wanyu/IteraTeR_v2 huggingface dataset:
Original:  However, recent studies highlight the importance of the higher-order network analysis, where complex structures called motifs are the first-class citizens.
Revised:  However, recent studies highlight the importance of higher-order network analysis, where complex structures called motifs are the first-class citizens.
Edit intent: fluency
Original:  We illustrate that existing link prediction schemes fail to predict the appearance of complex motifsin graph data.
Revised:  We first show that existing link prediction schemes fail to predict the appearance of complex motifsin graph data.
Edit intent: clarity
Original:  We establish the theoretical foundation of motif prediction and we propose several heuristics that , for a fixed set of nodes in a graph and a specified motif, assess the chances for this motif to appear.
Revised:  We establish the theoretical foundation of motif prediction and we propose several heuristics that assess the chances for this motif to appear.
Edit intent: clarity
Original:  We establish the theoretical foundation of motif prediction and we propose several heuristics that , for a fixed set of nodes in a graph and a specified motif, assess the chances for this motif to appear.
Revised:  We establish the theoretical foundation of motif prediction and we propose several heuristics that , for a fixed set of nodes in a graph and a specified motif, assess the chances for a specified motif to appear.
Edit intent: clarity
Original:  To make the scores realistic, our heuristics  - among others - consider correlations between links, i.e., the potential impact of some arriving links on the appearance of other parts of a given motif.
Revised:  To make the scores realistic, our heuristics - among others - correlations between links, i.e., the potential impact of some arriving links on the appearance of other parts of a given motif.
Edit intent: coherence
Original:  To make the scores realistic, our heuristics  - among others - consider correlations between links, i.e., the potential impact of some arriving links on the appearance of other parts of a given motif.
Revised:  To make the scores realistic, our heuristics - among others - consider correlations between links, i.e., the potential impact of some arriving links on the appearance of other links in a given motif.
Edit intent: clarity
Original:  \textit{Producer side measurement is more challenging because the producer experience depends on the treatment assignment of the consumers . Existing approaches for producer side measurement are either based on graph cluster-based randomization or on certain treatment propagation assumptions.
Revised:  \textit{Producer side measurement is more challenging because the producer experience depends on the treatment assignment of the consumers . Existing approaches for producer side measurement are either based on graph cluster-based randomization or on certain treatment propagation assumptions.
Edit intent: fluency
Original:  In this paper, we propose (i) a quantification of the quality of a producer side experiment  , and (ii) a new experiment design mechanism that generates high quality experiments based on this quantification.
Revised:  In this paper, we propose (i) a quantification of the quality of a producer side experiment design , and (ii) a new experiment design mechanism that generates high quality experiments based on this quantification.
Edit intent: clarity
Original:  In this paper, we propose (i) a quantification of the quality of a producer side experiment  , and (ii) a new experiment design mechanism that generates high quality experiments based on this quantification.
Revised:  In this paper, we propose (i) a quantification of the quality of a producer side experiment , and (ii) a new experiment design mechanism that generates high-quality experiments based on this quantification.
Edit intent: fluency
Original:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Revised:  Our approach, called UniCoRn ( fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Edit intent: fluency
Original:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Revised:  Our approach, called UniCoRn ( Uni %DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Edit intent: fluency
Original:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Revised:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Edit intent: fluency
Original:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Revised:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co %DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Edit intent: fluency
Original:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Revised:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Edit intent: fluency
Original:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Revised:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R %DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Edit intent: fluency
Original:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% n kings ), provides explicit control over the quality of the experiment and its computation cost.
Revised:  Our approach, called UniCoRn ( Uni fying%DIFDELCMD < {%%% Co unterfactual%DIFDELCMD < {%%% R a%DIFDELCMD < {%%% kings ), provides explicit control over the quality of the experiment and its computation cost.
Edit intent: fluency
Original:  We use simulations to thoroughly validate our approach and compare it against existing methods.
Revised:  We use simulations to validate our approach and compare it against existing methods.
Edit intent: clarity
Original:  We also implement UniCoRn in an edge recommendation application that serves tens of millions of members and billions of edge recommendations daily.
Revised:  We also deployed UniCoRn in an edge recommendation application that serves tens of millions of members and billions of edge recommendations daily.
Edit intent: clarity
Original: Machine earning algorithms are increasingly used for consequential decision making regarding individuals based on their relevant features.
Revised: Machine learning algorithms are increasingly used for consequential decision making regarding individuals based on their relevant features.
Edit intent: clarity
Original:  We first propose information theoretic measures for the impact of different subsets of features on the accuracy and discrimination of the model.
Revised:  We first propose information theoretic measures which quantify the impact of different subsets of features on the accuracy and discrimination of the model.
