wanyu/IteraTeR_v2 huggingface dataset:
Original:  This improvement is expected to increase in the deep networks, where several layers of pooling become necessary.
Revised:  This improvement is expected to increase in deeper networks, where several layers of pooling become necessary.
Edit intent: fluency
Original: In this paper, we propose an accurate finite difference method to discretize the two and three dimensional fractional Laplacian (-\Delta)^{   \alpha / 2 %DIFDELCMD < \MBLOCKRIGHTBRACE %%% in the hypersingular integral form and apply it to solve the fractional reaction-diffusion equations.
Revised: In this paper, we propose accurate and efficient finite difference methods to discretize the two and three dimensional fractional Laplacian (-\Delta)^{ \alpha / 2 %DIFDELCMD < \MBLOCKRIGHTBRACE %%% in the hypersingular integral form and apply it to solve the fractional reaction-diffusion equations.
Edit intent: clarity
Original: In this paper, we propose an accurate finite difference method to discretize the two and three dimensional fractional Laplacian (-\Delta)^{   \alpha / 2 %DIFDELCMD < \MBLOCKRIGHTBRACE %%% in the hypersingular integral form and apply it to solve the fractional reaction-diffusion equations.
Revised: In this paper, we propose an accurate finite difference method to discretize the two- and three-dimensional fractional Laplacian (-\Delta)^{ \alpha / 2 %DIFDELCMD < \MBLOCKRIGHTBRACE %%% in the hypersingular integral form and apply it to solve the fractional reaction-diffusion equations.
Edit intent: fluency
Original: In this paper, we propose an accurate finite difference method to discretize the two and three dimensional fractional Laplacian (-\Delta)^{   \alpha / 2 %DIFDELCMD < \MBLOCKRIGHTBRACE %%% in the hypersingular integral form and apply it to solve the fractional reaction-diffusion equations.
Revised: In this paper, we propose an accurate finite difference method to discretize the two and three dimensional fractional Laplacian (-\Delta)^{ \alpha < 2 %DIFDELCMD < \MBLOCKRIGHTBRACE %%% in the hypersingular integral form and apply it to solve the fractional reaction-diffusion equations.
Edit intent: coherence
Original: In this paper, we propose an accurate finite difference method to discretize the two and three dimensional fractional Laplacian (-\Delta)^{   \alpha / 2 %DIFDELCMD < \MBLOCKRIGHTBRACE %%% in the hypersingular integral form and apply it to solve the fractional reaction-diffusion equations.
Revised: In this paper, we propose an accurate finite difference method to discretize the two and three dimensional fractional Laplacian (-\Delta)^{ \alpha / 2 %DIFDELCMD < \MBLOCKRIGHTBRACE %%% ) in hypersingular integral form and apply it to solve the fractional reaction-diffusion equations.
Edit intent: fluency
Original:  It is proved that for\to  u \in C^{ 3 \lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), our method has an accuracy of O(h^2), uniformly for any \alpha \in ( } 0 , 2), while for\lfloor \rfloor  u \in C^{ 1\lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), the accuracy is O(h^{1-\alpha/2).
Revised:  It is proved that for\to u \in C^{ 3 \lfloor\alpha\rfloor , \alpha /2\lfloor\rfloor }( R ^d), our method has an accuracy of O(h^2), uniformly for any \alpha \in ( } 0 , 2), while for\lfloor \rfloor u \in C^{ 1\lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), the accuracy is O(h^{1-\alpha/2).
Edit intent: fluency
Original:  It is proved that for\to  u \in C^{ 3 \lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), our method has an accuracy of O(h^2), uniformly for any \alpha \in ( } 0 , 2), while for\lfloor \rfloor  u \in C^{ 1\lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), the accuracy is O(h^{1-\alpha/2).
Revised:  It is proved that for\to u \in C^{ 3 \lfloor\rfloor , \alpha /2\lfloor\alpha\rfloor }( R ^d), our method has an accuracy of O(h^2), uniformly for any \alpha \in ( } 0 , 2), while for\lfloor \rfloor u \in C^{ 1\lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), the accuracy is O(h^{1-\alpha/2).
Edit intent: fluency
Original:  It is proved that for\to  u \in C^{ 3 \lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), our method has an accuracy of O(h^2), uniformly for any \alpha \in ( } 0 , 2), while for\lfloor \rfloor  u \in C^{ 1\lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), the accuracy is O(h^{1-\alpha/2).
