wanyu/IteraTeR_v2 huggingface dataset:
Original: A graph G with a list of colors L(v) and weight \omega (v) for each vertex v is (L, \omega )-colorable if one can choose a subset of \omega (v) colors from L(v) for each vertex v, such that adjacent vertices receive disjoint color sets.
Revised: A graph G with a list of colors L(v) and weight \omega (v) for each vertex v is (L, w )-colorable if one can choose a subset of \omega (v) colors from L(v) for each vertex v, such that adjacent vertices receive disjoint color sets.
Edit intent: clarity
Original:  One application is to the bitsize of the eigenvalues and eigenvectors of an integer matrix, which also yields a new proof that the problem is strongly polynomial.
Revised:  One application is to the bitsize of the eigenvalues and eigenvectors of an integer matrix, which also yields a new proof that the problem is polynomial.
Edit intent: clarity
Original: Moral Foundation Theory (MFT) states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations on a subset of issues.
Revised: Moral Foundation Theory states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations on a subset of issues.
Edit intent: clarity
Original:  Here we use methods of statistical mechanics to characterize the collective behavior of an agent-based model society whose inter individual interactions due to information exchange in the form of opinions , are in qualitative agreement with neurocognitive and psychological data.
Revised:  Here we characterize the collective behavior of an agent-based model society whose inter individual interactions due to information exchange in the form of opinions , are in qualitative agreement with neurocognitive and psychological data.
Edit intent: clarity
Original:  Here we use methods of statistical mechanics to characterize the collective behavior of an agent-based model society whose inter individual interactions due to information exchange in the form of opinions , are in qualitative agreement with neurocognitive and psychological data.
Revised:  Here we use methods of statistical mechanics to characterize the collective behavior of an agent-based model whose inter individual interactions due to information exchange in the form of opinions , are in qualitative agreement with neurocognitive and psychological data.
Edit intent: clarity
Original:  Here we use methods of statistical mechanics to characterize the collective behavior of an agent-based model society whose inter individual interactions due to information exchange in the form of opinions , are in qualitative agreement with neurocognitive and psychological data.
Revised:  Here we use methods of statistical mechanics to characterize the collective behavior of an agent-based model society whose inter individual interactions due to information exchange in the form of opinions are in qualitative agreement with neurocognitive and psychological data.
Edit intent: fluency
Original:  Here we use methods of statistical mechanics to characterize the collective behavior of an agent-based model society whose inter individual interactions due to information exchange in the form of opinions , are in qualitative agreement with neurocognitive and psychological data.
Revised:  Here we use methods of statistical mechanics to characterize the collective behavior of an agent-based model society whose inter individual interactions due to information exchange in the form of opinions , are in qualitative agreement with data.
Edit intent: clarity
Original:  The main conclusion derived from the model is that the existence of diversity in the cognitive strategies yields different statistics for the sets of moral foundations and that these arise from the cognitive interactions of the agents.
Revised:  The main conclusion derived connects the existence of diversity in the cognitive strategies yields different statistics for the sets of moral foundations and that these arise from the cognitive interactions of the agents.
Edit intent: clarity
Original:  The main conclusion derived from the model is that the existence of diversity in the cognitive strategies yields different statistics for the sets of moral foundations and that these arise from the cognitive interactions of the agents.
Revised:  The main conclusion derived from the model is that the existence of diversity in the cognitive strategies and statistics of the sets of moral foundations and that these arise from the cognitive interactions of the agents.
Edit intent: clarity
Original:  The main conclusion derived from the model is that the existence of diversity in the cognitive strategies yields different statistics for the sets of moral foundations and that these arise from the cognitive interactions of the agents.
Revised:  The main conclusion derived from the model is that the existence of diversity in the cognitive strategies yields different statistics for the sets of moral foundations and suggests that this connection arises from interactions between agents.
Edit intent: clarity
Original:  Thus a simple interacting agent model, whose interactions are in accord with empirical data about moral dynamics , presents statistical signatures consistent with those that characterize opinions of conservatives and liberals.
Revised:  Thus a simple interacting agent model, whose interactions are in accord with empirical data about moral dynamics , presents statistical signatures consistent with those that characterize moral judgment patterns of conservatives and liberals.
Edit intent: clarity
Original:  Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with those that characterize moral judgment patterns of conservatives and liberals  .
Revised:  Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with moral judgment patterns of conservatives and liberals .
