wanyu/IteraTeR_v2 huggingface dataset:
Original:  The calculus exploits operators on sequents, in the style of ``nested'' or `` tree-sequent '' calculi;
Revised:  The calculus exploits operators on sequents, in the style of "nested" or " tree-sequent '' calculi;
Edit intent: fluency
Original:  The calculus exploits operators on sequents, in the style of ``nested'' or `` tree-sequent '' calculi;
Revised:  The calculus exploits operators on sequents, in the style of ``nested'' or `` tree-sequent " calculi;
Edit intent: fluency
Original: We establish a connection between observed scale-free topologies and hidden hyperbolic geometries of complex networks . Hidden geometries are coarse metric abstractions of the approximately hierarchical community structure of complex networks, used to estimate node similarities.
Revised: We establish a connection between observed scale-free topologies of complex networks . Hidden geometries are coarse metric abstractions of the approximately hierarchical community structure of complex networks, used to estimate node similarities.
Edit intent: clarity
Original:  Space expands exponentially in hyperbolic geometry, and scale-free topologies emerge as a consequence of this exponential expansion .
Revised:  Space expands exponentially in hyperbolic geometry, and scale-free topologies emerge as a consequence of the exponential expansion of hidden hyperbolic space .
Edit intent: clarity
Original: We introduce a simplified model of ecosystem  for which we are able to map out all assembly pathways generated by external invasions in an exact manner.
Revised: We introduce a simplified model of ecosystem assembly for which we are able to map out all assembly pathways generated by external invasions in an exact manner.
Edit intent: clarity
Original:  Second, we are able to prove that the endstate is always unique, so it does not depend on the assembly history.
Revised:  Second, we are able to prove that the endstate is independent on the assembly history.
Edit intent: clarity
Original: We investigate the distribution of flavonoid , a major category of plant secondary metabolites, across species.
Revised: We investigate the distribution of flavonoids , a major category of plant secondary metabolites, across species.
Edit intent: fluency
Original:  Flavonoid is known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of living organisms.
Revised:  Flavonoids are known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of living organisms.
Edit intent: fluency
Original:  Flavonoid is known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of living organisms.
Revised:  Flavonoid is known to show high species specificity, and were once considered as a chemical marker to understand adaptive evolution and characterization of living organisms.
Edit intent: fluency
Original:  Flavonoid is known to show high species specificity, and was once considered as a chemical marker to understand adaptive evolution and characterization of living organisms.
Revised:  Flavonoid is known to show high species specificity, and was once considered as chemical markers for understanding adaptive evolution and characterization of living organisms.
Edit intent: fluency
Original:  This work explores single solution clusters of random 3- and 4-SAT formulas through a random walk process SPINFLIP {\tt  .
Revised:  This paper explores single solution clusters of random 3- and 4-SAT formulas through a random walk process SPINFLIP {\tt .
Edit intent: clarity
Original:  This work explores single solution clusters of random 3- and 4-SAT formulas through a random walk process SPINFLIP {\tt  .
Revised:  This work explores single solution clusters of random 3- and 4-SAT formulas through a random walk process {\tt .
Edit intent: clarity
Original:  In the community-rich phase the number of unfrozen variables discovered by SPINFLIP {\tt  increases with time logarithmically for a large random formula . Based on these findings some of the recent theoretical and algorithmic results are discussed .
Revised:  In the community-rich phase the number of unfrozen variables discovered by {\tt increases with time logarithmically for a large random formula . Based on these findings some of the recent theoretical and algorithmic results are discussed .
Edit intent: clarity
Original:  In the community-rich phase the number of unfrozen variables discovered by SPINFLIP {\tt  increases with time logarithmically for a large random formula . Based on these findings some of the recent theoretical and algorithmic results are discussed .
Revised:  In the community-rich phase the number of unfrozen variables discovered by SPINFLIP {\tt increases with time logarithmically for a large random formula .
Edit intent: clarity
Original: The solution space of a K-satisfiability (K-SAT) formula is a collection of  clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips.
Revised: The solution space of a K-satisfiability (K-SAT) formula is a collection of solution clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips.
