wanyu/IteraTeR_v2 huggingface dataset:
Original:  By a very recent result of [Fearnley, Goldberg, Hollender, Savani 2020 ] , this implies that these problems are PPAD\capPLS-complete.
Revised:  By a very recent result of [Fearnley, Goldberg, Hollender, Savani '20 ] , this implies that these problems are PPAD\capPLS-complete.
Edit intent: clarity
Original:  By a very recent result of [Fearnley, Goldberg, Hollender, Savani 2020 ] , this implies that these problems are PPAD\capPLS-complete.
Revised:  By a very recent result of [Fearnley, Goldberg, Hollender, Savani 2020 ] this implies that these problems are PPAD\capPLS-complete.
Edit intent: fluency
Original: A  curve P with n vertices is said to be c-packed if the length of the curve within any disk of radius r is at most cr, for any r>0.
Revised: A curve P with n vertices is c-packed if the length of the curve within any disk of radius r is at most cr, for any r>0.
Edit intent: clarity
Original:  If the ratio \frac L \delta is fixed, where L is the total length of P and \delta is the minimum distance between any two points on P, other than the intersection points, a 2 (1+\epsilon)-approximation algorithm exists for disks, and a (1+\epsilon)-approximation algorithm exists for convex polygons  , with time complexities O(\frac{\log (L/\delta)}{\epsilon}n^3) and O( \frac{\log (L/\delta){\epsilon}} {\epsilon^{5/2}}} n^3\log n), respectively.
Revised:  If the ratio \frac L \delta is fixed, where L is the total length of P and \delta is the minimum distance between any pair of points on two non-intersecting edges of P, (1+\epsilon)-approximation algorithm exists for disks, and a (1+\epsilon)-approximation algorithm exists for convex polygons , with time complexities O(\frac{\log (L/\delta)}{\epsilon}n^3) and O( \frac{\log (L/\delta){\epsilon}} {\epsilon^{5/2}}} n^3\log n), respectively.
Edit intent: clarity
Original:  If the ratio \frac L \delta is fixed, where L is the total length of P and \delta is the minimum distance between any two points on P, other than the intersection points, a 2 (1+\epsilon)-approximation algorithm exists for disks, and a (1+\epsilon)-approximation algorithm exists for convex polygons  , with time complexities O(\frac{\log (L/\delta)}{\epsilon}n^3) and O( \frac{\log (L/\delta){\epsilon}} {\epsilon^{5/2}}} n^3\log n), respectively.
Revised:  If the ratio \frac L \delta is fixed, where L is the total length of P and \delta is the minimum distance between any two points on P, other than the intersection points, a 2 (1+\epsilon)-approximation algorithms exist for disks, and a (1+\epsilon)-approximation algorithm exists for convex polygons , with time complexities O(\frac{\log (L/\delta)}{\epsilon}n^3) and O( \frac{\log (L/\delta){\epsilon}} {\epsilon^{5/2}}} n^3\log n), respectively.
Edit intent: fluency
Original:  If the ratio \frac L \delta is fixed, where L is the total length of P and \delta is the minimum distance between any two points on P, other than the intersection points, a 2 (1+\epsilon)-approximation algorithm exists for disks, and a (1+\epsilon)-approximation algorithm exists for convex polygons  , with time complexities O(\frac{\log (L/\delta)}{\epsilon}n^3) and O( \frac{\log (L/\delta){\epsilon}} {\epsilon^{5/2}}} n^3\log n), respectively.
Revised:  If the ratio \frac L \delta is fixed, where L is the total length of P and \delta is the minimum distance between any two points on P, other than the intersection points, a 2 (1+\epsilon)-approximation algorithm exists for disks, and for convex polygons , with time complexities O(\frac{\log (L/\delta)}{\epsilon}n^3) and O( \frac{\log (L/\delta){\epsilon}} {\epsilon^{5/2}}} n^3\log n), respectively.
Edit intent: coherence
Original:  If the ratio \frac L \delta is fixed, where L is the total length of P and \delta is the minimum distance between any two points on P, other than the intersection points, a 2 (1+\epsilon)-approximation algorithm exists for disks, and a (1+\epsilon)-approximation algorithm exists for convex polygons  , with time complexities O(\frac{\log (L/\delta)}{\epsilon}n^3) and O( \frac{\log (L/\delta){\epsilon}} {\epsilon^{5/2}}} n^3\log n), respectively.
