hline \multicolumn{3}{c}{Feature extraction module} & \multicolumn{3}{c}{DI reconstruction module} \\ Layer & K-Size & K-Num & Layer & K-Size & K-Num \\ \hline DConv1 & 3$\times$3 & 64 & TConv6 & 2$\times$2 & 512 \\ Pooling1 & 2$\times$2 & - & DConv6 & 3$\times$3 & 512 \\ DConv2 & 3$\times$3 & 128 & TConv7 & 2$\times$2 & 256 \\ Pooling2 & 2$\times$2 & - & DConv7 & 3$\times$3 & 256 \\ DConv3 & 3$\times$3 & 256 & TConv8 & 2$\times$2 & 128 \\ Pooling3 & 2$\times$2 & - & DConv8 & 3$\times$3 & 128 \\ DConv4 & 3$\times$3 & 512 & TConv9 & 2$\times$2 & 64 \\ Pooling4 & 2$\times$2 & - & DConv9 & 3$\times$3 & 64 \\ DConv5 & 3$\times$3 & 1024 & Conv10 & 1$\times$1 & 16 \\ - & - & - & Conv11 & 1$\times$1 & 1 \\ - & - & - & Sigmoid & - & - \\ \hline \end{tabular}
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\begin{tabular}{cccccc} \hline \multirow{2}{*}{Dataset} & \multirow{2}{*}{Metrics} & \multicolumn{4}{c}{Size of filter} \\ & & 3 & 5 & 7 & 9 \\ \hline \multirow{3}{*}{S1} & Pr(\%) & 27.34 & \textbf{47.10} & 41.91 & 22.94 \\ & Rc(\%) & \textbf{41.59} & 31.93 & 27.97 & 36.85 \\ & F1(\%) & 32.99 & \textbf{38.06} & 33.55 & 28.27 \\ \hline \multirow{3}{*}{T3} & Pr(\%) & \textbf{95.09} & 89.60 & 86.57 & 94.19 \\ & Rc(\%) & 71.78 & 80.38 & \textbf{82.51} & 76.55 \\ & F1(\%) & 81.81 & \textbf{84.74} & 84.49 & 84.46 \\ \hline \end{tabular}
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\begin{tabular}{lccll} \hline \hline Datasets & Number & Resolution & Data type & Public \\ \hline DRIVE & 40 & $565 \times 584$ & Fundus & Public \\ STARE & 20 & $605 \times 700$ & Fundus & Public \\ IOSTAR & 30 & $1024 \times 1024$ & Fundus & Public \\ CORN-1 & 1698 & $384 \times 384$ & CCM & Public \\ OCTA & 30 & $1376 \times 968$ & OCTA & Private \\ OCT RPE & 36 & $384 \times 379$ & OCT & Private \\ \hline \end{tabular}
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\begin{tabular}{l|ccccc} \hline \hline \textbf{Methods} & \textbf{TPR} $\uparrow$ & \textbf{FNR} $\downarrow$ & \textbf{FPR} $\downarrow$ & \textbf{OR} $\downarrow$ & \textbf{UR} $\downarrow$\\ \hline Backbone & 0.9517 & 0.0493 & 0.0103 & 0.0877 & 0.0808 \\ Backbone+CAB & 0.9663 & 0.0310 & 0.0024 & 0.1082 & 0.0341 \\ Backbone+SAB & 0.9565 & 0.0413 & 0.0018 & 0.1147 & 0.0532 \\ \textbf{CS$^2$Net} & \textbf{0.9706} & \textbf{0.0285} & \textbf{0.0004} & \textbf{0.1027} & \textbf{0.0296} \\ \hline \end{tabular}
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\begin{tabular}{l|l} \toprule Symbol & Meaning\\ \midrule $\bm{X}^{(i)}$ & The $i$-th view of multi-view data. \\ \midrule $\bm{H}$ & Latent representation of multiple views. \\ \midrule $\bm{x}_a^{(i)}$ & Sample $a$ in the $i$-th view. \\ \midrule $\bm{h}_a^{(i)}$ & Sample $a$ in latent representation. \\ \midrule $n$ & The number of data samples. \\ \midrule $v$ & The number of views. \\ \midrule $m$ & The number of clusters. \\ \midrule $\rm{dim}_i$ & The dimensionality of the $i$-th view.\\ \midrule $d_{ab}^{(i)}$ & Cosine distance of $a$ and $b$ samples in the $i$-th view.\\ \midrule $d_{ab}^{*}$ & Cosine distance of $a$ and $b$ samples in latent representation.\\ \bottomrule \end{tabular}
