wanyu/IteraTeR_full_sent huggingface dataset:
Original:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 (  2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Revised:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . SIAM Review 49 ( 2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Edit intent: coherence
Original:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 (  2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Revised:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization, 49 ( 2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Edit intent: coherence
Original:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 (  2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Revised:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review From practical point of view, we propose an algorithm for numerically solving such problem. The proposed algorithm is a combination of ( 2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Edit intent: meaning-changed
Original:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 (  2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Revised:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 ( 1) a positive semidefinite program detecting whether the initial Hermitian matrices are simultaneously diagonalizable via *-congruence, and ( 2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Edit intent: meaning-changed
Original:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 (  2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Revised:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 ( 2) . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Edit intent: coherence
Original:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 (  2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Revised:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 ( 2) , 2007 a Jacobi-like algorithm for simultaneously diagonalizing via *-congruence the commuting normal matrices derived from the previous stage. Illustrating examples by hand/coding \textsc{ are also presented.
Edit intent: meaning-changed
Original:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 (  2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Revised:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 ( 2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding in\textsc{ are also presented.
Edit intent: fluency
Original:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 (  2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{ are also presented.
Revised:  As a consequence, this certainly solves such SDC-problem for collections of real symmetric matrices listed in J-B . Hiriart-Urruty, Potpourri of conjectures and open questions in nonlinear analysis and optimization,SIAM Review 49 ( 2) , 2007 . Corresponding algorithms and illustrating examples by hand/coding \textsc{Matlab are also presented.
Edit intent: meaning-changed
Original:  Essential equations to the conversion of a convex polygon to a voronoi polygonare derived along this paper . As a reference, a very standard convex PIP testing algorithm, the sign of offset \textit{ , is selected for comparison.
Revised:  The equations, essential to the conversion of a convex polygon to a voronoi polygonare derived along this paper . As a reference, a very standard convex PIP testing algorithm, the sign of offset \textit{ , is selected for comparison.
Edit intent: clarity
Original:  Essential equations to the conversion of a convex polygon to a voronoi polygonare derived along this paper . As a reference, a very standard convex PIP testing algorithm, the sign of offset \textit{ , is selected for comparison.
Revised:  Essential equations to the conversion of a convex polygon to a Voronoi polygon, are derived . As a reference, a very standard convex PIP testing algorithm, the sign of offset \textit{ , is selected for comparison.
Edit intent: clarity
Original:  Essential equations to the conversion of a convex polygon to a voronoi polygonare derived along this paper . As a reference, a very standard convex PIP testing algorithm, the sign of offset \textit{ , is selected for comparison.
Revised:  Essential equations to the conversion of a convex polygon to a voronoi polygonare derived along this paper . As a reference, a very standard convex PIP testing algorithm, \textit{ , is selected for comparison.
Edit intent: clarity
Original:  Essential equations to the conversion of a convex polygon to a voronoi polygonare derived along this paper . As a reference, a very standard convex PIP testing algorithm, the sign of offset \textit{ , is selected for comparison.
Revised:  Essential equations to the conversion of a convex polygon to a voronoi polygonare derived along this paper . As a reference, a very standard convex PIP testing algorithm, the sign of offset \textit{the sign of offset , is selected for comparison.
Edit intent: fluency
Original:  Morphologically-Rich Languages (MRLs) pose a challenge to this basic formulation, as the boundaries of Named Entities do not  coincide with token boundaries, rather, they respect morphological boundaries.
Revised:  Morphologically-Rich Languages (MRLs) pose a challenge to this basic formulation, as the boundaries of Named Entities do not necessarily coincide with token boundaries, rather, they respect morphological boundaries.
Edit intent: coherence
Original:  To address NER in MRLs we then need to answer two fundamental modeling questions: (i) What should be the basic units to be identified and labeled, are they token-based or morpheme-based? and (ii) How can morphological units be encoded and accurately obtained in realistic (non-gold) scenarios?
Revised:  To address NER in MRLs we then need to answer two fundamental modeling questions: (i) What should be the basic units to be labeled, and how can these units be detected and classified in realistic settings, i.e., where no gold morphology is available.