Revised:  It is proved that for\to u \in C^{ 3 \lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), our method has an accuracy of O(h^2), uniformly for any \alpha \in ( } 0 , 2), while for\lfloor \rfloor u \in C^{ 1\lfloor\alpha\rfloor , \alpha /2\lfloor\rfloor }( R ^d), the accuracy is O(h^{1-\alpha/2).
Edit intent: fluency
Original:  It is proved that for\to  u \in C^{ 3 \lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), our method has an accuracy of O(h^2), uniformly for any \alpha \in ( } 0 , 2), while for\lfloor \rfloor  u \in C^{ 1\lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), the accuracy is O(h^{1-\alpha/2).
Revised:  It is proved that for\to u \in C^{ 3 \lfloor\rfloor , \alpha /2\lfloor\rfloor }( R ^d), our method has an accuracy of O(h^2), uniformly for any \alpha \in ( } 0 , 2), while for\lfloor \rfloor u \in C^{ 1\lfloor\rfloor , \alpha /2\lfloor\alpha\rfloor }( R ^d), the accuracy is O(h^{1-\alpha/2).
Edit intent: fluency
Original:  It shows that our method is accurate and efficient in solving the higher dimensional fractional reaction-diffusion equation, and it can be easily applied to solve other fractional PDEs .
Revised:  It shows that our method is accurate and efficient in solving the high-dimensional fractional problems .
Edit intent: clarity
Original: We consider the problem of incrementally maintaining the triangle count query under single- tuple updates to the input relations.
Revised: We consider the problem of incrementally maintaining the triangle count query under single-tuple updates to the input relations.
Edit intent: fluency
Original:  In particular, they require linear- time update maintenance, which is suboptimal.
Revised:  In particular, they require linear-time update maintenance, which is suboptimal.
Edit intent: fluency
Original:  Given a fixed, deterministic signal, we assume that we use a random frame, whose analysis matrix has independent isotropic sub-Gaussian rows, to collect the measurements, which are consecutively quantized via MSQ. For this setting,  numerically observed decay rate seems to agree with the prediction by the WNH.
Revised:  Given a fixed, deterministic signal, we assume that we use a random frame, whose analysis matrix has independent isotropic sub-Gaussian rows, to collect the measurements, which are consecutively quantized via MSQ. For this setting, the numerically observed decay rate seems to agree with the prediction by the WNH.
Edit intent: fluency
Original:  We rigorously establish sharp non-asymptotic error bounds without using the WNH that explain the observed decay rate.
Revised:  We rigorously establish sharp non-asymptotic error bounds without using the WNH that explains the observed decay rate.
Edit intent: fluency
Original:  Here ~ b is an integer base and ~ P is a finite set of prime numbers.
Revised:  Here b is an integer base and ~ P is a finite set of prime numbers.
Edit intent: coherence
Original:  Here ~ b is an integer base and ~ P is a finite set of prime numbers.
Revised:  Here ~ b is an integer base and P is a finite set of prime numbers.
Edit intent: fluency
Original:  We show that almost every real number whose base b expansion is in ~ T_P is normal to base ~ b. In the case when P is the singleton set \{2\} we prove that more is true: almost every real number whose base b expansion is in T_P is normal to all integer bases.
Revised:  We show that almost every real number whose base b expansion is in T_P is normal to base ~ b. In the case when P is the singleton set \{2\} we prove that more is true: almost every real number whose base b expansion is in T_P is normal to all integer bases.
Edit intent: coherence
Original:  We show that almost every real number whose base b expansion is in ~ T_P is normal to base ~ b. In the case when P is the singleton set \{2\} we prove that more is true: almost every real number whose base b expansion is in T_P is normal to all integer bases.
Revised:  We show that almost every real number whose base b expansion is in ~ T_P is normal to base b. In the case when P is the singleton set \{2\} we prove that more is true: almost every real number whose base b expansion is in T_P is normal to all integer bases.
Edit intent: clarity
Original:  The proposed WSA-IC is compared with several state-of-the-art niching metaheuristic algorithms on CEC2015 niching benchmark test functions and five additional classical multimodal functions with high dimensions.
Revised:  The proposed WSA-IC is compared with several niching metaheuristic algorithms on CEC2015 niching benchmark test functions and five additional classical multimodal functions with high dimensions.
