wanyu/IteraTeR_v2 huggingface dataset:
Original:  Therefore , they can solve NP-complete problems in polynomial time , however requiring resources that only grow polynomially with the input size.
Revised:  Therefore they can solve NP-complete problems in polynomial time , however requiring resources that only grow polynomially with the input size.
Edit intent: fluency
Original:  Therefore  they can solve NP-complete problems in polynomial time and, using the appropriate architecture, with resources that only grow polynomially with the input size.
Revised:  Therefore , they can solve NP-complete problems in polynomial time and, using the appropriate architecture, with resources that only grow polynomially with the input size.
Edit intent: fluency
Original:  The reason for this computational power stems from three main properties inspired by the brain and shared by any universal memcomputing machine : intrinsic parallelism , functional polymorphism and information overhead, namely the capability of storing more information than the number of memory elements by using the collective state of the memprocessor network.
Revised:  The reason for this computational power stems from properties inspired by the brain and shared by any universal memcomputing machine : intrinsic parallelism , functional polymorphism and information overhead, namely the capability of storing more information than the number of memory elements by using the collective state of the memprocessor network.
Edit intent: clarity
Original:  The reason for this computational power stems from three main properties inspired by the brain and shared by any universal memcomputing machine : intrinsic parallelism , functional polymorphism and information overhead, namely the capability of storing more information than the number of memory elements by using the collective state of the memprocessor network.
Revised:  The reason for this computational power stems from three main properties inspired by the brain and shared by any universal memcomputing machine , in particular intrinsic parallelism and information overhead, namely the capability of storing more information than the number of memory elements by using the collective state of the memprocessor network.
Edit intent: clarity
Original:  The reason for this computational power stems from three main properties inspired by the brain and shared by any universal memcomputing machine : intrinsic parallelism , functional polymorphism and information overhead, namely the capability of storing more information than the number of memory elements by using the collective state of the memprocessor network.
Revised:  The reason for this computational power stems from three main properties inspired by the brain and shared by any universal memcomputing machine : intrinsic parallelism , functional polymorphism and information overhead, namely the capability of compressing information in the collective state of the memprocessor network.
Edit intent: clarity
Original:  We have fabricated this architecture using standard microelectronic technology so that it can be easily realized in any laboratory setting , whether academic or industrial .
Revised:  We have fabricated this architecture using standard microelectronic technology so that it can be easily realized in any laboratory setting .
Edit intent: clarity
Original:  However, works further analyzing the type of fractality and its origin still lack.
Revised:  However, works further analyzing the category of fractality and its origin still lack.
Edit intent: clarity
Original:  Herein,  DFA and MFDFA methods are applied in the analysis of time series of online reviewing activity from Movielens and Netflix.
Revised:  Herein, both the DFA and MFDFA methods are applied in the analysis of time series of online reviewing activity from Movielens and Netflix.
Edit intent: clarity
Original:  Herein,  DFA and MFDFA methods are applied in the analysis of time series of online reviewing activity from Movielens and Netflix.
Revised:  Herein, DFA and MFDFA are applied in the analysis of time series of online reviewing activity from Movielens and Netflix.
Edit intent: clarity
Original:  Results show the long-term correlation at individual and whole community level, while the strength of such correlation at individual level is restricted to activity level.
Revised:  Results show the long-term correlation at individual and whole community level, while the extent of correlation at individual level is restricted to activity level.
Edit intent: clarity
Original:  Such long-term correlation  reveals the fractality of online reviewing activity.
Revised:  Such long-term correlation also reveals the fractality of online reviewing activity.
Edit intent: clarity
Original:  In our further investigation of this fractality, we first demonstrate it is multifractality, which results from the dual effect of broad probability density function and long-term correlation of time series in online reviewing activity.
Revised:  In our further investigation of this fractality, we first demonstrate it is multifractality, which results from the dual effect of broad probability density function and long-term correlation of time series of online reviewing activity.
Edit intent: clarity
Original: Recent discoveries of human activity reveal the existence of long-term correlation and its relation with the fat-tailed distribution of inter-event times , which imply that there exists the fractality of human activity.
Revised: Although recent studies have found that the long-term correlation and its relation with the fat-tailed distribution of inter-event times , which imply that there exists the fractality of human activity.
