wanyu/IteraTeR_v2 huggingface dataset:
Original:  We prove another result in this line of work: The snowflake metric d^{1/2} of a doubling set S \subset l2 can be embedded with arbitrarily low distortion into l ^D2 , for dimension D that depends solely on the doubling constant of the metric.
Revised:  We prove another result in this line of work: The snowflake metric d^{1/2} of a doubling set S \subset l2 can be embedded with arbitrarily low distortion into l _2^D , for dimension D that depends solely on the doubling constant of the metric.
Edit intent: clarity
Original:  Our techniques are robust and extend to the more difficult spaces l1 and l\infty , although the dimension bounds here are quantitatively inferior than those for l2 .
Revised:  Our techniques are robust and extend to the more difficult spaces l_1 and l_\infty , although the dimension bounds here are quantitatively inferior than those for l2 .
Edit intent: fluency
Original:  Our techniques are robust and extend to the more difficult spaces l1 and l\infty , although the dimension bounds here are quantitatively inferior than those for l2 .
Revised:  Our techniques are robust and extend to the more difficult spaces l1 and l\infty , although the dimension bounds here are quantitatively inferior than those for l_2 .
Edit intent: clarity
Original:  We give a deterministic black-box identity testing algorithm for  polynomials of the form j=0^t c_j X^{\alpha_j} (a + b X)^{\beta_j} , and from there we derive a lower bound for representations of univariate polynomials under this form.
Revised:  We give a deterministic black-box identity testing algorithm for univariate polynomials of the form j=0^t c_j X^{\alpha_j} (a + b X)^{\beta_j} , and from there we derive a lower bound for representations of univariate polynomials under this form.
Edit intent: fluency
Original:  Here we report a study on the precision of SMID measurements.
Revised:  Here we report on the analysis of the precision of SMID measurements.
Edit intent: clarity
Original:  This standard deviation error is a function of the total number of detected photons, the background photon noise, and the camera pixel size , and it closely correlates with results of experimentalmeasurements, simulations ,  and numerical integrations . Using this expression, we show that single-molecule standard deviation analysis offers nanometer precision and is on average 1.25 times more precise than centroid analysis under comparable imaging conditions.
Revised:  We have developed an analytical expression for the standard deviation measurement error of a single image which is a function of the total number of detected photons, the background photon noise, and the camera pixel size , and it closely correlates with results of experimentalmeasurements, simulations , and numerical integrations . Using this expression, we show that single-molecule standard deviation analysis offers nanometer precision and is on average 1.25 times more precise than centroid analysis under comparable imaging conditions.
Edit intent: clarity
Original:  This standard deviation error is a function of the total number of detected photons, the background photon noise, and the camera pixel size , and it closely correlates with results of experimentalmeasurements, simulations ,  and numerical integrations . Using this expression, we show that single-molecule standard deviation analysis offers nanometer precision and is on average 1.25 times more precise than centroid analysis under comparable imaging conditions.
Revised:  This standard deviation error is a function of the total number of detected photons, the background photon noise, and the camera pixel size . The theoretical results agree well with the experimental , and numerical integrations . Using this expression, we show that single-molecule standard deviation analysis offers nanometer precision and is on average 1.25 times more precise than centroid analysis under comparable imaging conditions.
Edit intent: clarity
Original:  This standard deviation error is a function of the total number of detected photons, the background photon noise, and the camera pixel size , and it closely correlates with results of experimentalmeasurements, simulations ,  and numerical integrations . Using this expression, we show that single-molecule standard deviation analysis offers nanometer precision and is on average 1.25 times more precise than centroid analysis under comparable imaging conditions.
Revised:  This standard deviation error is a function of the total number of detected photons, the background photon noise, and the camera pixel size , and it closely correlates with results of experimentalmeasurements, simulations , simulation, and numerical integrations . Using this expression, we show that single-molecule standard deviation analysis offers nanometer precision and is on average 1.25 times more precise than centroid analysis under comparable imaging conditions.
Edit intent: fluency
Original:  This standard deviation error is a function of the total number of detected photons, the background photon noise, and the camera pixel size , and it closely correlates with results of experimentalmeasurements, simulations ,  and numerical integrations . Using this expression, we show that single-molecule standard deviation analysis offers nanometer precision and is on average 1.25 times more precise than centroid analysis under comparable imaging conditions.
Revised:  This standard deviation error is a function of the total number of detected photons, the background photon noise, and the camera pixel size , and it closely correlates with results of experimentalmeasurements, simulations , and numerical integration results . Using this expression, we show that single-molecule standard deviation analysis offers nanometer precision and is on average 1.25 times more precise than centroid analysis under comparable imaging conditions.
