wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( U \times%DIFDELCMD < } %%% V )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| U )) is characterized via a pasting property of the representing sets of probabilities .
Revised:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( \times%DIFDELCMD < } %%% V )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| U )) is characterized via a pasting property of the representing sets of probabilities .
Edit intent: coherence
Original:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( U \times%DIFDELCMD < } %%% V )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| U )) is characterized via a pasting property of the representing sets of probabilities .
Revised:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( U %DIFDELCMD < } %%% V )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| U )) is characterized via a pasting property of the representing sets of probabilities .
Edit intent: coherence
Original:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( U \times%DIFDELCMD < } %%% V )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| U )) is characterized via a pasting property of the representing sets of probabilities .
Revised:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( U \times%DIFDELCMD < } %%% \mathcal{F )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| U )) is characterized via a pasting property of the representing sets of probabilities .
Edit intent: meaning-changed
Original:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( U \times%DIFDELCMD < } %%% V )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| U )) is characterized via a pasting property of the representing sets of probabilities .
Revised:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( U \times%DIFDELCMD < } %%% V )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| \mathcal{G )) is characterized via a pasting property of the representing sets of probabilities .
Edit intent: meaning-changed
Original:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( U \times%DIFDELCMD < } %%% V )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| U )) is characterized via a pasting property of the representing sets of probabilities . As applications, we characterize under which conditions the product of a set of probabilities and a set of kernels is compact , and under which conditions a nonlinear version of Fubini's theorem holds true .
Revised:  Further, given another sublinear increasing functional \mathcal{E}(\cdot)\colon\mathcal{L}( U \times%DIFDELCMD < } %%% V )\to\mathbb{R} which leaves the constants invariant, the tower property \mathcal{E}(\cdot)=\mathcal{E}(\mathcal{E}(\cdot| U )) is characterized via a pasting property of the representing sets of probabilities , and the importance of analytic functions is explained. Finally, it is characterized when a nonlinear version of Fubini's theorem holds true and when the product of a set of probabilities and a set of kernels is compact , and under which conditions a nonlinear version of Fubini's theorem holds true .
Edit intent: meaning-changed
Original:  In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the  response to an antigen  of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Revised: Recent experimental studies have suggested the ratio between T-helper and T-suppressor lymphocytes as an index of immunosuppression in HIV, cancer, immunosenescence and inflammatory and auto-immune diseases. However, a quantitative understanding of the impact of this ratio on the immune response has lagged behind data and its validity as a tool for prognostic monitoring or therapeutic target remains an open question. In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the response to an antigen of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Edit intent: meaning-changed
Original:  In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the  response to an antigen  of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Revised:  In this work , we use statistical physics and dynamical systems approaches , to analyze the response to an antigen of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Edit intent: clarity
Original:  In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the  response to an antigen  of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Revised:  In this work we use a combination of statistical physics and dynamical systems approaches to analyze the response to an antigen of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Edit intent: fluency
Original:  In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the  response to an antigen  of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Revised:  In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the time-dependent response to an antigen of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Edit intent: meaning-changed
Original:  In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the  response to an antigen  of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Revised:  In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the response to an antigen , of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes.
Edit intent: fluency
Original:  In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the  response to an antigen  of a simplified model of the adaptive immune system, which comprises B, T helper and T regulatory lymphocytes. Results show that the model is remarkably robust against changes in the  kinetic parameters, noise levels, and mechanisms that activate T regulatory lymphocytes.
Revised:  In this work we use a combination of statistical physics and dynamical systems approaches , to analyze the response to an antigen of a simplified model of the adaptive immune system, which comprises B, T-helper and T-suppressor lymphocytes. The model is remarkably robust against changes in the kinetic parameters, noise levels, and mechanisms that activate T regulatory lymphocytes.
Edit intent: coherence
Original:  Results show that the model is remarkably robust against changes in the  kinetic parameters, noise levels, and mechanisms that activate T regulatory lymphocytes. In contrast, the model is extremely sensitive to changes in the ratio between T helper and T regulatory lymphocytes, exhibiting in particular a phase transition , from a responsive to an immuno-suppressed phase, when the ratio is lowered below a critical value .
