wanyu/IteraTeR_v2 huggingface dataset:
Original:  Just like discrete invariants are used to reason about correctness in discrete systems without unrolling their loopsforever , continuous invariants are used to reason about differential equations without having to solve them.
Revised:  Just like discrete invariants are used to reason about correctness in discrete systems without having to unroll their loops , continuous invariants are used to reason about differential equations without having to solve them.
Edit intent: clarity
Original:  Methodologically, we propose a temporal mixture ensemble model , capable of adaptively exploiting, for the forecasting, different sources of data and providing a volume point estimate, as well as its uncertainty.
Revised:  Methodologically, we propose a temporal mixture ensemble , capable of adaptively exploiting, for the forecasting, different sources of data and providing a volume point estimate, as well as its uncertainty.
Edit intent: clarity
Original: This paper analyzes the structure of the set of positive solutions of a class of one-dimensional symmetric superlinear indefinite bvp's.
Revised: This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp's.
Edit intent: clarity
Original: \infty in the region where a(x)<0   , and solve positively the conjecture of R. G\'{omez-Re\~{n}asco and J. L\'{o}pez-G\'{o}mez in two special cases of interest, where we show the existence of 2^{n+1}-1 positive solutions for sufficiently negative \lambda}  [  . On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.
Revised: \infty in the region where a(x)<0 0 , and solve positively the conjecture of R. G\'{omez-Re\~{n}asco and J. L\'{o}pez-G\'{o}mez in two special cases of interest, where we show the existence of 2^{n+1}-1 positive solutions for sufficiently negative \lambda} [ . On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.
Edit intent: fluency
Original: \infty in the region where a(x)<0   , and solve positively the conjecture of R. G\'{omez-Re\~{n}asco and J. L\'{o}pez-G\'{o}mez in two special cases of interest, where we show the existence of 2^{n+1}-1 positive solutions for sufficiently negative \lambda}  [  . On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.
Revised: \infty in the region where a(x)<0 , mez-Re\~{n}asco and J. L\'{o}pez-G\'{o}mez in two special cases of interest, where we show the existence of 2^{n+1}-1 positive solutions for sufficiently negative \lambda} [ . On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.
Edit intent: coherence
Original:  While temporal and local properties of social networks have been extensively studied, the origin of their global fluctuations is not yet well understood.
Revised:  While temporal and local properties of social networks have been extensively studied, the origin of their dynamical nature is not yet well understood.
Edit intent: clarity
Original:  A network may grow or shrink if a) the total population of nodes , including resting ones, changes and/or b) the chance of two nodes being connected varies over time.
Revised:  Networks may grow or shrink if a) the total population of nodes , including resting ones, changes and/or b) the chance of two nodes being connected varies over time.
Edit intent: clarity
Original:  A network may grow or shrink if a) the total population of nodes , including resting ones, changes and/or b) the chance of two nodes being connected varies over time.
Revised:  A network may grow or shrink if a) the total population of nodes changes and/or b) the chance of two nodes being connected varies over time.
Edit intent: clarity
Original:  Here, we develop a method that classifies the source of global fluctuations of temporal networks according to these two mechanisms.
Revised:  Here, we develop a method that allows us to classify the source of global fluctuations of temporal networks according to these two mechanisms.
Edit intent: clarity
Original:  Here, we develop a method that classifies the source of global fluctuations of temporal networks according to these two mechanisms.
Revised:  Here, we develop a method that classifies the source of time-varying nature of temporal networks according to these two mechanisms.
Edit intent: clarity
Original: We present Choral, the first framework for programming choreographies (multiparty protocols) that builds on top of mainstream programming abstractions: in Choral, choreographies are objects.
Revised: We present Choral, the first language for programming choreographies (multiparty protocols) that builds on top of mainstream programming abstractions: in Choral, choreographies are objects.
Edit intent: clarity
Original:  Then  we introduce the construction of a colimit induced by a map of 2-monads, show that we obtain the structure of a 2-monad and give a characterisation of its algebras.
Revised:  Then , we introduce the construction of a colimit induced by a map of 2-monads, show that we obtain the structure of a 2-monad and give a characterisation of its algebras.
Edit intent: fluency
Original:  Finally, we apply the construction to the map of 2-monads between free symmetric monoidal and the free cartesian 2-monads and combine them into a Linear Non-Linear 2-monad.
Revised:  Finally, we apply the construction to the map of 2-monads between free symmetric monoidal and the free cartesian 2-monads and combine them into a linear-non-linear 2-monad.
Edit intent: clarity
Original:  The social structures of these systems have in recent years been studied in many species by means of network analysis.
Revised:  The social structures of these systems can be studied in depth by means of network analysis.
