wanyu/IteraTeR_v2 huggingface dataset:
Original:  In contrast to existing methods, our model uses no additional information or resources about the task or language (e.g., parsers or seed lexicons) and still achieves the best results reported to-date on a benchmark single-sentence dataset and gives competitive results for the limited-training multi-sentence setting.
Revised:  In contrast to existing methods, our model uses no additional information or resources about the task or language (e.g., parsers or seed lexicons) and still achieves the best results reported to-date on a benchmark single-sentence dataset and competitive results for the limited-training multi-sentence setting.
Edit intent: clarity
Original:  We evaluate our model through a series of ablation studies that elucidate the contributions of the primary components of our model.
Revised:  We analyze our model through a series of ablation studies that elucidate the contributions of the primary components of our model.
Edit intent: clarity
Original:  We evaluate our model through a series of ablation studies that elucidate the contributions of the primary components of our model.
Revised:  We evaluate our model through a series of ablations that elucidate the contributions of the primary components of our model.
Edit intent: clarity
Original:  These include column planarity, universal point subsets, and partial simultaneous geomet- ric embeddings (with or without mappings).
Revised:  These include column planarity, universal point subsets, and partial simultaneous geometric embeddings (with or without mappings).
Edit intent: fluency
Original:  This extends the corresponding complexity result for  and-or precedence constraints aka the max-atoms problem.
Revised:  This extends the corresponding complexity result for and-or precedence constraints , or equivalently the max-atoms problem.
Edit intent: clarity
Original:  The model alleviates two shortcomings that  current models of growing multiplex networks suffer from: homogeneity (rate of link creation is the same for all layers) and independence (layers grow independent of one another) .
Revised:  The model alleviates two shortcomings that are present in the current models of growing multiplex networks suffer from: homogeneity (rate of link creation is the same for all layers) and independence (layers grow independent of one another) .
Edit intent: clarity
Original:  The model alleviates two shortcomings that  current models of growing multiplex networks suffer from: homogeneity (rate of link creation is the same for all layers) and independence (layers grow independent of one another) .
Revised:  The model alleviates two shortcomings that current models of growing multiplex networks : homogeneity of connections, and homogeneity of fitness .
Edit intent: clarity
Original:  In this paper, we posit and analyze a growth model that is heterogeneous and coupled .
Revised:  In this paper, we posit and analyze a growth model that is heterogeneous in both senses .
Edit intent: clarity
Original:  Casts can be integrated with the implicit coercion mechanism of Coq to support implicit cast insertion \`a la gradual typing.
Revised:  Casts can be integrated with the implicit coercion mechanism of Coq to support implicit cast insertion a la gradual typing.
Edit intent: fluency
Original: We consider relations between the size, treewidth, and local crossing number (maximum  crossings per edge) of graphs embedded on topological surfaces.
Revised: We consider relations between the size, treewidth, and local crossing number (maximum number of crossings per edge) of graphs embedded on topological surfaces.
Edit intent: clarity
Original:  Additionally , we show that for g<m, every m-edge graph can be embedded on a surface of genus  g with O((m/ g )\log^2 g) crossings per edge, which is tight to within a polylogarithmic factor.
Revised:  Additionally , we show that for g<m, every m-edge graph can be embedded on a surface of genus g with O((m/ g )\log^2 g) crossings per edge, which is tight to a polylogarithmic factor.
Edit intent: clarity
Original: We make use of ideas from the theory of complex networks to implement a machine learning classification of human DNA methylation data . DNA methylation patterns are known to be modified due to cancer development.
Revised: We make use of ideas from the theory of complex networks to implement a machine learning classification of human DNA methylation data , that carry signatures of cancer development.
Edit intent: clarity
Original:  Data obtained from patients with various kinds of cancers are represented as parenclictic networks, in which nodes correspond to genes, and edges are weighted according to pairwise variation from control group subjects.
Revised:  The data were obtained from patients with various kinds of cancers are represented as parenclictic networks, in which nodes correspond to genes, and edges are weighted according to pairwise variation from control group subjects.
Edit intent: clarity
Original:  Data obtained from patients with various kinds of cancers are represented as parenclictic networks, in which nodes correspond to genes, and edges are weighted according to pairwise variation from control group subjects.
