wanyu/IteraTeR_v2 huggingface dataset:
Original:  We present a topological model of this process, and  characterize all possible knot or catenane products that arise from the most common substrates : unknots, unlinks, and (2,m)-torus knots and catenanes .
Revised:  We develop a model of this process, and characterize all possible knot or catenane products that arise from the most common substrates : unknots, unlinks, and (2,m)-torus knots and catenanes .
Edit intent: clarity
Original:  We present a topological model of this process, and  characterize all possible knot or catenane products that arise from the most common substrates : unknots, unlinks, and (2,m)-torus knots and catenanes .
Revised:  We present a topological model of this process, and characterize all possible knot or catenane products that arise from the most common substrates .
Edit intent: coherence
Original: Tools of the theory of critical phenomena, namely the scaling analysis and universality  are argued to be applicable to the large complex web like network structures.
Revised: Tools of the theory of critical phenomena, namely the scaling analysis and universality , are argued to be applicable to the large complex web like network structures.
Edit intent: fluency
Original: Tools of the theory of critical phenomena, namely the scaling analysis and universality  are argued to be applicable to the large complex web like network structures.
Revised: Tools of the theory of critical phenomena, namely the scaling analysis and universality are argued to be applicable to large complex web-like network structures.
Edit intent: fluency
Original:  Using a detailed analysis of the real-data of the International Trade Network we argue that the scaled link weight distribution has an approximate log-normal distribution which remains robust over a period of 53 years.
Revised:  Using a detailed analysis of the real data of the International Trade Network we argue that the scaled link weight distribution has an approximate log-normal distribution which remains robust over a period of 53 years.
Edit intent: fluency
Original:  Another universal feature is observed in the power law growth of the trade-strength with Gross Domestic Product , the exponent being similar for all countries.
Revised:  Another universal feature is observed in the power-law growth of the trade-strength with Gross Domestic Product , the exponent being similar for all countries.
Edit intent: fluency
Original:  Another universal feature is observed in the power law growth of the trade-strength with Gross Domestic Product , the exponent being similar for all countries.
Revised:  Another universal feature is observed in the power law growth of the trade strength with gross domestic product , the exponent being similar for all countries.
Edit intent: fluency
Original:  Using the ` rich-club' coefficient measure of the weighted networks it has been shown that the size of the rich-club controlling half of the world's trade is actually shrinking.
Revised:  Using the ' rich-club' coefficient measure of the weighted networks it has been shown that the size of the rich-club controlling half of the world's trade is actually shrinking.
Edit intent: fluency
Original:  While the gravity law is known to describe well the social interactions in the static networks of population migration, international trades etc. here for the first time we studied a non-conservative dynamical model based on the gravity law which reproduce excellent many empirical features of the ITN.
Revised:  While the gravity law is known to describe well the social interactions in the static networks of population migration, international trade, etc, here for the first time we studied a non-conservative dynamical model based on the gravity law which reproduce excellent many empirical features of the ITN.
Edit intent: fluency
Original:  While the gravity law is known to describe well the social interactions in the static networks of population migration, international trades etc. here for the first time we studied a non-conservative dynamical model based on the gravity law which reproduce excellent many empirical features of the ITN.
Revised:  While the gravity law is known to describe well the social interactions in the static networks of population migration, international trades etc. here for the first time we studied a non-conservative dynamical model based on the gravity law which excellently reproduced many empirical features of the ITN.
Edit intent: clarity
Original:  In our formulation, the market moves continuously  but an investor trades in discrete times, which can depend on the past path of the market.
Revised:  In our formulation, the market moves continuously , but an investor trades in discrete times, which can depend on the past path of the market.
Edit intent: fluency
Original:  Our proof is based on embedding high-frequency discrete time games into the continuous time game and the use of the Bayesian strategy of Kumon, Takemura and Takeuchi ( 2007b) for discrete time coin-tossing games.
Revised:  Our proof is based on embedding high-frequency discrete-time games into the continuous time game and the use of the Bayesian strategy of Kumon, Takemura and Takeuchi ( 2007b) for discrete time coin-tossing games.
Edit intent: fluency
Original:  Our proof is based on embedding high-frequency discrete time games into the continuous time game and the use of the Bayesian strategy of Kumon, Takemura and Takeuchi ( 2007b) for discrete time coin-tossing games.