Revised:  Results show that the model is remarkably robust against changes in the kinetic parameters, but it is very sensitive to changes in the ratio between T helper and T regulatory lymphocytes, exhibiting in particular a phase transition , from a responsive to an immuno-suppressed phase, when the ratio is lowered below a critical value .
Edit intent: clarity
Original:  In contrast, the model is extremely sensitive to changes in the ratio between T helper and T regulatory lymphocytes, exhibiting in particular a phase transition , from a responsive to an immuno-suppressed phase, when the ratio is lowered below a critical value .
Revised:  In contrast, the model is extremely sensitive to changes in the ratio between T-helper and T-suppressor lymphocytes, exhibiting in particular a phase transition , from a responsive to an immuno-suppressed phase, when the ratio is lowered below a critical value .
Edit intent: clarity
Original:  In contrast, the model is extremely sensitive to changes in the ratio between T helper and T regulatory lymphocytes, exhibiting in particular a phase transition , from a responsive to an immuno-suppressed phase, when the ratio is lowered below a critical value .
Revised:  In contrast, the model is extremely sensitive to changes in the ratio between T helper and T regulatory lymphocytes, exhibiting , in particular, a transition from a responsive to an immuno-suppressed phase, when the ratio is lowered below a critical value .
Edit intent: clarity
Original:  In contrast, the model is extremely sensitive to changes in the ratio between T helper and T regulatory lymphocytes, exhibiting in particular a phase transition , from a responsive to an immuno-suppressed phase, when the ratio is lowered below a critical value .
Revised:  In contrast, the model is extremely sensitive to changes in the ratio between T helper and T regulatory lymphocytes, exhibiting in particular a phase transition , from a responsive to an immuno-suppressed phase, as the ratio is lowered below a critical value .
Edit intent: coherence
Original:  In contrast, the model is extremely sensitive to changes in the ratio between T helper and T regulatory lymphocytes, exhibiting in particular a phase transition , from a responsive to an immuno-suppressed phase, when the ratio is lowered below a critical value . To the best of our knowledge, this is the first mathematical study to support the validity of the T-helper/ T-regulator lymphocyte ratio as an index of immunosuppression , with a potential for prognostic monitoring .
Revised:  In contrast, the model is extremely sensitive to changes in the ratio between T helper and T regulatory lymphocytes, exhibiting in particular a phase transition , from a responsive to an immuno-suppressed phase, when the ratio is lowered below a critical value , which is in line with experiments. This result supports the validity of the T-helper/ T-regulator lymphocyte ratio as an index of immunosuppression , with a potential for prognostic monitoring .
Edit intent: meaning-changed
Original:  To the best of our knowledge, this is the first mathematical study to support the validity of the T-helper/ T-regulator lymphocyte ratio as an index of immunosuppression , with a potential for prognostic monitoring .
Revised:  To the best of our knowledge, this is the first mathematical study to support the validity of the T-helper/ T-suppressor ratio as an index of immunosuppression , with a potential for prognostic monitoring .
Edit intent: clarity
Original:  To the best of our knowledge, this is the first mathematical study to support the validity of the T-helper/ T-regulator lymphocyte ratio as an index of immunosuppression , with a potential for prognostic monitoring .
Revised:  To the best of our knowledge, this is the first mathematical study to support the validity of the T-helper/ T-regulator lymphocyte ratio as an index of immunosuppression and may provide a useful theoretical benchmark to interpret and compare experiments .
Edit intent: meaning-changed
Original: Background: The correct positioning of the mitotic spindle during the asymmetric division of the nematode C. elegans zygote relies on the combination of centering and corticalpulling forces. These forces, revealed by centrosome anaphase oscillations, are regulated through the dynamics of force generators, related to mitosis progression.
