wanyu/IteraTeR_v2 huggingface dataset:
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 the condition holds if and only if m > 1. Consequently, the construction of Budaghyan and Carlet produces APN polynomials for all m and n. 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: clarity
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 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.
Edit intent: coherence
Original:  We show that our method is correct and generalizes the class of nets generated by other hierarchical approaches.
Revised:  We show that this method is correct and generalizes the class of nets generated by other hierarchical approaches.
Edit intent: fluency
Original:  We also identify a new notion of soundness and prove that it is preserved by substitutions.
Revised:  The method involves a new notion of soundness and prove that it is preserved by substitutions.
Edit intent: clarity
Original:  We also identify a new notion of soundness and prove that it is preserved by substitutions.
Revised:  We also identify a new notion of soundness which is preserved by substitutions.
Edit intent: coherence
Original:  We claim that this notion is better suited than *-soundness for use with hierarchical methods, while showing examples that *-soundness in the general case } is not preserved by  substitution.
Revised:  We claim that this notion is better suited than *-soundness for use with hierarchical methods, while showing examples that *-soundness in the general case *} is not preserved by substitution.
Edit intent: fluency
Original:  We suggest that ZD strategies with an informational advantage over other players that allows them to recognize other ZD strategies will be evolutionarily stable (and able to exploit other players).
Revised:  We show that ZD strategies with an informational advantage over other players that allows them to recognize other ZD strategies will be evolutionarily stable (and able to exploit other players).
Edit intent: clarity
Original:  We suggest that ZD strategies with an informational advantage over other players that allows them to recognize other ZD strategies will be evolutionarily stable (and able to exploit other players).
Revised:  We suggest that ZD strategies with an informational advantage over other players that allows them to recognize other ZD strategies can be evolutionarily stable (and able to exploit other players).
Edit intent: clarity
Original:  However, such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition 
Revised:  However, such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition .
Edit intent: fluency
Original: Consistently predicting protein structure at atomic resolution from sequence alone remains an unsolved challenge in computational biophysics.
Revised: Consistently predicting biopolymer structure at atomic resolution from sequence alone remains an unsolved challenge in computational biophysics.
Edit intent: clarity
Original: We introduce various definitions for price momentum on financial instruments in quantitative and mathematical ways.
Revised: We introduce various definitions for price momentum of financial instruments in quantitative and mathematical ways.
Edit intent: fluency
Original:  Measurement of the equity price momentum derived from the concept of momentum in physics can be conducted by velocity and mass defined in diverse manners.
Revised:  Measurement of the price momentum derived from the concept of momentum in physics can be conducted by velocity and mass defined in diverse manners.
Edit intent: clarity
Original:  Measurement of the equity price momentum derived from the concept of momentum in physics can be conducted by velocity and mass defined in diverse manners.
Revised:  Measurement of the equity price momentum derived from the concept of momentum in physics can be conducted with velocity and mass defined in diverse manners.
Edit intent: fluency
Original:  By using the physical momentum of equities as a selection criterion, the momentum/contrarian strategies are implemented  in the South Korean stock market .
Revised:  By using the physical momentum of price as a selection criterion, the momentum/contrarian strategies are implemented in the South Korean stock market .
Edit intent: clarity
Original:  By using the physical momentum of equities as a selection criterion, the momentum/contrarian strategies are implemented  in the South Korean stock market .
Revised:  By using the physical momentum of equities as a selection criterion, the momentum/contrarian strategies are implemented with equities in the South Korean stock market .
Edit intent: clarity
Original:  The physical momentum strategies provide better expected returns and risk-reward ratios than those of the original momentum strategy in weekly scales and part of monthly scales.
Revised:  The physical momentum strategies provide better expected returns and risk-reward ratios than those of the original momentum strategy in weekly scales and short terms in monthly scales.
Edit intent: clarity
Original:  In addition to that, the spontaneously symmetry breaking of arbitrage is also tested for the physical momentum strategies and the strategies with symmetry breaking generate the stronger performance and increase stability of the portfolios  .
Revised:  In addition to that, the spontaneously symmetry breaking of arbitrage is also tested for the physical momentum strategies and the strategies with a scheme from the symmetry breaking of arbitrage generate the stronger performance and increase stability of the portfolios .
Edit intent: clarity
Original:  In addition to that, the spontaneously symmetry breaking of arbitrage is also tested for the physical momentum strategies and the strategies with symmetry breaking generate the stronger performance and increase stability of the portfolios  .
Revised:  In addition to that, the spontaneously symmetry breaking of arbitrage is also tested for the physical momentum strategies and the strategies with symmetry breaking generate the stronger performance and increase stability of the portfolios than the strategies without the scheme .
