wanyu/IteraTeR_v2 huggingface dataset:
Original:  We show that all read-once functions f over B have checking tests containing O(n^l) vectors, where n is the number of essential variables of f and l is the largest arity of functions in B  .
Revised:  We show that every read-once functions f over B have checking tests containing O(n^l) vectors, where n is the number of essential variables of f and l is the largest arity of functions in B .
Edit intent: fluency
Original:  We show that all read-once functions f over B have checking tests containing O(n^l) vectors, where n is the number of essential variables of f and l is the largest arity of functions in B  .
Revised:  We show that all read-once function f over B have checking tests containing O(n^l) vectors, where n is the number of essential variables of f and l is the largest arity of functions in B .
Edit intent: fluency
Original:  We show that all read-once functions f over B have checking tests containing O(n^l) vectors, where n is the number of essential variables of f and l is the largest arity of functions in B  .
Revised:  We show that all read-once functions f over B has a checking test containing O(n^l) vectors, where n is the number of essential variables of f and l is the largest arity of functions in B .
Edit intent: fluency
Original:  We show that all read-once functions f over B have checking tests containing O(n^l) vectors, where n is the number of essential variables of f and l is the largest arity of functions in B  .
Revised:  We show that all read-once functions f over B have checking tests containing O(n^l) vectors, where n is the number of relevant variables of f and l is the largest arity of functions in B .
Edit intent: clarity
Original: Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been found in neural systems, particularly, in neuronal cultures.
Revised: Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been observed in neural systems, particularly, in neuronal cultures.
Edit intent: clarity
Original:  In this case, the avalanches defined from nLFPs displayed power-law scaling in double logarithmic representations, as reported previously in monkey.
Revised:  In this case, the avalanches defined from nLFPs displayed power-law scaling in double log representations, as reported previously in monkey.
Edit intent: clarity
Original:  Closer examination of this scaling using the more reliable cumulative distribution function (CDF) and other rigorous statistical measures, did not confirm power-law scaling.
Revised:  Closer examination of this scaling using more reliable cumulative distribution function (CDF) and other rigorous statistical measures, did not confirm power-law scaling.
Edit intent: fluency
Original:  Closer examination of this scaling using the more reliable cumulative distribution function (CDF) and other rigorous statistical measures, did not confirm power-law scaling.
Revised:  Closer examination of this scaling using the more reliable cumulative distribution functions (CDF) and other rigorous statistical measures, did not confirm power-law scaling.
Edit intent: fluency
Original:  While simple exponentials yielded very good fits of the avalanche dynamics , the "sum of exponentials" provided the best fit to the data . Collectively, these results show no clear evidence for power-law scaling or self-organized critical states in the awake and sleeping brain of mammals, from cat to man.
Revised:  Multiple exponential fitting yielded optimal fits of the avalanche dynamics , the "sum of exponentials" provided the best fit to the data . Collectively, these results show no clear evidence for power-law scaling or self-organized critical states in the awake and sleeping brain of mammals, from cat to man.
Edit intent: clarity
Original:  While simple exponentials yielded very good fits of the avalanche dynamics , the "sum of exponentials" provided the best fit to the data . Collectively, these results show no clear evidence for power-law scaling or self-organized critical states in the awake and sleeping brain of mammals, from cat to man.
Revised:  While simple exponentials yielded very good fits of the avalanche dynamics with bi-exponential distributions . Collectively, these results show no clear evidence for power-law scaling or self-organized critical states in the awake and sleeping brain of mammals, from cat to man.
Edit intent: clarity
Original: Next-generation sequencing techniques have for the first time facilitated a large scale analysis of human genetic variation.
Revised: Next-generation sequencing techniques have facilitated a large scale analysis of human genetic variation.
Edit intent: clarity
Original:  However, despite the advances in sequencing speeds, achieved at ever lower costs, the computational discovery of structural variants is not yet standard.
Revised:  Despite the advances in sequencing speeds, achieved at ever lower costs, the computational discovery of structural variants is not yet standard.
