wanyu/IteraTeR_v2 huggingface dataset:
Original:  \] For various ranges of parameters (e.g., when m=\Theta(n) and q = o(n^{7/9})), this bound is smaller than the best known two-dimensional lower bound \Omega^*\Omega* (m^{2/3}n^{2/3}+m+n) .
Revised:  \] For various ranges of parameters (e.g., when m=\Theta(n) and q = o(n^{7/9})), this bound is smaller than the lower bound\Omega* (m^{2/3}n^{2/3}+m+n) .
Edit intent: clarity
Original:  Our result is obtained by applying the polynomial partitioning technique of Guth and Katz using a constant-degree partitioning polynomial , as was also recently used by Solymosi and Tao  .
Revised:  Our result is obtained by applying the polynomial partitioning technique of Guth and Katz using a constant-degree partitioning polynomial ( as was also recently used by Solymosi and Tao .
Edit intent: fluency
Original:  Our result is obtained by applying the polynomial partitioning technique of Guth and Katz using a constant-degree partitioning polynomial , as was also recently used by Solymosi and Tao  .
Revised:  Our result is obtained by applying the polynomial partitioning technique of Guth and Katz using a constant-degree partitioning polynomial , as was also recently used by Solymosi and Tao ) .
Edit intent: fluency
Original:  The previous best known bound, originally established for the planar case and later extended to any dimension \ge 2, is O*(m^{2/3}n^{2/3} + m^{6/11}n^{9/11}+m+n) ( where the O*(\cdot) notation hides sub-polynomial factors ) . Since all the points and circles may lie on a common plane (or sphere), it is impossible to improve the bound in R^3 without first improving it in the plane.
Revised:  The previous best known bound, originally established for the planar case and later extended to any dimension \ge 2, is O*(m^{2/3}n^{2/3} + m^{6/11}n^{9/11}+m+n) , where the O*(\cdot) notation hides sub-polynomial factors ) . Since all the points and circles may lie on a common plane (or sphere), it is impossible to improve the bound in R^3 without first improving it in the plane.
Edit intent: fluency
Original:  The previous best known bound, originally established for the planar case and later extended to any dimension \ge 2, is O*(m^{2/3}n^{2/3} + m^{6/11}n^{9/11}+m+n) ( where the O*(\cdot) notation hides sub-polynomial factors ) . Since all the points and circles may lie on a common plane (or sphere), it is impossible to improve the bound in R^3 without first improving it in the plane.
Revised:  The previous best known bound, originally established for the planar case and later extended to any dimension \ge 2, is O*(m^{2/3}n^{2/3} + m^{6/11}n^{9/11}+m+n) ( where the O*(\cdot) notation hides sub-polynomial factors . Since all the points and circles may lie on a common plane (or sphere), it is impossible to improve the bound in R^3 without first improving it in the plane.
Edit intent: fluency
Original:  We further prove that the median score attains the lower bound exactly on the triples of genomes that can be obtained from a single genome with optimal rearrangements.
Revised:  We further prove that the median score attains the lower bound exactly on the triples of genomes that can be obtained from a single genome with strong rearrangements.
Edit intent: clarity
Original: A polygon representing transportation network is given, together with a point p in its interior .
Revised: Given a polygon representing a transportation network together with a point p in its interior .
Edit intent: clarity
Original:  Geometric dilation of some point q on the boundary is the ratio between the length of the shortest path from p to q through the extended network  and their Euclidean distance.
Revised:  Geometric dilation of some point q on the boundary is the ratio between the length of the shortest path from p to q through the extended network , and their Euclidean distance.
Edit intent: fluency
Original:  We give a linear time algorithm for computing the feed-link with the minimum overall dilation, thus improving upon the previously known algorithm of complexity close to O(n log n).
Revised:  We give a linear time algorithm for computing the feed-link with the minimum overall dilation, thus improving upon the previously known algorithm of complexity that is roughly O(n log n).