Edit intent: clarity
Original: Recent discoveries of human activity reveal the existence of long-term correlation and its relation with the fat-tailed distribution of inter-event times , which imply that there exists the fractality of human activity.
Revised: Recent discoveries of human activity reveal the existence of long-term correlations relating to the fat-tailed distribution of inter-event times , which imply that there exists the fractality of human activity.
Edit intent: clarity
Original:  Herein, both the DFA and MFDFA are applied in the analysis of time series of online reviewing activity from Movielens and Netflix.
Revised:  Herein, both the DFA and MFDFA to analyze the time series in online viewing activity separating from Movielens and Netflix.
Edit intent: clarity
Original:  Results show the long-term correlation at individual and whole community level, while the extent of correlation at  individual level is restricted to activity level.
Revised:  We find long-term correlation at individual and whole community level, while the extent of correlation at individual level is restricted to activity level.
Edit intent: clarity
Original:  Results show the long-term correlation at individual and whole community level, while the extent of correlation at  individual level is restricted to activity level.
Revised:  Results show the long-term correlations at both the individual and communal level, and that the extent of correlation at individual level is restricted to activity level.
Edit intent: clarity
Original:  Results show the long-term correlation at individual and whole community level, while the extent of correlation at  individual level is restricted to activity level.
Revised:  Results show the long-term correlation at individual and whole community level, while the extent of correlation at the individual level is restricted to activity level.
Edit intent: fluency
Original:  Results show the long-term correlation at individual and whole community level, while the extent of correlation at  individual level is restricted to activity level.
Revised:  Results show the long-term correlation at individual and whole community level, while the extent of correlation at individual level is determined by the activity level.
Edit intent: clarity
Original:  Such long-term correlation also reveals the fractality of online reviewing activity.
Revised:  These long-term correlation also reveals the fractality of online reviewing activity.
Edit intent: fluency
Original:  In our further investigation of this fractality, wefirst demonstrate it is multifractality , which results from the dual effect of broad probability density function and long-term correlation of time series of online reviewing activity .
Revised:  In our further investigation of this fractality, we demonstrate it is multifractality , which results from the dual effect of broad probability density function and long-term correlation of time series of online reviewing activity .
Edit intent: coherence
Original:  Therefore, we conclude that the combining impact of both broad probability density function and long-term correlation is the origin of multifractality behaving in human online activity .
Revised:  Therefore, it can be concluded that the multifractality in online viewing activity is caused by both the fat-tailed distribution of inter-event times and the long-term correlation is the origin of multifractality behaving in human online activity .
Edit intent: clarity
Original:  We show that for p=\Omega(\log n/n), the eigenvalues of each of the matrices are a.a.s. concentrated around two values.
Revised:  We show that for p=\Omega(\log n/n), the eigenvalues of these matrices are a.a.s. concentrated around two values.
Edit intent: clarity
Original:  It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the eigenvalues of the higher-dimensional Laplacian  capture the notion of coboundary expansion - a higher-dimensional generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov.
Revised:  It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the higher-dimensional Laplacian capture the notion of coboundary expansion - a higher-dimensional generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov.
Edit intent: clarity
Original:  It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the eigenvalues of the higher-dimensional Laplacian  capture the notion of coboundary expansion - a higher-dimensional generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov.
Revised:  It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the eigenvalues of the higher-dimensional Laplacian spectra capture the notion of coboundary expansion - a higher-dimensional generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov.
Edit intent: clarity
Original:  It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the eigenvalues of the higher-dimensional Laplacian  capture the notion of coboundary expansion - a higher-dimensional generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov.
Revised:  It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the eigenvalues of the higher-dimensional Laplacian capture the notion of coboundary expansion - a generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov.
Edit intent: fluency
Original:  In this paper, we propose a novel index partitioning technique based on  speed values of the moving objects.
Revised:  In this paper, we propose a novel speed partitioning technique based on speed values of the moving objects.
Edit intent: clarity
Original:  We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on the query performance of the indexing structure . Next we formulate the optimal speed partitioning problem based on the search space expansion analysis and then compute  optimal solution using dynamic programming.
Revised:  We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on query performance of the indexing structure . Next we formulate the optimal speed partitioning problem based on the search space expansion analysis and then compute optimal solution using dynamic programming.
