wanyu/IteraTeR_v2 huggingface dataset:
Original:  \bullet Reinterpretations of reduction techniques developed for kernelization algorithms for%DIFDELCMD < {\sc %%% Dominating Set and%DIFDELCMD < {\sc %%% Connected Dominating Set from%DIFDELCMD < [%%% SODA 2012 . A protrusion is a subgraph of constant treewidth separated from the remaining vertices by a constant number of vertices.
Revised:  \bullet Reinterpretations of reduction techniques developed for kernelization algorithms for%DIFDELCMD < {\sc %%% Dominating Set and%DIFDELCMD < {\sc %%% Connected Dominating Set %DIFDELCMD < [%%% SODA 2012 . A protrusion is a subgraph of constant treewidth separated from the remaining vertices by a constant number of vertices.
Edit intent: fluency
Original: We give the first linear kernels for Dominating Set and Connected Dominating Set problems on graphs excluding a fixed graph H as a topological minor .
Revised: We give the first linear kernels for the (Connected) Dominating Set problems on graphs excluding a fixed graph H as a topological minor .
Edit intent: coherence
Original:  In other words, we give polynomial time algorithms that, for a given H-topological-minor-free graph G and a positive integer k, output an H-topological-minor-free graph G' on O(k) vertices such that G has a (connected) dominating set of size k if and only if G' has  .
Revised:  In other words, we give polynomial time algorithms that, for a given H-topological-minor-free graph G and a positive integer k, output an H-topological-minor-free graph G' on O(k) vertices such that G has a (connected) dominating set of size k iff G' has .
Edit intent: clarity
Original:  In other words, we give polynomial time algorithms that, for a given H-topological-minor-free graph G and a positive integer k, output an H-topological-minor-free graph G' on O(k) vertices such that G has a (connected) dominating set of size k if and only if G' has  .
Revised:  In other words, we give polynomial time algorithms that, for a given H-topological-minor-free graph G and a positive integer k, output an H-topological-minor-free graph G' on O(k) vertices such that G has a (connected) dominating set of size k if and only if G' has one .
Edit intent: clarity
Original:  Our results extend the known classes of graphs on which  Dominating Set and Connected Dominating Set problems admit linear kernels.
Revised:  Our results extend the known classes of graphs on which the Dominating Set and Connected Dominating Set problems admit linear kernels.
Edit intent: fluency
Original:  Prior to our work, it was known that these prob- lems admit linear kernels on graphs excluding a fixed apex graph H as a minor.
Revised:  Prior to our work, it was known that these problems admit linear kernels on graphs excluding a fixed apex graph H as a minor.
Edit intent: clarity
Original:  Moreover, for Dominating Set, a kernel of size k^c (H), where c(H) is a constant depending on the size of H, follows from a more general result on the kernelization of Dominating Set on graphs of bounded degeneracy.
Revised:  Moreover, for Dominating Set, a kernel of size kc (H), where c(H) is a constant depending on the size of H, follows from a more general result on the kernelization of Dominating Set on graphs of bounded degeneracy.
Edit intent: clarity
Original:  Alon and Gutner asked explicitly , whether one can obtain a linear kernel for Dominating Set on H-minor-free graphs.
Revised:  Alon and Gutner explicitly asked whether one can obtain a linear kernel for Dominating Set on H-minor-free graphs.
Edit intent: fluency
Original:  We answer this question in  affirmative and in fact prove a more general result.
Revised:  We answer this question in the affirmative and in fact prove a more general result.
Edit intent: fluency
Original:  ] Our results are based on a generic reduction rule producing an equivalent instance (in case the input graph is H-minor-free) of the problem  with treewidth O( sqrt k%DIFDELCMD < }%%% ). .. .
Revised:  ]; Our results are based on a generic reduction rule producing an equivalent instance (in case the input graph is H-minor-free) of the problem with treewidth O( sqrt k%DIFDELCMD < }%%% ). .. .
Edit intent: fluency
Original:  ] Our results are based on a generic reduction rule producing an equivalent instance (in case the input graph is H-minor-free) of the problem  with treewidth O( sqrt k%DIFDELCMD < }%%% ). .. .
