wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our method is implemented and produces cartograms that, while not  perfectly accurate, achieve  the desired areas for many real-world examples.
Revised:  Our method is implemented and produces cartograms that, while not perfectly accurate, achieve many of the desired areas for many real-world examples.
Edit intent: clarity
Original:  Our method is implemented and produces cartograms that, while not  perfectly accurate, achieve  the desired areas for many real-world examples.
Revised:  Our method is implemented and produces cartograms that, while not perfectly accurate, achieve the desired areas in our real-world examples.
Edit intent: clarity
Original: We solve four intertwined problems, motivated by mathematical finance, concerning degenerate-parabolic partial differential operators and degenerate diffusion processes.
Revised: Motivated by applications to probability and mathematical finance, concerning degenerate-parabolic partial differential operators and degenerate diffusion processes.
Edit intent: clarity
Original:  This study examines the effectiveness of several HMA overlay mix design strategies for the purpose of controlling the development of reflective cracking.
Revised:  This study examines the effectiveness of HMA overlay design strategies for the purpose of controlling the development of reflective cracking.
Edit intent: clarity
Original:  A parametric study was conducted using a 3D Finite Element (FE) model of a rigid pavement section including a Linear Viscoelastic (LVE) model for Hot Mix Asphalt (HMA) materials and non-uniform tire-pavement contact stresses.
Revised:  A parametric study was conducted using a 3D Finite Element (FE) model of a rigid pavement section including Linear Viscoelastic (LVE) model for Hot Mix Asphalt (HMA) materials and non-uniform tire-pavement contact stresses.
Edit intent: fluency
Original:  A parametric study was conducted using a 3D Finite Element (FE) model of a rigid pavement section including a Linear Viscoelastic (LVE) model for Hot Mix Asphalt (HMA) materials and non-uniform tire-pavement contact stresses.
Revised:  A parametric study was conducted using a 3D Finite Element (FE) model of a rigid pavement section including a Linear Viscoelastic (LVE) material properties for the Hot Mix Asphalt (HMA) materials and non-uniform tire-pavement contact stresses.
Edit intent: clarity
Original:  A parametric study was conducted using a 3D Finite Element (FE) model of a rigid pavement section including a Linear Viscoelastic (LVE) model for Hot Mix Asphalt (HMA) materials and non-uniform tire-pavement contact stresses.
Revised:  A parametric study was conducted using a 3D Finite Element (FE) model of a rigid pavement section including a Linear Viscoelastic (LVE) model for Hot Mix Asphalt (HMA) overlay and non-uniform tire-pavement contact stresses.
Edit intent: clarity
Original:  As compared to the SB mix, the use of PM asphalt mixture in the leveling course reduced the level of longitudinal tensile stresses at the bottom of the HMA overlay above the PCC joint by approximately 30\%.
Revised:  As compared to the SB mix, the use of PM asphalt mixture in the leveling course reduced the level of longitudinal tensile stress at the bottom of the HMA overlay above the PCC joint by approximately 30\%.
Edit intent: fluency
Original:  Shortly after, it was proven that the languages enerated by (finite) splicing systems form a proper subclass of the class of regular languages.
Revised:  Shortly after, it was proven that the languages generated by (finite) splicing systems form a proper subclass of the class of regular languages.
Edit intent: fluency
Original:  We namely prove that  if a language is generated by a splicing system, then it is also generated by a splicing system whose size is a function of the size of the syntactic monoid of the input language, and which can be effectively constructed.
Revised:  We namely prove that , if a language is generated by a splicing system, then it is also generated by a splicing system whose size is a function of the size of the syntactic monoid of the input language, and which can be effectively constructed.
Edit intent: fluency
Original:  Shortly after , it was proven that the languages generated by (finite) splicing systems form a proper subclass of the class of regular languages.
Revised:  Shortly thereafter , it was proven that the languages generated by (finite) splicing systems form a proper subclass of the class of regular languages.
Edit intent: fluency
Original:  We namely prove that, if a language is generated by a splicing system, then it is also generated by a splicing system whose size is a function of the size of the syntactic monoid of the input language, and which can be effectively constructed.
