wanyu/IteraTeR_v2 huggingface dataset:
Original:  The main objective of this paper is to identify necessary and sufficient conditions on failed events under which a decomposable global task can still be achieved successfully between two cooperative agents .
Revised:  The main objective of this paper is to identify necessary and sufficient conditions on failed events under which a decomposable global task can still be achieved successfully .
Edit intent: clarity
Original:  For such a purpose, a notion called passivity for the failed events is introduced , based on which necessary and sufficient conditions for the reliability of cooperative tasking under  failures are derived, followed by illustrative examples and remarks for the derived conditions.
Revised:  For such a purpose, a notion called passivity for the failed events is introduced , based on which necessary and sufficient conditions for the reliability of cooperative tasking under event failures are derived, followed by illustrative examples and remarks for the derived conditions.
Edit intent: fluency
Original:  The latter result answers Steel's Quartet Challenge on the difficulty of finding additional solutions \sc  to Quartet Compatibility  .
Revised:  The latter result shows that Steel's Quartet Challenge on the difficulty of finding additional solutions \sc to Quartet Compatibility .
Edit intent: clarity
Original:  The latter result answers Steel's Quartet Challenge on the difficulty of finding additional solutions \sc  to Quartet Compatibility  .
Revised:  The latter result answers Steel's \sc to Quartet Compatibility .
Edit intent: coherence
Original:  The basic set-up consists of a system with multiple agents corresonding to the nodes of a graph whose edges represent the information that is available to the agents.
Revised:  The basic set-up consists of a system with multiple agents corresponding to the nodes of a graph whose edges represent the information that is available to the agents.
Edit intent: fluency
Original:  The basic set-up consists of a system with multiple agents corresonding to the nodes of a graph whose edges represent the information that is available to the agents.
Revised:  The basic set-up consists of a system with multiple agents corresonding to the nodes of a graph whose edges encode the information that is available to the agents.
Edit intent: clarity
Original:  Formation control is concerned with problems in which agents are required to stabilize at a given distance of other agents.
Revised:  Formation control is concerned with problems in which agents are required to stabilize at a given distance from other agents.
Edit intent: fluency
Original:  Said otherwise: is minimal rigidity sufficient for global stabilization?
Edit intent: coherence
Original:  The control of directed formations has proven  more difficult than initially thought, as is exemplified by the lack of global result for formations with n >3 agents.
Revised:  The control of directed formations has proven to be more difficult than initially thought, as is exemplified by the lack of global result for formations with n >3 agents.
Edit intent: fluency
Original:  We established in part I that the space of planar formations had a non-trivial  topology.
Revised:  We established in part I that the space of planar formations has a non-trivial topology.
Edit intent: fluency
Original:  We apply this framework to the study of a directed formation with n = 4 agents and show that the agents do not have enough information to evaluate locally stabilizing feedback laws.
Revised:  We apply this framework to the study of a directed formation with n = 4 agents and show that the agents do not have enough information to implement locally stabilizing feedback laws.
Edit intent: clarity
Original:  A sizable literature exists on the ultimate fixation .
Revised:  Both the ultimate fixation .
Edit intent: clarity
Original:  Interesting issues relating to the transient dynamics , with multiple time scales , Maxwell-type construction borrowed from statistical physics, and the dilemma diffusion approximation faces, are discussed .
Revised:  Several issues relating to the transient dynamics , with multiple time scales , Maxwell-type construction borrowed from statistical physics, and the dilemma diffusion approximation faces, are discussed .
Edit intent: clarity
Original:  It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that  made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.
Revised:  It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.
Edit intent: coherence
Original: Location distinction is defined as determining when a device has changed its position .
Revised: Location distinction is defined as determining whether or not the position of a device has changed its position .
Edit intent: clarity
Original: Location distinction is defined as determining when a device has changed its position .
Revised: Location distinction is defined as determining when a device has changed .