Edit intent: clarity
Original:  Closing some gaps in the literature, we show that some fundamental problems in this context are NP-hard, W[1]-hard, and  the known (partially brute-force) exact algorithms are essentially close to optimality assuming the Exponential Time Hypothesis.
Revised:  Closing some gaps in the literature, we show that several fundamental problems in this context are NP-hard, W[1]-hard, and the known (partially brute-force) exact algorithms are essentially close to optimality assuming the Exponential Time Hypothesis.
Edit intent: clarity
Original:  Closing some gaps in the literature, we show that some fundamental problems in this context are NP-hard, W[1]-hard, and  the known (partially brute-force) exact algorithms are essentially close to optimality assuming the Exponential Time Hypothesis.
Revised:  Closing some gaps in the literature, we show that some fundamental problems in this context are NP- and W[1]-hard, and the known (partially brute-force) exact algorithms are essentially close to optimality assuming the Exponential Time Hypothesis.
Edit intent: clarity
Original:  Closing some gaps in the literature, we show that some fundamental problems in this context are NP-hard, W[1]-hard, and  the known (partially brute-force) exact algorithms are essentially close to optimality assuming the Exponential Time Hypothesis.
Revised:  Closing some gaps in the literature, we show that some fundamental problems in this context are NP-hard, W[1]-hard, and that the known (partially brute-force) exact algorithms are essentially close to optimality assuming the Exponential Time Hypothesis.
Edit intent: fluency
Original:  Closing some gaps in the literature, we show that some fundamental problems in this context are NP-hard, W[1]-hard, and  the known (partially brute-force) exact algorithms are essentially close to optimality assuming the Exponential Time Hypothesis.
Revised:  Closing some gaps in the literature, we show that some fundamental problems in this context are NP-hard, W[1]-hard, and the known (partially brute-force) algorithms are close to optimality assuming the Exponential Time Hypothesis.
Edit intent: clarity
Original:  We introduce a much more general ] family of circular consensus string problems that also serves as a key for our hardness reductions, and proves to be of independent ( also practical) interest on its own .
Revised:  We introduce a much more general ] family of circular string alignment problems that serves as a key for our hardness reductions, and proves to be of independent ( also practical) interest on its own .
Edit intent: clarity
Original:  We introduce a much more general ] family of circular consensus string problems that also serves as a key for our hardness reductions, and proves to be of independent ( also practical) interest on its own .
Revised:  We introduce a much more general ] family of circular consensus string problems that also serves as a key for our hardness reductions, and is of independent ( also practical) interest on its own .
Edit intent: coherence
Original:  We introduce a much more general ] family of circular consensus string problems that also serves as a key for our hardness reductions, and proves to be of independent ( also practical) interest on its own .
Revised:  We introduce a much more general ] family of circular consensus string problems that also serves as a key for our hardness reductions, and proves to be of independent ( practical) interest on its own .
Edit intent: fluency
Original:  In particular, our work answers the main open question concerning the computational complexity of exact mean computation in dynamic time warping spaces Brill et al., SDM 2018 .
Revised:  In particular, Brill et al., SDM 2018 .
Edit intent: clarity
Original: Consensus problems for strings and sequences appear in numerous application contexts, ranging from bioinformatics over data mining to speech recognition . Closing some gaps in the literature, we show that several fundamental problems in this context are NP- and W[1]-hard, and that the known (partially brute-force) algorithms are close to optimality assuming the Exponential Time Hypothesis.
Revised: Consensus problems for strings and sequences appear in numerous application contexts, ranging from bioinformatics over data mining to machine learning . Closing some gaps in the literature, we show that several fundamental problems in this context are NP- and W[1]-hard, and that the known (partially brute-force) algorithms are close to optimality assuming the Exponential Time Hypothesis.
Edit intent: clarity
Original:  Our main contribution is to settle the complexity status of computing a mean in dynamic time warping spaces which, as pointed out by Brill et al. [SDM 2018], suffered from many unproven or false assumptions in the literature.
Revised:  Among our main contributions is to settle the complexity status of computing a mean in dynamic time warping spaces which, as pointed out by Brill et al. [SDM 2018], suffered from many unproven or false assumptions in the literature.
Edit intent: clarity
Original:  In this context, we introduce a broad family of circular string alignment problems that serves as a key for our hardness reductions, and  is of independent (practical) interest in bioinformatics .
