wanyu/IteraTeR_v2 huggingface dataset:
Original: An (n,r,h,a,q) -LRC is a linear code over F_q of length n, whose codeword symbols are partitioned into n/r local groups each of size r. Each local group satisfies `a' local parity checks to recover from `a' erasures in that local group and there are further h global parity checks to provide fault tolerance from more global erasure patterns.
Revised: An (n,r,h,a,q) -Local Reconstruction Code is a linear code over F_q of length n, whose codeword symbols are partitioned into n/r local groups each of size r. Each local group satisfies `a' local parity checks to recover from `a' erasures in that local group and there are further h global parity checks to provide fault tolerance from more global erasure patterns.
Edit intent: clarity
Original:  Such an LRC is Maximally Recoverable (MR), if it  can correct all erasure patterns which are information-theoretically correctable given this structure---these are precisely patterns with up to `a' erasures in each local group and an additional h erasures anywhere in the codeword .
Revised:  Such an LRC is Maximally Recoverable (MR), if it can correct all erasure patterns whose recovery is information-theoretically correctable given this structure---these are precisely patterns with up to `a' erasures in each local group and an additional h erasures anywhere in the codeword .
Edit intent: clarity
Original:  Such an LRC is Maximally Recoverable (MR), if it  can correct all erasure patterns which are information-theoretically correctable given this structure---these are precisely patterns with up to `a' erasures in each local group and an additional h erasures anywhere in the codeword .
Revised:  Such an LRC is Maximally Recoverable (MR), if it can correct all erasure patterns which are information-theoretically feasible given the locality structure (these are precisely patterns with up to `a' erasures in each local group and an additional h erasures anywhere in the codeword .
Edit intent: clarity
Original:  This significantly improves upon known constructions in most parameter ranges.
Revised:  This improves upon known constructions in most parameter ranges.
Edit intent: clarity
Original:  Moreover, it matches the best known lower bound from ~\mbox{ gopi2020maximally in an interesting special case when r=\Theta(n) and h,a are constants with h\le a+2, achieving the optimal field size of a, h(n^{h/2}).
Revised:  Moreover, it matches the lower bound from ~\mbox{ gopi2020maximally in an interesting special case when r=\Theta(n) and h,a are constants with h\le a+2, achieving the optimal field size of a, h(n^{h/2}).
Edit intent: clarity
Original:  Moreover, it matches the best known lower bound from ~\mbox{ gopi2020maximally in an interesting special case when r=\Theta(n) and h,a are constants with h\le a+2, achieving the optimal field size of a, h(n^{h/2}).
Revised:  Moreover, it matches the best known lower bound from Gopi et al. (2020) in an interesting special case when r=\Theta(n) and h,a are constants with h\le a+2, achieving the optimal field size of a, h(n^{h/2}).
Edit intent: clarity
Original:  Moreover, it matches the best known lower bound from ~\mbox{ gopi2020maximally in an interesting special case when r=\Theta(n) and h,a are constants with h\le a+2, achieving the optimal field size of a, h(n^{h/2}).
Revised:  Moreover, it matches the best known lower bound from ~\mbox{ gopi2020maximally in an interesting range of parameters where r=\Theta(n) and h,a are constants with h\le a+2, achieving the optimal field size of a, h(n^{h/2}).
Edit intent: clarity
Original:  Moreover, it matches the best known lower bound from ~\mbox{ gopi2020maximally in an interesting special case when r=\Theta(n) and h,a are constants with h\le a+2, achieving the optimal field size of a, h(n^{h/2}).
Revised:  Moreover, it matches the best known lower bound from ~\mbox{ gopi2020maximally in an interesting special case when r=\Theta(n) and h,a are constants with h\le a+2, achieving the optimal field size of (n^{h/2}).
Edit intent: coherence
Original: While the open-source model for software development has led to successful large-scale collaborations in building software systems, data science projects are frequently developed by individuals or small groups .
Revised: While the open-source software development model has led to successful large-scale collaborations in building software systems, data science projects are frequently developed by individuals or small groups .
Edit intent: clarity
Original: While the open-source model for software development has led to successful large-scale collaborations in building software systems, data science projects are frequently developed by individuals or small groups .