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\begin{tabular}{l|c|c|c} \toprule Datasets & \# Views & \# Samples & \# Clusters\\ \midrule 100leaves & 3 & 1600 & 100 \\ \midrule BBCSport & 2 & 544 & 5 \\ \midrule Caltech101 & 6 & 9144 & 102 \\ \midrule Football & 9 & 248 & 20 \\ \midrule NottingHill & 3 & 4660 & 5 \\ \midrule Olympics & 9 & 464 & 28 \\ \midrule ORL & 3 & 400 & 40 \\ \midrule Politicsie & 9 & 348 & 7 \\ \midrule UCI & 3 & 2000 & 10 \\ \bottomrule \end{tabular}
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\begin{tabular}{l|ccccccccc} \toprule ACC & 100leaves & BBCSport & Caltech101 & Football & NottingHill & Olympics & ORL & Politicsie & UCI\\ \midrule k-means & 0.617 & 0.408 & 0.258 & 0.651 & 0.822 & 0.569 & 0.729 & 0.621 & 0.732 \\ \midrule LRR (TPAMI'13) & 0.462 & 0.797 & 0.241 & 0.834 & 0.794 & 0.780 & 0.812 & 0.681 & 0.871 \\ \midrule RMSC (AAAI'14) & 0.775 & 0.856 & 0.173 & 0.715 & 0.807 & 0.637 & 0.704 & 0.410 & 0.915 \\ \midrule LT-MSC (ICCV'15) & 0.729 & \underline{0.926} & 0.267 & 0.870 & \underline{0.868} & \underline{0.865} & \underline{0.821} & \underline{0.888} & 0.803 \\ \midrule AMGL (IJCAI'16) & 0.727 & 0.919 & 0.238 & 0.744 & 0.358 & 0.689 & 0.725 & 0.816 & 0.764\\ \midrule LMSC (CVPR'17) & 0.748 & 0.918 & 0.251 & 0.795 & 0.816 & 0.804 & 0.819 & 0.690 & 0.859\\ \midrule BMVC (TPAMI'18) & 0.776 & 0.774 & \underline{0.288} & 0.685 & 0.319 & 0.724 & 0.593 & 0.721 & 0.783 \\ \midrule GMC (TKDE'19) & \underline{0.824} & 0.739 & 0.195 & \underline{0.883} & 0.312 & 0.819 & 0.635 & 0.856 & 0.733 \\ \midrule COMIC (ICML'19) & 0.407 & 0.793 & 0.111 & 0.772 & 0.707 & 0.759 & 0.567 & 0.713 & \underline{0.940}\\ \midrule LVMSC (AAAI'20) & 0.561 & 0.605 & 0.112 & 0.657 & 0.726 & 0.631 & 0.555 & 0.569 & 0.714\\ \midrule MHC & \bf{0.868} & \bf{0.965} & \bf{0.378} & \bf{0.919} & \bf{0.970} & \bf{0.946} & \bf{0.858} & \bf{0.891} & \bf{0.958}\\ \bottomrule \end{tabular}
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\begin{tabular}{l|ccccccccc} \toprule NMI & 100leaves & BBCSport & Caltech101 & Football & NottingHill & Olympics & ORL & Politicsie & UCI\\ \midrule k-means & 0.818 & 0.136 & 0.496 & 0.717 & 0.723 & 0.713 & 0.876 & 0.623 & 0.738 \\ \midrule LRR (TPAMI'13) & 0.736 & 0.700 & 0.495 & 0.850 & 0.579 & 0.867 & \underline{0.924} & 0.779 & 0.768 \\ \midrule RMSC (AAAI'14) & 0.919 & 0.812 & 0.395 & 0.779 & 0.585 & 0.760 & 0.854 & 0.053 & 0.822 \\ \midrule LT-MSC (ICCV'15) & 0.868 & 0.803 & \bf{0.512} & 0.891 & \underline{0.779} & \underline{0.940} & 0.921 & \underline{0.820} & 0.775\\ \midrule AMGL (IJCAI'16) & 0.890 & \underline{0.864} & 0.391 & 0.802 & 0.129 & 0.810 & 0.883 & 0.764 & 0.798\\ \midrule LMSC (CVPR'17) & 0.877 & 0.839 & 0.485 & 0.840 & 0.697 & 0.891 & 0.921 & 0.684 & 0.782\\ \midrule BMVC (TPAMI'18) & 0.909 & 