wanyu/IteraTeR_v2 huggingface dataset:
Original: In this short note, the author shows that the gap problem of k-CSP with no negations and the support of its predicate the ground of a uniformly positive correlated distribution can be solved by Hast's Algorithm in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three truncated biased pairwise independent distributions and the three biases satisfy certain conditions.
Revised: In this short note, the author shows that a gap problem of k-CSP with no negations and the support of its predicate the ground of a uniformly positive correlated distribution can be solved by Hast's Algorithm in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three truncated biased pairwise independent distributions and the three biases satisfy certain conditions.
Edit intent: fluency
Original: In this short note, the author shows that a gap problem of k-CSP with no negations and the support of its predicate the ground of a uniformly positive correlated distribution can be solved by  Hast's Algorithm in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three truncated biased pairwise independent distributions and the three biases satisfy certain conditions.
Revised: In this short note, the author shows that a gap problem of k-CSP with no negations and the support of its predicate the ground of a balanced pairwise independent distribution can be solved by Hast's Algorithm in polynomial time, when k is sufficiently large, the support of its predicate is combined by the grounds of three truncated biased pairwise independent distributions and the three biases satisfy certain conditions.
Edit intent: clarity
Original:  We discussed the difference between the phases on which the networks depend.
Revised:  We discuss the difference between the phases on which the networks depend.
Edit intent: fluency
Original: We formulate an analytically tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand , and order cancellation is not a prominent feature .
Revised: We formulate an analytically tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand .
Edit intent: coherence
Original: We formulate an analytically tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand.
Revised: We analyze a tractable model of a limit order book on short time scales, where the dynamics are driven by stochastic fluctuations between supply and demand.
Edit intent: clarity
Original:  We use our model to analyze various high-frequency trading strategies, and comment on the Nash equilibria that emerge between high-frequency traders when a market in continuous time is replaced by frequent batch auctions.
Revised:  We use the model to analyze various high-frequency trading strategies, and comment on the Nash equilibria that emerge between high-frequency traders when a market in continuous time is replaced by frequent batch auctions.
Edit intent: fluency
Original:  It is challenging as fine-grained actions take place in the same activities or events, share similar contexts and tend to be localized within videos.
Edit intent: coherence
Original:  Convincing results are shown on the FGA-240 data set, as well as the public THUMOS 2014 localization data set with only untrimmed training videos.
Revised:  Convincing results are shown on the FGA-240 data set, as well as the THUMOS 2014 localization data set with only untrimmed training videos.
Edit intent: clarity
Original:  Convincing results are shown on the FGA-240 data set, as well as the public THUMOS 2014 localization data set with only untrimmed training videos.
Revised:  Convincing results are shown on the FGA-240 data set, as well as the public THUMOS 2014 localization data set with untrimmed training videos.
Edit intent: clarity
Original:  Several modifications of this portfolio, which outperform the market under milder versions of this  no-failure  condition, are put forward, one of which is rank-based.
Revised:  Several modifications of this portfolio, which outperform the market under milder versions of this " no-failure condition, are put forward, one of which is rank-based.
Edit intent: fluency
Original:  Several modifications of this portfolio, which outperform the market under milder versions of this  no-failure  condition, are put forward, one of which is rank-based.
Revised:  Several modifications of this portfolio, which outperform the market under milder versions of this no-failure " condition, are put forward, one of which is rank-based.
Edit intent: fluency
Original:  Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to  orders of magnitude faster than traditional simulation schemes based on rejection sampling.
Revised:  Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling.
Edit intent: clarity
Original:  To understand the fundamental mechanisms which determine the fate of online social networks at the system level, we recently introduced a general ecological theory of the digital world  .
Revised:  To understand the fundamental mechanisms which determine the fate of online social networks at the system level, we describe the digital world .
Edit intent: clarity
Original:  In this paper, we discuss the impact of heterogeneity in the network intrinsic fitness and present how the general theory can be applied to understand the competition between an international network, like Facebook, and local services.
Revised:  In this paper, we discuss the impact of heterogeneity in network intrinsic fitnesses induced by the competition between an international network, like Facebook, and local services.
Edit intent: clarity
Original:  We find that above a certain threshold the level of global connectivity can lead to the extinction of local networks .
Revised:  We show how inter-country social ties induce an increased intrinsic fitness of the international network. Under certain conditions this leads to the extinction of local networks .
Edit intent: clarity
Original:  To  understand the fundamental mechanisms which determine the fate of online social networks at the system level, we describe the digital world as a complex ecosystem of interacting networks.
Revised:  To help understand the fundamental mechanisms which determine the fate of online social networks at the system level, we describe the digital world as a complex ecosystem of interacting networks.