Revised:  Our proof is based on embedding high-frequency discrete time games into the continuous-time game and the use of the Bayesian strategy of Kumon, Takemura and Takeuchi ( 2007b) for discrete time coin-tossing games.
Edit intent: fluency
Original:  We also clarify that the main growth part of the investor's capital processes is lucidly described by the information quantities, which are derived from the Kullback-Leibler information with respect to the empirical fluctuation of the asset price.
Revised:  We also show that the main growth part of the investor's capital processes is lucidly described by the information quantities, which are derived from the Kullback-Leibler information with respect to the empirical fluctuation of the asset price.
Edit intent: coherence
Original:  We also clarify that the main growth part of the investor's capital processes is lucidly described by the information quantities, which are derived from the Kullback-Leibler information with respect to the empirical fluctuation of the asset price.
Revised:  We also clarify that the main growth part of the investor's capital processes is clearly described by the information quantities, which are derived from the Kullback-Leibler information with respect to the empirical fluctuation of the asset price.
Edit intent: clarity
Original:  We also clarify that the main growth part of the investor's capital processes is lucidly described by the information quantities, which are derived from the Kullback-Leibler information with respect to the empirical fluctuation of the asset price.
Revised:  We also clarify that the main growth part of the investor's capital processes is lucidly described by the information quantities, which are derived from the Kullback--Leibler information with respect to the empirical fluctuation of the asset price.
Edit intent: fluency
Original: Biochemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes.
Revised: Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes.
Edit intent: clarity
Original:  These systems are oftentimes simulated using the Gillespie Algorithm or the Next Reaction Method , which are exact simulation methods .
Revised:  These systems are oftentimes simulated using the Gillespie Algorithm or the Next Reaction Method .
Edit intent: coherence
Original:  In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function.
Revised:  In this paper we make explicit use of the fact that the initiation times of the reactions can be represented as the firing times of an independent, unit Poisson process with integrated propensity function.
Edit intent: clarity
Original:  In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function.
Revised:  In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of independent, unit Poisson process with integrated propensity function.
Edit intent: fluency
Original:  These results together with our earlier study of Engrailed Homeodomain and recent experimental studies provide a comprehensive, atomic-level picture of folding mechanics of three-helix bundle proteins 
Revised:  These results together with our earlier study of Engrailed Homeodomain and recent experimental studies provide a comprehensive, atomic-level picture of folding mechanics of three-helix bundle proteins .
Edit intent: fluency
Original: Continuous time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution.
Revised: Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution.
Edit intent: fluency
Original:  Our approach leads to option prices that fulfil the financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for considering more exotic market conditions.
Revised:  Our approach leads to option prices that fulfil financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for considering more exotic market conditions.
Edit intent: fluency
Original:  Our approach leads to option prices that fulfil the financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for considering more exotic market conditions.
Revised:  Our approach leads to option prices that fulfil the financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for more exotic market conditions.
Edit intent: clarity
Original: A  finite-state automaton (FSA) is an abstract machine with finite working memory, whose input is a string from a finite alphabet, which reads the input one character at a time , and which has a deterministic transition function .
Revised: A finite-state automaton (FSA) is an abstract sequential machine that reads the symbols comprising an input word one at a time , and which has a deterministic transition function .
Edit intent: clarity
Original: A  finite-state automaton (FSA) is an abstract machine with finite working memory, whose input is a string from a finite alphabet, which reads the input one character at a time , and which has a deterministic transition function .
Revised: A finite-state automaton (FSA) is an abstract machine with finite working memory, whose input is a string from a finite alphabet, which reads the input one character at a time .
Edit intent: coherence
Original:  We show that, given a symmetric FSA A , there is a deterministic divide-and-conquer process that simulates A whose intermediate results are no larger than the size of A's memory.
Revised:  We show that, given a symmetric FSA A into an automaton-like divide-and-conquer process that simulates A whose intermediate results are no larger than the size of A's memory.
Edit intent: clarity
Original:  We show that, given a symmetric FSA A , there is a deterministic divide-and-conquer process that simulates A whose intermediate results are no larger than the size of A's memory.
Revised:  We show that, given a symmetric FSA A , there is a deterministic divide-and-conquer process whose intermediate results are no larger than the size of A's memory.
Edit intent: clarity
Original:  In comparison, for a general (not necessarily symmetric) FSA, a similar divide-and-conquer implementation has long been known via functional composition  but entails an exponential increase in the sizeof the state space.