Edit intent: clarity
Original:  We empirically investigate these questions on a novel parallel NER benchmarkwe deliver , with parallel token-level and morpheme-level NER annotations  for Modern Hebrew, a morphologically complex language.
Revised:  We empirically investigate these questions on a novel parallel NER benchmarkwe deliver , with parallel token-level and morpheme-level NER annotations for Modern Hebrew, a morphologically rich-and-ambiguous language.
Edit intent: meaning-changed
Original:  Our results show that explicitly modeling morphological boundaries consistently leads to improved NER performance, and that a novel hybrid architecture that we propose , in which NER precedes and prunes the morphological decomposition(MD) space , greatly outperforms the standard pipeline approach, on both Hebrew NER and Hebrew MD in realistic scenarios .
Revised:  Our results show that explicitly modeling morphological boundaries leads to improved NER performance, and that a novel hybrid architecture that we propose , in which NER precedes and prunes the morphological decomposition(MD) space , greatly outperforms the standard pipeline approach, on both Hebrew NER and Hebrew MD in realistic scenarios .
Edit intent: clarity
Original:  Our results show that explicitly modeling morphological boundaries consistently leads to improved NER performance, and that a novel hybrid architecture that we propose , in which NER precedes and prunes the morphological decomposition(MD) space , greatly outperforms the standard pipeline approach, on both Hebrew NER and Hebrew MD in realistic scenarios .
Revised:  Our results show that explicitly modeling morphological boundaries consistently leads to improved NER performance, and that a novel hybrid architecture , in which NER precedes and prunes the morphological decomposition(MD) space , greatly outperforms the standard pipeline approach, on both Hebrew NER and Hebrew MD in realistic scenarios .
Edit intent: clarity
Original:  Our results show that explicitly modeling morphological boundaries consistently leads to improved NER performance, and that a novel hybrid architecture that we propose , in which NER precedes and prunes the morphological decomposition(MD) space , greatly outperforms the standard pipeline approach, on both Hebrew NER and Hebrew MD in realistic scenarios .
Revised:  Our results show that explicitly modeling morphological boundaries consistently leads to improved NER performance, and that a novel hybrid architecture that we propose , in which NER precedes and prunes morphological decomposition , greatly outperforms the standard pipeline approach, on both Hebrew NER and Hebrew MD in realistic scenarios .
Edit intent: clarity
Original:  Our results show that explicitly modeling morphological boundaries consistently leads to improved NER performance, and that a novel hybrid architecture that we propose , in which NER precedes and prunes the morphological decomposition(MD) space , greatly outperforms the standard pipeline approach, on both Hebrew NER and Hebrew MD in realistic scenarios .
Revised:  Our results show that explicitly modeling morphological boundaries consistently leads to improved NER performance, and that a novel hybrid architecture that we propose , in which NER precedes and prunes the morphological decomposition(MD) space , greatly outperforms the standard pipeline , where morphological decomposition strictly precedes NER, setting a new performance bar for both Hebrew NER and Hebrew MD in realistic scenarios .
Edit intent: meaning-changed
Original:  Our results show that explicitly modeling morphological boundaries consistently leads to improved NER performance, and that a novel hybrid architecture that we propose , in which NER precedes and prunes the morphological decomposition(MD) space , greatly outperforms the standard pipeline approach, on both Hebrew NER and Hebrew MD in realistic scenarios .
Revised:  Our results show that explicitly modeling morphological boundaries consistently leads to improved NER performance, and that a novel hybrid architecture that we propose , in which NER precedes and prunes the morphological decomposition(MD) space , greatly outperforms the standard pipeline approach, on both Hebrew NER and Hebrew morphological decomposition tasks .
Edit intent: clarity
Original:  This differs from traditional graph or hypergraph partitioning models which minimize total communication under a work balance constraint. We address regimes where partitions of the row space and column space are expected to match (the symmetric case) or are allowed to differ (the nonsymmetric case) .
Revised:  This differs from traditional graph or hypergraph partitioning models which minimize total communication , or from traditional load balancing models which only balance work. One can view our algorithms as optimally rounding one-dimensional embeddings of direct K-way noncontiguous partitioning problems .