Edit intent: fluency
Original:  We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on the query performance of the indexing structure . Next we formulate the optimal speed partitioning problem based on the search space expansion analysis and then compute  optimal solution using dynamic programming.
Revised:  We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on the query performance of the indexes . Next we formulate the optimal speed partitioning problem based on the search space expansion analysis and then compute optimal solution using dynamic programming.
Edit intent: clarity
Original:  We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on the query performance of the indexing structure . Next we formulate the optimal speed partitioning problem based on the search space expansion analysis and then compute  optimal solution using dynamic programming.
Revised:  We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on the query performance of the indexing structure . Next we formulate the optimal speed partitioning problem based on search space expansion analysis and then compute optimal solution using dynamic programming.
Edit intent: fluency
Original:  We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on the query performance of the indexing structure . Next we formulate the optimal speed partitioning problem based on the search space expansion analysis and then compute  optimal solution using dynamic programming.
Revised:  We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on the query performance of the indexing structure . Next we formulate the optimal speed partitioning problem based on the search space expansion analysis and then compute the optimal solution using dynamic programming.
Edit intent: fluency
Original:  We  build the partitioned indexing system where queries are duplicated and processed in each index partition either concurrently or sequentially .
Revised:  We then build the partitioned indexing system where queries are duplicated and processed in each index partition either concurrently or sequentially .
Edit intent: coherence
Original:  We  build the partitioned indexing system where queries are duplicated and processed in each index partition either concurrently or sequentially .
Revised:  We build the partitioned indexing system where queries are duplicated and processed in each index partition .
Edit intent: clarity
Original:  Extensive experiments demonstrate that our methods dramatically improve the query performance of the indexing structures and outperforms other state-of-the-art velocity-based partitioning methods .
Revised:  Extensive experiments demonstrate that our methods dramatically improve the query performance of the indexing structures and outperforms other state-of-the-art velocity-based partitioning approaches .
Edit intent: clarity
Original:  We show FIXP-hardness of computing equilibria in Arrow-Debreu exchange markets under Leontief utility functions, and Arrow-Debreu markets under linear utility functions and Leontief production sets , thereby settling these open questions (Vazirani and Yannakakis, 2009).
Revised:  We show FIXP-hardness of computing equilibria in Arrow-Debreu markets under Leontief utility functions, and Arrow-Debreu markets under linear utility functions and Leontief production sets , thereby settling these open questions (Vazirani and Yannakakis, 2009).
Edit intent: clarity
Original:  If all instances are under consideration, then in all cases we prove that the problem of deciding if a given instance admits an equilibrium is ETR-complete, where ETR \Exists\Exists is the class  Existential Theory of Reals.
Revised:  If all instances are under consideration, then in all cases we prove that the problem of deciding if a given instance admits an equilibrium is \Exists\Exists is the class Existential Theory of Reals.
Edit intent: clarity
Original: For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two field system of equations with velocity and pressure  unknowns.
Revised: For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two-field system of equations with velocity and pressure unknowns.
Edit intent: fluency
Original: For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two field system of equations with velocity and pressure  unknowns.
Revised: For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two field system of equations with velocity and pressure as unknowns.
Edit intent: clarity
Original:  Previous work has shown that while optimal preconditioners for the two field formulation can be constructed , the construction of preconditioners that are uniform with respect to model parameters is difficult.
Revised:  Previous work has shown that while optimal preconditioners for the two-field formulation can be constructed , the construction of preconditioners that are uniform with respect to model parameters is difficult.
Edit intent: fluency
Original:  Previous work has shown that while optimal preconditioners for the two field formulation can be constructed , the construction of preconditioners that are uniform with respect to model parameters is difficult.
Revised:  Previous work has shown that while optimal preconditioners for the two field formulation can be obtained , the construction of preconditioners that are uniform with respect to model parameters is difficult.
Edit intent: clarity
Original:  This limits the applicability of two field preconditioners in certain regimes of practical interest.
Revised:  This limits the applicability of two-field preconditioners in certain regimes of practical interest.
Edit intent: fluency
Original:  We address this issue by reformulating the governing equations as a three field problem, which removes a term that was problematic in the two field formulation in favour of an additional equation for a pressure-like field.
