wanyu/IteraTeR_v2 huggingface dataset:
Original:  We formulate a conjecture on graph connections, whose validity follows by the successful avoidance of an explicit cut-type obstacle that we call "cut-obstacle" .
Revised:  We formulate a conjecture on graph connections, whose validity follows by the successful avoidance of an explicit cut-type obstacle that we call cut-obstacles .
Edit intent: fluency
Original:  It has been reported in a number of studies that the protein sectors found by SCA are functionally significant, with different sectors controlling different biochemical properties of the protein.
Revised:  It has been asserted that the protein sectors found by SCA are functionally significant, with different sectors controlling different biochemical properties of the protein.
Edit intent: clarity
Original:  It has been reported in a number of studies that the protein sectors found by SCA are functionally significant, with different sectors controlling different biochemical properties of the protein.
Revised:  It has been reported in a number of studies that the protein sectors identified by SCA are functionally significant, with different sectors controlling different biochemical properties of the protein.
Edit intent: fluency
Original:  We analyze the available experimental data and show that for proteins where a single SCA sectoris identified, the functionally-significant residues can also be found using single-site statistics such as conservation.
Revised:  Here we reconsider the available experimental data and show that for proteins where a single SCA sectoris identified, the functionally-significant residues can also be found using single-site statistics such as conservation.
Edit intent: clarity
Original: If a graph has no induced subgraph isomorphic to any graph in a finite family \{H_1, \ldots ,H_p\}, it is said to be (H_1, \ldots ,H_p)-free.
Revised: If a graph has no induced subgraph isomorphic to any graph in a finite family \{H_1, \ldots ,H_p\}, it is said to be (H_1, ... ,H_p)-free.
Edit intent: coherence
Original:  To reduce the number of open cases we also determine a number of new graph classes of bounded clique-width as well as a number of new graph classes of unbounded clique-width.
Revised:  To reduce the number of open cases we determine new graph classes of bounded clique-width as well as a number of new graph classes of unbounded clique-width.
Edit intent: coherence
Original:  To reduce the number of open cases we also determine a number of new graph classes of bounded clique-width as well as a number of new graph classes of unbounded clique-width.
Revised:  To reduce the number of open cases we also determine a number of new graph classes of bounded clique-width and new graph classes of unbounded clique-width.
Edit intent: coherence
Original:  Finally, we show algorithmic consequences of our results for the graph colouring problem restricted to (H_1,H_2)-free graphs.
Revised:  Finally, we show algorithmic consequences of our results for the graph colour
Edit intent: clarity
Original:  We briefly revisit the notions and instead propose a more general formulation of roles based on the similarity of a feature representation (in contrast to the graph representation).
Revised:  We briefly revisit these early notions and instead propose a more general formulation of roles based on the similarity of a feature representation (in contrast to the graph representation).
Edit intent: clarity
Original:  This leads us to propose a taxonomy of two general classes of techniques for discovering roles which includes (i) graph-based roles and (ii) feature-based roles .
Revised:  This leads us to propose a taxonomy of two general classes of techniques for discovering roles that includes (i) graph-based roles and (ii) feature-based roles .
Edit intent: fluency
Original:  This leads us to propose a taxonomy of two general classes of techniques for discovering roles which includes (i) graph-based roles and (ii) feature-based roles .
Revised:  This leads us to propose a taxonomy of two general classes of techniques for discovering roles which includes (i) graph-based roles , (ii) feature-based roles .
Edit intent: fluency
Original:  In particular, we also introduce a flexible framework for discovering roles using the notion of structural similarity on a feature-based representation.
Revised:  In particular, we also introduce a flexible framework for discovering roles using the notion of similarity on a feature-based representation.
Edit intent: clarity
Original:  The framework consists of two fundamental components: ( 1 ) role feature construction and ( 2 ) role assignment using the learned feature representation.
Revised:  The framework consists of two fundamental components: ( a ) role feature construction and ( 2 ) role assignment using the learned feature representation.