Revised:  Namely, we prove that, if a language is generated by a splicing system, then it is also generated by a splicing system whose size is a function of the size of the syntactic monoid of the input language, and which can be effectively constructed.
Edit intent: coherence
Original:  It  also found that the finite fluid domain has a significant impact on the behaviour of the wave run-up.
Revised:  It is also found that the finite fluid domain has a significant impact on the behaviour of the wave run-up.
Edit intent: coherence
Original:  It  also found that the finite fluid domain has a significant impact on the behaviour of the wave run-up.
Revised:  It also found that the finite fluid domain has a significant impact on the behavior of the wave run-up.
Edit intent: fluency
Original:  We investi- gate the impact of recurrent partial sweeps on levels of neutral diversity, and show that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequency reached by these partial sweeps.
Revised:  We investigate the impact of recurrent partial sweeps on levels of neutral diversity, and show that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequency reached by these partial sweeps.
Edit intent: fluency
Original:  This general- ized model goes some way towards providing a more flexible framework to describe genomic patterns of diversity.
Revised:  This generalized model goes some way towards providing a more flexible framework to describe genomic patterns of diversity.
Edit intent: fluency
Original: Two major sources of stochasticity in the dynamics of neutral alleles result from the sampling due to finite population size (genetic drift) and the ran- dom genetic background of  selected alleles on which  neutral alleles are found (linked selection).
Revised: Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the ran- dom genetic background of selected alleles on which neutral alleles are found (linked selection).
Edit intent: clarity
Original: Two major sources of stochasticity in the dynamics of neutral alleles result from the sampling due to finite population size (genetic drift) and the ran- dom genetic background of  selected alleles on which  neutral alleles are found (linked selection).
Revised: Two major sources of stochasticity in the dynamics of neutral alleles result from the sampling due to finite population size (genetic drift) and the random genetic background of selected alleles on which neutral alleles are found (linked selection).
Edit intent: fluency
Original: Two major sources of stochasticity in the dynamics of neutral alleles result from the sampling due to finite population size (genetic drift) and the ran- dom genetic background of  selected alleles on which  neutral alleles are found (linked selection).
Revised: Two major sources of stochasticity in the dynamics of neutral alleles result from the sampling due to finite population size (genetic drift) and the ran- dom genetic background of selected alleles on which the neutral alleles are found (linked selection).
Edit intent: fluency
Original:  However, the bulk of selected alleles that sweep into the population may not be destined for rapid fixation in the species .
Revised:  However, the bulk of selected alleles that sweep into the population may not be destined for rapid fixation .
Edit intent: clarity
Original:  We investigate the impact of recurrent partial sweeps on levels of neutral diversity, and show that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequency reached by these partial sweeps.
Revised:  We investigate the impact of recurrent partial sweeps on levels of neutral diversity, and find that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequency reached by these partial sweeps.
Edit intent: clarity
Original:  Indeed we show that in the limit of a high rate of sweeps to low frequency , the resulting coalescent model is identical to the standard neutral model.
Revised:  In fact, the limiting coalescent model under a high rate of sweeps to low frequency , the resulting coalescent model is identical to the standard neutral model.
Edit intent: clarity
Original:  Indeed we show that in the limit of a high rate of sweeps to low frequency , the resulting coalescent model is identical to the standard neutral model.
Revised:  Indeed we show that in the limit of a high rate of sweeps to low frequency is identical to the standard neutral model.
Edit intent: clarity
Original: This paper studies the possibility of introducing parallelism into Cylindrical Algebraic Decomposition (CAD)  . CAD is the most elaborate way to perform Quantifier Elimination over real closed fields.
Revised: In this paper we propose a parallel approach to quantifier elimination on real closed fields through a modification in the cylindrical algebraic decomposition (CAD) . CAD is the most elaborate way to perform Quantifier Elimination over real closed fields.
Edit intent: clarity
Original:  When the labels of vertices of these graphs are unavailable, graph matching (GM)---the process of determining which permutation assigns vertices of one graph to those of another---is a computationally daunting problem.