Edit intent: clarity
Original: We develop a simple theoretical framework for the evolution of weighted network that is consistent with a number of stylized features of real-world data.
Revised: We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data.
Edit intent: fluency
Original:  Our model is verify by means of simulations and real world trade data.
Revised:  Our model is verified by means of simulations and real world trade data.
Edit intent: fluency
Original:  The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such  the sum of the weighted edges, seen as vectors, cancel at every point.
Revised:  The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point.
Edit intent: fluency
Original:  But all the edges are considered  the same in almost all these studies.
Revised:  But all the edges are considered to be the same in almost all these studies.
Edit intent: fluency
Original:  In this paper, we present a simple classification method, which can divide the edges of an undirectedunweighted nework into two types: p2c and p2p.
Revised:  In this paper, we present a simple classification method, which divides the edges of an undirectedunweighted nework into two types: p2c and p2p.
Edit intent: clarity
Original:  In this paper, we present a simple classification method, which can divide the edges of an undirectedunweighted nework into two types: p2c and p2p.
Revised:  In this paper, we present a simple classification method, which can divide the edges of undirected, unweighted networks into two types: p2c and p2p.
Edit intent: fluency
Original:  It is surprising and unexpected that for a wide variety of real-world networks, the p2c degree distribution follows the power law more strictly than the total degree distribution, while the p2p degree distribution follows the Weibull distribution very well.
Revised:  It is surprising and unexpected that for a wide variety of real-world networks, the p2c degree distribution follows a power law more strictly than the total degree distribution, while the p2p degree distribution follows the Weibull distribution very well.
Edit intent: fluency
Original:  Thus, the total degree distribution can be seen as a mixture of the power-law and Weibull distribution.
Revised:  Thus, the total degree distribution can be seen as a mixture of a power-law and Weibull distribution.
Edit intent: fluency
Original:  Our results provide new insight into complex networks and may have potential impact on future studies in this field.
Revised:  Our results provide new insight into complex networks and may impact on future studies in this field.
Edit intent: clarity
Original:  Thus, the total degree distribution can be seen as a mixture of a power-law and Weibull distribution .
Revised:  Thus, the total degree distribution can be seen as a mixture of power-law and Weibull distribution .
Edit intent: fluency
Original: We  report a development of a new fast surface-based method (FSBE) for numerical calculations of  solvation energy of biomolecules with charged groups.
Revised: We report a development of a new fast surface-based method (FSBE) for numerical calculations of the solvation energy of biomolecules with charged groups.
Edit intent: fluency
Original:  The procedure is only a few percent wrong for any molecular configurations of arbitrary sizes, gives explicit value for the reaction field potential at any point , provides both the solvation energy  and its derivatives suitable for Molecular Dynamics (MD) simulations.
Revised:  The procedure is only a few percents wrong for molecular configurations of arbitrary sizes, gives explicit value for the reaction field potential at any point , provides both the solvation energy and its derivatives suitable for Molecular Dynamics (MD) simulations.
Edit intent: fluency
Original:  The procedure is only a few percent wrong for any molecular configurations of arbitrary sizes, gives explicit value for the reaction field potential at any point , provides both the solvation energy  and its derivatives suitable for Molecular Dynamics (MD) simulations.
Revised:  The procedure is only a few percent wrong for any molecular configurations of arbitrary sizes, provides explicit values for the reaction field potential at any point , provides both the solvation energy and its derivatives suitable for Molecular Dynamics (MD) simulations.
Edit intent: clarity
Original:  The procedure is only a few percent wrong for any molecular configurations of arbitrary sizes, gives explicit value for the reaction field potential at any point , provides both the solvation energy  and its derivatives suitable for Molecular Dynamics (MD) simulations.
Revised:  The procedure is only a few percent wrong for any molecular configurations of arbitrary sizes, gives explicit value for the reaction field potential at any point , provides both the solvation energy value and its derivatives suitable for Molecular Dynamics (MD) simulations.
Edit intent: clarity
Original:  The method works well both for large and small molecules and thus gives stable energy differences for quantities such as solvation energies of molecular complex formation.
Revised:  The method works well both for large and small molecules and thus gives stable energy differences for quantities such as solvation energies contributions to a molecular complex formation.
Edit intent: clarity
Original:  Here we extend this approach in several ways, by including the dynamics of both ends , by comparing two possible mechanisms of ATP hydrolysis , and by introducing mass conservation for the monomers .
Revised:  Here we extend this approach in several ways, by including the dynamics of both ends and by comparing two possible mechanisms of ATP hydrolysis , and by introducing mass conservation for the monomers .
Edit intent: coherence
Original:  Here we extend this approach in several ways, by including the dynamics of both ends , by comparing two possible mechanisms of ATP hydrolysis , and by introducing mass conservation for the monomers .