Edit intent: clarity
Original: It has been suggested that a Random Tree Puzzle (RTP) process leads to a Yule--Harding (YH) distribution, when the number of taxa becomes large.
Revised: It has been suggested that a Random Tree Puzzle (RTP) process leads to a Yule-Harding (YH) distribution, when the number of taxa becomes large.
Edit intent: fluency
Original:  Specifically, rather than taking coefficients from an arbitrary semiring S we instead take them from S ^\mathbb{N . Doing this is useful because it gives us information about how the weight of an infinite word does or does not diverge, and if it does diverge what form the divergence takes --- e.g., polynomial, exponential, etc.
Revised:  Specifically, rather than taking coefficients from an arbitrary semiring S we instead take them from S ^N . Doing this is useful because it gives us information about how the weight of an infinite word does or does not diverge, and if it does diverge what form the divergence takes --- e.g., polynomial, exponential, etc.
Edit intent: coherence
Original:  In this paper we introduce a new kind of automaton which we call a diverging automaton that maps infinite words to sequences of weights from a semiring and which employs a B\"uchi-like boundary condition.
Revised:  In this paper we introduce a new kind of automaton which we call a diverging automaton that maps infinite words to sequences of weights from a semiring and which employs a Buchi-like boundary condition.
Edit intent: fluency
Original: We study kinetic model of reversible enzyme reaction and compare two techniques for analytic approximate solutions of the model.
Revised: We study kinetic models of reversible enzyme reaction and compare two techniques for analytic approximate solutions of the model.
Edit intent: fluency
Original: We study kinetic model of reversible enzyme reaction and compare two techniques for analytic approximate solutions of the model.
Revised: We study kinetic model of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model.
Edit intent: fluency
Original:  Analytic approximate solutions of non-linear reaction equations for reversible enzyme reaction are calculated by Homotopy perturbation method (HPM) and Simple iteration method (SIM).
Revised:  Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and Simple iteration method (SIM).
Edit intent: fluency
Original:  Analytic approximate solutions of non-linear reaction equations for reversible enzyme reaction are calculated by Homotopy perturbation method (HPM) and Simple iteration method (SIM).
Revised:  Analytic approximate solutions of non-linear reaction equations for reversible enzyme reaction are calculated by Homotopy perturbation method (HPM) and the Simple Iteration Method (SIM).
Edit intent: fluency
Original:  The Matlab program are included in appendixes .
Revised:  The Matlab programs are included in appendixes .
Edit intent: fluency
Original:  The Matlab program are included in appendixes .
Revised:  The Matlab program are included in appendices .
Edit intent: fluency
Original:  Majority of previous methods for this problem are still restricted to graph-based interference models.
Revised:  Majority of previous methods are restricted to graph-based interference models.
Edit intent: clarity
Original:  Through some key observations about this model, we discover some intrinsic connections between these two interference models, and then we can indirectly apply results on graph-based interference models to develop efficient link scheduling algorithms for physical interference model  .
Revised:  Through some key observations about this model, we develop efficient link scheduling algorithms for physical interference model .
Edit intent: coherence
Original:  Through some key observations about this model, we discover some intrinsic connections between these two interference models, and then we can indirectly apply results on graph-based interference models to develop efficient link scheduling algorithms for physical interference model  .
Revised:  Through some key observations about this model, we discover some intrinsic connections between these two interference models, and then we can indirectly apply results on graph-based interference models to develop efficient link scheduling algorithms by exploiting the intrinsic connections between the physical interference model .
Edit intent: clarity
Original: In this paper the complex systems are discussed from the business and economics point of view .
Revised: In this chapter the complex systems are discussed from the business and economics point of view .
Edit intent: clarity
Original: In this paper the complex systems are discussed from the business and economics point of view .
Revised: In this paper the complex systems are discussed in the context of economic and business policy and decision making .
Edit intent: clarity
Original:  It will be showed and motivated that social systems are typically chaotic  and/or non-linear and therefore non-equilibrium or complex systems.
