wanyu/IteraTeR_v2 huggingface dataset:
Original: We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment-matching conditions.
Revised: We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions.
Edit intent: fluency
Original:  The polynomial property allows us to study the existence of such rules using algebraic techniques.
Revised:  The polynomial property allows us to study such rules using algebraic techniques.
Edit intent: clarity
Original: We present a non-commutative algorithm for multiplying 5 \times 5 matrices using 99 multiplications.
Revised: We present a non-commutative algorithm for multiplying 5x5 matrices using 99 multiplications.
Edit intent: fluency
Original:  This algorithm is a minor modification of Makarov algorithm 4 .
Revised:  This algorithm is a minor modification of Makarov 4 .
Edit intent: clarity
Original: We propose a population-based optimization algorithm  inspired by two main thinking modes in philosophy . Particles are regarded as thinkers and their locations are interpreted as the theses.
Revised: A population-based optimization algorithm inspired by two main thinking modes in philosophy . Particles are regarded as thinkers and their locations are interpreted as the theses.
Edit intent: coherence
Original:  The result is a delicate balance between the thinkers without any requirement for adjustment of the step-size coefficients.
Revised:  The result is a delicate balance without any requirement for adjustment of the step-size coefficients.
Edit intent: clarity
Original:  The result is a delicate balance between the thinkers without any requirement for adjustment of the step-size coefficients.
Revised:  The result is a delicate balance between the thinkers without any requirement for adjustment of step-size coefficients.
Edit intent: fluency
Original:  An additional integer parameter is defined to boost the stability of the final algorithm in facing with some specific problems.
Revised:  An additional integer parameter is defined to boost the stability of the final algorithm in some particular problems.
Edit intent: clarity
Original:  The results indicate efficiency and in some cases superiority of performance of the proposed algorithm in comparison with a variety of well-known  algorithms . Low runtime is another remarkable advantage of the proposed algorithm .
Revised:  The results indicate fast and efficient performance in comparison with a variety of well-known algorithms . Low runtime is another remarkable advantage of the proposed algorithm .
Edit intent: clarity
Original:  The results indicate efficiency and in some cases superiority of performance of the proposed algorithm in comparison with a variety of well-known  algorithms . Low runtime is another remarkable advantage of the proposed algorithm .
Revised:  The results indicate efficiency and in some cases superiority of performance of the proposed algorithm in comparison with well-known algorithms . Low runtime is another remarkable advantage of the proposed algorithm .
Edit intent: clarity
Original:  The results indicate efficiency and in some cases superiority of performance of the proposed algorithm in comparison with a variety of well-known  algorithms . Low runtime is another remarkable advantage of the proposed algorithm .
Revised:  The results indicate efficiency and in some cases superiority of performance of the proposed algorithm in comparison with a variety of well-known algorithms .
Edit intent: coherence
Original:  Therefore, it is important to maintain the connectivity of IoT networks and make them secure and resistant to malicious attacks.
Edit intent: coherence
Original:  In this work, we present a heterogeneous IoT network design problem in which a network designer can add links to provide additional communication paths between two nodes or secure links against failures by investing resources.
Revised:  In this work, we develop a heterogeneous IoT network design problem in which a network designer can add links to provide additional communication paths between two nodes or secure links against failures by investing resources.
Edit intent: clarity
Original:  In this work, we present a heterogeneous IoT network design problem in which a network designer can add links to provide additional communication paths between two nodes or secure links against failures by investing resources.
Revised:  In this work, we present a heterogeneous IoT network design framework in which a network designer can add links to provide additional communication paths between two nodes or secure links against failures by investing resources.
Edit intent: clarity
Original:  In this work, we present a heterogeneous IoT network design problem in which a network designer can add links to provide additional communication paths between two nodes or secure links against failures by investing resources.
Revised:  In this work, we present a heterogeneous IoT network design problem in which a network designer can add links to provide additional communication paths between two nodes or secure links against attacks by investing resources.