Edit intent: clarity
Original:  To address this problem, we propose a decentralized Q-learning approach, where each UAV-BS is equipped with an autonomous agent that maximizes the connectivity to ground devices while improving its energy utilization.
Revised:  To address this problem, we propose a decentralized Q-learning approach, where each UAV-BS is equipped with an autonomous agent that maximizes the connectivity of mobile ground devices while improving its energy utilization.
Edit intent: clarity
Original:  The recent mixture invariant training (MixIT) method enables training on in-the wild data;
Revised:  The recent mixture invariant training (MixIT) method enables training on in-the-wild data;
Edit intent: fluency
Original:  These problems interact: increasing the number of output sources exacerbates over-separation.
Edit intent: coherence
Original:  To extend MixIT to larger numbers of sources, we introduce an efficient approximation using a fast least-squares solution, projected onto the MixIT constraint set.
Revised:  To handle larger numbers of sources, we introduce an efficient approximation using a fast least-squares solution, projected onto the MixIT constraint set.
Edit intent: clarity
Original:  We give overwhelming evidence that %DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP , defined originally by Kleinberg et al., is the natural complexity class associated with explicit constructions for objects whose existence follows from the probabilistic method, by proving that a host of well-studied explicit construction problems lie in this class.
Revised:  We give overwhelming evidence that %DIFDELCMD < {\bf %DIFDELCMD < %%% , defined originally by Kleinberg et al., is the natural complexity class associated with explicit constructions for objects whose existence follows from the probabilistic method, by proving that a host of well-studied explicit construction problems lie in this class.
Edit intent: clarity
Original:  We give overwhelming evidence that %DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP , defined originally by Kleinberg et al., is the natural complexity class associated with explicit constructions for objects whose existence follows from the probabilistic method, by proving that a host of well-studied explicit construction problems lie in this class.
Revised:  We give overwhelming evidence that %DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP , defined originally by Kleinberg et al., is the natural complexity class associated with explicit constructions of objects whose existence follows from the probabilistic method, by proving that a host of well-studied explicit construction problems lie in this class.
Edit intent: fluency
Original:  We give overwhelming evidence that %DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP , defined originally by Kleinberg et al., is the natural complexity class associated with explicit constructions for objects whose existence follows from the probabilistic method, by proving that a host of well-studied explicit construction problems lie in this class.
Revised:  We give overwhelming evidence that %DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP , defined originally by Kleinberg et al., is the natural complexity class associated with explicit constructions for objects whose existence follows from the probabilistic method, by placing a variety of such construction problems in this class.
Edit intent: clarity
Original:  We then observe that a result of Jer\'{a}bek on provability in Bounded Arithmetic, when reinterpreted as a reduction between search problems, shows that constructing a truth table of high circuit complexity is complete for %DIFDELCMD < {\bf %%% APEPP under%DIFDELCMD < {\bf %%% P ^{ %DIFDELCMD < \bf %%% NP } reductions.
Revised:  We then demonstrate that a result of Jer\'{a}bek on provability in Bounded Arithmetic, when reinterpreted as a reduction between search problems, shows that constructing a truth table of high circuit complexity is complete for %DIFDELCMD < {\bf %%% APEPP under%DIFDELCMD < {\bf %%% P ^{ %DIFDELCMD < \bf %%% NP } reductions.
Edit intent: clarity
Original:  We then observe that a result of Jer\'{a}bek on provability in Bounded Arithmetic, when reinterpreted as a reduction between search problems, shows that constructing a truth table of high circuit complexity is complete for %DIFDELCMD < {\bf %%% APEPP under%DIFDELCMD < {\bf %%% P ^{ %DIFDELCMD < \bf %%% NP } reductions.
Revised:  We then observe that a result of Jer\'{a}bek on provability in Bounded Arithmetic, when reinterpreted as a reduction between search problems, shows that constructing a truth table of high circuit complexity is complete for %DIFDELCMD < {\bf %%% APEPP %DIFDELCMD < {\bf %%% P ^{ %DIFDELCMD < \bf %%% NP } reductions.
Edit intent: fluency
Original:  We then observe that a result of Jer\'{a}bek on provability in Bounded Arithmetic, when reinterpreted as a reduction between search problems, shows that constructing a truth table of high circuit complexity is complete for %DIFDELCMD < {\bf %%% APEPP under%DIFDELCMD < {\bf %%% P ^{ %DIFDELCMD < \bf %%% NP } reductions.
