wanyu/IteraTeR_v2 huggingface dataset:
Original:  Surprisingly, when mapped as networks, the architectural patterns emergent across these different phenomena show consistent features.
Revised:  When mapped as networks, the architectural patterns emergent across these different phenomena show consistent features.
Edit intent: coherence
Original:  Surprisingly, when mapped as networks, the architectural patterns emergent across these different phenomena show consistent features.
Revised:  Surprisingly, when mapped as networks, connectivity patterns across such different phenomena show consistent features.
Edit intent: clarity
Original:  A theory providing a simple set of mechanisms to explain this topological universality has seemed plausible yet tantalisingly out of reach .
Revised:  A theory providing a simple set of mechanisms to explain this remains elusive .
Edit intent: clarity
Original:  The proposed fundamental formulation establishes new foundations from which to understand, analyse, deconstruct and interpret network phenomena.
Revised:  The proposed theory establishes new foundations from which to understand, analyse, deconstruct and interpret network phenomena.
Edit intent: clarity
Original:  Here, we pose a new theory which considerably outperforms current mechanistic theories of complex network emergence in network modelling accuracy.
Revised:  We pose a new theory which considerably outperforms current mechanistic theories of complex network emergence in network modelling accuracy.
Edit intent: coherence
Original: Our world is abundant with interdependent interactions occurring at all levels-- be it in the global ecology, human social institutions, within the human brain, or in micro-scale protein interactions.
Revised: Networks of disparate phenomena-- be it the global ecology, human social institutions, within the human brain, or in micro-scale protein interactions.
Edit intent: clarity
Original:  Here, link probability is defined by a log-normal node fitness (surface) factor and a latent Euclidean space-embedded node similarity (depth) factor.
Revised:  Here, link probability is modelled by a log-normal node fitness (surface) factor and a latent Euclidean space-embedded node similarity (depth) factor.
Edit intent: clarity
Original:  Topological modelling based on this theory strongly outperforms power-law fitness and hyperbolic geometry explanations across 110 networks.
Revised:  Modelling based on this theory strongly outperforms power-law fitness and hyperbolic geometry explanations across 110 networks.
Edit intent: clarity
Original:  Importantly, due to the intrinsic scaling properties of log-normal distributions in their right-tails, the degree distributions of the model resemble power-laws at small densities and log-normal distributions at larger densities .
Revised:  Importantly, the degree distributions of the model resemble power-laws at small densities and log-normal distributions at larger densities .
Edit intent: coherence
Original:  The proposed theory establishes new foundations from which to understand, analyse, deconstruct and interpret network phenomena.
Revised:  This establishes new foundations from which to understand, analyse, deconstruct and interpret network phenomena.
Edit intent: clarity
Original: Accurate segmentation of brain tissue in magnetic resonance images (MRI) is a difficult task due to different types of brain abnormalities .
Revised: Accurate super-resolution medical image is vital for doctor's diagnosis and quantitative analysis .
Edit intent: clarity
Original: Accurate super-resolution medical image is vital for doctor's diagnosis and quantitative analysis .
Revised: During the growing popularity of electronic medical records, electronic medical record (EMR) data has exploded increasingly. It is very meaningful to retrieve high quality EMR in mass data .
Edit intent: coherence
Original:  We present an antagonistic crowd simulation model, ACSEE, which is integrated with  emotional contagion and evolutionary game theories.
Revised:  We present an antagonistic crowd simulation model, ACSEE, which is integrated with antagonistic emotional contagion and evolutionary game theories.
Edit intent: fluency
Original:  Our evolutionary game  approach incorporates antagonistic emotional contagion through deterrent force which modelled by a mixture of emotional and physical forces defeating the opponents.
Revised:  Our evolutionary game theoretic approach incorporates antagonistic emotional contagion through deterrent force which modelled by a mixture of emotional and physical forces defeating the opponents.
Edit intent: clarity
Original:  Our evolutionary game  approach incorporates antagonistic emotional contagion through deterrent force which modelled by a mixture of emotional and physical forces defeating the opponents.
Revised:  Our evolutionary game approach incorporates antagonistic emotional contagion through deterrent force , which is modelled by a mixture of emotional and physical forces defeating the opponents.
Edit intent: fluency
Original:  We also compare the simulated crowd behaviors with real-world crowd videos and use our approach to predict the incidents of crowd violence .
Revised:  We also compare the simulated crowd behaviors with real-world crowd videos and use our approach to predict the trends of crowd movements in violence incidents .
Edit intent: clarity
Original:  Antagonistic emotions between different opposing groups and the way they spread through contagion in a crowd are important causes of such behaviors.
Revised:  Antagonistic emotions between different opposing groups and the way they spread through contagion in a crowd are important causes of crowd antagonistic behaviors.