Edit intent: coherence
Original:  In this paper, we discuss the impact of heterogeneity in network intrinsic fitnesses induced by the competition between an international network, like Facebook, and local services.
Revised:  In this paper, we discuss the impact of heterogeneity in network fitnesses induced by the competition between an international network, like Facebook, and local services.
Edit intent: clarity
Original:  In this paper, we discuss the impact of heterogeneity in network intrinsic fitnesses induced by the competition between an international network, like Facebook, and local services.
Revised:  In this paper, we discuss the impact of heterogeneity in network intrinsic fitnesses induced by competition between an international network, like Facebook, and local services.
Edit intent: fluency
Original:  In this paper, we discuss the impact of heterogeneity in network intrinsic fitnesses induced by the competition between an international network, like Facebook, and local services.
Revised:  In this paper, we discuss the impact of heterogeneity in network intrinsic fitnesses induced by the competition between an international network, such as Facebook, and local services.
Edit intent: fluency
Original: To this end, we construct a 1:1000 scale model of the digital world enclosing the 80 countries with  most Internet users.
Revised: To this end, we construct a 1:1000 scale model of the digital world , consisting of the 80 countries with most Internet users.
Edit intent: clarity
Original: To this end, we construct a 1:1000 scale model of the digital world enclosing the 80 countries with  most Internet users.
Revised: To this end, we construct a 1:1000 scale model of the digital world enclosing the 80 countries with the most Internet users.
Edit intent: fluency
Original:  We show how inter-country social ties induce an increased intrinsic fitness of the international network.
Revised:  We show how inter-country social ties induce increased fitness of the international network.
Edit intent: clarity
Original:  Under certain conditions  this leads to the extinction of local networks  whereas under different conditions  local networks can persist and even dominate the international network completely.
Revised:  Under certain conditions , this leads to the extinction of local networks whereas under different conditions local networks can persist and even dominate the international network completely.
Edit intent: fluency
Original:  Under certain conditions  this leads to the extinction of local networks  whereas under different conditions  local networks can persist and even dominate the international network completely.
Revised:  Under certain conditions this leads to the extinction of local networks ; whereas under different conditions local networks can persist and even dominate the international network completely.
Edit intent: fluency
Original:  Under certain conditions  this leads to the extinction of local networks  whereas under different conditions  local networks can persist and even dominate the international network completely.
Revised:  Under certain conditions this leads to the extinction of local networks whereas under different conditions , local networks can persist and even dominate the international network completely.
Edit intent: fluency
Original:  These findings provide new insights into the possibilities to preserve digital diversity.
Revised:  These findings provide new insights into the possibilities for preserving digital diversity.
Edit intent: fluency
Original: The overwhelming success of online social networks, the key actors in the cosmos of the Web 2.0  , has reshaped human interactions on a worldwide scale .
Revised: The overwhelming success of online social networks, the key actors in the Web 2.0 , has reshaped human interactions on a worldwide scale .
Edit intent: clarity
Original: The overwhelming success of online social networks, the key actors in the cosmos of the Web 2.0  , has reshaped human interactions on a worldwide scale .
Revised: The overwhelming success of online social networks, the key actors in the cosmos of the Web 2.0 , has reshaped human interactions globally .
Edit intent: clarity
Original:  In this paper, we discuss the impact of heterogeneity in network fitnesses induced by competition between an international network, such as Facebook, and local services.
Revised:  In this paper, we study the impact of heterogeneity in network fitnesses induced by competition between an international network, such as Facebook, and local services.
Edit intent: fluency
Original:  In this paper, we discuss the impact of heterogeneity in network fitnesses induced by competition between an international network, such as Facebook, and local services.
Revised:  In this paper, we discuss the impact of heterogeneity in network fitnesses on the competition between an international network, such as Facebook, and local services.
Edit intent: clarity
Original:  To this end , we construct a 1:1000 scale model of the digital world, consisting of the 80 countries with the most Internet users.
Revised:  The higher fitness of international networks is induced by their ability to attract users from all over the world, which can then establish social interactions without the limitations of local networks. In other words, inter-country social ties lead to increased fitness of the international network. To study the competition between an international network and local ones , we construct a 1:1000 scale model of the digital world, consisting of the 80 countries with the most Internet users.
Edit intent: coherence
Original:  We show how inter-country social ties induce increased fitness of the international network.
Edit intent: coherence
Original:  Specifically, several noisy measurements of x_{i -x _{j is represented by a graph with an edge set E such that x _{i -x _{j only if (i,j)\inE.
Revised:  Imagine we acquire a few observations taking the form of x_i -x _{j is represented by a graph with an edge set E such that x _{i -x _{j only if (i,j)\inE.
