wanyu/IteraTeR_v2 huggingface dataset:
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the\textit{  form c(x,y)= \Psi(x-y) for some convex function \Psi .
Revised:  We consider the problem of transporting \mu to \nu with respect to a cost function c: X \times Y \to R of the\textit{ form c(x,y)= \Psi(x-y) for some convex function \Psi .
Edit intent: clarity
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the\textit{  form c(x,y)= \Psi(x-y) for some convex function \Psi .
Revised:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the\textit{ . For cost functions of the form c(x,y)= \Psi(x-y) for some convex function \Psi .
Edit intent: clarity
Original:  For cost functions of the form c(x,y)= \Psi(x-y) for some convex function \Psi, we find an associated K\"ahler manifold whose orthogonal holomorphic bisectional curvature is proportional to the MTW tensor.
Revised:  For cost functions of the form c(x,y)= \Psi(x-y) for some convex function \Psi, we find an associated K\"ahler manifold whose orthogonal anti-bisectional curvature is proportional to the MTW tensor.
Edit intent: clarity
Original:  Our main contributions are competitive algorithms for this problem and a near-matching hardness bound.
Revised:  Our main contributions are competitive algorithms for this problem that are close to or match a hardness bound.
Edit intent: clarity
Original:  The competitive ratio of the algorithms nicely interpolates between the truly offline setting ( i.e., no adversarial part) and the truly online setting ( i.e., no predictable part).
Revised:  The competitive ratio of the algorithms nicely interpolates between the truly offline setting ( no adversarial part) and the truly online setting ( i.e., no predictable part).
Edit intent: fluency
Original:  The competitive ratio of the algorithms nicely interpolates between the truly offline setting ( i.e., no adversarial part) and the truly online setting ( i.e., no predictable part).
Revised:  The competitive ratio of the algorithms nicely interpolates between the truly offline setting ( i.e., no adversarial part) and the truly online setting ( no predictable part).
Edit intent: fluency
Original:  QS is ubiquitous in nature and enables microorganisms to respond to fluctuations of living environments by working together.
Revised:  QS is ubiquitous in nature and enables microorganisms to respond to fluctuations in living environments by working together.
Edit intent: fluency
Original:  In this work , a QS-based  communication system within a microbial population in a two-dimensional (2D) environment is analytically modeled.
Revised:  In this study , a QS-based communication system within a microbial population in a two-dimensional (2D) environment is analytically modeled.
Edit intent: clarity
Original:  Notably, the diffusion and degradation of signaling molecules within the population is characterized.
Edit intent: coherence
Original:  Using this analysis and some approximation, the expected density of cooperating bacteria is derived.
Revised:  Using this analysis and some approximation, the expected density of cooperative bacteria is derived.
Edit intent: fluency
Original:  The model can be used to predict and control behavioral dynamics of microscopic populations that have imperfect signal propagation .
Revised:  The model can be used to predict the density of cooperative bacteria in a variety of QS-coordinated activities, e.g., biofilm formation and antibiotic resistance .
Edit intent: clarity
Original:  Furthermore, we combine human intuition with our algorithm by performing modified counterfactual inference over the possible inherited gene alleles for any individual .
Revised:  Furthermore, we make use of human intuition by providing a method to assign hypothetical evidence to any inherited gene alleles for any individual .
Edit intent: clarity
Original:  Furthermore, we combine human intuition with our algorithm by performing modified counterfactual inference over the possible inherited gene alleles for any individual .
Revised:  Furthermore, we combine human intuition with our algorithm by performing modified counterfactual inference over the possible inherited gene alleles .
Edit intent: clarity
Original:  Moreover, we also present cache-aware strategies to further improve the time efficiency while theoretically retaining the time complexity of BFC-VP.
Revised:  Secondly, we present cache-aware strategies to further improve the time efficiency while theoretically retaining the time complexity of BFC-VP.
Edit intent: coherence
Original:  These not only resolve the issue that the existing techniques cannot finish on some real datasets but also extensive empirical studies demonstrate that our techniques can speed up the state-of-the-art techniques by up to two orders of magnitude for the real datasets when the existing techniques can finish .