Edit intent: fluency
Original:  Knowledge on the fine structure of solution clusters is indispensable for a complete understanding of the solution space structure and the computational complexity of the random K-SAT problem.
Revised:  Knowledge on the fine structure of solution clusters is valuable for a complete understanding of the solution space structure and the computational complexity of the random K-SAT problem.
Edit intent: clarity
Original:  This paper explores single solution clusters of random 3- and 4-SAT formulas through a random walk process%DIFDELCMD < {\tt %%% SPINFLIP .
Revised:  This paper explores single solution clusters of random 3- and 4-SAT formulas through %DIFDELCMD < {\tt %%% SPINFLIP .
Edit intent: clarity
Original:  This paper explores single solution clusters of random 3- and 4-SAT formulas through a random walk process%DIFDELCMD < {\tt %%% SPINFLIP .
Revised:  This paper explores single solution clusters of random 3- and 4-SAT formulas through a random walk process%DIFDELCMD < {\tt %%% .
Edit intent: clarity
Original:  In the community-rich phase the number of unfrozen variables discovered by%DIFDELCMD < {\tt %DIFDELCMD < %%% SPINFLIP increases with time logarithmically for a large random formula .
Revised:  In the community-rich phase the number of unfrozen variables discovered by%DIFDELCMD < {\tt %DIFDELCMD < %%% increases with time logarithmically for a large random formula .
Edit intent: clarity
Original:  It is therefore conceivable that also neural information processing in the brain should operate close to criticality.
Revised:  It is therefore conceivable that also neural information processing operates close to criticality.
Edit intent: clarity
Original:  An important open question is how the brain can remain close to a critical point while undergoing  continual change in the course of development, adaptation, learning, and more.
Revised:  An important open question is how the brain can remain close to a critical point while undergoing a continual change in the course of development, adaptation, learning, and more.
Edit intent: fluency
Original:  Here  we address the question whether this mechanism is relevant for real neural networks ;
Revised:  Here , we address the question whether this mechanism is relevant for real neural networks ;
Edit intent: fluency
Original:  These results suggest that the interplay between dynamics and topology is essential for neural information processing.
Revised:  These results suggest that the interplay between dynamics and topology may be essential for neural information processing.
Edit intent: clarity
Original:  However, highly overlapping community structure, present in many real networks including social and biological networks, interferes with discovery of hierarchy since a node's membership in multiple communities precludes a unique hierarchical position.
Revised:  However, the fact that many real networks including social and biological networks, interferes with discovery of hierarchy since a node's membership in multiple communities precludes a unique hierarchical position.
Edit intent: coherence
Original:  One crucial step when studying the structure and dynamics of networks is to identify communities ;
Revised:  One crucial step when studying the structure and dynamics of networks is to identify communities :
Edit intent: fluency
Original:  Meanwhile, many networks are known to possess multi-scale, hierarchical organisation , where communities are recursively grouped into a hierarchical structure.
Revised:  Meanwhile, many networks are known to possess hierarchical organization , where communities are recursively grouped into a hierarchical structure.
Edit intent: clarity
Original:  Here we reinvent communities as groups of links rather than nodes and show that this unorthodox approach successfully reconciles the antagonistic organising principles of overlapping communities and hierarchy.
Revised:  Here we reinvent communities as groups of links rather than nodes and show that this unorthodox approach successfully reconciles the antagonistic organizing principles of overlapping communities and hierarchy.
Edit intent: fluency
Original:  In contrast to the existing literature, which has entirely focused on grouping nodes, link communities naturally incorporate overlap while revealing hierarchical organisation .
Revised:  In contrast to the existing literature, which has entirely focused on grouping nodes, link communities naturally incorporate overlap while revealing hierarchical organization .
Edit intent: fluency
Original:  We find biologically relevant link communities in  protein-protein interaction and metabolic networks  and show that a large social network contains hierarchically organised, community structures spanning inner-city to regional scales while maintaining pervasive overlap.
Revised:  We find relevant link communities in protein-protein interaction and metabolic networks and show that a large social network contains hierarchically organised, community structures spanning inner-city to regional scales while maintaining pervasive overlap.