Revised:  Here we extend this approach in several ways, by including the dynamics of both ends , by comparing two possible mechanisms of ATP hydrolysis .
Edit intent: coherence
Original: The empirical evidence that human color categorization exhibits  universal patterns beyond superficial discrepancies across different cultures has been a major breakthrough in the study of cognitive sciences .
Revised: The empirical evidence that human color categorization exhibits some universal patterns beyond superficial discrepancies across different cultures has been a major breakthrough in the study of cognitive sciences .
Edit intent: clarity
Original: The empirical evidence that human color categorization exhibits  universal patterns beyond superficial discrepancies across different cultures has been a major breakthrough in the study of cognitive sciences .
Revised: The empirical evidence that human color categorization exhibits universal patterns beyond superficial discrepancies across different cultures is a major breakthrough in the study of cognitive sciences .
Edit intent: fluency
Original: The empirical evidence that human color categorization exhibits  universal patterns beyond superficial discrepancies across different cultures has been a major breakthrough in the study of cognitive sciences .
Revised: The empirical evidence that human color categorization exhibits universal patterns beyond superficial discrepancies across different cultures has been a major breakthrough in cognitive science .
Edit intent: clarity
Original:  Here  we reproduce the WCS in a numerical model where different populations independently develop their own categorization systems by playing elementary language games.
Revised:  Here , we reproduce the WCS in a numerical model where different populations independently develop their own categorization systems by playing elementary language games.
Edit intent: fluency
Original:  Here  we reproduce the WCS in a numerical model where different populations independently develop their own categorization systems by playing elementary language games.
Revised:  Here we reproduce the WCS in a numerical model in which different populations develop independently their own categorization systems by playing elementary language games.
Edit intent: fluency
Original:  The introduction of a simple perceptive constraint , namely the human Just Noticeable Difference (JND) as a function of wavelength, common to all humans, is sufficient to trigger the emergence of universal patterns , which unconstrained cultural interaction is unable to establish .
Revised:  We find that a simple perceptual constraint shared by all humans , namely the human Just Noticeable Difference (JND) as a function of wavelength, common to all humans, is sufficient to trigger the emergence of universal patterns , which unconstrained cultural interaction is unable to establish .
Edit intent: clarity
Original:  The introduction of a simple perceptive constraint , namely the human Just Noticeable Difference (JND) as a function of wavelength, common to all humans, is sufficient to trigger the emergence of universal patterns , which unconstrained cultural interaction is unable to establish .
Revised:  The introduction of a simple perceptive constraint , namely the human Just Noticeable Difference (JND) , is sufficient to trigger the emergence of universal patterns , which unconstrained cultural interaction is unable to establish .
Edit intent: clarity
Original:  The introduction of a simple perceptive constraint , namely the human Just Noticeable Difference (JND) as a function of wavelength, common to all humans, is sufficient to trigger the emergence of universal patterns , which unconstrained cultural interaction is unable to establish .
Revised:  The introduction of a simple perceptive constraint , namely the human Just Noticeable Difference (JND) as a function of wavelength, common to all humans, is sufficient to trigger the emergence of universal patterns that unconstrained cultural interaction is unable to establish .
Edit intent: fluency
Original:  The introduction of a simple perceptive constraint , namely the human Just Noticeable Difference (JND) as a function of wavelength, common to all humans, is sufficient to trigger the emergence of universal patterns , which unconstrained cultural interaction is unable to establish .
Revised:  The introduction of a simple perceptive constraint , namely the human Just Noticeable Difference (JND) as a function of wavelength, common to all humans, is sufficient to trigger the emergence of universal patterns , which unconstrained cultural interaction fails to produce .
Edit intent: clarity
Original:  We test the outcome of our experiment against real data by performing the same statistical analysis proposed to quantify the universal tendencies present in the WCS [  Proc.
Revised:  We test the results of our experiment against real data by performing the same statistical analysis proposed to quantify the universal tendencies present in the WCS [ Proc.
Edit intent: clarity
Original:  We test the outcome of our experiment against real data by performing the same statistical analysis proposed to quantify the universal tendencies present in the WCS [  Proc.
Revised:  We test the outcome of our experiment against real data by performing the same statistical analysis proposed to quantify the universal tendencies shown in the WCS [ Proc.
Edit intent: clarity
Original:  Sci. USA 100 (15) : 9085-9089 , 2003 ], and find an excellent quantitative agreement.
Revised:  Sci. USA 100 (15) : 9085-9089 ], and find an excellent quantitative agreement.
Edit intent: coherence
Original:  Sci. USA 100 (15) : 9085-9089 , 2003 ], and find an excellent quantitative agreement.
