wanyu/IteraTeR_v2 huggingface dataset:
Original:  We define " autocatalytic networks, " and conjecture that  weakly-reversible reaction networks have critical siphons if and only if they are autocatalytic.
Revised:  We define " autocatalytic networks, " and conjecture that weakly-reversible reaction network has critical siphons if and only if they are autocatalytic.
Edit intent: fluency
Original:  We define " autocatalytic networks, " and conjecture that  weakly-reversible reaction networks have critical siphons if and only if they are autocatalytic.
Revised:  We define " autocatalytic networks, " and conjecture that weakly-reversible reaction networks have critical siphons if and only if it is autocatalytic.
Edit intent: clarity
Original: Queries that constrain multiple dimensions simultaneously are difficult to express and compute efficiently in both Structured Query Language (SQL) and multidimensional languages.
Revised: Many queries that constrain multiple dimensions simultaneously are difficult to express and compute efficiently in both Structured Query Language (SQL) and multidimensional languages.
Edit intent: clarity
Original:  We show that our custom implementation is more than twenty-five times faster, on a large data set, than popular database engines .
Revised:  We show that our custom implementation is more than twenty-five times faster, on a large data set, than a popular database engine .
Edit intent: fluency
Original: A conspicuous flaw in evaluation programmes such as the UK's Research Assessment Exercise is the absence of a method to compare research quality across academic disciplines.
Revised: Peer-evaluation based measures of group research quality such as the UK's Research Assessment Exercise is the absence of a method to compare research quality across academic disciplines.
Edit intent: clarity
Original:  The approach is based upon a recently established relationship between research quality and group size which facilitates determination of discipline-dependent critical masses.
Revised:  The approach is based upon a mathematical model for the relationship between research quality and group size which facilitates determination of discipline-dependent critical masses.
Edit intent: clarity
Original:  A sensible normalization procedure is then to pitch these plateaus at similar levels.
Revised:  A possible normalization procedure is then to pitch these plateaus at similar levels.
Edit intent: clarity
Original:  We examine the consequence of this procedure at RAE for a multitude of academic disciplines, corresponding to a range of critical masses.
Revised:  We examine the consequences of this procedure at RAE for a multitude of academic disciplines, corresponding to a range of critical masses.
Edit intent: fluency
Original:  In agreement with previous results, three phases are identified: the phase in which both hosts and parasites are extinct (S _0 ), the phase in which hosts survive but parasites are extinct (S_{01}), and the phase in which both hosts and parasites survive (S_{012}).
Revised:  In agreement with previous results, three phases are identified: the phase in which both hosts and parasites are extinct (S _{0 ), the phase in which hosts survive but parasites are extinct (S_{01}), and the phase in which both hosts and parasites survive (S_{012}).
Edit intent: fluency
Original:  In this model, it has been suggested that an excessively large reproduction rate of parasites paradoxically extinguishes hosts and parasites and results in S _0 . We show that this paradoxical extinction is a finite size effect;
Revised:  In this model, it has been suggested that an excessively large reproduction rate of parasites paradoxically extinguishes hosts and parasites and results in S _{0 . We show that this paradoxical extinction is a finite size effect;
Edit intent: fluency
Original:  Analysis of targeted immunization strategies revealed that in the absence of contact network data , preferential immunization of students is the most effective strategy .
Revised:  Analysis of targeted immunization strategies suggested that contact network data , preferential immunization of students is the most effective strategy .
Edit intent: clarity
Original:  Analysis of targeted immunization strategies revealed that in the absence of contact network data , preferential immunization of students is the most effective strategy .
Revised:  Analysis of targeted immunization strategies revealed that in the absence of contact network data are required to design strategies that are significantly more effective than random immunization .
Edit intent: clarity
Original: In their paper on the `` chasm at depth four '' , Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m).
Revised: In their paper on the " chasm at depth four '' , Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m).
Edit intent: fluency
Original: In their paper on the `` chasm at depth four '' , Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m).
Revised: In their paper on the `` chasm at depth four " , Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m).
Edit intent: fluency
Original: In their paper on the " chasm at depth four " , Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m).
Revised: In their paper on the `` chasm at depth four " , Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m).
Edit intent: fluency
Original: In their paper on the " chasm at depth four " , Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m).