Edit intent: clarity
Original:  Specifically, several noisy measurements of x_{i -x _{j is represented by a graph with an edge set E such that x _{i -x _{j only if (i,j)\inE.
Revised:  Specifically, several noisy measurements of x_{i -x _{j is represented by a graph with an edge set E such that x _i -x _{j only if (i,j)\inE.
Edit intent: fluency
Original:  Specifically, several noisy measurements of x_{i -x _{j is represented by a graph with an edge set E such that x _{i -x _{j only if (i,j)\inE.
Revised:  Specifically, several noisy measurements of x_{i -x _{j is represented by a graph with an edge set E such that x _{i -x _j is observed if and only if (i,j)\inE.
Edit intent: clarity
Original:  The distributions of the noisy measurements are modeled by a set of communication channels with given input/output transition measures.
Revised:  To account for noisy measurements in a general manner, we model the data acquisition process by a set of communication channels with given input/output transition measures.
Edit intent: clarity
Original:  The distributions of the noisy measurements are modeled by a set of communication channels with given input/output transition measures.
Revised:  The distributions of the noisy measurements are modeled by a set of channels with given input/output transition measures.
Edit intent: clarity
Original:  Using information-theoretic tools applied to the channel decoding problem , we develop a \textit{unified framework to characterize the region where information recovery is possible , which accommodates general graph structures, alphabet sizes, and channel transition measures.
Revised:  Employing information-theoretic tools applied to the channel decoding problem , we develop a \textit{unified framework to characterize the region where information recovery is possible , which accommodates general graph structures, alphabet sizes, and channel transition measures.
Edit intent: fluency
Original:  Using information-theoretic tools applied to the channel decoding problem , we develop a \textit{unified framework to characterize the region where information recovery is possible , which accommodates general graph structures, alphabet sizes, and channel transition measures.
Revised:  Using information-theoretic tools applied to channel decoding problems , we develop a \textit{unified framework to characterize the region where information recovery is possible , which accommodates general graph structures, alphabet sizes, and channel transition measures.
Edit intent: fluency
Original:  Using information-theoretic tools applied to the channel decoding problem , we develop a \textit{unified framework to characterize the region where information recovery is possible , which accommodates general graph structures, alphabet sizes, and channel transition measures.
Revised:  Using information-theoretic tools applied to the channel decoding problem , we develop a \textit{unified framework to characterize the region where information recovery is possible , which accommodates general graph structures, alphabet sizes, and channel transition measures.
Edit intent: fluency
Original:  In particular, we isolate and highlight a family of \textit{minimum distance measures underlying the channel transition probabilities, which plays a central role in determining the recovery limits.
Revised:  In particular, our results isolate a family of \textit{minimum distance measures underlying the channel transition probabilities, which plays a central role in determining the recovery limits.
Edit intent: clarity
Original:  For a very broad class of homogeneous graphs, our results are tight up to some explicit constant factor, and depend only on the graph edge sparsity irrespective of other second-order graphical metricslike the spectral gap .
Revised:  For a very broad class of homogeneous graphs, the recovery condition depends almost only on the graph edge sparsity irrespective of other second-order graphical metricslike the spectral gap .
Edit intent: clarity
Original:  For a very broad class of homogeneous graphs, our results are tight up to some explicit constant factor, and depend only on the graph edge sparsity irrespective of other second-order graphical metricslike the spectral gap .
Revised:  For a very broad class of homogeneous graphs, our results are tight up to some explicit constant factor, and depend only on the edge sparsity irrespective of other second-order graphical metricslike the spectral gap .
Edit intent: clarity
Original:  Our theory leads to order-wise optimal recovery conditions for all these cases, while improving upon existing results in certain regimes .
Revised:  Our theory leads to order-wise tight recovery conditions for all these cases, while improving upon existing results in certain regimes .
Edit intent: clarity
Original:  Our theory leads to order-wise optimal recovery conditions for all these cases, while improving upon existing results in certain regimes .
Revised:  Our theory leads to order-wise optimal recovery conditions for all these scenarios .
Edit intent: clarity
Original:  On the contrary , little has been published about soft errors in uncore components, such as memory subsystem and I/O controllers, in a System-on-Chip (SoC).
Revised:  On the contrary , little has been published about soft errors in uncore components, such as memory subsystem and I/O controllers, of a System-on-a-Chip (SoC).
Edit intent: clarity
Original:  We have created a new mixed-mode simulation platform that combines simulators at two different levels of abstraction  and achieves 20,000x speedup over RTL-only simulation.
