wanyu/IteraTeR_v2 huggingface dataset:
Original: This paper is motivated by the problem of error-free communication through the i.i.d. duplication channel which acts on the transmitted sequence by inserting a random number of duplicates of each symbol \cdots x_i of length \ell is inserted } next to the original symbol.
Revised: This paper is concerned with the problem of error-free communication through the i.i.d. duplication channel which acts on the transmitted sequence by inserting a random number of duplicates of each symbol \cdots x_i of length \ell is inserted } next to the original symbol.
Edit intent: clarity
Original: This paper is motivated by the problem of error-free communication through the i.i.d. duplication channel which acts on the transmitted sequence by inserting a random number of duplicates of each symbol \cdots x_i of length \ell is inserted } next to the original symbol.
Revised: This paper is motivated by the problem of error-free communication over an i.i.d. duplication channel which acts on the transmitted sequence by inserting a random number of duplicates of each symbol \cdots x_i of length \ell is inserted } next to the original symbol.
Edit intent: clarity
Original:  A construction of optimal codes correcting all patterns of errors of this type is described, and the zero-error capacity of the duplication channel is determined . A generalization of these results to channel models in which blocks of \ell consecutive symbols are being duplicated, and which are inspired by DNA-based data storage systems where the stored molecules are subject to tandem-duplication mutations, is also given .
Revised:  A construction of optimal codes correcting all patterns of errors of this type is described, and the zero-error capacity of the duplication channel is determined .
Edit intent: coherence
Original: This paper is concerned with the problem of error-free communication over an i.i.d. duplication channel whose action on a transmitted string x_1 \cdots x_n can be described as follows: for every i = \ell, \ldots, n , a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted }  next to the original substring (independently of everything else) .
Revised: This paper is concerned with the problem of error-free communication over the i.i.d. duplication channel whose action on a transmitted string x_1 \cdots x_n can be described as follows: for every i = \ell, \ldots, n , a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted } next to the original substring (independently of everything else) .
Edit intent: fluency
Original: This paper is concerned with the problem of error-free communication over an i.i.d. duplication channel whose action on a transmitted string x_1 \cdots x_n can be described as follows: for every i = \ell, \ldots, n , a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted }  next to the original substring (independently of everything else) .
Revised: This paper is concerned with the problem of error-free communication over an i.i.d. duplication channel which acts on a transmitted string x_1 \cdots x_n can be described as follows: for every i = \ell, \ldots, n , a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted } next to the original substring (independently of everything else) .
Edit intent: fluency
Original: This paper is concerned with the problem of error-free communication over an i.i.d. duplication channel whose action on a transmitted string x_1 \cdots x_n can be described as follows: for every i = \ell, \ldots, n , a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted }  next to the original substring (independently of everything else) .
Revised: This paper is concerned with the problem of error-free communication over an i.i.d. duplication channel whose action on a transmitted sequence x_1 \cdots x_n can be described as follows: for every i = \ell, \ldots, n , a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted } next to the original substring (independently of everything else) .
Edit intent: clarity
Original: This paper is concerned with the problem of error-free communication over an i.i.d. duplication channel whose action on a transmitted string x_1 \cdots x_n can be described as follows: for every i = \ell, \ldots, n , a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted }  next to the original substring (independently of everything else) .
Revised: This paper is concerned with the problem of error-free communication over an i.i.d. duplication channel whose action on a transmitted string x_1 \cdots x_n by inserting a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted } next to the original substring (independently of everything else) .
Edit intent: clarity
Original: This paper is concerned with the problem of error-free communication over an i.i.d. duplication channel whose action on a transmitted string x_1 \cdots x_n can be described as follows: for every i = \ell, \ldots, n , a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted }  next to the original substring (independently of everything else) .
Revised: This paper is concerned with the problem of error-free communication over an i.i.d. duplication channel whose action on a transmitted string x_1 \cdots x_n can be described as follows: for every i = \ell, \ldots, n , a random number of copies of the substring x_{i-\ell+1 \cdots x_i of length \ell is inserted } next to the original symbol .