Revised: While the open-source model for software development has led to successful large-scale collaborations in building software systems, data science projects are frequently developed by individuals or small teams .
Edit intent: clarity
Original:  We describe challenges to scaling data science collaborations and present a novel conceptual framework and ML programming model to address them.
Revised:  We describe challenges to scaling data science collaborations and present a conceptual framework and ML programming model to address them.
Edit intent: clarity
Original:  We instantiate these ideas in Ballet, a lightweight software framework for collaborative  open-source data science and a cloud-based development environment , with a plugin for collaborative feature engineering .
Revised:  We instantiate these ideas in Ballet, a lightweight framework for collaborative open-source data science and a cloud-based development environment , with a plugin for collaborative feature engineering .
Edit intent: clarity
Original:  We instantiate these ideas in Ballet, a lightweight software framework for collaborative  open-source data science and a cloud-based development environment , with a plugin for collaborative feature engineering .
Revised:  We instantiate these ideas in Ballet, a lightweight software framework for collaborative , open-source data science and a cloud-based development environment , with a plugin for collaborative feature engineering .
Edit intent: fluency
Original:  We instantiate these ideas in Ballet, a lightweight software framework for collaborative  open-source data science and a cloud-based development environment , with a plugin for collaborative feature engineering .
Revised:  We instantiate these ideas in Ballet, a lightweight software framework for collaborative open-source data science and a cloud-based development environment .
Edit intent: clarity
Original:  We leverage Ballet to conduct an extensive case study analysis of a real-world income prediction problem  , and discuss implications for  collaborative projects.
Revised:  We leverage Ballet to conduct a case study analysis of a real-world income prediction problem , and discuss implications for collaborative projects.
Edit intent: clarity
Original:  We leverage Ballet to conduct an extensive case study analysis of a real-world income prediction problem  , and discuss implications for  collaborative projects.
Revised:  We leverage Ballet to conduct an extensive case study analysis of an income prediction problem , and discuss implications for collaborative projects.
Edit intent: clarity
Original:  In this paper, we prove constructively that the cone of sums of nonnegative circuits (SONC) admits an SOC representation.
Revised:  In this paper, we prove constructively that the cone of sums of nonnegative circuits (SONC) admits a SOC representation.
Edit intent: fluency
Original: The performance of graph programs depends highly on the algorithm, size, and structure of the input graphs, as well as the features of the underlying hardware.
Revised: The performance of graph programs depends highly on the algorithm, the size and structure of the input graphs, as well as the features of the underlying hardware.
Edit intent: fluency
Original:  To achieve high performance, the programmer must carefully select which set optimizations as well as the hardware platform to use.
Revised:  To achieve high performance, the programmer must carefully select which set of optimizations and hardware platforms to use.
Edit intent: coherence
Original:  We propose the GGGPU compiler, a new graph processing framework that achieves high performance on both CPUs and GPUs using the same algorithm specification.
Revised:  We propose GG, an extension to the GraphIt compiler framework, that achieves high performance on both CPUs and GPUs using the same algorithm specification.
Edit intent: clarity
Original:  GG significantly expands the optimization space of GPU graph processing frameworks with a novel GPU scheduling language and compiler that enables combining load balancing, edge traversal direction, active vertex set creation, active vertex set processing ordering, and kernel fusion optimizations . GG also introduces two performance optimizations, Edge-based Thread Warps CTAs load balancing (ETWC) and EdgeBlocking, to expand the optimization space for GPUs.
Revised:  GG significantly expands the optimization space of GPU graph processing frameworks with a novel GPU scheduling language and compiler that enables combining graph optimizations for GPUs . GG also introduces two performance optimizations, Edge-based Thread Warps CTAs load balancing (ETWC) and EdgeBlocking, to expand the optimization space for GPUs.
Edit intent: clarity
Original:  ETWC improves load balance by dynamically partitioning the edges of each vertex into blocks that are assigned to threads, warps, and CTAs for execution.
Revised:  ETWC improves load balancing by dynamically partitioning the edges of each vertex into blocks that are assigned to threads, warps, and CTAs for execution.
