wanyu/IteraTeR_full_sent huggingface dataset:
Original: Jeandel and Rao proved that 11 is the size of the smallest set of Wang tiles, i.e., unit squares with colored edges, that admit valid  (contiguous edges of adjacent tiles have the same color) tilings of the plane  none of them being invariant under a nontrivial translation.
Revised: Jeandel and Rao proved that 11 is the size of the smallest set of Wang tiles, i.e., unit squares with colored edges, that admit valid (contiguous edges of adjacent tiles have the same color) tilings of the plane , none of them being invariant under a nontrivial translation.
Edit intent: fluency
Original:  In this contribution, we study the Wang shift \Omega_0 made of all valid tilings using the set T_0 of 11 aperiodic Wang tiles discovered by Jeandel and Rao.
Revised:  We study herein the Wang shift \Omega_0 made of all valid tilings using the set T_0 of 11 aperiodic Wang tiles discovered by Jeandel and Rao.
Edit intent: clarity
Original:  We show that there exists a minimal subshift X_0 of \Omega_0 such that any tiling in X_0 can be decomposed uniquely into 19 distinct patches of sizes ranging from 45 to 112 that are equivalent to a set of  self-similar and aperiodic 19 Wang tiles.
Revised:  We show that there exists a minimal subshift X_0 of \Omega_0 such that every tiling in X_0 can be decomposed uniquely into 19 distinct patches of sizes ranging from 45 to 112 that are equivalent to a set of self-similar and aperiodic 19 Wang tiles.
Edit intent: fluency
Original:  We show that there exists a minimal subshift X_0 of \Omega_0 such that any tiling in X_0 can be decomposed uniquely into 19 distinct patches of sizes ranging from 45 to 112 that are equivalent to a set of  self-similar and aperiodic 19 Wang tiles.
Revised:  We show that there exists a minimal subshift X_0 of \Omega_0 such that any tiling in X_0 can be decomposed uniquely into 19 distinct patches of sizes ranging from 45 to 112 that are equivalent to a set of 19 self-similar and aperiodic 19 Wang tiles.
Edit intent: meaning-changed
Original:  We show that there exists a minimal subshift X_0 of \Omega_0 such that any tiling in X_0 can be decomposed uniquely into 19 distinct patches of sizes ranging from 45 to 112 that are equivalent to a set of  self-similar and aperiodic 19 Wang tiles.
Revised:  We show that there exists a minimal subshift X_0 of \Omega_0 such that any tiling in X_0 can be decomposed uniquely into 19 distinct patches of sizes ranging from 45 to 112 that are equivalent to a set of self-similar and aperiodic Wang tiles.
Edit intent: meaning-changed
Original:  We think that this gives an almost complete description of the substitutive structure of Jeandel-Rao tilings  as we believe that \Omega_0\setminus X_0 is a null set for any shift-invariant probability measure on \Omega_0.
Revised:  We suggest that this provides an almost complete description of the substitutive structure of Jeandel-Rao tilings as we believe that \Omega_0\setminus X_0 is a null set for any shift-invariant probability measure on \Omega_0.
Edit intent: clarity
Original:  We think that this gives an almost complete description of the substitutive structure of Jeandel-Rao tilings  as we believe that \Omega_0\setminus X_0 is a null set for any shift-invariant probability measure on \Omega_0.
Revised:  We think that this gives an almost complete description of the substitutive structure of Jeandel-Rao tilings , as we believe that \Omega_0\setminus X_0 is a null set for any shift-invariant probability measure on \Omega_0.
Edit intent: fluency
Original:  Starting in a neutral strategy with constant exercise rate then allows us to globally optimize this function in a gradual manner . Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method  both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of  exercise rates.
Revised:  The global optimum of this function can be approached gradually when starting from a constant exercise rate then allows us to globally optimize this function in a gradual manner . Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of exercise rates.
Edit intent: clarity
Original:  Starting in a neutral strategy with constant exercise rate then allows us to globally optimize this function in a gradual manner . Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method  both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of  exercise rates.
Revised:  Starting in a neutral strategy with constant exercise rate . Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of exercise rates.
Edit intent: clarity
Original:  Starting in a neutral strategy with constant exercise rate then allows us to globally optimize this function in a gradual manner . Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method  both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of  exercise rates.
Revised:  Starting in a neutral strategy with constant exercise rate then allows us to globally optimize this function in a gradual manner . Numerical experiments on vanilla put options in the multivariate Black-Scholes model and a preliminary theoretical analysis underline the efficiency of our method both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of exercise rates.
