wanyu/IteraTeR_full_sent huggingface dataset:
Original:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0,  \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{X , and derive the probability of a large drawdown preceding a small rally.
Revised:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0, \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X %DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{X , and derive the probability of a large drawdown preceding a small rally.
Edit intent: meaning-changed
Original:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0,  \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{X , and derive the probability of a large drawdown preceding a small rally.
Revised:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0, \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% at the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{X , and derive the probability of a large drawdown preceding a small rally.
Edit intent: coherence
Original:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0,  \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{X , and derive the probability of a large drawdown preceding a small rally.
Revised:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0, \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% \underline{X , and derive the probability of a large drawdown preceding a small rally.
Edit intent: clarity
Original:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0,  \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{X , and derive the probability of a large drawdown preceding a small rally.
Revised:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0, \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{ , and derive the probability of a large drawdown preceding a small rally.
Edit intent: fluency
Original:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0,  \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{X , and derive the probability of a large drawdown preceding a small rally. These results are applied to the Carr%DIFDELCMD < & %%% Wu \mbox{%DIFAUXCMD \cite{CarrWu }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% P 500. and supremum }\ovl  of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.
Revised:  } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0, \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{X %DIFDELCMD < & %%% Wu \mbox{%DIFAUXCMD \cite{CarrWu }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% P 500. and supremum }\ovl of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.
Edit intent: meaning-changed
Original:  These results are applied to the Carr%DIFDELCMD < & %%% Wu \mbox{%DIFAUXCMD \cite{CarrWu }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% P 500. and supremum }\ovl  of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.
Revised:  These results are applied to the Carr%DIFDELCMD < & %%% }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% P 500. and supremum }\ovl of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.
Edit intent: clarity
Original:  These results are applied to the Carr%DIFDELCMD < & %%% Wu \mbox{%DIFAUXCMD \cite{CarrWu }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% P 500. and supremum }\ovl  of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.
Revised:  These results are applied to the Carr%DIFDELCMD < & %%% Wu \mbox{%DIFAUXCMD \cite{CarrWu }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% _{\tau_a and supremum }\ovl of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.
Edit intent: meaning-changed
Original:  These results are applied to the Carr%DIFDELCMD < & %%% Wu \mbox{%DIFAUXCMD \cite{CarrWu }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% P 500. and supremum }\ovl  of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.
Revised:  These results are applied to the Carr%DIFDELCMD < & %%% Wu \mbox{%DIFAUXCMD \cite{CarrWu }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% P 500. and supremum }\ovl X_{\tau_a of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.
Edit intent: fluency
Original:  Variations of data processing or modeling do not mitigate these errors. Instead, as evaluated by bootstrapping, the information content of SHAPE data appears insufficient to define these RNAs' structures.
Revised:  Variations of data processing , normalization, and modeling parameters did not significantly mitigate modeling errors. Only one varation, filtering out data collected with deoxyinosine triphosphate during primer extension, gave a modest improvement (FNR = 12\%, and FDR = 14\%). The residual structure modeling errors are explained by the insufficient information content of SHAPE data appears insufficient to define these RNAs' structures.
Edit intent: meaning-changed
Original:  Instead, as evaluated by bootstrapping, the information content of SHAPE data appears insufficient to define these RNAs' structures.
Revised:  Instead, as evaluated by bootstrapping, the information content of SHAPE data appears insufficient to define these RNAs' SHAPE data, as evaluated by a nonparametric bootstrapping analysis. Beyond these benchmark cases, bootstrapping suggests a low level of confidence (<50\%) in the majority of helices in a previously proposed SHAPE-directed model for the HIV-1 RNA genome.
Edit intent: meaning-changed
Original:  According to our model, structure analysis can be formally defined as decomposing a traffic matrix into low-rank, sparse, and noise sub-matrixes , which is equal to the Robust Principal Component Analysis (RPCA) problem defined in [13].
Revised:  According to this model, we carry out the structural analysis by decomposing the network traffic matrix into low-rank, sparse, and noise sub-matrixes , which is equal to the Robust Principal Component Analysis (RPCA) problem defined in [13].
Edit intent: clarity
Original:  According to our model, structure analysis can be formally defined as decomposing a traffic matrix into low-rank, sparse, and noise sub-matrixes , which is equal to the Robust Principal Component Analysis (RPCA) problem defined in [13].
Revised:  According to our model, structure analysis can be formally defined as decomposing a traffic matrix into three sub-matrices, namely, the deterministic traffic, the anomaly traffic and the noise traffic matrix , which is equal to the Robust Principal Component Analysis (RPCA) problem defined in [13].
Edit intent: meaning-changed
Original:  According to our model, structure analysis can be formally defined as decomposing a traffic matrix into low-rank, sparse, and noise sub-matrixes , which is equal to the Robust Principal Component Analysis (RPCA) problem defined in [13].
