wanyu/IteraTeR_v2 huggingface dataset:
Original:  This algorithm considerably extends the class of games which admit parallel solutions and demonstrates for the first time the existence of a parallel algorithm for \emph{any game (classical or quantum) in which one player reacts adaptively to the other.
Revised:  This algorithm considerably extends the class of games which admit parallel solutions and demonstrates for the first time the existence of a parallel algorithm for \emph{any game (classical or quantum) in which one party reacts adaptively to the other.
Edit intent: clarity
Original:   A special case of our result is a parallel approximation scheme for a new class of semidefinite programs whose feasible region consists of n-tuples of semidefinite matrices that satisfy a certain consistency condition.
Revised:  A special case of our result is a parallel approximation scheme for a specific class of semidefinite programs whose feasible region consists of n-tuples of semidefinite matrices that satisfy a certain consistency condition.
Edit intent: clarity
Original:   A special case of our result is a parallel approximation scheme for a new class of semidefinite programs whose feasible region consists of n-tuples of semidefinite matrices that satisfy a certain consistency condition.
Revised:  A special case of our result is a parallel approximation scheme for a new class of semidefinite programs whose feasible region consists of lists of semidefinite matrices that satisfy a certain consistency condition.
Edit intent: clarity
Original:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%%  .
Revised:  called the\emph{min-max \emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%% .
Edit intent: coherence
Original:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%%  .
Revised:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{ approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%% .
Edit intent: clarity
Original:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%%  .
Revised:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual %DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%% .
Edit intent: clarity
Original:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%%  .
Revised:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% %DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%% .
Edit intent: coherence
Original:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%%  .
Revised:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% %DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%% .
Edit intent: coherence
Original:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%%  .
Revised:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% %DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%% .
Edit intent: fluency
Original:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%%  .
Revised:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% %DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%% .
Edit intent: coherence
Original:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%%  .
Revised:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% %DIFDELCMD < \cls{DQIP}%%% .
Edit intent: coherence
Original:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%%  .
Revised:  called the\emph{min-max approach, to solve SDPs in contrast to the\emph{primal-dual approach to SDPs used in the original proof of%DIFDELCMD < \cls{QIP}%%% =%DIFDELCMD < \cls{PSPACE}%%% . It also follows from our work that several competing-provers complexity classes collapse to%DIFDELCMD < \cls{PSPACE} %%% such as%DIFDELCMD < \cls{QRG}(2)%%% ,%DIFDELCMD < \cls{SQG} %%% and two new classes called%DIFDELCMD < \cls{DIP} %%% and%DIFDELCMD < \cls{DQIP}%%% PSPACE .
Edit intent: coherence
Original:  Why are such models successful in some casesbut not others ? Here, we study the ability of pairwise maximum entropy models to capture the activity patterns of feedforward circuits with different architectures and inputs.
Revised:  Why are such models successful in some casesbut not others ? Here, we study the emergence of higher-order correlations in feedforward circuits with different architectures and inputs.
Edit intent: clarity
Original:  Responses to bimodal input signals shared by all circuit elements deviated substantially from maximum entropy predictions, while responses of unimodal inputs, regardless of connectivity, did not.
Revised:  Responses to bimodal input signals shared by all circuit elements deviated substantially from maximum entropy predictions, while responses to unimodal inputs, regardless of connectivity, did not.
Edit intent: fluency
Original:  Here, we study the emergence of higher-order correlations in feedforward circuits with different architectures and inputs.
Revised:  Here, we study the emergence of higher-order interactions in simple circuits with different architectures and inputs.
Edit intent: clarity
Original:  "null" descriptions in which all higher-than pairwise correlations have been removed , known as pairwise maximum entropy models.
Revised:  "null" descriptions in which all higher-than-pairwise correlations have been removed , known as pairwise maximum entropy models.
Edit intent: fluency
Original:  We find that responses to bimodal input signals shared by all circuit elements deviate substantially from purely pairwise predictions , while responses to unimodal inputs , regardless of connectivity, do not .
Revised:  We find that bimodal input signals shared by all circuit elements deviate substantially from purely pairwise predictions , while responses to unimodal inputs , regardless of connectivity, do not .
Edit intent: fluency
Original:  We find that responses to bimodal input signals shared by all circuit elements deviate substantially from purely pairwise predictions , while responses to unimodal inputs , regardless of connectivity, do not .