0.557 & 0.505 & 0.749 & 0.071 & 0.807 & 0.746 & 0.636 & 0.796 \\ \midrule GMC (TKDE'19) & \underline{0.929} & 0.795 & 0.345 & \underline{0.879} & 0.092 & 0.875 & 0.857 & 0.753 & 0.812 \\ \midrule COMIC (ICML'19) & 0.700 & 0.701 & 0.288 & 0.797 & 0.695 & 0.832 & 0.785 & 0.720 & \underline{0.892}\\ \midrule LVMSC (AAAI'20) & 0.785 & 0.436 & 0.263 & 0.708 & 0.681 & 0.745 & 0.789 & 0.501 & 0.712\\ \midrule MHC & \bf{0.950} & \bf{0.890} & \underline{0.509} & \bf{0.909} & \bf{0.926} & \bf{0.947} & \bf{0.953} & \bf{0.857} & \bf{0.916}\\ \bottomrule \end{tabular}
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\begin{tabular}{l|ccccccccc} \toprule F-measure & 100leaves & BBCSport & Caltech101 & Football & NottingHill & Olympics & ORL & Politicsie & UCI\\ \midrule k-means & 0.505 & 0.409 & 0.224 & 0.452 & 0.753 & 0.302 & 0.645 & 0.542 & 0.681 \\ \midrule LRR (TPAMI'13) & 0.352 & 0.761 & 0.179 & 0.745 & 0.653 & 0.710 & 0.765 & 0.676 & 0.763 \\ \midrule RMSC (AAAI'14) & 0.730 & 0.851 & 0.136 & 0.623 & 0.603 & 0.572 & 0.623 & 0.398 & 0.811 \\ \midrule LT-MSC (ICCV'15) & 0.636 & 0.858 & 0.197 & \underline{0.800} & \underline{0.825} & \underline{0.844} & \underline{0.767} & \bf{0.907} & 0.753\\ \midrule AMGL (IJCAI'16) & 0.410 & \underline{0.901} & 0.066 & 0.610 & 0.369 & 0.584 & 0.535 & 0.776 & 0.722\\ \midrule LMSC (CVPR'17) & 0.675 & 0.900 & 0.192 & 0.704 & 0.761 & 0.787 & 0.762 & 0.652 & 0.764\\ \midrule BMVC (TPAMI'18) & \underline{0.717} & 0.665 & \underline{0.237} & 0.579 & 0.254 & 0.699 & 0.431 & 0.634 & 0.750 \\ \midrule GMC (TKDE'19) & 0.502 & 0.721 & 0.050 & 0.709 & 0.369 & 0.701 & 0.360 & 0.778 & 0.708 \\ \midrule COMIC (ICML'19) & 0.282 & 0.766 & 0.070 & 0.636 & 0.692 & 0.671 & 0.408 & 0.694 & \underline{0.888}\\ \midrule LVMSC (AAAI'20) & 0.448 & 0.478 & 0.064 & 0.420 & 0.696 & 0.357 & 0.439 & 0.450 & 0.653\\ \midrule MHC & \bf{0.826} & \bf{0.931} & \bf{0.425} & \bf{0.843} & \bf{0.952} & \bf{0.928} & \bf{0.809} & \underline{0.883} & \bf{0.918}\\ \bottomrule \end{tabular}
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\begin{tabular}{l|c|c|c} \toprule Datasets & True \# Clusters & Closed \# Clusters & NMI \\ \midrule 100leaves & 100 & 114 & 0.647\\ \midrule BBCSport & 5 & 5 & 0.890\\ \midrule Caltech101 & 102 & 56 & 0.473 \\ \midrule Football & 20 & 17 & 0.855 \\ \midrule NottingHill & 5 & 3 & 0.721 \\ \midrule Olympics & 28 & 29 & 0.803 \\ \midrule ORL & 40 & 42 & 0.957 \\ \midrule Politicsie & 7 & 3 & 0.591 \\ \midrule UCI & 10 & 9 & 0.900 \\ \bottomrule \end{tabular}
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\begin{tabular}{l|c|c|c} \toprule Datasets & ~~BMVC~~ & ~~LVMSC~~ & ~~MHC~~ \\ \midrule 100leaves & 0.665 & 9.417 & 1.220 \\ \midrule BBCSport & 0.082 & 1.385 & 0.548 \\ \midrule Caltech101 & 8.157 & 139.75 & 26.628 \\ \midrule Football & 0.061 & 2.306 & 1.007 \\ \midrule NottingHill & 2.532 & 9.08 & 60.431 \\ \midrule Olympics & 0.120 & 4.433 & 2.982 \\ \midrule ORL & 0.080 & 3.668 & 1.079 \\ \midrule Politicsie & 0.076 & 0.611 & 0.902 \\ \midrule UCI & 0.659 & 2.799 & 0.377 \\ \bottomrule \end{tabular}