Revised:  ] Our results are based on a generic reduction rule that produces an equivalent instance (in case the input graph is H-minor-free) of the problem with treewidth O( sqrt k%DIFDELCMD < }%%% ). .. .
Edit intent: fluency
Original:  ] Our results are based on a generic reduction rule producing an equivalent instance (in case the input graph is H-minor-free) of the problem  with treewidth O( sqrt k%DIFDELCMD < }%%% ). .. .
Revised:  ] Our results are based on a generic reduction rule producing an equivalent instance (in case the input graph is H-minor-free) of the problem , with treewidth O( sqrt k%DIFDELCMD < }%%% ). .. .
Edit intent: fluency
Original:  It has been observed that performances of various speech based tasks are very much dependent to the efficiency of the SAD.
Revised:  It has been observed that performances of various speech based tasks are very much dependent on the efficiency of the SAD.
Edit intent: fluency
Original:  The network approach not only gives a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design.
Revised:  Network description and analysis not only gives a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design.
Edit intent: clarity
Original:  Here we give a comprehensive assessment of the analytical tools of network topology and dynamics.
Revised:  We give a comprehensive assessment of the analytical tools of network topology and dynamics.
Edit intent: coherence
Original:  We summarize the current knowledge and the state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets .
Revised:  The state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets .
Edit intent: clarity
Original:  Finally, summarizing more than 1100 cited references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality.
Revised:  Summarizing >1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality.
Edit intent: clarity
Original:  Finally, we highlight network-related drug development trends both at protein structure and cellular levels helping to achieve these hallmarks by a cohesive, global approach.
Revised:  Finally, we highlight network-related drug development trends helping to achieve these hallmarks by a cohesive, global approach.
Edit intent: coherence
Original:  Network description and analysis not only gives a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design.
Revised:  Network description and analysis not only give a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design.
Edit intent: fluency
Original:  The central hit strategy selectively targets central node /edges of the flexible networks of infectious agents or cancer cells to kill them.
Revised:  The central hit strategy selectively targets central nodes /edges of the flexible networks of infectious agents or cancer cells to kill them.
Edit intent: fluency
Original:  Summarizing > 1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality.
Revised:  Summarizing more than 1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality.
Edit intent: fluency
Original:  We classified them numerically according to their similarity to sphere and icosahedron and a set of shapes in between, all  obtained from the theory of elasticity of shells.
Revised:  We classified them numerically according to their similarity to sphere and icosahedron and a set of shapes in between, all of them obtained from the theory of elasticity of shells.
Edit intent: fluency
Original:  Using such a procedure we performed statistical analysis of a series of virus shapes and we found strong similarities between the capsid elastic properties of even very different viruses.
Revised:  Using such a procedure we performed statistical analysis of a series of virus shapes and we found similarities between the capsid elastic properties of even very different viruses.
Edit intent: clarity
Original:  We focus on those structures Gamma that contain the inequality relation, the graph of addition,and a unary relation that only contains the element 1. }  } Hence, all CSPs studied in this article are at least as expressive as the feasibility problem for linear programs.
Revised:  We focus on those structures Gamma that contain the inequality relation, the graph of addition,and a unary relation that only contains the element 1. } and } Hence, all CSPs studied in this article are at least as expressive as the feasibility problem for linear programs.
Edit intent: coherence
Original:  We focus on those structures Gamma that contain the inequality relation, the graph of addition,and a unary relation that only contains the element 1. }  } Hence, all CSPs studied in this article are at least as expressive as the feasibility problem for linear programs.
Revised:  We focus on those structures Gamma that contain the inequality relation, the graph of addition,and a unary relation that only contains the element 1. } }. Hence, all CSPs studied in this article are at least as expressive as the feasibility problem for linear programs.
Edit intent: fluency
Original:  The central concept in our investigation is essential convexity: a relation S is essentially convex if for all a,b in S \inS , there are only finitely many points on the line segment between a and b that are not in S. If Gamma contains a relation S that is not essentially convex and this is witnessed by rational points a,b, then we show that the CSP for Gamma is NP-hard.