Revised: In their paper on the " chasm at depth four '' , Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m).
Edit intent: fluency
Original: A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix, bifix, factor , and subword-free languages are defined similarly, where by "subword" we mean "subsequence".
Revised: A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix-, bifix-, factor- , and subword-free languages are defined similarly, where by "subword" we mean "subsequence".
Edit intent: fluency
Original: A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix, bifix, factor , and subword-free languages are defined similarly, where by "subword" we mean "subsequence".
Revised: A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix, bifix, factor , and subword-free languages are defined similarly, where "subword" we mean "subsequence".
Edit intent: clarity
Original: A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix, bifix, factor , and subword-free languages are defined similarly, where by "subword" we mean "subsequence".
Revised: A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix, bifix, factor , and subword-free languages are defined similarly, where by "subword" means "subsequence".
Edit intent: clarity
Original:  We study the quotient complexity, more commonly known as state complexity, of regular operations in the classes of bifix-, factor-, and subword-free  languages.
Revised:  We study the quotient complexity, more commonly known as state complexity, of operations in the classes of bifix-, factor-, and subword-free languages.
Edit intent: clarity
Original:  We find tight upper bounds on the complexity of intersection, union, difference, symmetric difference, concatenation, star, and reversal in bifix-, factor-, and subword-free languages.
Revised:  We find tight upper bounds on the complexity of intersection, union, difference, symmetric difference, concatenation, star, and reversal in these three classes of languages.
Edit intent: clarity
Original: A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix-, bifix-, factor-, and subword-free languages are defined similarly, where "subword" means "subsequence".
Revised: A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix-, factor-, and subword-free languages are defined similarly, where "subword" means "subsequence".
Edit intent: fluency
Original: In this work, we introduce a new algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system .
Revised: In this work, we introduce an algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system .
Edit intent: clarity
Original:  Finally, we compare the new methodto the finite-differences approach in three molecules of biological relevance: methanol, N-methyl-acetamide and a tri-glycine peptide .
Revised:  Finally, and in order to validate the method, which, as far as we are aware, is the first of its kind in the literature, we compare it to the natural and straightforward finite-differences approach in three molecules of biological relevance: methanol, N-methyl-acetamide and a tri-glycine peptide .
Edit intent: coherence
Original:  While not unique, regular control surfaces are exactly the possible limiting positions of a Bezier patch when the weights are allowed to vary , but the control points are fixed .
Revised:  While not unique, regular control surfaces are exactly the possible limiting positions of a Bezier patch when the weights are allowed to vary .
Edit intent: coherence
Original:  In this paper we develop a bisimulation technique for proving behavioural equivalence of such systems modelled in the higher-order pi-calculus with passivation (and restriction).
Revised:  In this paper we propose a bisimulation technique for proving behavioural equivalence of such systems modelled in the higher-order pi-calculus with passivation (and restriction).
Edit intent: clarity
Original:  In contrast, we provide a sound and useful definition of environmental bisimulations \emph{ , with several non-trivial examples.
Revised:  In contrast, we provide a sound and useful definition of \emph{ , with several non-trivial examples.
Edit intent: clarity
Original:  The model is based on the clinical evidence, which states that antobodies can directly kill cancerous cells [ 18 ].
Revised:  The model is based on the clinical evidence, which states that antibodies can directly kill cancerous cells [ 18 ].
Edit intent: fluency
Original:  We assume that hyperbolic geometry underlies these networks, and  show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry.
Revised:  We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry.
Edit intent: fluency
Original:  This mapping interprets edges in a network as non-interacting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies / distances.
Revised:  This mapping interprets edges in a network as non-interacting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances.
Edit intent: fluency
Original:  The case gamma= 0 corresponds to the infinite-temperature limit of the Potts model, and is computationally trivial.
Revised:  The case gamma= 0.
Edit intent: clarity
Original:  It is known that there is no FPRAS unless NP=RP in the in-between region -2<=gamma<0, apart from at two "special points '' where the polynomial can be computed exactly in polynomial time.
Revised:  It is known that there is no FPRAS unless NP=RP in the in-between region -2<=gamma<0, apart from at two "special points " where the polynomial can be computed exactly in polynomial time.