Edit intent: clarity
Original: The numerical method for study of hydrodynamic flows over an arbitrary bed profile in the presence of external force is proposed in this paper .
Revised: The numerical method for study of hydrodynamic flows over an arbitrary bed profile in the presence of external force is proposed .
Edit intent: clarity
Original:  This method takes into account the external force effect, it uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with consideration of features of the flow near the step.
Revised:  This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with consideration of features of the flow near the step.
Edit intent: coherence
Original:  This method takes into account the external force effect, it uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with consideration of features of the flow near the step.
Revised:  This method takes into account the external force effect, it uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with advanced consideration of the flow features near the step.
Edit intent: clarity
Original:  The quasi-two-layer approach allows to determine the size of the dry zone of the vertical component of the step.
Revised:  The quasi-two-layer approach determines the size of the dry zone of the vertical component of the step.
Edit intent: clarity
Original:  There are performed the numerical simulations based on the proposed algorithm of various physical phenomena, such as a breakdown of the rectangular fluid column over an inclined plane, the large-scale motion of fluid in the gravitational field in the presence of Coriolis force over an underlying mountain-like surface.
Revised:  There are performed the numerical simulations based on the proposed algorithm of various physical phenomena, such as a breakdown of the rectangular fluid column over an inclined plane, large-scale motion of fluid in the gravitational field in the presence of Coriolis force over an underlying mountain-like surface.
Edit intent: fluency
Original:  There are performed the numerical simulations based on the proposed algorithm of various physical phenomena, such as a breakdown of the rectangular fluid column over an inclined plane, the large-scale motion of fluid in the gravitational field in the presence of Coriolis force over an underlying mountain-like surface.
Revised:  There are performed the numerical simulations based on the proposed algorithm of various physical phenomena, such as a breakdown of the rectangular fluid column over an inclined plane, the large-scale motion of fluid in the gravity field in the presence of Coriolis force over an underlying mountain-like surface.
Edit intent: fluency
Original:  We then show that, in the same time complexity, we can attain approximation factors of O(log opt ) for simple polygons and O((1+ log( h+1)) log opt ) for polygons with holes . Some of these results were obtained independently by Jang and Kwon (2011) .
Revised:  We then show that, in the same time complexity, we can attain approximation factors of O(log opt ) for simple polygons and O((1+ log( h+1)) log opt ) for polygons with holes .
Edit intent: coherence
Original: Due to the vast space of possible networks and the relatively small amount of data available, inferring genetic networks from gene expression data is one of the most challenging work in the post-genomic era  .
Revised: Inferring genetic networks from gene expression data is one of the most challenging work in the post-genomic era .
Edit intent: clarity
Original:  In this paper, we propose an original approach for inferring gene regulation network using a robust biological prior on  structure in order to limit the set of candidate networks.
Revised:  In this paper, we propose an original approach for inferring gene regulation networks using a robust biological prior on structure in order to limit the set of candidate networks.
Edit intent: fluency
Original:  In this paper, we propose an original approach for inferring gene regulation network using a robust biological prior on  structure in order to limit the set of candidate networks.
Revised:  In this paper, we propose an original approach for inferring gene regulation network using a robust biological prior on their structure in order to limit the set of candidate networks.
Edit intent: clarity
Original:  Our approach enables to compare the network inferred between two conditions of interest (for instance case and control networks) and help along the biological interpretation of results.
Revised:  Our approach enables to compare the networks inferred between two conditions of interest (for instance case and control networks) and help along the biological interpretation of results.
Edit intent: fluency
Original:  We illustrate the proposed approach by applying our method to Network Inference in breast cancer's response to treatment study .
Revised:  We illustrate the proposed approach by applying our method to a study of breast cancer's response to treatment study .
Edit intent: clarity
Original:  We illustrate the proposed approach by applying our method to Network Inference in breast cancer's response to treatment study .
Revised:  We illustrate the proposed approach by applying our method to Network Inference in breast cancer's response to treatment .