Revised:  In this context, we study a broad family of circular string alignment problems that serves as a key for our hardness reductions, and is of independent (practical) interest in bioinformatics .
Edit intent: clarity
Original:  In this context, we introduce a broad family of circular string alignment problems that serves as a key for our hardness reductions, and  is of independent (practical) interest in bioinformatics .
Revised:  In this context, we introduce a broad family of circular string alignment problems . This family also serves as a key for our hardness reductions, and is of independent (practical) interest in bioinformatics .
Edit intent: clarity
Original:  In this context, we introduce a broad family of circular string alignment problems that serves as a key for our hardness reductions, and  is of independent (practical) interest in bioinformatics .
Revised:  In this context, we introduce a broad family of circular string alignment problems that serves as a key for our hardness reductions, and it is of independent (practical) interest in bioinformatics .
Edit intent: coherence
Original:  In particular, we show  hardness and running time lower bounds for CIRCULAR CONSENSUS STRING ;
Revised:  In particular, we show hardness and running time lower bounds for Circular Consensus String ;
Edit intent: fluency
Original:  In particular, we show almost tight hardness and running time lower bounds for Circular Consensus String;
Revised:  In particular, we show tight hardness and running time lower bounds for Circular Consensus String;
Edit intent: clarity
Original: In this paper, a system architecture is proposed that closely models the functionality of metabolic networks.
Revised: In this paper, a system architecture is proposed that approximately models the functionality of metabolic networks.
Edit intent: clarity
Original:  The system is implemented on a graphical processing unit (GPU) as the hardware platform using CUDA environment.
Revised:  The system is implemented on a graphics processing unit (GPU) as the hardware platform using CUDA environment.
Edit intent: fluency
Original: Data on the molecular phylogeny of the Colias complex of South America (SA), obtained via barcoding a mitochondrial part of genome, are reported.
Revised: The data on molecular phylogeny of the Colias complex of South America (SA), obtained via barcoding a mitochondrial part of genome, are reported.
Edit intent: fluency
Original:  It also reveals the occurrence of 3 well-established ( i.e. notably diverged genetically) species (C. dimera, C. vauthierii, and C. alticola, the latter re-raised to sp. level), plus a complex of 3 emerging species (C. lesbia, C. euxanthe, and C. flaveola) which are weakly differentiated genetically.
Revised:  It also reveals the occurrence of 3 well-established ( notably diverged genetically) species (C. dimera, C. vauthierii, and C. alticola, the latter re-raised to sp. level), plus a complex of 3 emerging species (C. lesbia, C. euxanthe, and C. flaveola) which are weakly differentiated genetically.
Edit intent: coherence
Original:  It also reveals the occurrence of 3 well-established ( i.e. notably diverged genetically) species (C. dimera, C. vauthierii, and C. alticola, the latter re-raised to sp. level), plus a complex of 3 emerging species (C. lesbia, C. euxanthe, and C. flaveola) which are weakly differentiated genetically.
Revised:  It also reveals the occurrence of 3 well-established ( i.e. notably diverged genetically) species (C. dimera, C. vauthierii, and C. alticola, the latter re-raised to sp. level), plus a complex of 3 'emerging' species (C. lesbia, C. euxanthe, and C. flaveola) which are weakly differentiated genetically.
Edit intent: clarity
Original:  Furthermore, it disregards the sp. status of taxa weberbaueri, mossi, nigerrima, erika, blameyi  and mendozina, as certain evidences are being brought to consider them ssp. of a clinal type of super-sp.
Revised:  Furthermore, it disregards the sp. status of taxa weberbaueri, mossi, nigerrima, erika, blameyi , and mendozina, as certain evidences are being brought to consider them ssp. of a clinal type of super-sp.
Edit intent: fluency
Original:  Importantly, the clade formed by South-American Colias is found to be sister to the one comprising Colias sp. occurring outside the region (in Eurasia, North America, and Africa).
Revised:  Importantly, the clade formed by SA Colias is found to be sister to the one comprising Colias sp. occurring outside the region (in Eurasia, North America, and Africa).
Edit intent: clarity
Original:  A direct comparison of the results obtained for SA Colias with those for worldwide Colias (GenBank data) led to the conclusion that these are largely divergent autonomous subcomplexes, being in fact  s. lat. subgenera of genus Colias.
