wanyu/IteraTeR_v2 huggingface dataset:
Original:  Finally  we introduce a new class of non-necessarily representable matroids  described by a grammar , on which MSOM is decidable in linear time.
Revised:  Finally we introduce a new class of non-necessarily representable matroids , described by a grammar , on which MSOM is decidable in linear time.
Edit intent: fluency
Original:  As a result of this consistence , the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of non-existence are verified: (i) There is no axisymmetric open membrane being a part of torus satisfying the shape equation;
Revised:  As a result of this consistency , the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of non-existence are verified: (i) There is no axisymmetric open membrane being a part of torus satisfying the shape equation;
Edit intent: fluency
Original:  Additionally, the shape equation is reduced to a second-order differential equation while the boundary conditions are reduced to two equations due to this consistence .
Revised:  Additionally, the shape equation is reduced to a second-order differential equation while the boundary conditions are reduced to two equations due to this consistency .
Edit intent: fluency
Original:  Numerical solutions to the reduced shape equation and boundary conditions agree well with the experimental data [A. Saitoh et al. , Proc.
Revised:  Numerical solutions to the reduced shape equation and boundary conditions agree well with the experimental data [A. Saitoh et al. , Proc.
Edit intent: fluency
Original:  Sci. USA 95 , 1026 (1998)].
Revised:  Sci. USA 95 , 1026 (1998)].
Edit intent: fluency
Original: Only some special open surfaces satisfying the shape equation of lipid membranes can be consistent with the boundary conditions.
Revised: Only some special open surfaces satisfying the shape equation of lipid membranes can be compatible with the boundary conditions.
Edit intent: clarity
Original:  As a result of this consistency , the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of non-existence are verified: (i) There is no axisymmetric open membrane being a part of torus satisfying the shape equation;
Revised:  As a result of this compatibility , the first integral of the shape equation should vanish for axisymmetric lipid membranes, from which two theorems of non-existence are verified: (i) There is no axisymmetric open membrane being a part of torus satisfying the shape equation;
Edit intent: clarity
Original:  Additionally, the shape equation is reduced to a second-order differential equation while the boundary conditions are reduced to two equations due to this consistency .
Revised:  Additionally, the shape equation is reduced to a second-order differential equation while the boundary conditions are reduced to two equations due to this compatibility .
Edit intent: clarity
Original: Coupled human balancing tasks are investigated on the basis of both pseudo-neural controllers characterized by time-delayed feedback with random gain and natural human balancing tasks.
Revised: Coupled human balancing tasks are investigated based on both pseudo-neural controllers characterized by time-delayed feedback with random gain and natural human balancing tasks.
Edit intent: fluency
Original:  It is numerically shown that in comparison to single balancing tasks, balancing tasks coupled by mechanical structures increase the stability of balancing errors in terms of both amplitude and velocity and also improve the tracking ability of the controllers.
Revised:  It is shown numerically that, compared to single balancing tasks, balancing tasks coupled by mechanical structures increase the stability of balancing errors in terms of both amplitude and velocity and also improve the tracking ability of the controllers.
Edit intent: fluency
Original:  It is numerically shown that in comparison to single balancing tasks, balancing tasks coupled by mechanical structures increase the stability of balancing errors in terms of both amplitude and velocity and also improve the tracking ability of the controllers.
Revised:  It is numerically shown that in comparison to single balancing tasks, balancing tasks coupled by mechanical structures exhibit enhanced stability against balancing errors in terms of both amplitude and velocity and also improve the tracking ability of the controllers.
Edit intent: clarity
Original:  We then perform an experiment in which the numerical pseudo-neural controllers are replaced with natural human balancing tasks carried out using computer mice.
Revised:  We then perform an experiment in which numerical pseudo-neural controllers are replaced with natural human balancing tasks carried out using computer mice.
Edit intent: fluency
Original:  The result shows that the coupling structure generates asymmetric tracking abilities in the subjects whose tracking abilities are nearly symmetric in their single balancing tasks.