Revised:  If the ratio \frac L \delta is fixed, where L is the total length of P and \delta is the minimum distance between any two points on P, other than the intersection points, a 2 (1+\epsilon)-approximation algorithm exists for disks, and a (1+\epsilon)-approximation algorithm exists for convex polygons , with time complexities O(\frac{\log (L/\delta)}{\epsilon}n^3) and O( \frac{\log (L/\delta){\epsilon}} \frac{\log (L/\delta){\epsilon^{5/2}}} n^3\log n), respectively.
Edit intent: fluency
Original:  Using an example, we show that c-packedness and relative c-packedness are not within a constant factor of each other .
Revised:  Using an example, we show that c-packedness and relative c-packedness .
Edit intent: clarity
Original:  Assuming L is the total length of P and \delta is the minimum distance between any pair of points on two non-intersecting edges of P, ( 1+\epsilon ) -approximation algorithms exist for disks, and for convex polygons of constant size, with time complexities O(\frac{\log (L/\delta){\epsilon}n ^3) and O(\log (L/\delta){\epsilon^{5/2}}n^3\log} )^{\frac 4 3}}\polylog  n ), respectively.
Revised:  Assuming L is the diameter of P and \delta is the minimum distance between any pair of points on two non-intersecting edges of P, ( 1+\epsilon ) -approximation algorithms exist for disks, and for convex polygons of constant size, with time complexities O(\frac{\log (L/\delta){\epsilon}n ^3) and O(\log (L/\delta){\epsilon^{5/2}}n^3\log} )^{\frac 4 3}}\polylog n ), respectively.
Edit intent: clarity
Original:  Assuming L is the total length of P and \delta is the minimum distance between any pair of points on two non-intersecting edges of P, ( 1+\epsilon ) -approximation algorithms exist for disks, and for convex polygons of constant size, with time complexities O(\frac{\log (L/\delta){\epsilon}n ^3) and O(\log (L/\delta){\epsilon^{5/2}}n^3\log} )^{\frac 4 3}}\polylog  n ), respectively.
Revised:  Assuming L is the total length of P and \delta is the minimum distance between points on disjoint edges of P, ( 1+\epsilon ) -approximation algorithms exist for disks, and for convex polygons of constant size, with time complexities O(\frac{\log (L/\delta){\epsilon}n ^3) and O(\log (L/\delta){\epsilon^{5/2}}n^3\log} )^{\frac 4 3}}\polylog n ), respectively.
Edit intent: clarity
Original:  Assuming L is the total length of P and \delta is the minimum distance between any pair of points on two non-intersecting edges of P, ( 1+\epsilon ) -approximation algorithms exist for disks, and for convex polygons of constant size, with time complexities O(\frac{\log (L/\delta){\epsilon}n ^3) and O(\log (L/\delta){\epsilon^{5/2}}n^3\log} )^{\frac 4 3}}\polylog  n ), respectively.
Revised:  Assuming L is the total length of P and \delta is the minimum distance between any pair of points on two non-intersecting edges of P, ( 1+\epsilon -approximation algorithms exist for disks, and for convex polygons of constant size, with time complexities O(\frac{\log (L/\delta){\epsilon}n ^3) and O(\log (L/\delta){\epsilon^{5/2}}n^3\log} )^{\frac 4 3}}\polylog n ), respectively.
Edit intent: fluency
Original:  Assuming L is the total length of P and \delta is the minimum distance between any pair of points on two non-intersecting edges of P, ( 1+\epsilon ) -approximation algorithms exist for disks, and for convex polygons of constant size, with time complexities O(\frac{\log (L/\delta){\epsilon}n ^3) and O(\log (L/\delta){\epsilon^{5/2}}n^3\log} )^{\frac 4 3}}\polylog  n ), respectively.
Revised:  Assuming L is the total length of P and \delta is the minimum distance between any pair of points on two non-intersecting edges of P, ( 1+\epsilon ) -approximation {\epsilon}n ^3) and O(\log (L/\delta){\epsilon^{5/2}}n^3\log} )^{\frac 4 3}}\polylog n ), respectively.
Edit intent: coherence
Original:  We also give a data-structure for computing the length of the curve inside arbitrary query disk, known as the length-query problem .
Revised:  We also give a data-structure for computing the curve-length inside query disks .
