wanyu/IteraTeR_v2 huggingface dataset:
Original: Extending the previous 2-gender dioecious biploid gene-mating evolution model  , we attempt to answer "whether the Hardy-Weinberg global stability and the exact analytic dynamical solutions can be found in the generalized N-gender polyploid gene-mating system ?' " For a 2-gender gene-mating evolution model, a pair of male and female determines the trait of their offspring.
Revised: Extending the previous 2-gender dioecious diploid gene-mating evolution model , we attempt to answer "whether the Hardy-Weinberg global stability and the exact analytic dynamical solutions can be found in the generalized N-gender polyploid gene-mating system ?' " For a 2-gender gene-mating evolution model, a pair of male and female determines the trait of their offspring.
Edit intent: fluency
Original: Extending the previous 2-gender dioecious biploid gene-mating evolution model  , we attempt to answer "whether the Hardy-Weinberg global stability and the exact analytic dynamical solutions can be found in the generalized N-gender polyploid gene-mating system ?' " For a 2-gender gene-mating evolution model, a pair of male and female determines the trait of their offspring.
Revised: Extending the previous 2-gender dioecious biploid gene-mating evolution model , we attempt to answer "whether the Hardy-Weinberg global stability and the exact analytic dynamical solutions can be found in the generalized N-gender N-polyploid gene-mating system ?' " For a 2-gender gene-mating evolution model, a pair of male and female determines the trait of their offspring.
Edit intent: fluency
Original:  Hence, for an N-gender polypoid gene-mating model, each of N different genders contributes one allele to combine into the genotype of their offspring.
Revised:  Hence, for an N-gender N-polypoid gene-mating model, each of N different genders contributes one allele to combine into the genotype of their offspring.
Edit intent: fluency
Original:  The 2-gender to N-gender gene-mating equation generalization is analogues to the 2-body collision to the N-body collision Boltzmann equations with discretized distribution .
Revised:  The 2-gender to N-gender gene-mating equation generalization is analogs to the 2-body collision to the N-body collision Boltzmann equations with discretized distribution .
Edit intent: fluency
Original: Simulating a binary black hole  coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time.
Revised: Simulating a binary black hole (BBH) coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time.
Edit intent: clarity
Original:  In this paper , we construct an accurate and fast-to-evaluate surrogate model for numerical relativity (NR) waveforms from non-spinning binary black hole coalescences with mass ratios from 1 to 10 and durations corresponding to about 15 orbits before merger.
Revised:  In this paper , we construct an accurate and fast-to-evaluate surrogate model for numerical relativity (NR) waveforms from non-spinning BBH coalescences with mass ratios from 1 to 10 and durations corresponding to about 15 orbits before merger.
Edit intent: clarity
Original:  In this paper , we construct an accurate and fast-to-evaluate surrogate model for numerical relativity (NR) waveforms from non-spinning binary black hole coalescences with mass ratios from 1 to 10 and durations corresponding to about 15 orbits before merger.
Revised:  In this paper , we construct an accurate and fast-to-evaluate surrogate model for numerical relativity (NR) waveforms from non-spinning binary black hole coalescences with mass ratios in 1 to 10 and durations corresponding to about 15 orbits before merger.
Edit intent: clarity
Original:  In this paper , we construct an accurate and fast-to-evaluate surrogate model for numerical relativity (NR) waveforms from non-spinning binary black hole coalescences with mass ratios from 1 to 10 and durations corresponding to about 15 orbits before merger.
Revised:  In this paper , we construct an accurate and fast-to-evaluate surrogate model for numerical relativity (NR) waveforms from non-spinning binary black hole coalescences with mass ratios from 1 , 10 and durations corresponding to about 15 orbits before merger.
Edit intent: fluency
Original:  In particular, we show that our modeling strategy produces surrogates which can correctly predict NR waveforms that were {\em not} used for the surrogate's training .
Revised:  In particular, we show that our modeling strategy predicts NR waveforms {\em not} used for the surrogate's training .