Revised:  In comparison, a similar result for general FSA's has been long known via functional composition but entails an exponential increase in the sizeof the state space.
Edit intent: clarity
Original:  In comparison, for a general (not necessarily symmetric) FSA, a similar divide-and-conquer implementation has long been known via functional composition  but entails an exponential increase in the sizeof the state space.
Revised:  In comparison, for a general (not necessarily symmetric) FSA, a similar divide-and-conquer implementation has long been known via functional composition , but entails an exponential increase in the sizeof the state space.
Edit intent: fluency
Original:  Our result has applications to parallel processing and to symmetric FSA networks .
Revised:  Our result has applications to parallel processing and symmetric FSA networks .
Edit intent: fluency
Original: Neurons in brains are subject to various kinds of noises.
Revised: Neurons are subject to various kinds of noises.
Edit intent: clarity
Original:  Here we investigated the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses.
Revised:  In this paper, we studied the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses.
Edit intent: clarity
Original:  Here we investigated the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses.
Revised:  Here we investigated the response of a stochastic Hodgkin-Huxley neuron to transient input pulses.
Edit intent: clarity
Original:  Whereas in network level, the detection ability of the network was optimized versus the number of neurons involved in .
Revised:  Whereas in network level, the detection ability of networks can be optimized for the number of neurons involved in .
Edit intent: clarity
Original:  Whereas in network level, the detection ability of the network was optimized versus the number of neurons involved in .
Revised:  Whereas in network level, the detection ability of the network was optimized versus the number of neurons comprising the network .
Edit intent: clarity
Original:  We also introduce, and compute, two new measures of %DIFDELCMD < {\it %%% fluctuations in the synthesis of RNA. Analyzing these fluctuations, we show how the level of intrinsic noise {\it  in mRNA synthesis depends on the concentrations of the RNAPs as well as on those of some of the reactants and the products of the enzymatic reactions catalyzed by RNAP.
Revised:  We also introduce, and compute, two new measures of %DIFDELCMD < {\it %%% fluctuations in the synthesis of RNA. Analyzing these fluctuations, we show how the level of intrinsic noise {\it in mRNA synthesis depends on the concentrations of the RNAPs as well as on those of some of the reactants and the products of the enzymatic reactions catalyzed by RNAP.
Edit intent: fluency
Original:  We also introduce, and compute, two new measures of %DIFDELCMD < {\it %%% fluctuations in the synthesis of RNA. Analyzing these fluctuations, we show how the level of intrinsic noise {\it  in mRNA synthesis depends on the concentrations of the RNAPs as well as on those of some of the reactants and the products of the enzymatic reactions catalyzed by RNAP.
Revised:  We also introduce, and compute, two new measures of %DIFDELCMD < {\it %%% fluctuations in the synthesis of RNA. Analyzing these fluctuations, we show how the level of {\it in mRNA synthesis depends on the concentrations of the RNAPs as well as on those of some of the reactants and the products of the enzymatic reactions catalyzed by RNAP.
Edit intent: clarity
Original:  We show that fast and slow searches differ significantly in average search time and the variability of search time.
Revised:  We show that these searches differ significantly in average search time and the variability of search time.
Edit intent: clarity
Original:  We also use experimentally measured parameter values to estimate the balance between time spent in 3D and 1D diffusion and the total search time.
Revised:  Using experimentally measured parameter values to estimate the balance between time spent in 3D and 1D diffusion and the total search time.
Edit intent: clarity
Original:  We also use experimentally measured parameter values to estimate the balance between time spent in 3D and 1D diffusion and the total search time.
Revised:  We also use experimentally measured parameter values , we also show that 1D diffusion and the total search time.
Edit intent: coherence
Original: The diversity in wealth and social status is obvious not just amongst humans, but also throughout the animal world.
Revised: The diversity in wealth and social status is present not only among humans, but also throughout the animal world.
Edit intent: clarity
Original: The diversity in wealth and social status is obvious not just amongst humans, but also throughout the animal world.
Revised: The diversity in wealth and social status is obvious not just amongst humans, but throughout the animal world.
Edit intent: coherence
Original:  We accommodate this observation by generating random surfaces that determine the social diversity of players engaging in the prisoner's dilemma game.
Revised:  We account for this observation by generating random surfaces that determine the social diversity of players engaging in the prisoner's dilemma game.