Edit intent: clarity
Original:  Animal social networks is now a well-established research area that has provided important insights into animal behaviour, ecology, and social evolution.
Revised:  A large number of studies on animal social networks in many species have in recent years been carried out within the biological research field of animal behaviour and have provided new insights into behaviour, ecology, and social evolution.
Edit intent: clarity
Original:  Animal social network research , however, seems to not be well known by scientists outside of the animal behaviour field .
Revised:  This line of research is currently not well connected to the field of complex systems .
Edit intent: clarity
Original:  Here we provide an introduction to animal social networks for complex systems researchers .
Revised:  Here we provide an introduction to animal social networks for complex systems scientists .
Edit intent: clarity
Original:  We believe that a better integration of animal social networks with the interdisciplinary field of complex systems would be mutually beneficial for various reasons.
Revised:  We believe that an increased integration of animal social networks with the interdisciplinary field of complex systems would be mutually beneficial for various reasons.
Edit intent: clarity
Original:  We believe that a better integration of animal social networks with the interdisciplinary field of complex systems would be mutually beneficial for various reasons.
Revised:  We believe that a better integration of animal social networks with the interdisciplinary field of complex systems networks would be beneficial for various reasons.
Edit intent: clarity
Original:  Furthermore, high-resolution datasets of social networks from different animal species can potentially be very useful for investigating general hypotheses about complex systems.
Revised:  Furthermore, high-resolution datasets of social networks from different animal species can be useful for investigating general hypotheses about complex systems.
Edit intent: clarity
Original:  and finally we highlight challenges in the study of animal social networks where interaction between animal social network research and general complex systems research could be particularly valuable.
Revised:  and finally we highlight challenges in the study of animal social networks where input from researchers with expertise in complex systems could be particularly valuable.
Edit intent: clarity
Original:  We hope that this will help to facilitate future interdisciplinary collaborations involving animal social networks, and lead to better integration of these networks into the field of complex systems.
Revised:  We hope that this will help to facilitate further interdisciplinary collaborations involving animal social networks, and lead to better integration of these networks into the field of complex systems.
Edit intent: fluency
Original:  A large number of studies on animal social networks in many species have in recent years been carried out within the biological research field of animal behaviour and have provided new insights into behaviour, ecology, and social evolution.
Revised:  A large number of studies on animal social networks in many species have in recent years been carried out in the biological research field of animal behaviour and have provided new insights into behaviour, ecology, and social evolution.
Edit intent: clarity
Original:  This line of research is currently not  well connected to the field of complex systems .
Revised:  This line of research is currently not so well connected to the field of complex systems .
Edit intent: coherence
Original:  We believe that an increased integration of animal social networks with the interdisciplinary field of complex systems  networks would be beneficial for various reasons.
Revised:  We believe that an increased integration of animal social networks with the interdisciplinary field of complex systems and networks would be beneficial for various reasons.
Edit intent: clarity
Original:  Increased collaboration between researchers in this field and biologists studying animal social systems could be valuable in solving challenges of particular importance to animal social network research.
Revised:  Increased collaboration between researchers in this field and biologists studying animal social systems could be valuable in solving challenges that are of importance to animal social network research.
Edit intent: clarity
Original:  Furthermore, high-resolution datasets of social networks from different animal species can be useful for investigating general hypotheses about complex systems  .
Revised:  Furthermore, animal social networks provide the opportunity to investigate hypotheses about complex systems .
Edit intent: clarity
Original:  and finally we highlight challenges in the study of animal social networks where input from researchers with expertise in complex systems could be particularly valuable  .
Revised:  we highlight challenges in the study of animal social networks where input from researchers with expertise in complex systems could be particularly valuable .
Edit intent: coherence
Original:  and finally we highlight challenges in the study of animal social networks where input from researchers with expertise in complex systems could be particularly valuable  .
Revised:  and finally we highlight challenges in the study of animal social networks where complex systems expertise may be particularly valuable .
Edit intent: clarity
Original:  We hope that this will help to facilitate further interdisciplinary collaborations involving animal social networks, and lead to better integration of these networks into the field of complex systems.
Revised:  We hope that this will help to facilitate further interdisciplinary collaborations involving animal social networks, and further integration of these networks into the field of complex systems.
Edit intent: clarity
Original: Drastic difference in the COVID-19  infection and fatality counts , observed between Hubei (Wuhan) and other Mainland China provinces raised public controversies.
Revised: Drastic difference in the COVID-19 infection and fatality counts ( observed between Hubei (Wuhan) and other Mainland China provinces raised public controversies.
Edit intent: fluency
Original:  Case Fatality Rate is five times larger in Hubei, but our estimated Infection Fatality Rates  are much more uniform/consistent across all provinces.