Edit intent: clarity
Original: We propose a very simple (almost linear) stochastic map model of economic dynamics.
Revised: We propose a stochastic map model of economic dynamics.
Edit intent: coherence
Original:  Our proposed model can generate the Gamma-like and the power law distributions as has been observed in the real data of income and wealth distributions .
Revised:  The proposed model attempts to produce positively skewed distributions and the power law distributions as has been observed in the real data of income and wealth distributions .
Edit intent: clarity
Original:  Our proposed model can generate the Gamma-like and the power law distributions as has been observed in the real data of income and wealth distributions .
Revised:  Our proposed model can generate the Gamma-like and the power law distributions as has been observed in the real data of income and wealth .
Edit intent: fluency
Original:  Also, it is able to produce a non-trivial phase transition in the opinion of a society (opinion formation).
Revised:  Also, it shows a non-trivial phase transition in the opinion of a society (opinion formation).
Edit intent: clarity
Original:  Therefore, we compare the results obtained from these two approaches and point out a number of new features obtained from the map model.
Revised:  Therefore, we compare the results obtained from these two approaches and discuss a number of new features obtained from the map model.
Edit intent: clarity
Original:  Our goal is to find an accurate clustering while keeping the number of queriessmall .
Revised:  Our goal is to find an accurate clustering using few queries .
Edit intent: clarity
Original:  We model the problem as a point set S with an unknown metric d on S, and assume that we have access to one versus all distance queries that given a point s in S return the distances between s and all other points.
Revised:  We model the problem as a point set S with an unknown metric d on S, and assume that we have access to one versus all distance queries that given a point s in S return the distances between s and all other points.
Edit intent: fluency
Original:  Given a natural assumption about the approximation stability of the min-sum objective function for clustering, we design a provably accurate clustering algorithm that uses few one versus all queries.
Revised:  Given a natural assumption about the approximation stability of the min-sum objective function for clustering, we design a provably accurate clustering algorithm that uses few one versus all queries.
Edit intent: fluency
Original:  In our empirical study we compare our clusterings to gold-standard classifications and show that our method compares favorably to well-established clustering algorithms  .
Revised:  In our empirical study we show that our method compares favorably to well-established clustering algorithms .
Edit intent: coherence
Original:  By known lower bounds on resolution refutations, this implies an exponential separation of TC^0-Frege from resolution in the average case.
Edit intent: coherence
Original:  The idea is based on demonstrating efficient propositional correctness proofs of the random 3CNF unsatisfiability witnesses given by Feige, Kim and Ofek FOCS'06 . Since the soundness of these witnesses is verified using spectral techniques, we develop an appropriate way to reason about eigenvectors in propositional systems.
Revised:  The idea is based on demonstrating efficient propositional correctness proofs of the random 3CNF unsatisfiability witnesses given by Feige, Kim and Ofek (2006) . Since the soundness of these witnesses is verified using spectral techniques, we develop an appropriate way to reason about eigenvectors in propositional systems.
Edit intent: clarity
Original:  To carry out the full argument we work inside weak formal systems of arithmetic , use a general translation scheme to propositional proofs and then show how to turn these proofs into random 3CNF refutations .
Revised:  To carry out the full argument we work inside weak formal systems of arithmetic and use a general translation scheme to propositional proofs and then show how to turn these proofs into random 3CNF refutations .
Edit intent: fluency
Original:  To carry out the full argument we work inside weak formal systems of arithmetic , use a general translation scheme to propositional proofs and then show how to turn these proofs into random 3CNF refutations .
Revised:  To carry out the full argument we work inside weak formal systems of arithmetic , use a general translation scheme to propositional proofs .
Edit intent: coherence
Original: We extend languages of dot-depth one to infinite words.
Revised: Over finite words, languages of dot-depth one to infinite words.