Revised:  Data obtained from patients with various kinds of cancers and represented as parenclictic networks, in which nodes correspond to genes, and edges are weighted according to pairwise variation from control group subjects.
Edit intent: coherence
Original:  Data obtained from patients with various kinds of cancers are represented as parenclictic networks, in which nodes correspond to genes, and edges are weighted according to pairwise variation from control group subjects.
Revised:  Data obtained from patients with various kinds of cancers are represented as parenclictic networks, wherein nodes correspond to genes, and edges are weighted according to pairwise variation from control group subjects.
Edit intent: clarity
Original:  We demonstrate that for 12 out of the 14 types of cancer we studied , it is possible to obtain  high performance of binary classification between cancer-positive and negative samples based on network measures.
Revised:  We demonstrate that for 12 out of the 14 types of cancer under study , it is possible to obtain high performance of binary classification between cancer-positive and negative samples based on network measures.
Edit intent: clarity
Original:  We demonstrate that for 12 out of the 14 types of cancer we studied , it is possible to obtain  high performance of binary classification between cancer-positive and negative samples based on network measures.
Revised:  We demonstrate that for 12 out of the 14 types of cancer we studied , it is possible to obtain a high performance of binary classification between cancer-positive and negative samples based on network measures.
Edit intent: fluency
Original:  Remarkably, an accuracy as high as 90-100 \\%DIF < is achieved with only 12 network topology indices, in a dramatic %DIF > is achieved with only  reduction of complexity from the original 15295 gene methylation levels.
Revised:  Remarkably, an accuracy as high as 90-100 \\%DIF < is achieved with only 12 network topology indices, in a dramatic %DIF > is achieved with only 12 network topology indices, in a dramatic reduction of complexity from the original 15295 gene methylation levels.
Edit intent: fluency
Original:  Moreover, it was found that the parenclictic networks are scale-free in norm, and do not follow a power-law distribution for these 12 cancertypes.
Revised:  Moreover, it was found that the parenclictic networks are scale-free in cancer-negative subjects, and deviate from the power-law distribution for these 12 cancertypes.
Edit intent: clarity
Original:  The obtained node centrality ranking and the modular structure which arises could provide insights into  systems biology of cancer.
Revised:  The obtained node centrality ranking and arising modular structure could provide insights into systems biology of cancer.
Edit intent: clarity
Original:  The obtained node centrality ranking and the modular structure which arises could provide insights into  systems biology of cancer.
Revised:  The obtained node centrality ranking and the modular structure which arises could provide insights into the systems biology of cancer.
Edit intent: fluency
Original: The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1957, A. A. Markov determined the inversion complexity of every Boolean function and particularly proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) ~--- maximum value changes from 1 to 0 over all increasing chains of tuples  ).
Revised: The minimum number of NOT gates in a Boolean circuit computing a Boolean function is called the inversion complexity of f . In 1957, A. A. Markov determined the inversion complexity of every Boolean function and particularly proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) ~--- maximum value changes from 1 to 0 over all increasing chains of tuples ).
Edit intent: fluency
Original: The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1957, A. A. Markov determined the inversion complexity of every Boolean function and particularly proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) ~--- maximum value changes from 1 to 0 over all increasing chains of tuples  ).
Revised: The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of the function . In 1957, A. A. Markov determined the inversion complexity of every Boolean function and particularly proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) ~--- maximum value changes from 1 to 0 over all increasing chains of tuples ).
Edit intent: clarity
Original: The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1957, A. A. Markov determined the inversion complexity of every Boolean function and particularly proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) ~--- maximum value changes from 1 to 0 over all increasing chains of tuples  ).
Revised: The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) ~--- maximum value changes from 1 to 0 over all increasing chains of tuples ).
Edit intent: coherence
Original: The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1957, A. A. Markov determined the inversion complexity of every Boolean function and particularly proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) ~--- maximum value changes from 1 to 0 over all increasing chains of tuples  ).
Revised: The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1957, A. A. Markov determined the inversion complexity of every Boolean function and particularly proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) is maximum number of value changes from 1 to 0 over all increasing chains of tuples ).
