wanyu/IteraTeR_v2 huggingface dataset:
Original:  there is a color that appears exactly once in H. If one were considering all connected subgraphs of G instead, then such a coloring is known as a centered coloring, and the minimum achievable number of colors  is the treedepth of G . Classes of graphs with bounded treedepth are exactly those that exclude a fixed path as a subgraph, or equivalently, as a minor.
Revised:  there is a color that appears exactly once in H. If one were considering all connected subgraphs of G instead, then such a coloring is known as a centered coloring, and the minimum achievable number of colors in a centered coloring of G is the treedepth of G . Classes of graphs with bounded treedepth are exactly those that exclude a fixed path as a subgraph, or equivalently, as a minor.
Edit intent: clarity
Original:  there is a color that appears exactly once in H. If one were considering all connected subgraphs of G instead, then such a coloring is known as a centered coloring, and the minimum achievable number of colors  is the treedepth of G . Classes of graphs with bounded treedepth are exactly those that exclude a fixed path as a subgraph, or equivalently, as a minor.
Revised:  there is a color that appears exactly once in H. If one were considering all connected subgraphs of G instead, then such a coloring is known as a centered coloring, and the minimum achievable number of colors is the treedepth of G , and it is known that classes of graphs with bounded treedepth are exactly those that exclude a fixed path as a subgraph, or equivalently, as a minor.
Edit intent: coherence
Original:  We show that every \(3\)-connected graph with sufficiently many vertex-disjoint subgraphs each containing a \(k\)-ladder minor has a \((k+1)\)-ladder minor.
Revised:  We show that every \(3\)-connected graph with sufficiently many vertex-disjoint copies of a 2 \times k grid has a 2 \times (k+1) grid minor.
Edit intent: clarity
Original:  The observation of other traffic participants , and the inference of their possible next actions depending on the own action is considered cooperative prediction and planning.
Revised:  The observation of other traffic participants and the inference of their possible next actions depending on the own action is considered cooperative prediction and planning.
Edit intent: fluency
Original:  However, the search space for cooperative plans is so large that the vast amount of the computational budget is spent on exploring the search space in unpromising regions that are far away from the solution.
Revised:  However, the search space for cooperative plans is so large that most of the computational budget is spent on exploring the search space in unpromising regions that are far away from the solution.
Edit intent: clarity
Original:  To accelerate the planning process, we combined learned heuristics with a cooperative planning method in order to guide the search towards regions with promising actions, yielding better results at lower computational costs.
Revised:  To accelerate the planning process, we combined learned heuristics with a cooperative planning method to guide the search towards regions with promising actions, yielding better results at lower computational costs.
Edit intent: coherence
Original:  To accelerate the planning process, we combined learned heuristics with a cooperative planning method in order to guide the search towards regions with promising actions, yielding better results at lower computational costs.
Revised:  To accelerate the planning process, we combined learned heuristics with a cooperative planning method in order to guide the search towards regions with promising actions, yielding better solutions at lower computational costs.
Edit intent: clarity
Original:  Australian languages have been characterised as having a high degree of phonotactic homogeneity.
Revised:  Australian languages have been characterized as having a high degree of phonotactic homogeneity.
Edit intent: fluency
Original:  Phylogenetic signal is higher in finer-grained frequency data than in binary data, and highest in natural-class-based data.
Revised:  Phylogenetic signal is greater in finer-grained frequency data than in binary data, and highest in natural-class-based data.
Edit intent: clarity
Original:  Phylogenetic signal is higher in finer-grained frequency data than in binary data, and highest in natural-class-based data.
Revised:  Phylogenetic signal is higher in finer-grained frequency data than in binary data, and greatest in natural-class-based data.