Revised:  It will be showed and motivated that social systems are typically chaotic , non-linear and/or non-linear and therefore non-equilibrium or complex systems.
Edit intent: fluency
Original:  It will be showed and motivated that social systems are typically chaotic  and/or non-linear and therefore non-equilibrium or complex systems.
Revised:  It will be showed and motivated that social systems are typically chaotic and/or non-equilibrium and therefore complex systems.
Edit intent: clarity
Original:  It is discussed that the rapid change  global consumer behaviour is underway, that further increases the complexity in the business and management.
Revised:  It is discussed that the rapid change in global consumer behaviour is underway, that further increases the complexity in the business and management.
Edit intent: fluency
Original:  It is discussed that the rapid change  global consumer behaviour is underway, that further increases the complexity in the business and management.
Revised:  It is discussed that the rapid change global consumer behaviour is underway, that further increases the complexity in business and management.
Edit intent: fluency
Original:  For successful management under complexity, a following principles are offered: openness and international competition, tolerance and variety of the ideas, self-reliability and low dependence on external help.
Revised:  For policy making under complexity, a following principles are offered: openness and international competition, tolerance and variety of the ideas, self-reliability and low dependence on external help.
Edit intent: clarity
Original:  For successful management under complexity, a following principles are offered: openness and international competition, tolerance and variety of the ideas, self-reliability and low dependence on external help.
Revised:  For successful management under complexity, following principles are offered: openness and international competition, tolerance and variety of the ideas, self-reliability and low dependence on external help.
Edit intent: fluency
Original:  For successful management under complexity, a following principles are offered: openness and international competition, tolerance and variety of the ideas, self-reliability and low dependence on external help.
Revised:  For successful management under complexity, a following principles are offered: openness and international competition, tolerance and variety of ideas, self-reliability and low dependence on external help.
Edit intent: clarity
Original:  It is motivated that small economies have good prospects to gain from the global processes underway, if they can demonstrate flexible production , reliable business ethics and good risk management.
Revised:  It is motivated that small economies have good prospects to gain from the global processes underway, if they can demonstrate production flexibility , reliable business ethics and good risk management.
Edit intent: clarity
Original:   In this environment, the challenges for corporate managements are being also permanently changed: the balance between short term noise and long term chaos whose attractor includes customers, shareholders and employees must be found.
Revised:  In this environment, the challenges for corporate management are being also permanently changed: the balance between short term noise and long term chaos whose attractor includes customers, shareholders and employees must be found.
Edit intent: fluency
Original: The open question about the power of centralized PC systems of pushdown automata (PCPA) working in returning mode is settled by showing them to be universal.
Revised: Parallel communicating systems of pushdown automata (PCPA) working in returning mode is settled by showing them to be universal.
Edit intent: clarity
Original:  Furthermore, taking both the download of keywords and publication of articles into consideration, we design a method to detect the emerging research trends.
Revised:  Furthermore, taking both the download of keywords and articles into consideration, we design a method to detect the emerging research trends.
Edit intent: clarity
Original:  We find that in scientometrics field, social media, new indices to quantify scientific productivity (g-index), webometrics, semantic, text mining, open access are emerging fields that information scientists are focusing on.
Revised:  We find that in scientometrics field, social media, new indices to quantify scientific productivity (g-index), webometrics, semantic, text mining, open access are emerging fields that scientometrics researchers are focusing on.
Edit intent: clarity
Original:  The routing strategies are compared using two generic models, i.e., Barabasi-Albert scale-free network and scale-free network on lattice, and academic router networks of the Netherlands and France.
Revised:  The routing strategies are compared using two generic models, i.e., Barab\`asi-Albert scale-free network and scale-free network on lattice, and academic router networks of the Netherlands and France.
Edit intent: fluency
Original: In this paper, we are interested in optimization of complex network without changing average connectivity or total network capacity .
Revised: In this paper, we are exploring strategies for the reduction of the congestion in the complex networks. The nodes without buffers are considered, so, if the congestion occurs, the information packets will be dropped .