Edit intent: clarity
Original:  Measurement of the price momentum derived from the concept of momentum in physics can be conducted with velocity and mass defined in diverse manners . By using the physical momentum of price as a selection criterion, the momentum/ contrarian strategies are implemented with equities in the South Korean stock markets including the KOSPI 200 and its subuniverses.
Revised:  Measurement of the price momentum derived from the concept of momentum in physics is quantified with velocity and mass defined in diverse manners . By using the physical momentum of price as a selection criterion, the momentum/ contrarian strategies are implemented with equities in the South Korean stock markets including the KOSPI 200 and its subuniverses.
Edit intent: clarity
Original:  Measurement of the price momentum derived from the concept of momentum in physics can be conducted with velocity and mass defined in diverse manners . By using the physical momentum of price as a selection criterion, the momentum/ contrarian strategies are implemented with equities in the South Korean stock markets including the KOSPI 200 and its subuniverses.
Revised:  Measurement of the price momentum derived from the concept of momentum in physics can be conducted with velocity and mass defined in diverse ways . By using the physical momentum of price as a selection criterion, the momentum/ contrarian strategies are implemented with equities in the South Korean stock markets including the KOSPI 200 and its subuniverses.
Edit intent: fluency
Original:  Measurement of the price momentum derived from the concept of momentum in physics can be conducted with velocity and mass defined in diverse manners . By using the physical momentum of price as a selection criterion, the momentum/ contrarian strategies are implemented with equities in the South Korean stock markets including the KOSPI 200 and its subuniverses.
Revised:  Measurement of the price momentum derived from the concept of momentum in physics can be conducted with velocity and mass defined in diverse manners . By using the physical momentum of price as a selection criterion, the momentum/ contrarian strategies are implemented in South Korea KOSPI 200 and its subuniverses.
Edit intent: clarity
Original: The physical momentum strategies provide  better expected returns and risk-reward ratios than those of the traditional momentum strategy at many lookback-holding pairs in weekly scales and short terms in monthly scales.
Revised: The physical momentum strategies provide better expected returns and reward-risk measures than those of the traditional momentum strategy at many lookback-holding pairs in weekly scales and short terms in monthly scales.
Edit intent: clarity
Original:  The price momentum originated from the concept of momentum in physics is quantified with velocity and mass defined in diverse ways .
Revised:  The price momentum is quantified with velocity and mass defined in diverse ways .
Edit intent: coherence
Original:  The price momentum originated from the concept of momentum in physics is quantified with velocity and mass defined in diverse ways .
Revised:  The price momentum originated from the concept of momentum in physics is quantified with velocity and mass concepts originated from the momentum in physics .
Edit intent: clarity
Original:  By using the physical momentum of price as a selection criterion, the weekly contrarian strategies are implemented in South Korea KOSPI 200 and U.S. S&P 500 universes.
Revised:  By using the physical momentum of price as a selection criterion, the weekly contrarian strategies are implemented in South Korea KOSPI 200 and US S&P 500 universes.
Edit intent: fluency
Original: Two words have a reverse if they have the same pair of distinct letters on the same pair of positions  in reversed order.
Revised: Two words have a reverse if they have the same pair of distinct letters on the same pair of positions , but in reversed order.
Edit intent: coherence
Original:  Moreover, a subset of force-extension trajectories reveals a mechanical hierarchy in which the rupture of domain-domain interactions at high forces ( >300 pN) liberates the unfolding of individual domains at low forces ( ~ 100 pN).
Revised:  Moreover, a subset of force-extension trajectories reveals a mechanical hierarchy in which the rupture of domain-domain interactions at high forces ( >300 pN) liberates the unfolding of individual domains at low forces ( 100 pN).
Edit intent: clarity
Original:  For other non-zero characteristic, we show that a stronger form of Dietzfelbinger et al.'s inequality (implicit in their proof) for "weighted " adjacency matrices is tight.
Revised:  For other non-zero characteristic, we show that a stronger form of Dietzfelbinger et al.'s inequality (implicit in their proof) for weighted adjacency matrices is tight.
Edit intent: fluency
Original: In a bipartite graph, a "cross-free matching" or "fooling set" is a matching no two of whose edges induce a C_4  M_{\ell,k} = 0 for every k}\ne  . Dietzfelbinger, Hromkovi \v{c , and Schnitger ( 1994 ) showed that the maximum cardinality of a cross-free matching is at most the square of the rank of the bipartite adjacency matrix of the graph (\le  regardless of over which field the rank is computed ) , and asked , whether this bound can be improved.