Revised:  Case Fatality Rate is significantly larger for Hubei, we find that Infection Fatality Rates are much more uniform/consistent across all provinces.
Edit intent: clarity
Original:  However, COVID-19 has brought unprecedented social distancing measures, with a challenge on how to include these in a manner that can explain the data , but avoid overfitting in parameter inference.
Revised:  However, COVID-19 has brought unprecedented social distancing measures, with a challenge on how to include these in a manner that can explain the data but avoid overfitting in parameter inference.
Edit intent: fluency
Original:  We here develop a simple non-homologous model, where social distancing effects are introduced analogous to course grained models of gene expression control in systems biology.
Revised:  We here develop a simple non-homologous model, where social distancing effects are introduced analogous to coarse-grained models of gene expression control in systems biology.
Edit intent: fluency
Original:  3) Use of personal protective equipment (PPE) to reduce viral shedding and resultant infectivity .
Revised:  3) Viral shedding rate .
Edit intent: clarity
Original:  These results suggest that higher compliance with PPE usage and personal hygiene has the potential to decrease the number of infections and shorten epidemic duration.
Edit intent: coherence
Original:  Among our results, we show the condition number of non--symmetric random Toeplitz matrix of dimension n under the existence of moment generating function of the random entries is \kappa\left( \mathcal{T _n\right) = O\left( 1{\varepsilon} n^{\rho+1/2} \left(\log n\right)^{1/2} \right) with probability 1-O\left((\varepsilon^2 + \varepsilon) n^{-2\rho} + n^{-1/2+o(1)}\right) for any \varepsilon >0, \rho\in(0,1/4).
Revised:  Among our results, we show the condition number of non--symmetric random circulant matrix of dimension n under the existence of moment generating function of the random entries is \kappa\left( \mathcal{T _n\right) = O\left( 1{\varepsilon} n^{\rho+1/2} \left(\log n\right)^{1/2} \right) with probability 1-O\left((\varepsilon^2 + \varepsilon) n^{-2\rho} + n^{-1/2+o(1)}\right) for any \varepsilon >0, \rho\in(0,1/4).
Edit intent: clarity
Original:  Also, Cauchy Interlacing Theorem permits to analyze the condition number of a symmetric random Toeplitz matrix.
Revised:  For the condition number of a symmetric random Toeplitz matrix.
Edit intent: coherence
Original:  In this case, the condition number \kappa\left(\mathcal{T} ^{sym _n\right) = \mbox{O \left( \frac{1{\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left(  \right) ^{1/2}%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( \varepsilon n^{-1/10 + n^{-77/300+\scriptstyle{o}(1)}}  \right) , when the random entries have moment generating function.
Revised:  In this case, the condition number \kappa\left(\mathcal{T} _n\right) = \mbox{O \left( \frac{1{\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left( \right) ^{1/2}%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( \varepsilon n^{-1/10 + n^{-77/300+\scriptstyle{o}(1)}} \right) , when the random entries have moment generating function.
Edit intent: fluency
Original:  In this case, the condition number \kappa\left(\mathcal{T} ^{sym _n\right) = \mbox{O \left( \frac{1{\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left(  \right) ^{1/2}%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( \varepsilon n^{-1/10 + n^{-77/300+\scriptstyle{o}(1)}}  \right) , when the random entries have moment generating function.
Revised:  In this case, the condition number \kappa\left(\mathcal{T} ^{sym _n\right) \leq \kappa \left( \frac{1{\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left( \right) ^{1/2}%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( \varepsilon n^{-1/10 + n^{-77/300+\scriptstyle{o}(1)}} \right) , when the random entries have moment generating function.
Edit intent: clarity
Original:  In this case, the condition number \kappa\left(\mathcal{T} ^{sym _n\right) = \mbox{O \left( \frac{1{\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left(  \right) ^{1/2}%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( \varepsilon n^{-1/10 + n^{-77/300+\scriptstyle{o}(1)}}  \right) , when the random entries have moment generating function.
Revised:  In this case, the condition number \kappa\left(\mathcal{T} ^{sym _n\right) = \mbox{O \left( {\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left( \right) ^{1/2}%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( \varepsilon n^{-1/10 + n^{-77/300+\scriptstyle{o}(1)}} \right) , when the random entries have moment generating function.
Edit intent: fluency
Original:  In this case, the condition number \kappa\left(\mathcal{T} ^{sym _n\right) = \mbox{O \left( \frac{1{\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left(  \right) ^{1/2}%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( \varepsilon n^{-1/10 + n^{-77/300+\scriptstyle{o}(1)}}  \right) , when the random entries have moment generating function.
Revised:  In this case, the condition number \kappa\left(\mathcal{T} ^{sym _n\right) = \mbox{O \left( \frac{1{\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left( \right) }%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( \varepsilon n^{-1/10 + n^{-77/300+\scriptstyle{o}(1)}} \right) , when the random entries have moment generating function.