Edit intent: clarity
Original:  Our model includes all spherical-harmonic {}_{-2}Y_{\ell m} waveform modes that can be resolved by the NR code up to \ell= 8, including modes that are typically difficult to model with other approaches.
Revised:  Our model includes all spherical-harmonic {}_{-2}Y_{\ell m} waveform modes resolved by the NR code up to \ell= 8, including modes that are typically difficult to model with other approaches.
Edit intent: clarity
Original:  We carry out experiments using trilateration for 2D localization, and quadrilateration for 3D localization, algorithm and experimentally verified that exploiting the clustering information leads to a more precise localization than mere quadrilateration.
Revised:  We have carried out experiments using trilateration for 2D localization, and quadrilateration for 3D localization, algorithm and experimentally verified that exploiting the clustering information leads to a more precise localization than mere quadrilateration.
Edit intent: style
Original:  We carry out experiments using trilateration for 2D localization, and quadrilateration for 3D localization, algorithm and experimentally verified that exploiting the clustering information leads to a more precise localization than mere quadrilateration.
Revised:  We carry out experiments using trilateration for 2D localization, and quadrilateration for 3D localization, and experimentally verified that exploiting the clustering information leads to a more precise localization than mere quadrilateration.
Edit intent: clarity
Original: A definition of p-volume of rectangular matrices is given.
Revised: A generalized and applicable to rectangular matrices definition of a volume of a matrix is given.
Edit intent: clarity
Original:  We generalize the results for square maximum-volume submatrices to the case  rectangular maximal-volume submatrices and provide estimates for the growth of the coefficients  .
Revised:  We generalize the results for square maximum-volume submatrices to the case of rectangular maximal-volume submatrices and provide estimates for the growth of the coefficients .
Edit intent: fluency
Original:  The code is available online at URL
Revised:  The code is available online .
Edit intent: coherence
Original:  Our approach is computationally fast and shows in the analysis of a large-scale drug discovery test data set equivalent prediction accuracy as random forests .
Revised:  Our approach is computationally inexpensive and shows in the analysis of a large-scale drug discovery test data set equivalent prediction accuracy as random forests .
Edit intent: clarity
Original:  Our approach is computationally fast and shows in the analysis of a large-scale drug discovery test data set equivalent prediction accuracy as random forests .
Revised:  Our approach is computationally fast and shows in the analysis of a large-scale drug discovery test data set equivalent prediction accuracy as a random forest .
Edit intent: fluency
Original: Understanding the spatial networks formed by the trajectories of mobile users can be beneficial to applications ranging from epidemiology to local search in modern mobile applications . Despite the potential for impact in a number of fields, several aspects of human mobility networks remain largely unexplored due to the lack of large-scale data at a fine spatiotemporal resolution.
Revised: Understanding the spatial networks formed by the trajectories of mobile users can be beneficial to applications ranging from epidemiology to local search . Despite the potential for impact in a number of fields, several aspects of human mobility networks remain largely unexplored due to the lack of large-scale data at a fine spatiotemporal resolution.
Edit intent: coherence
Original:  Using a longitudinal dataset from the location-based service Foursquare, we perform an empirical analysis on the growth patterns, temporal dynamics and topological properties of place networks in urban environments.
Revised:  Using a longitudinal dataset from the location-based service Foursquare, we perform an empirical analysis of the topological properties of place networks in urban environments.
Edit intent: clarity
Original:  In terms of topological properties, place networks are similar to online social networks , being characterized by heavy-tailed degree distributions, triadic closure mechanisms and the small world property.
Revised:  In terms of topological properties, place networks are similar to online social networks in terms of heavy-tailed degree distributions, triadic closure mechanisms and the small world property.
Edit intent: clarity
Original: Ostrowski type and the corrected version of the Brauer type theorems are derived for the left eigenvalues of quaternionic matrix.
Revised: Ostrowski type and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix.
Edit intent: clarity
Original:   Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems, respectively, for  left and right eigenvalues of quaternionic matrix.