Revised:  When the labels of vertices of these graphs are unavailable, graph matching (GM)---the process of finding an optimal permutation of the vertices of one graph to those of another---is a computationally daunting problem.
Edit intent: clarity
Original:  This work presents an inexact strategy for GM . Specifically, we frame GM as a quadratic assignment problem, and then relax the feasible region to its convex hull.
Revised:  This work presents an inexact strategy for GM can be formulated as a quadratic assignment problem, and then relax the feasible region to its convex hull.
Edit intent: clarity
Original:  Performance exceeds the previous state-of-the-art in all of 16 benchmark tests .
Revised:  Performance exceeds the previous state-of-the-art on nearly all benchmarks .
Edit intent: clarity
Original: Graph matching (GM) ---the process of finding an optimal permutation of the vertices of one graph to minimize adjacency disagreements with the vertices of another---is rapidly becoming an increasingly important computational problem, arising in fields ranging from machine vision to chemical engineering to neuroscience.
Revised: Graph matching (GM) - the process of finding an optimal permutation of the vertices of one graph to minimize adjacency disagreements with the vertices of another---is rapidly becoming an increasingly important computational problem, arising in fields ranging from machine vision to chemical engineering to neuroscience.
Edit intent: fluency
Original: Graph matching (GM) ---the process of finding an optimal permutation of the vertices of one graph to minimize adjacency disagreements with the vertices of another---is rapidly becoming an increasingly important computational problem, arising in fields ranging from machine vision to chemical engineering to neuroscience.
Revised: Graph matching (GM) ---the process of finding an optimal permutation of the vertices of one graph to minimize adjacency disagreements with the vertices of another - is rapidly becoming an increasingly important computational problem, arising in fields ranging from machine vision to chemical engineering to neuroscience.
Edit intent: fluency
Original: Graph matching (GM) ---the process of finding an optimal permutation of the vertices of one graph to minimize adjacency disagreements with the vertices of another---is rapidly becoming an increasingly important computational problem, arising in fields ranging from machine vision to chemical engineering to neuroscience.
Revised: Graph matching (GM) ---the process of finding an optimal permutation of the vertices of one graph to minimize adjacency disagreements with the vertices of another---is rapidly becoming an increasingly important computational problem, arising in fields ranging from machine vision to neuroscience.
Edit intent: clarity
Original:  We develop a fast approximate quadratic  (FAQ) assignment algorithm to approximately solve a relaxed quadratic program with only linear constraints . FAQ scales cubicly with the number of vertices, and demonstrates marked improvements over previous state-of-the-art on nearly all benchmarks .
Revised:  We develop a fast approximate quadratic (FAQ) . FAQ scales cubicly with the number of vertices, and demonstrates marked improvements over previous state-of-the-art on nearly all benchmarks .
Edit intent: clarity
Original:  Unfortunately, the computational complexity of FAQ scales too poorly to use it for mammalian brain-graphs, with millions or billions of vertices.
Revised:  Unfortunately, the computational complexity of FAQ to be able to match mammalian brain-graphs, with millions or billions of vertices.
Edit intent: clarity
Original:  To inspire further development of approximate solutions to these problems, this work is available from on the first author's website, URL
Edit intent: coherence
Original:  Because GM is NP-hard, exact algorithms are unsuitable for today's large graphs (with >1000 vertices) .
Revised:  Because GM is NP-hard, exact algorithms are intractable .
Edit intent: clarity
Original:  Approximate algorithms necessarily employ a accuracy/efficiency trade-off.
Revised:  Approximate algorithms necessarily employ an accuracy/efficiency trade-off.
Edit intent: fluency
Original: Cre-Lox system is used as a genetic tool to control site specific recombination events in genomic DNA.
Revised: Cre-lox and other systems are used as genetic tools to control site-specific recombination (SSR) events in genomic DNA.
Edit intent: clarity
Original:  If multiple recombination sites are organized in a compact cluster within the same genome, a series of stochastic recombination events may generate substantial cell specific genomic diversity.