Edit intent: clarity
Original:  The results show that the two proposed strategies deliver an improved performance, characterized by (1) a higher accumulated reward within a finite number of time steps;
Revised:  The results show that the two proposed strategies deliver improved performance, characterized by (1) a higher accumulated reward within a finite number of time steps;
Edit intent: fluency
Original:  Existing methods commonly involve the trials of multiple strategies and then reward better-performing one with more resources based on their previous performance.
Revised:  Existing methods commonly involve the trials of multiple strategies and then rewards better-performing one with more resources based on their previous performance.
Edit intent: fluency
Original:  Existing methods commonly involve the trials of multiple strategies and then reward better-performing one with more resources based on their previous performance.
Revised:  Existing methods commonly involve the trials of multiple strategies and then reward better-performing ones with more resources based on their previous performance.
Edit intent: fluency
Original:  EaDE divides the evolution process into several SCSS ( Selective-candidate with similarity selection ) generations and adaptive generations.
Revised:  EaDE divides the evolution process into several Selective-candidate with similarity selection ) generations and adaptive generations.
Edit intent: clarity
Original:  EaDE divides the evolution process into several SCSS ( Selective-candidate with similarity selection ) generations and adaptive generations.
Revised:  EaDE divides the evolution process into several SCSS ( Selective-candidate with Similarity Selection (SCSS ) generations and adaptive generations.
Edit intent: clarity
Original:  Exploitation and exploration needs are learned in the SCSS generations by a relatively balanced strategy.
Revised:  In the SCSS generations, the exploitation and exploration needs are learned in the SCSS generations by a relatively balanced strategy.
Edit intent: coherence
Original:  Exploitation and exploration needs are learned in the SCSS generations by a relatively balanced strategy.
Revised:  Exploitation and exploration needs are learnt by utilizing a balanced strategy.
Edit intent: clarity
Original:  While in the adaptive generations, to meet these needs, two other alternative strategies, an exploitative one or an explorative one is employed . Experimental studies on 28 benchmark functions confirm the effectiveness of the proposed method .
Revised:  To meet these needs, two other alternative strategies, an exploitative one or an explorative one is employed . Experimental studies on 28 benchmark functions confirm the effectiveness of the proposed method .
Edit intent: coherence
Original:  While in the adaptive generations, to meet these needs, two other alternative strategies, an exploitative one or an explorative one is employed . Experimental studies on 28 benchmark functions confirm the effectiveness of the proposed method .
Revised:  While in the adaptive generations, to meet these needs, in adaptive generations, two other strategies, exploitative or explorative is adaptively used . Experimental studies on 28 benchmark functions confirm the effectiveness of the proposed method .
Edit intent: clarity
Original:  While in the adaptive generations, to meet these needs, two other alternative strategies, an exploitative one or an explorative one is employed . Experimental studies on 28 benchmark functions confirm the effectiveness of the proposed method .
Revised:  While in the adaptive generations, to meet these needs, two other alternative strategies, an exploitative one or an explorative one is employed . Experimental studies on benchmark functions demonstrate the effectiveness of the proposed method .
Edit intent: clarity
Original: With regard to formalizing mathematics in proof assistants, the hierarchy of mathematical structure that allows for the sharing of notations and theories , and makes subtyping of structures implicit, is a key ingredient of infrastructure to support the users .
Revised: Sharing of notations and theories , and makes subtyping of structures implicit, is a key ingredient of infrastructure to support the users .
Edit intent: coherence
Original:  The packed classes method is a generic design pattern to define and combine mathematical structures in a dependent type theory with records.
Revised:  The packed classes methodology is a generic design pattern to define and combine mathematical structures in a dependent type theory with records.
Edit intent: fluency
Original:  In this paper, we identify the invariants of hierarchies that ensure the modularity of reasoning and the predictability of inference with packed classes, propose checking tools for those invariants , and show that our tools significantly improve the development process of Mathematical Components, a formalized mathematics library for Coq .
Revised:  In this paper, we identify the invariants of hierarchies that ensure the modularity of reasoning and predictability of inference with packed classes, propose checking tools for those invariants , and show that our tools significantly improve the development process of Mathematical Components, a formalized mathematics library for Coq .