Edit intent: clarity
Original:  In this note, we consider circuits over arbitrary basis that consist of all monotone functions (with zero weight) and finite nonempty set of nonmonotone functions (with unit weight).
Revised:  In this note, we consider circuits over arbitrary basis that consists of all monotone functions (with zero weight) and finite nonempty set of nonmonotone functions (with unit weight).
Edit intent: fluency
Original:  In this note, we consider circuits over arbitrary basis that consist of all monotone functions (with zero weight) and finite nonempty set of nonmonotone functions (with unit weight).
Revised:  In this note, we consider circuits over arbitrary basis that consist of all monotone functions (with zero weight) and finite nonempty set of non-monotone functions (with unit weight).
Edit intent: fluency
Original:  It was shown that minimal sufficient for  Boolean function f realization number of nonmonotone elements is equal to \lceil\log_{2}(d(f)+1)\rceil - O(1).
Revised:  It is shown that the minimal sufficient for Boolean function f realization number of nonmonotone elements is equal to \lceil\log_{2}(d(f)+1)\rceil - O(1).
Edit intent: fluency
Original:  It was shown that minimal sufficient for  Boolean function f realization number of nonmonotone elements is equal to \lceil\log_{2}(d(f)+1)\rceil - O(1).
Revised:  It was shown that minimal sufficient for a realization of the Boolean function f realization number of nonmonotone elements is equal to \lceil\log_{2}(d(f)+1)\rceil - O(1).
Edit intent: clarity
Original:  It was shown that minimal sufficient for  Boolean function f realization number of nonmonotone elements is equal to \lceil\log_{2}(d(f)+1)\rceil - O(1).
Revised:  It was shown that minimal sufficient for Boolean function f number of non-monotone gates is equal to \lceil\log_{2}(d(f)+1)\rceil - O(1).
Edit intent: clarity
Original:  Similar extends of a classical result of A. A. Markov for  inversion complexity of system of Boolean functions has been obtained.
Revised:  Similar extends of another classical result of A. A. Markov for inversion complexity of system of Boolean functions has been obtained.
Edit intent: clarity
Original:  Similar extends of a classical result of A. A. Markov for  inversion complexity of system of Boolean functions has been obtained.
Revised:  Similar extends of a classical result of A. A. Markov for the inversion complexity of system of Boolean functions has been obtained.
Edit intent: fluency
Original: In real societies individuals are constantly subject to external stimuli, such as peer and media pressure, which often have a substantial impact on the formation of their opinions . Normally, in a social system , each agent interacts with other agents on different topics , such as politics, religion, economy, and is subject to the pressure of exogenous forces, including mass media.
Revised: The formation of agents' opinions in a social system , each agent interacts with other agents on different topics , such as politics, religion, economy, and is subject to the pressure of exogenous forces, including mass media.
Edit intent: clarity
Original:  Here we propose a simple model in which coherent agents , interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhoods, and are at the same time subject to external fields which play the role of mass media pressure .
Revised:  Here we propose a model in which coherent agents , interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhoods, and are at the same time subject to external fields which play the role of mass media pressure .
Edit intent: clarity
Original:  Here we propose a simple model in which coherent agents , interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhoods, and are at the same time subject to external fields which play the role of mass media pressure .
Revised:  Here we propose a simple model in which coherent agents , interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhoods, and are at the same time subject to external fields , resembling the pressure of mass media pressure .
Edit intent: clarity
Original:  Here we propose a simple model in which coherent agents , interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhoods, and are at the same time subject to external fields which play the role of mass media pressure .
Revised:  Here we propose a simple model in which coherent agents , interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhoods, and are at the same time subject to external fields which play the role of mass media .
Edit intent: clarity
Original:  We show that the presence of heterogeneity in the relative weight assigned by agents to social pressure and internal coherence allows to obtain a rich variety of consensuspatterns.
Revised:  We show that the presence of heterogeneity in the internal coupling assigned by agents to social pressure and internal coherence allows to obtain a rich variety of consensuspatterns.
Edit intent: clarity
Original:  In particular , we show that the introduction of thermal noise qualitatively preserves all the observed features  up to a critical temperature, after which global consensus in not attainableany more.