Revised:  Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems, respectively, for the left and right eigenvalues of quaternionic matrix.
Edit intent: fluency
Original:  In addition, generalizations of the Gerschgorin type theorems are discussed for both the left and right eigenvalues of quater- nionic matrix, and finally, we show that our framework is so developed that generalizes the existing results in the literatures.
Revised:  In addition, generalizations of the Gerschgorin type theorems are discussed for both the left and right eigenvalues of quaternionic matrix, and finally, we show that our framework is so developed that generalizes the existing results in the literatures.
Edit intent: fluency
Original:  In addition, generalizations of the Gerschgorin type theorems are discussed for both the left and right eigenvalues of quater- nionic matrix, and finally, we show that our framework is so developed that generalizes the existing results in the literatures.
Revised:  In addition, generalizations of the Gerschgorin type theorems are discussed for both the left and right eigenvalues of quater- nionic matrix, and finally, we see that our framework is so developed that generalizes the existing results in the literatures.
Edit intent: fluency
Original: Ostrowski type and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix.
Revised: In this paper, Ostrowski and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix.
Edit intent: clarity
Original:  Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems , respectively, for the left and  right eigenvalues of  quaternionic matrix.
Revised:  Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems , respectively, for the left and the right eigenvalues of quaternionic matrix.
Edit intent: fluency
Original:  Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems , respectively, for the left and  right eigenvalues of  quaternionic matrix.
Revised:  Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems , respectively, for the left and right eigenvalues of a quaternionic matrix.
Edit intent: fluency
Original:  In addition, generalizations of the Gerschgorin type theorems are discussed for both the left and right eigenvalues of quaternionic matrix, and finally, we see that our framework is so developed that generalizes the existing results in the literatures .
Revised:  Thereafter a sufficient condition for the stability of a quaternionic matrix is given that generalizes the existing results in the literatures .
Edit intent: clarity
Original: It was reported that buffalo is a low susceptibility species resisting to TSEs ( Transmissible Spongiform Encephalopathies  ) (same as rabbits, horses and dogs).
Revised: It was reported that buffalo is a low susceptibility species resisting to Transmissible Spongiform Encephalopathies ) (same as rabbits, horses and dogs).
Edit intent: clarity
Original:  This paper studies the molecular structure and structural dynamics of buffalo prion protein, in order to find out the reason why buffaloes are resistant to prion diseases.
Revised:  This paper studies the molecular structure and structural dynamics of buffalo prion protein, in order to reveal the reason why buffaloes are resistant to prion diseases.
Edit intent: clarity
Original:  This paper studies the molecular structure and structural dynamics of buffalo prion protein, in order to find out the reason why buffaloes are resistant to prion diseases.
Revised:  This paper studies the molecular structure and structural dynamics of buffalo prion protein, in order to find out the reason why buffalo are resistant to prion diseases.
Edit intent: fluency
Original:  We first did molecular modeling  a homology structure constructed by one mutation at residue 143 from the Nuclear Magnetic Resonance structure of bovine and cattle PrP(124-227);
Revised:  We first did molecular modeling of a homology structure constructed by one mutation at residue 143 from the Nuclear Magnetic Resonance structure of bovine and cattle PrP(124-227);
Edit intent: fluency
Original:  immediately we found for buffalo PrPC(124-227) there are 5 hydrogen bonds at Asn143, but at this position bovine and cattle do not have such hydrogen bonds.
Revised:  immediately we found for buffalo PrPC(124-227) there are 5 hydrogen bonds at Asn143, but at this position bovine / cattle do not have such hydrogen bonds.
Edit intent: fluency
Original:  TSEs, also called prion diseases,  are invariably fatal and highly infectious neurodegenerative diseases that affect a wide variety of species.
Revised:  TSEs, also called prion diseases, which are invariably fatal and highly infectious neurodegenerative diseases that affect a wide variety of species.