Edit intent: fluency
Original:  Starting in a neutral strategy with constant exercise rate then allows us to globally optimize this function in a gradual manner . Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method  both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of  exercise rates.
Revised:  Starting in a neutral strategy with constant exercise rate then allows us to globally optimize this function in a gradual manner . Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method , both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of exercise rates.
Edit intent: fluency
Original:  Starting in a neutral strategy with constant exercise rate then allows us to globally optimize this function in a gradual manner . Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method  both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of  exercise rates.
Revised:  Starting in a neutral strategy with constant exercise rate then allows us to globally optimize this function in a gradual manner . Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of the exercise rates.
Edit intent: fluency
Original:  Finally,  the flexibility of our method is demonstrated by numerical experiments on max call options in the Black--Scholes model and vanilla put options in  Heston model and the non-Markovian rough Bergomi model.
Revised:  Finally, we demonstrate the flexibility of our method is demonstrated by numerical experiments on max call options in the Black--Scholes model and vanilla put options in Heston model and the non-Markovian rough Bergomi model.
Edit intent: clarity
Original:  Finally,  the flexibility of our method is demonstrated by numerical experiments on max call options in the Black--Scholes model and vanilla put options in  Heston model and the non-Markovian rough Bergomi model.
Revised:  Finally, the flexibility of our method through numerical experiments on max call options in the Black--Scholes model and vanilla put options in Heston model and the non-Markovian rough Bergomi model.
Edit intent: clarity
Original:  Finally,  the flexibility of our method is demonstrated by numerical experiments on max call options in the Black--Scholes model and vanilla put options in  Heston model and the non-Markovian rough Bergomi model.
Revised:  Finally, the flexibility of our method is demonstrated by numerical experiments on max call options in the classical Black-Scholes model, and vanilla put options in Heston model and the non-Markovian rough Bergomi model.
Edit intent: meaning-changed
Original:  Finally,  the flexibility of our method is demonstrated by numerical experiments on max call options in the Black--Scholes model and vanilla put options in  Heston model and the non-Markovian rough Bergomi model.
Revised:  Finally, the flexibility of our method is demonstrated by numerical experiments on max call options in the Black--Scholes model and vanilla put options in both the Heston model and the non-Markovian rough Bergomi model.
Edit intent: clarity
Original: In this paper we consider the classical min--\# curve simplification problem in three different variants. Let \delta>0, P be  a polygonal curve  with n vertices in \mathbb{R^d, and D(\cdot,\cdot) be a distance measure.
Revised: Due to its many applications, a polygonal curve with n vertices in \mathbb{R^d, and D(\cdot,\cdot) be a distance measure.
Edit intent: meaning-changed
Original:  Let \delta>0, P be  a polygonal curve  with n vertices in \mathbb{R^d, and D(\cdot,\cdot) be a distance measure.
Revised:  Let \delta>0, P be is a long-studied problem in computational geometry and adjacent disciplines, such as graphics, geographical information science, etc. Given a polygonal curve with n vertices in \mathbb{R^d, and D(\cdot,\cdot) be a distance measure.
Edit intent: meaning-changed
Original:  We aim to simplify P by }  another polygonal curve P' with minimum number of vertices satisfying D(P,P' ) \leq \delta. We obtain three main results for this problem: (1) An O(n^4)-time algorithm when D(P,P') is the Fr\'echet distance and vertices in P' are selected from a subsequence of vertices in P. (2) An   \emph{  NP-hardness result for the case that D(P ,P')
Revised:  We aim to simplify P by } another polygonal curve P' with minimum number of vertices such that P' is sufficiently similar to P. Quality guarantees of a simplification are usually given in a \emph{ NP-hardness result for the case that D(P ,P')
Edit intent: meaning-changed
Original:  An   \emph{  NP-hardness result for the case that D(P ,P') is the directed Hausdorff distance from P' to P and the vertices of P' can lie anywhere on P while respecting the order of edges along P. (3) For any \epsilon>0, an O^*(n^2\log n \log \log n)-time algorithm that computes P'whose vertices can lie anywhere in the space and whose Fr\'echet distance to P is at most (1+\epsilon)\delta with at most 2m+1 links, where m is the number of links in the optimal simplified curve and O^* hides polynomial factors of 1/\epsilon .
Revised:  An \emph{ NP-hardness for other variants. Through this systematic study we observe, for the first time, some surprising patterns, and suggest directions for future research in this important area .
Edit intent: meaning-changed
Original:  I show that in both cases the coefficient on treatment is identical to a convex combination of two other parameters(different for OLS and 2SLS), which can be interpreted as the average treatment effects on the treated and controls under additional assumptions.
