wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Second, we study fully implementable Euler-Maruyama-type schemes for the particle system to approximate the solution of the  McKean-Vlasov SDEs . Here, we will prove strong convergence results in terms of  number of time-steps and number of particles.
Revised:  Second, we study fully implementable Euler-Maruyama type schemes for the particle system to approximate the solution of the McKean-Vlasov SDEs . Here, we will prove strong convergence results in terms of number of time-steps and number of particles.
Edit intent: fluency
Original:  Second, we study fully implementable Euler-Maruyama-type schemes for the particle system to approximate the solution of the  McKean-Vlasov SDEs . Here, we will prove strong convergence results in terms of  number of time-steps and number of particles.
Revised:  Second, we study fully implementable Euler-Maruyama-type schemes for the particle system to approximate the solution of the one-dimensional McKean-Vlasov SDEs . Here, we will prove strong convergence results in terms of number of time-steps and number of particles.
Edit intent: meaning-changed
Original:  Second, we study fully implementable Euler-Maruyama-type schemes for the particle system to approximate the solution of the  McKean-Vlasov SDEs . Here, we will prove strong convergence results in terms of  number of time-steps and number of particles.
Revised:  Second, we study fully implementable Euler-Maruyama-type schemes for the particle system to approximate the solution of the McKean-Vlasov SDE . Here, we will prove strong convergence results in terms of number of time-steps and number of particles.
Edit intent: fluency
Original:  Second, we study fully implementable Euler-Maruyama-type schemes for the particle system to approximate the solution of the  McKean-Vlasov SDEs . Here, we will prove strong convergence results in terms of  number of time-steps and number of particles.
Revised:  Second, we study fully implementable Euler-Maruyama-type schemes for the particle system to approximate the solution of the McKean-Vlasov SDEs . Here, we will prove strong convergence results in terms of the number of time-steps and number of particles.
Edit intent: fluency
Original:  Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual 1/2 strong convergence order  known for the Lipschitz case cannot be recovered for all presented schemes.
Revised:  Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual strong convergence order known for the Lipschitz case cannot be recovered for all presented schemes.
Edit intent: clarity
Original:  Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual 1/2 strong convergence order  known for the Lipschitz case cannot be recovered for all presented schemes.
Revised:  Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual 1/2 strong convergence order 1/2 known for the Lipschitz case cannot be recovered for all presented schemes.
Edit intent: meaning-changed
Original:  Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual 1/2 strong convergence order  known for the Lipschitz case cannot be recovered for all presented schemes.
Revised:  Due to the discontinuity of the drift, the convergence analysis is non-standard and the usual 1/2 strong convergence order known for the Lipschitz case cannot be recovered for all schemes.
Edit intent: clarity
Original: Once past the lockdown stage in many parts of the world, the important question now concerns the effects of relaxing the lockdown and finding the best ways to implement further lockdown(s), if required, to control the spread.
Revised: One of the important measures to control infectious diseases is a lockdown. As once past the lockdown stage in many parts of the world, the important question now concerns the effects of relaxing the lockdown and finding the best ways to implement further lockdown(s), if required, to control the spread.
Edit intent: coherence
Original:  In the present workwe study a modified SEIRS model with population migration between two cities: a fraction of population in each city is allowed to migrate. Possible infection during transit is also incorporated - a fraction of exposed population becomes infected during transit .
Revised:  In this work, we present the population migration model for n-cities and apply the model for migration between two and three cities. The reproduction number is calculated and the effect of the migration rate is being analyzed .
Edit intent: meaning-changed
Original:  This paper analyzes the market behavior and optimal investment strategies to attain relative arbitrage both in the N investors and mean field regimes  .
Revised: The relative arbitrage portfolio, formulated in Stochastic Portfolio Theory (SPT), outperforms a benchmark portfolio over a given time-horizon with probability one. This paper analyzes the market behavior and optimal investment strategies to attain relative arbitrage both in the N investors and mean field regimes .
Edit intent: meaning-changed
Original:  With market price of risk processes depending on the stock market and investors respectively, the minimal initial capital required is the optimal cost in the N-player games and mean field games. It can be characterized as the smallest nonnegative continuous solution of a Cauchy problem.
Revised:  With market price of risk processes depending on the market portfolio and investors, we develop a systematic way to solve multi-agent optimization problem within SPT's framework. The objective can be characterized as the smallest nonnegative continuous solution of a Cauchy problem.
Edit intent: meaning-changed
Original:  We modify the extended mean field game with common noise and its notion of the uniqueness of Nash equilibrium . There is a unique equilibrium in N-player games and mean field games with mild conditions on the equity market.
Revised:  We modify the extended mean field game with common noise and its notion of the uniqueness of Nash equilibrium , we show a unique equilibrium in N-player games and mean field games with mild conditions on the equity market.
Edit intent: coherence
Original: We study the real-time signals provided by the Aruoba-Diebold-Scotti Index of Business conditions (ADS) for tracking economic activity at high frequency.