Edit intent: coherence
Original:  linking alpha-helices H2 and H1 (if mutation H187R is made at position 187 then the hydrophobic core of PrPC will be exposed), (ii) at D178, there is a hydrogen bond Y169-D178 and a polar contact R164-D178 for BufPrPC instead of a polar contact Q168-D178 for bovine PrPC, (iii) BufPrPC owns 3-10 helices at 125-127, 152-156 and in the beta2-alpha2 loop respectively,  (iv) in beta2-alpha2 loop there are strong pi-contacts, etc, has been discovered.
Revised:  linking alpha-helices H2 and H1 (if mutation H187R is made at position 187 then the hydrophobic core of PrPC will be exposed), (ii) at D178, there is a hydrogen bond Y169-D178 and a polar contact R164-D178 for BufPrPC instead of a polar contact Q168-D178 for bovine PrPC, (iii) BufPrPC owns 3-10 helices at 125-127, 152-156 and in the beta2-alpha2 loop respectively, and (iv) in beta2-alpha2 loop there are strong pi-contacts, etc, has been discovered.
Edit intent: fluency
Original:  We show that the interdependence of countries' economies are strictly (anti)correlated to the price of oil.
Revised:  We show that over that time period the international division of labor and trade patterns are tightly linked to the price of oil.
Edit intent: clarity
Original:  We give polynomial (in the dimension of the ambient space) bounds on the number of irreducible representations of the symmetric group which acts on these sets, as well as their multiplicities , appearing in the isotypic decomposition of their cohomology moduleswith coefficients in a field of characteristic 0.
Revised:  We give polynomial (in the dimension of the ambient space) bound on the number of irreducible representations of the symmetric group which acts on these sets, as well as their multiplicities , appearing in the isotypic decomposition of their cohomology moduleswith coefficients in a field of characteristic 0.
Edit intent: fluency
Original:  We also give some applications of our methods in proving lower bounds on the degrees of defining polynomials of certain symmetric semi-algebraic sets, as well as better bounds on the Betti numbers of the images under projections of (not necessarily symmetric) bounded real algebraic sets .
Revised:  We also give some applications of our methods in proving lower bounds on the degrees of defining polynomials of certain symmetric semi-algebraic sets, as well as improved bounds on the Betti numbers of the images under projections of (not necessarily symmetric) bounded real algebraic sets .
Edit intent: clarity
Original: We study the activation process in undirected graphs known as bootstrap percolation: A vertex is active either if it belongs to a set of initially activated vertices or if at some point it had at least r active neighbors, for a threshold r that is identical for all vertices.
Revised: We study the activation process in undirected graphs known as bootstrap percolation: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it had at least r active neighbors, for a threshold r that is identical for all vertices.
Edit intent: fluency
Original:  With respect to the minimum degree, we prove that if G has minimum degree n / 2 then m(G,2)=2. We also provide tight upper bounds on the number of rounds  until all nodes are active.
Revised:  With respect to the minimum degree, we prove that if G has minimum degree n / 2 then m(G,2)=2. We also provide tight upper bounds on the number of rounds it takes until all nodes are active.
Edit intent: clarity
Original:  We determine the precise value of M(n,k,2) and M(n,k,k)  assuming that n is sufficiently large compared to k.
Revised:  We determine the precise value of M(n,k,2) and M(n,k,k) , assuming that n is sufficiently large compared to k.
Edit intent: fluency
Original:  Complementing this, we show that general comparator circuits of polynomial size over arbitrary fixed finite lattices exactly characterizes P and that when the comparator circuit is skew they characterize NL . In addition, we show a characterization of the class NP by a family of polynomial sized comparator circuits over fixed {\em finite bounded posets}.
Revised:  Complementing this, we show that general comparator circuits of polynomial size over arbitrary fixed finite lattices exactly characterizes P even when the comparator circuit is skew they characterize NL . In addition, we show a characterization of the class NP by a family of polynomial sized comparator circuits over fixed {\em finite bounded posets}.