Edit intent: clarity
Original:  Moreover, games between different opposing groups determine the level of crowd violence.
Revised:  Moreover, games , which refers to the interaction between opposing groups adopting different strategies to obtain higher benefits and less casualties, determine the level of crowd violence.
Edit intent: coherence
Original:  Our evolutionary game theoretic approach incorporates antagonistic emotional contagion through deterrent force, which is modelled by a mixture of emotional  and physical forces defeating the opponents.
Revised:  Our evolutionary game theoretic approach incorporates antagonistic emotional contagion through deterrent force, which is modelled by a mixture of emotional forces and physical forces defeating the opponents.
Edit intent: fluency
Original:  Using the sparse synthesis prior, we minimize the \ell^1-Tikhonov functional  which is the sum of a data fitting term and the \ell^1-norm of the synthesis coefficients  .
Revised:  Using the sparse synthesis prior, we propose minimizing the \ell^1-Tikhonov functional which is the sum of a data fitting term and the \ell^1-norm of the synthesis coefficients .
Edit intent: clarity
Original:  Using the sparse synthesis prior, we minimize the \ell^1-Tikhonov functional  which is the sum of a data fitting term and the \ell^1-norm of the synthesis coefficients  .
Revised:  Using the sparse synthesis prior, we minimize the \ell^1-Tikhonov functional , which is the sum of a data fitting term and the \ell^1-norm of the synthesis coefficients .
Edit intent: fluency
Original:  They are posed in an up to 3+3 dimensional phase space and thus solving this problem is extremely expensive from a computational point of view.
Revised:  As they are posed in an up to 3+3 dimensional phase space and thus solving this problem is extremely expensive from a computational point of view.
Edit intent: fluency
Original:  They are posed in an up to 3+3 dimensional phase space and thus solving this problem is extremely expensive from a computational point of view.
Revised:  They are posed in an up to 3+3 dimensional phase space , solving this problem is extremely expensive from a computational point of view.
Edit intent: coherence
Original:  In this paper  we exploit the low-rank structure shown by the solution of the Vlasov equation.
Revised:  In this paper , we exploit the low-rank structure shown by the solution of the Vlasov equation.
Edit intent: fluency
Original:  In this paper  we exploit the low-rank structure shown by the solution of the Vlasov equation.
Revised:  In this paper we exploit the low-rank structure in the solution of the Vlasov equation.
Edit intent: clarity
Original:  More specifically, we consider the Vlasov-Maxwell system and propose a dynamic low-rank integrator.
Revised:  More specifically, we consider the Vlasov--Maxwell system and propose a dynamic low-rank integrator.
Edit intent: fluency
Original:  The key idea is to constrain the dynamics of the system  to a low-rank manifold by means of a projection on the tangent space.
Revised:  The key idea is to approximate the dynamics of the system to a low-rank manifold by means of a projection on the tangent space.
Edit intent: clarity
Original:  The key idea is to constrain the dynamics of the system  to a low-rank manifold by means of a projection on the tangent space.
Revised:  The key idea is to constrain the dynamics of the system by constraining it to a low-rank manifold by means of a projection on the tangent space.
Edit intent: clarity
Original:  The key idea is to constrain the dynamics of the system  to a low-rank manifold by means of a projection on the tangent space.
Revised:  The key idea is to constrain the dynamics of the system to a low-rank manifold . This is accomplished by a projection onto the tangent space.
Edit intent: clarity
Original:  The dynamics of the system is then represented by the low-rank factors, which are determined by solving lower-dimensional partial differential equations.
Revised:  There, the dynamics is represented by the low-rank factors, which are determined by solving lower-dimensional partial differential equations.
Edit intent: clarity
Original:  The  scheme performs well in numerical experiments and succeeds in capturing the main features of the plasma dynamics.
Revised:  The proposed scheme performs well in numerical experiments and succeeds in capturing the main features of the plasma dynamics.
Edit intent: clarity
Original:  The coupling of the Vlasov equation with the Maxwell system  introduces additional challenges.
Revised:  The coupling of the Vlasov equation with the Maxwell system , however, introduces additional challenges.
Edit intent: coherence
Original:  We propose a correction based on Lagrange multipliers which enforces Gauss' s law up to machine precision.
Revised:  We propose a correction based on Lagrange multipliers which enforces Gauss' law up to machine precision.
Edit intent: fluency
Original: The reachability problem is to determine if there exists a path from one vertex to the other in a graph.
Revised: The reachability problem is to determine if there exists a path from one vertex to another in a graph.
Edit intent: fluency
Original:  In this paper, we further improve the space bound and present a polynomial time algorithm that uses O(n^{1/4 + \epsilon}) space to solve reachability in a grid graph with n vertices .