Edit intent: clarity
Original: As the development of Quantum computers becomes reality, the implementation of quantum algorithms is accelerating in a great pace . Grover's  algorithm in a binary quantum system is one such quantum algorithm which solves search problems with numeric speed-ups than the conventional classical computers .
Revised: The progress in building quantum computers to execute quantum algorithms has recently been remarkable . Grover's algorithm in a binary quantum system is one such quantum algorithm which solves search problems with numeric speed-ups than the conventional classical computers .
Edit intent: clarity
Original: As the development of Quantum computers becomes reality, the implementation of quantum algorithms is accelerating in a great pace . Grover's  algorithm in a binary quantum system is one such quantum algorithm which solves search problems with numeric speed-ups than the conventional classical computers .
Revised: As the development of Quantum computers becomes reality, the implementation of quantum algorithms is accelerating in a great pace . Grover's search algorithm in a binary quantum system is one such quantum algorithm which solves search problems with numeric speed-ups than the conventional classical computers .
Edit intent: fluency
Original: As the development of Quantum computers becomes reality, the implementation of quantum algorithms is accelerating in a great pace . Grover's  algorithm in a binary quantum system is one such quantum algorithm which solves search problems with numeric speed-ups than the conventional classical computers .
Revised: As the development of Quantum computers becomes reality, the implementation of quantum algorithms is accelerating in a great pace . Grover's algorithm in a binary quantum system provides considerable speed-up over classical paradigm .
Edit intent: clarity
Original:  Further, Grover's algorithm is extended to a d-ary  quantum system for utilizing the advantage of larger state space.
Revised:  Further, Grover's algorithm can be extended to a d-ary quantum system for utilizing the advantage of larger state space.
Edit intent: clarity
Original:  In qudit or d-ary quantum system n-qudit Toffoli gate plays a significant role in the accurate implementation of Grover's algorithm.
Revised:  In a qudit quantum system, an n-qudit Toffoli gate plays a significant role in the accurate implementation of Grover's algorithm.
Edit intent: clarity
Original:  Further, the circuit for Grover's algorithm has  been designed for any d-ary quantum system, where d >= \ge 2, with the proposed n-qudit Toffoli gate so as to get optimized depth as compared to state-of-the-art approaches.
Revised:  The circuit for Grover's algorithm has been designed for any d-ary quantum system, where d >= \ge 2, with the proposed n-qudit Toffoli gate so as to get optimized depth as compared to state-of-the-art approaches.
Edit intent: coherence
Original:  Further, the circuit for Grover's algorithm has  been designed for any d-ary quantum system, where d >= \ge 2, with the proposed n-qudit Toffoli gate so as to get optimized depth as compared to state-of-the-art approaches.
Revised:  Further, the circuit for Grover's algorithm has then been designed for any d-ary quantum system, where d >= \ge 2, with the proposed n-qudit Toffoli gate so as to get optimized depth as compared to state-of-the-art approaches.
Edit intent: coherence
Original:  Therefore, the performance of this decomposition for the unitary and erasure models of leakage noise has been studied as well.
Revised:  The performance of the decomposition for the unitary and erasure models of leakage noise has been studied as well.
Edit intent: coherence
Original: We consider the problem of active portfolio management where a loss-averse and/or gain-seeking investor aims to outperform a benchmark strategy's risk profile while not deviating too much from it.
Revised: We study the problem of active portfolio management where a loss-averse and/or gain-seeking investor aims to outperform a benchmark strategy's risk profile while not deviating too much from it.
Edit intent: clarity
Original: We consider the problem of active portfolio management where a loss-averse and/or gain-seeking investor aims to outperform a benchmark strategy's risk profile while not deviating too much from it.
Revised: We consider the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too much from it.
Edit intent: clarity
Original: We consider the problem of active portfolio management where a loss-averse and/or gain-seeking investor aims to outperform a benchmark strategy's risk profile while not deviating too much from it.
Revised: We consider the problem of active portfolio management where a loss-averse and/or gain-seeking investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it.
Edit intent: clarity
Original:  Specifically, an investor considers alternative strategies that co-move with the benchmark and whose terminal wealth lies within a Wasserstein ball surrounding  it.
Revised:  Specifically, an investor considers alternative strategies whose terminal wealth lies within a Wasserstein ball surrounding it.