Edit intent: clarity
Original: In order to appreciate how good we as mathematicians and scientists have it today, with extremely fast hardware and lots and lots of memory, as well as with readily available high-level software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and carefully examine , as a case study, a problem that was considered a huge challenge back then, and compare notes.
Revised: In order to appreciate how well off we mathematicians and scientists have it today, with extremely fast hardware and lots and lots of memory, as well as with readily available high-level software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and carefully examine , as a case study, a problem that was considered a huge challenge back then, and compare notes.
Edit intent: clarity
Original: In order to appreciate how good we as mathematicians and scientists have it today, with extremely fast hardware and lots and lots of memory, as well as with readily available high-level software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and carefully examine , as a case study, a problem that was considered a huge challenge back then, and compare notes.
Revised: In order to appreciate how good we as mathematicians and scientists are today, with extremely fast hardware and lots and lots of memory, as well as with readily available high-level software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and carefully examine , as a case study, a problem that was considered a huge challenge back then, and compare notes.
Edit intent: clarity
Original: In order to appreciate how good we as mathematicians and scientists have it today, with extremely fast hardware and lots and lots of memory, as well as with readily available high-level software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and carefully examine , as a case study, a problem that was considered a huge challenge back then, and compare notes.
Revised: In order to appreciate how good we as mathematicians and scientists have it today, with extremely fast hardware and lots and lots of memory, as well as with powerful software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and carefully examine , as a case study, a problem that was considered a huge challenge back then, and compare notes.
Edit intent: clarity
Original: In order to appreciate how good we as mathematicians and scientists have it today, with extremely fast hardware and lots and lots of memory, as well as with readily available high-level software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and carefully examine , as a case study, a problem that was considered a huge challenge back then, and compare notes.
Revised: In order to appreciate how good we as mathematicians and scientists have it today, with extremely fast hardware and lots and lots of memory, as well as with readily available high-level software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and compare how things went then. We have chosen , as a case study, a problem that was considered a huge challenge back then, and compare notes.
Edit intent: clarity
Original:  We chose C.L. Pekeris' 1958 seminal work on the ground state energies of two-electron atoms.
Revised:  We chose C.L. Pekeris' s seminal 1958 work on the ground state energies of two-electron atoms.
Edit intent: fluency
Original:  All computations will be done ab initio with today's software and hardware, with a special emphasis on the symbolic computations which in 1958 had to be made by hand, and which nowadays can be automated and generalized.
Revised:  We went through all the computations ab initio with today's software and hardware, with a special emphasis on the symbolic computations which in 1958 had to be made by hand, and which nowadays can be automated and generalized.
Edit intent: clarity
Original:  Performance of these protocols is affected by many physical layer (PHY) parameters, which are not well studied in the literature .
Revised:  For the most part, the works appearing in the literature make idealized and simplifying assumptions about the underlying physical layer as well as some aspects of the link adaptation protocol. The result is that the performance predicted by such works may not necessarily be a good predictor of actual performance in a fully deployed system .
Edit intent: clarity
Original:  This letter places bounds on the degree and quality of such oscillations when the system in question is homogeneous and has discrete states.
Revised:  The question of the number of possible oscillations and the coherent quality of those oscillations remain unanswered. This paper proves the upper-bounds on the number and quality of such oscillations when the system in question is homogeneous and has discrete states.
Edit intent: clarity
Original:  This letter places bounds on the degree and quality of such oscillations when the system in question is homogeneous and has discrete states.
Revised:  This letter places bounds on the degree and quality of such oscillations when the system in question is homogeneously driven and has discrete states.
Edit intent: clarity
Original:  This fundamental limit serves as a key design principle for engineered dynamics in chemical systems and nano-scale machines .
Revised:  I also prove that homogeneously driven systems with discrete states must have a loop topology to allow oscillations. The consequences of this limit are explored in the context of chemical clocks and limit cycles .
Edit intent: coherence
Original:  The question of the number of possible oscillations and the coherent quality of those oscillations remain unanswered.
Revised:  The questions of the number of possible oscillations and the coherent quality of those oscillations remain unanswered.
Edit intent: fluency
Original:  The questions of the number of possible oscillations and the coherent quality of those oscillations remain unanswered.
Revised:  The question of the number of possible oscillations and the coherent quality of those oscillations remain unanswered.
Edit intent: fluency
Original:  The questions of the number of possible oscillations and the coherent quality of those oscillations remain unanswered.
Revised:  The questions of the number of possible oscillations and the coherent quality of these oscillations remain unanswered.
Edit intent: clarity
Original:  This paper proves the upper-bounds on the number and quality of such oscillations when the system in question is homogeneously driven and has discrete states.