Revised:  We have created a new mixed-mode simulation platform that combines simulators at two different levels of abstraction , and achieves 20,000x speedup over RTL-only simulation.
Edit intent: fluency
Original:  We also demonstrate that uncore soft errors can create major challenges for traditional system-level checkpoint-based recovery techniques.
Revised:  We also demonstrate that uncore soft errors can create major challenges for traditional system-level checkpoint recovery techniques.
Edit intent: clarity
Original:  Evidence for the nonexistence of efficient algorithms was given in a result of Lee (JACM'01) , who showed that any algorithm for a more general parsing problem with running time O(| G | n ^{ 3-eps }) , that works even in the unusual case that |G|=Omega(n^6), can be converted into a surprising subcubic algorithm for Boolean Matrix Multiplication.
Revised:  Lee (JACM'01) , who showed that any algorithm for a more general parsing problem with running time O(| G | n ^{ 3-eps }) , that works even in the unusual case that |G|=Omega(n^6), can be converted into a surprising subcubic algorithm for Boolean Matrix Multiplication.
Edit intent: coherence
Original:  Evidence for the nonexistence of efficient algorithms was given in a result of Lee (JACM'01) , who showed that any algorithm for a more general parsing problem with running time O(| G | n ^{ 3-eps }) , that works even in the unusual case that |G|=Omega(n^6), can be converted into a surprising subcubic algorithm for Boolean Matrix Multiplication.
Revised:  Evidence for the nonexistence of efficient algorithms was given in a result of Lee (JACM'01) , who showed that any algorithm for a more general parsing problem with running time O(| G | n ^{ 3-eps }) can be converted into a surprising subcubic algorithm for Boolean Matrix Multiplication.
Edit intent: coherence
Original:  In this work, we make the first progress on the constant size grammar case in 40 years, and prove that any improvement on Valiant's algorithm,  either in terms of runtime or by avoiding the inefficiencies of fast matrix multiplication, would imply a breakthrough algorithm for the k-Clique problem: given a graph of n nodes, decide if there are k that form a clique.
Revised:  In this work, we prove that any improvement on Valiant's algorithm, either in terms of runtime or by avoiding the inefficiencies of fast matrix multiplication, would imply a breakthrough algorithm for the k-Clique problem: given a graph of n nodes, decide if there are k that form a clique.
Edit intent: coherence
Original:  In this work, we make the first progress on the constant size grammar case in 40 years, and prove that any improvement on Valiant's algorithm,  either in terms of runtime or by avoiding the inefficiencies of fast matrix multiplication, would imply a breakthrough algorithm for the k-Clique problem: given a graph of n nodes, decide if there are k that form a clique.
Revised:  In this work, we make the first progress on the constant size grammar case in 40 years, and prove that any improvement on Valiant's algorithm, even for constant size grammars, either in terms of runtime or by avoiding the inefficiencies of fast matrix multiplication, would imply a breakthrough algorithm for the k-Clique problem: given a graph of n nodes, decide if there are k that form a clique.
Edit intent: clarity
Original:  In this work, we make the first progress on the constant size grammar case in 40 years, and prove that any improvement on Valiant's algorithm,  either in terms of runtime or by avoiding the inefficiencies of fast matrix multiplication, would imply a breakthrough algorithm for the k-Clique problem: given a graph of n nodes, decide if there are k that form a clique.
Revised:  In this work, we make the first progress on the constant size grammar case in 40 years, and prove that any improvement on Valiant's algorithm, either in terms of runtime or by avoiding the inefficiencies of fast matrix multiplication, would imply a breakthrough algorithm for the k-Clique problem: given a graph on n nodes, decide if there are k that form a clique.
Edit intent: fluency
Original: A better understanding of how people move in space is of fundamental importance for many areas such as prevention of epidemics , urban planningand wireless network engineering, to name a few.
Revised: In recent years, we have seen scientists attempt to model and explain human dynamics and, in particular, human movement. Many aspects of our complex life are affected by human movements such as disease spread and epidemics modeling, city planning, wireless network development, and disaster relief, to name a few.
Edit intent: clarity
Original:  In this work, we explore a rank-based approach for the characterization of human trajectories and unveil a visitation bias toward recently visited locations.
Revised:  In this work, we focus on the concept of recency. We propose a model in which exploitation in human movement also considers recently-visited locations and not solely frequently-visited locations.
Edit intent: clarity
Original: Two-player , zero-sum games of infinite duration and their quantitative versions are often used in verification to model the interaction between a controller (Eve) and an antagonistic environment (Adam).
Revised: Two-player zero-sum games of infinite duration and their quantitative versions are often used in verification to model the interaction between a controller (Eve) and an antagonistic environment (Adam).
Edit intent: fluency