Edit intent: coherence
Original:  However, despite the advances in sequencing speeds, achieved at ever lower costs, the computational discovery of structural variants is not yet standard.
Revised:  However, despite the advances in sequencing speeds, the computational discovery of structural variants is not yet standard.
Edit intent: clarity
Original:  It is likely that a considerable amount of variants have remained undiscovered in many sequenced individuals.
Revised:  It is likely that many variants have remained undiscovered in many sequenced individuals.
Edit intent: clarity
Original:  It is likely that a considerable amount of variants have remained undiscovered in many sequenced individuals.
Revised:  It is likely that a considerable amount of variants have remained undiscovered in most sequenced individuals.
Edit intent: clarity
Original:  On very short indels (10-29 bp) we outperform all prior insert size approaches, while our unique predictions favorably complement the predictions of the split-read aligner considered.
Revised:  On very short indels (10-29 bp) we outperform all prior insert size approaches, while our unique predictions favorably complement the predictions of split-read aligner considered.
Edit intent: fluency
Original:  Our implementation is available from URL as open source software under the terms of the GNU General Public License.
Revised:  Our implementation is available from URL 
Edit intent: clarity
Original:  We also define a new class of words, \emph{semicentral words}, and show that they are characterized by the property that they can be written as uxyu, for a central Sturmian word u and two different letters x,y.
Revised:  We also define a new class of words, \emph{semicentral words}, and show that they are characterized by the property that they can be written as uxyu, for a central word u and two different letters x,y.
Edit intent: fluency
Original:  The model requires two important changes compared to related recent work on the downlink .
Revised:  Compared to related recent work on the downlink .
Edit intent: clarity
Original:  First, dependence is introduced between the user and base station point processes to make sure each base station serves a single mobile in the given resource block.
Revised:  First, dependence is considered between the user and base station point processes to make sure each base station serves a single mobile in the given resource block.
Edit intent: clarity
Original:  First, dependence is considered between the user and base station point processes to make sure each base station serves a single mobile in the given resource block.
Revised:  First, dependence is considered between user and base station point processes to make sure each base station serves a single mobile in the given resource block.
Edit intent: fluency
Original:  Second, per-mobile power control is included, which further couples the transmission of mobiles due to location dependent channel inversion.
Revised:  Second, per-mobile power control is included, which further couples the transmission of mobiles due to location-dependent channel inversion.
Edit intent: fluency
Original: The fixed point subgroup of an endomorphism of a finitely generated virtually free group is proved to be finitely generated.
Revised: The fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated.
Edit intent: clarity
Original:  We find that the max norm of the error matrix achieved with a tolerance of below 2 \times 10^{-8} is lower than that of the single-precision {\tt SGEMM} for quantum chemical test matrices, while outperforming {\tt SGEMM} with a cross-over already for small matrices (n \sim 1000).
Revised:  We find that the max norm of the max norm achieved with a tolerance of below 2 \times 10^{-8} is lower than that of the single-precision {\tt SGEMM} for quantum chemical test matrices, while outperforming {\tt SGEMM} with a cross-over already for small matrices (n \sim 1000).
Edit intent: clarity
Original:  We find that the max norm of the max norm achieved with a tolerance of below 2 \times 10^{-8} is lower than that of the single-precision {\tt SGEMM} for quantum chemical test matrices, while outperforming {\tt SGEMM} with a cross-over already for small matrices (n \sim 1000).
Revised:  We find that the max norm of the error achieved with a tolerance of below 2 \times 10^{-8} is lower than that of the single-precision {\tt SGEMM} for quantum chemical test matrices, while outperforming {\tt SGEMM} with a cross-over already for small matrices (n \sim 1000).
Edit intent: clarity
Original:  We find that the max norm of the max norm achieved with a tolerance of below 2 \times 10^{-8} is lower than that of the single-precision {\tt SGEMM} for quantum chemical test matrices, while outperforming {\tt SGEMM} with a cross-over already for small matrices (n \sim 1000).
Revised:  We find that the max norm of the max norm achieved with a tolerance below 2 \times 10^{-8} is lower than that of the single-precision {\tt SGEMM} for quantum chemical test matrices, while outperforming {\tt SGEMM} with a cross-over already for small matrices (n \sim 1000).