Edit intent: clarity
Original:  We characterize the optimal strategy of the secure network design problem by first providing a lower bound on the number of links a secure network requires for a given budget of protected links, and then developing a method to construct networks that satisfy the heterogeneous network design specifications.
Revised:  We characterize the optimal design of secure IoT network by first providing a lower bound on the number of links a secure network requires for a given budget of protected links, and then developing a method to construct networks that satisfy the heterogeneous network design specifications.
Edit intent: clarity
Original:  Case studies on the Internet of Battlefield Things (IoBT) are used to corroborate our results.
Revised:  Case studies on the Internet of Battlefield Things (IoBT) to corroborate and illustrate our obtained results.
Edit intent: clarity
Original:  Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, while many previous extrinsic methods lack theoretical justification.
Revised:  Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification.
Edit intent: coherence
Original:  Instead, we propose a systematic approach by considering the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume.
Revised:  Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume.
Edit intent: clarity
Original:  A remarkable property of this operator is that it encodes the volumetric geometry.
Revised:  A remarkable property of this operator is that it completely encodes volumetric geometry.
Edit intent: clarity
Original: The motion of social insects constitute beautiful examples of adaptive collective dynamics born out of apparent purposeless individual behavior.
Revised: The motion of social insects is often used a paradigmatic example of complex adaptive dynamics arising from decentralized individual behavior.
Edit intent: clarity
Original:  The analysis, done over previously reported data, reconsider the proposed causation arrows,  not finding any link between the duration of the ants  activity and its moving speed.
Revised:  The analysis, done over previously reported data, reconsider the causation arrows, not finding any link between the duration of the ants activity and its moving speed.
Edit intent: clarity
Original:  The analysis, done over previously reported data, reconsider the proposed causation arrows,  not finding any link between the duration of the ants  activity and its moving speed.
Revised:  The analysis, done over previously reported data, reconsider the proposed causation arrows, not finding any link between the duration of the ants ' activity and its moving speed.
Edit intent: fluency
Original:  One feature that can change spreading dynamics substantially is heterogeneous behavior among different types of individuals in a social network.
Edit intent: coherence
Original:  In this paper, we explore how anti-establishment nodes (e.g., hipsters) influence  spreading dynamics of two competing products.
Revised:  In this paper, we explore how anti-establishment nodes (e.g., hipsters) influence the spreading dynamics of two competing products.
Edit intent: fluency
Original:  We consider a model in which spreading follows a deterministic rule for updating node states  in which an adjustable fraction p_{\rm Hip} of the nodes in a network are hipsters, who always choose to adopt the product that they believe is the less popular of the two.
Revised:  We consider a model in which spreading follows a deterministic rule for updating node states in which an adjustable fraction p_{\rm Hip} of the nodes in a network are hipsters, who choose to adopt the product that they believe is the less popular of the two.
Edit intent: clarity
Original:  The remaining nodes are conformists, who choose which product to adopt by considering only which products their immediate neighbors have adopted.
Revised:  The remaining nodes are conformists, who choose which product to adopt by considering which products their immediate neighbors have adopted.
Edit intent: clarity
Original:  Our simple model and analysis may help shed light on the road to success for anti-establishment choices in elections, as such success --- and qualitative differences in final outcomes between competing products, political candidates, and so on --- can arise rather generically  from a small number of anti-establishment individuals and ordinary processes of social influence on normal individuals.
Revised:  Our simple model and analysis may help shed light on the road to success for anti-establishment choices in elections, as such success can arise rather generically from a small number of anti-establishment individuals and ordinary processes of social influence on normal individuals.
Edit intent: clarity
Original: A family \mathcal F%DIFDELCMD < } %%% of graphs has the Erd\H{os-P\'osa property if for every graph G, the maximum number of pairwise disjoint subgraphs isomorphic to members of }%DIFDELCMD < {%%% \mathcal F contained in G and the minimum size of a set of vertices of G hitting all such subgraphs are bounded by functions of each other.