Revised:  A direct comparison of the results obtained for SA Colias with those for worldwide Colias (GenBank data) leads to the conclusion that these are largely divergent autonomous subcomplexes, being in fact s. lat. subgenera of genus Colias.
Edit intent: fluency
Original:  A direct comparison of the results obtained for SA Colias with those for worldwide Colias (GenBank data) led to the conclusion that these are largely divergent autonomous subcomplexes, being in fact  s. lat. subgenera of genus Colias.
Revised:  A direct comparison of the results obtained for SA Colias with those for worldwide Colias (GenBank data) led to the conclusion that these are largely divergent autonomous subcomplexes, being in fact subgenera s. lat. subgenera of genus Colias.
Edit intent: clarity
Original:  A direct comparison of the results obtained for SA Colias with those for worldwide Colias (GenBank data) led to the conclusion that these are largely divergent autonomous subcomplexes, being in fact  s. lat. subgenera of genus Colias.
Revised:  A direct comparison of the results obtained for SA Colias with those for worldwide Colias (GenBank data) led to the conclusion that these are largely divergent autonomous subcomplexes, being in fact s. lat. of genus Colias.
Edit intent: clarity
Original:  The first subgenus comprising all SA Colias sp. and named Aucolias (Austral Colias, or of Southern hemisphere stem) is sister to the second one (comprising all Colias sp. from the Old and New Worlds), for which the name Colias (Colias) s. str. is preserved.
Revised:  The first subgenus comprising all SA Colias sp. and named Aucolias (Austral Colias, or of southern hemisphere stem) is sister to the second one (comprising all Colias sp. from the Old and New Worlds), for which the name Colias (Colias) s. str. is preserved.
Edit intent: fluency
Original:  However, on massively parallel hardware their performance is typically limited by communication latency rather than floating point performance.
Revised:  However, on massively parallel hardware the performance of these methods is typically limited by communication latency rather than floating point performance.
Edit intent: clarity
Original:  With HPC hardware advancing towards the exascale regime the gap between computation (i.e. flops) and communication (i.e. internode communication, as well as data movement within the memory hierarchy) keeps steadily increasing, imposing the need for scalable alternatives to traditional Krylov subspace methods.
Revised:  With HPC hardware advancing towards the exascale regime the gap between computation and communication keeps steadily increasing, imposing the need for scalable alternatives to traditional Krylov subspace methods.
Edit intent: clarity
Original:  One such approach are  pipelined Krylov subspace methods, which reduce the number of global synchronization points and overlap global communication latency with local arithmetic operations, thus `hiding ' the global reduction phases behind useful computations.
Revised:  One such approach are the so-called pipelined Krylov subspace methods, which reduce the number of global synchronization points and overlap global communication latency with local arithmetic operations, thus `hiding ' the global reduction phases behind useful computations.
Edit intent: clarity
Original:  One such approach are  pipelined Krylov subspace methods, which reduce the number of global synchronization points and overlap global communication latency with local arithmetic operations, thus `hiding ' the global reduction phases behind useful computations.
Revised:  One such approach are pipelined Krylov subspace methods, which reduce the number of global synchronization points and overlap global communication latency with local arithmetic operations, thus hiding the global reduction phases behind useful computations.
Edit intent: fluency
Original:  Although pipelined Krylov subspace methods are equivalent to traditional Krylov subspace methods in exact arithmetic, the behavior of local rounding errors induced by the multi-term recurrence relations in finite precision may in practice affect convergence significantly.
Revised:  Although pipelined Krylov subspace methods are equivalent to traditional Krylov subspace methods in exact arithmetic, local rounding errors induced by the multi-term recurrence relations in finite precision may in practice affect convergence significantly.
Edit intent: clarity
Original:  This numerical stability study aims to characterize the effect of local rounding errors  in various pipelined versions of the popular Conjugate Gradient method.
Revised:  This numerical stability study aims to characterize the effect of local rounding errors on attainable accuracy in various pipelined versions of the popular Conjugate Gradient method.
Edit intent: clarity
Original:  We derive expressions for the gaps between the true and (recursively ) computed variables that are used to update the search directions in the different CG variants  .
Revised:  Expressions for the gaps between the true and (recursively ) computed variables that are used to update the search directions in the different CG variants .
Edit intent: coherence