Revised:  The central concept in our investigation is essential convexity: a relation S is essentially convex if for all a,b \inS , there are only finitely many points on the line segment between a and b that are not in S. If Gamma contains a relation S that is not essentially convex and this is witnessed by rational points a,b, then we show that the CSP for Gamma is NP-hard.
Edit intent: clarity
Original:  The central concept in our investigation is essential convexity: a relation S is essentially convex if for all a,b in S \inS , there are only finitely many points on the line segment between a and b that are not in S. If Gamma contains a relation S that is not essentially convex and this is witnessed by rational points a,b, then we show that the CSP for Gamma is NP-hard.
Revised:  The central concept in our investigation is essential convexity: a relation S is essentially convex if for all a,b in S \inS , there are only finitely many points on the line segment between a and b that are not in S. If \Gamma contains a relation S that is not essentially convex and this is witnessed by rational points a,b, then we show that the CSP for Gamma is NP-hard.
Edit intent: fluency
Original:  The central concept in our investigation is essential convexity: a relation S is essentially convex if for all a,b in S \inS , there are only finitely many points on the line segment between a and b that are not in S. If Gamma contains a relation S that is not essentially convex and this is witnessed by rational points a,b, then we show that the CSP for Gamma is NP-hard.
Revised:  The central concept in our investigation is essential convexity: a relation S is essentially convex if for all a,b in S \inS , there are only finitely many points on the line segment between a and b that are not in S. If Gamma contains a relation S that is not essentially convex and this is witnessed by rational points a,b, then we show that the CSP for \Gamma is NP-hard.
Edit intent: fluency
Original:  The analysis focuses on three fields : Cardiac cardiovascular systems, Clinical neurology, and Surgery .
Revised:  The analysis focuses on three fields cardiovascular systems, Clinical neurology, and Surgery .
Edit intent: clarity
Original:  The analysis focuses on three fields : Cardiac cardiovascular systems, Clinical neurology, and Surgery .
Revised:  The analysis focuses on three fields : Cardiac .
Edit intent: clarity
Original:  In particular, it is found that clinical research is generally cited less frequently than basic and non-interventional research . Conclusions: Popular bibliometric indicators, such as the h-index and the impact factor, do not correct for differences in citation practices between medical fields.
Revised:  In particular, it is found that clinical research . Conclusions: Popular bibliometric indicators, such as the h-index and the impact factor, do not correct for differences in citation practices between medical fields.
Edit intent: coherence
Original:  The worst-case result size may be determined by the fractional edge cover method (Atserias, Grohe, and Marx, 2008).
Revised:  The worst-case result size may be determined using the fractional edge cover method (Atserias, Grohe, and Marx, 2008).
Edit intent: fluency
Original: We recently had occasion to study and admire the join algorithm of Ngo, Porat, R{\'e} and Rudra ( Ngo et al., 2012) ( henceforth NPRR) . Given bounds on the input relation sizes, the running time of NPRR is bounded by the largest possible result size, which may be determined using the fractional edge cover method (Atserias, Grohe, and Marx, 2008)  .
Revised: We recently had occasion to study and admire the join algorithm of Ngo, Porat, R{\'e} and Rudra ( henceforth NPRR) . Given bounds on the input relation sizes, the running time of NPRR is bounded by the largest possible result size, which may be determined using the fractional edge cover method (Atserias, Grohe, and Marx, 2008) .
Edit intent: clarity
Original: We recently had occasion to study and admire the join algorithm of Ngo, Porat, R{\'e} and Rudra ( Ngo et al., 2012) ( henceforth NPRR) . Given bounds on the input relation sizes, the running time of NPRR is bounded by the largest possible result size, which may be determined using the fractional edge cover method (Atserias, Grohe, and Marx, 2008)  .
Revised: We recently had occasion to study and admire the join algorithm of Ngo, Porat, R{\'e} and Rudra ( Ngo et al., 2012) ( henceforth NPRR) devised a groundbreaking join algorithm with worst-case running time proportional to the AGM bound .
Edit intent: clarity
Original:  We establish that leapfrog triejoin is also worst-case optimal for fully conjunctive queries, and in fact satisfies a more exacting optimality criterion.