Revised:  \mathcal F%DIFDELCMD < } %%% of graphs has the Erd\H{os-P\'osa property if for every graph G, the maximum number of pairwise disjoint subgraphs isomorphic to members of }%DIFDELCMD < {%%% \mathcal F contained in G and the minimum size of a set of vertices of G hitting all such subgraphs are bounded by functions of each other.
Edit intent: clarity
Original: A family \mathcal F%DIFDELCMD < } %%% of graphs has the Erd\H{os-P\'osa property if for every graph G, the maximum number of pairwise disjoint subgraphs isomorphic to members of }%DIFDELCMD < {%%% \mathcal F contained in G and the minimum size of a set of vertices of G hitting all such subgraphs are bounded by functions of each other.
Revised: A family %DIFDELCMD < } %%% of graphs has the Erd\H{os-P\'osa property if for every graph G, the maximum number of pairwise disjoint subgraphs isomorphic to members of }%DIFDELCMD < {%%% \mathcal F contained in G and the minimum size of a set of vertices of G hitting all such subgraphs are bounded by functions of each other.
Edit intent: clarity
Original: A family \mathcal F%DIFDELCMD < } %%% of graphs has the Erd\H{os-P\'osa property if for every graph G, the maximum number of pairwise disjoint subgraphs isomorphic to members of }%DIFDELCMD < {%%% \mathcal F contained in G and the minimum size of a set of vertices of G hitting all such subgraphs are bounded by functions of each other.
Revised: A family \mathcal F%DIFDELCMD < } %%% s-P\'osa property if for every graph G, the maximum number of pairwise disjoint subgraphs isomorphic to members of }%DIFDELCMD < {%%% \mathcal F contained in G and the minimum size of a set of vertices of G hitting all such subgraphs are bounded by functions of each other.
Edit intent: clarity
Original:  Robertson and Seymour proved that if \mathcal F%DIFDELCMD < } %%% consists of H-minors for some fixed graph H, then the planarity of H is equivalent with the Erdo s-P\'osa property.
Revised:  Robertson and Seymour proved that \mathcal F%DIFDELCMD < } %%% consists of H-minors for some fixed graph H, then the planarity of H is equivalent with the Erdo s-P\'osa property.
Edit intent: coherence
Original:  Robertson and Seymour proved that if \mathcal F%DIFDELCMD < } %%% consists of H-minors for some fixed graph H, then the planarity of H is equivalent with the Erdo s-P\'osa property.
Revised:  Robertson and Seymour proved that if %DIFDELCMD < } %%% consists of H-minors for some fixed graph H, then the planarity of H is equivalent with the Erdo s-P\'osa property.
Edit intent: coherence
Original:  Robertson and Seymour proved that if \mathcal F%DIFDELCMD < } %%% consists of H-minors for some fixed graph H, then the planarity of H is equivalent with the Erdo s-P\'osa property.
Revised:  Robertson and Seymour proved that if \mathcal F%DIFDELCMD < } %%% consists of H-minors for any fixed graph H, then the planarity of H is equivalent with the Erdo s-P\'osa property.
Edit intent: clarity
Original:  Robertson and Seymour proved that if \mathcal F%DIFDELCMD < } %%% consists of H-minors for some fixed graph H, then the planarity of H is equivalent with the Erdo s-P\'osa property.
Revised:  Robertson and Seymour proved that if \mathcal F%DIFDELCMD < } %%% consists of H-minors for some fixed graph H, the planarity of H is equivalent with the Erdo s-P\'osa property.
Edit intent: coherence
Original:  Robertson and Seymour proved that if \mathcal F%DIFDELCMD < } %%% consists of H-minors for some fixed graph H, then the planarity of H is equivalent with the Erdo s-P\'osa property.