Revised: An n\times n matrix M is called a M_{\ell,k} = 0 for every k}\ne . Dietzfelbinger, Hromkovi \v{c , and Schnitger ( 1994 ) showed that the maximum cardinality of a cross-free matching is at most the square of the rank of the bipartite adjacency matrix of the graph (\le regardless of over which field the rank is computed ) , and asked , whether this bound can be improved.
Edit intent: clarity
Original: In a bipartite graph, a "cross-free matching" or "fooling set" is a matching no two of whose edges induce a C_4  M_{\ell,k} = 0 for every k}\ne  . Dietzfelbinger, Hromkovi \v{c , and Schnitger ( 1994 ) showed that the maximum cardinality of a cross-free matching is at most the square of the rank of the bipartite adjacency matrix of the graph (\le  regardless of over which field the rank is computed ) , and asked , whether this bound can be improved.
Revised: In a bipartite graph, a "cross-free matching" or "fooling set" is a matching no two of whose edges induce a C_4 M_{\ell,k} = 0 for every k}\ne . Dietzfelbinger, Hromkovi \v{c , and Schnitger ( 1994 ) showed that the maximum cardinality of a cross-free matching is at most the square of the rank of the bipartite adjacency matrix of the graph (\le regardless of over which field the rank is computed ) , and asked , whether this bound can be improved.
Edit intent: fluency
Original: In a bipartite graph, a "cross-free matching" or "fooling set" is a matching no two of whose edges induce a C_4  M_{\ell,k} = 0 for every k}\ne  . Dietzfelbinger, Hromkovi \v{c , and Schnitger ( 1994 ) showed that the maximum cardinality of a cross-free matching is at most the square of the rank of the bipartite adjacency matrix of the graph (\le  regardless of over which field the rank is computed ) , and asked , whether this bound can be improved.
Revised: In a bipartite graph, a "cross-free matching" or "fooling set" is a matching no two of whose edges induce a C_4 M_{\ell,k} = 0 for every k}\ne . Dietzfelbinger, Hromkovi \v{c , and Schnitger ( 1994 ) showed that the maximum cardinality of a cross-free matching is at most the square of the rank of the bipartite adjacency matrix of the graph (\le regardless of over which field the rank is computed , and asked , whether this bound can be improved.
Edit intent: fluency
Original: In a bipartite graph, a "cross-free matching" or "fooling set" is a matching no two of whose edges induce a C_4  M_{\ell,k} = 0 for every k}\ne  . Dietzfelbinger, Hromkovi \v{c , and Schnitger ( 1994 ) showed that the maximum cardinality of a cross-free matching is at most the square of the rank of the bipartite adjacency matrix of the graph (\le  regardless of over which field the rank is computed ) , and asked , whether this bound can be improved.
Revised: In a bipartite graph, a "cross-free matching" or "fooling set" is a matching no two of whose edges induce a C_4 M_{\ell,k} = 0 for every k}\ne . Dietzfelbinger, Hromkovi \v{c , and Schnitger ( 1994 ) showed that the maximum cardinality of a cross-free matching is at most the square of the rank of the bipartite adjacency matrix of the graph (\le regardless of over which field the rank is computed ) , and asked whether the exponent on \mbox{rk can be improved.
Edit intent: clarity
Original:  Our model is designed to explain a  behavior of the market when new information a?ecting the market arrives.
Revised:  Our model is designed to explain a collective behavior of the market when new information a?ecting the market arrives.
Edit intent: clarity
Original:  Our model is designed to explain a  behavior of the market when new information a?ecting the market arrives.
Revised:  Our model is designed to explain a behavior of the market when new information affecting the market arrives.
Edit intent: fluency
Original:  Our model is designed to explain a collective behavior of the market when new information affecting the market arrives.
Revised:  Our model is designed to explain the collective behavior of the market when new information affecting the market arrives.
Edit intent: fluency
Original:  Our model is designed to explain a collective behavior of the market when new information affecting the market arrives.
Revised:  Our model is designed to explain a collective behavior of the market when new information a?ecting the market arrives.
Edit intent: fluency
Original:  The model has two additional parameters which we call slow parameters .
Revised:  The model has two additional parameters which we call slow vari- ables .
Edit intent: fluency
Original:  These parameters measure  mood of two groups of investors, namely, bulls and bears.
Revised:  These parameters measure the mood of two groups of investors, namely, bulls and bears.
Edit intent: fluency
Original:   We explain the intuition behind the equations and present numerical simulations which show that behavior of the model is similar to the behavior of the real market .
Revised:  We explain the intuition behind the equations and present numerical simulations which show that the behavior of our model is similar to the behavior of the real market .
Edit intent: fluency
Original:  Our model is designed to explain the collective behavior of the market when new information a?ecting the market arrives.