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\begin{tabular}{clc} \textbf{Symbol} & \textbf{Description} & \textbf{Units}\\ \hline $\theta$ & Hopper's angle & \textit{degrees}\\ $\beta$ & Surface slope & \textit{degrees}\\ $l$ & Spike's length & $m$\\ $I_f$ & Flywheel's rotational inertia & $kg \cdot m^2$\\ $I_p$ & Platform's rotational inertia & $kg \cdot m^2$\\ $\tau$ & Flywheel's torque & $N \cdot m$\\ $2 \alpha$ & Angle between spikes & \textit{degrees}\\ $\omega_f$ & Flywheel angular speed & $rad/s$\\ $g$ & Gravity acceleration & $m/s^2$\\ $m_p$ & Platform's mass & $kg$ \end{tabular}
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\begin{tabular}{clc} \textbf{Symbol} & \textbf{Description} & \textbf{Value}\\ \hline $g$ & Itokawa's mean gravity acceleration & 77 $\mu m/s^2$\\ $\beta$ & Surface inclination & -30º$< \beta <$30º\\ $\alpha$ & Half the angle between spikes & 45º\\ $l$ & Spike's length & 0.071 $m$\\ $m_p$ & \textit{Hopper}'s mass & 1.5 $kg$\\ $m_f$ & Flywheel's mass & 0.076 $kg$\\ $I_p$ & \textit{Hopper}'s rotational inertia & 25e-4 $kg m^2$\\ $I_f$ & Flywheel's rotational inertia & 3.42e-5 $kg m^2$ \end{tabular}
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\begin{tabular}{llrrrrrr} \textbf{Distance} & $\mathbf{d_h}\textbf{[m]}$ & \textbf{5} & \textbf{10} & \textbf{30} & \textbf{50} & \textbf{70} & \textbf{100}\\ \hline \textbf{Angular speed} & $\omega_f$[rad/s] & 81.3 & 115.0 & 198.9 & 256.7 & 303.7 & 363.0\\ \textbf{Speed-up time} & $T_{min}$[s] & 375.0 & 531.0 & 919.0 & 1186.0 & 1403.0 & 1677.0\\ \textbf{Braking time} & $\Delta t$[s] & 2.78 & 1.97 & 0.97 & 0.80 & 0.69 & 0.56\\ \textbf{Launch speed} & $L_s$[cm/s] & 2.0 & 2.8 & 4.8 & 6.2 & 7.3 & 8.8\\ \textbf{Launch angle} & $\theta_h$[degrees] & 43.0 & 43.0 & 46.0 & 45.0 & 44.0 & 45.0\\ \textbf{Fly time} & $T_f$[s] & 347.0 & 491.0 & 900.0 & 1139.0 & 1335.0 & 1610.0 \end{tabular}
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\begin{tabular}{clrc} \bf{Symbol} & \bf{Description} & \bf{Value} & \bf{Units}\\ \hline $J$ & Moment of inertia of the flywheel & 3.42e-5 & $kg\ m^2$\\ $b$ & Friction coefficient of the rotor & 2.20e-5 & $N\ m\ s$\\ $K$ & Back electro-motive force constant & 47.96e-3 & $\frac{V}{rad/s}$\\ $L$ & Motor winding inductance & 7.75e-3 & $H$\\ $R$ & Motor winding resistance & 11.36 & $\Omega$ \end{tabular}
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\begin{tabular}{crrrr} \textbf{Test} & $\omega_f\ [rad/s]$ & $\beta\ [degrees]$ & $\Delta t\ [s]$ & $d_h\ [m]$\\ \hline 2 & 81.16 & 0 & 0.00 & 5\\ 3 & 114.88 & 10 & 0.98 & 10\\ 4 & 198.76 & 5 & 0.26 & 30\\ 5 & 199.49 & 30 & 1.37 & 30\\ 6 & 256.67 & 20 & 0.80 & 50\\ 7 & 389.98 & -15 & 0.00 & 100 \end{tabular}