Edit intent: coherence
Original:  In this case, the condition number \kappa\left(\mathcal{T} ^{sym _n\right) = \mbox{O \left( \frac{1{\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left(  \right) ^{1/2}%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( \varepsilon n^{-1/10 + n^{-77/300+\scriptstyle{o}(1)}}  \right) , when the random entries have moment generating function.
Revised:  In this case, the condition number \kappa\left(\mathcal{T} ^{sym _n\right) = \mbox{O \left( \frac{1{\varepsilon} n^{1.01} } _{2n}}\right) \left( \log n}\left( \right) ^{1/2}%DIFDELCMD < \right) %%% with probability 1- \mbox{O \left( + n^{-77/300+\scriptstyle{o}(1)}} \right) , when the random entries have moment generating function.
Edit intent: clarity
Original:  We use  label propagation technique focused on hashtag cooccurences to find polarizing tweets and users.
Revised:  We use a label propagation technique focused on hashtag cooccurences to find polarizing tweets and users.
Edit intent: fluency
Original:  We use  label propagation technique focused on hashtag cooccurences to find polarizing tweets and users.
Revised:  We use label propagation technique focused on hashtag co-occurrences to find polarizing tweets and users.
Edit intent: fluency
Original:  for  performing denoising, dereverberation, and source separation (DN+DR+SS) at the same time . Conventionally, cascade configuration composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response (MVDR) beamformer has been used as the state-of-the-art frontend of far-field speech recognition, however, overall optimality of this approach is not guaranteed.
Revised:  for jointly performing denoising, dereverberation, and source separation (DN+DR+SS) at the same time . Conventionally, cascade configuration composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response (MVDR) beamformer has been used as the state-of-the-art frontend of far-field speech recognition, however, overall optimality of this approach is not guaranteed.
Edit intent: clarity
Original:  for  performing denoising, dereverberation, and source separation (DN+DR+SS) at the same time . Conventionally, cascade configuration composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response (MVDR) beamformer has been used as the state-of-the-art frontend of far-field speech recognition, however, overall optimality of this approach is not guaranteed.
Revised:  for performing denoising, dereverberation, and source separation (DN+DR+SS) in a computationally efficient way . Conventionally, cascade configuration composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response (MVDR) beamformer has been used as the state-of-the-art frontend of far-field speech recognition, however, overall optimality of this approach is not guaranteed.
Edit intent: clarity
Original:  for  performing denoising, dereverberation, and source separation (DN+DR+SS) at the same time . Conventionally, cascade configuration composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response (MVDR) beamformer has been used as the state-of-the-art frontend of far-field speech recognition, however, overall optimality of this approach is not guaranteed.
Revised:  for performing denoising, dereverberation, and source separation (DN+DR+SS) at the same time . Conventionally, cascade configuration composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response beamformer has been used as the state-of-the-art frontend of far-field speech recognition, however, overall optimality of this approach is not guaranteed.
Edit intent: clarity
Original:  for  performing denoising, dereverberation, and source separation (DN+DR+SS) at the same time . Conventionally, cascade configuration composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response (MVDR) beamformer has been used as the state-of-the-art frontend of far-field speech recognition, however, overall optimality of this approach is not guaranteed.
Revised:  for performing denoising, dereverberation, and source separation (DN+DR+SS) at the same time . Conventionally, cascade configuration composed of a Weighted Prediction Error minimization (WPE) dereverberation filter followed by a Minimum Variance Distortionless Response (MVDR) beamformer has been usedas the state-of-the-art frontend of far-field speech recognition, however, overall optimality of this approach is not guaranteed.
Edit intent: fluency
Original: In this paper, we propose a modeling approach on these apparently various phenomena through the example of the dynamics of social unrest.
Revised: In this paper, we propose a modeling approach for these apparently diverse phenomena through the example of the dynamics of social unrest.
Edit intent: clarity
Original:  Here we place the emphasis on two subclasses of systems defined in 17 : tension inhibiting and tension enhancing.
Revised:  We particularly emphasize here two subclasses of systems defined in 17 : tension inhibiting and tension enhancing.
Edit intent: clarity
Original:  Here we place the emphasis on two subclasses of systems defined in 17 : tension inhibiting and tension enhancing.
Revised:  Here we place the emphasis on two subclasses of systems 17 : tension inhibiting and tension enhancing.
Edit intent: clarity
Original:  Here we place the emphasis on two subclasses of systems defined in 17 : tension inhibiting and tension enhancing.
Revised:  Here we place the emphasis on two subclasses of systems defined in : tension inhibiting and tension enhancing.
Edit intent: fluency