Revised:  These not only resolve the issue that the existing techniques cannot finish on some real datasets but also extensive empirical studies demonstrate that our techniques can speed up the state-of-the-art techniques by up to two orders of magnitude for the real datasets .
Edit intent: clarity
Original:  In this paper, we study the problem of efficiently counting the number of butterflies in a bipartite network.
Revised:  In this paper, we study the problem of efficient counting the number of butterflies in a bipartite network.
Edit intent: fluency
Original:  Secondly , we present cache-aware strategies to further improve the time efficiency while theoretically retaining the time complexity of BFC-VP.
Revised:  Secondly , we present cache-aware strategies to further improve time efficiency while theoretically retaining the time complexity of BFC-VP.
Edit intent: fluency
Original:  Moreover, we also present efficient external algorithms and parallel algorithms .
Revised:  Moreover, we also show that our proposed techniques can work efficiently in external and parallel contexts .
Edit intent: clarity
Original:  Our extensive empirical studies demonstrate that our techniques can speed up the state-of-the-art techniques by up to two orders of magnitude for the real datasets.
Revised:  Our extensive empirical studies demonstrate that the proposed techniques can speed up the state-of-the-art techniques by up to two orders of magnitude for the real datasets.
Edit intent: clarity
Original: The explosive growth in fake news and its erosion to democracy, justice, and public trust has increased the demand for fake news analysis, detection and intervention.
Revised: The explosive growth in fake news and its erosion to democracy, justice, and public trust has increased the demand for fake news detection and intervention.
Edit intent: clarity
Original:  For the deterministic algorithms, we introduce an SST construction algorithm that takes O(n (\log \frac{n{|B|}+\log^*n) }  ) time (for |B|=\Omega(\log n \log^*n )).
Revised:  For the deterministic algorithms, we introduce an SST construction algorithm that takes O(n {|B|}+\log^*n) } ) time (for |B|=\Omega(\log n \log^*n )).
Edit intent: clarity
Original: Distributed ledger technologies rely on consensus protocols confronting traders with random waiting times until the transfer of ownership is accomplished.
Revised: Distributed ledger technologies replace trusted clearing counterparties and security depositories with time-consuming consensus protocols to record the transfer of ownership is accomplished.
Edit intent: clarity
Original:  We derive theoretical arbitrage boundaries under general assumptions and show that they increase with expected latency, latency uncertainty, spot volatility , and risk aversion.
Revised:  We derive theoretical arbitrage boundaries under general assumptions and show that they increase with expected latency, latency uncertainty, volatility and risk aversion.
Edit intent: clarity
Original:  Using high-frequency data from the Bitcoin network , we estimate arbitrage boundaries due to settlement latency of on average 124 basis points, covering 88 percent of the observed cross-exchange price differences.
Revised:  Using Bitcoin orderbook and network data , we estimate arbitrage boundaries due to settlement latency of on average 124 basis points, covering 88 percent of the observed cross-exchange price differences.
Edit intent: clarity
Original:  Using high-frequency data from the Bitcoin network , we estimate arbitrage boundaries due to settlement latency of on average 124 basis points, covering 88 percent of the observed cross-exchange price differences.
Revised:  Using high-frequency data from the Bitcoin network , we estimate arbitrage bounds of on average 124 basis points, covering 88 percent of the observed cross-exchange price differences.
Edit intent: clarity
Original:  Using high-frequency data from the Bitcoin network , we estimate arbitrage boundaries due to settlement latency of on average 124 basis points, covering 88 percent of the observed cross-exchange price differences.
Revised:  Using high-frequency data from the Bitcoin network , we estimate arbitrage boundaries due to settlement latency of on average 124 basis points, covering 88 percent of the observed cross-market price differences.
Edit intent: clarity
Original:  Settlement through decentralized systems thus induces non-trivial frictions affecting market efficiency and price formation .
Revised:  Settlement through decentralized systems thus induces non-trivial friction that impedes arbitrage activity .