Edit intent: clarity
Original:  As for finite words, this class of languages corresponds to BSigma1, the first level of the quantifier alternation hierarchy of first-order  logic FO = FO <, +1, min, max%DIFDELCMD < ]%%% . We give a decidable characterization of BSigma1 <, +1,min over infinite words ;
Revised:  As for finite words, this class of languages corresponds to BSigma1, the first level of the quantifier alternation hierarchy of first-order logic <, +1, min, max%DIFDELCMD < ]%%% . We give a decidable characterization of BSigma1 <, +1,min over infinite words ;
Edit intent: coherence
Original:  As for finite words, this class of languages corresponds to BSigma1, the first level of the quantifier alternation hierarchy of first-order  logic FO = FO <, +1, min, max%DIFDELCMD < ]%%% . We give a decidable characterization of BSigma1 <, +1,min over infinite words ;
Revised:  As for finite words, this class of languages corresponds to BSigma1, the first level of the quantifier alternation hierarchy of first-order logic FO = FO %DIFDELCMD < ]%%% . We give a decidable characterization of BSigma1 <, +1,min over infinite words ;
Edit intent: coherence
Original:  As for finite words, this class of languages corresponds to BSigma1, the first level of the quantifier alternation hierarchy of first-order  logic FO = FO <, +1, min, max%DIFDELCMD < ]%%% . We give a decidable characterization of BSigma1 <, +1,min over infinite words ;
Revised:  As for finite words, this class of languages corresponds to BSigma1, the first level of the quantifier alternation hierarchy of first-order logic FO = FO <, +1, min, max%DIFDELCMD < ]%%% <, +1,min over infinite words ;
Edit intent: coherence
Original:  We prove a decidable characterization for BSigma1 <,+1,min as well as for BSigma1 <,+1,min,max%DIFDELCMD < ] %%% over finite and infinite words .
Revised:  We <,+1,min as well as for BSigma1 <,+1,min,max%DIFDELCMD < ] %%% over finite and infinite words .
Edit intent: clarity
Original:  We prove a decidable characterization for BSigma1 <,+1,min as well as for BSigma1 <,+1,min,max%DIFDELCMD < ] %%% over finite and infinite words .
Revised:  We prove a decidable characterization for BSigma1 then obtain the results for infinite words as well as for BSigma1 <,+1,min,max%DIFDELCMD < ] %%% over finite and infinite words .
Edit intent: clarity
Original:  We prove a decidable characterization for BSigma1 <,+1,min as well as for BSigma1 <,+1,min,max%DIFDELCMD < ] %%% over finite and infinite words .
Revised:  We prove a decidable characterization for BSigma1 <,+1,min as well as for <,+1,min,max%DIFDELCMD < ] %%% over finite and infinite words .
Edit intent: fluency
Original:  In particular, a new combinatorial proof of Knast's Theorem concerning languages of dot-depth one over finite words is included .
Revised:  In particular, we give a new proof of Knast's Theorem concerning languages of dot-depth one over finite words is included .
Edit intent: clarity
Original:  In particular, a new combinatorial proof of Knast's Theorem concerning languages of dot-depth one over finite words is included .
Revised:  In particular, a new combinatorial proof of Knast's Theorem on languages of dot-depth one over finite words is included .
Edit intent: clarity
Original:  In particular, a new combinatorial proof of Knast's Theorem concerning languages of dot-depth one over finite words is included .
Revised:  In particular, a new combinatorial proof of Knast's Theorem concerning languages of dot-depth one over finite words .
Edit intent: clarity
Original: A directed graph is called Eulerian, if it contains a walk that traverses every arc in the graph exactly once.
Revised: A directed graph is called Eulerian, if it contains a tour that traverses every arc in the graph exactly once.
Edit intent: clarity
Original:  We study the problem of Eulerian Extension (EE) where a directed multigraph G and a weight function is given and it is asked whether G can be made Eulerian by adding arcs whose total weight does not exceed a given threshold.