Revised:  Sci. USA 100 (15) : 9085-9089 , 2003 ], and obtain an excellent quantitative agreement.
Edit intent: clarity
Original:  Our work confirms that synthetic modeling has nowadays reached the maturity to contribute effectively to the ongoing debate in cognitive sciences .
Revised:  This work confirms that synthetic modeling has nowadays reached the maturity to contribute effectively to the ongoing debate in cognitive sciences .
Edit intent: fluency
Original:  Our work confirms that synthetic modeling has nowadays reached the maturity to contribute effectively to the ongoing debate in cognitive sciences .
Revised:  Our work confirms that synthetic modeling has nowadays reached the maturity to contribute significantly to the ongoing debate in cognitive sciences .
Edit intent: clarity
Original:  Our work confirms that synthetic modeling has nowadays reached the maturity to contribute effectively to the ongoing debate in cognitive sciences .
Revised:  Our work confirms that synthetic modeling has nowadays reached the maturity to contribute effectively to the ongoing debate in cognitive science .
Edit intent: clarity
Original:  We then demonstrate a very close link between such threshold models and queueing theory, with the largest price changes corresponding to the busy period in a single-server queue.
Revised:  We then demonstrate a close link between such threshold models and queueing theory, with the largest price changes corresponding to the busy period in a single-server queue.
Edit intent: clarity
Original:  We then demonstrate a very close link between such threshold models and queueing theory, with the largest price changes corresponding to the busy period in a single-server queue.
Revised:  We then demonstrate a very close link between such threshold models and queueing theory, with large price changes corresponding to the busy period in a single-server queue.
Edit intent: fluency
Original:  We then demonstrate a very close link between such threshold models and queueing theory, with the largest price changes corresponding to the busy period in a single-server queue.
Revised:  We then demonstrate a very close link between such threshold models and queueing theory, with the largest price changes corresponding to the busy periods of a single-server queue.
Edit intent: clarity
Original:  The distribution of this busy period is known to have excess kurtosis and non-exponential decay under various assumptions on the queue parameters.
Revised:  The distribution of the busy periods is known to have excess kurtosis and non-exponential decay under various assumptions on the queue parameters.
Edit intent: fluency
Original:  Such an approach may also prove useful in the development of mathematical models for rapid deleveraging  in financial markets  and the stress-testing of financial institutions.
Revised:  Such an approach may prove useful in the development of mathematical models for rapid deleveraging in financial markets and the stress-testing of financial institutions.
Edit intent: clarity
Original:  Such an approach may also prove useful in the development of mathematical models for rapid deleveraging  in financial markets  and the stress-testing of financial institutions.
Revised:  Such an approach may also prove useful in the development of mathematical models for rapid deleveraging in financial markets , and the stress-testing of financial institutions.
Edit intent: fluency
Original: We develop a new theory for pricing call type American options in complete markets which do not necessarily admit an equivalent local martingale measure.
Revised: We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure.
Edit intent: clarity
Original:  The frequent appearance of a motif may be an indication of some network-specific utility for that motif, such as speeding up the response times of gene circuits .
Revised:  The frequent appearance of a motif may be an indication of some network-specific functions .
Edit intent: clarity
Original:  However, the precise nature of the connection between motifs and the global structure and function of networks remains unclear .
Revised:  However, the precise nature of the connection between motifs and the global structure and function of networks remains elusive .
Edit intent: clarity
Original:  Here we show that the global structure of some real networks is statistically determined by the distributions of local motifs of size at most 3, once we augment motifs to include node degree information.
Revised:  Here we show that the global structure of some real networks is statistically determined by the probability of connections within motifs of size at most 3, once we augment motifs to include node degree information.
Edit intent: clarity
Original:  In all cases except the power grid, random networks that maintain the degree-enriched connectivity profiles for node triples in the original network reproduce all its local and global properties.
Revised:  In all cases except the power grid, random networks that maintain the degree-enriched connectivity profiles for node triples in these networks capture all their local and global properties.
Edit intent: clarity
Original:  Our results also show that in the presence of remnants microtubule dynamics can be regulated by changing the depolymerisation rate .
Revised:  Under conditions for which this alternative mechanism dominates, an increasing depolymerization rate leads to a decrease in dissociation rate and thus a net increase in assembly .
Edit intent: coherence
Original:  This current is demonstrated to  add directly to the longitudinal current  resulting from an external voltage source, and could be significant in amplifying low-intensity endogenous currents within the cellular environment  .
Revised:  This effect is demonstrated to add directly to the longitudinal current resulting from an external voltage source, and could be significant in amplifying low-intensity endogenous currents within the cellular environment .
Edit intent: clarity