Edit intent: fluency
Original:  In this paper, we identify the invariants of hierarchies that ensure the modularity of reasoning and the predictability of inference with packed classes, propose checking tools for those invariants , and show that our tools significantly improve the development process of Mathematical Components, a formalized mathematics library for Coq .
Revised:  In this paper, we identify the invariants of hierarchies that ensure the modularity of reasoning and the predictability of inference with packed classes, propose checking tools for those invariants , and show that they significantly improve the development process of Mathematical Components, a formalized mathematics library for Coq .
Edit intent: clarity
Original:  While the solution of the linear system is relatively straightforward for simple finite-difference- and finite-volume- discretisations, it is much more challenging for advanced finite element discretisations, which have recently been explored in atmospheric modelling.
Edit intent: coherence
Original: Cross-lingual document alignment aims to identify pairs of documents in two distinct languages that are of comparable content or translations of each other.
Revised: Document alignment aims to identify pairs of documents in two distinct languages that are of comparable content or translations of each other.
Edit intent: clarity
Original:  Such aligned data can be used for a variety of NLP tasks from training cross-lingual representations to mining parallel bitexts for machine translation training .
Revised:  Such aligned data can be used for a variety of NLP tasks from training cross-lingual representations to mining parallel data for machine translation training .
Edit intent: fluency
Original:  Such aligned data can be used for a variety of NLP tasks from training cross-lingual representations to mining parallel bitexts for machine translation training .
Revised:  Such aligned data can be used for a variety of NLP tasks from training cross-lingual representations to mining parallel bitexts for machine translation .
Edit intent: clarity
Original:  Early approaches relied on utilizing each user's first-order social neighbors' interests for better user modeling , and failed to model the social influence diffusion process from the global social network structure.
Revised:  Early approaches relied on utilizing each user's first-order social neighbors' interests for better user modeling and failed to model the social influence diffusion process from the global social network structure.
Edit intent: fluency
Original:  Recently, we propose a preliminary work of a neural influence diffusion network ~ (i.e., DiffNet) for social recommendation ~ (Diffnet), which models the recursive social diffusion process to capture the higher-order relationships for each user.
Revised:  Recently, we propose a preliminary work of a neural influence diffusion network (i.e., DiffNet) for social recommendation ~ (Diffnet), which models the recursive social diffusion process to capture the higher-order relationships for each user.
Edit intent: fluency
Original:  Recently, we propose a preliminary work of a neural influence diffusion network ~ (i.e., DiffNet) for social recommendation ~ (Diffnet), which models the recursive social diffusion process to capture the higher-order relationships for each user.
Revised:  Recently, we propose a preliminary work of a neural influence diffusion network ~ (i.e., DiffNet) for social recommendation (Diffnet), which models the recursive social diffusion process to capture the higher-order relationships for each user.
Edit intent: fluency
Original: Spike-based neuromorphic hardware is a promising option for reducing the energy consumption of image classification , or more generally of inference in large neural networks that have been trained by deep learning .
Revised: Spike-based neuromorphic hardware is a promising option for reducing the energy consumption of image classification and other deep learning applications .
Edit intent: clarity
Original:  However direct training of deep feedforward spiking neural networks is difficult, and previous methods for converting trained artificial neural networks to spiking neurons required too many spikes.
Revised:  However direct training of deep spiking neural networks is difficult, and previous methods for converting trained artificial neural networks to spiking neurons required too many spikes.
Edit intent: clarity
Original:  However direct training of deep feedforward spiking neural networks is difficult, and previous methods for converting trained artificial neural networks to spiking neurons required too many spikes.
Revised:  However direct training of deep feedforward spiking neural networks is difficult, and previous methods for converting trained artificial neural networks to spiking neurons were inefficient because the neurons had to emit too many spikes.
