wanyu/IteraTeR_v2 huggingface dataset:
Original:  Global cooperation by exploring a rapidly changing environment may cause an occasional over-perturbation exhausting system-resources, causing rapid degradation, ageing and death of an otherwise forever-young network in a necrosis-like process.
Revised:  Global cooperation by exploring a rapidly changing environment may cause an occasional over-perturbation exhausting system-resources, and causing death in a necrosis-like process.
Edit intent: clarity
Original: Peer-to-peer  locality has recently raised a lot of interest in the community.
Revised: Peer-to-peer (P2P) locality has recently raised a lot of interest in the community.
Edit intent: clarity
Original:  Indeed, whereas peer-to-peer content distribution enables financial saving for the content providers who do not have to maintain a dedicated infrastructure , it dramatically increases the traffic on inter-ISP links.
Revised:  Indeed, whereas P2P content distribution enables financial saving for the content providers who do not have to maintain a dedicated infrastructure , it dramatically increases the traffic on inter-ISP links.
Edit intent: fluency
Original:  Indeed, whereas peer-to-peer content distribution enables financial saving for the content providers who do not have to maintain a dedicated infrastructure , it dramatically increases the traffic on inter-ISP links.
Revised:  Indeed, whereas peer-to-peer content distribution enables financial savings for the content providers who do not have to maintain a dedicated infrastructure , it dramatically increases the traffic on inter-ISP links.
Edit intent: fluency
Original:  Indeed, whereas peer-to-peer content distribution enables financial saving for the content providers who do not have to maintain a dedicated infrastructure , it dramatically increases the traffic on inter-ISP links.
Revised:  Indeed, whereas peer-to-peer content distribution enables financial saving for the content providers , it dramatically increases the traffic on inter-ISP links.
Edit intent: clarity
Original:  To solve this issue, the idea to keep a fraction of the peer-to-peer traffic local to each ISP was introduced a few years ago.
Revised:  To solve this issue, the idea to keep a fraction of the P2P traffic local to each ISP was introduced a few years ago.
Edit intent: clarity
Original:  Since then, peer-to-peer solutions exploiting locality have been introduced.
Revised:  Since then, P2P solutions exploiting locality have been introduced.
Edit intent: clarity
Original:  For instance , how far can we push locality for a peer-to-peer distribution without impacting its robustness ?
Revised:  In particular , how far can we push locality for a peer-to-peer distribution without impacting its robustness ?
Edit intent: clarity
Original:  In particular, we show that high locality values enable up to two orders of magnitude saving on inter-ISP links without any significant impact on peers download completion time  .
Revised:  In particular, we show that high locality values enable up to two orders of magnitude inter-ISP links without any significant impact on peers download completion time .
Edit intent: clarity
Original:  < (g'')^2 and h'''h' < (h'')^2) , the level sets of f form a family of pseudocircles in the plane, the minimization diagram of translates of f has linear complexity and can be constructed in O(n log n) randomized expected time, all cells in the minimization diagram are connected, and the set of bisectors separating any one cell in the diagram from each of the others forms an arrangement of pseudolines in the plane.
Revised:  < (g'')^2 and h'''h' < (h'')^2) , the level sets of f form a family of pseudocircles in the plane, all cells in the minimization diagram are connected, and the set of bisectors separating any one cell in the diagram from each of the others forms an arrangement of pseudolines in the plane.
Edit intent: coherence
Original:  We also experiment with using a variant of Lloyd's algorithm, adapted to smoothed distance, to find uniformly spaced point samples with exponentially decreasing density around a point o .
Revised:  We also experiment with a variant of Lloyd's algorithm, adapted to smoothed distance, to find uniformly spaced point samples with exponentially decreasing density around a point o .
Edit intent: fluency
Original:  We also experiment with using a variant of Lloyd's algorithm, adapted to smoothed distance, to find uniformly spaced point samples with exponentially decreasing density around a point o .
Revised:  We also experiment with using a variant of Lloyd's algorithm, adapted to smoothed distance, to find uniformly spaced point samples with exponentially decreasing density around a given point .
Edit intent: clarity
Original: The enormous successes have been made by quantum algorithms during the last decade.