Revised:  I show that the treatment coefficient is a convex combination of two other parameters(different for OLS and 2SLS), which can be interpreted as the average treatment effects on the treated and controls under additional assumptions.
Edit intent: clarity
Original:  I show that in both cases the coefficient on treatment is identical to a convex combination of two other parameters(different for OLS and 2SLS), which can be interpreted as the average treatment effects on the treated and controls under additional assumptions.
Revised:  I show that in both cases the coefficient on treatment is identical to a convex combination of two parameters, which under certain conditions can be interpreted as the average treatment effects on the treated and controls under additional assumptions.
Edit intent: clarity
Original:  I show that in both cases the coefficient on treatment is identical to a convex combination of two other parameters(different for OLS and 2SLS), which can be interpreted as the average treatment effects on the treated and controls under additional assumptions. Importantly, the OLS and 2SLS weights on these parameters are inversely related to the proportion of  each group.
Revised:  I show that in both cases the coefficient on treatment is identical to a convex combination of two other parameters(different for OLS and 2SLS), which can be interpreted as the average treatment effects on the treated and untreated. The weights on these parameters are inversely related to the proportion of each group.
Edit intent: clarity
Original:  What follows, the reliance on these implicit weights can have serious consequences for applied work . I illustrate some of these issues in four empirical applicationsfrom different fields of economics. I also develop a weighted least squares correction and simple diagnostic tools that applied researchers can use to avoid potential biases  .
Revised:  What follows, the reliance on these implicit weights can have serious consequences for applied work , as I illustrate with two well-known applications. I develop simple diagnostic tools that applied researchers can use to avoid potential biases .
Edit intent: meaning-changed
Original:  It was studied the DNA damage in a single strain and in double strain, SSB and DSB respectively as a product of ionising radiation from X-rays when interacting with the DNA immersed in water.
Revised:  Once the strands are generated, it is studied the DNA damage in a single strain and in double strain, SSB and DSB respectively as a product of ionising radiation from X-rays when interacting with the DNA immersed in water.
Edit intent: meaning-changed
Original:  It was studied the DNA damage in a single strain and in double strain, SSB and DSB respectively as a product of ionising radiation from X-rays when interacting with the DNA immersed in water.
Revised:  It was studied the DNA damage in a single strain and in double strain, SSB and DSB respectively as a product of ionising radiation of X-rays when interacting with the DNA immersed in water.
Edit intent: clarity
Original:  This is a theoretical and experimental study in-vitro  that quantifies the SSB and DSB with respect to different Gy's of radiation, this allows the understanding and prediction about the exact risks of the exposition.
Revised:  This is a theoretical and experimental in-vitro that quantifies the SSB and DSB with respect to different Gy's of radiation, this allows the understanding and prediction about the exact risks of the exposition.
Edit intent: clarity
Original:  This is a theoretical and experimental study in-vitro  that quantifies the SSB and DSB with respect to different Gy's of radiation, this allows the understanding and prediction about the exact risks of the exposition.
Revised:  This is a theoretical and experimental study in-vitro study that quantifies the SSB and DSB with respect to different Gy's of radiation, this allows the understanding and prediction about the exact risks of the exposition.
Edit intent: clarity
Original:  This is a theoretical and experimental study in-vitro  that quantifies the SSB and DSB with respect to different Gy's of radiation, this allows the understanding and prediction about the exact risks of the exposition. It has been developed for energies corresponding to the 17.6 KeV however the energy parameters are also variable which allows the simulation of all type of ionising radiation. For this simulation it is also taken into account the indirect damage as a product of the free electrons and radicals from the water effects.
Revised:  This is a theoretical and experimental study in-vitro that quantifies the SSB and DSB with respect to different Gy's of radiation, this allows the understanding and prediction about the exact risks of expositions to radiations. In simulations, it is taken into account the indirect damage as a product of the free electrons and radicals from the water effects.
Edit intent: clarity
Original:  For this simulation it is also taken into account the indirect damage as a product of the free electrons and radicals from the water effects. The information of the spatial distribution of the electrones is obtained form Geant4 and afterwards it is implemented in Matlab where rays are created with tri-dimensional random trajectories through Monte Carlo simulations.
Revised:  For this simulation it is also taken into account the damage caused by free electrons generated by the effect of the interaction with the water molecules, this is different to the effect considered in radiobiology, where indirect damages are due to chemical reactions. The spatial distribution of the electrones is obtained form Geant4 and afterwards it is implemented in Matlab where rays are created with tri-dimensional random trajectories through Monte Carlo simulations.