Edit intent: fluency
Original:  The framework consists of two fundamental components: ( 1 ) role feature construction and ( 2 ) role assignment using the learned feature representation.
Revised:  The framework consists of two fundamental components: ( 1 ) role feature construction and ( b ) role assignment using the learned feature representation.
Edit intent: clarity
Original:  We discuss the relevant decisions for discovering feature-based roles and highlight the advantages and disadvantages of the many techniques that can be used for this purpose .
Revised:  We discuss the different possibilities for discovering feature-based roles and highlight the advantages and disadvantages of the many techniques that can be used for this purpose .
Edit intent: clarity
Original:  We discuss the relevant decisions for discovering feature-based roles and highlight the advantages and disadvantages of the many techniques that can be used for this purpose .
Revised:  We discuss the relevant decisions for discovering feature-based roles and the tradeoffs of the many techniques that can be used for this purpose .
Edit intent: clarity
Original:  We discuss the relevant decisions for discovering feature-based roles and highlight the advantages and disadvantages of the many techniques that can be used for this purpose .
Revised:  We discuss the relevant decisions for discovering feature-based roles and highlight the advantages and disadvantages of the many techniques for computing them .
Edit intent: clarity
Original:  The flocking of animals is perhaps a behavior of the species of prey only , but not the one of the predator.
Revised:  The flocking of animals is an universal behavior of the species of prey only , but not the one of the predator.
Edit intent: clarity
Original:  The flocking of animals is perhaps a behavior of the species of prey only , but not the one of the predator.
Revised:  The flocking of animals is perhaps a behavior of the species of prey , but not the one of the predator.
Edit intent: clarity
Original: Dynamic spectrum access (DSA) is a new paradigm in radio frequency spectrum sharing.
Revised: Dynamic spectrum access (DSA) is a new paradigm of secondary spectrum utilization and sharing.
Edit intent: clarity
Original:  It allows unlicensed secondary users (SUs) to access the spectrum licensed to primary spectrum owners (POs) opportunistically.
Revised:  It allows unlicensed secondary users (SUs) to exploit the under-utilized radio spectrum licensed to primary spectrum owners (POs) opportunistically.
Edit intent: clarity
Original:  Market-driven secondary spectrum trading is an effective way to provide proper economic incentive for DSA, andto achieve high spectrum secondary utilization efficiency in DSA . In this paper, we consider the short-term secondary spectrum trading between one PO and multiple SUs in a hybrid spectrum market consisting of both the futures market (with contract buyers) and the spot market (with spot transaction buyers) .
Revised:  Market-driven secondary spectrum trading is an effective way to provide proper economic incentive for DSA, andto achieve high spectrum secondary utilization efficiency in DSA . In this paper, we propose and study a hybrid secondary spectrum market consisting of both the futures market (with contract buyers) and the spot market (with spot transaction buyers) .
Edit intent: clarity
Original:  Market-driven secondary spectrum trading is an effective way to provide proper economic incentive for DSA, andto achieve high spectrum secondary utilization efficiency in DSA . In this paper, we consider the short-term secondary spectrum trading between one PO and multiple SUs in a hybrid spectrum market consisting of both the futures market (with contract buyers) and the spot market (with spot transaction buyers) .
Revised:  Market-driven secondary spectrum trading is an effective way to provide proper economic incentive for DSA, andto achieve high spectrum secondary utilization efficiency in DSA . In this paper, we consider the short-term secondary spectrum trading between one PO and multiple SUs in a hybrid spectrum market consisting of both the futures market and the spot market (with spot transaction buyers) .
Edit intent: clarity
Original:  To solve this problem, we first compute an optimal policy that maximizes the ex-ante expected spectrum  efficiency based on the stochastic distribution of network information , and then design a VCG-based mechanism that determines the real-time allocation and pricing under information asymmetry.
Revised:  To solve this problem, we first compute an optimal policy that maximizes the ex-ante expected spectrum efficiency based on the stochastic distribution of network information . We then propose an on-line VCG auction that determines the real-time allocation and pricing under information asymmetry.