Revised:  Weleapfrog triejoin establish that leapfrog triejoin is also worst-case optimal for fully conjunctive queries, and in fact satisfies a more exacting optimality criterion.
Edit intent: clarity
Original:  In 2012, Ngo, Porat, R{\'e} and Rudra (henceforth NPRR) devised a groundbreaking join algorithm with worst-case running time proportional to the AGM bound 9 . Our commercial Datalog system LogicBlox employs a novel join algorithm, leapfrog triejoin, which compared conspicuously well to the NPRR algorithm in preliminary benchmarks.
Revised:  In 2012, Ngo, Porat, R{\'e} and Rudra (henceforth NPRR) devised a join algorithm with worst-case running time proportional to the AGM bound 9 . Our commercial Datalog system LogicBlox employs a novel join algorithm, leapfrog triejoin, which compared conspicuously well to the NPRR algorithm in preliminary benchmarks.
Edit intent: clarity
Original:  In 2012, Ngo, Porat, R{\'e} and Rudra (henceforth NPRR) devised a groundbreaking join algorithm with worst-case running time proportional to the AGM bound 9 . Our commercial Datalog system LogicBlox employs a novel join algorithm, leapfrog triejoin, which compared conspicuously well to the NPRR algorithm in preliminary benchmarks.
Revised:  In 2012, Ngo, Porat, R{\'e} and Rudra (henceforth NPRR) devised a groundbreaking join algorithm with worst-case running time proportional to the AGM bound . Our commercial Datalog system LogicBlox employs a novel join algorithm, leapfrog triejoin, which compared conspicuously well to the NPRR algorithm in preliminary benchmarks.
Edit intent: clarity
Original:  Moreover, leapfrog triejoin achieves worst-case optimality for finer-grained classes , for example, those defined by constraints on the size of projections of the input relations .
Revised:  Moreover, leapfrog triejoin achieves worst-case optimality for finer-grained classes , for example, those defined by constraints on projection cardinalities .
Edit intent: clarity
Original:  We show that leapfrog triejoin is asymptotically faster than NPRR for some such classes  .
Revised:  We show that NPRR is .
Edit intent: clarity
Original:  Using self-financed strategy and duplication we are able to derive a Random Partial Differential Equation (RPDE) that any claim whose value depends on firm value and time should satisfy.
Revised:  Using self-financed strategy and replication we are able to derive a Random Partial Differential Equation (RPDE) that any claim whose value depends on firm value and time should satisfy.
Edit intent: fluency
Original:  Using self-financed strategy and duplication we are able to derive a Random Partial Differential Equation (RPDE) that any claim whose value depends on firm value and time should satisfy.
Revised:  Using self-financed strategy and duplication we are able to derive a Random Partial Differential Equation (RPDE) satisfied by any corporate claim whose value depends on firm value and time should satisfy.
Edit intent: clarity
Original:  Using self-financed strategy and duplication we are able to derive a Random Partial Differential Equation (RPDE) that any claim whose value depends on firm value and time should satisfy.
Revised:  Using self-financed strategy and duplication we are able to derive a Random Partial Differential Equation (RPDE) that any claim whose value is a function of firm value and time should satisfy.
Edit intent: clarity
Original:  Furthermore, the resulting ROQ rule converges exponentially with the number of nodes, and a factor of ~50 savings, without loss of accuracy, is observed in evaluations of inner products when ROQ are used as a downsampling strategy for equidistant samples using the trapezoidal rule.
Revised:  Furthermore, the resulting ROQ rule is found to converge exponentially with the number of nodes, and a factor of ~50 savings, without loss of accuracy, is observed in evaluations of inner products when ROQ are used as a downsampling strategy for equidistant samples using the trapezoidal rule.
Edit intent: clarity
Original:  While the primary focus of this paper is on quadrature rules for inner products of parameterized functions, our method can be easily adapted to integrations of single parameterized functions, and some examples of this type are also considered.
Revised:  While the primary focus of this paper is on quadrature rules for inner products of parameterized functions, our method can be easily adapted to integrations of single parameterized functions, and some examples of this type are considered.