Edit intent: coherence
Original:  The focus is on  efficient routing.
Revised:  The focus is on the efficient routing.
Edit intent: fluency
Original:  The routing strategies are compared using two generic models, i.e., Barab\`asi-Albert scale-free network and scale-free network on lattice, and  academic router networks of the Netherlands and France.
Revised:  The routing strategies are compared using two generic models, i.e., Barab\`asi-Albert scale-free network and scale-free network on lattice, and the academic router networks of the Netherlands and France.
Edit intent: fluency
Original:  The nodes without buffers are considered, so, if congestion occurs, packets will be dropped.
Edit intent: coherence
Original:  Simulation results indicate that proposed routing strategy can further reduce number of dropped packets in a combination with the efficient path routing proposed by Yan et al.
Revised:  The simulation results indicate that proposed routing strategy can further reduce number of dropped packets in a combination with the efficient path routing proposed by Yan et al.
Edit intent: clarity
Original:  After setting up the master equation associated to the stochastic dynamics we develop a truncation scheme to solve the evolution equations from which we get the epidemic curve and the threshold of the disease as well as the reproductive ratio.
Revised:  We develop a truncation scheme to solve the evolution equations from which we get the epidemic curve and the threshold of the disease as well as the reproductive ratio.
Edit intent: coherence
Original:  After setting up the master equation associated to the stochastic dynamics we develop a truncation scheme to solve the evolution equations from which we get the epidemic curve and the threshold of the disease as well as the reproductive ratio.
Revised:  After setting up the master equation associated to the stochastic dynamics we develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease as well as the reproductive ratio.
Edit intent: clarity
Original:  After setting up the master equation associated to the stochastic dynamics we develop a truncation scheme to solve the evolution equations from which we get the epidemic curve and the threshold of the disease as well as the reproductive ratio.
Revised:  After setting up the master equation associated to the stochastic dynamics we develop a truncation scheme to solve the evolution equations from which we get the epidemic curve and the threshold of the disease and the reproductive ratio.
Edit intent: coherence
Original:  Therefore for random variables assuming values in a finite set, our contributions are two-fold: (i) In the case of the alpha-mixing coefficient, we show that determining whether or not it exceeds a prespecified threshold is NP-complete . and provide efficiently computable upper and lower bounds.
Revised:  Therefore for random variables assuming values in a finite set, our contributions are two-fold: (i) In the case of the alpha-mixing coefficient, we show that determining whether or not it exceeds a prespecified threshold is NP-complete , and provide efficiently computable upper and lower bounds.
Edit intent: fluency
Original:  Instant interactive proofs effect a fragile epistemic impact in their intended communities of peer reviewers that consists in the impermanent induction of the knowledge of their proof goal by means of the knowledge of the proof with the interpreting reviewer: If my peer reviewer knew my proof then she would at least then  know that its proof goal is true.
Revised:  Instant interactive proofs effect a fragile epistemic impact in their intended communities of peer reviewers that consists in the impermanent induction of the knowledge of their proof goal by means of the knowledge of the proof with the interpreting reviewer: If my peer reviewer knew my proof then she would at least then (in that instant) know that its proof goal is true.
Edit intent: clarity
Original: Given a planar graph G on n vertices and an integer parameter r<n, an r--division of G with few holes is a decomposition of G into O(n/r) regions of size at most r such that each region contains at most a constant number of faces that are not faces of G (also called holes), and such that, for each region, the total number of vertices on these faces is O( \sqrt r ).
Revised: Given a planar graph G on n vertices and an integer parameter r<n, an r-division of G with few holes is a decomposition of G into O(n/r) regions of size at most r such that each region contains at most a constant number of faces that are not faces of G (also called holes), and such that, for each region, the total number of vertices on these faces is O( \sqrt r ).
Edit intent: fluency
Original: Given a planar graph G on n vertices and an integer parameter r<n, an r--division of G with few holes is a decomposition of G into O(n/r) regions of size at most r such that each region contains at most a constant number of faces that are not faces of G (also called holes), and such that, for each region, the total number of vertices on these faces is O( \sqrt r ).