Edit intent: clarity
Original:  With the spatial spectrum reuse, the VCG mechanism is NP-hard .
Revised:  With the spatial spectrum reuse, the proposed VCG auction is NP-hard .
Edit intent: clarity
Original:  Thus, we further propose a heuristics solution based on an  VCG-like mechanism with polynomial complexity, and quantify the associated efficiency loss systematically.
Revised:  Thus, we further propose a heuristics approach based on an VCG-like mechanism with polynomial complexity, and quantify the associated efficiency loss systematically.
Edit intent: clarity
Original: Dynamic spectrum access (DSA) is a new paradigm of secondary spectrum utilization and sharing.
Revised: Dynamic spectrum access is a new paradigm of secondary spectrum utilization and sharing.
Edit intent: clarity
Original:  It allows unlicensed secondary users (SUs) to exploit  the under-utilized radio spectrum licensed to primary users opportunistically . Market mechanism is a widely-used promising means to regulate the consuming behaviours of users and, hence, achieve the efficient allocation and consumption of limited resources.
Revised:  It allows unlicensed secondary users (SUs) to exploit the under-utilized licensed spectrum . Market mechanism is a widely-used promising means to regulate the consuming behaviours of users and, hence, achieve the efficient allocation and consumption of limited resources.
Edit intent: clarity
Original:  It allows unlicensed secondary users (SUs) to exploit  the under-utilized radio spectrum licensed to primary users opportunistically . Market mechanism is a widely-used promising means to regulate the consuming behaviours of users and, hence, achieve the efficient allocation and consumption of limited resources.
Revised:  It allows unlicensed secondary users (SUs) to exploit the under-utilized radio spectrum licensed to primary users opportunistically . Market mechanism is a widely-used promising means to regulate the consuming behaviours of users and, hence, achieves the efficient allocation and consumption of limited resources.
Edit intent: fluency
Original:  In this paper, we propose and study a hybrid secondary spectrum market consisting of both the futures market and the spot market, in which SUs (buyers) purchase under-utilized licensed spectrum from a primary spectrum regulator(PR) , either through predefined contracts via the futures market, or through spot transactions via the spot market.
Revised:  In this paper, we propose and study a hybrid secondary spectrum market consisting of both the futures market and the spot market, in which SUs (buyers) purchase under-utilized licensed spectrum from a spectrum regulator , either through predefined contracts via the futures market, or through spot transactions via the spot market.
Edit intent: clarity
Original:  To solve this problem, we first derive an o?ff-line optimal allocation policy that maximizes the ex-ante expected spectrum utilization efficiency based on the stochastic distribution of network information.
Revised:  To solve this problem, we first derive an off-line optimal allocation policy that maximizes the ex-ante expected spectrum utilization efficiency based on the stochastic distribution of network information.
Edit intent: fluency
Original:  With this aim we apply two methods , Markov chains and Google matrix, for the analysis of the hyperlink networks of 24 Wikipedia language editions, and rank all their articles by PageRank, 2DRank , and CheiRank algorithms.
Revised:  With this aim , we apply methods of Markov chains and Google matrix, for the analysis of the hyperlink networks of 24 Wikipedia language editions, and rank all their articles by PageRank, 2DRank , and CheiRank algorithms.
Edit intent: clarity
Original:  With this aim we apply two methods , Markov chains and Google matrix, for the analysis of the hyperlink networks of 24 Wikipedia language editions, and rank all their articles by PageRank, 2DRank , and CheiRank algorithms.
Revised:  With this aim we apply two methods , Markov chains and Google matrix, for the analysis of the hyperlink networks of 24 Wikipedia language editions, and rank all their articles by PageRank, 2DRank and CheiRank algorithms.
Edit intent: fluency
Original:  Using automatic extraction of people names  we obtain the top 100 historical figures  for each edition and for each algorithm.
Revised:  Using automatic extraction of people names , we obtain the top 100 historical figures for each edition and for each algorithm.