Revised: Enormous successes have been made by quantum algorithms during the last decade.
Edit intent: clarity
Original:  In this paper, we combine the quantum game with the problem of data clustering, and develop clustering algorithms based on it , in which data points in a dataset are considered as players who can make decisions and play quantum strategies in quantum games.
Revised:  In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm , in which data points in a dataset are considered as players who can make decisions and play quantum strategies in quantum games.
Edit intent: coherence
Original:  In this paper, we combine the quantum game with the problem of data clustering, and develop clustering algorithms based on it , in which data points in a dataset are considered as players who can make decisions and play quantum strategies in quantum games.
Revised:  In this paper, we combine the quantum game with the problem of data clustering, and develop clustering algorithms based on it , in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games.
Edit intent: clarity
Original:  After playing quantum games , each player's expected payoff is calculated and then he uses an link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them for maximizing his payoff.
Revised:  After each round of a quantum game , each player's expected payoff is calculated and then he uses an link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them for maximizing his payoff.
Edit intent: clarity
Original:  After playing quantum games , each player's expected payoff is calculated and then he uses an link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them for maximizing his payoff.
Revised:  After playing quantum games , each player's expected payoff is calculated . Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them for maximizing his payoff.
Edit intent: coherence
Original:  After playing quantum games , each player's expected payoff is calculated and then he uses an link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them for maximizing his payoff.
Revised:  After playing quantum games , each player's expected payoff is calculated and then he uses an link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff.
Edit intent: clarity
Original:  Thanks to Weitz's self-avoiding tree, we extends the result for graphs which are sparse in some average sense, which makes in our framework part of the recent work of Mossel and SlyMS08, who proved the strong spatial mixing property for ferromagnetic Ising model.
Revised:  Thanks to Weitz's self-avoiding tree, we extends the result for sparse on average graphs, which generalizes part of the recent work of Mossel and SlyMS08, who proved the strong spatial mixing property for ferromagnetic Ising model.
Edit intent: clarity
Original:  (2) we give a polynomial-time O(k(n_{1 algorithm to determine whether any given two multi-letter QFAs for accepting unary languages are equivalent, and, indeed, we prove that a k_{1}-letter QFA {\cal A}_1 and another k_{2}-letter QFA {\cal A}_2 are equivalent if and only if they are k (n_{1}+n_{2})^{ 2 } -equivalent , where n_{1} and n_{2} are the numbers of states of {\cal A}_{1} and {\cal A}_{2}, respectively, and k=\max(k_{1},k_{2}).
Revised:  (2) we give a polynomial-time algorithm to determine whether any given two multi-letter QFAs for accepting unary languages are equivalent, and, indeed, we prove that a k_{1}-letter QFA {\cal A}_1 and another k_{2}-letter QFA {\cal A}_2 are equivalent if and only if they are k (n_{1}+n_{2})^{ 2 } -equivalent , where n_{1} and n_{2} are the numbers of states of {\cal A}_{1} and {\cal A}_{2}, respectively, and k=\max(k_{1},k_{2}).
Edit intent: clarity
Original:  (2) we give a polynomial-time O(k(n_{1 algorithm to determine whether any given two multi-letter QFAs for accepting unary languages are equivalent, and, indeed, we prove that a k_{1}-letter QFA {\cal A}_1 and another k_{2}-letter QFA {\cal A}_2 are equivalent if and only if they are k (n_{1}+n_{2})^{ 2 } -equivalent , where n_{1} and n_{2} are the numbers of states of {\cal A}_{1} and {\cal A}_{2}, respectively, and k=\max(k_{1},k_{2}).
Revised:  (2) we give a polynomial-time O(k(n_{1 algorithm to determine whether any given two multi-letter QFAs for accepting unary languages are equivalent, and, indeed, we prove that a k_{1}-letter QFA {\cal A}_1 and another k_{2}-letter QFA {\cal A}_2 are equivalent if and only if they are (n_{1}+n_{2})^{ 2 } -equivalent , where n_{1} and n_{2} are the numbers of states of {\cal A}_{1} and {\cal A}_{2}, respectively, and k=\max(k_{1},k_{2}).