Edit intent: fluency
Original:  We show that for binary matroids there is no FPRAS in the region gamma<-2 unless NP=RP . Also, in the region gamma>0  the approximation problem is hard for the complexity class #RHPi_1 under approximation-preserving (AP) reducibility.
Revised:  We show that for binary matroids there is no FPRAS in the region gamma<-2 unless NP=RP , and (ii) in the region gamma>0 the approximation problem is hard for the complexity class #RHPi_1 under approximation-preserving (AP) reducibility.
Edit intent: coherence
Original:  We show that for binary matroids there is no FPRAS in the region gamma<-2 unless NP=RP . Also, in the region gamma>0  the approximation problem is hard for the complexity class #RHPi_1 under approximation-preserving (AP) reducibility.
Revised:  We show that for binary matroids there is no FPRAS in the region gamma<-2 unless NP=RP . Also, in the region gamma>0 , the approximation problem is hard for the complexity class #RHPi_1 under approximation-preserving (AP) reducibility.
Edit intent: fluency
Original:  Our result implies that it is computationally difficult to approximate the weight enumerator of a binary linear code, apart from at the special weights for which the problem is exactly solvable in polynomial time.
Revised:  Our result implies that it is computationally difficult to approximate the weight enumerator of a binary linear code, apart from at the special weights at which the problem is exactly solvable in polynomial time.
Edit intent: clarity
Original:  As a consequence, we show that approximating the cycle index polynomial of a permutation group is hard for #RHPi_1 under AP-reducibility, partially resolving a question  first posed in 1992.
Revised:  As a consequence, we show that approximating the cycle index polynomial of a permutation group is hard for #RHPi_1 under AP-reducibility, partially resolving a question that we first posed in 1992.
Edit intent: fluency
Original: The famous F5 algorithm for computing Gr\"obner \gr basis was presented by Faug\`ere in 2002.
Revised: The famous F5 algorithm for computing \gr basis was presented by Faug\`ere in 2002.
Edit intent: fluency
Original:  The original  F5 algorithm is described by codes, so it is a bit difficult to understand.
Revised:  The original version of F5 algorithm is described by codes, so it is a bit difficult to understand.
Edit intent: clarity
Original:  The original  F5 algorithm is described by codes, so it is a bit difficult to understand.
Revised:  The original F5 is given in programming codes, so it is a bit difficult to understand.
Edit intent: clarity
Original:  In this paper, the F5 algorithm is simplified  in a Buchberger's style (F5B algorithm) such that it is easy to understand and implement.
Revised:  In this paper, the F5 algorithm is simplified in a Buchberger's style such that it is easy to understand and implement.
Edit intent: coherence
Original:  The equivalence between the original F5 algorithm and F5B algorithm is shown, and some versions of  F5 algorithm are illustrated by F5B algorithm .
Revised:  The equivalence between the original F5 algorithm and F5B is also shown. At last, some versions of F5 algorithm are illustrated by F5B algorithm .
Edit intent: coherence
Original:  The equivalence between the original F5 algorithm and F5B algorithm is shown, and some versions of  F5 algorithm are illustrated by F5B algorithm .
Revised:  The equivalence between the original F5 algorithm and F5B algorithm is shown, and some versions of the F5 algorithm are illustrated by F5B algorithm .
Edit intent: fluency
Original:  The equivalence between the original F5 algorithm and F5B algorithm is shown, and some versions of  F5 algorithm are illustrated by F5B algorithm .
Revised:  The equivalence between the original F5 algorithm and F5B algorithm is shown, and some versions of F5 algorithm are illustrated .
Edit intent: clarity
Original:  A key application of our techniques yields the result that it is also PSPACE-complete to compute any of the equilibria that could be found via the classical Lemke-Howson algorithm  ] .
Revised:  A key application of our techniques yields the result that it is PSPACE-complete to compute any of the equilibria that could be found via the classical Lemke-Howson algorithm ] .
Edit intent: clarity
Original: We provide an exhaustive analysis of the features of the simple model of species assembly introduced in ( Capitan et al. , 2009).
Revised: We provide an exhaustive analysis of the features of the simple model of species assembly introduced in Capitan et al. , 2009).
Edit intent: fluency
Original: We provide an exhaustive analysis of the features of the simple model of species assembly introduced in ( Capitan et al. , 2009).