Edit intent: clarity
Original:  This model is inspired by channels with certain types of synchronization errors, as well as by DNA-based data storage systems where the stored DNA sequences are subject to tandem-duplication mutations  .
Revised:  This model is inspired by DNA-based data storage systems where the stored DNA sequences are subject to tandem-duplication mutations .
Edit intent: clarity
Original:  This model is inspired by channels with certain types of synchronization errors, as well as by DNA-based data storage systems where the stored DNA sequences are subject to tandem-duplication mutations  .
Revised:  This model is inspired by channels with certain types of synchronization errors, as well as by DNA-based data storage systems wherein the stored molecules are subject to tandem-duplication mutations .
Edit intent: clarity
Original:  This revelation is made possible by ND, which provides a computationally light way to explore partially folded proteins via incomplete SCN0s. ND analysis affirms the presence of NS topology in its TS structures , and finds C to be a better measure of protein topology than RCO, to shed light on the hypothesized relationship between NS structure and folding rate.
Revised:  This revelation is made possible by ND, which provides a computationally light way to explore partially folded proteins via incomplete SCN0s. ND analysis affirms the presence of NS topology in its TS SCN0s , and finds C to be a better measure of protein topology than RCO, to shed light on the hypothesized relationship between NS structure and folding rate.
Edit intent: clarity
Original: A dynamic network-centric approach to study two-state folding from native structure called network dynamics (ND) is introduced.
Revised: The Network Dynamics (ND) is introduced.
Edit intent: coherence
Original:  Taken together, the two influences on the ordering of PRN0 contacts , result in more route-like formation of native shortcut networks, and hence more two-state like folding.
Revised:  The two influences on the ordering of PRN0 contacts , result in more route-like formation of native shortcut networks, and hence more two-state like folding.
Edit intent: coherence
Original:  Taken together, the two influences on the ordering of PRN0 contacts , result in more route-like formation of native shortcut networks, and hence more two-state like folding.
Revised:  Taken together, the two influences on the ordering of PRN0 contacts also result in more route-like formation of native shortcut networks, and hence more two-state like folding.
Edit intent: clarity
Original:  Of the five ND variants tested, the best results at  the macroscopic, mesoscopic and microscopic levels, were produced by a single variant.
Revised:  Of the five ND variants tested, the best results at each of the macroscopic, mesoscopic and microscopic levels, were produced by a single variant.
Edit intent: clarity
Original:  Of the five ND variants tested, the best results at  the macroscopic, mesoscopic and microscopic levels, were produced by a single variant.
Revised:  Of the five ND variants tested, the best results at the macroscopic, mesoscopic and microscopic levels, is produced by a single variant.
Edit intent: fluency
Original:  Correlation between experimental folding rates and ND simulated folding rates is strongest when the probability of edge creation is higher for contacts with smaller sequence separation, and when the probability of node selection is higher for nodes with larger remaining degree within a local neighborhood .
Revised:  Correlation between experimental folding rates . Over proteins of different chain fold types, this basic requirement is best satisfied when a recipe favours earlier restoration of edges with smaller sequence separation, and when the probability of node selection is higher for nodes with larger remaining degree within a local neighborhood .
Edit intent: clarity
Original:  These two conditions also induce a wider range of simulated folding rates, which is a sign of cooperative folding for two-state folders;
Revised:  These two conditions also induce a wider range of simulated folding rates, both of which signal cooperative two-state folders;
Edit intent: clarity
Original:  and better correspondence between experimental phi-values and calculated phi-values .
Revised:  and better correspondence between ND calculated phi-values and calculated phi-values .
Edit intent: clarity
Original:  and better correspondence between experimental phi-values and calculated phi-values .
Revised:  and better correspondence between experimental phi-values and experimental phi-values .
Edit intent: clarity
Original:  Further preliminary exploration of mixed ND variants by chain fold type suggests that these results could be improved with context-sensitive model parameters, and that the ND model could be extended to multi-state folders .
