wanyu/IteraTeR_v2 huggingface dataset:
Original:  We find that decreasing N or m promotes evolution toward altruism, and if this evolution is exactly balanced outby evolution towards selfishness, N and m satisfy a scaling relation N\,\propto\, m ^{ -
Revised:  We find that decreasing N or m promotes evolution toward altruism, and if this evolution is exactly balanced outby evolution towards selfishness, N and m satisfy a scaling relation N\,\propto\, m ^{ 
Edit intent: fluency
Original:  \alpha} such that evolution becomes increasingly independent of m as s decreases (i.e., \alpha%DIFDELCMD < \downarrow0 %%% as s%DIFDELCMD < \downarrow0%%% ) . This relation markedly differs from that predicted by a binary-trait model, where evolution becomes increasingly dependent on m as s decreases.
Revised:  \alpha} %DIFDELCMD < \downarrow0 %%% as s%DIFDELCMD < \downarrow0%%% ) . This relation markedly differs from that predicted by a binary-trait model, where evolution becomes increasingly dependent on m as s decreases.
Edit intent: clarity
Original:  \alpha} such that evolution becomes increasingly independent of m as s decreases (i.e., \alpha%DIFDELCMD < \downarrow0 %%% as s%DIFDELCMD < \downarrow0%%% ) . This relation markedly differs from that predicted by a binary-trait model, where evolution becomes increasingly dependent on m as s decreases.
Revised:  \alpha} such that evolution becomes increasingly independent of m as s decreases (i.e., \alpha%DIFDELCMD < \downarrow0 %%% %DIFDELCMD < \downarrow0%%% ) . This relation markedly differs from that predicted by a binary-trait model, where evolution becomes increasingly dependent on m as s decreases.
Edit intent: coherence
Original:  The developed approach can potentially be applied to related problems that involve stiff computations such as those arising in compressible high-speed flows.
Edit intent: coherence
Original:  Nowadays, many works become widely disseminated even before publication, in the form of preprints.
Revised:  Nowadays, many works are widely disseminated even before publication, in the form of preprints.
Edit intent: clarity
Original:  Another important new element concerns the visualizations of published articles.
Revised:  Another important new element concerns the views of published articles.
Edit intent: clarity
Original:  Thanks to the availability of respective data by some journals,  it became possible to develop investigations on how papers are viewed along time, often before the first citations appear.
Revised:  Thanks to the availability of respective data by some journals, it became possible to develop investigations on how scientific works are viewed along time, often before the first citations appear.
Edit intent: clarity
Original:  Our research was initiated in observations that the view profiles along time tend to present a piecewise linear nature.
Revised:  More specifically, our research was motivated by preliminary observations that the view profiles along time tend to present a piecewise linear nature.
Edit intent: clarity
Original:  A methodology was then delineated that in order to identify the main segments in the view profiles, which allowed to obtain several related measurements  .
Revised:  A methodology was then delineated in order to identify the main segments in the view profiles, which allowed to obtain several related measurements .
Edit intent: fluency
Original:  A methodology was then delineated that in order to identify the main segments in the view profiles, which allowed to obtain several related measurements  .
Revised:  A methodology was then delineated that in order to identify the main segments in the view profiles, which allowed several related measurements .
Edit intent: clarity
Original:  A methodology was then delineated that in order to identify the main segments in the view profiles, which allowed to obtain several related measurements  .
Revised:  A methodology was then delineated that in order to identify the main segments in the view profiles, which allowed to obtain several related measurements to be derived .
Edit intent: clarity
Original:  Basic statistics indicated that the inclination tends to decrease along subsequent segments, while the segment lengths resulted more stable.
Revised:  Basic statistics indicated that the inclination can vary substantially along subsequent segments, while the segment lengths resulted more stable.
Edit intent: clarity
Original:  We demonstrated that this framework is flexible and unified enough to incorporate a family of problems spanning Multi-armed bandits (MAB), contextual bandits (CB) and reinforcement learning (RL), which decompose the sequential decision making process in different levels.