Revised:  We find that responses to bimodal input signals produce larger deviations from pairwise predictions than unimodal inputs for circuits with local and global connectivity. Moreover, recurrent coupling can accentuate these deviations, if coupling strengths are neither too weak nor too strong .
Edit intent: clarity
Original:  A circuit model based on intracellular recordings from  retinal ganglion cells further shows that a broad range of light signals induce unimodal inputs to spike generators, providing a simple explanation for the success of pairwise models in this system.
Revised:  A circuit model based on intracellular recordings from retinal ganglion cells shows that a broad range of light signals induce unimodal inputs to spike generators, providing a simple explanation for the success of pairwise models in this system.
Edit intent: clarity
Original:  These findings identify circuit-level mechanisms that produce  higher-order spiking statistics in neural ensembles , and specific mechanisms that do not .
Revised:  Overall, our findings identify circuit-level mechanisms that produce higher-order spiking statistics in neural ensembles , and specific mechanisms that do not .
Edit intent: coherence
Original:  These findings identify circuit-level mechanisms that produce  higher-order spiking statistics in neural ensembles , and specific mechanisms that do not .
Revised:  These findings identify circuit-level mechanisms that produce higher-order spiking statistics in neural ensembles .
Edit intent: clarity
Original:  IM accuracy is not satisfied since neither MMRs nor DT records contain complete information on interference and traffic distribution.
Revised:  IM accuracy is not satisfactory since neither MMRs nor DT records contain complete information on interference and traffic distribution.
Edit intent: fluency
Original:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi of statements ( ``constraints'' ) about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi of allowed  formulas;
Revised:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi of statements ( ``constraints'' ) about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi of allowed formulas;
Edit intent: fluency
Original:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi of statements ( ``constraints'' ) about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi of allowed  formulas;
Revised:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi of statements ( "constraints" ) about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi of allowed formulas;
Edit intent: fluency
Original:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi of statements ( ``constraints'' ) about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi of allowed  formulas;
Revised:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi of statements ( ``constraints'' ) about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi formulas;
Edit intent: clarity
Original:  the question is whether \Phi is satisfiable in a graph.
Revised:  the question is whether \Phi is satisfiable in a graph.
Edit intent: fluency
Original:  We prove that either \Psi is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time, or the problem is NP-complete.
Revised:  We prove that either \Psi is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time, or the problem is NP-complete.
Edit intent: fluency
Original:  Our method to then classify the computational complexity of those CSPs produces many statements of independent mathematical interest.
Revised:  Our method to classify the computational complexity of those CSPs produces many statements of independent mathematical interest.
Edit intent: clarity
Original:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi of statements ("constraints") about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi of allowed quantifier-free first-order formulas;
Revised:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi\ of statements ("constraints") about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi of allowed quantifier-free first-order formulas;
Edit intent: fluency
Original:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi of statements ("constraints") about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi of allowed quantifier-free first-order formulas;
Revised:  In this generalization of Schaefer's result, the input consists of a set W of variables and a conjunction \Phi of statements ("constraints") about these variables in the language of graphs, where each statement is taken from a fixed finite set \Psi\ of allowed quantifier-free first-order formulas;
Edit intent: fluency
Original:  the question is whether \Phi is satisfiable in a graph.
Revised:  the question is whether \Phi\ is satisfiable in a graph.
Edit intent: fluency
Original:  We prove that either \Psi is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time, or the problem is NP-complete.
Revised:  We prove that either \Psi\ is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time, or the problem is NP-complete.
Edit intent: fluency
Original:  The transferability of the research technology in cognitive terms--that is, the transition from "mode-1" to "mode-2" research--is suggested as the crucial difference in explaining the different rates of diffusion between siRNA and NCSC.
Revised:  The transferability of the research technology in cognitive terms--that is, the transition from "mode-1" to "mode-2" ) research is suggested as the crucial difference in explaining the different rates of diffusion between siRNA and NCSC.
Edit intent: fluency
Original: We realize a biochemical filtering process based on the introduction of a small quantity of a buffer in a biocatalytic signal-transduction logic system based on the function of an enzyme, esterase.
Revised: We realize a biochemical filtering process by introducing a buffer in a biocatalytic signal-transduction logic system based on the function of an enzyme, esterase.