Edit intent: meaning-changed
Original:  The experimental confirmation was developed by radiating DNA samples immersed in water with a X-rays unit with Molibdeno targetand it is observed and quantified the damage level through Atomic Force Microscopy (AFM).
Revised:  It is also presented the experimental DNA damage through radiating DNA samples immersed in water with a X-rays unit with Molibdeno targetand it is observed and quantified the damage level through Atomic Force Microscopy (AFM).
Edit intent: coherence
Original:  The experimental confirmation was developed by radiating DNA samples immersed in water with a X-rays unit with Molibdeno targetand it is observed and quantified the damage level through Atomic Force Microscopy (AFM).
Revised:  The experimental confirmation was developed by radiating DNA samples immersed in water with a X-rays unit with Molybdenum target. The damage level is quantified through Atomic Force Microscopy (AFM).
Edit intent: coherence
Original:  It was obtained a direct relation between the damage and the radiation dose in the experiment and in the model and it is concluded that for 17.6 KeV the deterioration for interaction is observed very low doses but the mutagenic damage only appears until the 17 Gy .
Revised:  It is possible to conclude a direct relation between the damage and the radiation dose in the experiment and in the model and it is concluded that for 17.6 KeV the deterioration for interaction is observed very low doses but the mutagenic damage only appears until the 17 Gy .
Edit intent: clarity
Original: The analysis of neuroimaging data poses several strong challenges, in particular, due to its high dimensionality, its strong spatio-temporal correlation and the comparably small sample sizes of the respective datasets.
Revised: The application of deep learning (DL) models to neuroimaging data poses several strong challenges, in particular, due to its high dimensionality, its strong spatio-temporal correlation and the comparably small sample sizes of the respective datasets.
Edit intent: meaning-changed
Original: The analysis of neuroimaging data poses several strong challenges, in particular, due to its high dimensionality, its strong spatio-temporal correlation and the comparably small sample sizes of the respective datasets. To address these challenges, conventional decoding approaches such as the searchlight reduce the complexity of the decoding problem by considering local clusters of voxels only. Thereby, neglecting the distributed spatial patterns of brain activity underlying many cognitive states. In this work , we introduce the DLight framework, which overcomes these challenges by utilizing a long short-term memory unit (LSTM) based deep neural network architecture to analyze the spatial dependency structure of whole-brain fMRI data.
Revised: The analysis of neuroimaging data poses several strong challenges, in particular, due to its high dimensionality, low sample size and complex temporo-spatial dependency structure of these datasets. Even further, DL models act as as black-box models, impeding insight into the association of cognitive state and brain activity. To approach these challenges , we introduce the DLight framework, which overcomes these challenges by utilizing a long short-term memory unit (LSTM) based deep neural network architecture to analyze the spatial dependency structure of whole-brain fMRI data.
Edit intent: coherence
Original:  In this work , we introduce the DLight framework, which overcomes these challenges by utilizing a long short-term memory unit (LSTM) based deep neural network architecture to analyze the spatial dependency structure of whole-brain fMRI data.
Revised:  In this work , we introduce the DeepLight framework, which overcomes these challenges by utilizing a long short-term memory unit (LSTM) based deep neural network architecture to analyze the spatial dependency structure of whole-brain fMRI data.
Edit intent: fluency
Original:  In this work , we introduce the DLight framework, which overcomes these challenges by utilizing a long short-term memory unit (LSTM) based deep neural network architecture to analyze the spatial dependency structure of whole-brain fMRI data.
Revised:  In this work , we introduce the DLight framework, which utilizes long short-term memory unit (LSTM) based deep neural network architecture to analyze the spatial dependency structure of whole-brain fMRI data.
Edit intent: coherence
Original:  In this work , we introduce the DLight framework, which overcomes these challenges by utilizing a long short-term memory unit (LSTM) based deep neural network architecture to analyze the spatial dependency structure of whole-brain fMRI data.
Revised:  In this work , we introduce the DLight framework, which overcomes these challenges by utilizing a long short-term memory (LSTM) based deep neural network architecture to analyze the spatial dependency structure of whole-brain fMRI data.
Edit intent: clarity
Original:  In this work , we introduce the DLight framework, which overcomes these challenges by utilizing a long short-term memory unit (LSTM) based deep neural network architecture to analyze the spatial dependency structure of whole-brain fMRI data.
Revised:  In this work , we introduce the DLight framework, which overcomes these challenges by utilizing a long short-term memory unit (LSTM) based DL models to analyze whole-brain fMRI data.
Edit intent: clarity