wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Finally, a numerical study is done based on P_1-finite element approximation for space discretization and implicit Euler scheme for time discretization , where we study the stability of the scheme, analysis of the error and obtained some numerical simulations  .
Revised:  Finally, a numerical study is done based on P_1-finite element approximation for space discretization and implicit Euler scheme for time discretization , where we study the stability of the scheme, analysis of the error and obtained some numerical simulations are presented .
Edit intent: meaning-changed
Original: The structures, including technologies, industries, infrastructure and institutions, in a country have three attributes , namely, structurality, durationality, and transformality .
Revised: This paper proposes a framework to model how a country develops its economy by endogenous structural transformation and efficient resource allocation in a market mechanism. To achieve this goal, the paper first summarizes three attributes of economic structures from the literature , namely, structurality, durationality, and transformality .
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Original: The structures, including technologies, industries, infrastructure and institutions, in a country have three attributes , namely, structurality, durationality, and transformality . The paper proposes a novel method to model the structural transformation in a market economy. With the common knowledge assumption, the paper proposes a generic model combining optimal control and optimal switching to study the static equilibrium and dynamic equilibrium of resource allocations under a given industrial structureand the equilibrium when the condition for transforming industrial structures arises by a social planner to maximize the representative household's utility in a market economy .
Revised: The structures, including technologies, industries, infrastructure and institutions, in a country have three attributes , namely, structurality, durationality, and transformality , and discuss their implications for methods of economic modeling. Then, with the common knowledge assumption, the paper proposes a generic model combining optimal control and optimal switching to study the static equilibrium and dynamic equilibrium of resource allocations under a given industrial structureand the equilibrium when the condition for transforming industrial structures arises by a social planner to maximize the representative household's utility in a market economy .
Edit intent: coherence
Original:  With the common knowledge assumption, the paper proposes a generic model combining optimal control and optimal switching to study the static equilibrium and dynamic equilibrium of resource allocations under a given industrial structureand the equilibrium when the condition for transforming industrial structures arises by a social planner to maximize the representative household's utility in a market economy .
Revised:  With the common knowledge assumption, the paper studies a Ramsey growth model with endogenous structural transformation in which the social planner chooses the optimal industrial structure, recource allocation with the chosen structure, and consumption to maximize the representative household's utility in a market economy .
Edit intent: meaning-changed
Original:  With the common knowledge assumption, the paper proposes a generic model combining optimal control and optimal switching to study the static equilibrium and dynamic equilibrium of resource allocations under a given industrial structureand the equilibrium when the condition for transforming industrial structures arises by a social planner to maximize the representative household's utility in a market economy .
Revised:  With the common knowledge assumption, the paper proposes a generic model combining optimal control and optimal switching to study the static equilibrium and dynamic equilibrium of resource allocations under a given industrial structureand the equilibrium when the condition for transforming industrial structures arises by a social planner to maximize the representative household's total utility subject to the resource constraint .
Edit intent: clarity
Original:  The paper  establishes the mathematical underpinning of the static equilibrium, dynamicequilibrium and structural equilibrium. The generic model and its equilibria are then extended to economies with complicated economic structures consisting of hierarchical production, composite consumption, technology adoption and innovation, infrastructure, and economic and political institutions.
Revised:  The paper establishes the mathematical underpinning of the static , dynamic, and structural equilibria. The Ramsey growth model and its equilibria are then extended to economies with complicated economic structures consisting of hierarchical production, composite consumption, technology adoption and innovation, infrastructure, and economic and political institutions.
Edit intent: meaning-changed
Original:  In 2019 Mastrolilli ]  initiated a systematic study of IMPs arising from Constraint Satisfaction Problems (CSP) of the form CSP(\Gamma), that is, CSPs in which the type of constraints is limited to relations from a set \Gamma.
Revised:  The first part of this paper follows the work of Mastrolilli ] initiated a systematic study of IMPs arising from Constraint Satisfaction Problems (CSP) of the form CSP(\Gamma), that is, CSPs in which the type of constraints is limited to relations from a set \Gamma.