Revised:  The results reveal that the coupling structure generates asymmetric tracking abilities in the subjects whose tracking abilities are nearly symmetric in their single balancing tasks.
Edit intent: clarity
Original:  The result shows that the coupling structure generates asymmetric tracking abilities in the subjects whose tracking abilities are nearly symmetric in their single balancing tasks.
Revised:  The result shows that the coupling structure generates asymmetric tracking abilities in subjects whose tracking abilities are nearly symmetric in their single balancing tasks.
Edit intent: fluency
Original:  Hidden Markov models are widely employed by numerous Bioinformatics programs used today.
Revised:  Hidden Markov models are widely employed by numerous bioinformatics programs used today.
Edit intent: fluency
Original: Molecular dynamics simulations are performed to determine the binding affinities between  the hormone 17 beta-estradiol (E2) and different estrogen receptor (ER) isoforms in the rainbow trout (Oncorhynchus mykiss).
Revised: Molecular dynamics simulations were used to determine the binding affinities between the hormone 17 beta-estradiol (E2) and different estrogen receptor (ER) isoforms in the rainbow trout (Oncorhynchus mykiss).
Edit intent: clarity
Original: Molecular dynamics simulations are performed to determine the binding affinities between  the hormone 17 beta-estradiol (E2) and different estrogen receptor (ER) isoforms in the rainbow trout (Oncorhynchus mykiss).
Revised: Molecular dynamics simulations are performed to determine the binding affinities between between the hormone 17 beta-estradiol (E2) and different estrogen receptor (ER) isoforms in the rainbow trout (Oncorhynchus mykiss).
Edit intent: fluency
Original:  Previous studies have demonstrated that a recent, unique gene duplication of the ER alpha subtype created two isoforms ER alpha 1 and ER alpha 2, and an early secondary split of ER beta produced two distinct isoformsof ER beta 1 and ER beta 2 based on the phylogenetic analysis.
Revised:  Previous studies have demonstrated that a recent, unique gene duplication of the ER alpha subtype created two isoforms ER alpha 1 and ER beta 2, and an early secondary split of ER beta produced two distinct isoformsof ER beta 1 and ER beta 2 based on the phylogenetic analysis.
Edit intent: fluency
Original:  Previous studies have demonstrated that a recent, unique gene duplication of the ER alpha subtype created two isoforms ER alpha 1 and ER alpha 2, and an early secondary split of ER beta produced two distinct isoformsof ER beta 1 and ER beta 2 based on the phylogenetic analysis.
Revised:  Previous studies have demonstrated that a recent, unique gene duplication of the ER alpha subtype created two isoforms ER alpha 1 and ER alpha 2, and an early secondary split of ER beta produced two distinct isoformsof ER beta 1 and ER alpha 2.
Edit intent: clarity
Original:  We quantify the degree of fluctuations in oscillation periods and amplitudes, as well as the noise propagation along the regulatory cascade using the exact stochastic simulations with the Gillespie algorithm in the stable oscillation regime  .
Revised:  We quantify the degree of fluctuations in oscillation periods and amplitudes, as well as the noise propagation along the regulatory cascade in the stable oscillation regime .
Edit intent: coherence
Original:  Correlations between successive periods and between successive amplitudes respectively are measured to assess the noise propagation properties, which are found to decay faster for the amplitude than for the period.
Revised:  Correlations between successive periods and between successive amplitudes , respectively, are measured to assess the noise propagation properties, which are found to decay faster for the amplitude than for the period.
Edit intent: fluency
Original:  Local fluctuation property is also studied.
Revised:  The local fluctuation property is also studied.
Edit intent: clarity
Original: {\it   In this paper, we develop a new computing model of 1QFA, namely, {\it one-way quantum finite automata together with classical states} (1QFAC for short).
Revised: {\it One-way quantum finite automata In this paper, we develop a new computing model of 1QFA, namely, {\it one-way quantum finite automata together with classical states} (1QFAC for short).
Edit intent: fluency
Original:  In this model, the component of classical states together with their transformations is added, and the choice of unitary evolution of quantum states at each step is closely related to the current classical state.