Edit intent: meaning-changed
Original:  Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log( /(c_{low}\epsilon)) is O(N^C) for C < } 1  and c_{low} are upper and lower bounds on the optimal cost.
Revised:  Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log( c_{high/(c_{low}\epsilon)) is O(N^C) for C < } 1 and c_{low} are upper and lower bounds on the optimal cost.
Edit intent: meaning-changed
Original:  Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log( /(c_{low}\epsilon)) is O(N^C) for C < } 1  and c_{low} are upper and lower bounds on the optimal cost.
Revised:  Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log( /(c_{low}\epsilon)) is O(N^C) for C < } 1 , where c_{high and c_{low} are upper and lower bounds on the optimal cost.
Edit intent: meaning-changed
Original:  We also propose a simpler version of our (1 + \epsilon)-approximate algorithm which runs in a factor of \log(c_{high}} / \epsilon) is sublinear. We\epsilon)) from linear time, but is faster in practice.
Revised:  We also propose a simpler version of our (1 + \epsilon)-approximate algorithm which runs in a factor of \log(c_{high}} / (c_{low\epsilon)) from linear time, but is faster in practice.
Edit intent: meaning-changed
Original:  We specialize Chazelle's dominance counting algorithm to points in the bounded integer plane and generalize it to trade reduced construction time for increased query time, since our partitioners make very few queries. Our algorithms split the original row (or column) ordering into parts to optimize diverse cost models. Combined with reordering or embedding techniques, our algorithms might be used to build more general heuristic partitioners, as they can optimally round one-dimensional embeddings of direct K-way noncontiguous partitioning problems .
Revised:  We specialize Chazelle's dominance counting algorithm to points in the bounded integer plane and generalize it to trade reduced construction time for increased query time, resulting in an overall linear runtime .
Edit intent: meaning-changed
Original:  We propose exact and approximate contiguous partitioners that minimize the maximum runtime of any processor under a diverse family of cost models that combine work and hypergraph communication terms in symmetric or asymmetric settings. This differs from traditional partitioning models which minimize total communication, or from traditional load balancing models which only balance work. One can view our algorithms as optimally rounding one-dimensional embeddings of direct K-way noncontiguous partitioning problems. Our algorithms use linear space.
Revised:  We propose the first near-linear time algorithms for several graph partitioning problems in the contiguous regime. Traditional objectives such as the simple edge cut, hyperedge cut, or hypergraph connectivity minimize the total cost of all parts under a balance constraint. Our total partitioners use O(Km + N) space. They run in O((Km\log(m) + N)\log(N)) time, a significant improvement over prior O(K(m^2 + N)) time algorithms due to Kernighan and Grandjean et. al. Bottleneck partitioning minimizes the maximum cost of any part. We propose a new bottleneck cost which reflects the sum of communication and computation on each part. Our bottleneck partitioners use linear space.
Edit intent: meaning-changed
Original:  Our exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ \text{high }/(c_{ \text{low }\epsilon)) is O(N^C) for C < 1, where c_{ \text{high } and c_{ \text{low } are upper and lower bounds on the optimal cost.
Revised:  The exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ \text{high }/(c_{ \text{low }\epsilon)) is O(N^C) for C < 1, where c_{ \text{high } and c_{ \text{low } are upper and lower bounds on the optimal cost.
Edit intent: fluency
Original:  Our exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ \text{high }/(c_{ \text{low }\epsilon)) is O(N^C) for C < 1, where c_{ \text{high } and c_{ \text{low } are upper and lower bounds on the optimal cost.
Revised:  Our exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ high }/(c_{ \text{low }\epsilon)) is O(N^C) for C < 1, where c_{ \text{high } and c_{ \text{low } are upper and lower bounds on the optimal cost.
Edit intent: fluency
Original:  Our exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ \text{high }/(c_{ \text{low }\epsilon)) is O(N^C) for C < 1, where c_{ \text{high } and c_{ \text{low } are upper and lower bounds on the optimal cost.