Edit intent: coherence
Original:  Complementing this, we show that general comparator circuits of polynomial size over arbitrary fixed finite lattices exactly characterizes P and that when the comparator circuit is skew they characterize NL . In addition, we show a characterization of the class NP by a family of polynomial sized comparator circuits over fixed {\em finite bounded posets}.
Revised:  Complementing this, we show that general comparator circuits of polynomial size over arbitrary fixed finite lattices exactly characterizes P and that when the comparator circuit is skew . In addition, we show a characterization of the class NP by a family of polynomial sized comparator circuits over fixed {\em finite bounded posets}.
Edit intent: clarity
Original:  We show that Spira's theorem (1971) can be extended to this setting as well and show that polynomial sized Boolean formulae over finite fixed lattices capture exactly NC^1 . Our results indicate potential new approaches towards the problems P vs CC and NL vs L using lattice theoretic methods .
Revised:  We show that Spira's theorem (1971) can be extended to this setting as well and show that polynomial sized Boolean formulae over finite fixed lattices capture exactly NC^1 .
Edit intent: clarity
Original:  The second method is a faster approximation to the solution path on a grid of logarithmically-spaced values that uses an interesting application of bucket sort to make the process efficient   .
Revised:  The second method is a faster approximation to the solution path on a grid of logarithmically-spaced values that uses an interesting application of bucket sort to make the process efficient or .
Edit intent: coherence
Original:  We demonstrate that both of these algorithms are fast and local on large networks .
Revised:  We demonstrate that these methods identify refined clustering structure on a number of real-world networks with up to 2 billion edges .
Edit intent: clarity
Original:  This procedure provides an accurate estimate of the quasi-stationary probability distribution of population sizes in the pre-colonization state, and of the mean time to colonization, for a wide range of immigration rates.
Revised:  This procedure provides an accurate evaluation of the quasi-stationary probability distribution of population sizes in the pre-colonization state, and of the mean time to colonization, for a wide range of immigration rates.
Edit intent: clarity
Original: A major difficulty of choosing an optimal radiation schedule is the uncertainty of model parameters due to geometric and patient specific uncertainties .
Revised: We consider the effects of parameter uncertainty on the optimal radiation schedule is the uncertainty of model parameters due to geometric and patient specific uncertainties .
Edit intent: clarity
Original:  We performed substantial numerical experiments for head-and-neck tumor including six normal tissues, spinal cord, brain stem, skin, oral cavity, mandible and larynx to reveal the effect of parameter uncertainty on optimal schedules  .
Revised:  We performed substantial numerical experiments for head-and-neck tumors to reveal the effect of parameter uncertainty on optimal schedules .
Edit intent: clarity
Original:  We here analyze a recently proposed measure called Surprise , which assesses the quality of the partition of a network into communities.
Revised:  We here analyze a recently proposed measure called surprise , which assesses the quality of the partition of a network into communities.
Edit intent: fluency
Original:  Given that, in its current form, its formulation is rather difficult to analyze , we develop an accurate asymptotic approximation.
Revised:  In its current form, its formulation is rather difficult to analyze , we develop an accurate asymptotic approximation.
Edit intent: coherence
Original:  Given that, in its current form, its formulation is rather difficult to analyze , we develop an accurate asymptotic approximation.
Revised:  Given that, in its current form, its formulation is rather difficult to analyze . We here therefore develop an accurate asymptotic approximation.
Edit intent: coherence
Original:  This allows for the development of an efficient algorithm for optimizing Surprise .
Revised:  This allows for the development of an efficient algorithm for optimizing surprise .
Edit intent: fluency
Original:  Incidentally, this leads to a straightforward extension of Surprise to weighted graphs.
Revised:  Incidentally, this leads to a straightforward extension of surprise to weighted graphs.
Edit intent: fluency
Original:  However, this function might be inefficient because of the following two reasons\emph{  : (a) it involves a lot of computations or (b) a huge amount of auxiliary randomness is required.
Revised:  However, it might be\emph{ : (a) it involves a lot of computations or (b) a huge amount of auxiliary randomness is required.
Edit intent: clarity