Edit intent: coherence
Original: Multi-letter {\it quantum finite automata} (QFAs) were a new one-way QFA model proposed recently by Belovs, Rosmanis, and Smotrovs \mbox{ BRS07 and they showed that multi-letter QFAs can precisely accept some regular languages ((a+b)^{*}b) that are unacceptable by the usual one-way QFAs.
Revised: Multi-letter {\it quantum finite automata} (QFAs) were a new one-way QFA model proposed recently by Belovs, Rosmanis, and Smotrovs \mbox{ BRS07 and they showed that multi-letter QFAs can accept with no error some regular languages ((a+b)^{*}b) that are unacceptable by the usual one-way QFAs.
Edit intent: clarity
Original: Multi-letter {\it quantum finite automata} (QFAs) were a new one-way QFA model proposed recently by Belovs, Rosmanis, and Smotrovs \mbox{ BRS07 and they showed that multi-letter QFAs can precisely accept some regular languages ((a+b)^{*}b) that are unacceptable by the usual one-way QFAs.
Revised: Multi-letter {\it quantum finite automata} (QFAs) were a new one-way QFA model proposed recently by Belovs, Rosmanis, and Smotrovs \mbox{ BRS07 and they showed that multi-letter QFAs can precisely accept some regular languages ((a+b)^{*}b) that are unacceptable by the one-way QFAs.
Edit intent: clarity
Original:  In this paper, we continue to deal with multi-letter QFAs , and we mainly focus on two issues: (1) we show that (k+1)-letter QFAs are computationally more powerful than k-letter QFAs, that is, (k+1)-letter QFAs can accept some regular languages  unacceptable by any k-letter QFA.
Revised:  In this paper, we continue to study multi-letter QFAs , and we mainly focus on two issues: (1) we show that (k+1)-letter QFAs are computationally more powerful than k-letter QFAs, that is, (k+1)-letter QFAs can accept some regular languages unacceptable by any k-letter QFA.
Edit intent: clarity
Original:  In this paper, we continue to deal with multi-letter QFAs , and we mainly focus on two issues: (1) we show that (k+1)-letter QFAs are computationally more powerful than k-letter QFAs, that is, (k+1)-letter QFAs can accept some regular languages  unacceptable by any k-letter QFA.
Revised:  In this paper, we continue to deal with multi-letter QFAs . We mainly focus on two issues: (1) we show that (k+1)-letter QFAs are computationally more powerful than k-letter QFAs, that is, (k+1)-letter QFAs can accept some regular languages unacceptable by any k-letter QFA.
Edit intent: coherence
Original:  In this paper, we continue to deal with multi-letter QFAs , and we mainly focus on two issues: (1) we show that (k+1)-letter QFAs are computationally more powerful than k-letter QFAs, that is, (k+1)-letter QFAs can accept some regular languages  unacceptable by any k-letter QFA.
Revised:  In this paper, we continue to deal with multi-letter QFAs , and we mainly focus on two issues: (1) we show that (k+1)-letter QFAs are computationally more powerful than k-letter QFAs, that is, (k+1)-letter QFAs can accept some regular languages that are unacceptable by any k-letter QFA.
Edit intent: fluency
Original:  A comparison to the usual one-way QFAs is made by some examples;
Revised:  A comparison with the one-way QFAs is made by some examples;
Edit intent: clarity
Original:  (2) we give a polynomial-time algorithm to determine whether any given two multi-letter QFAs for accepting unary languages are equivalent, and, indeed, we prove that a k_{1}-letter QFA {\cal A}_1 and another k_{2}-letter QFA {\cal A}_2 are equivalent if and only if they are (n_{1}+n_{2})^{4}+k-1-equivalent,  where n_{1} and n_{2} are the numbers of states of {\cal A}_{1} and {\cal A}_{2}, respectively, and k=\max(k_{1},k_{2}).
Revised:  (2) we prove that a k_{1}-letter QFA {\cal A}_1 and another k_{2}-letter QFA {\cal A}_2 are equivalent if and only if they are (n_{1}+n_{2})^{4}+k-1-equivalent, where n_{1} and n_{2} are the numbers of states of {\cal A}_{1} and {\cal A}_{2}, respectively, and k=\max(k_{1},k_{2}).