Revised:  In this paper, we show that reachability in an n vertex grid graph can be decided by an algorithm using O(n^{1/4 + \epsilon}) space to solve reachability in a grid graph with n vertices .
Edit intent: clarity
Original:  There has been an increasing interest in the modeling and analysis of how opinions spread as a function of these relationships.
Revised:  There has been an increasing interest in the modeling and analysis of how opinions evolve as a function of these relationships.
Edit intent: clarity
Original:  In this paper, we propose a new  simple and intuitive model that incorporates the socio-psychological phenomenon of the boomerang effect for driving the opinions of the members of the network.
Revised:  In this paper, we propose a new , simple and intuitive model that incorporates the socio-psychological phenomenon of the boomerang effect for driving the opinions of the members of the network.
Edit intent: fluency
Original:  We prove the important result that, under certain conditions on the sign structures of the network for which structural balance is a particular case , the opinions in the network polarize.
Revised:  We prove the important result that, under certain conditions on the structure of the signed network that corresponds to the so-called structural balance property , the opinions in the network polarize.
Edit intent: clarity
Original:  Compared to other models in the literature, our model displays a richer and perhaps more intuitive behavior of the opinions whenever the social network is not structurally balanced .
Revised:  Compared to other models in the literature, our model displays a richer and perhaps more intuitive behavior of the opinions when the social network is not structurally balanced .
Edit intent: coherence
Original:  Compared to other models in the literature, our model displays a richer and perhaps more intuitive behavior of the opinions whenever the social network is not structurally balanced .
Revised:  Compared to other models in the literature, our model displays a richer and perhaps more intuitive behavior of the opinions whenever the social network does not satisfy structural balance .
Edit intent: clarity
Original:  In particular, we present some results whenever the network displays more than two factions (also known as clustering balance) and more arbitrary sign structures as a result of perturbation of initially balanced networks .
Revised:  In particular, we analyze signed networks in which the opinions show persistent fluctuations (including the case of the so-called clustering balance) and more arbitrary sign structures as a result of perturbation of initially balanced networks .
Edit intent: clarity
Original:  In particular, we present some results whenever the network displays more than two factions (also known as clustering balance) and more arbitrary sign structures as a result of perturbation of initially balanced networks .
Revised:  In particular, we present some results whenever the network displays more than two factions (also known as clustering balance) .
Edit intent: coherence
Original:  Here, we evaluate the applicability of MAP-Elites to "illuminate" constrained search spaces by mapping them into features spaces where each feature corresponds to a different constraint.
Revised:  Here, we evaluate the applicability of MAP-Elites to `illuminate' constrained search spaces by mapping them into features spaces where each feature corresponds to a different constraint.
Edit intent: fluency
Original:  Nevertheless, it has a higher potential at finding constraint violations vs. objective trade-offs solutions and providing new problem information.
Revised:  Nevertheless, it has a higher potential at finding constraint violations vs. objective trade-offs and providing new problem information.
Edit intent: clarity
Original:  As such, it could be used in the future as an effective building-block for designing new constraint optimization algorithms.
Revised:  As such, it could be used in the future as an effective building-block for designing new constrained optimization algorithms.
Edit intent: fluency
Original:  Here, we evaluate the applicability of MAP-Elites to `illuminate' constrained search spaces by mapping them into features spaces where each feature corresponds to a different constraint.
Revised:  Here, we evaluate the applicability of MAP-Elites to "illuminate" constrained search spaces by mapping them into features spaces where each feature corresponds to a different constraint.
Edit intent: fluency
Original:  Here, we evaluate the applicability of MAP-Elites to `illuminate' constrained search spaces by mapping them into features spaces where each feature corresponds to a different constraint.
Revised:  Here, we evaluate the applicability of MAP-Elites to `illuminate' constrained search spaces by mapping them into feature spaces where each feature corresponds to a different constraint.
Edit intent: fluency
Original:  On the other  , it provides an effective visualization that facilitates a better understanding of how constraint violations correlate with the objective function.
Revised:  On the other hand , it provides an effective visualization that facilitates a better understanding of how constraint violations correlate with the objective function.
Edit intent: fluency
Original:  As expected, numerical results show that a basic version of MAP-Elites cannot compete on all problems (especially those with equality constraints) with state-of-the-art algorithms which use gradient or advanced constraint handling techniques.
Revised:  As expected, numerical results show that a basic version of MAP-Elites cannot compete on all problems (especially those with equality constraints) with state-of-the-art algorithms that use gradient information or advanced constraint handling techniques.
Edit intent: clarity
Original:  Nevertheless, it has a higher potential at finding constraint violations vs. objective trade-offs and providing new problem information.