Revised:  We then observe that a result of Jer\'{a}bek on provability in Bounded Arithmetic, when reinterpreted as a reduction between search problems, shows that constructing a truth table of high circuit complexity is complete for %DIFDELCMD < {\bf %%% APEPP under%DIFDELCMD < {\bf %%% under ^{ %DIFDELCMD < \bf %%% NP } reductions.
Edit intent: coherence
Original:  We then observe that a result of Jer\'{a}bek on provability in Bounded Arithmetic, when reinterpreted as a reduction between search problems, shows that constructing a truth table of high circuit complexity is complete for %DIFDELCMD < {\bf %%% APEPP under%DIFDELCMD < {\bf %%% P ^{ %DIFDELCMD < \bf %%% NP } reductions.
Revised:  We then observe that a result of Jer\'{a}bek on provability in Bounded Arithmetic, when reinterpreted as a reduction between search problems, shows that constructing a truth table of high circuit complexity is complete for %DIFDELCMD < {\bf %%% APEPP under%DIFDELCMD < {\bf %%% P ^{ %DIFDELCMD < \bf %%% } reductions.
Edit intent: clarity
Original:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% E ^{\bf NP: the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP has a%DIFDELCMD < {\bf %%% P ^{\bf NP algorithm if and only if such a lower bound holds.
Revised:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% ^{\bf NP: the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP has a%DIFDELCMD < {\bf %%% P ^{\bf NP algorithm if and only if such a lower bound holds.
Edit intent: clarity
Original:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% E ^{\bf NP: the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP has a%DIFDELCMD < {\bf %%% P ^{\bf NP algorithm if and only if such a lower bound holds.
Revised:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% E : the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP has a%DIFDELCMD < {\bf %%% P ^{\bf NP algorithm if and only if such a lower bound holds.
Edit intent: fluency
Original:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% E ^{\bf NP: the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP has a%DIFDELCMD < {\bf %%% P ^{\bf NP algorithm if and only if such a lower bound holds.
Revised:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% E ^{\bf NP: the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP %DIFDELCMD < {\bf %%% P ^{\bf NP algorithm if and only if such a lower bound holds.
Edit intent: fluency
Original:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% E ^{\bf NP: the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP has a%DIFDELCMD < {\bf %%% P ^{\bf NP algorithm if and only if such a lower bound holds.
Revised:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% E ^{\bf NP: the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP has a%DIFDELCMD < {\bf %%% ^{\bf NP algorithm if and only if such a lower bound holds.
Edit intent: clarity
Original:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% E ^{\bf NP: the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP has a%DIFDELCMD < {\bf %%% P ^{\bf NP algorithm if and only if such a lower bound holds.
Revised:  This result in fact gives a precise algorithmic characterization of proving 2^{\Omega(n) circuit lower bounds for }%DIFDELCMD < {\bf %%% E ^{\bf NP: the complete problem for }%DIFDELCMD < {\bf %DIFDELCMD < %%% APEPP has a%DIFDELCMD < {\bf %%% P algorithm if and only if such a lower bound holds.
Edit intent: fluency
Original:  Together with our proof that pseudorandom generators can be constructed in }%DIFDELCMD < {\bf %%% APEPP , this also yields a self-contained and significantly simplified proof of the celebrated result of Impagliazzo and Wigderson that worst-case-hard truth tables can be used to derandomize algorithms (although the conclusion is weaker as our derandomization requires an%DIFDELCMD < {\bf %%% NP oracle).
Revised:  Together with our proof that pseudorandom generators can be constructed in }%DIFDELCMD < {\bf %%% , this also yields a self-contained and significantly simplified proof of the celebrated result of Impagliazzo and Wigderson that worst-case-hard truth tables can be used to derandomize algorithms (although the conclusion is weaker as our derandomization requires an%DIFDELCMD < {\bf %%% NP oracle).
Edit intent: clarity
Original:  Together with our proof that pseudorandom generators can be constructed in }%DIFDELCMD < {\bf %%% APEPP , this also yields a self-contained and significantly simplified proof of the celebrated result of Impagliazzo and Wigderson that worst-case-hard truth tables can be used to derandomize algorithms (although the conclusion is weaker as our derandomization requires an%DIFDELCMD < {\bf %%% NP oracle).
Revised:  Together with our proof that pseudorandom generators can be constructed in }%DIFDELCMD < {\bf %%% APEPP %DIFDELCMD < {\bf %%% NP oracle).
Edit intent: coherence
Original:  Together with our proof that pseudorandom generators can be constructed in }%DIFDELCMD < {\bf %%% APEPP , this also yields a self-contained and significantly simplified proof of the celebrated result of Impagliazzo and Wigderson that worst-case-hard truth tables can be used to derandomize algorithms (although the conclusion is weaker as our derandomization requires an%DIFDELCMD < {\bf %%% NP oracle).