Edit intent: meaning-changed
Original:  In 2019 Mastrolilli ]  initiated a systematic study of IMPs arising from Constraint Satisfaction Problems (CSP) of the form CSP(\Gamma), that is, CSPs in which the type of constraints is limited to relations from a set \Gamma.
Revised:  In 2019 Mastrolilli SODA'19] initiated a systematic study of IMPs arising from Constraint Satisfaction Problems (CSP) of the form CSP(\Gamma), that is, CSPs in which the type of constraints is limited to relations from a set \Gamma.
Edit intent: meaning-changed
Original:  In 2019 Mastrolilli ]  initiated a systematic study of IMPs arising from Constraint Satisfaction Problems (CSP) of the form CSP(\Gamma), that is, CSPs in which the type of constraints is limited to relations from a set \Gamma.
Revised:  In 2019 Mastrolilli ] who initiated a systematic study of IMPs arising from Constraint Satisfaction Problems (CSP) of the form CSP(\Gamma), that is, CSPs in which the type of constraints is limited to relations from a set \Gamma.
Edit intent: coherence
Original:  He described sets \Gamma on a 2-element set that give rise to polynomial time solvable IMPs and showed that for the remaining ones the problem is hard. We continue this line of research. First, we show that many CSP techniques can be translated to IMPs thus allowing us to significantly improve the methods of studying the complexity of the IMP.
Revised:  We show that many CSP techniques can be translated to IMPs thus allowing us to significantly improve the methods of studying the complexity of the IMP.
Edit intent: coherence
Original:  The sufficient conditions include IMPs arising from systems of linear equations over GF(p), p prime, and also some conditions defined through special kinds of polymorphisms  .
Revised:  The sufficient conditions include IMPs arising from systems of linear equations over GF(p), p prime, and also some conditions defined through special kinds of polymorphisms . Our work has several consequences and applications in terms of bit complexity of sum-of-squares (SOS) proofs and their automatizability, and studying (construction of) theta bodies of combinatorial problems .
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Original:  Our results indicate that the 4-states Non-Homogeneous Hidden Markov model has the best one-step-ahead forecasting performance among all the competing models for all three series.
Revised:  Our results indicate that the 4-states Non-Homogeneous Hidden Markov (NHHM) model with four states has the best one-step-ahead forecasting performance among all the competing models for all three series.
Edit intent: meaning-changed
Original:  Here, we quantitatively synthesized 850 observations from field studies that were conducted in  common garden or monoculture plantations to assess how tree species type (broadleaf vs. conifer), mycorrhizal association (arbuscular mycorrhizal (AM) vs. ectomycorrhizal (ECM)), and N-fixing ability (N-fixing vs. non-N-fixing), directly and indirectly, affect soil C concentration and stock, and how such effects were influenced by environmental variables such as geographical location and climate.
Revised:  Here, we quantitatively synthesized 850 observations from field studies that were conducted in a common garden or monoculture plantations to assess how tree species type (broadleaf vs. conifer), mycorrhizal association (arbuscular mycorrhizal (AM) vs. ectomycorrhizal (ECM)), and N-fixing ability (N-fixing vs. non-N-fixing), directly and indirectly, affect soil C concentration and stock, and how such effects were influenced by environmental variables such as geographical location and climate.
Edit intent: fluency
Original:  Here, we quantitatively synthesized 850 observations from field studies that were conducted in  common garden or monoculture plantations to assess how tree species type (broadleaf vs. conifer), mycorrhizal association (arbuscular mycorrhizal (AM) vs. ectomycorrhizal (ECM)), and N-fixing ability (N-fixing vs. non-N-fixing), directly and indirectly, affect soil C concentration and stock, and how such effects were influenced by environmental variables such as geographical location and climate.
Revised:  Here, we quantitatively synthesized 850 observations from field studies that were conducted in common garden or monoculture plantations to assess how tree species type (broadleaf vs. conifer), mycorrhizal association (arbuscular mycorrhizal (AM) vs. ectomycorrhizal (ECM)), and N-fixing ability (N-fixing vs. non-N-fixing), directly and indirectly, affect topsoil (with a median depth of 10 cm) C concentration and stock, and how such effects were influenced by environmental variables such as geographical location and climate.