Revised:  Robertson and Seymour proved that if \mathcal F%DIFDELCMD < } %%% consists of H-minors for some fixed graph H, then the planarity of H is equivalent with the Erdo s-P\'{o property.
Edit intent: fluency
Original:  Thomas conjectured that the planarity is no longer required if the requirement for those H-minors being pairwise disjoint is replaced with being half-integrally disjoint .
Revised:  Thomas conjectured that the planarity is no longer required if the solution of the packing problem is allowed to be half-integral .
Edit intent: clarity
Original:  In this paper, we prove that this half-integral version of Erdo s-P\'osa property holds with respect to the topological minor containment, which easily implies Thomas' conjecture.
Revised:  In this paper, we prove that this half-integral version of Erdo s-P\'{o property holds with respect to the topological minor containment, which easily implies Thomas' conjecture.
Edit intent: fluency
Original:  Robertson and Seymour proved that when packing and covering H-minors for any fixed graph H, the planarity of H is equivalent with the Erdos-P\'{o}sa property.
Revised:  Robertson and Seymour proved that when packing and covering H-minors for any fixed graph H, the planarity of H is equivalent to the Erdos-P\'{o}sa property.
Edit intent: fluency
Original:  Indeed , we prove an even stronger statement in which those subdivisions are rooted at any choice of prescribed subsets of vertices.
Revised:  In fact , we prove an even stronger statement in which those subdivisions are rooted at any choice of prescribed subsets of vertices.
Edit intent: coherence
Original:  Applications of this theorem include generalizations of algorithmic meta-theorems and structure theorems for H-topological minor free ( or H-minor free ) graphs to graphs that do not half-integrally pack many H-topological minors ( or H-minors ) .
Revised:  Applications of this theorem include generalizations of algorithmic meta-theorems and structure theorems for H-topological minor free or H-minor free ) graphs to graphs that do not half-integrally pack many H-topological minors ( or H-minors ) .
Edit intent: fluency
Original:  Applications of this theorem include generalizations of algorithmic meta-theorems and structure theorems for H-topological minor free ( or H-minor free ) graphs to graphs that do not half-integrally pack many H-topological minors ( or H-minors ) .
Revised:  Applications of this theorem include generalizations of algorithmic meta-theorems and structure theorems for H-topological minor free ( or H-minor free graphs that do not half-integrally pack many H-topological minors ( or H-minors ) .
Edit intent: fluency
Original:  Applications of this theorem include generalizations of algorithmic meta-theorems and structure theorems for H-topological minor free ( or H-minor free ) graphs to graphs that do not half-integrally pack many H-topological minors ( or H-minors ) .
Revised:  Applications of this theorem include generalizations of algorithmic meta-theorems and structure theorems for H-topological minor free ( or H-minor free ) graphs to graphs that do not half-integrally pack many H-topological minors or H-minors ) .
Edit intent: fluency
Original: results on H-topological minor free or H-minor free graphs have conclusions or requirements tied to properties of H. Classes of graphs that can half-integrally pack only a bounded number of H-topological minors or H-minors are more general topological minor-closed or minor-closed families whose minimal obstructions are more complicated than H. Our theorem provides a general machinery to extend those results to those more general classes of graphs without losing their tight connection to H.
Revised: results on H-topological minor free or H-minor free graphs have conclusions or requirements tied to properties of H. Classes of graphs that can half-integrally pack only a bounded number of H-topological minors or H-minors are more general topological minor-closed or minor-closed families whose minimal obstructions are more complicated than H. Our theorem provides a general machinery to extend those results to those more general classes of graphs without losing their tight connections to H.
Edit intent: fluency
Original:  Examples of such "order-incomplete" data include integrated event sequences such as log entries ;
Revised:  Examples of such "order-incomplete" data include integrated event sequences such as log entries ,
Edit intent: fluency
Original:  lists of properties (e.g., hotels and restaurants) ranked by an unknown function reflecting relevance or customer ratings ;
Revised:  lists of properties (e.g., hotels and restaurants) ranked by an unknown function reflecting relevance or customer ratings ,
Edit intent: fluency
Original:  We have tested the proposed method through applications to two real-world biological collectives , termites in an experimental setting and human pedestrians in an open space .