Revised: Entering the Pandemic Recession, we study the high-frequency real-activity signals provided by the Aruoba-Diebold-Scotti Index of Business conditions (ADS) for tracking economic activity at high frequency.
Edit intent: meaning-changed
Original: We study the real-time signals provided by the Aruoba-Diebold-Scotti Index of Business conditions (ADS) for tracking economic activity at high frequency. We start with exit from the Great Recession, comparing the evolution of real-time vintage beliefs to a "final" late-vintage chronology.
Revised: We study the real-time signals provided by the Aruoba-Diebold-Scotti Index of Business Conditions produced and released in real time by the Federal Reserve Bank of Philadelphia. We track the evolution of real-time vintage beliefs to a "final" late-vintage chronology.
Edit intent: meaning-changed
Original:  We start with exit from the Great Recession, comparing the evolution of real-time vintage beliefs to a "final" late-vintage chronology. We then consider entry into the Pandemic Recession, again tracking the evolution of real-time vintage beliefs. ADS swings widely as its underlying economic indicators swing widely , but the emerging ADS path as of this writing (late June) indicates a return to growth in May.
Revised:  We start with exit from the Great Recession, comparing the evolution of real-time vintage beliefs and compare them to a later-vintage chronology. Real-time ADS plunges and then swings as its underlying economic indicators swing widely , but the emerging ADS path as of this writing (late June) indicates a return to growth in May.
Edit intent: meaning-changed
Original:  ADS swings widely as its underlying economic indicators swing widely , but the emerging ADS path as of this writing (late June) indicates a return to growth in May. The trajectory of the nascent recovery, however, is highly uncertain -- particularly as COVID-19 spreads in the South and West -- and could be revised or eliminated as new data arrive .
Revised:  ADS swings widely as its underlying economic indicators swing widely , but the emerging ADS path as of this writing (late June) indicates a return to brisk positive growth by mid-May. We show, moreover, that the daily real activity path was extremely highly correlated with the daily COVID-19 spreads in the South and West -- and could be revised or eliminated as new data arrive .
Edit intent: meaning-changed
Original: Entering  the Pandemic Recession, we study the high-frequency real-activity signals provided by a leading nowcast, the ADS Index of Business Conditions produced and released in real time by the Federal Reserve Bank of Philadelphia.
Revised: Entering and exiting the Pandemic Recession, we study the high-frequency real-activity signals provided by a leading nowcast, the ADS Index of Business Conditions produced and released in real time by the Federal Reserve Bank of Philadelphia.
Edit intent: meaning-changed
Original: Entering  the Pandemic Recession, we study the high-frequency real-activity signals provided by a leading nowcast, the ADS Index of Business Conditions produced and released in real time by the Federal Reserve Bank of Philadelphia.
Revised: Entering the Pandemic Recession, I study the high-frequency real-activity signals provided by a leading nowcast, the ADS Index of Business Conditions produced and released in real time by the Federal Reserve Bank of Philadelphia.
Edit intent: clarity
Original:  We show, moreover, that the daily real activity path was extremely highly correlated with the daily COVID-19 path . Finally, we provide a comparative assessment of the real-time ADS signals provided when exiting the Great Recession.
Revised:  We show, moreover, that daily real activity path was extremely highly correlated with the daily COVID-19 path . Finally, we provide a comparative assessment of the real-time ADS signals provided when exiting the Great Recession.
Edit intent: fluency
Original:  We show, moreover, that the daily real activity path was extremely highly correlated with the daily COVID-19 path . Finally, we provide a comparative assessment of the real-time ADS signals provided when exiting the Great Recession.
Revised:  We show, moreover, that the daily real activity path was highly correlated with the daily COVID-19 path . Finally, we provide a comparative assessment of the real-time ADS signals provided when exiting the Great Recession.
Edit intent: coherence
Original:  We show, moreover, that the daily real activity path was extremely highly correlated with the daily COVID-19 path . Finally, we provide a comparative assessment of the real-time ADS signals provided when exiting the Great Recession.
Revised:  We show, moreover, that the daily real activity path was extremely highly correlated with the daily COVID-19 cases . Finally, we provide a comparative assessment of the real-time ADS signals provided when exiting the Great Recession.
Edit intent: clarity
Original:  We show, moreover, that the daily real activity path was extremely highly correlated with the daily COVID-19 path . Finally, we provide a comparative assessment of the real-time ADS signals provided when exiting the Great Recession.
Revised:  We show, moreover, that the daily real activity path was extremely highly correlated with the daily COVID-19 path . Finally, I provide a comparative assessment of the real-time ADS signals provided when exiting the Great Recession.