Revised:  We address this issue by reformulating the governing equations as a three-field problem, which removes a term that was problematic in the two field formulation in favour of an additional equation for a pressure-like field.
Edit intent: fluency
Original:  We address this issue by reformulating the governing equations as a three field problem, which removes a term that was problematic in the two field formulation in favour of an additional equation for a pressure-like field.
Revised:  We address this issue by reformulating the governing equations as a three field problem, which removes a term that was problematic in the two-field formulation in favour of an additional equation for a pressure-like field.
Edit intent: fluency
Original:  For the three-field problem, we develop and analyse new preconditioners and we show numerically that the new three-field preconditioners are optimal in terms of problem size and less sensitive to model parameters  compared to the two-field preconditioner.
Revised:  For the three-field problem, we develop and analyse new preconditioners and we show numerically that they are optimal in terms of problem size and less sensitive to model parameters compared to the two-field preconditioner.
Edit intent: coherence
Original:  For the three-field problem, we develop and analyse new preconditioners and we show numerically that the new three-field preconditioners are optimal in terms of problem size and less sensitive to model parameters  compared to the two-field preconditioner.
Revised:  For the three-field problem, we develop and analyse new preconditioners and we show numerically that the new three-field preconditioners are optimal in terms of problem size and less sensitive to model parameters , compared to the two-field preconditioner.
Edit intent: fluency
Original:  This extends the applicability of optimal preconditioners for coupled mantle/magma dynamics into parameter regimes of important physical interest.
Revised:  This extends the applicability of optimal preconditioners for coupled mantle/magma dynamics into parameter regimes of physical interest.
Edit intent: clarity
Original:  We experimentally demonstrate \mu%DIFDELCMD < }%%% s precision of neuronal response timings under low stimulation frequencies, whereas moderate frequencies result in a chaotic neuronal phase characterized by degraded precision.
Revised:  We \mu%DIFDELCMD < }%%% s precision of neuronal response timings under low stimulation frequencies, whereas moderate frequencies result in a chaotic neuronal phase characterized by degraded precision.
Edit intent: clarity
Original:  We experimentally demonstrate \mu%DIFDELCMD < }%%% s precision of neuronal response timings under low stimulation frequencies, whereas moderate frequencies result in a chaotic neuronal phase characterized by degraded precision.
Revised:  We experimentally demonstrate %DIFDELCMD < }%%% s precision of neuronal response timings under low stimulation frequencies, whereas moderate frequencies result in a chaotic neuronal phase characterized by degraded precision.
Edit intent: clarity
Original:  This intrinsic neuronal response impedance mechanism , as opposed to links distribution, counter-intuitively leads to cooperation on a network level, such that firing rates are suppressed towards the lowest neuronal critical frequencies simultaneously with neuronal \mu s precision .
Revised:  This intrinsic neuronal response impedance mechanism leads to cooperation on a network level, such that firing rates are suppressed towards the lowest neuronal critical frequencies simultaneously with neuronal \mu s precision .
Edit intent: coherence
Original:  This intrinsic neuronal response impedance mechanism , as opposed to links distribution, counter-intuitively leads to cooperation on a network level, such that firing rates are suppressed towards the lowest neuronal critical frequencies simultaneously with neuronal \mu s precision .
Revised:  This intrinsic neuronal response impedance mechanism , as opposed to links distribution, counter-intuitively leads to cooperation on a network level, such that firing rates are suppressed towards the lowest neuronal critical frequency simultaneously with neuronal \mu s precision .
Edit intent: fluency
Original: There has been great interest in recent years in the development of statistical models for dynamic networks.
Revised: There has been great interest in recent years on statistical models for dynamic networks.
Edit intent: clarity
Original:  We propose a stochastic block transition model (SBTM) for dynamic networks that is inspired by the well-known stochastic block model (SBM) for static networks and several recent dynamic extensions of the SBM.
Revised:  We propose a stochastic block transition model (SBTM) for dynamic networks that is inspired by the well-known stochastic block model (SBM) for static networks and previous dynamic extensions of the SBM.
Edit intent: clarity
Original:  We demonstrate that the proposed SBTM is significantly better at reproducing durations of edges in real social network data between edges while retaining the interpretability of the SBM .
Revised:  We demonstrate that the proposed SBTM is significantly better at reproducing durations of edges in real social network data .
Edit intent: clarity