Revised:  We have tested the proposed method through applications to two real-world biological collectives : termites in an experimental setting and human pedestrians in an open space .
Edit intent: fluency
Original: The main of this paper is to introduce a family of risk measures which generalizes the Gini-type measures of risk and variability, by taking into consideration the psychological behavior .
Revised: The aim of this paper is to introduce a family of risk measures which generalizes the Gini-type measures of risk and variability, by taking into consideration the psychological behavior .
Edit intent: fluency
Original: The main of this paper is to introduce a family of risk measures which generalizes the Gini-type measures of risk and variability, by taking into consideration the psychological behavior .
Revised: The main of this paper is to introduce a risk measure that extends the Gini-type measures of risk and variability, by taking into consideration the psychological behavior .
Edit intent: clarity
Original:  Our risk measures family is coherent and catches variability with respect to the decision-maker attitude towards risk .
Revised:  Our risk measure is coherent and catches variability with respect to the decision-maker attitude towards risk .
Edit intent: clarity
Original:  We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain are the superposition of the direct transitions and the indirect transitions via all the fast transition paths.
Revised:  We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths.
Edit intent: clarity
Original:  We also give the precise mathematical conditions for  mRNAs and proteins to yield random bursts .
Revised:  We give the precise mathematical conditions for mRNAs and proteins to yield random bursts .
Edit intent: clarity
Original:  We also give the precise mathematical conditions for  mRNAs and proteins to yield random bursts .
Revised:  We also give the precise mathematical conditions for mRNAs and proteins .
Edit intent: clarity
Original:  It turns out the the random bursts exactly correspond to the fast transition paths of the Markov model.
Revised:  It turns out that random bursts exactly correspond to the fast transition paths of the Markov model.
Edit intent: fluency
Original:  This helps us gain a better understanding of the physics behind random bursts as an emergent behavior from the complex biochemical reaction kinetics  .
Revised:  This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the complex biochemical reaction kinetics .
Edit intent: clarity
Original: The emerging field of  compartmentalized in vitro evolution , where selection is carried out by differential reproduction in each compartment, is a promising new approach to protein engineering.
Revised: The emerging field of compartmentalized in vitro evolution is a promising new approach to protein engineering.
Edit intent: coherence
Original:  From practical point of view  , it is important to know the effect of the increase in the average number of genotype bearing agents per compartment.
Revised:  From practical point of view , it is important to know the impact of the increase in the average number of genotype bearing agents per compartment.
Edit intent: clarity
Original:  We carried out a theoretical investigation of this problem in the context of selection dynamics for a simple model with an infinite population that is periodically redistributed among infinite  number of identical compartments, inside which all molecules are copied without distinction with the success rate as a function of the total genomic composition in the compartment.
Revised:  We carried out a theoretical investigation of this problem in the context of selection dynamics for an infinite number of identical compartments, inside which all molecules are copied without distinction with the success rate as a function of the total genomic composition in the compartment.
Edit intent: clarity
Original:  Using the obtained update equation, we demonstrated that, for the linear additive fitness function , the best genotype is still selected regardless of the average number of individuals per compartment .
Revised:  Using the obtained update equation, we demonstrated that, for the linear additive fitness , the best genotype is still selected regardless of the average number of individuals per compartment .
Edit intent: clarity
Original:  Using the obtained update equation, we demonstrated that, for the linear additive fitness function , the best genotype is still selected regardless of the average number of individuals per compartment .
Revised:  Using the obtained update equation, we demonstrated that, for the linear additive fitness function , the best genotype is still selected regardless of the mean occupancy .
Edit intent: clarity