Revised: We provide an exhaustive analysis of the features of the simple model of species assembly introduced in ( Capitan et al. ( 2009).
Edit intent: fluency
Original:  Our approach is based on the construction of an assembly graph containing all viable configurations of the species community, and the definition of a Markov chain whose transitions are the transformations of communities induced by invasion of a new species .
Revised:  Our approach is based on the construction of an assembly graph containing all viable configurations of the community, and the definition of a Markov chain whose transitions are the transformations of communities induced by invasion of a new species .
Edit intent: fluency
Original:  The chain also provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables in an exact manner as well as the time variation of these magnitudes during succession  . Since the times to absorption to the recurrent set are found to be small compared to the size of the system, the end state is quickly reached (in units of the invasion time)
Revised:  The chain also provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables as well as the time variation of these magnitudes during succession . Since the times to absorption to the recurrent set are found to be small compared to the size of the system, the end state is quickly reached (in units of the invasion time)
Edit intent: clarity
Original:  The chain also provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables in an exact manner as well as the time variation of these magnitudes during succession  . Since the times to absorption to the recurrent set are found to be small compared to the size of the system, the end state is quickly reached (in units of the invasion time)
Revised:  The chain also provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables in an exact manner as well as the time variation of these magnitudes during succession , in an exact manner . Since the times to absorption to the recurrent set are found to be small compared to the size of the system, the end state is quickly reached (in units of the invasion time)
Edit intent: coherence
Original:  The chain also provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables in an exact manner as well as the time variation of these magnitudes during succession  . Since the times to absorption to the recurrent set are found to be small compared to the size of the system, the end state is quickly reached (in units of the invasion time)
Revised:  The chain also provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables in an exact manner as well as the time variation of these magnitudes during succession . Since the absorption times into the recurrent set are found to be small compared to the size of the system, the end state is quickly reached (in units of the invasion time)
Edit intent: clarity
Original:  The chain also provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables in an exact manner as well as the time variation of these magnitudes during succession  . Since the times to absorption to the recurrent set are found to be small compared to the size of the system, the end state is quickly reached (in units of the invasion time)
Revised:  The chain also provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables in an exact manner as well as the time variation of these magnitudes during succession . Since the times to absorption to the recurrent set are found to be comparable to the size of the system, the end state is quickly reached (in units of the invasion time)
Edit intent: clarity
Original:  and the ecosystem can be regarded as a fluctuating complex system where species get continually replaced by newcomers without ever leaving the set of recurrent patterns.
Revised:  and the ecosystem can be regarded as a fluctuating complex system where species are continually replaced by newcomers without ever leaving the set of recurrent patterns.
Edit intent: fluency
Original:  However, it has been shown that in FitzHugh-Nagumo model there exist alternative stable vortices with distinct periods.
Revised:  Here we show that in FitzHugh-Nagumo model there exist alternative stable vortices with distinct periods.
Edit intent: clarity
Original:  Furthermore, there exist hysteresis loops in the vortex period at a certain range of parameters.
Edit intent: coherence
Original:  In this paper, we use the Response Functions (RFs), that is the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues {\lambda} = 0, +/- i{\omega} , to predict the filament tension of the alternative vortices.
Revised:  In this paper, we use the Response Functions (RFs), that is the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues {\lambda} = 0, +/- i{\omega} to predict the filament tension of the alternative vortices.
Edit intent: fluency
Original:  It appears that the slower vortex has negative filament tension, while the faster, shorter period vortex changes sign of its filament tension within the hysteresis loop .
Revised:  It appears that the slower vortex has negative filament tension, while the faster, shorter period vortex changes sign of its filament tension within the parametric region .
Edit intent: clarity
Original:  The slower scrolls display features similar to delayed after-depolarisation (DAD) and tend to develop into turbulence similar to Ventricular Fibrillation (VF).
Edit intent: coherence
Original:  In this paper, we use the Response Functions (RFs), that is the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues \lambda%DIFDELCMD < } %%% = 0, +/- i \omega%DIFDELCMD < } %%% to predict the filament tension of the alternative vortices.
Revised:  \lambda%DIFDELCMD < } %%% = 0, +/- i \omega%DIFDELCMD < } %%% to predict the filament tension of the alternative vortices.
Edit intent: coherence