Edit intent: clarity
Original: Distributed ledger technologies replace trusted clearing counterparties and security depositories with time-consuming consensus protocols to record the transfer of ownership.
Revised: Distributed ledger technologies replace central counterparties with time-consuming consensus protocols to record the transfer of ownership.
Edit intent: clarity
Original:  This settlement latency exposes cross-market  arbitrageurs to price risk.
Revised:  This settlement latency exposes cross-market trading and exposes arbitrageurs to price risk.
Edit intent: clarity
Original:  The core of our method is a support-effective volume decomposition algorithm that targets on minimizing the usage of support-structures for the regions with large overhang .
Revised:  The core of our method is a support-effective volume decomposition algorithm that targets on minimizing the area of the regions with large overhang .
Edit intent: clarity
Original:  The core of our method is a support-effective volume decomposition algorithm that targets on minimizing the usage of support-structures for the regions with large overhang .
Revised:  The core of our method is a support-effective volume decomposition algorithm that targets on minimizing the usage of support-structures for the regions with large overhangs .
Edit intent: fluency
Original:  Different from existing approaches that need  manually assemble 3D printed components into a final model, regions decomposed by our algorithm can be automatically fabricated in a collision-free way on a multi-directional 3D printing system.
Revised:  Different from existing approaches that need to manually assemble 3D printed components into a final model, regions decomposed by our algorithm can be automatically fabricated in a collision-free way on a multi-directional 3D printing system.
Edit intent: fluency
Original:  Different from existing approaches that need  manually assemble 3D printed components into a final model, regions decomposed by our algorithm can be automatically fabricated in a collision-free way on a multi-directional 3D printing system.
Revised:  Different from existing approaches that need manually assemble 3D printed components into a final model, regions decomposed by our algorithm can be automatically fabricated on a multi-directional 3D printing system.
Edit intent: clarity
Original:  For those models that cannot completely eliminate support for large overhang , an algorithm is developed to generate special supporting structures for multi-directional 3D printing.
Revised:  For those models that cannot completely eliminate supporting structures for large overhangs , an algorithm is developed to generate special supporting structures for multi-directional 3D printing.
Edit intent: fluency
Original: We present a method to fabricate general models by multi-directional 3D printing systems , in which different regions of a model are printed along different directions.
Revised: We present a method for fabricating general models with multi-directional 3D printing systems , in which different regions of a model are printed along different directions.
Edit intent: clarity
Original: We present a method to fabricate general models by multi-directional 3D printing systems , in which different regions of a model are printed along different directions.
Revised: We present a method to fabricate general models by multi-directional 3D printing systems by printing different model regions along with different directions.
Edit intent: clarity
Original:  The core of our method is a support-effective volume decomposition algorithm that targets on minimizing the area of the regions with large overhangs.
Revised:  The core of our method is a support-effective volume decomposition algorithm that minimizes the area of the regions with large overhangs.
Edit intent: clarity
Original:  Optimal volume decomposition represented by a sequence of clipping planes is determined by a beam-guided searching algorithm according to manufacturing constraints.
Revised:  A beam-guided searching algorithm with manufacturing constraints determines the optimal volume decomposition, which is represented by a sequence of clipping planes is determined by a beam-guided searching algorithm according to manufacturing constraints.
Edit intent: coherence
Original:  For those models that cannot completely eliminate supporting structures for large overhangs, an algorithm is developed to generate special supporting structures for multi-directional 3D printing.
Revised:  A supplementary algorithm generates special supporting structures for large overhangs, an algorithm is developed to generate special supporting structures for multi-directional 3D printing.
Edit intent: clarity
Original:  For those models that cannot completely eliminate supporting structures for large overhangs, an algorithm is developed to generate special supporting structures for multi-directional 3D printing.
Revised:  For those models that cannot completely eliminate supporting structures for models where supporting structures for multi-directional 3D printing.
Edit intent: clarity
Original:  We developed two different hardware systems to physically verify the effectiveness of our method  : a Cartesian-motion based system and an angular-motion based system.