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\begin{tabular}{ccrr|r} \textbf{Slope} & \textbf{Parameter} & \textbf{Exp. Response} & \textbf{Real Response} & \textbf{Error}\\ \hline 0º & $d_h\ [m]$ & \textbf{5} & \textbf{3.00} & 40.00 \%\\ & $\omega_f\ [rad/s]$ & 81.16 & 62.83\\ & $\Delta t\ [s]$ & 0.00 & 0.06\\ \hline 10º & $d_h\ [m]$ & \textbf{10} & \textbf{8.29} & 17.10\%\\ & $\omega_f\ [rad/s]$ & 114.88 & 104.51\\ & $\Delta t\ [s]$ & 0.98 & 0.86\\ \hline 5º & $d_h\ [m]$ & \textbf{30} & \textbf{28.96} & 3.47\%\\ & $\omega_f\ [rad/s]$ & 198.76 & 195.3\\ & $\Delta t\ [s]$ & 0.26 & 0.30\\ \hline 30º & $d_h\ [m]$ & \textbf{30} & \textbf{32.62} & 8.73\%\\ & $\omega_f\ [rad/s]$ & 199.49 & 207.97\\ & $\Delta t\ [s]$ & 1.37 & 1.31\\ \hline 20º & $d_h\ [m]$ & \textbf{50} & \textbf{51.35} & 2.7\%\\ & $\omega_f\ [rad/s]$ & 256.67 & 260.02\\ & $\Delta t\ [s]$ & 0.80 & 0.79\\ \hline -15º & $d_h\ [m]$ & \textbf{100} & \textbf{89.59}\\ & $\omega_f\ [rad/s]$ & 389.98 & 400.13 & 10.41\%\\ & $\Delta t\ [s]$ & 0.00 & 0.16 \end{tabular}
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\begin{tabular}{crrr} \textbf{Target Distance} & \textbf{Mean Distance} & \textbf{Std Deviation} & \textbf{Relative Error}\\ \hline 5 $m$ & 3.6 $m$ & $\pm0.2\ m$ & \textbf{27.2\%}\\ 10 $m$ & 8.5 $m$ & $\pm0.2\ m$ & \textbf{15.5\%}\\ 30 $m$ & 35.7 $m$ & $\pm1.6\ m$ & \textbf{19.1\%}\\ 50 $m$ & 51.9 $m$ & $\pm0.4\ m$ & \textbf{3.7\%}\\ 70 $m$ & 73.6 $m$ & $\pm0.2\ m$ & \textbf{5.1\%}\\ 100 $m$ & 106.3 $m$ & $\pm0.9\ m$ & \textbf{6.2\%} \end{tabular}
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\begin{tabular}{crrr} \textbf{Target Distance} & \textbf{Mean Distance} & \textbf{Std Deviation} & \textbf{Relative Error}\\ \hline 5 $m$ & 3.8 $m$ & $\pm0.2\ m$ & \textbf{23.0\%}\\ 10 $m$ & 8.5 $m$ & $\pm0.2\ m$ & \textbf{14.8\%}\\ 30 $m$ & 31.4 $m$ & $\pm1.9\ m$ & \textbf{4.8\%}\\ 50 $m$ & 51.4 $m$ & $\pm0.5\ m$ & \textbf{2.7\%}\\ 70 $m$ & 73.0 $m$ & $\pm0.4\ m$ & \textbf{4.2\%}\\ 100 $m$ & 105.3 $m$ & $\pm1.0\ m$ & \textbf{5.3\%} \end{tabular}
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\begin{tabular}{crrr} \textbf{Target Distance} & \textbf{Mean Distance} & \textbf{Std Deviation} & \textbf{Relative Error}\\ \hline 5 $m$ & 3.9 $m$ & $\pm0.1\ m$ & \textbf{23.1\%}\\ 10 $m$ & 8.4 $m$ & $\pm0.3\ m$ & \textbf{16.1\%}\\ 30 $m$ & 34.1 $m$ & $\pm2.2\ m$ & \textbf{13.7\%}\\ 50 $m$ & 49.6 $m$ & $\pm1.2\ m$ & \textbf{0.8\%}\\ 70 $m$ & 66 $m$ & $\pm0.7\ m$ & \textbf{5.7\%}\\ 100 $m$ & 93.8 $m$ & $\pm1.4\ m$ & \textbf{6.2\%} \end{tabular}
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\begin{tabular}{cr|r} \textbf{Target Distance $[m]$} & \textbf{Resultant Distance $[m]$} & \textbf{Error} [\%]\\ \hline 100 & 102.41 & 2.41\\ 100 & 102.18 & 2.18\\ 100 & 105.67 & 5.67\\ 75 & 73.95 & 1.40\\ \textbf{385} & \textbf{384.33} & 0.17 \end{tabular}