Revised:  In particular , we show that all the observed features up to a critical temperature, after which global consensus in not attainableany more.
Edit intent: clarity
Original:  This model demonstrates also how mass media can be effectively used to favour the propagation of a chosen opinion , thus polarising the consensus of an entire population.
Revised:  This model demonstrates also how mass media can be effectively used to favour the propagation of a chosen set of opinions , thus polarising the consensus of an entire population.
Edit intent: clarity
Original: We present a detailed and easily accessible proof of Gromov's Topological Overlap Theorem : Let X is a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension \dim X= d.
Revised: We give a detailed and easily accessible proof of Gromov's Topological Overlap Theorem : Let X is a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension \dim X= d.
Edit intent: clarity
Original: We present a detailed and easily accessible proof of Gromov's Topological Overlap Theorem : Let X is a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension \dim X= d.
Revised: We present a detailed and easily accessible proof of Gromov's : Let X is a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension \dim X= d.
Edit intent: coherence
Original: We present a detailed and easily accessible proof of Gromov's Topological Overlap Theorem : Let X is a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension \dim X= d.
Revised: We present a detailed and easily accessible proof of Gromov's Topological Overlap Theorem Topological Overlap Theorem. Let X be a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension \dim X= d.
Edit intent: fluency
Original: We present a detailed and easily accessible proof of Gromov's Topological Overlap Theorem : Let X is a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension \dim X= d.
Revised: We present a detailed and easily accessible proof of Gromov's Topological Overlap Theorem : Let X is a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension d.
Edit intent: clarity
Original:  Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are  terms of cellular cochains of X) then X has the following topological overlap property : for every continuous map X\rightarrow R ^d there exists a point p\in R^d whose preimage meets a positive fraction \mu>0 of the d-cells of X.
Revised:  Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are terms of cellular cochains of X) then X has the following topological overlap property : for every continuous map X\rightarrow R ^d there exists a point p\in R^d whose preimage meets a positive fraction \mu>0 of the d-cells of X.
Edit intent: fluency
Original:  Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are  terms of cellular cochains of X) then X has the following topological overlap property : for every continuous map X\rightarrow R ^d there exists a point p\in R^d whose preimage meets a positive fraction \mu>0 of the d-cells of X.
Revised:  Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are defined in terms of cellular cochains of X) then X has the following topological overlap property : for every continuous map X\rightarrow R ^d there exists a point p\in R^d whose preimage meets a positive fraction \mu>0 of the d-cells of X.
Edit intent: clarity
Original: Reaction-diffusion systems involving a large number of unknowns and a wide spectrum of scales in space and time model various phenomena across disciplines such as combustion dynamics, atmospheric science, or biomedical engineering.
Revised: Reaction-diffusion systems involving a large number of unknowns and a wide spectrum of scales in space and time model various complex phenomena across different disciplines such as combustion dynamics, atmospheric science, or biomedical engineering.
Edit intent: clarity
Original:  A new generation of techniques featuring adaptation in space and time as well as error control has been introduced recently  . Based on operator splitting, finite volume adaptive multiresolution  and high order time integrators with specific stability properties for each operator, these methods yield a high computational efficiency for stiff reaction-diffusion problems  .
Revised:  A new generation of techniques featuring adaptation in space and time as well as error control has been introduced recently . Based on operator splitting, finite volume adaptive multiresolution , and high order time integrators with specific stability properties for each operator, these methods yield a high computational efficiency for stiff reaction-diffusion problems .
Edit intent: fluency
Original:  yielding accurate solutions to such complex models while considering the entire spectrum of scales . Based on operator splitting, finite volume adaptive multiresolution , and high order time integrators with specific stability properties for each operator, these methods yield a high computational efficiency for stiff reaction-diffusion problems and were specifically designed to carry out large multidimensional simulations on standard architectures such as powerful workstations.
Revised:  yielding accurate solutions to such complex models while considering the entire spectrum of scales . Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, these methods yield a high computational efficiency for stiff reaction-diffusion problems and were specifically designed to carry out large multidimensional simulations on standard architectures such as powerful workstations.
Edit intent: fluency