Edit intent: meaning-changed
Original:  Here, we quantitatively synthesized 850 observations from field studies that were conducted in  common garden or monoculture plantations to assess how tree species type (broadleaf vs. conifer), mycorrhizal association (arbuscular mycorrhizal (AM) vs. ectomycorrhizal (ECM)), and N-fixing ability (N-fixing vs. non-N-fixing), directly and indirectly, affect soil C concentration and stock, and how such effects were influenced by environmental variables such as geographical location and climate.
Revised:  Here, we quantitatively synthesized 850 observations from field studies that were conducted in common garden or monoculture plantations to assess how tree species type (broadleaf vs. conifer), mycorrhizal association (arbuscular mycorrhizal (AM) vs. ectomycorrhizal (ECM)), and N-fixing ability (N-fixing vs. non-N-fixing), directly and indirectly, affect soil C concentration and stock, and how such effects were influenced by environmental factors such as geographical location and climate.
Edit intent: fluency
Original:  Insights into the underlying mechanisms of tree species effects found in our study would be useful to e.g. inform tree species selection in forest management or afforestation aiming to sequester more atmospheric C in soil for mitigation of climate change.
Revised:  Insights into the underlying mechanisms of tree species effects found in our study would be useful to inform tree species selection in forest management or afforestation aiming to sequester more atmospheric C in soil for mitigation of climate change.
Edit intent: coherence
Original:  This improves the previously smallest dependence on \varepsilon in the running time (1/\varepsilon)^{ \mathcal{O (1/\varepsilon^{d-1})}n \log n of the algorithm by Rao and Smith (STOC 1998).
Revised:  This improves the previously smallest dependence on \varepsilon in the running time (1/\varepsilon)^{ O (1/\varepsilon^{d-1})}n \log n of the algorithm by Rao and Smith (STOC 1998).
Edit intent: clarity
Original:  We also show that a 2^{o(1/\varepsilon^{d-1})} \text{poly (n) algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH).
Revised:  We also show that a 2^{o(1/\varepsilon^{d-1})} \mathrm{poly (n) algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH).
Edit intent: meaning-changed
Original:  Our new algorithm builds upon the celebrated quadtree-based methods initially proposed by Arora (J. ACM 1998), but it adds a simple new idea that we call sparsity-sensitive patching .
Revised:  Our new algorithm builds upon the celebrated quadtree-based methods initially proposed by Arora (J. ACM 1998), but it adds a new idea that we call sparsity-sensitive patching .
Edit intent: clarity
Original:  Our new algorithm builds upon the celebrated quadtree-based methods initially proposed by Arora (J. ACM 1998), but it adds a simple new idea that we call sparsity-sensitive patching .
Revised:  Our new algorithm builds upon the celebrated quadtree-based methods initially proposed by Arora (J. ACM 1998), but it adds a simple new idea that we call sparsity-sensitive patching .
Edit intent: fluency
Original:  Our approach is (arguably) simpler than the one by Rao and Smith since it can work without geometric spanners. We demonstrate the technique extends easily to other problems, by showing as an example that it also yields a Gap-ETH-tight approximation scheme for Rectilinear Steiner Tree.
Revised:  We demonstrate that our technique extends to other problems, by showing as an example that it also yields a Gap-ETH-tight approximation scheme for Rectilinear Steiner Tree.
Edit intent: clarity
Original:  We demonstrate the technique extends easily to other problems, by showing as an example that it also yields a Gap-ETH-tight approximation scheme for Rectilinear Steiner Tree.
Revised:  We demonstrate the technique extends easily to other problems, by showing that for Steiner Tree and Rectilinear Steiner Tree it yields the same running time. We complement our results with a matching Gap-ETH lower bound for Rectilinear Steiner Tree.
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Original:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Revised:  We give an asymptotic answer to the open question for a wide range of commonly studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Edit intent: fluency
Original:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Revised:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models (especially IC) -- the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Edit intent: clarity
Original:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Revised:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Edit intent: meaning-changed
Original:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Revised:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 by Xia that was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Edit intent: meaning-changed
Original:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Revised:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis by Spielman and Teng . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Edit intent: meaning-changed
Original:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under a large class of voting rules .