Edit intent: clarity
Original:  We find biologically relevant link communities in  protein-protein interaction and metabolic networks  and show that a large social network contains hierarchically organised, community structures spanning inner-city to regional scales while maintaining pervasive overlap.
Revised:  We find biologically relevant link communities in protein-protein interaction and metabolic networks , and show that a large social network contains hierarchically organised, community structures spanning inner-city to regional scales while maintaining pervasive overlap.
Edit intent: fluency
Original:  We find biologically relevant link communities in  protein-protein interaction and metabolic networks  and show that a large social network contains hierarchically organised, community structures spanning inner-city to regional scales while maintaining pervasive overlap.
Revised:  We find biologically relevant link communities in protein-protein interaction and metabolic networks and show that a large social network contains hierarchically organized community structures spanning inner-city to regional scales while maintaining pervasive overlap.
Edit intent: fluency
Original:  Our results imply that link communities are fundamental building blocks that reveal overlap and multi-scale hierarchical organisation in networks to be two aspects of the same phenomenon.
Revised:  Our results imply that link communities are fundamental building blocks that reveal overlap and hierarchical organization in networks to be two aspects of the same phenomenon.
Edit intent: clarity
Original:  The flexible spectrum management provides new opportunities for the licensed primary user and the unlicensed secondary users to reallocate the spectrum resource efficiently.
Revised:  The flexible spectrum management provides new opportunities for licensed primary user and the unlicensed secondary users to reallocate the spectrum resource efficiently.
Edit intent: fluency
Original:  The flexible spectrum management provides new opportunities for the licensed primary user and the unlicensed secondary users to reallocate the spectrum resource efficiently.
Revised:  The flexible spectrum management provides new opportunities for the licensed primary user and unlicensed secondary users to reallocate the spectrum resource efficiently.
Edit intent: fluency
Original:  In this paper, we present an oligopoly pricing framework for dynamic spectrum allocation in which the primary users sell the excessive spectrum to the secondary users for monetary return.
Revised:  In this paper, we present an oligopoly pricing framework for dynamic spectrum allocation in which the primary users sell excessive spectrum to the secondary users for monetary return.
Edit intent: fluency
Original:  In the oligopoly model with strict constraints, we propose a low-complexity searching method to obtain the Nash Equilibrium and prove the uniqueness.
Revised:  In the oligopoly model with strict constraints, we propose a low-complexity searching method to obtain the Nash Equilibrium and prove its uniqueness.
Edit intent: clarity
Original: The concept of matching dependencies ( MDs ) is recently proposed for specifying matching rules for object identification.
Revised: The concept of matching dependencies ( mds ) is recently proposed for specifying matching rules for object identification.
Edit intent: fluency
Original: The concept of matching dependencies ( MDs ) is recently proposed for specifying matching rules for object identification.
Revised: The concept of matching dependencies ( MDs ) is recently pro- posed for specifying matching rules for object identification.
Edit intent: fluency
Original:  Similar to the functional dependencies (with conditions), MDs can also be applied to various data quality applications such as violation detection.
Revised:  Similar to the functional dependencies (with conditions), mds can also be applied to various data quality applications such as violation detection.
Edit intent: fluency
Original:  Then we consider the problem of quickly distinguishing boards positions that can be reduced to one peg ("winning" board positions) from those that cannot be solved to one peg ("losing" board positions).
Revised:  Then we consider the problem of quickly distinguishing boards positions that can be reduced to one peg ("winning" board positions) from those that cannot ("losing" board positions).
Edit intent: clarity
Original:  Two popular board shapes are the 33-hole cross-shaped board, and the 15-hole triangular board - we use them as examples throughout.
Revised:  Two popular board shapes are the 33-hole cross-shaped board, and the 15-hole triangle board---we use them as examples throughout.
Edit intent: fluency
Original:  The basic game begins from a full board with one peg missing and finishes at a board position with one peg.
Revised:  The basic game begins from a full board with one peg missing and the goal is to finish at a board position with one peg.