Edit intent: coherence
Original: Protecting against link failures in autonomic communication networks is essential to increase robustness, accessibility, and reliability of data transmission.
Revised: Agile recovery from link failures in autonomic communication networks is essential to increase robustness, accessibility, and reliability of data transmission.
Edit intent: clarity
Original:   Recently, network coding has been proposed as a solution to provide agile and cost efficient network self-healing and self-protection against link failures, which does not require data rerouting, or packet retransmission .
Revised:  Recently, network coding has been proposed as a solution to provide agile and cost efficient network self-healing against link failures, which does not require data rerouting, or packet retransmission .
Edit intent: clarity
Original:   Recently, network coding has been proposed as a solution to provide agile and cost efficient network self-healing and self-protection against link failures, which does not require data rerouting, or packet retransmission .
Revised:  Recently, network coding has been proposed as a solution to provide agile and cost efficient network self-healing and self-protection against link failures, in a manner that does not require data rerouting, or packet retransmission .
Edit intent: clarity
Original:  In this paper we introduce autonomic self-healing and self-protection network strategies based on network coding and reduced capacity, a technique known asnetwork protection codes (NPC).
Revised:  In this paper we introduce autonomic self-healing and self-protection network strategies based on network coding and reduced capacity, network protection codes (NPC).
Edit intent: clarity
Original:  In these strategies, an autonomic communication is able to provide self-protection and self-recovery from various network failures affecting network operations .
Revised:  In these strategies, an autonomic network is able to provide self-protection and self-recovery from various network failures affecting network operations .
Edit intent: clarity
Original:  In these strategies, an autonomic communication is able to provide self-protection and self-recovery from various network failures affecting network operations .
Revised:  In these strategies, an autonomic communication is able to provide self-healing from various network failures affecting network operations .
Edit intent: clarity
Original:  In these strategies, an autonomic communication is able to provide self-protection and self-recovery from various network failures affecting network operations .
Revised:  In these strategies, an autonomic communication is able to provide self-protection and self-recovery from various network failures affecting network operation .
Edit intent: fluency
Original:  The techniques improve services and enhance reliability of autonomic communication.
Revised:  The techniques improve service and enhance reliability of autonomic communication.
Edit intent: fluency
Original:  The network protection codes are extended to be self-healing and self-protecting against multiple link failures and can be implemented at an overlay layer in autonomic communication networks.
Revised:  The network protection codes are extended to provide self-healing and self-protecting against multiple link failures and can be implemented at an overlay layer in autonomic communication networks.
Edit intent: clarity
Original:  The network protection codes are extended to be self-healing and self-protecting against multiple link failures and can be implemented at an overlay layer in autonomic communication networks.
Revised:  The network protection codes are extended to be self-healing from multiple link failures and can be implemented at an overlay layer in autonomic communication networks.
Edit intent: coherence
Original:  We present bounds and network protection code constructions , furthermore tables of the best known self-healing codes are presented .
Revised:  We present bounds and network protection code constructions .
Edit intent: clarity
Original: We study the relationship between the computational hardness of two  well-studied problems in algorithmic semi-algebraic geometry -- namely the problem of deciding sentences in the first order theory of  reals with a constant number of quantifier alternations, and that of computing Betti numbers of semi-algebraic sets.
Revised: We study the relationship between the computational hardness of two well-studied problems in algorithmic semi-algebraic geometry -- namely the problem of deciding sentences in the first order theory of the reals with a constant number of quantifier alternations, and that of computing Betti numbers of semi-algebraic sets.
Edit intent: fluency
Original:  An analogous result in the complexity theory over the reals (in the sense of Blum-Shub-Smale real Turing machines) has been missing so far.
Revised:  An analogous result in the complexity theory over the reals (in the sense of Blum-Shub-Smale real machines) has been missing so far.
Edit intent: clarity
Original:  We present a deterministic (Delta + 1)-coloring distributed algorithm with running time O( \Delta ) + 1/2 \log ^* n.
Revised:  We present a deterministic (Delta + 1)-coloring distributed algorithm with running time O( Delta ) + 1/2 \log ^* n.
Edit intent: fluency
Original:  We present a deterministic (Delta + 1)-coloring distributed algorithm with running time O( \Delta ) + 1/2 \log ^* n.