Edit intent: clarity
Original:  Relative to naive implementations of using optimized versions of%DIFDELCMD < {\tt %%% SGEMM , such as those found in Intel's Math Kernel Library ({\tt MKL}) or AMD's Core Math Library ({\tt ACML}), our optimized version is found to be significantly faster.
Revised:  Relative to naive implementations of using %DIFDELCMD < {\tt %%% SGEMM , such as those found in Intel's Math Kernel Library ({\tt MKL}) or AMD's Core Math Library ({\tt ACML}), our optimized version is found to be significantly faster.
Edit intent: clarity
Original:  Relative to naive implementations of using optimized versions of%DIFDELCMD < {\tt %%% SGEMM , such as those found in Intel's Math Kernel Library ({\tt MKL}) or AMD's Core Math Library ({\tt ACML}), our optimized version is found to be significantly faster.
Revised:  Relative to naive implementations of using optimized versions of%DIFDELCMD < {\tt %%% , such as those found in Intel's Math Kernel Library ({\tt MKL}) or AMD's Core Math Library ({\tt ACML}), our optimized version is found to be significantly faster.
Edit intent: clarity
Original:  Relative to naive implementations of using optimized versions of%DIFDELCMD < {\tt %%% SGEMM , such as those found in Intel's Math Kernel Library ({\tt MKL}) or AMD's Core Math Library ({\tt ACML}), our optimized version is found to be significantly faster.
Revised:  Relative to naive implementations of using optimized versions of%DIFDELCMD < {\tt %%% SGEMM Intel's Math Kernel Library ({\tt MKL}) or AMD's Core Math Library ({\tt ACML}), our optimized version is found to be significantly faster.
Edit intent: clarity
Original:  Detailed performance comparisons are made with for quantum chemical matrices of RHF/STO-2G and RHF/6-31G ^{** .
Revised:  Detailed performance comparisons are made for quantum chemical matrices of RHF/STO-2G and RHF/6-31G ^{** .
Edit intent: fluency
Original:  Detailed performance comparisons are made with for quantum chemical matrices of RHF/STO-2G and RHF/6-31G ^{** .
Revised:  Detailed performance comparisons are made with for quantum chemical matrices ^{** .
Edit intent: clarity
Original:  Finally, we discuss the potential of improved hardware prefetch to yield 2--3x speedups.
Revised:  Finally, we discuss the potential of improved hardware prefetch to yield 2-3x speedups.
Edit intent: fluency
Original:  Finally, we discuss the potential of improved hardware prefetch to yield 2-3x speedups.
Revised:  Finally, we discuss the potential of improved hardware prefetch to yield 2--3x speedups.
Edit intent: fluency
Original:  [JEA 2008]  shown a set of simple rules that reduce the number of vertices of G to 2^k, and no algorithm is known with significantly better running time bound than a brute-force search on this reduced instance.
Revised:  [JEA 2008] have shown a set of simple rules that reduce the number of vertices of G to 2^k, and no algorithm is known with significantly better running time bound than a brute-force search on this reduced instance.
Edit intent: clarity
Original:  In this paper we show that the approach of Gramm et al. is essentially optimal: we present a polynomial time algorithm that reduces an arbitrary 3-CNF-SAT formula with n variables and m clauses to an equivalent EDGE CLIQUE COVER instance (G,k) with k = O(log n) and |V(G)| = O(n + m)  .
Revised:  In this paper we show that the approach of Gramm et al. is essentially optimal: we present a polynomial time algorithm that reduces an arbitrary 3-CNF-SAT formula with n variables and m clauses to an equivalent ECC instance (G,k) with k = O(log n) and |V(G)| = O(n + m) .
Edit intent: fluency
Original: An increasing number of retail energy markets exhibit price fluctuationsand provide customers such as data centers and residential users the opportunity to buy energy at lower than average prices.
Revised: An increasing number of retail energy markets show price fluctuations, providing users with the opportunity to buy energy at lower than average prices.