Revised:  We study the problem of Eulerian extension (EE) where a directed multigraph G and a weight function is given and it is asked whether G can be made Eulerian by adding arcs whose total weight does not exceed a given threshold.
Edit intent: fluency
Original:  However, EE is NP- hard and thus we use the parameterized complexity framework to analyze it.
Revised:  However, EE is NP-hard and thus we use the parameterized complexity framework to analyze it.
Edit intent: coherence
Original:  In parameterized complexity, the running time of algorithms is considered not only with respect to input length, but also with respect to other properties of the input-called "parameters".
Revised:  In parameterized complexity, the running time of algorithms is considered not only with respect to input length, but also with respect to other properties of the input - called "parameters".
Edit intent: fluency
Original:  Dorn et  al. proved that EE can be solved in O(4^k n^4) time, where k denotes the parameter "number of arcs that have to be added".
Revised:  Dorn et . al. proved that EE can be solved in O(4^k n^4) time, where k denotes the parameter "number of arcs that have to be added".
Edit intent: fluency
Original: The paper is devoted to complete proofs of theorems on consistency on cubic lattices for 3 x 3 determinants.
Revised: The paper is devoted to complete proofs of theorems on consistency on cubic lattices for 3 \times 3 determinants.
Edit intent: clarity
Original:  The discrete nonlinear equations on Z ^2 defined by the condition that the determinants of all 3 x 3 matrices of values of the scalar field at the points of the lattice Z ^2 that form elementary 3 x 3 squares vanish are considered;
Revised:  The discrete nonlinear equations on Z ^2 defined by the condition that the determinants of all 3 \times 3 matrices of values of the scalar field at the points of the lattice Z ^2 that form elementary 3 x 3 squares vanish are considered;
Edit intent: clarity
Original:  The discrete nonlinear equations on Z ^2 defined by the condition that the determinants of all 3 x 3 matrices of values of the scalar field at the points of the lattice Z ^2 that form elementary 3 x 3 squares vanish are considered;
Revised:  The discrete nonlinear equations on Z ^2 defined by the condition that the determinants of all 3 x 3 matrices of values of the scalar field at the points of the lattice Z ^2 that form elementary 3 \times 3 squares vanish are considered;
Edit intent: clarity
Original:  and for arbitrary initial data satisfying these concrete conditions of general position, theorems on consistency on cubic lattices  for the considered discrete nonlinear equations on Z ^2 defined by 3 x 3 determinants are proved.
Revised:  and for arbitrary initial data satisfying these concrete conditions of general position, theorems on consistency on cubic lattices for the considered discrete nonlinear equations on Z ^2 defined by 3 \times 3 determinants are proved.
Edit intent: clarity
Original:  In this paper, we examine -- for a suitably-scaled set of parameters -- the complex interaction occurring between several classes of traffic when an unstable class is penalized proportionally to its level of congestion .
Revised:  In this paper, we examine the complex interaction occurring between several classes of traffic when an unstable class is penalized proportionally to its level of congestion .
Edit intent: clarity
Original:  We characterize the evolution of the performance measures of the network from the moment the initial surge takes place until the system reaches its equilibrium.
Revised:  We characterize the evolution of the network from the moment the initial surge takes place until the system reaches its equilibrium.
Edit intent: clarity
Original:  Using a time-space-transition-scaling , we show that the trajectories of the temporarily unstable class can be described by a differential equation, while those of the stable classes retain their stochastic nature.
Revised:  Using an appropriate scaling , we show that the trajectories of the temporarily unstable class can be described by a differential equation, while those of the stable classes retain their stochastic nature.
Edit intent: clarity
Original:  We show that the free energy of the system possessing a wider binding energy spectrum is almost surely lower compared to the system possessing a narrower energy spectrum.
Revised:  We show that the free energy of the system possessing a wider binding energy spectrum is almost surely lower compared with the system possessing a narrower energy spectrum.
Edit intent: fluency