Revised:  Together with our proof that pseudorandom generators can be constructed in }%DIFDELCMD < {\bf %%% APEPP , this also yields a self-contained and significantly simplified proof of the celebrated result of Impagliazzo and Wigderson that worst-case-hard truth tables can be used to derandomize algorithms (although the conclusion is weaker as our derandomization requires an%DIFDELCMD < {\bf %%% oracle).
Edit intent: clarity
Original:  As another corollaryof this completeness result, we show that%DIFDELCMD < {\bf %%% E\textit{ \bf{EXP} ^{ %DIFDELCMD < \bf %DIFDELCMD < %%% NP \bf{NP} } contains a language of circuit complexity 2^{ \Omega( n ) } if and only if it contains a language of circuit complexity \frac{2^n . Finally, for several of the problems shown to lie in %DIFDELCMD < {\bf %%% APEPP \bf{APEPP} , we demonstrate direct polynomial time reductions to the explicit construction of hard truth tables.
Revised:  As another corollaryof this completeness result, we show that%DIFDELCMD < {\bf %%% E\textit{ \bf{EXP} ^{ %DIFDELCMD < \bf %DIFDELCMD < %%% \bf{NP} } contains a language of circuit complexity 2^{ \Omega( n ) } if and only if it contains a language of circuit complexity \frac{2^n . Finally, for several of the problems shown to lie in %DIFDELCMD < {\bf %%% APEPP \bf{APEPP} , we demonstrate direct polynomial time reductions to the explicit construction of hard truth tables.
Edit intent: clarity
Original:  As another corollaryof this completeness result, we show that%DIFDELCMD < {\bf %%% E\textit{ \bf{EXP} ^{ %DIFDELCMD < \bf %DIFDELCMD < %%% NP \bf{NP} } contains a language of circuit complexity 2^{ \Omega( n ) } if and only if it contains a language of circuit complexity \frac{2^n . Finally, for several of the problems shown to lie in %DIFDELCMD < {\bf %%% APEPP \bf{APEPP} , we demonstrate direct polynomial time reductions to the explicit construction of hard truth tables.
Revised:  As another corollaryof this completeness result, we show that%DIFDELCMD < {\bf %%% E\textit{ \bf{EXP} ^{ %DIFDELCMD < \bf %DIFDELCMD < %%% NP \bf{NP} } contains a language of circuit complexity 2^{ n ) } if and only if it contains a language of circuit complexity \frac{2^n . Finally, for several of the problems shown to lie in %DIFDELCMD < {\bf %%% APEPP \bf{APEPP} , we demonstrate direct polynomial time reductions to the explicit construction of hard truth tables.
Edit intent: clarity
Original:  As another corollaryof this completeness result, we show that%DIFDELCMD < {\bf %%% E\textit{ \bf{EXP} ^{ %DIFDELCMD < \bf %DIFDELCMD < %%% NP \bf{NP} } contains a language of circuit complexity 2^{ \Omega( n ) } if and only if it contains a language of circuit complexity \frac{2^n . Finally, for several of the problems shown to lie in %DIFDELCMD < {\bf %%% APEPP \bf{APEPP} , we demonstrate direct polynomial time reductions to the explicit construction of hard truth tables.
Revised:  As another corollaryof this completeness result, we show that%DIFDELCMD < {\bf %%% E\textit{ \bf{EXP} ^{ %DIFDELCMD < \bf %DIFDELCMD < %%% NP \bf{NP} } contains a language of circuit complexity 2^{ \Omega( n ) } if and only if it contains a language of circuit complexity \frac{2^n . Finally, for several of the problems shown to lie in %DIFDELCMD < {\bf %%% APEPP \bf{APEPP} , we demonstrate direct polynomial time reductions to the explicit construction of hard truth tables.
Edit intent: fluency
Original:  Recently, there has been an increasing amount of literature that employs mean-field partial differential equations (PDEs) to model the time-evolution of the probability density of swarm robotic systems and uses mean-field feedback to design stable control laws that act on individuals such that their density converges to a target profile.
Revised:  Recently, there has been an increasing amount of literature that employs partial differential equations (PDEs) to model the time-evolution of the probability density of swarm robotic systems and uses mean-field feedback to design stable control laws that act on individuals such that their density converges to a target profile.
Edit intent: clarity
Original:  Specially , we propose new mean-field control laws which use the real-time density and its gradient as feedback, and prove that they are globally input-to-state stable (ISS)  to estimation errors.
Revised:  Specifically , we propose new mean-field control laws which use the real-time density and its gradient as feedback, and prove that they are globally input-to-state stable (ISS) to estimation errors.
Edit intent: fluency