Revised:  If multiple recombination sites are organized in a compact cluster within the same genome, a series of random recombination events may generate substantial cell specific genomic diversity.
Edit intent: clarity
Original:  Both of these events are available in the Cre-Lox system.
Revised:  Both of these events are available in the Cre-lox system.
Edit intent: fluency
Original:  In this paper, we further develop a mathematical model of bone cell interactions by Pivonka et al. (2008) by introducing proliferation of precursor osteoblasts into the model , and then quantify the anabolic response of boneunder different rates of proliferation to calibrate the new model .
Revised:  In this paper, we further develop a mathematical model of bone cell interactions by Pivonka et al. (2008) to include the proliferation of precursor osteoblasts into the model , and then quantify the anabolic response of boneunder different rates of proliferation to calibrate the new model .
Edit intent: clarity
Original:  However, modelling these different processes separately enables the new model to represent recent experimental discoveries such as the role of Wnt signalling in bone biology and the recruitment of osteoblast progenitor cells by transforming growth factor \beta .
Revised:  However, modelling these different processes separately enables the new model to represent recent experimental discoveries such as the role of Wnt signalling in bone biology and the recruitment of osteoblast progenitor cells by transforming growth factor \beta .
Edit intent: fluency
Original:  We demonstrate that the new computational model developed here is capable of capturing some key observations made on the evolution of the bone mass due to metastasis of prostate cancer to the bone microenvironment .
Revised:  We demonstrate that the new computational model developed here is capable of capturing some key observations made on the evolution of the bone mass due to metastasis of prostate cancer to the bone microenvironment 
Edit intent: fluency
Original:  A decision effect is any consequence of putting a decision outcome into effect .
Revised:  Decision outcomes are seen by an audience and autonomous actions from the audience is supposed to realize the putting into effect of a decision outcome into effect .
Edit intent: clarity
Original:  A decision effect is any consequence of putting a decision outcome into effect .
Revised:  A decision effect is any consequence of putting a decision outcome , thus leading to so-called decision effects .
Edit intent: clarity
Original:  Decision outcomes must be expected by the decider to lead to certain decision effects, by way of their being put into effect.
Revised:  Decision outcomes are supposedly expected by the decider to lead to certain decision effects, by way of their being put into effect.
Edit intent: clarity
Original:  The availability of a model or of a theory of the causal chain leading from a decision outcome to one or more decision effects is assumed for the decision taker , otherwise the decision outcome is merely an utterance.
Revised:  The availability of a model or a theory concerning the causal chain leading from a decision outcome to one or more decision effects is assumed for the decision taker , otherwise the decision outcome is merely an utterance.
Edit intent: clarity
Original:  Decision taking is positioned amidst many similar notions including: decision making, decision process, decision making process, decision process making, decision engineering, decision progression, and decision progression production .
Revised:  Decision taking is positioned amidst many related notions including: decision making, decision process, decision making process, decision process making, decision engineering, decision progression, and decision progression production .
Edit intent: fluency
Original: We show the border rank of the matrix multiplication operator for n by n matrices has growth at least like (2-c)n^2as n goes to infinity, for all c>0.
Revised: The border rank of the matrix multiplication operator for n by n matrices has growth at least like (2-c)n^2as n goes to infinity, for all c>0.
Edit intent: clarity
Original:  We give an explicit lower bound as a function of n that beats the previous lower bound (due to Lickteig in 1985) of 3/2 n^2+ n/ 2-1 for all n greater than 2. 
Revised:  We give an explicit lower bound as a function of n that beats the previous lower bound (due to Lickteig in 1985) of 3/2 n^2+ n/ 2 -1 for all n greater than 2. 
Edit intent: fluency
Original:  We give an explicit lower bound as a function of n that beats the previous lower bound (due to Lickteig in 1985) of 3/2 n^2+ n/ 2-1 for all n greater than 2. 
Revised:  We give an explicit lower bound as a function of n that beats the previous lower bound (due to Lickteig in 1985) of 3/2 n^2+ n/ 2-1 for all n > 2. 