Edit intent: clarity
Original:  Then we consider the problem of quickly distinguishing boards positions that can be reduced to one peg ("winning" board positions) from those that cannot("losing" board positions) .
Revised:  Then we consider the problem of quickly distinguishing boards positions that can be reduced to one peg ("winning" board positions) from those where it cannot .
Edit intent: clarity
Original:  On the 15-hole triangular board, it is possible to identify all winning board positions (from any single vacancy start) by storing a key set of 437 board positions.
Revised:  On the 15-hole triangle board, it is possible to identify all winning board positions (from any single vacancy start) by storing a key set of 437 board positions.
Edit intent: fluency
Original: The Linear-Algebraic Lambda-Calculus (arXiv:quant-ph/0612199) extends the lambda-calculus with the possibility of making arbitrary linear combinations of  terms a.t+b.u.
Revised: The linear-algebraic lambda-calculus (arXiv:quant-ph/0612199) extends the lambda-calculus with the possibility of making arbitrary linear combinations of terms a.t+b.u.
Edit intent: fluency
Original:  In this paper we provide a System F like type system for the Linear-Algebraic Lambda-Calculus, which guarantees normalisation and hence no need for such restrictions, t-t always reduces to 0.
Revised:  In this paper we provide a System F -like type system for the Linear-Algebraic Lambda-Calculus, which guarantees normalisation and hence no need for such restrictions, t-t always reduces to 0.
Edit intent: fluency
Original:  Moreover this type system keeps track of 'the amount of a type' . As such it can be seen as probabilistic type system, guaranteeing that terms define correct probabilistic functions.
Revised:  Moreover this type system keeps track of 'the amount of a type' . As such it can be seen as probabilistic type system, which guarantees that terms define correct probabilistic functions.
Edit intent: coherence
Original: The  ]  linear-algebraic lambda-calculus (arXiv:quant-ph/0612199) extends the lambda-calculus ]  with the possibility of making arbitrary linear combinations of lambda-calculus terms a.t+b. u.\alphai In this paper we provide a System F -like type system for the linear-algebraic lambda-calculus, which keeps track of 'the amount of a type' that is present in a term .
Revised: The ] linear-algebraic \lambda-calculus ] with the possibility of making arbitrary linear combinations of lambda-calculus terms a.t+b. u.\alphai In this paper we provide a System F -like type system for the linear-algebraic lambda-calculus, which keeps track of 'the amount of a type' that is present in a term .
Edit intent: clarity
Original: The  ]  linear-algebraic lambda-calculus (arXiv:quant-ph/0612199) extends the lambda-calculus ]  with the possibility of making arbitrary linear combinations of lambda-calculus terms a.t+b. u.\alphai In this paper we provide a System F -like type system for the linear-algebraic lambda-calculus, which keeps track of 'the amount of a type' that is present in a term .
Revised: The ] linear-algebraic lambda-calculus (arXiv:quant-ph/0612199) extends the lambda-calculus ] with the possibility of making arbitrary linear combinations of lambda-calculus terms a.t+b. u.\alphai In this paper we provide a fine-grained, System F-like type system for the linear-algebraic lambda-calculus, which keeps track of 'the amount of a type' that is present in a term .
Edit intent: clarity
Original:  We show that this scalar type system enjoys both the subject-reduction property and the strong-normalisation property, which constitute our main technical results.
Revised:  We show that this "scalar" type system enjoys both the subject-reduction property and the strong-normalisation property, which constitute our main technical results.
Edit intent: fluency
Original:  The latter yields a significant simplification of the linear-algebraic lambda-calculus itself, by removing the need for some restrictions in its reduction rules - and thus leaving it more intuitive.
Revised:  The latter yields a significant simplification of the linear-algebraic lambda-calculus itself, by removing the need for some restrictions in its reduction rules -- and thus leaving it more intuitive.
Edit intent: fluency
Original:  Thus we are able to specialize the linear-algebraic lambda-calculus into a\alphai higher-order , probabilisticlambda-calculus .
Revised:  Thus we are able to specialize the linear-algebraic lambda-calculus into a\alphai higher-order \lambda-calculus .