Edit intent: clarity
Original:  Such cost savings however are hard to obtain in practice because they require users to observe the price fluctuations and shift their consumption to low price periods.
Edit intent: coherence
Original:  We propose to use energy storage to allow users to satisfy demand at times when prices are high with energy previously bought during low-price periods.
Revised:  We propose to temporarily store this inexpensive energy in a battery, and use it to satisfy demand when energy prices are high with energy previously bought during low-price periods.
Edit intent: clarity
Original:  For Mario and Donkey Kong, we show NP-completeness.
Edit intent: coherence
Original:  Our results apply to generalized versions of Super Mario Bros. 1, 3, Lost Levels, and Super Mario World;
Revised:  Our results apply to generalized versions of Super Mario Bros. 1-3, The Lost Levels, and Super Mario World;
Edit intent: clarity
Original:  all Legend of Zelda games except Zelda II: The Adventure of Link ;
Revised:  all Legend of Zelda games ;
Edit intent: coherence
Original:  Specifically, we show that the node degree distribution of causal sets in de Sitter spacetime is described by a power law with exponent 2 , similar to many complex networks .
Revised:  Specifically, we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering , similar to many complex networks .
Edit intent: clarity
Original:  These findings suggest that unexpectedly similar mechanisms may shape the large-scale structure and dynamics of complex systems as different as the brain, the Internet, and the universe .
Revised:  These findings suggest that unexpectedly similar laws govern the dynamics of complex systems as different as the brain, the Internet, and the universe .
Edit intent: clarity
Original:  In this paper, we address robustness questions about the k-core . Given a k-core, remove one edge uniformly at random and find its new k-core.
Revised:  In this paper, we address robustness questions about k-cores . Given a k-core, remove one edge uniformly at random and find its new k-core.
Edit intent: fluency
Original:  We define a constant c _k ' such that when k+ %DIFDELCMD < \eps%%%  < c < c _k '- %DIFDELCMD < \eps%%%  , the new k-core is empty with probability bounded away from zero and, if c > c _k' + \psi(n)with \psi(n) = \omega (n^{-1/4}), \psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Revised:  We define a constant c (k) ' such that when k+ %DIFDELCMD < \eps%%% < c < c _k '- %DIFDELCMD < \eps%%% , the new k-core is empty with probability bounded away from zero and, if c > c _k' + \psi(n)with \psi(n) = \omega (n^{-1/4}), \psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Edit intent: clarity
Original:  We define a constant c _k ' such that when k+ %DIFDELCMD < \eps%%%  < c < c _k '- %DIFDELCMD < \eps%%%  , the new k-core is empty with probability bounded away from zero and, if c > c _k' + \psi(n)with \psi(n) = \omega (n^{-1/4}), \psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Revised:  We define a constant c _k ' such that when k+ %DIFDELCMD < \eps%%% < c < c (k) '- %DIFDELCMD < \eps%%% , the new k-core is empty with probability bounded away from zero and, if c > c _k' + \psi(n)with \psi(n) = \omega (n^{-1/4}), \psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Edit intent: coherence
Original:  We define a constant c _k ' such that when k+ %DIFDELCMD < \eps%%%  < c < c _k '- %DIFDELCMD < \eps%%%  , the new k-core is empty with probability bounded away from zero and, if c > c _k' + \psi(n)with \psi(n) = \omega (n^{-1/4}), \psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Revised:  We define a constant c _k ' such that when k+ %DIFDELCMD < \eps%%% < c < c _k '- %DIFDELCMD < \eps%%% , the new k-core is empty with probability bounded away from zero and, if c > c (k)' + \psi(n)with \psi(n) = \omega (n^{-1/4}), \psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Edit intent: fluency
Original:  We define a constant c _k ' such that when k+ %DIFDELCMD < \eps%%%  < c < c _k '- %DIFDELCMD < \eps%%%  , the new k-core is empty with probability bounded away from zero and, if c > c _k' + \psi(n)with \psi(n) = \omega (n^{-1/4}), \psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Revised:  We define a constant c _k ' such that when k+ %DIFDELCMD < \eps%%% < c < c _k '- %DIFDELCMD < \eps%%% , the new k-core is empty with probability bounded away from zero and, if c > c _k' + \psi(n)with \psi(n) = omega (n^{-1/4}), \psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Edit intent: clarity
Original:  We define a constant c _k ' such that when k+ %DIFDELCMD < \eps%%%  < c < c _k '- %DIFDELCMD < \eps%%%  , the new k-core is empty with probability bounded away from zero and, if c > c _k' + \psi(n)with \psi(n) = \omega (n^{-1/4}), \psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Revised:  We define a constant c _k ' such that when k+ %DIFDELCMD < \eps%%% < c < c _k '- %DIFDELCMD < \eps%%% , the new k-core is empty with probability bounded away from zero and, if c > c _k' + \psi(n)with \psi(n) = \omega (n^{-1/4}), psi (n) > 0 and c is bounded, then the probability that the new k-core has less than n-h(n) vertices goes to zero, for every h(n) = \omega(\psi(n)^{-1 ).