Edit intent: clarity
Original:  We accommodate this observation by generating random surfaces that determine the social diversity of players engaging in the prisoner's dilemma game.
Revised:  We accommodate this observation by generating random variables that determ ine the social diversity of players engaging in the prisoner's dilemma game.
Edit intent: clarity
Original:  In particular, we consider different distributions of diversity and find that the power-law distribution warrants the best promotion of cooperation.
Revised:  In particular, we consider different distributions of diversity and find that the power-law distribution enables the best promotion of cooperation.
Edit intent: clarity
Original:  The facilitative effect relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to conquer attacking defectors even by high temptations to defect.
Revised:  The facilitation of the cooperative str ategy relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to conquer attacking defectors even by high temptations to defect.
Edit intent: clarity
Original:  The facilitative effect relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to conquer attacking defectors even by high temptations to defect.
Revised:  The facilitative effect relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to prevail against the defectors even when there is a large temptation to defect.
Edit intent: clarity
Original:  To confirm this, we also study the impact of spatially correlated social diversity and find that cooperation deteriorates as the spatial correlation length increases.
Revised:  To confirm this, we also study the impact of spatially correlated social diversity and find that coopera tion deteriorates as the spatial correlation length increases.
Edit intent: fluency
Original: Following Obizhaeva and Wang (2005), we consider optimal execution strategies for block market orders placed in a limit order book (LOB).
Revised: We consider optimal execution strategies for block market orders placed in a limit order book (LOB).
Edit intent: clarity
Original:  In this setting, there are now two possibilities of modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread.
Revised:  We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread.
Edit intent: clarity
Original: Thermal shape fluctuations of grafted microtubules were studied using high resolution particle tracking on attached fluorescent beads.
Revised: Thermal shape fluctuations of grafted microtubules were studied using high resolution particle tracking of attached fluorescent beads.
Edit intent: fluency
Original:  Motivated by these fundamental questions on intracellular biological processes, we have developed a model for searching a specific site on a self-avoiding walk (SAW) by a single particle .
Revised:  Motivated by these fundamental questions on intracellular biological processes, we have developed a model for searching a specific site on a self-avoiding walk (SAW) by a single protein .
Edit intent: clarity
Original:  We have made a comparative quantitative study of the efficiencies of sliding, inter-segmental hoppings and detachment/re-attachments of the particle during its search for the specific site on the SAW{\it  {\it   .
Revised:  We have made a comparative quantitative study of the efficiencies of sliding, inter-segmental hoppings and detachment/re-attachments of the particle during its search for the specific site on the SAW{\it efficiency {\it .
Edit intent: fluency
Original:  We have made a comparative quantitative study of the efficiencies of sliding, inter-segmental hoppings and detachment/re-attachments of the particle during its search for the specific site on the SAW{\it  {\it   .
Revised:  We have made a comparative quantitative study of the efficiencies of sliding, inter-segmental hoppings and detachment/re-attachments of the particle during its search for the specific site on the SAW{\it {\it experiments .
Edit intent: fluency
Original: A zone diagram of order n is a relatively new concept which was first defined and studied by T. Asano, J. Matousek and T.
Revised: A zone diagram is a relatively new concept which was first defined and studied by T. Asano, J. Matousek and T.
Edit intent: clarity
Original:  Tokuyama. It can be interpreted as a state of equilibrium between n mutually hostile kingdoms.
Revised:  Tokuyama. It can be interpreted as a state of equilibrium between several mutually hostile kingdoms.
Edit intent: clarity
Original:  We consider  m-spaces (a simple generalization of metric spaces) and prove some existence and (non)uniqueness results there .
Revised:  We consider m-spaces (a simple generalization of metric spaces) and prove several existence and (non)uniqueness results there .
Edit intent: clarity
Original:  Learning and innovation help to preserve cooperation during network re-organization  , and may be key mechanisms promoting the evolution of self-organizing, complex systems.
Revised:  These results suggest that a balanced duo of learning and innovation may help to preserve cooperation during network re-organization , and may be key mechanisms promoting the evolution of self-organizing, complex systems.
Edit intent: clarity
Original:  Learning and innovation help to preserve cooperation during network re-organization  , and may be key mechanisms promoting the evolution of self-organizing, complex systems.
Revised:  Learning and innovation help to preserve cooperation during the re-organization , and may be key mechanisms promoting the evolution of self-organizing, complex systems.
Edit intent: clarity