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\begin{tabular}{c|c|c|ccccc} \hline \multirow{2}{*}{Dataset}& \multirow{2}{*}{T}& \multirow{2}{*}{Metric}& \multicolumn{5}{c}{Hidden size} \\ \cline{4-8} &&&8&16&32&64&128\\ \hline\hline \multirow{5}{*}{SZ-taxi}& \multirow{5}{*}{60min} &RMSE& 4.0630 & 4.0490& 4.0510& \textbf{4.0270}& 4.1090\\ &&MAE& 2.7220 & 2.7000& \textbf{2.6870}& 2.7010& 2.7270\\ &&ACC& 0.7170 & 0.7179& 0.7178& \textbf{0.7195}& 0.7137\\ &&R$^{2}$& 0.8446& 0.8496& 0.8495& \textbf{0.8513}& 0.8451\\ &&VAR& 0.8489 & 0.8499& 0.8499& \textbf{0.8515}& 0.8451\\ \hline \multirow{5}{*}{Los-loop}& \multirow{5}{*}{60min} &RMSE& 10.810 & 7.7330 &7.5140 & \textbf{7.0840} &7.0980 \\ &&MAE& 6.9610 & 4.7280 &4.4720 &\textbf{4.1350} &4.2290 \\ &&ACC& 0.8156 & 0.8682 &0.8720 &\textbf{0.8793} &0.8790 \\ &&R$^{2}$& 0.3992 & 0.6924 &0.7096 &\textbf{0.7418 } &0.7409 \\ &&VAR& 0.4053 & 0.694 &0.7096 &\textbf{0.7418} &0.7414 \\ \hline \end{tabular}
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\begin{tabular}{c|c|c|ccccc} \hline \multirow{2}{*}{Dataset}& \multirow{2}{*}{T}& \multirow{2}{*}{Metric}& \multicolumn{5}{c}{Monte Carlo dropout probability} \\ \cline{4-8} &&&0.1&0.3&0.5&0.7&0.9\\ \hline\hline \multirow{5}{*}{SZ-taxi}& \multirow{5}{*}{60min} &RMSE& \textbf{4.0270}& 4.0350& 4.0470 & 4.1020& 4.6620\\ &&MAE& 2.6860 & \textbf{2.6720} & 2.7050 & 2.7290& 3.1970\\ &&ACC& \textbf{0.7195}& 0.7189& 0.7181 & 0.7143& 0.6752\\ &&R$^{2}$& \textbf{0.8513}& 0.8507& 0.8498 & 0.8457& 0.8006\\ &&VAR& \textbf{0.8514}& 0.8507& 0.85 & 0.8457& 0.8008\\ \hline \multirow{5}{*}{Los-loop}& \multirow{5}{*}{60min} &RMSE& 6.9940 & 6.8370 & \textbf{6.7330} &\text{6.7760} & 6.9580\\ &&MAE& 4.0460 & 3.9340 & \textbf{3.9180} &3.9740 & 4.1390\\ &&ACC& 0.8808 & 0.8835 & \textbf{0.8853} &\text{0.8845} & 0.8814\\ &&R$^{2}$& 0.7483 &0.7596 & \textbf{0.7668} &\text{0.7638} & 0.7509\\ &&VAR& 0.7485 &0.7601 & \textbf{0.7669} &\text{0.7638} & 0.7511\\ \hline \end{tabular}
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\begin{tabular}{c|c|c|cc} \hline \multirow{2}{*}{Dataset}& \multirow{2}{*}{T}& \multirow{2}{*}{Metric}& \multicolumn{2}{c}{Activation function} \\ \cline{4-5} &&&Identity&Sigmoid\\ \hline\hline \multirow{5}{*}{SZ-taxi}& \multirow{5}{*}{60min} &RMSE&4.0280&\textbf{4.0270}\\ &&MAE&2.7020&\textbf{2.6860}\\ &&ACC&0.7194&\textbf{0.7195}\\ &&R$^{2}$&0.8512&\textbf{0.8513}\\ &&VAR&\textbf{0.8516}&0.8514\\ \hline \multirow{5}{*}{Los-loop}& \multirow{5}{*}{60min} &RMSE&\textbf{6.5900}&{6.7330}\\ &&MAE&\textbf{3.8420}&{3.9180}\\ &&ACC&\textbf{0.8877}&{0.8853}\\ &&R$^{2}$&\textbf{0.7766}&{0.7668}\\ &&VAR&\textbf{0.7767}&{0.7669}\\ \hline \end{tabular}
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\begin{tabular}{c|ccc|ccc|ccc} \hline & \multicolumn{3}{c|}{ Case 1} & \multicolumn{3}{c|}{ Case 2} & \multicolumn{3}{c}{ Case 3} \\ \hline $\vert g_t \vert$, $v_t$ & \multicolumn{3}{c|}{S} & \multicolumn{3}{c|}{L} & \multicolumn{3}{c}{L} \\ \hline $\vert g_t - g_{t-1} \vert$, $s_t$ & \multicolumn{3}{c|}{S} & \multicolumn{3}{c|}{ L} & \multicolumn{3}{c}{S} \\ \hline $\vert \Delta \theta_t \vert_{ideal}$ & \multicolumn{3}{c|}{L} & \multicolumn{3}{c|}{S} & \multicolumn{3}{c}{L} \\ \hline \multicolumn{1}{c|}{\multirow{2}{*}{$\vert \Delta \theta_t \vert$}} & SGD & Adam & \multicolumn{1}{c|}{AdaBelief} & SGD & Adam & \multicolumn{1}{c|}{AdaBelief} & SGD & Adam & AdaBelief \\ \cline{2-10} \multicolumn{1}{c|}{} & S & L & \multicolumn{1}{c|}{L} & L & S & \multicolumn{1}{c|}{S} & L & S & L \\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c|c|c|c} \hline AdaBelief & SGD & AdaBound & Yogi & Adam & MSVAG & RAdam & AdamW \\ \hline \textbf{70.08} & 70.23$^\dag$ & 68.13$^\dag$ & 68.23$^\dag$ & 63.79$^\dag$ (66.54$^\ddag$) & 65.99 & 67.62$^\ddag$ & 67.93$^\dag$ \\ \hline \end{tabular}
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\begin{tabular}{c|c} \hline Generator & Discriminator \\ \hline \hline ConvTranspose ({[}inchannel = 100, outchannel = 512, kernel = 4$\times$4, stride = 1{]}) & Conv2D({[}inchannel=3, outchannel=64, kernel = 4$\times$4, stride=2{]}) \\ \hline BN-ReLU & LeakyReLU \\ \hline ConvTranspose ({[}inchannel = 512, outchannel = 256, kernel = 4$\times$4, stride = 2{]}) & Conv2D({[}inchannel=64, outchannel=128, kernel = 4$\times$4, stride=2{]}) \\ \hline BN-ReLU & BN-LeakyReLU \\ \hline ConvTranspose ({[}inchannel = 256, outchannel = 128, kernel = 4$\times$4, stride = 2{]}) & Conv2D({[}inchannel=128, outchannel=256, kernel = 4$\times$4, stride=2{]}) \\ \hline BN-ReLU & BN-LeakyReLU \\ \hline ConvTranspose ({[}inchannel = 128, outchannel = 64, kernel = 4$\times$4, stride = 2{]}) & Conv2D({[}inchannel=256, outchannel=512, kernel = 4$\times$4, stride=2{]}) \\ \hline BN-ReLU & BN-LeakyReLU \\ \hline ConvTranspose ({[}inchannel = 64, outchannel = 3, kernel = 4$\times$4, stride = 2{]}) & Linear(-1, 1) \\ \hline Tanh & \\ \hline \end{tabular}
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\begin{tabular}{ccccc} \hline Cases & \multicolumn{4}{c}{Service Type} \\ & 1 & 2 & 3 & 4 \\ \hline Case a & 0 & 0 & 40 & 40 \\ Case b & 10 & 10 & 30 & 30 \\ Case c & 20 & 20 & 20 & 20 \\ Case d & 30 & 30 & 10 & 10 \\ Case e & 40 & 40 & 0 & 0 \\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c} \hline \multirow{3}{2.1cm}{The maximum $\langle M_{1}M_{2} \rangle$ at the first $n.n.$} & \multicolumn{3}{c}{Host semiconductors} \\ \cline{2-4} &InSb &InAs &GaSb \\ &(gap=0.17eV) &(gap=0.42eV) &(gap=0.75eV) \\ \hline \multirow{2}*{Fe} &0.07 (p-type) &0.14 (p-type) &0.1 (p-type) \\ &0.09 (n-type) & &\\ \hline \multirow{2}*{Mn} &0.14 (p-type) &0.13 (p-type) &0.13 (p-type) \\ &0.07 (n-type) & &\\ \hline \multirow{2}*{Cr} &0.13 (p-type) &0.12 (p-type) &0.12 (p-type) \\ &0.08 (n-type) & &\\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c} \hline the $i$-th $n.n.$ &first &second &third &fourth \\ \hline $\langle M_1^zM_2^z \rangle$ (10$^{-2}$ $\mu_B^2$) &0.467 &0.231 &0.155 &0.124\\ \hline $J_i/k_B$ (K) &6.757 &3.334 &2.235 &1.788\\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c} \hline doping concentration &12.5$\%$ &25$\%$ &37.5$\%$ \\ \hline Tc (K) &120 &245 &379\\ \hline \end{tabular}