Revised:  It is designed to explain the collective behavior of the market when new information a?ecting the market arrives.
Edit intent: clarity
Original:  Our model is designed to explain the collective behavior of the market when new information a?ecting the market arrives.
Revised:  Our model is designed to explain collective behaviour of the market when new information a?ecting the market arrives.
Edit intent: fluency
Original:  Our model is designed to explain the collective behavior of the market when new information a?ecting the market arrives.
Revised:  Our model is designed to explain the collective behavior of the market when new information affecting the market arrives.
Edit intent: fluency
Original:  Second, our model captures the interaction between trading agents and constitutes a nonlinear Markov process which exhibits long term cor- relations .
Revised:  Second, our model captures the interaction between trading agents and constitutes a nonlinear Markov process which exhibits long term correlations .
Edit intent: fluency
Original:  We explain the intuition behind the equations and present numerical simulations which show that the behavior of our model is similar to the behavior of the real market  .
Revised:  We explain the intuition behind the equations and present numerical simulations which show that the behaviour of our model is similar to the behavior of the real market .
Edit intent: fluency
Original:  We explain the intuition behind the equations and present numerical simulations which show that the behavior of our model is similar to the behavior of the real market  .
Revised:  We explain the intuition behind the equations and present numerical simulations which show that the behavior of our model is similar to the behaviour of the real market .
Edit intent: fluency
Original: A new method for visualizing the relatedness of scientific fields is developed that is based on measuring the overlap of researchers between fields .
Revised: A new method for visualizing the relatedness of scientific areas is developed that is based on measuring the overlap of researchers between fields .
Edit intent: clarity
Original: A new method for visualizing the relatedness of scientific fields is developed that is based on measuring the overlap of researchers between fields .
Revised: A new method for visualizing the relatedness of scientific fields is developed that is based on measuring the overlap of researchers between areas .
Edit intent: clarity
Original:  It is found that closely related fields have a high propensity to share a larger number of common authors.
Revised:  It is found that closely related areas have a high propensity to share a larger number of common authors.
Edit intent: clarity
Original:  A methodology for comparing fields of vastly different sizes and to handle name homonymy is constructed, allowing for the robust deployment of this method on real data sets.
Revised:  A methodology for comparing areas of vastly different sizes and to handle name homonymy is constructed, allowing for the robust deployment of this method on real data sets.
Edit intent: clarity
Original:  This is demonstrated on two case studies, complexity science and neutrino physics, where the level of relatedness of fields within each area is expected to vary greatly.
Revised:  This is demonstrated on two case studies, complexity science and neutrino physics, where the level of relatedness of areas within each area is expected to vary greatly.
Edit intent: clarity
Original:  It is found that the results returned by this method closely match the intuitive expectation that the broad, multidisciplinary area of complexity science possesses fields that are weakly related to each other while the much narrower area of neutrino physics shows very strongly related fields .
Revised:  It is found that the results returned by this method closely match the intuitive expectation that the broad, multidisciplinary area of complexity science possesses areas that are weakly related to each other while the much narrower area of neutrino physics shows very strongly related fields .
Edit intent: clarity
Original:  It is found that the results returned by this method closely match the intuitive expectation that the broad, multidisciplinary area of complexity science possesses fields that are weakly related to each other while the much narrower area of neutrino physics shows very strongly related fields .
Revised:  It is found that the results returned by this method closely match the intuitive expectation that the broad, multidisciplinary area of complexity science possesses fields that are weakly related to each other while the much narrower area of neutrino physics shows very strongly related areas .
Edit intent: clarity
Original: Modeling molecules as undirected graphs and chemical reactions asgraph rewriting operations is a natural and convenient approach tomodeling chemistry.
Revised: Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach tomodeling chemistry.
Edit intent: fluency
Original: Modeling molecules as undirected graphs and chemical reactions asgraph rewriting operations is a natural and convenient approach tomodeling chemistry.
Revised: Modeling molecules as undirected graphs and chemical reactions asgraph rewriting operations is a natural and convenient approach tom odeling chemistry.
Edit intent: fluency
Original:  Graph grammar rules are most naturally employed tomodel elementary reactions like merging, splitting, and isomerisationof molecules.
Revised:  Graph grammar rules are most naturally employed to model elementary reactions like merging, splitting, and isomerisationof molecules.
Edit intent: fluency
Original:  Graph grammar rules are most naturally employed tomodel elementary reactions like merging, splitting, and isomerisationof molecules.
Revised:  Graph grammar rules are most naturally employed tomodel elementary reactions like merging, splitting, and isomerisation of molecules.
Edit intent: fluency