Revised:  Further preliminary exploration of mixed ND variants by chain fold type suggests that concocting further context-sensitive model parameters, and that the ND model could be extended to multi-state folders .
Edit intent: clarity
Original: Limited lookahead has been studied for decades in complete-information games.
Revised: Limited lookahead has been studied for decades in perfect-information games.
Edit intent: clarity
Original:  We initiate a new direction via two simultaneous deviation points: generalization to incomplete-information games and a game-theoretic approach.
Revised:  We initiate a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach.
Edit intent: clarity
Original:  We study this for opponents that differ based on their lookahead depth, based on whether they, too, have incomplete information, and based on how they break ties.
Revised:  We study this for opponents that differ based on their lookahead depth, based on whether they, too, have imperfect information, and based on how they break ties.
Edit intent: fluency
Original:  We characterize the hardness of finding a Nash equilibrium or an optimal commitment strategy for either player, showing that in some of these variations the problem can be solved in polynomial time while in others it is PPAD-hard or NP-hard  .
Revised:  We characterize the hardness of finding a Nash equilibrium or an optimal commitment strategy for either player, showing that in some of these variations the problem can be solved in polynomial time while in others it is PPAD-hard , NP-hard .
Edit intent: fluency
Original:  In this paper we propose a simple and natural version of IRLS for solving \ell_\infty and \ell_1 regression, which provably converges to a (1+\epsilon)-approximate solution in O(m^{1/3}\log(1/\epsilon)/\epsilon  + \log ( m/\epsilon )/\epsilon ^2) iterations, where m is the number of rows of the input matrix.
Revised:  In this paper we propose a simple and natural version of IRLS for solving \ell_\infty and \ell_1 regression, which provably converges to a (1+\epsilon)-approximate solution in O(m^{1/3}\log(1/\epsilon)/\epsilon + \log m/\epsilon )/\epsilon ^2) iterations, where m is the number of rows of the input matrix.
Edit intent: fluency
Original:  In this paper we propose a simple and natural version of IRLS for solving \ell_\infty and \ell_1 regression, which provably converges to a (1+\epsilon)-approximate solution in O(m^{1/3}\log(1/\epsilon)/\epsilon  + \log ( m/\epsilon )/\epsilon ^2) iterations, where m is the number of rows of the input matrix.
Revised:  In this paper we propose a simple and natural version of IRLS for solving \ell_\infty and \ell_1 regression, which provably converges to a (1+\epsilon)-approximate solution in O(m^{1/3}\log(1/\epsilon)/\epsilon + \log ( m/\epsilon ^2) iterations, where m is the number of rows of the input matrix.
Edit intent: fluency
Original:  Interestingly, this running time is independent of the conditioning of the input, and the dominant term of the running time depends only linearly in \epsilon^{-1}, despite the fact that the problem it is solving is non-smooth , and the algorithm is not using any regularization .
Revised:  Interestingly, this running time is independent of the conditioning of the input, and the dominant term of the running time depends sublinearly in \epsilon^{-1}, despite the fact that the problem it is solving is non-smooth , and the algorithm is not using any regularization .
Edit intent: clarity
Original:  Interestingly, this running time is independent of the conditioning of the input, and the dominant term of the running time depends only linearly in \epsilon^{-1}, despite the fact that the problem it is solving is non-smooth , and the algorithm is not using any regularization .
Revised:  Interestingly, this running time is independent of the conditioning of the input, and the dominant term of the running time depends only linearly in \epsilon^{-1}, despite the fact that the problem it is solving is non-smooth functions .
Edit intent: clarity
Original:  To best exploit information from these environments, organisms must evolve the ability to correctly anticipate consequences of unknown stimuli, and act on these predictions.
Revised:  To best exploit information from these environments, organisms must evolve the ability to anticipate consequences of unknown stimuli, and act on these predictions.
Edit intent: clarity
Original:  Through in-vitro and in-silico experiments, we define the minimal conditions necessary in a network with spike-timing dependent plasticity for the organism to go from reactive to proactive behavior.