Edit intent: clarity
Original:  Specifically, an investor considers alternative strategies that co-move with the benchmark and whose terminal wealth lies within a Wasserstein ball surrounding  it.
Revised:  Specifically, an investor considers alternative strategies that co-move with the benchmark and whose terminal wealth lie within a Wasserstein ball surrounding it.
Edit intent: fluency
Original:  The investor then chooses the alternative strategy that minimises their personal risk preferences, modelled in terms of a distortion risk measure  .
Revised:  The investor then chooses the alternative strategy that minimises a distortion risk measure .
Edit intent: clarity
Original:  In a general  market model, we prove that an optimal dynamic strategy exists and is unique, and provide its characterisation through the notion of isotonic projections.
Revised:  In a general market model, we prove that an optimal dynamic strategy exists and provide its characterisation through the notion of isotonic projections.
Edit intent: clarity
Original:  We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving some aspects of the benchmark .
Revised:  We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving the benchmark's structure .
Edit intent: clarity
Original:  First we prove existence of unique solutions to this equation with particular attention paid to the handling of the fractional derivative.
Revised:  First we prove existence of a unique solution to this equation with particular attention paid to the handling of the fractional derivative.
Edit intent: fluency
Original:   A number of numerical results are presented to support the error analysis for both smooth and nonsmooth solutions .
Revised:  A number of numerical results are presented to support the error analysis .
Edit intent: clarity
Original:  \%Benefiting from this design, CLADE greatly reduces the computation cost while being able to preserve the semantic information in the generation.
Edit intent: coherence
Original: Predicting the dynamics of neural network parameters during training is one of the key challenges in building a theoretical foundation for deep learning.
Revised: Understanding the dynamics of neural network parameters during training is one of the key challenges in building a theoretical foundation for deep learning.
Edit intent: clarity
Original:  We empirically validate our analytic predictions for learning dynamics on VGG-16 trained on Tiny ImageNet.
Revised:  We empirically validate our analytic expressions for learning dynamics on VGG-16 trained on Tiny ImageNet.
Edit intent: clarity
Original: Noun phrases and relation phrases in open knowledge graphs are not canonicalized, leading to an explosion of redundant and ambiguous subject-relation-object triples.
Revised: Noun phrases and Relation phrases in open knowledge graphs are not canonicalized, leading to an explosion of redundant and ambiguous subject-relation-object triples.
Edit intent: fluency
Original:  Existing approaches to face this problem take a two-step approach : first , they generate embedding representations for both noun and relation phrases, then a clustering algorithm is used to group them using the embeddings as features.
Revised:  Existing approaches to solve this problem take a two-step approach : first , they generate embedding representations for both noun and relation phrases, then a clustering algorithm is used to group them using the embeddings as features.
Edit intent: clarity
Original:  Existing approaches to face this problem take a two-step approach : first , they generate embedding representations for both noun and relation phrases, then a clustering algorithm is used to group them using the embeddings as features.
Revised:  Existing approaches to face this problem take a two-step approach . First , they generate embedding representations for both noun and relation phrases, then a clustering algorithm is used to group them using the embeddings as features.
Edit intent: fluency
Original:  In this work, we propose Canonicalizing Using Variational AutoEncoders (CUVA), a joint model to learn both embeddings and cluster assignments in an end-to-end approach, which leads to a better vector representation for the noun and relation phrases.
Revised:  In this work, we propose Canonicalizing Using Variational Autoencoders (CUVA), a joint model to learn both embeddings and cluster assignments in an end-to-end approach, which leads to a better vector representation for the noun and relation phrases.
Edit intent: fluency
Original:  Our evaluation over multiple benchmarks shows that CUVA outperforms the existing state of the art approaches.
Revised:  Our evaluation over multiple benchmarks shows that CUVA outperforms the existing state-of-the-art approaches.
Edit intent: fluency
Original:  Moreover, we introduce CanonicNell  a novel dataset to evaluate entity canonicalization systems.
Revised:  Moreover, we introduce CanonicNell , a novel dataset to evaluate entity canonicalization systems.
Edit intent: fluency
Original:  With the advances in cloud technologies, disaggregated Radio Access Network (RAN) architectures emerged in the past decade , where Network Functions (NFs) are ripped away from specialized hardware and placed on bare metal servers.
Revised:  With the advances in cloud technologies, disaggregated Radio Access Network (RAN) architectures have significantly evolved in the past decade , where Network Functions (NFs) are ripped away from specialized hardware and placed on bare metal servers.