Edit intent: fluency
Original:  Using automatic extraction of people names  we obtain the top 100 historical figures  for each edition and for each algorithm.
Revised:  Using automatic extraction of people names we obtain the top 100 historical figures , for each edition and for each algorithm.
Edit intent: fluency
Original:  Our study demonstrates not only the existence of skewness with local figures, mainly recognized only in their own culture , but also the existence of global historical figures appearing in a large number of editions.
Revised:  Our study demonstrates not only the existence of skewness with local figures, mainly recognized only in their own cultures , but also the existence of global historical figures appearing in a large number of editions.
Edit intent: fluency
Original:  Considering historical figures who appear in multiple editions as interactions between cultures, we construct a network of cultures and identify the most influential cultures according to such network.
Revised:  Considering historical figures who appear in multiple editions as interactions between cultures, we construct a network of cultures and identify the most influential cultures according to this network.
Edit intent: clarity
Original: The computational cost of counting the number of solutions satisfying a boolean formula, which is a problem instance of #SAT, has proven subtle to quantify.
Revised: The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify.
Edit intent: fluency
Original:  By these methods, we give an algorithm using an axiomatic tensor contraction language for n-variable #SAT instances with complexity O(( n\log(n)) ^{O(1)} 2^c) , where c is the number of COPY-tensors in the network.
Revised:  By these methods, we give an algorithm using an axiomatic tensor contraction language for n-variable #SAT instances with complexity O(( n\log(n)) ^{O(1)} 2^c) where c is the number of COPY-tensors in the network.
Edit intent: fluency
Original:  Therefore the counting problems can be solved efficiently when a specific tensor network expression has at most O(\log c) COPY-tensors and polynomial fan-out .
Revised:  Therefore the counting problems can be solved efficiently when their tensor network expression has at most O(\log c) COPY-tensors and polynomial fan-out .
Edit intent: clarity
Original:  We consider computations acting on abstract "distributions" , in which probabilities are replaced by "amplitudes" drawn from a semiring S.
Revised:  We consider computations acting on abstract "distributions" . In these distributions, probabilities are replaced by "amplitudes" drawn from a semiring S.
Edit intent: clarity
Original:  Wilcock and Sabry [arXiv:1102.3587] show that UNIQUE-SAT is efficiently solvable using invertible transformations in the case S = \mathbb F_2. Extending this result, we show that for prime powers k%DIFDELCMD < \geqslant %%% 2, the decision problems solvable in polynomial time using either invertible or "unitary" transformations over  S = \mathbb F_kare those in the class Mod_{\mathit kP .
Revised:  Wilcock and Sabry [arXiv:1102.3587] show that UNIQUE-SAT is %DIFDELCMD < \geqslant %%% 2, the decision problems solvable in polynomial time using either invertible or "unitary" transformations over S = \mathbb F_kare those in the class Mod_{\mathit kP .
Edit intent: clarity
Original:  Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for N-th order tensors.
Revised:  Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for N^{th order tensors.
Edit intent: fluency
Original:  Results: We present\betaada an integrated approach to study signatures of local adaptation, providing rapid processing of whole genome data and enabling assessment of spatial association using molecular markers.
Revised:  Results: We present\betaada, an integrated approach to study signatures of local adaptation, providing rapid processing of whole genome data and enabling assessment of spatial association using molecular markers.
Edit intent: fluency
Original:  Availabilty: Sam \ss%DIFDELCMD < }%%% ada\betaada\betaada is an open source software written in C++ available at URL (under the license GNU GPL 3).
Revised:  \ss%DIFDELCMD < }%%% ada\betaada\betaada is an open source software written in C++ available at URL (under the license GNU GPL 3).
Edit intent: coherence
Original:  Availabilty: Sam \ss%DIFDELCMD < }%%% ada\betaada\betaada is an open source software written in C++ available at URL (under the license GNU GPL 3).
Revised:  Availabilty: Sam %DIFDELCMD < }%%% ada\betaada\betaada is an open source software written in C++ available at URL (under the license GNU GPL 3).