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\begin{tabular}{c|c|c|c|c} \hline &doping concentration &12.5$\%$ &25$\%$ &37.5$\%$ \\ \hline \multirow{3}*{Tc (K)} &(In,Cr)Sb &62 &214 &406 \\ \cline{2-5} &(In,Cr)As &17 &129 &264 \\ \cline{2-5} &(Ga,Cr)Sb &242 &534 &851 \\ \hline \end{tabular}
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\begin{tabular}{lccc} \hline Datasets &NYT10&CoNLL04&ADE\\ \hline Relation types &29&5&2 \\ Entity types &7&4&3 \\ Training set &70339&910&3416 \\ Training triplets &87739&1273&5650 \\ Test set &4006&288&854 \\ Test triplets &5859&422&1450 \\ \hline \end{tabular}
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\begin{tabular}{||c|c|c|c||} \hline \hline Domains sequence & Burgers vectors & $N_{Si}$ & E per Si atom (meV) \\ \hline \hline $abcda$ & $\vec{b}_+ \times 2$, $\vec{b}_- \times 2 $ &104 & 0 \\ $abcda$, Adatoms at the boundaries & $\vec{b}_+ \times 2$, $\vec{b}_- \times 2 $ & 108 & 66.9 \\ $abcda$, Adatoms at the domains & $\vec{b}_+ \times 2$, $\vec{b}_- \times 2 $ & 108 & 65.0 \\ $a$ & none & 108 & 30.5 \\ $aa$ & $2(\vec{b}_{+}+\vec{b}_{-})=a_{Si}\vec{u}_x $ &104 & 15.8 \\ $acda$ & $\vec{b}_{+} +\vec{b}_-$, $\vec{b}_+$, $\vec{b}_-$ & 104 & 3.8 \\ $ada$ & $2\vec{b}_{+} +\vec{b}_-$, $\vec{b}_-$ & 104 & 7.9 \\ $ada$ & $-\vec{b}_-$, $\vec{b}_-$ & 108 & 39.7 \\ \hline \hline \end{tabular}
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\begin{tabular}{cc} \hline\hline Total COM energy T$_{c}$ (GeV) & Total cross section $\sigma$ (mb) \\ [0.5ex] \hline 0.01 & 1.33 \\ 0.02 & 1.06 \\ 0.03 & 0.852 \\ 0.1 & 0.158 \\ 0.19 & 0.00886 \\ 0.2 & 0.00570 \\ \hline \end{tabular}
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\begin{tabular}{cc} \hline\hline Total COM energy T$_{c}$ (GeV) & Total cross section $\sigma$ (mb) \\ [0.5ex] \hline 0.02 & 0.15 \\ 0.04 & 0.11 \\ 0.1 & 0.07 \\ 0.2 & 0.03 \\ 0.3 & 0.01 \\ 0.5 & 0 \\ \hline \end{tabular}
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\begin{tabular}{cc} \hline\hline Total COM energy T$_{c}$ (GeV) & Total cross section $\sigma$ (mb) \\ [0.5ex] \hline 0.01 & 0.282 \\ 0.02 & 0.269 \\ 0.03 & 0.244 \\ 0.04 & 0.222 \\ 0.1 & 0.121 \\ 0.2 & 0.0472 \\ 0.3 & 0.0173 \\ 0.4 & 0.00544 \\ 0.5 & 0.00121 \\ \hline \end{tabular}
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\begin{tabular}{ccc} \toprule Term & \# of tweets & \# of tweets localized in U.S. \\ \midrule \#dinner & 6,007,037 & 1,520,573 \\ \#breakfast & 5,736,525 & 1,335,432 \\ \#lunch & 5,514,638 & 1,213,171 \\ \#brunch & 2,160,015 & 768,577 \\ \#snack & 898,178 & 246,842 \\ \#meal & 553,214 & 115,101 \\ \#supper & 138,658 & 24,860 \\ \midrule Total & 28,854,023 & 5,198,387 \\ \bottomrule \end{tabular}
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\begin{tabular}{cc} \toprule Year (March-May) & \# of tweets localized in U.S. \\ \midrule 2020 & 63,898 \\ 2019 & 81,036 \\ 2018 & 131,418 \\ 2017 & 135,734 \\ 2016 & 174,792 \\ 2015 & 185,264 \\ \bottomrule \end{tabular}
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