Edit intent: clarity
Original:  We show that a substantially more efficient conversion from artificial neural networks to spike-based networks is possible if one optimizes the spiking neuron model for that purpose, and enables it to use the timing of spikes to encode information .
Revised:  We show that a substantially more efficient conversion arises when one optimizes the spiking neuron model for that purpose, and enables it to use the timing of spikes to encode information .
Edit intent: clarity
Original:  In addition  our new conversion method drastically improves latency and throughput of the resulting spiking networks.
Revised:  In addition , our new conversion method drastically improves latency and throughput of the resulting spiking networks.
Edit intent: fluency
Original: Spike-based neuromorphic hardware is a promising option for reducing the energy consumption of image classification and other deep learning applications .
Revised: Spike-based neuromorphic hardware promises to reduce the energy consumption of image classification and other deep learning applications .
Edit intent: clarity
Original:  However  direct training of deep spiking neural networks is difficult, and previous methods for converting trained artificial neural networks to spiking neurons were inefficient because the neurons had to emit too many spikes.
Revised:  However , direct training of deep spiking neural networks is difficult, and previous methods for converting trained artificial neural networks to spiking neurons were inefficient because the neurons had to emit too many spikes.
Edit intent: fluency
Original:  In addition, our new conversion method drastically improves latency and throughput of the resulting spiking networks.
Revised:  In addition, our new conversion method improves latency and throughput of the resulting spiking networks.
Edit intent: clarity
Original: Stochastically evolving geometric systems are studied in geometric mechanics for modelling turbulence parts of multi-scale fluid flows and in shape analysis for stochastic evolutions of shapes of  e.g. \ human organs.
Revised: Stochastically evolving geometric systems are studied in geometric mechanics for modelling turbulence parts of multi-scale fluid flows and in shape analysis for stochastic evolutions of shapes of , e.g. \ human organs.
Edit intent: fluency
Original: Stochastically evolving geometric systems are studied in geometric mechanics for modelling turbulence parts of multi-scale fluid flows and in shape analysis for stochastic evolutions of shapes of  e.g. \ human organs.
Revised: Stochastically evolving geometric systems are studied in geometric mechanics for modelling turbulence parts of multi-scale fluid flows and in shape analysis for stochastic evolutions of shapes of e.g. , human organs.
Edit intent: fluency
Original: Stochastically evolving geometric systems are studied in  geometric mechanics for modelling turbulence parts of multi-scale fluid flows and in shape analysis for stochastic evolutions of shapes of, e. g., human organs.
Revised: Stochastically evolving geometric systems are studied in geometric mechanics for modelling turbulence parts of multi-scale fluid flows .
Edit intent: clarity
Original:  Recently introduced models involve stochastic differential equations that govern the dynamics of a diffusion process X . In applications X is only partially observed at times 0 and T>0.
Revised:  Recently introduced models involve stochastic differential equations that govern the dynamics of a diffusion process X where, in applications, X is only partially observed at times 0 and T>0.
Edit intent: clarity
Original:  Conditional on these observations, interest lies in inferring parameters in the dynamics of the diffusion and reconstructing the path (X_t,\, t\in [0,T]).
Revised:  Conditional on these observations, the challenge is to infer parameters of the dynamics of the diffusion and reconstructing the path (X_t,\, t\in [0,T]).
Edit intent: clarity
Original:  Conditional on these observations, interest lies in inferring parameters in the dynamics of the diffusion and reconstructing the path (X_t,\, t\in [0,T]).
Revised:  Conditional on these observations, interest lies in inferring parameters in the dynamics of the diffusion and to reconstruct the path (X_t,\, t\in [0,T]).
Edit intent: fluency
Original:  We develop a general scheme for bridge sampling in the case of finite dimensional systems of shape landmarks and singular solutions in fluid dynamics.