Revised:  We demonstrated that this framework is flexible and unified enough to incorporate a family of problems spanning multi-armed bandits (MAB), contextual bandits (CB) and reinforcement learning (RL), which decompose the sequential decision making process in different levels.
Edit intent: fluency
Original: Recent years have witnessed growing interests in solving partial differentialequationsbydeepneuralnetworks, especiallyinthehigh-dimensional case.
Revised: Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case.
Edit intent: fluency
Original:  In the work, we conduct a comprehensive study of four different boundary conditions, i.e., Dirichlet, Neumann, Robin, and periodic boundary conditions, using two representative methods: deep Ritz method and deep Galerkin method.
Revised:  In the work, we conduct a comprehensive study of four different boundary conditions, i.e., Dirichlet, Neumann, Robin, and periodic boundary conditions, using two representative methods: deep Galerkin method and deep Galerkin method.
Edit intent: clarity
Original:  However, by a number of examples, we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for lowregularity solutions.
Revised:  However, by a number of examples, we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for low-regularity solutions.
Edit intent: fluency
Original:  We show that the catchbond behaviour of individual dynein motors manifests as a generic mechanism of generating spontaneous oscillations in such complexes.
Revised:  We show that catchbonding behaviour of motor proteins provides a generic mechanism of generating spontaneous oscillations in such complexes.
Edit intent: clarity
Original:  This has dramatic effects on the extrapolation of a disease's progression when the data collected comes from the early, exponential-like region, and may remove a systematic bias from such models .
Revised:  This has dramatic effects on the extrapolation of a disease's progression when the data collected comes from the early, exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak .
Edit intent: clarity
Original: The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in disease susceptibility.
Revised: The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in infection susceptibility.
Edit intent: fluency
Original:  Moreover, our proofs cover the actual Agda implementations of the libraries , not just an abstract model .
Revised:  Moreover, our proofs cover the actual Agda implementations of the libraries in terms of type abstraction .
Edit intent: clarity
Original: Network alignment, the process of finding correspondences between nodes in different graphs, has significant scientific and industrial applications.
Revised: Network alignment, the process of finding correspondences between nodes in different graphs, has many scientific and industrial applications.
Edit intent: clarity
Original:  We find that many existing network alignment methods fail to achieve accurate alignments because they break up node neighborhoods during alignment, failing to preserve matched neighborhood consistency.
Revised:  Existing unsupervised network alignment methods fail to achieve accurate alignments because they break up node neighborhoods during alignment, failing to preserve matched neighborhood consistency.
Edit intent: clarity
Original:  We find that many existing network alignment methods fail to achieve accurate alignments because they break up node neighborhoods during alignment, failing to preserve matched neighborhood consistency.
Revised:  We find that many existing network alignment methods find suboptimal alignments that break up node neighborhoods during alignment, failing to preserve matched neighborhood consistency.
Edit intent: clarity
Original:  We find that many existing network alignment methods fail to achieve accurate alignments because they break up node neighborhoods during alignment, failing to preserve matched neighborhood consistency.
Revised:  We find that many existing network alignment methods fail to achieve accurate alignments because they break up node neighborhoods , i.e. do not preserve matched neighborhood consistency.
Edit intent: clarity
Original:  In a special case the integral equation is equivalent to the Bernoulli differential equation and implies the classic SIR model under an appropriate scaling  .
Revised:  In a special case the integral equation is equivalent to the Bernoulli differential equation . Another result of the paper is that, under an appropriate scaling .
Edit intent: coherence
Original:  We show that the distribution of the time before infection can be expressed in terms of the solution of an integral equation, special cases of which are equivalent to the Bernoulli differential equation .
Revised:  We show that the distribution of the infection time in terms of the solution of an integral equation, special cases of which are equivalent to the Bernoulli differential equation .
Edit intent: clarity
Original:  Another resultof the paper is that, under an appropriate scaling, the single equation of the model implies the system of three equations of the classic SIR model.
Revised:  Another resultof the paper is that, under an appropriate scaling, the single equation of the system of three equations of the classic SIR model.