Revised: Background: The correct positioning of the mitotic spindle during the asymmetric division of the Caenorhabditis elegans nematode zygote, the polarity cues distribution and daughter cell fates depend on the correct positioning of the mitotic spindle which results from both centering and cortical pulling forces. Revealed by spindle rocking, these pulling forces are regulated by the force generator dynamics, which are related to mitosis progression.
Edit intent: meaning-changed
Original:  Recently, we reported the control of oscillation onset by the posterior spindle pole position in related speciesC. briggsae, necessitating a re-evaluation of the role of astral microtubules dynamics.
Revised:  This may be combined with a second regulation, this one by the posterior spindle pole position in related speciesC. briggsae, necessitating a re-evaluation of the role of astral microtubules dynamics.
Edit intent: clarity
Original:  Results: After exhibiting such a positional switch in C. elegans, we mapped the microtubule ends at the cortex and observed a correlation between the proximity of the centrosomes and the density of microtubule contacts.
Revised:  Results: After delaying anaphase onset, we identified a positional pulling force regulation in C. elegans, we mapped the microtubule ends at the cortex and observed a correlation between the proximity of the centrosomes and the density of microtubule contacts.
Edit intent: meaning-changed
Original:  Results: After exhibiting such a positional switch in C. elegans, we mapped the microtubule ends at the cortex and observed a correlation between the proximity of the centrosomes and the density of microtubule contacts.
Revised:  Results: After exhibiting such a positional switch in C. elegans, which we ascribed to microtubule dynamics at the cortex and observed a correlation between the proximity of the centrosomes and the density of microtubule contacts.
Edit intent: clarity
Original:  Results: After exhibiting such a positional switch in C. elegans, we mapped the microtubule ends at the cortex and observed a correlation between the proximity of the centrosomes and the density of microtubule contacts.
Revised:  Results: After exhibiting such a positional switch in C. elegans, we mapped the microtubule ends at the cortex . Indeed, in mapping the contacts we found a correlation between the proximity of the centrosomes and the density of microtubule contacts.
Edit intent: coherence
Original:  Results: After exhibiting such a positional switch in C. elegans, we mapped the microtubule ends at the cortex and observed a correlation between the proximity of the centrosomes and the density of microtubule contacts. To explore the functional consequences, we extended the tug-of-war model and successfully accounted for the positional switch. We predicted and experimentally validated that the control of oscillation onset was robust to changes in cell geometry or maximum number of attached force generators.
Revised:  Results: After exhibiting such a positional switch in C. elegans, we mapped the microtubule ends at the cortex and observed a correlation between the centrosome-cortex distance and the microtubule contact density. This density in turn modulates pulling force generator activity. We expanded our model of spindle rocking and predicted then experimentally validated that the control of oscillation onset was robust to changes in cell geometry or maximum number of attached force generators.
Edit intent: clarity
Original:  We also predicted that the final position of the posterior centrosome and thus the spindle has a reduced dependence upon the force generator dynamics or number . Conclusion: The outburst of forces responsible of spindle anaphase oscillations and positioning is regulated by the spindle position through the spatial modulation of microtubule contactsat the cortex .
Revised:  Consistent with final spindle position measurements, this new model accounts for a lower dependence on force generator dynamics or number . Conclusion: The outburst of forces responsible of spindle anaphase oscillations and positioning is regulated by the spindle position through the spatial modulation of microtubule contactsat the cortex .
Edit intent: clarity
Original:  We also predicted that the final position of the posterior centrosome and thus the spindle has a reduced dependence upon the force generator dynamics or number . Conclusion: The outburst of forces responsible of spindle anaphase oscillations and positioning is regulated by the spindle position through the spatial modulation of microtubule contactsat the cortex .
Revised:  We also predicted that the final position of the posterior centrosome and thus the spindle has a reduced dependence upon the force generator dynamics and quantities than predicted by the previous model . Conclusion: The outburst of forces responsible of spindle anaphase oscillations and positioning is regulated by the spindle position through the spatial modulation of microtubule contactsat the cortex .