Revised:  Through in-vitro and in-silico experiments, we define the conditions necessary in a network with spike-timing dependent plasticity for the organism to go from reactive to proactive behavior.
Edit intent: clarity
Original:  Our results support the existence of small evolutionary steps and four necessary conditions allowing embodied neural networks to evolve predictive and inductive abilities from an initial reactive strategy.
Revised:  Our results support the existence of specific evolutionary steps and four necessary conditions allowing embodied neural networks to evolve predictive and inductive abilities from an initial reactive strategy.
Edit intent: clarity
Original:  Our results support the existence of small evolutionary steps and four necessary conditions allowing embodied neural networks to evolve predictive and inductive abilities from an initial reactive strategy.
Revised:  Our results support the existence of small evolutionary steps and four conditions necessary for embodied neural networks to evolve predictive and inductive abilities from an initial reactive strategy.
Edit intent: clarity
Original: We consider paths with low "exposure" to a  polygonal domain, i.e., paths which are seen as little as possible;
Revised: We consider paths with low exposure polygonal domain, i.e., paths which are seen as little as possible;
Edit intent: clarity
Original:  We also highlight connection of the problem to minimum satisfiability and settle hardness of variants of planar min- and max-SAT.
Revised:  We also highlight connections of the problem to minimum satisfiability and settle hardness of variants of planar min- and max-SAT.
Edit intent: fluency
Original:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Revised:  that every planar hamiltonian graph G with \delta \geq %DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Edit intent: clarity
Original:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Revised:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% {4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Edit intent: clarity
Original:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Revised:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% %DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Edit intent: fluency
Original:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Revised:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% %DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Edit intent: fluency
Original:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Revised:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% {4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Edit intent: fluency
Original:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)|, and that if | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Revised:  that every planar hamiltonian graph G with \delta \geq 5 has a cycle of length k for every k \in \{%DIFDELCMD < \lfloor %%% \frac{1{4}{|V(G)|} }%DIFDELCMD < \rfloor%%% ,%DIFDELCMD < \dots%%% ,%DIFDELCMD < \lceil %%% \frac{3{4}{|V(G)|} }%DIFDELCMD < \rceil %DIFDELCMD < %%% + 3\} with 3 \leq k \leq | V(G)| \geq 8 is even , every 3-connected planar hamiltonian graph G with \delta \geq 4 has a cycle of length \frac{|V(G)|}{2} -
Edit intent: coherence
Original:  Another interesting consequence follows from our tool is that, given an instance of the number partitioning problem, i.e. a multiset of positive integers \{a_1,%DIFDELCMD < \dots%%% , a_N\}, if \sum_{i = 1^{N} a_i \leq 2N - 2, then a partition always exists and can be found in linear time}  .
Revised:  %DIFDELCMD < \dots%%% , a_N\}, if \sum_{i = 1^{N} a_i \leq 2N - 2, then a partition always exists and can be found in linear time} .
Edit intent: coherence
Original:  However, most of  models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism, which prevents the model from obtaining adequate global information.
Revised:  However, most of these models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism, which prevents the model from obtaining adequate global information.
Edit intent: clarity
Original:  Instead of merely aggregating one- or two-hop neighborhood information, the proposed coarsening procedure enlarges the receptive field for each original node, hence more global information can be learned.
Revised:  Instead of merely aggregating one- or two-hop neighborhood information, the proposed coarsening procedure enlarges the receptive field for each node, hence more global information can be learned.
Edit intent: clarity
Original:  Comprehensive experiments conducted on public datasets demonstrate  effectiveness of the proposed method over the state-of-art methods.
Revised:  Comprehensive experiments conducted on public datasets demonstrate the effectiveness of the proposed method over the state-of-art methods.
Edit intent: fluency
Original:  Notably, our model gains substantial improvements when only very few labeled samples are provided.
Revised:  Notably, our model gains substantial improvements when only a few labeled samples are provided.
Edit intent: clarity