Revised:  We develop a general scheme for bridge simulation in the case of finite dimensional systems of shape landmarks and singular solutions in fluid dynamics.
Edit intent: clarity
Original:  This scheme allows for subsequent statistical inference of properties of the fluid flow or the evolution of observed shapes.
Revised:  The scheme allows for subsequent statistical inference of properties of the fluid flow or the evolution of observed shapes.
Edit intent: fluency
Original:  It covers stochastic landmark models for which no suitable simulation method has been proposed in the literature , that removes restrictions of earlier approaches , improves the handling of the nonlinearity of the configuration space leading to more effective sampling schemes and allows to generalise the common inexact matching scheme to the stochastic setting.
Revised:  It covers stochastic landmark models for which no suitable simulation method has been proposed in the literature ; that it removes restrictions of earlier approaches , improves the handling of the nonlinearity of the configuration space leading to more effective sampling schemes and allows to generalise the common inexact matching scheme to the stochastic setting.
Edit intent: coherence
Original:  It covers stochastic landmark models for which no suitable simulation method has been proposed in the literature , that removes restrictions of earlier approaches , improves the handling of the nonlinearity of the configuration space leading to more effective sampling schemes and allows to generalise the common inexact matching scheme to the stochastic setting.
Revised:  It covers stochastic landmark models for which no suitable simulation method has been proposed in the literature , that removes restrictions of earlier approaches ; that it improves the handling of the nonlinearity of the configuration space leading to more effective sampling schemes and allows to generalise the common inexact matching scheme to the stochastic setting.
Edit intent: coherence
Original:  It covers stochastic landmark models for which no suitable simulation method has been proposed in the literature , that removes restrictions of earlier approaches , improves the handling of the nonlinearity of the configuration space leading to more effective sampling schemes and allows to generalise the common inexact matching scheme to the stochastic setting.
Revised:  It covers stochastic landmark models for which no suitable simulation method has been proposed in the literature , that removes restrictions of earlier approaches , improves the handling of the nonlinearity of the configuration space leading to more effective sampling schemes ; and that it allows to generalise the common inexact matching scheme to the stochastic setting.
Edit intent: coherence
Original: Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling stochastic evolution of human organ shapes , and in geometric mechanics for modelling turbulence parts of multi-scale fluid flows.
Revised: Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes , and in geometric mechanics for modelling turbulence parts of multi-scale fluid flows.
Edit intent: clarity
Original:  Conditional on these observations, the challenge is to infer parameters of the dynamics of the diffusion and to reconstruct the path (X_t,\, t\in 0,T%DIFDELCMD < ]%%% ).
Revised:  Conditional on these observations, the challenge is to infer parameters of the dynamics of the diffusion and to reconstruct the path (X_t,\, t\in %DIFDELCMD < ]%%% ).
Edit intent: clarity
Original:  both of them turn out to be power-laws and an arithmetic, testable relationship between the respective exponents naturally appears .
Revised:  both of them turn out to be power-laws , whose respective exponents are in an arithmetic, testable relationship between the respective exponents naturally appears .
Edit intent: clarity
Original:  both of them turn out to be power-laws and an arithmetic, testable relationship between the respective exponents naturally appears .
Revised:  both of them turn out to be power-laws and an arithmetic, testable relationship .
Edit intent: clarity
Original:  The values of the free parameters of the model are estimated by a Bayesian maximum likelihood inference which keeps into account the prior distribution of the parameters making use of theorems from Information Geometry .
Revised:  The values of the free parameters of the model are estimated by a Bayesian maximum likelihood inference which keeps into account the prior distribution of the parameters .
Edit intent: coherence
Original: In smooth strongly convex optimization, or in the presence of H\"olderian error bounds, knowledge of the curvature parameter is critical for obtaining simple methods with accelerated rates.
Revised: In smooth strongly convex optimization, knowledge of the curvature parameter is critical for obtaining simple methods with accelerated rates.
Edit intent: clarity