Edit intent: fluency
Original:  EdgeBlocking improves the locality of the program by reordering the edges and restricting random memory accesses to fit within  L2 cache.
Revised:  EdgeBlocking improves the locality of the program by reordering the edges and restricting random memory accesses to fit within the L2 cache.
Edit intent: fluency
Original:  We evaluate GG on 5 algorithms and 9 input graphs on both Pascal and Volta generation NVIDIA GPUs, and show that it achieves up to 5.11x speedup over state-of-the-art GPU graph processing frameworks, and is the fastest on 62 out of the 90 experiment
Revised:  We evaluate GG on 5 algorithms and 9 input graphs on both Pascal and Volta generation NVIDIA GPUs, and show that it achieves up to 5.11x speedup over state-of-the-art GPU graph processing frameworks, and is the fastest on 62 out of the 90 experiments.
Edit intent: fluency
Original:  The name "Friedrichs learning" is for Friedrichs' contribution to the minimax framework for PDEsin a weak form .
Revised:  The name "Friedrichs learning" is for highlighting the close relationship between our learning strategy and Friedrichs theory on symmetric systems of PDEs .
Edit intent: clarity
Original:  Using this metric, Fis, which depends on the frequency response of each complex component, we find that initial Vh influences intersection frequency ;
Revised:  Using this metric, Fis, which depends on the frequency response of each complex component, we find that initial Vh influences Fis ;
Edit intent: clarity
Original:  Whereas the negative group evidences shifts to higher frequencies for increasing tension, the opposite occurs for the positive group.
Revised:  Whereas the negative group exhibits shifts to higher frequencies for increasing tension, the opposite occurs for the positive group.
Edit intent: fluency
Original:  Pivotal noveltiesof the designed cognitive architecture include:
Revised:  Regarding pivotal novelties, the designed cognitive architecture include:
Edit intent: fluency
Original:  Motivated by the fact that different optimizers work well on different problems, our approach switches between different optimizers.
Revised:  Motivated by the fact that different optimizers work well on different problems, our approach switches between different optimizers.
Edit intent: fluency
Original:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Revised:  \footnote{chaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Edit intent: clarity
Original:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Revised:  \footnote{Switching between algorithms also relates to work on oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Edit intent: fluency
Original:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Revised:  \footnote{Switching between algorithms also relates to work onchaining algorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Edit intent: fluency
Original:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Revised:  \footnote{Switching between algorithms also relates to work onchaining or . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Edit intent: clarity
Original:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Revised:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Edit intent: fluency
Original:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Revised:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Edit intent: fluency
Original:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, Squirrel .
Revised:  \footnote{Switching between algorithms also relates to work onchaining oralgorithm schedules . Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel , or here, short, .
Edit intent: coherence
Original: Probabilistic solvers for ordinary differential equations (ODEs) assign a posterior measure to the solution of an initial value problem.
Revised: Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem.
Edit intent: clarity
Original:  But its explicit numerical value for a certain step size , which depends on certain parameters of this class of solvers, is not automatically a good estimate of the explicit error.
Revised:  But its explicit numerical value for a certain step size is not automatically a good estimate of the explicit error.
Edit intent: clarity
Original:  We obtain a direct and a dual description of market-consistent prices with acceptable risk based on superreplication prices and pricing densities .
Revised:  We obtain a direct and a dual description of market-consistent prices with acceptable risk .
Edit intent: clarity
Original: We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular , we investigate the VXX notes tracking the short-end part of the futures term structure.
Revised: We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular we investigate the VXX notes tracking the short-end part of the futures term structure.
Edit intent: fluency
Original: A Path Graph is the intersection graph of vertex paths in an undirected tree.
Revised: A path graph is the intersection graph of vertex paths in an undirected tree.
Edit intent: fluency
Original:  It has the same worst-case time complexity as the faster recognition algorithm known so far A.A. Sch\"affer, A faster algorithm to recognize undirected path graphs, Discrete Applied Mathematics, 43 (1993), pp. 261-295. but it has an easier and more intuitive implementation based on a new characterization of Path Graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, CoRR, abs/ 1911.09069, (2019).].