Revised:  We present a deterministic (Delta + 1)-coloring distributed algorithm with running time O( \Delta ) + 1/2 log ^* n.
Edit intent: fluency
Original:  On the way to this result we introduce a generalization of the notion of graph coloring, which we call relaxed coloring.
Revised:  On the way to this result we study a generalization of the notion of graph coloring, which we call relaxed coloring.
Edit intent: clarity
Original:  We also develop a technique to employ multiple relaxed colorings of various subgraphs of the original graph G for computing a (Delta+1)-coloring of G. We believe that these techniques and the notion of relaxed coloring are of independent interest.
Revised:  We also develop a technique to employ multiple defect colorings of various subgraphs of the original graph G for computing a (Delta+1)-coloring of G. We believe that these techniques and the notion of relaxed coloring are of independent interest.
Edit intent: fluency
Original:  We also develop a technique to employ multiple relaxed colorings of various subgraphs of the original graph G for computing a (Delta+1)-coloring of G. We believe that these techniques and the notion of relaxed coloring are of independent interest.
Revised:  We also develop a technique to employ multiple relaxed colorings of various subgraphs of the original graph G for computing a (Delta+1)-coloring of G. We believe that these techniques are of independent interest.
Edit intent: clarity
Original:  In other words , there is no polynomial-time algorithm for SCARF unless PPAD is a subset of P.
Revised:  Hence , there is no polynomial-time algorithm for SCARF unless PPAD is a subset of P.
Edit intent: coherence
Original:  However, the complexity of the computational version of Scarf's lemma (SCARF) is unknown .
Revised:  However, the complexity of the computational version of Scarf's lemma (SCARF) remained open .
Edit intent: clarity
Original: Actin networks in certain single-celled organisms exhibit a complex pattern-forming dynamics that starts with the appearance of static `spots ' of actin on the cell cortex.
Revised: Actin networks in certain single-celled organisms exhibit a complex pattern-forming dynamics that starts with the appearance of static spots of actin on the cell cortex.
Edit intent: fluency
Original:  Spots soon become mobile,  and eventually give rise to , and coexist with, traveling waves of actin.
Revised:  Spots soon become mobile, and eventually give rise to traveling waves of actin.
Edit intent: clarity
Original:  Waves confer motility upon the cell by impinging on its periphery.
Edit intent: clarity
Original:  By contrast, we find no evidence to support a homophilic version of the model , nor does conventional time-aggregated network analysis help unravel the dynamics .
Revised:  By contrast, we find no evidence to support a version of the model , nor does conventional time-aggregated network analysis help unravel the dynamics .
Edit intent: clarity
Original:  Starting from simple principles, we show that the impact of a trade on prices is directly proportional to the size of the transaction and the amount of liquidityof the asset.
Revised:  We show that the impact of a trade on prices is directly proportional to the size of the transaction and the amount of liquidityof the asset.
Edit intent: coherence
Original:  Starting from simple principles, we show that the impact of a trade on prices is directly proportional to the size of the transaction and the amount of liquidityof the asset.
Revised:  Starting from simple principles, we show that the impact of a market order on prices depends on the size of the transaction and the amount of liquidityof the asset.
Edit intent: clarity
Original:  We  show that, with the use of volatility swaps, contingent claims whose payoffs depend on the value of the asset can be approximately replicated  .
Revised:  We show that, with the use of variance swaps, contingent claims whose payoffs depend on the value of the asset can be approximately replicated .
Edit intent: fluency
Original:  The numbers of balls with a given color are i.i.d. random variables with a specific probability distribution, for instance a Pareto or a Weibull distribution.
Revised:  The numbers of balls with a given color are i.i.d. random variables with a heavy tailed probability distribution, for instance a Pareto or a Weibull distribution.
Edit intent: clarity
Original:  By means of Le Cam's inequality and Chen-Stein method, we establish bounds in total variation norm between the distribution of the number of balls drawn with a given color and the Poisson distribution with the same mean  .
Revised:  By means of Le Cam's inequality and Chen-Stein method, bounds for the total variation norm between the distribution of the number of balls drawn with a given color and the Poisson distribution with the same mean .
Edit intent: clarity