Edit intent: meaning-changed
Original:  We also predicted that the final position of the posterior centrosome and thus the spindle has a reduced dependence upon the force generator dynamics or number . Conclusion: The outburst of forces responsible of spindle anaphase oscillations and positioning is regulated by the spindle position through the spatial modulation of microtubule contactsat the cortex .
Revised:  We also predicted that the final position of the posterior centrosome and thus the spindle has a reduced dependence upon the force generator dynamics or number . Conclusion: The spindle position regulates the rapid increase in forces needed for anaphase oscillation and positioning through the spatial modulation of microtubule contactsat the cortex .
Edit intent: clarity
Original:  We also predicted that the final position of the posterior centrosome and thus the spindle has a reduced dependence upon the force generator dynamics or number . Conclusion: The outburst of forces responsible of spindle anaphase oscillations and positioning is regulated by the spindle position through the spatial modulation of microtubule contactsat the cortex .
Revised:  We also predicted that the final position of the posterior centrosome and thus the spindle has a reduced dependence upon the force generator dynamics or number . Conclusion: The outburst of forces responsible of spindle anaphase oscillations and positioning is regulated by the spindle position through the spatial modulation of microtubule-cortex contacts .
Edit intent: clarity
Original:  We propose a new estimator of VaR contributions , that utilizes Markov chain Monte Carlo (MCMC) method. Unlike the existing estimators, our MCMC-based estimator is computed by samples of conditional loss distribution given the rare event of our interest.
Revised:  We propose a new estimator of VaR contributions , that utilizes Markov chain Monte Carlo (MCMC) methods. Unlike existing estimators, our MCMC-based estimator is computed by samples of conditional loss distribution given the rare event of our interest.
Edit intent: fluency
Original:  Unlike the existing estimators, our MCMC-based estimator is computed by samples of conditional loss distribution given the rare event of our interest. MCMC method enables to generate such samples without evaluating the density of total risk. Thanks to these features, our estimator has improved sample-efficiency compared with the crude Monte Carlo method.
Revised:  Unlike the existing estimators, our MCMC-based estimator is computed by samples of conditional loss distribution given the rare event of interest. This feature enhances sample efficiency compared with the crude Monte Carlo method.
Edit intent: clarity
Original:  In this paper, we show that our MCMC-based estimator has several attractive properties, such as consistency and asymptotic normality. Our numerical experiment also demonstrates that , in various risk models used in practice, our MCMC estimator has smaller bias and MSE compared with these of existing estimators.
Revised:  Our numerical experiments based on simulation and real-world data demonstrate that in various risk models used in practice, our MCMC estimator has smaller bias and MSE compared with these of existing estimators.
Edit intent: clarity
Original: Motivated by map labeling, we study the problem in which ]  we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Revised: Motivated by map labeling, Funke, Krumpe, and Storandt ] we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Edit intent: meaning-changed
Original: Motivated by map labeling, we study the problem in which ]  we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Revised: Motivated by map labeling, we study the problem in which IWOCA 2016] we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Edit intent: meaning-changed
Original: Motivated by map labeling, we study the problem in which ]  we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Revised: Motivated by map labeling, we study the problem in which ] introduced the following problem: we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Edit intent: meaning-changed
Original: Motivated by map labeling, we study the problem in which ]  we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Revised: Motivated by map labeling, we study the problem in which ] we are given a sequence of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Edit intent: clarity
Original: Motivated by map labeling, we study the problem in which ]  we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Revised: Motivated by map labeling, we study the problem in which ] we are given a collection of n disks %DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Edit intent: meaning-changed
Original: Motivated by map labeling, we study the problem in which ]  we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Revised: Motivated by map labeling, we study the problem in which ] we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% in the plane that grow at possibly different speeds.
Edit intent: clarity
Original: Motivated by map labeling, we study the problem in which ]  we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane that grow at possibly different speeds.
Revised: Motivated by map labeling, we study the problem in which ] we are given a collection of n disks D_1,%DIFDELCMD < \dots%%% , D_n in the plane . Initially, all disks have radius 0, and they grow at constant, but possibly different, speeds.
Edit intent: meaning-changed