Edit intent: clarity
Original:  This is an affirmative answer to the question of Hoyer and Spalek and implies that QNC^0_f=QAC^0_f in contrast to the fact that NC^0 \subsetneq AC^0 , where \subsetneq  QNC^0_f and QAC^0_f are the quantum circuit complexity classes corresponding to the classical ones NC^0and AC^0, respectively.
Revised:  This is an affirmative answer to the question of Hoyer and Spalek . In sharp contrast to the fact that NC^0 \subsetneq AC^0 , where \subsetneq QNC^0_f and QAC^0_f are the quantum circuit complexity classes corresponding to the classical ones NC^0and AC^0, respectively.
Edit intent: clarity
Original:  This is an affirmative answer to the question of Hoyer and Spalek and implies that QNC^0_f=QAC^0_f in contrast to the fact that NC^0 \subsetneq AC^0 , where \subsetneq  QNC^0_f and QAC^0_f are the quantum circuit complexity classes corresponding to the classical ones NC^0and AC^0, respectively.
Revised:  This is an affirmative answer to the question of Hoyer and Spalek and implies that QNC^0_f=QAC^0_f in contrast to the fact that NC^0 \subsetneq AC^0 \subsetneq QNC^0_f and QAC^0_f are the quantum circuit complexity classes corresponding to the classical ones NC^0and AC^0, respectively.
Edit intent: coherence
Original:  We also show that there exists an O(1)-depth small-size quantum circuit for the threshold function on n bits with a threshold 1 \leq t \leq n, where the size is O(n log n) when t is close to 1 or n, and it is O(n sqrt n log n%DIFDELCMD < }%%% ) when t is around n/2.
Revised:  We also show that there exists an O(1)-depth small-size quantum circuit for the n log n%DIFDELCMD < }%%% ) when t is around n/2.
Edit intent: clarity
Original:  We also show that there exists an O(1)-depth small-size quantum circuit for the threshold function on n bits with a threshold 1 \leq t \leq n, where the size is O(n log n) when t is close to 1 or n, and it is O(n sqrt n log n%DIFDELCMD < }%%% ) when t is around n/2.
Revised:  We also show that there exists an O(1)-depth small-size quantum circuit for the threshold function on n bits with a threshold 1 \leq t \leq n, where the size is O(n log n) when t is close to 1 or n, and it is O(n sqrt %DIFDELCMD < }%%% ) when t is around n/2.
Edit intent: fluency
Original:  We find that the probability density function (PDF) of relative price levels where cancellations allocate obeys the log-normal distribution.
Revised:  We find that the profiles of relative price levels where cancellations allocate obeys the log-normal distribution.
Edit intent: clarity
Original:  We find that the probability density function (PDF) of relative price levels where cancellations allocate obeys the log-normal distribution.
Revised:  We find that the probability density function (PDF) of relative price levels where cancellations occur obey a log-normal distribution.
Edit intent: clarity
Original:  We then analyze the PDF of normalized relative price levels by removing the factor of order numbers stored at the price level, and find that the PDF has a power-law behavior in the tails for both buy and sell orders.
Revised:  After normalizing the relative price level by removing the factor of order numbers stored at the price level, and find that the PDF has a power-law behavior in the tails for both buy and sell orders.
Edit intent: clarity
Original:  In addtion, the PDF of cancellation positions can be fitted by the exponent function for both buy and sell orders  .
Revised:  In addtion, the PDF of cancellation positions can be fitted by an exponent function for both buy and sell orders .
Edit intent: fluency
Original:  they take turns in moving to adjacent vertices (or staying), cops inside the guarded region, the robber on the remaining vertices (the robber-region).
Revised:  they take turns in moving to adjacent vertices (or staying), cops inside the guarded region, Robber on the remaining vertices (the robber-region).
Edit intent: fluency
Original:  The goal of the robber is to enter the guarded region at a vertex with no cop on it.
Revised:  The goal of Robber is to enter the guarded region at a vertex with no cop on it.
Edit intent: fluency