Revised:  Nevertheless, it has a higher potential at finding constraint violations vs. objectives trade-offs and providing new problem information.
Edit intent: fluency
Original:  Here, we argue that the presence of centrality anomalies in complex networks provides a diagnosis of model over-simplification.
Revised:  Here, we argue that the presence of centrality anomalies in complex networks is a result of model over-simplification.
Edit intent: clarity
Original:  Using four large datasets , we show that the unweighted projection of the structure of the inter-city bus transportation network and the worldwide air transportation network exhibit a significant fraction of anomalous nodes compared to a random null model.
Revised:  Using four large datasets , we show that the unweighted projection of the structure of these networks can exhibit a significant fraction of anomalous nodes compared to a random null model.
Edit intent: clarity
Original:  However, the weighted projection of these networks, compared with an appropriated null model, no longer show these anomalies , suggesting that centrality anomalies are a symptom of model over-simplification.
Revised:  However, the weighted projection of these networks, compared with an appropriated null model, significantly reduces the fraction of anomalies observed , suggesting that centrality anomalies are a symptom of model over-simplification.
Edit intent: clarity
Original:  Our study provides analytically tractable examples of localization transitions in path-dependent, reinforced stochastic processes, which can also be useful to understanding spatial learning by living organisms.
Revised:  Our study provides analytically tractable examples of localization transitions in path-dependent, reinforced stochastic processes, which can be also useful for understanding spatial learning by living organisms.
Edit intent: clarity
Original: We study the K-item knapsack problem (\ie, 1.5-dimensional knapsack problem ), which is a generalization of the famous 0-1 knapsack problem (\ie, 1-dimensional knapsack problem ) in which an upper bound K is imposed on the number of items selected.
Revised: We study the K-item knapsack problem (\ie, 1.5-dimensional knapsack problem ), which is a generalization of the famous 0-1 knapsack problem (\ie, 1-dimensional KP ) in which an upper bound K is imposed on the number of items selected.
Edit intent: clarity
Original:  The current best results are due to \mbox{ mastrolilli2006hybrid , in which two schemes are presented exhibiting a space-time tradeoff--one scheme with time complexity O(n+Kz^{2}/\varepsilon^{2}) and space complexity O(n+z^{3}/\varepsilon), while another scheme requires a run-time of O(n+(Kz^{2}+z^{4})/\varepsilon^{2})  but only needs O(n+z^{2}/\varepsilon) space, where z=\min\{K,1/\varepsilon\}.
Revised:  The current best results are due to \mbox{ mastrolilli2006hybrid , in which two schemes are presented exhibiting a space-time tradeoff--one scheme with time complexity O(n+Kz^{2}/\varepsilon^{2}) and space complexity O(n+z^{3}/\varepsilon), while another scheme requires a run-time of O(n+(Kz^{2}+z^{4})/\varepsilon^{2}) but only needs O(n+z^{2}/\varepsilon) space, where z=\min\{K,1/\varepsilon\}.
Edit intent: fluency
Original:  The current best results are due to \mbox{ mastrolilli2006hybrid , in which two schemes are presented exhibiting a space-time tradeoff--one scheme with time complexity O(n+Kz^{2}/\varepsilon^{2}) and space complexity O(n+z^{3}/\varepsilon), while another scheme requires a run-time of O(n+(Kz^{2}+z^{4})/\varepsilon^{2})  but only needs O(n+z^{2}/\varepsilon) space, where z=\min\{K,1/\varepsilon\}.
Revised:  The current best results are due to \mbox{ mastrolilli2006hybrid , in which two schemes are presented exhibiting a space-time tradeoff--one scheme with time complexity O(n+Kz^{2}/\varepsilon^{2}) and space complexity O(n+z^{3}/\varepsilon), while another scheme requires O(n+(Kz^{2}+z^{4})/\varepsilon^{2}) but only needs O(n+z^{2}/\varepsilon) space, where z=\min\{K,1/\varepsilon\}.
Edit intent: clarity
Original:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n)  + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Revised:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n) + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Edit intent: fluency
Original:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n)  + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Revised:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a run-time of + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Edit intent: fluency
Original:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n)  + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Revised:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n) + \cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Edit intent: coherence
Original:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n)  + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Revised:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n) + (z^{2\cdot \max\{K,\varepsilon} z^{2/\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Edit intent: fluency
Original:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n)  + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } \} ), while simultaneously reaching the O(n+z^{2/\varepsilon) space complexity .
Revised:  In this paper we close the space-time tradeoff exhibited in \mbox{ mastrolilli2006hybrid by designing a new FPTAS with a running time of O(n) + (z^{2\cdot \max\{K,\varepsilon} /\varepsilon} ^{ -2 } /\varepsilon) space complexity .
Edit intent: coherence