Revised:  Our exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ \text{high }/(c_{ low }\epsilon)) is O(N^C) for C < 1, where c_{ \text{high } and c_{ \text{low } are upper and lower bounds on the optimal cost.
Edit intent: fluency
Original:  Our exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ \text{high }/(c_{ \text{low }\epsilon)) is O(N^C) for C < 1, where c_{ \text{high } and c_{ \text{low } are upper and lower bounds on the optimal cost.
Revised:  Our exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ \text{high }/(c_{ \text{low }\epsilon)) is O(N^C) for C < 1, where c_{ high } and c_{ \text{low } are upper and lower bounds on the optimal cost.
Edit intent: fluency
Original:  Our exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ \text{high }/(c_{ \text{low }\epsilon)) is O(N^C) for C < 1, where c_{ \text{high } and c_{ \text{low } are upper and lower bounds on the optimal cost.
Revised:  Our exact algorithm runs in linear time when K^2 is O(N^C) for C < 1. Our (1 + \epsilon)-approximate algorithm runs in linear time when K\log(c_{ \text{high }/(c_{ \text{low }\epsilon)) is O(N^C) for C < 1, where c_{ \text{high } and c_{ low } are upper and lower bounds on the optimal cost.
Edit intent: clarity
Original:  We also propose a simpler (1 + \epsilon)-approximate algorithm which runs in a factor of \log(c_{ \text{high }/(c_{ \text{low }\epsilon)) from linear time , but is faster in practice .
Revised:  We also propose a simpler (1 + \epsilon)-approximate algorithm which runs in a factor of \log(c_{ high }/(c_{ \text{low }\epsilon)) from linear time , but is faster in practice .
Edit intent: fluency
Original:  We also propose a simpler (1 + \epsilon)-approximate algorithm which runs in a factor of \log(c_{ \text{high }/(c_{ \text{low }\epsilon)) from linear time , but is faster in practice .
Revised:  We also propose a simpler (1 + \epsilon)-approximate algorithm which runs in a factor of \log(c_{ \text{high }/(c_{ low }\epsilon)) from linear time , but is faster in practice .
Edit intent: fluency
Original:  We also propose a simpler (1 + \epsilon)-approximate algorithm which runs in a factor of \log(c_{ \text{high }/(c_{ \text{low }\epsilon)) from linear time , but is faster in practice .
Revised:  We also propose a simpler (1 + \epsilon)-approximate algorithm which runs in a factor of \log(c_{ \text{high }/(c_{ \text{low }\epsilon)) from linear time .
Edit intent: coherence
Original:  We empirically demonstrate that all of our algorithms efficiently produce high-quality contiguous partitions  .
Revised:  We empirically demonstrate that all of our algorithms efficiently produce high-quality contiguous partitions on a test suite of 42 test matrices. When K = 8, our hypergraph connectivity partitioner achieved a speedup of 53\times (mean 15.1\times) over prior algorithms. The mean runtime of our bottleneck partitioner was 5.15 SpMVs .
Edit intent: meaning-changed
Original:  In the context of one-shot robot teaching, the contributions of the paper is to propose a framework that 1) covers various tasks in grasp-manipulation-release class household operations and 2) mimics human postures during the operations .
Revised:  Within the context of one-shot robot teaching, the contributions of the paper is to propose a framework that 1) covers various tasks in grasp-manipulation-release class household operations and 2) mimics human postures during the operations .
Edit intent: fluency
Original:  In the context of one-shot robot teaching, the contributions of the paper is to propose a framework that 1) covers various tasks in grasp-manipulation-release class household operations and 2) mimics human postures during the operations .
Revised:  In the context of one-shot robot teaching, the contribution of this study is a framework that 1) covers various tasks in grasp-manipulation-release class household operations and 2) mimics human postures during the operations .
Edit intent: clarity
Original:  In the context of one-shot robot teaching, the contributions of the paper is to propose a framework that 1) covers various tasks in grasp-manipulation-release class household operations and 2) mimics human postures during the operations .
Revised:  In the context of one-shot robot teaching, the contributions of the paper is to propose a framework that 1) covers various tasks in grasp-manipulation-release class household operations and 2) mimics human postures during operation .
Edit intent: fluency