Edit intent: fluency
Original: Subspace clustering and feature extraction are two of the most extensive unsupervised visual learning tasks in computer vision and pattern recognition.
Revised: Subspace clustering and feature extraction are two of the most commonly used unsupervised learning techniques in computer vision and pattern recognition.
Edit intent: clarity
Original:  Experimental results on both synthetic data and real applications validate our theoretical analysis and demonstrate the power of FRR for unsupervised visual learning.
Revised:  Experimental results on both synthetic data and real applications validate our theoretical analysis and demonstrate the benefits of FRR for unsupervised visual learning.
Edit intent: clarity
Original:  The process consists of expressing the specification of a function body as an initial code matrix , growing the matrix by adding rows and columns until the completed matrix is translated in a routine fashion to compilable code.
Revised:  The process consists of expressing the specification of a function body as an initial code matrix and then growing the matrix by adding rows and columns until the completed matrix is translated in a routine fashion to compilable code.
Edit intent: coherence
Original: In this paper, we present a technique for generating Leslie transition matrices from simple age/ sex population counts, using an implementation of "Wood's Method" [Wood , 1997 ];
Revised: In this paper, we present a technique for generating Leslie transition matrices from simple age/ sex population counts, using an implementation of "Wood's Method" [Wood 97 ];
Edit intent: fluency
Original:  This approach improves on previous methods for creating Leslie matrices in two respects: it eliminates the need to calculate the elements of a Leslie matrix directly from demographic rates , and a new format for the fitted Leslie matrix more elegantly reveals the population's demographic components of change (fertility, mortality, and migration).
Revised:  Our approach improves on previous methods for creating Leslie matrices in two respects: it eliminates the need to calculate the elements of a Leslie matrix directly from demographic rates , and a new format for the fitted Leslie matrix more elegantly reveals the population's demographic components of change (fertility, mortality, and migration).
Edit intent: fluency
Original:  This approach improves on previous methods for creating Leslie matrices in two respects: it eliminates the need to calculate the elements of a Leslie matrix directly from demographic rates , and a new format for the fitted Leslie matrix more elegantly reveals the population's demographic components of change (fertility, mortality, and migration).
Revised:  This approach improves on previous methods for creating Leslie matrices in two respects: it eliminates the need to calculate input demographic rates from "raw" data, and our new format for the fitted Leslie matrix more elegantly reveals the population's demographic components of change (fertility, mortality, and migration).
Edit intent: clarity
Original:  This approach improves on previous methods for creating Leslie matrices in two respects: it eliminates the need to calculate the elements of a Leslie matrix directly from demographic rates , and a new format for the fitted Leslie matrix more elegantly reveals the population's demographic components of change (fertility, mortality, and migration).
Revised:  This approach improves on previous methods for creating Leslie matrices in two respects: it eliminates the need to calculate the elements of a Leslie matrix directly from demographic rates , and a new format for the Leslie matrix more elegantly reveals the population's demographic components of change (fertility, mortality, and migration).
Edit intent: clarity