Edit intent: clarity
Original:  Although the concept of RAN evolution has been around for some time starting from Cloud Radio Access Networks (C-RANs), continuing with Virtual Radio Access Networks (vRANs) and most recently Open Radio Access Networks (ORANs), we are seeing commercial implementations and tests of disaggregated, virtualized and open RANs only since the beginning of 2020.
Revised:  Although the concept of RAN evolution has been around for some time starting from Cloud Radio Access Networks (C-RANs), continuing with Virtual Radio Access Networks (vRANs) and most recently Open Radio Access Networks (ORANs), we are seeing commercial implementations and tests of disaggregated, virtualized and open RANs , with numerous tests and deployments world wide.
Edit intent: coherence
Original:  One unique aspect that motivates this paper is the availability of new opportunities that arise from applying machine learning to optimize the RAN in closed-loop, i.e. without human intervention, where the complexity of disaggregation and virtualization makes well-known Self-Organized Networking (SON) solutions inadequate.
Revised:  One unique aspect that motivates this paper is the availability of new opportunities that arise from using machine learning to optimize the RAN in closed-loop, i.e. without human intervention, where the complexity of disaggregation and virtualization makes well-known Self-Organized Networking (SON) solutions inadequate.
Edit intent: fluency
Original:  In particular, Multi-agent systems (MASs) is expected to play an essential role in the control and coordination of  near-real-time and nonreal-time RAN Intelligent Controller (RIC).
Revised:  In our view, Multi-Agent Systems (MASs) is expected to play an essential role in the control and coordination of near-real-time and nonreal-time RAN Intelligent Controller (RIC).
Edit intent: clarity
Original:  In particular, Multi-agent systems (MASs) is expected to play an essential role in the control and coordination of  near-real-time and nonreal-time RAN Intelligent Controller (RIC).
Revised:  In particular, Multi-agent systems (MASs) is expected to play an essential role in the control and coordination of near-real-time and non-real-time RAN Intelligent Controller (RIC).
Edit intent: fluency
Original:  In this visionary article, we first present the state-of-the-art research in multiagent systems and team learning, then we provide an overview of the landscape in RAN disaggregation , virtualization, as well as ORAN which emphasizes the open interfaces introduced by the O-RAN Alliance.
Revised:  In this article, we first present the state-of-the-art research in multiagent systems and team learning, then we provide an overview of the landscape in RAN disaggregation , virtualization, as well as ORAN which emphasizes the open interfaces introduced by the O-RAN Alliance.
Edit intent: coherence
Original:  In this visionary article, we first present the state-of-the-art research in multiagent systems and team learning, then we provide an overview of the landscape in RAN disaggregation , virtualization, as well as ORAN which emphasizes the open interfaces introduced by the O-RAN Alliance.
Revised:  In this visionary article, we first present the state-of-the-art research in multi-agent systems and team learning, then we provide an overview of the landscape in RAN disaggregation , virtualization, as well as ORAN which emphasizes the open interfaces introduced by the O-RAN Alliance.
Edit intent: fluency
Original:  In this visionary article, we first present the state-of-the-art research in multiagent systems and team learning, then we provide an overview of the landscape in RAN disaggregation , virtualization, as well as ORAN which emphasizes the open interfaces introduced by the O-RAN Alliance.
Revised:  In this visionary article, we first present the state-of-the-art research in multiagent systems and team learning, then we provide an overview of the landscape in RAN disaggregation and virtualization, as well as ORAN which emphasizes the open interfaces introduced by the O-RAN Alliance.
Edit intent: fluency
Original:  In this visionary article, we first present the state-of-the-art research in multiagent systems and team learning, then we provide an overview of the landscape in RAN disaggregation , virtualization, as well as ORAN which emphasizes the open interfaces introduced by the O-RAN Alliance.
Revised:  In this visionary article, we first present the state-of-the-art research in multiagent systems and team learning, then we provide an overview of the landscape in RAN disaggregation , virtualization, as well as O-RAN which emphasizes the open interfaces introduced by the O-RAN Alliance.
Edit intent: fluency
Original:  Anyway, despite hopes placed in this field are high, Quantum Computing is still in an incipient stage of development.
Revised:  Anyway, Quantum Computing is still in an incipient stage of development.
Edit intent: coherence