Revised:  According to our model, structure analysis can be formally defined as decomposing a traffic matrix into low-rank, sparse, and noise sub-matrixes , which is similar to the Robust Principal Component Analysis (RPCA) problem defined in [13].
Edit intent: clarity
Original:  According to our model, structure analysis can be formally defined as decomposing a traffic matrix into low-rank, sparse, and noise sub-matrixes , which is equal to the Robust Principal Component Analysis (RPCA) problem defined in [13].
Revised:  According to our model, structure analysis can be formally defined as decomposing a traffic matrix into low-rank, sparse, and noise sub-matrixes , which is equal to the Robust Principal Component Analysis (RPCA) problem previously studied in [13].
Edit intent: clarity
Original:  Based on the Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated Proximal Gradient (APG) algorithm, an iterative algorithm for decomposing a traffic matrix is presented, and our experiment results demonstrate its efficiency and flexibility  .
Revised:  Based on the Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated Proximal Gradient (APG) algorithm, we present an iterative approach for decomposing a traffic matrix is presented, and our experiment results demonstrate its efficiency and flexibility .
Edit intent: clarity
Original:  Based on the Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated Proximal Gradient (APG) algorithm, an iterative algorithm for decomposing a traffic matrix is presented, and our experiment results demonstrate its efficiency and flexibility  .
Revised:  Based on the Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated Proximal Gradient (APG) algorithm, an iterative algorithm for decomposing a traffic matrix , and demonstrate its efficiency and flexibility .
Edit intent: coherence
Original:  Based on the Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated Proximal Gradient (APG) algorithm, an iterative algorithm for decomposing a traffic matrix is presented, and our experiment results demonstrate its efficiency and flexibility  .
Revised:  Based on the Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated Proximal Gradient (APG) algorithm, an iterative algorithm for decomposing a traffic matrix is presented, and our experiment results demonstrate its efficiency and flexibility by experimental results. Finally, we further discuss several features of the deterministic and noise traffic .
Edit intent: meaning-changed
Original:  In assembly state, the growth of microtubule includes two processes:  GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Revised:  In assembly state, the growth of MTs includes two processes: GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Edit intent: clarity
Original:  In assembly state, the growth of microtubule includes two processes:  GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Revised:  In assembly state, the growth of microtubule includes two processes: free GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Edit intent: meaning-changed
Original:  In assembly state, the growth of microtubule includes two processes:  GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Revised:  In assembly state, the growth of microtubule includes two processes: GTP-tubulin binding to the tip of protofilament (PF) and conformation change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Edit intent: fluency
Original:  In assembly state, the growth of microtubule includes two processes:  GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Revised:  In assembly state, the growth of microtubule includes two processes: GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Edit intent: coherence
Original:  In assembly state, the growth of microtubule includes two processes:  GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Revised:  In assembly state, the growth of microtubule includes two processes: GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit which curls outwards is rearranged into MT surface using the energy released from GTP hydrolysis .
Edit intent: clarity
Original:  In assembly state, the growth of microtubule includes two processes:  GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from GTP hydrolysis .
Revised:  In assembly state, the growth of microtubule includes two processes: GTP-tubulin binding to the tip of protofilament (PF) and conformational change of PF, during which the penultimate GTP is hydrolyzed and the first tubulin unit that curls out the MT surface is rearranged into MT surface using the energy released from the hydrolysis of GTP in the penultimate tubulin unit .
Edit intent: clarity
Original:  In disassembly state, the shortening of microtubule is also described by two processes, the release of GDP-tibulin from the tip of PF and one new tubulin unit curls out from the MT surface.
Revised:  In disassembly state, the shortening of MTs includes also two processes, the release of GDP-tibulin from the tip of PF and one new tubulin unit curls out from the MT surface.
Edit intent: clarity
Original:  In disassembly state, the shortening of microtubule is also described by two processes, the release of GDP-tibulin from the tip of PF and one new tubulin unit curls out from the MT surface.
Revised:  In disassembly state, the shortening of microtubule is also described by two processes, the release of GDP-tibulin from the tip of PF and one new tubulin unit curls out of the MT surface.
Edit intent: fluency
Original:  To know more about the external force and GTP concentration dependent MT growth properties , and for the sake of  experimental verification of this two-state model, eight {\it critical forces} are defined and numerically discussed.
Revised:  To know more about the external force and GTP-tubulin concentration dependent properties of MT growth , and for the sake of experimental verification of this two-state model, eight {\it critical forces} are defined and numerically discussed.
Edit intent: meaning-changed
Original:  To know more about the external force and GTP concentration dependent MT growth properties , and for the sake of  experimental verification of this two-state model, eight {\it critical forces} are defined and numerically discussed.