Edit intent: clarity
Original: In this paper, we present, to our knowledge, the first known I/O efficient solutions for computing the k-bisimulation \kbisimnormal partition of a massive  graph, and performing maintenance of such a partition upon updates to the underlying graph.
Revised: In this paper, we present, to our knowledge, the first known I/O efficient solutions for computing the k-bisimulation \kbisimnormal\ partition of a massive graph, and performing maintenance of such a partition upon updates to the underlying graph.
Edit intent: fluency
Original:  We consider in particular k-bisimulation \kbisimnormal , which is the standard variant of bisimulation where the topological features of nodes are only considered within a local neighborhood of radius k\geqslant 0.
Revised:  We consider in particular \kbisimnormal , which is the standard variant of bisimulation where the topological features of nodes are only considered within a local neighborhood of radius k\geqslant 0.
Edit intent: clarity
Original:  The I/O cost of our partition construction algorithm is bounded by O(k\cdot sort(|\et|) + k\cdot scan(|\nt|) + sort(|\nt|)), while our maintenance algorithms are bounded by O(k\cdot sort(|\et|) + k\cdot sort(|\nt|)) \nt\et\nt\et .
Revised:  The I/O cost of our partition construction algorithm is bounded by O(k\cdot sort(|\et|) + k\cdot scan(|\nt|) + sort(|\nt|)), while our maintenance algorithms are bounded by O(k\cdot sort(|\et|) + k\cdot sort(|\nt|)) \nt\et\nt\et|), resp. .
Edit intent: coherence
Original:  Bisimulation is a robust notion of node equivalence which is ubiquitous in the theory and application of graph data .
Revised:  Ubiquitous in the theory and application of graph data .
Edit intent: coherence
Original:  It defines an intuitive notion of nodes in a graph sharing fundamental structural features.
Revised:  It defines an intuitive notion of nodes in a graph which share fundamental structural features.
Edit intent: clarity
Original:  We consider in particular%DIFDELCMD < \kbisimnormal%%% , which is the standard variant of bisimulation where the topological features of nodes are only considered within a local neighborhood of radius k\geqslant 0.
Revised:  %DIFDELCMD < \kbisimnormal%%% , which is the standard variant of bisimulation where the topological features of nodes are only considered within a local neighborhood of radius k\geqslant 0.
Edit intent: coherence
Original:  The space complexity bounds are O(|\nt|+|\et|) and O(k\cdot|\nt|+k\cdot|\et|), resp. . Here, |\et| and |\nt| are the number of disk pages occupied by the input graph's edge set and node set, resp., and sort (n) and scan (n) are the cost of sorting and scanning, resp., a file occupying n pages in external memory.
Revised:  The space complexity bounds are O(|\nt|+|\et|) and O(k\cdot|\nt|+k\cdot|\et|), resp. Here, |\et| and |\nt| are the number of disk pages occupied by the input graph's edge set and node set, resp., and sort (n) and scan (n) are the cost of sorting and scanning, resp., a file occupying n pages in external memory.
Edit intent: fluency
Original: Our problem is to accurately solve linear systems of modest dimensions (typically, the number of variables equals 32) on a general purpose graphics processing unit  .
Revised: Our problem is to accurately solve linear systems on a general purpose graphics processing unit .
Edit intent: clarity
Original:  The linear systems originate from the application of Newton's method on polynomial systems of (moderately) large degrees .
Revised:  The linear systems originate from the application of Newton's method on polynomial systems .
Edit intent: clarity
Original: This paper presents a model of spontaneous economic order within the framework of general equilibrium theory .
Revised: This paper provides an attempt to formalize Hayek's notion of spontaneous order within the framework of general equilibrium theory .
Edit intent: clarity
Original:  Our study shows that if a competitive economy is enough free and fair , then a spontaneous economic order shall emerge in long-period competitive equilibrium so that social members together occupy an optimally economic allocation .
Revised:  Our study shows that if a competitive economy is enough fair and free , then a spontaneous economic order shall emerge in long-period competitive equilibrium so that social members together occupy an optimally economic allocation .
Edit intent: fluency