Revised:  In this model, a component of classical states together with their transformations is added, and the choice of unitary evolution of quantum states at each step is closely related to the current classical state.
Edit intent: fluency
Original:  In this model, the component of classical states together with their transformations is added, and the choice of unitary evolution of quantum states at each step is closely related to the current classical state.
Revised:  In this model, the component of classical states is added, and the choice of unitary evolution of quantum states at each step is closely related to the current classical state.
Edit intent: clarity
Original:  (2) Then, we show that, for any  m\geq 2, there exists a regular language L _m whose minimal DFA needs O(m) states and that can not be accepted by  1QFA  , but there exists 1QFAC accepting L _m with only constant classical states and O(\log(m)) quantum basis states.
Revised:  (2) We show that, for any m\geq 2, there exists a regular language L _m whose minimal DFA needs O(m) states and that can not be accepted by 1QFA , but there exists 1QFAC accepting L _m with only constant classical states and O(\log(m)) quantum basis states.
Edit intent: coherence
Original: (4)We design {\cal  {\cal   a polynomial-time  n_{1})^2+ (k_{2}n_{2})^2}] algorithm for determining the equivalenceof any two 1QFAC.
Revised: (4)We design {\cal {\cal A a polynomial-time n_{1})^2+ (k_{2}n_{2})^2}] algorithm for determining the equivalenceof any two 1QFAC.
Edit intent: fluency
Original: (4)We design {\cal  {\cal   a polynomial-time  n_{1})^2+ (k_{2}n_{2})^2}] algorithm for determining the equivalenceof any two 1QFAC.
Revised: (4)We design {\cal {\cal a polynomial-time (k_{1n_{1})^2+ (k_{2}n_{2})^2}] algorithm for determining the equivalenceof any two 1QFAC.
Edit intent: fluency
Original:  The same technique can be used to minimize other quantum automata and probabilistic automata and n_{2} are the numbers of quantum basis states of }{\cal   and }{\cal   .
Revised:  The same technique can be used to minimize other quantum automata and probabilistic automata and n_{2} are the numbers of quantum basis states of }{\cal A and }{\cal .
Edit intent: fluency
Original: %DIFDELCMD < {\it %%% One-way quantum finite automata (1QFA) proposed by Moore and Crutchfield and by Kondacs and Watrous accept only subsets of regular languages with bounded error.
Revised: %DIFDELCMD < {\it %%% (1QFA) proposed by Moore and Crutchfield and by Kondacs and Watrous accept only subsets of regular languages with bounded error.
Edit intent: clarity
Original: %DIFDELCMD < {\it %%% One-way quantum finite automata (1QFA) proposed by Moore and Crutchfield and by Kondacs and Watrous accept only subsets of regular languages with bounded error.
Revised: %DIFDELCMD < {\it %%% One-way quantum finite automata 
Edit intent: coherence
Original: In this paper, we develop a new computing model of {\it   1QFA  , namely, {\it one-way quantum finite automata together with classical states} (1QFAC for short).
Revised: In this paper, we develop a new computing model of {\it one-way quantum finite automata 1QFA , namely, {\it one-way quantum finite automata together with classical states} (1QFAC for short).
Edit intent: fluency
Original: In this paper, we develop a new computing model of {\it   1QFA  , namely, {\it one-way quantum finite automata together with classical states} (1QFAC for short).
Revised: In this paper, we develop a new computing model of {\it 1QFA ) , namely, {\it one-way quantum finite automata together with classical states} (1QFAC for short).
Edit intent: fluency
Original:  In this model, a component of classical states is added, and the choice of unitary evolution of quantum states at each step is closely related to the current classical state . 1QFAC can accept all regular languages with no error, and in particular, 1QFAC can accept some languages with essentially less number of states than%DIFDELCMD < {\em %%% deterministic finite automata (DFA).