Revised:  To know more about the external force and GTP concentration dependent MT growth properties , and for the sake of the future experimental verification of this two-state model, eight {\it critical forces} are defined and numerically discussed.
Edit intent: clarity
Original:  To know more about the external force and GTP concentration dependent MT growth properties , and for the sake of  experimental verification of this two-state model, eight {\it critical forces} are defined and numerically discussed.
Revised:  To know more about the external force and GTP concentration dependent MT growth properties , and for the sake of experimental verification of this two-state model, eleven {\it critical forces} are defined and numerically discussed.
Edit intent: meaning-changed
Original:  We derive some necessary and sufficient first order conditions for optimality and we characterize the optimal solution of the investment problem in terms of the "base capacity " process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui .
Revised:  We derive some first order conditions for optimality and we characterize the optimal solution of the investment problem in terms of the "base capacity " process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui .
Edit intent: clarity
Original:  We derive some necessary and sufficient first order conditions for optimality and we characterize the optimal solution of the investment problem in terms of the "base capacity " process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui .
Revised:  We derive some necessary and sufficient first order conditions for optimality and we characterize the optimal solution in terms of the "base capacity " process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui .
Edit intent: clarity
Original:  We derive some necessary and sufficient first order conditions for optimality and we characterize the optimal solution of the investment problem in terms of the "base capacity " process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui .
Revised:  We derive some necessary and sufficient first order conditions for optimality and we characterize the optimal solution of the investment problem in terms of the base capacity process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui .
Edit intent: fluency
Original:  We derive some necessary and sufficient first order conditions for optimality and we characterize the optimal solution of the investment problem in terms of the "base capacity " process, i.e. the unique solution of a Representation Problem \`a la Bank-El Karoui . Under Markovian assumption, we show that the base capacity is in fact deterministic and coincides with the free boundary of the  optimal stopping problem naturally associated to the singular control one.
Revised:  We derive some necessary and sufficient first order conditions for optimality and we characterize the optimal solution of the investment problem in terms of the "base capacity " process, i.e. the unique solution of a representation problem in the spirit of Bank and El Karoui (2004). We show that the base capacity is in fact deterministic and coincides with the free boundary of the optimal stopping problem naturally associated to the singular control one.
Edit intent: meaning-changed
Original:  Under Markovian assumption, we show that the base capacity is in fact deterministic and coincides with the free boundary of the  optimal stopping problem naturally associated to the singular control one. For a Cobb-Douglas production function, if the diffusion's coefficients are constant, we are able to show that the free boundary is a continuous function of the time so to remove Assumption- Cfb%DIFDELCMD < ] %%% in Chiarolla and Haussmann (2009) .
Revised:  Under Markovian assumption, we show that the base capacity is in fact deterministic and coincides with the free boundary of the optimal stopping problem , when the coefficients of the controlled diffusion are deterministic functions of time. This is a novelty in the literature on finite horizon singular stochastic control problems. As a subproduct this result allows us to obtain an integral equation for the free boundary is a continuous function of the time so to remove Assumption- Cfb%DIFDELCMD < ] %%% in Chiarolla and Haussmann (2009) .
Edit intent: meaning-changed
Original:  For a Cobb-Douglas production function, if the diffusion's coefficients are constant, we are able to show that the free boundary is a continuous function of the time so to remove Assumption- Cfb%DIFDELCMD < ] %%% in Chiarolla and Haussmann (2009) .
Revised:  For a Cobb-Douglas production function, if the diffusion's coefficients are constant, we are able to show that the free boundary Cfb%DIFDELCMD < ] %%% in Chiarolla and Haussmann (2009) .
Edit intent: coherence
Original:  For a Cobb-Douglas production function, if the diffusion's coefficients are constant, we are able to show that the free boundary is a continuous function of the time so to remove Assumption- Cfb%DIFDELCMD < ] %%% in Chiarolla and Haussmann (2009) .
Revised:  For a Cobb-Douglas production function, if the diffusion's coefficients are constant, we are able to show that the free boundary is a continuous function of the time so to remove Assumption- %DIFDELCMD < ] %%% in Chiarolla and Haussmann (2009) .
Edit intent: clarity
Original:  For a Cobb-Douglas production function, if the diffusion's coefficients are constant, we are able to show that the free boundary is a continuous function of the time so to remove Assumption- Cfb%DIFDELCMD < ] %%% in Chiarolla and Haussmann (2009) .
Revised:  For a Cobb-Douglas production function, if the diffusion's coefficients are constant, we are able to show that the free boundary is a continuous function of the time so to remove Assumption- Cfb%DIFDELCMD < ] %%% , which we explicitly solve in the infinite horizon case for a Cobb-Douglas production function and constant coefficients in the controlled capacity process .
Edit intent: meaning-changed