Revised:  This paper proves the upper-bounds on the number and quality of such oscillations when the system in question is homogeneously driven and has a discrete network of states.
Edit intent: clarity
Original:  In a closed system, the maximum number of oscillations is bounded by the system dimension .
Revised:  In a closed system, the maximum number of oscillations is bounded by the number of states in the network .
Edit intent: clarity
Original:  In open systems, the system size bounds the quality factor of oscillation.
Revised:  In open systems, the size of the network bounds the quality factor of oscillation.
Edit intent: clarity
Original:  Each controller acts on many targets, and target nodes are controlled by many controllers in a strongly overlapping many-to-many network structure.
Revised:  Each controller acts on many targets, and targets affected by many controllers in a strongly overlapping many-to-many network structure.
Edit intent: clarity
Original:  Each controller acts on many targets, and target nodes are controlled by many controllers in a strongly overlapping many-to-many network structure.
Revised:  Each controller acts on many targets, and target nodes are controlled by many controllers , but these " many-to-many network structure.
Edit intent: coherence
Original:  We present a quantitative analysis of the network properties of three key biological systems for which sufficiently comprehensive datasets are now available: transcription factors, microRNAs  and protein kinases .
Revised:  We present a quantitative analysis of the network properties of three key biological systems for which sufficiently comprehensive datasets are now available: transcription factors, microRNAs , and protein kinases .
Edit intent: fluency
Original: For every \epsilon > 0 and large enough k we construct unsatisfiable k-CNF formulas where every clause has k distinct literals and every variable appears in at most (2/e + \epsilon) 2 ^k /k clauses.
Revised: We construct unsatisfiable k-CNF formulas where every clause has k distinct literals and every variable appears in at most (2/e + \epsilon) 2 ^k /k clauses.
Edit intent: coherence
Original: For every \epsilon > 0 and large enough k we construct unsatisfiable k-CNF formulas where every clause has k distinct literals and every variable appears in at most (2/e + \epsilon) 2 ^k /k clauses.
Revised: For every \epsilon > 0 and large enough k we construct unsatisfiable k-CNF formulas where every clause has k distinct literals and every variable appears in at most (2/e + \epsilon) 2 ^{k /k clauses.
Edit intent: fluency
Original:  Using a result of Berman, Karpinski and Scott we also show that our result is asymptotically best possible : every k-CNF formula where every variable appears in at most 2^{k+1 .
Revised:  Using a result of Berman, Karpinski and Scott we also show that our result is asymptotically best possible .
Edit intent: coherence
Original:  We establish that the  bound on l(k) obtained from the local lemma is asymptotically optimal, i.e., l(k) = ( e^{-1 + o(1))2 ^k.
Revised:  We establish that the bound on l(k) obtained from the Local Lemma is asymptotically optimal, i.e., l(k) = ( e^{-1 + o(1))2 ^k.
Edit intent: fluency
Original:  The ]  constructed formulas are all in the class MU(1)of minimal unsatisfiable formulas having one more clause than variablesand thus they resolve these asymptotic questions within that class as well ]  .
Revised:  The ] and thus the constructed formulas are all in the class MU(1)of minimal unsatisfiable formulas having one more clause than variablesand thus they resolve these asymptotic questions within that class as well ] .
Edit intent: coherence
Original:  The ]  constructed formulas are all in the class MU(1)of minimal unsatisfiable formulas having one more clause than variablesand thus they resolve these asymptotic questions within that class as well ]  .
Revised:  The ] constructed formulas are in the class MU(1)of minimal unsatisfiable formulas having one more clause than variablesand thus they resolve these asymptotic questions within that class as well ] .
Edit intent: clarity
Original:  The Lopsided Local Lemma , applied with assignment of random values according to counterintuitive probabilities, shows that our result is asymptotically best possible.
Revised:  The Lopsided Local Lemma shows that this is asymptotically best possible.
Edit intent: clarity
Original:  The determination of this extremal function is particularly important as it represents the value where the  k-SAT problem exhibits its complexity hardness jump: from having every instance being a YES-instance it becomes NP-hard just by allowing each variable to occur in one more clause.
Revised:  The determination of this extremal function is particularly important as it represents the value where the k-SAT problem exhibits a complexity hardness jump: from having every instance being a YES-instance it becomes NP-hard just by allowing each variable to occur in one more clause.
Edit intent: clarity
Original:  To obtain the asymptotically optimal binary trees we consider a continuous approximation of the problem , set up a differential equation and estimate its solution .