Revised: Given a planar graph G on n vertices and an integer parameter r<n, an r--division of G with few holes is a decomposition of G into O(n/r) regions of size at most r such that each region contains at most a constant number of faces that are not faces of G (also called holes), and such that, for each region, the total number of vertices on these faces is O( sqrt r ).
Edit intent: coherence
Original:  We provide a linear-time algorithm for computing r--divisions with few holes.
Revised:  We provide a linear-time algorithm for computing r-divisions with few holes.
Edit intent: fluency
Original:  In fact, our algorithm computes a structure, called decomposition tree, which represents a recursive decomposition of G that includes r--divisions for essentially all values of r.
Revised:  In fact, our algorithm computes a structure, called decomposition tree, which represents a recursive decomposition of G that includes r-divisions for essentially all values of r.
Edit intent: fluency
Original:  In particular, given an increasing sequence%DIFDELCMD < {\bm %%% r = (r_1,r_2,...), our algorithm can produce a recursive %DIFDELCMD < {\bm %DIFDELCMD < %%% r --division with few holes in linear time.
Revised:  In particular, given an %DIFDELCMD < {\bm %%% r = (r_1,r_2,...), our algorithm can produce a recursive %DIFDELCMD < {\bm %DIFDELCMD < %%% r --division with few holes in linear time.
Edit intent: clarity
Original:  In particular, given an increasing sequence%DIFDELCMD < {\bm %%% r = (r_1,r_2,...), our algorithm can produce a recursive %DIFDELCMD < {\bm %DIFDELCMD < %%% r --division with few holes in linear time.
Revised:  In particular, given an increasing sequence%DIFDELCMD < {\bm %%% r = (r_1,r_2,...), our algorithm can produce a recursive %DIFDELCMD < {\bm %DIFDELCMD < %%% --division with few holes in linear time.
Edit intent: fluency
Original:  In particular, given an increasing sequence%DIFDELCMD < {\bm %%% r = (r_1,r_2,...), our algorithm can produce a recursive %DIFDELCMD < {\bm %DIFDELCMD < %%% r --division with few holes in linear time.
Revised:  In particular, given an increasing sequence%DIFDELCMD < {\bm %%% r = (r_1,r_2,...), our algorithm can produce a recursive %DIFDELCMD < {\bm %DIFDELCMD < %%% r r-division with few holes in linear time.
Edit intent: fluency
Original:  Our linear-time algorithm improves upon the decomposition algorithm used in the state-of-the-art algorithm for minimum st--cut (Italiano, Nussbaum, Sankowski, and Wulff-Nilsen, STOC 2011), removing one of the bottlenecks in the overall running time of their algorithm (analogously for minimum cut in planar and bounded-genus graphs).
Revised:  Our linear-time algorithm improves upon the decomposition algorithm used in the state-of-the-art algorithm for minimum st-cut (Italiano, Nussbaum, Sankowski, and Wulff-Nilsen, STOC 2011), removing one of the bottlenecks in the overall running time of their algorithm (analogously for minimum cut in planar and bounded-genus graphs).
Edit intent: fluency
Original:  In this article, we prove the condition holds if and only if m > 1. Consequently, the construction of Budaghyan and Carlet produces APN polynomials for all values of r,s having m > 1 and GCD(m,n) = 1. In the case where GCD(m,n) = k >  1, Budaghyan and Carlet showed that the nonzero derivatives of the hexanomials are 2^k-to-one maps from F_{r^2} to F_{r^2}, provided the same technical condition holds.
Revised:  In this article, we prove that the construction of Budaghyan and Carlet produces APN polynomials for all values of r,s having m > 1 and GCD(m,n) = 1. In the case where GCD(m,n) = k > 1, Budaghyan and Carlet showed that the nonzero derivatives of the hexanomials are 2^k-to-one maps from F_{r^2} to F_{r^2}, provided the same technical condition holds.
Edit intent: coherence