Edit intent: clarity
Original:  Another resultof the paper is that, under an appropriate scaling, the single equation of the model implies the system of three equations of the classic SIR model.
Revised:  Another resultof the paper is that, under an appropriate scaling, the single equation of the model implies the system of equations of the classic SIR model.
Edit intent: clarity
Original:  in other cases, it is a topological matter (meagre vs. co-meagre) , or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre , in the sense of Mehlhorn (1973) ).
Revised:  in other cases, it is a topological matter (meagre vs. co-meagre) or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre , in the sense of Mehlhorn (1973) ).
Edit intent: fluency
Original:  in other cases, it is a topological matter (meagre vs. co-meagre) , or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre , in the sense of Mehlhorn (1973) ).
Revised:  in other cases, it is a topological matter (meagre vs. co-meagre) , or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre ).
Edit intent: coherence
Original:  In addition, we prove that for every metric space (X,d) it holds that 2-1\le\beta^*_{(X,d)}, and show that there exist a metric space for which \beta^*_{(X,d)}\le \frac{1}{2}.
Revised:  In addition, we prove that for every metric space (X,d) it holds that 2-1\le\beta^*_{(X,d)}, and show that there exists a metric space for which \beta^*_{(X,d)}\le \frac{1}{2}.
Edit intent: fluency
Original: To understand the hidden physical concepts from observed data is the most basic but challenging problem in many fields.
Revised: To derive the hidden dynamics from observed data is the most basic but challenging problem in many fields.
Edit intent: clarity
Original: To understand the hidden physical concepts from observed data is the most basic but challenging problem in many fields.
Revised: To understand the hidden physical concepts from observed data is one of the fundamental but also challenging problems in many different fields.
Edit intent: clarity
Original:  In this study, we propose a new type of interpretable neural network called the ordinary differential equation network (ODENet) to reveal the hidden dynamics buried in the massive time-series data.
Revised:  In this study, we propose a new type of interpretable network called the ordinary differential equation network (ODENet) to reveal the hidden dynamics buried in the massive time-series data.
Edit intent: clarity
Original:  From classical Lotka-Volterra equations to chaotic Lorenz equations, the ODENet demonstrates its remarkable capability to deal with time-series data .
Revised:  From classical Lotka-Volterra equations to chaotic Lorenz equations, the ODENet exhibits its remarkable capability to deal with time-series data .
Edit intent: fluency
Original:  From classical Lotka-Volterra equations to chaotic Lorenz equations, the ODENet demonstrates its remarkable capability to deal with time-series data .
Revised:  From classical Lotka-Volterra equations to chaotic Lorenz equations, the ODENet demonstrates its remarkable capability in handling time-series data .
Edit intent: clarity
Original:  In the end, we apply the ODENet to real actin aggregation data observed by experimentalists, and it shows an impressive performance as well  .
Revised:  In the end, we apply the ODENet to real actin aggregation data , which shows an impressive performance as well .
Edit intent: clarity
Original:  Aggregating these data to derive scientific insights often faces the challenge that fMRI data are high dimensional , heterogeneous across people, and noisy.
Revised:  Aggregating these data to derive scientific insights often faces the challenge that fMRI data are high-dimensional , heterogeneous across people, and noisy.
Edit intent: fluency
Original:  Such approaches can avoid erroneous findings, reduce the impact of noise, better utilize known properties of the data, and  aggregate data across groups of subjects.
Revised:  Such approaches can avoid erroneous findings, reduce the impact of noise, better utilize known properties of the data, and better aggregate data across groups of subjects.
Edit intent: fluency
Original:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Revised:  In this paper, we study the problem of estimating the state propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Edit intent: clarity
Original:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Revised:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the individuals . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Edit intent: clarity
Original:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Revised:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between individuals by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Edit intent: clarity
Original:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Revised:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of the time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Edit intent: clarity
Original:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Revised:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of one individual's state positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Edit intent: clarity
Original:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other cell averaged over the minimum cost alignments and show how to calculate it efficiently.