Edit intent: fluency
Original: The Gale-Shapely algorithm for the Stable Marriage Problem is known to take \Theta(n^2) steps to find a stable marriage in the worst case, but only \Theta(n \log n) steps in the average case (with n women and n men).
Revised: The Gale-Shapley algorithm for the Stable Marriage Problem is known to take \Theta(n^2) steps to find a stable marriage in the worst case, but only \Theta(n \log n) steps in the average case (with n women and n men).
Edit intent: fluency
Original:   Using a reduction to the communication complexity of the disjointness problem, we prove a significantly more general - albeit slightly weaker - result, showing that \Omega(n^2) Boolean queries of any type are required.
Revised:  Using a reduction to the communication complexity of the disjointness problem, we give a far simpler, yet significantly more powerful argument showing that \Omega(n^2) Boolean queries of any type are required.
Edit intent: clarity
Original:  Our lower boundgeneralizes to (A) randomized algorithms, (B) even just verifying the stability  of a proposed marriage, ( C) even allowing arbitrary separate preprocessing of the women's preferences  and of the men's preferences  , and ( D ) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage.
Revised:  Our lower boundgeneralizes to (A) randomized algorithms, (B) even just verifying the stability of a proposed marriage, ( D) allowing arbitrary separate preprocessing of the women's preferences and of the men's preferences , and ( D ) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage.
Edit intent: coherence
Original:  Our lower boundgeneralizes to (A) randomized algorithms, (B) even just verifying the stability  of a proposed marriage, ( C) even allowing arbitrary separate preprocessing of the women's preferences  and of the men's preferences  , and ( D ) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage.
Revised:  Our lower boundgeneralizes to (A) randomized algorithms, (B) even just verifying the stability of a proposed marriage, ( C) even allowing arbitrary separate preprocessing of the women's preferences and of the men's preferences profile , and ( D ) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage.
Edit intent: clarity
Original:  A significantly more general - albeit slightly weaker - lower bound follows from Segal's elaborate analysis of communication complexity, namely that \Omega(n^2) Boolean queries are required in order to find a stable marriage, regardless of the set of allowed Boolean queries.
Revised:  A significantly more general - albeit slightly weaker - lower bound follows from Segal's general analysis of communication complexity, namely that \Omega(n^2) Boolean queries are required in order to find a stable marriage, regardless of the set of allowed Boolean queries.
Edit intent: clarity
Original:  Notably, unlike Segal's lower bound, our lower bound generalizes also to (A) randomized algorithms, (B) finding approximately-stable marriages (C) verifying the stability (or the approximate stability) of a proposed marriage, (D) allowing arbitrary separate preprocessing of the women's preferences profile and of the men's preferences profile, and (E ) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage  .
Revised:  Notably, unlike Segal's lower bound, our lower bound generalizes also to (A) randomized algorithms, (B) allowing arbitrary separate preprocessing of the women's preferences profile and of the men's preferences profile, and (E ) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage .
Edit intent: coherence
Original:  Notably, unlike Segal's lower bound, our lower bound generalizes also to (A) randomized algorithms, (B) finding approximately-stable marriages (C) verifying the stability (or the approximate stability) of a proposed marriage, (D) allowing arbitrary separate preprocessing of the women's preferences profile and of the men's preferences profile, and (E ) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage  .
Revised:  Notably, unlike Segal's lower bound, our lower bound generalizes also to (A) randomized algorithms, (B) finding approximately-stable marriages (C) verifying the stability (or the approximate stability) of a proposed marriage, (D) allowing arbitrary separate preprocessing of the women's preferences profile and of the men's preferences profile, (C ) several variants of the basic problem, such as whether a given pair is married in every/some stable marriage .
Edit intent: coherence
Original: Uncovering urban mobility patterns is crucial for further predicting and controlling spatially embedded events.
Revised: The identification of urban mobility patterns is crucial for further predicting and controlling spatially embedded events.
Edit intent: clarity