Revised:  The main novelty of our approach here comes in setting up an appropriate continuous approximation of the problem , set up a differential equation and estimate its solution .
Edit intent: clarity
Original:  To obtain the asymptotically optimal binary trees we consider a continuous approximation of the problem , set up a differential equation and estimate its solution .
Revised:  To obtain the asymptotically optimal binary trees we consider a continuous approximation of the problem . This leads us to a differential equation and estimate its solution .
Edit intent: coherence
Original:  The  binary trees constructed also give asymptotically precise answers for seemingly unrelated problems like the European Tenure Game introduced by Doerr [9] and the search problem with bounded number of consecutive lies , considered in a problem of the 2012 IMO contest.
Revised:  The importance of the binary trees constructed also give asymptotically precise answers for seemingly unrelated problems like the European Tenure Game introduced by Doerr [9] and the search problem with bounded number of consecutive lies , considered in a problem of the 2012 IMO contest.
Edit intent: clarity
Original:  The  binary trees constructed also give asymptotically precise answers for seemingly unrelated problems like the European Tenure Game introduced by Doerr [9] and the search problem with bounded number of consecutive lies , considered in a problem of the 2012 IMO contest.
Revised:  The binary trees constructed also give asymptotically precise answers for seemingly unrelated problems like the European Tenure Game introduced by Doerr [9] and a search problem allowing a limited number of consecutive lies , considered in a problem of the 2012 IMO contest.
Edit intent: clarity
Original:  Starting from an educated guess for the odometer, we successively correct under- and overestimates and provably arrive at the correct final state.
Revised:  Starting from an approximation for the odometer, we successively correct under- and overestimates and provably arrive at the correct final state.
Edit intent: clarity
Original:  Without  Allee effect, the transition is continuous and the width w of the hull scales as in conventional (i.e., uncorrelated) gradient percolation, proportional to g^(-0.57).
Revised:  Without the Allee effect, the transition is continuous and the width w of the hull scales as in conventional (i.e., uncorrelated) gradient percolation, proportional to g^(-0.57).
Edit intent: fluency
Original:  However, with a strong Allee effect the transition is first-order and w is proportional to g^(-0.26).
Revised:  However, with a strong Allee effect the transition is first order and w is proportional to g^(-0.26).
Edit intent: fluency
Original: We introduce the algorithm NTRFinder to find a complex repetitive structure in DNA we call a nested tandem repeat (NTR).
Revised: We introduce the software tool NTRFinder to find a complex repetitive structure in DNA we call a nested tandem repeat (NTR).
Edit intent: clarity
Original: We introduce the algorithm NTRFinder to find a complex repetitive structure in DNA we call a nested tandem repeat (NTR).
Revised: We introduce the algorithm NTRFinder to find the complex repetitive structure in DNA we call a nested tandem repeat (NTR).
Edit intent: fluency
Original:  An NTR is a recurrence of two  distinct tandem motifs interspersed with each other.
Revised:  An NTR is a recurrence of two or more distinct tandem motifs interspersed with each other.
Edit intent: clarity
Original:  We discuss how one of these may assist in determining the cultivation prehistory of the ancient staple food crop taro (Colocasia esculenta).
Revised:  We discuss how one of these may assist in determining the cultivation prehistory of this ancient staple food crop taro (Colocasia esculenta).
Edit intent: fluency
Original: This paper investigates the role of two ordering principles, homophily and focus constraint , in shaping collaborative scientific research.
Revised: This paper investigates the role of homophily and focus constraint , in shaping collaborative scientific research.
Edit intent: clarity
Original: This paper investigates the role of two ordering principles, homophily and focus constraint , in shaping collaborative scientific research.
Revised: This paper investigates the role of two ordering principles, homophily and focus constraint in shaping collaborative scientific research.
Edit intent: fluency
Original:  A community-detection algorithm for formalising this perspective will be proposed and applied to the co-authorship network of the scientists that submitted to the 2001 Research Assessment Exercise in Business and Management in the UK . While results only partially support research-based homophily, they indicate that scientists use status positions for discriminating between potential partners by selecting collaborators from institutions with a rating similar to their own.
Revised:  A community-detection algorithm is applied to the co-authorship network of the scientists that submitted to the 2001 Research Assessment Exercise in Business and Management in the UK . While results only partially support research-based homophily, they indicate that scientists use status positions for discriminating between potential partners by selecting collaborators from institutions with a rating similar to their own.
Edit intent: clarity