Edit intent: clarity
Original:  The input, ethyl butyrate, is converted into butyric acid: the output signal, which in turn is measured by the drop in the pH value.
Revised:  The input, ethyl butyrate, is converted into butyric acid-the output signal, which in turn is measured by the drop in the pH value.
Edit intent: fluency
Original:  It appears that in order to bridge these two complementary approaches to proteins, conceptually novel tools need to be introduced.
Revised:  In order to bridge these two complementary approaches to proteins, conceptually novel tools need to be introduced.
Edit intent: coherence
Original:  Our scheme shows how to `` convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p).
Revised:  Our scheme shows how to " convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p).
Edit intent: fluency
Original:  It is shown here how the value of this hitherto mysterious timescale governing the memetic phase is explicable in terms of what happenned in the preceding genetic phase.
Revised:  It is shown here how the value of this hitherto mysterious timescale governing the memetic phase is explicable in terms of what happened in the preceding genetic phase.
Edit intent: fluency
Original:  The outcome is that the order of magnitude of the Foerster timescale can be accounted for as the product, \star\approx \g\,I\, of the relevant (human) generation timescale, \g\simeq 20 years, with the number of bits of information in the genome, I\approx 10^{10}  .
Revised:  The outcome is that the order of magnitude of the Foerster timescale can be accounted for as the product, \star\approx \g\,I\, of the relevant (human) generation timescale, \g\simeq 20 years, with the number of bits of information in the genome, I\approx 10^{10} . The automatic nature of the process involved implies that it was not a hard-step .
Edit intent: coherence
Original:  This has been followed by a phase of even more rapid technological evolution and concomitant expansion of the size of the population, that began when our own particular "sapiens" species emerged, just a few hundred thousand years ago.
Revised:  This has been followed by a phase of even more rapid technological evolution and concomitant expansion of the size of the population, that began when our own particular `sapiens' species emerged, just a few hundred thousand years ago.
Edit intent: fluency
Original:  From the outset of the latter until very recently -- about the year 2000 -- the growth of the global population N was roughly governed by an equation of the form %DIFDELCMD < \dot %%% N = N ^2 / \tau_{\star\, }  , in which \tau_{\star is a coefficient introduced (in 1960) by von Foerster, who evaluated it empirically as about 2\times 10^{11 years.
Revised:  From the outset of the latter until very recently -- about the year 2000 -- the growth of the global population N was roughly governed by an equation of the form %DIFDELCMD < \dot %%% N = N / \tau_{\star\, } , in which \tau_{\star is a coefficient introduced (in 1960) by von Foerster, who evaluated it empirically as about 2\times 10^{11 years.
Edit intent: clarity
Original:  From the outset of the latter until very recently -- about the year 2000 -- the growth of the global population N was roughly governed by an equation of the form %DIFDELCMD < \dot %%% N = N ^2 / \tau_{\star\, }  , in which \tau_{\star is a coefficient introduced (in 1960) by von Foerster, who evaluated it empirically as about 2\times 10^{11 years.
Revised:  From the outset of the latter until very recently -- about the year 2000 -- the growth of the global population N was roughly governed by an equation of the form %DIFDELCMD < \dot %%% N = N ^2 / \, } , in which \tau_{\star is a coefficient introduced (in 1960) by von Foerster, who evaluated it empirically as about 2\times 10^{11 years.
Edit intent: fluency
Original:  It is shown here how the value of this hitherto mysterious timescale governing the memetic phase is explicable in terms of what happened in the preceding genetic phase.
Revised:  It is shown here how the value of this hitherto mysterious timescale governing the memetic phase is explicable in terms of what happenned in the preceding genetic phase.
Edit intent: fluency
Original:  The outcome is that the order of magnitude of the Foerster timescale can be accounted for as the product , \tau_{\star\approx \g\,I\, } of the relevant (human) generation timescale, \tau_{\g\simeq }  20 years, with the number of bits of information in the genome, I\approx 10^{10 .
Revised:  The outcome is that the order of magnitude of the Foerster timescale can be accounted for as the product \approx \g\,I\, } of the relevant (human) generation timescale, \tau_{\g\simeq } 20 years, with the number of bits of information in the genome, I\approx 10^{10 .
Edit intent: fluency