Revised:  We give an asymptotic answer to the open question for a wide range of commonly-studied voting rules under a model that is much more general and realistic than i.i.d. models including IC--the smoothed social choice framework Xia20 , which was inspired by the celebrated smoothed complexity analysis ST09 . We prove dichotomy theorems on the smoothed likelihood of ties under positional scoring rules, edge-order-based rules, and some multi-round score-based elimination rules, which include commonly studied voting rules such as plurality, Borda, veto, maximin, Copeland, ranked pairs, Schulze, STV, and Coombs as special cases. We also complement the theoretical results by experiments on synthetic data and real-world rank data on Preflib .
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Original:  To mitigate this problem, we propose PairRE, a model with improved expressiveness and low computational requirement. PairRE represents each relation with paired vectors , where these paired vectors project connected two entities to relation specific locations. Beyond its ability to solve the aforementioned two problems ,
Revised:  To mitigate this problem, we propose PairRE, a model with paired vectors for each relation representation. The paired vectors enable an adaptive adjustment of the margin in loss function to fit for complex relations. Besides ,
Edit intent: meaning-changed
Original:  PairRE is advantageous to represent subrelation as it can capture both the similarities and differences of subrelations effectively . Given simple constraints on relation representations, PairRE can be the first model that is capable of encoding symmetry/antisymmetry, inverse, composition and subrelation relations . Experiments on link prediction benchmarks show PairREcan achieve either state-of-the-art or highly competitive performances.
Revised:  PairRE is capable of encoding three important relation patterns, symmetry/antisymmetry, inverse and composition . Given simple constraints on relation representations, PairRE can be the first model that is capable of encoding symmetry/antisymmetry, inverse, composition and subrelation relations . Experiments on link prediction benchmarks show PairREcan achieve either state-of-the-art or highly competitive performances.
Edit intent: clarity
Original:  PairRE is advantageous to represent subrelation as it can capture both the similarities and differences of subrelations effectively . Given simple constraints on relation representations, PairRE can be the first model that is capable of encoding symmetry/antisymmetry, inverse, composition and subrelation relations . Experiments on link prediction benchmarks show PairREcan achieve either state-of-the-art or highly competitive performances.
Revised:  PairRE is advantageous to represent subrelation as it can capture both the similarities and differences of subrelations effectively . Given simple constraints on relation representations, PairRE can encode subrelation further . Experiments on link prediction benchmarks show PairREcan achieve either state-of-the-art or highly competitive performances.
Edit intent: clarity
Original:  PairRE is advantageous to represent subrelation as it can capture both the similarities and differences of subrelations effectively . Given simple constraints on relation representations, PairRE can be the first model that is capable of encoding symmetry/antisymmetry, inverse, composition and subrelation relations . Experiments on link prediction benchmarks show PairREcan achieve either state-of-the-art or highly competitive performances.
Revised:  PairRE is advantageous to represent subrelation as it can capture both the similarities and differences of subrelations effectively . Given simple constraints on relation representations, PairRE can be the first model that is capable of encoding symmetry/antisymmetry, inverse, composition and subrelation relations . Experiments on link prediction benchmarks demonstrate the proposed key capabilities of PairRE. Moreover, We set a new state-of-the-art or highly competitive performances.
Edit intent: coherence
Original:  PairRE is advantageous to represent subrelation as it can capture both the similarities and differences of subrelations effectively . Given simple constraints on relation representations, PairRE can be the first model that is capable of encoding symmetry/antisymmetry, inverse, composition and subrelation relations . Experiments on link prediction benchmarks show PairREcan achieve either state-of-the-art or highly competitive performances. In addition, PairRE has shown encouraging results for encoding subrelation .
Revised:  PairRE is advantageous to represent subrelation as it can capture both the similarities and differences of subrelations effectively . Given simple constraints on relation representations, PairRE can be the first model that is capable of encoding symmetry/antisymmetry, inverse, composition and subrelation relations . Experiments on link prediction benchmarks show PairREcan achieve either state-of-the-art on two knowledge graph datasets of the challenging Open Graph Benchmark .
Edit intent: meaning-changed