Revised:  We developed two different hardware systems to physically verify the effectiveness of our method using two hardware systems : a Cartesian-motion based system and an angular-motion based system.
Edit intent: clarity
Original:  We show that when the permeability , K, is small the pressure Schur complement must also be addressed for H(div)-based preconditioners.
Revised:  We show that when the permeability , K, is small the pressure Schur complement can also be utilised for H(div)-based preconditioners.
Edit intent: clarity
Original:  The proposed approach is based on the operator preconditioning framework .
Revised:  The proposed approach employs an operator preconditioning framework .
Edit intent: clarity
Original: We introduce the problems of goodness-of-fit and two-sample testing of the latent community structure in a 2-community, symmetric, stochastic block model \textit{  (SBM), in the regime where recovery of the structure is difficult.
Revised: We introduce the problems of \textit{ (SBM), in the regime where recovery of the structure is difficult.
Edit intent: coherence
Original: We introduce the problems of goodness-of-fit and two-sample testing of the latent community structure in a 2-community, symmetric, stochastic block model \textit{  (SBM), in the regime where recovery of the structure is difficult.
Revised: We introduce the problems of goodness-of-fit and two-sample testing of the latent community structure in a 2-community, symmetric, stochastic block model \textit{ for stochastic block models (SBM), in the regime where recovery of the structure is difficult.
Edit intent: clarity
Original:  Given graphs G,H drawn according to SBMs with partitions x,y, respectively, we wish to test the hypothesis x = y against d(x,y)%DIFDELCMD < \ge %%% s, for agiven Hamming distortion parameter s \ll n . Prior work showed that `partial ' recovery of these partitions up to distortion s with vanishing error probability requires that the signal-to-noise ratio  (SNR) is%DIFDELCMD < \gtrsim %%% C \log (n/s).
Revised:  Given graphs G,H drawn according to SBMs with partitions x,y, respectively, we wish to test the hypothesis x = y against d(x,y)%DIFDELCMD < \ge %%% s, for agiven Hamming distortion parameter s \ll n . Prior work showed that `partial ' recovery of these partitions up to distortion s with vanishing error probability requires that the signal-to-noise ratio ' (SNR) is%DIFDELCMD < \gtrsim %%% C \log (n/s).
Edit intent: fluency
Original:  Given graphs G,H drawn according to SBMs with partitions x,y, respectively, we wish to test the hypothesis x = y against d(x,y)%DIFDELCMD < \ge %%% s, for agiven Hamming distortion parameter s \ll n . Prior work showed that `partial ' recovery of these partitions up to distortion s with vanishing error probability requires that the signal-to-noise ratio  (SNR) is%DIFDELCMD < \gtrsim %%% C \log (n/s).
Revised:  Given graphs G,H drawn according to SBMs with partitions x,y, respectively, we wish to test the hypothesis x = y against d(x,y)%DIFDELCMD < \ge %%% s, for agiven Hamming distortion parameter s \ll n . Prior work showed that `partial ' recovery of these partitions up to distortion s with vanishing error probability requires that the signal-to-noise ratio (SNR) %DIFDELCMD < \gtrsim %%% C \log (n/s).
Edit intent: fluency
Original:  Motivated by practical applications, we consider the challenging sparse SBM regime, where degree-per-node is constant, and the inter-community mean degree (b) scales proportionally to intra-community mean degree (a).
Revised:  Motivated by practical applications, we consider the challenging sparse regime, where degree-per-node is constant, and the inter-community mean degree (b) scales proportionally to intra-community mean degree (a).
Edit intent: clarity
Original:  Motivated by practical applications, we consider the challenging sparse SBM regime, where degree-per-node is constant, and the inter-community mean degree (b) scales proportionally to intra-community mean degree (a).
Revised:  Motivated by practical applications, we consider the challenging sparse SBM regime, where expected node degrees are constant, and the inter-community mean degree (b) scales proportionally to intra-community mean degree (a).