Edit intent: clarity
Original: The algebraic \lambda-calculus [Vau07] and the linear-algebraic \lambda-calculus [AD08] extend the \lambda-calculus with the possibility of making arbitrary linear combinations of \lambda-calculus terms (preserving \Sigma%DIFDELCMD < \alphai%%% .ti ).
Revised: The algebraic lambda-calculus [Vau07] and the linear-algebraic \lambda-calculus [AD08] extend the \lambda-calculus with the possibility of making arbitrary linear combinations of \lambda-calculus terms (preserving \Sigma%DIFDELCMD < \alphai%%% .ti ).
Edit intent: fluency
Original: The algebraic \lambda-calculus [Vau07] and the linear-algebraic \lambda-calculus [AD08] extend the \lambda-calculus with the possibility of making arbitrary linear combinations of \lambda-calculus terms (preserving \Sigma%DIFDELCMD < \alphai%%% .ti ).
Revised: The algebraic \lambda-calculus [Vau07] and the linear-algebraic lambda-calculus [AD08] extend the \lambda-calculus with the possibility of making arbitrary linear combinations of \lambda-calculus terms (preserving \Sigma%DIFDELCMD < \alphai%%% .ti ).
Edit intent: fluency
Original: The algebraic \lambda-calculus [Vau07] and the linear-algebraic \lambda-calculus [AD08] extend the \lambda-calculus with the possibility of making arbitrary linear combinations of \lambda-calculus terms (preserving \Sigma%DIFDELCMD < \alphai%%% .ti ).
Revised: The algebraic \lambda-calculus [Vau07] and the linear-algebraic \lambda-calculus [AD08] extend the lambda-calculus with the possibility of making arbitrary linear combinations of \lambda-calculus terms (preserving \Sigma%DIFDELCMD < \alphai%%% .ti ).
Edit intent: fluency
Original: The algebraic \lambda-calculus [Vau07] and the linear-algebraic \lambda-calculus [AD08] extend the \lambda-calculus with the possibility of making arbitrary linear combinations of \lambda-calculus terms (preserving \Sigma%DIFDELCMD < \alphai%%% .ti ).
Revised: The algebraic \lambda-calculus [Vau07] and the linear-algebraic \lambda-calculus [AD08] extend the \lambda-calculus with the possibility of making arbitrary linear combinations of lambda-calculus terms (preserving \Sigma%DIFDELCMD < \alphai%%% .ti ).
Edit intent: fluency
Original:  In this paper we provide a fine-grained, System F-like type system for the linear-algebraic \lambda-calculus (Lineal).
Revised:  In this paper we provide a fine-grained, System F-like type system for the linear-algebraic lambda-calculus (Lineal).
Edit intent: fluency
Original:  We show that this "scalar" type system enjoys both the subject-reduction property and the strong-normalisation property, which constitute our main technical results.
Revised:  We show that this 'scalar' type system enjoys both the subject-reduction property and the strong-normalisation property, which constitute our main technical results.
Edit intent: fluency
Original:  The latter yields a significant simplification of the linear-algebraic \lambda-calculus itself, by removing the need for some restrictions in its reduction rules -- and thus leaving it more intuitive .
Revised:  The latter yields a significant simplification of the linear-algebraic lambda-calculus itself, by removing the need for some restrictions in its reduction rules -- and thus leaving it more intuitive .
Edit intent: coherence
Original:  The latter yields a significant simplification of the linear-algebraic \lambda-calculus itself, by removing the need for some restrictions in its reduction rules -- and thus leaving it more intuitive .
Revised:  The latter yields a significant simplification of the linear-algebraic \lambda-calculus itself, by removing the need for some restrictions in its reduction rules .
Edit intent: coherence
Original:  As an example , we show how to use this type system in order to guarantee the well-definiteness of probabilistic functions (\Sigma%DIFDELCMD < \alphai%%%  =1) -- thereby specializing Lineal into a probabilistic, higher-order \lambda-calculus.
Revised:  As an example %DIFDELCMD < \alphai%%% =1) -- thereby specializing Lineal into a probabilistic, higher-order \lambda-calculus.
Edit intent: coherence