Revised:  In this model, a component of classical states is added, and the choice of unitary evolution of quantum states at each step is closely related to the current classical state . 1QFAC can accept all regular languages with no error, and in particular, 1QFAC can accept some languages with essentially less number of states than%DIFDELCMD < {\em %%% (DFA).
Edit intent: clarity
Original:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2 are equivalent if and only if they are (k_{1 a polynomial-time O( (k_{1n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Revised:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% _1 and%DIFDELCMD < {\cal %%% A _2 are equivalent if and only if they are (k_{1 a polynomial-time O( (k_{1n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Edit intent: fluency
Original:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2 are equivalent if and only if they are (k_{1 a polynomial-time O( (k_{1n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Revised:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% A %DIFDELCMD < {\cal %%% A _2 are equivalent if and only if they are (k_{1 a polynomial-time O( (k_{1n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Edit intent: coherence
Original:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2 are equivalent if and only if they are (k_{1 a polynomial-time O( (k_{1n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Revised:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% _2 are equivalent if and only if they are (k_{1 a polynomial-time O( (k_{1n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Edit intent: fluency
Original:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2 are equivalent if and only if they are (k_{1 a polynomial-time O( (k_{1n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Revised:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2 are equivalent if and only if they are (k_{1 a polynomial-time (k_{1n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Edit intent: clarity
Original:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2 are equivalent if and only if they are (k_{1 a polynomial-time O( (k_{1n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Revised:  (3) By a bilinearization technique we prove that any two 1QFAC%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2 are equivalent if and only if they are (k_{1 a polynomial-time O( n_{1})^2+ (k_{2}n_{2})^2}%DIFDELCMD < ]%%% ^4)
Edit intent: fluency
Original:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Revised:  algorithm for determining and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Edit intent: clarity
Original:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Revised:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Edit intent: fluency
Original:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Revised:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A %DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Edit intent: fluency
Original:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Revised:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Edit intent: fluency
Original:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Revised:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Edit intent: coherence
Original:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Revised:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Edit intent: fluency
Original:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Revised:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Edit intent: fluency
Original:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% A _{2 of 1QFAC is in EXPSPACE.
Revised:  algorithm for determining their equivalence, where k_{1 and k_{2} are the numbers of classical states of }%DIFDELCMD < {\cal %%% A _1 and%DIFDELCMD < {\cal %%% A _2, as well as n_{1 and n_{2} are the numbers of quantum basis states of }%DIFDELCMD < {\cal %%% A _{1 and }%DIFDELCMD < {\cal %DIFDELCMD < %%% _{2 of 1QFAC is in EXPSPACE.
Edit intent: fluency
Original: The genetic code is known to have a high level of error robustness and has been shown to be very error robust compared to randomly selected codes, but to be significantly less error robust than a certain code found by a heuristic algorithm.
Revised: The genetic code has been shown to be very error robust compared to randomly selected codes, but to be significantly less error robust than a certain code found by a heuristic algorithm.
Edit intent: coherence
Original:  We formulate this optimisation problem as a Quadratic Assignment Problem and use this to formally verify that the code found by the heuristic algorithm is the global optimum.
Revised:  We formulate this optimisation problem as a Quadratic Assignment Problem and thus verify that the code found by the heuristic algorithm is the global optimum.
Edit intent: clarity
Original:  We formulate this optimisation problem as a Quadratic Assignment Problem and use this to formally verify that the code found by the heuristic algorithm is the global optimum.
Revised:  We formulate this optimisation problem as a Quadratic Assignment Problem and use this to formally verify that the code found by the heuristic is the global optimum.
Edit intent: clarity
Original:  This has consequences for the kind of mechanisms we envisage as having shaped the genetic code.
Edit intent: clarity
Original:  As an application , we improve the running time of an algorithm of Edmonds for embedding finite metrics into the Manhattan-metric plane , from O(n^2 \log^2 n)to O(n ^2 ).
Revised:  As an application of this construction, we show how to test whether a given finite metric space embeds isometrically into the Manhattan plane in time O(n^2 \log^2 n)to O(n ^2 ).
Edit intent: clarity