Edit intent: clarity
Original:  Prior work has sharply characterized partial or full recovery of SBM community in terms of a ` signal-to-noise ratio ' (SNR) based on a and b.
Revised:  Prior work has sharply characterized partial or full community recovery in terms of a ` signal-to-noise ratio ' (SNR) based on a and b.
Edit intent: clarity
Original:  Prior work has sharply characterized partial or full recovery of SBM community in terms of a ` signal-to-noise ratio ' (SNR) based on a and b.
Revised:  Prior work has sharply characterized partial or full recovery of SBM community in terms of a " signal-to-noise ratio ' (SNR) based on a and b.
Edit intent: fluency
Original:  Prior work has sharply characterized partial or full recovery of SBM community in terms of a ` signal-to-noise ratio ' (SNR) based on a and b.
Revised:  Prior work has sharply characterized partial or full recovery of SBM community in terms of a ` signal-to-noise ratio " (SNR) based on a and b.
Edit intent: fluency
Original:  Conversely, in the small change regime, s \ll n, via an information theoretic lower bound, we show surprisingly that no algorithm can do better than the na\"ive algorithm that first recovers the full community and then detects changes.
Revised:  Conversely, in the small change regime, s \ll n, via an information-theoretic lower bound, we show surprisingly that no algorithm can do better than the na\"ive algorithm that first recovers the full community and then detects changes.
Edit intent: coherence
Original:  Conversely, in the small change regime, s \ll n, via an information theoretic lower bound, we show surprisingly that no algorithm can do better than the na\"ive algorithm that first recovers the full community and then detects changes.
Revised:  Conversely, in the small change regime, s \ll n, via an information theoretic lower bound, we show that, surprisingly, no algorithm can do better than the na\"ive algorithm that first recovers the full community and then detects changes.
Edit intent: coherence
Original: Networks and graphs arise naturally in many complex systems, often exhibiting dynamic behavior that can be modeled using dynamic networks.
Revised: In many complex systems, networks and graphs arise naturally in many complex systems, often exhibiting dynamic behavior that can be modeled using dynamic networks.
Edit intent: fluency
Original:  Two major research problems in dynamic networks are (1) community detection , which aims to find specific sub-structures within the networks, and (2) change point detection , which tries to find the time points at which sub-structures change.
Revised:  Two major research problems in network analysis are community detection and change-point detection. Community detection aims at finding specific sub-structures within the networks, and (2) change point detection , which tries to find the time points at which sub-structures change.
Edit intent: clarity
Original:  Two major research problems in dynamic networks are (1) community detection , which aims to find specific sub-structures within the networks, and (2) change point detection , which tries to find the time points at which sub-structures change.
Revised:  Two major research problems in dynamic networks are (1) community detection , which aims to find specific sub-structures within the networks, and change-point detection tries to find the time points at which sub-structures change.
Edit intent: coherence
Original:  The derived detection algorithm is compatible with many existing methods, and is supported by empirical results and data analysis.
Revised:  The promising practical performance of the proposed method is illustrated via a series of numerical experiments and real data analysis.
Edit intent: clarity
Original:  Multirate time integration strategies are able to efficiently and accurately propagate these equations in time .
Revised:  Implicit-explicit (IMEX) methods, multirate methods, and other multimethods combine different methods or timesteps to efficiently solve these systems .
Edit intent: clarity
Original:  In this work  we extend the derivation of  multirate infinitesimal GARK schemes to include coupled implicit stages that involve both the fast and slow components of the multirate system.
Revised:  In this work , we extend the derivation of multirate infinitesimal GARK schemes to include coupled implicit stages that involve both the fast and slow components of the multirate system.
Edit intent: fluency
Original:  Although the coupled stages computed over large timesteps may not provide the desired accuracy for the fast components of the system, they capture the slow dynamics and can be used to steer one or more MIS integrations with the goal of resolving the fast system more accurately.
Revised:  The coupled stages allow the slow tendencies to be interpolated as opposed to extrapolated, which can offer improved accuracy. Further, we show this coupled approach consistently offers improved stability.
Edit intent: clarity