Revised:  In this paper, we study the problem of estimating the firing propagation order of cells from the \{0,1 \ sequences of all the cells, where '1' at the i-th position means the firing state of the cell at time step i . We propose a method to estimate the propagation direction between cells by the sum of one cell's time delay of the matched positions from the other individual's matched state position averaged over the minimum cost alignments and show how to calculate it efficiently.
Edit intent: clarity
Original:  The propagation order estimated by our proposed method is demonstrated to be correct for our synthetic datasets, and also to be consistent with visually recognizable firing order for the dataset of soil-dwelling amoeba's chemical signal emitting state sequences.
Revised:  The propagation order estimated by our proposed method is demonstrated to be correct for our synthetic datasets, and also to be consistent with visually recognizable propagation orders for the dataset of soil-dwelling amoeba's chemical signal emitting state sequences.
Edit intent: clarity
Original:  This is breaking the\emph{kissing number barrier of 3^n that is inherent in the previous best approaches tackling this problem .
Revised:  This \emph{kissing number barrier of 3^n that is inherent in the previous best approaches tackling this problem .
Edit intent: coherence
Original:  This is breaking the\emph{kissing number barrier of 3^n that is inherent in the previous best approaches tackling this problem .
Revised:  This is breaking the\emph{ of 3^n that is inherent in the previous best approaches tackling this problem .
Edit intent: clarity
Original: For an empirical signed measure \mu = 1{N} \left(i=1^P \delta_{ %DIFDELCMD < \bx%%%  _i} -
Revised: For an empirical signed measure \mu = 1{N} \left(i=1^P \delta_{ %DIFDELCMD < \bx%%% x _i} -
Edit intent: fluency
Original:  i=1^M \delta_{ %DIFDELCMD < \by%%%  _i}\right), particle annihilation (PA)
Revised:  i=1^M \delta_{ %DIFDELCMD < \by%%% y _i}\right), particle annihilation (PA)
Edit intent: fluency
Original:  removes N_A particles from both \{ %DIFDELCMD < \bx%%%  _i\}_{i=1}^P and \{ %DIFDELCMD < \by%%%  _i\}_{i=1}^M simultaneously, yielding another empirical signed measure \nu such that \int f %DIFDELCMD < \D %%%  \nu approximates to \int f %DIFDELCMD < \D %%%  \mu within an acceptable accuracy for suitable test functions f. 62G09 Such annihilation of particles carrying opposite importance weights has been extensively utilized for alleviating the numerical sign problem in particle simulations.
Revised:  removes N_A particles from both \{ %DIFDELCMD < \bx%%% x _i\}_{i=1}^P and \{ %DIFDELCMD < \by%%% _i\}_{i=1}^M simultaneously, yielding another empirical signed measure \nu such that \int f %DIFDELCMD < \D %%% \nu approximates to \int f %DIFDELCMD < \D %%% \mu within an acceptable accuracy for suitable test functions f. 62G09 Such annihilation of particles carrying opposite importance weights has been extensively utilized for alleviating the numerical sign problem in particle simulations.
Edit intent: clarity
Original:  removes N_A particles from both \{ %DIFDELCMD < \bx%%%  _i\}_{i=1}^P and \{ %DIFDELCMD < \by%%%  _i\}_{i=1}^M simultaneously, yielding another empirical signed measure \nu such that \int f %DIFDELCMD < \D %%%  \nu approximates to \int f %DIFDELCMD < \D %%%  \mu within an acceptable accuracy for suitable test functions f. 62G09 Such annihilation of particles carrying opposite importance weights has been extensively utilized for alleviating the numerical sign problem in particle simulations.
Revised:  removes N_A particles from both \{ %DIFDELCMD < \bx%%% _i\}_{i=1}^P and \{ %DIFDELCMD < \by%%% y _i\}_{i=1}^M simultaneously, yielding another empirical signed measure \nu such that \int f %DIFDELCMD < \D %%% \nu approximates to \int f %DIFDELCMD < \D %%% \mu within an acceptable accuracy for suitable test functions f. 62G09 Such annihilation of particles carrying opposite importance weights has been extensively utilized for alleviating the numerical sign problem in particle simulations.
Edit intent: clarity