Edit intent: coherence
Original: In this paper, we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 3 ] . Such work aims to introduce the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Revised: In this paper, we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 4 ] . Such work aims to introduce the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Edit intent: meaning-changed
Original: In this paper, we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 3 ] . Such work aims to introduce the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Revised: In this paper, we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 3 ] , which aimed at introducing the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Edit intent: coherence
Original:  Our methods, which use the network morphism framework introduced in [ 2 ]  , can analyze forty times as many architectures as the fastest methods in the literature [ 2,10 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Revised:  Our methods, which use the network morphism framework introduced in [ 3 ] , can analyze forty times as many architectures as the fastest methods in the literature [ 2,10 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Edit intent: meaning-changed
Original:  Our methods, which use the network morphism framework introduced in [ 2 ]  , can analyze forty times as many architectures as the fastest methods in the literature [ 2,10 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Revised:  Our methods, which use the network morphism framework introduced in [ 2 ] as a baseline , can analyze forty times as many architectures as the fastest methods in the literature [ 2,10 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Edit intent: meaning-changed
Original:  Our methods, which use the network morphism framework introduced in [ 2 ]  , can analyze forty times as many architectures as the fastest methods in the literature [ 2,10 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Revised:  Our methods, which use the network morphism framework introduced in [ 2 ] , can analyze forty times as many architectures as the hill climbing methods [ 2,10 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Edit intent: meaning-changed
Original:  Our methods, which use the network morphism framework introduced in [ 2 ]  , can analyze forty times as many architectures as the fastest methods in the literature [ 2,10 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Revised:  Our methods, which use the network morphism framework introduced in [ 2 ] , can analyze forty times as many architectures as the fastest methods in the literature [ 3,11 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Edit intent: meaning-changed
Original: In this paper , we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 4 ] , which aimed at introducing the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Revised: In this paper we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 4 ] , which aimed at introducing the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Edit intent: fluency
Original: In this paper , we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 4 ] , which aimed at introducing the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Revised: In this paper , we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 5 ] , which aimed at introducing the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Edit intent: meaning-changed
Original: In this paper , we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 4 ] , which aimed at introducing the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Revised: In this paper , we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 4 ] which used the geometric structure of optimal transport to introduce the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory.
Edit intent: meaning-changed
Original: In this paper , we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 4 ] , which aimed at introducing the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space using ideas from optimal transport theory. Our methods , which use the network morphism framework introduced in [ 3 ] as a baseline, can analyze forty times as many architectures as the hill climbing methods [ 3, 11 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Revised: In this paper , we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [ 4 ] , which aimed at introducing the conceptual basis for new notions of traditional and accelerated gradient descent algorithms for the optimization of a function on a semi-discrete space . Our algorithms , which use the network morphism framework introduced in [ 3 ] as a baseline, can analyze forty times as many architectures as the hill climbing methods [ 3, 11 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Edit intent: coherence
Original:  Our methods , which use the network morphism framework introduced in [ 3 ] as a baseline, can analyze forty times as many architectures as the hill climbing methods [ 3, 11 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Revised:  Our methods , which use the network morphism framework introduced in [ 2 ] as a baseline, can analyze forty times as many architectures as the hill climbing methods [ 3, 11 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Edit intent: meaning-changed
Original:  Our methods , which use the network morphism framework introduced in [ 3 ] as a baseline, can analyze forty times as many architectures as the hill climbing methods [ 3, 11 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Revised:  Our methods , which use the network morphism framework introduced in [ 3 ] as a baseline, can analyze forty times as many architectures as the hill climbing methods [ 2, 14 ] while using the same computational resources and time and achieving comparable levels of accuracy.
Edit intent: meaning-changed
Original:  We show that attention  (1) captures the folding structure of proteins, connecting amino acids that are far apart in the underlying sequence, but spatially close in the three-dimensional structure, (2) targets binding sites, a key functional component of proteins, and (3) focuses on progressively more complex biophysical properties with increasing layer depth.
Revised:  We show that attention : (1) captures the folding structure of proteins, connecting amino acids that are far apart in the underlying sequence, but spatially close in the three-dimensional structure, (2) targets binding sites, a key functional component of proteins, and (3) focuses on progressively more complex biophysical properties with increasing layer depth.
Edit intent: fluency
Original:  This is motivated from computational biology, data protection, and computer security settings, which can be abstracted in terms of two parties, a responder , Alice, who must correctly answer queries of a given type regarding a degree-d tree, T, and a querier , Bob, who issues batches of queries, with each query in a batch being independent of the others, so as to eventually infer the structure of T.
Revised:  This is motivated from computational biology, data protection, and computer security settings, which can be abstracted in terms of two parties, a responder , Alice, who must correctly answer queries of a given type regarding a degree-d tree, T, and a querier , Bob, who issues batches of queries, with each query in a batch being independent of the others, so as to eventually infer the structure of T.
Edit intent: fluency
Original:  We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries andpath queries .
Revised:  We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including andpath queries .
Edit intent: clarity
Original:  We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries andpath queries .
Revised:  We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries path queries .
Edit intent: meaning-changed
Original:  We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries andpath queries .
Revised:  We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries andrelative-distance queries and path queries .
Edit intent: meaning-changed