Revised:  It has the same worst-case time complexity as the faster recognition algorithms known so far A.A. Sch\"affer, A faster algorithm to recognize undirected path graphs, Discrete Applied Mathematics, 43 (1993), pp. 261-295. but it has an easier and more intuitive implementation based on a new characterization of Path Graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, CoRR, abs/ 1911.09069, (2019).].
Edit intent: fluency
Original:  It has the same worst-case time complexity as the faster recognition algorithm known so far A.A. Sch\"affer, A faster algorithm to recognize undirected path graphs, Discrete Applied Mathematics, 43 (1993), pp. 261-295. but it has an easier and more intuitive implementation based on a new characterization of Path Graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, CoRR, abs/ 1911.09069, (2019).].
Revised:  It has the same worst-case time complexity as the faster recognition algorithm known so far but it has an easier and more intuitive implementation based on a new characterization of Path Graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, CoRR, abs/ 1911.09069, (2019).].
Edit intent: coherence
Original:  It has the same worst-case time complexity as the faster recognition algorithm known so far A.A. Sch\"affer, A faster algorithm to recognize undirected path graphs, Discrete Applied Mathematics, 43 (1993), pp. 261-295. but it has an easier and more intuitive implementation based on a new characterization of Path Graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, CoRR, abs/ 1911.09069, (2019).].
Revised:  It has the same worst-case time complexity as the faster recognition algorithm known so far A.A. Sch\"affer, A faster algorithm to recognize undirected path graphs, Discrete Applied Mathematics, 43 (1993), pp. 261-295. but it does not require complex data structures and it has an easy and intuitive implementation based on a new characterization of Path Graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, CoRR, abs/ 1911.09069, (2019).].
Edit intent: clarity
Original:  It has the same worst-case time complexity as the faster recognition algorithm known so far A.A. Sch\"affer, A faster algorithm to recognize undirected path graphs, Discrete Applied Mathematics, 43 (1993), pp. 261-295. but it has an easier and more intuitive implementation based on a new characterization of Path Graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, CoRR, abs/ 1911.09069, (2019).].
Revised:  It has the same worst-case time complexity as the faster recognition algorithm known so far A.A. Sch\"affer, A faster algorithm to recognize undirected path graphs, Discrete Applied Mathematics, 43 (1993), pp. 261-295. but it has an easier and more intuitive implementation based on a new characterization of path graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, CoRR, abs/ 1911.09069, (2019).].
Edit intent: fluency
Original:  In this work, we present a justification for using fictitious domains to study obstacles immersed in incompressible viscous fluids through a simplified version of Brinkham 's law for porous media.
Revised:  In this work, we present a justification for using fictitious domains to study obstacles immersed in incompressible viscous fluids through a simplified version of Brinkman 's law for porous media.
Edit intent: clarity
Original:  The strong convergence of the solution of the perturbed problem to the solution of the strong problem is studied, also considering error estimates that depend on the penalty parameter, both for fluids modeled with the Stokes and Navier-Stokes equations with non-homogeneous boundary conditions.
Revised:  The strong convergence of the solution of the perturbed problem to the solution of the strong problem is studied, also considering error estimates that depend on the penalty parameter, both for fluids modeled with the Stokes and Navier-Stokes equations with inhomogeneous boundary conditions.
Edit intent: clarity
Original: Thanks to the fast learning capability of a new task with small datasets, online meta-learning has become an appealing technique for enabling edge computing in the IoT ecosystems .
Revised: Online meta-learning has become an appealing technique for enabling edge computing in the IoT ecosystems .
Edit intent: coherence
Original: Thanks to the fast learning capability of a new task with small datasets, online meta-learning has become an appealing technique for enabling edge computing in the IoT ecosystems .
Revised: Thanks to the fast learning capability of a new task with small datasets, online meta-learning is emerging as an enabling technique for achieving edge intelligence in the IoT ecosystems .
Edit intent: clarity
Original: Thanks to the fast learning capability of a new task with small datasets, online meta-learning has become an appealing technique for enabling edge computing in the IoT ecosystems .
Revised: Thanks to the fast learning capability of a new task with small datasets, online meta-learning has become an appealing technique for enabling edge computing in the IoT ecosystem .
Edit intent: fluency