wanyu/IteraTeR_full_sent huggingface dataset:
Original: Networks of planar Hamiltonian systems closely resemble Hamiltonian system in R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a number called the Turing instability parameter.
Revised: Certain dissipative physical systems closely resemble Hamiltonian system in R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a number called the Turing instability parameter.
Edit intent: meaning-changed
Original: Networks of planar Hamiltonian systems closely resemble Hamiltonian system in R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a number called the Turing instability parameter.
Revised: Networks of planar Hamiltonian systems closely resemble Hamiltonian systems in R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a number called the Turing instability parameter.
Edit intent: fluency
Original: Networks of planar Hamiltonian systems closely resemble Hamiltonian system in R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a number called the Turing instability parameter.
Revised: Networks of planar Hamiltonian systems closely resemble Hamiltonian system in R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a real parameter.
Edit intent: meaning-changed
Original:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their physical interpretation motivates new problems in Floer theory, mirror symmetry, and the study of \mathbb{D-K\"{a}hler manifolds}  .
Revised:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their physical interpretation motivates new problems in -K\"{a}hler manifolds} .
Edit intent: clarity
Original:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their physical interpretation motivates new problems in Floer theory, mirror symmetry, and the study of \mathbb{D-K\"{a}hler manifolds}  .
Revised:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their physical interpretation motivates new problems in Floer theory, mirror symmetry, and the study of \mathbb{D-K\"{a}hler manifolds} mathematics .
Edit intent: clarity
Original:  (1) The size of avalanches are diverse depending on sectors where demands are given . (2) The simulated avalanche size for the policies actually conducted correspond well to the ex-post evaluations of the policies.
Revised:  (1) The size of avalanches follows power law . (2) The simulated avalanche size for the policies actually conducted correspond well to the ex-post evaluations of the policies.
Edit intent: meaning-changed
Original:  (1) The size of avalanches are diverse depending on sectors where demands are given . (2) The simulated avalanche size for the policies actually conducted correspond well to the ex-post evaluations of the policies. (3) The expectation to get involved into avalanches are diverse depending on sectors. (4) Service sectors and small firms are difficult to be indirectly affected by fiscal policies. On the other hand, construction, manufacturing, and wholesale sectors are well affected by fiscal policies. (5) If we need to clip a network without losing the effect of the fiscal policy, we can clip the network by the descending order of firms' capital size .
Revised:  (1) The size of avalanches are diverse depending on sectors where demands are given . (2) The mean sizes of avalanches for industries are diverse but their standard deviations highly overlap. (3) We compare the simulation with an input-output table and with the actual policies. They are compatible .
Edit intent: clarity
Original:  This theory includes (i) a cell-specific reference state that enables mechanosensing cells to gauge a mechanical stimulus and to respond to it; (ii) a rapid, but partial desensitisation of the mechanosensing cells to the mechanical stimulus;
Revised:  This theory assumes that osteocytes are formed adapted to their current local mechanical environment through modulation of morphological and genotypic osteocyte properties involved in mechanical sensitivity. We distinguish two main types of physiological responses by which osteocytes subsequently modify the reference mechanical state. One is the mechanosensing cells to the mechanical stimulus;
Edit intent: meaning-changed
Original:  (ii) a rapid, but partial desensitisation of the mechanosensing cells to the mechanical stimulus; and (iii) the replacement of the mechanosensing cells during bone remodelling, which resets the cell-specific reference state.
Revised:  (ii) a rapid, but partial desensitisation of the replacement of the mechanosensing cells during bone remodelling, which resets the cell-specific reference state.
Edit intent: coherence
Original:  and (iii) the replacement of the mechanosensing cells during bone remodelling, which resets the cell-specific reference state. The cell-specific reference state we propose is assumed to be encoded in the cells during their formation. It provides a long-lasting memory of the current mechanical stimulus gradually reset by bone remodelling.
Revised:  and (iii) the replacement of the mechanosensing cells during bone remodelling, which occurs over the long timescales of bone turnover. The other is cell desensitisation responses, which occur more rapidly and reversibly during an osteocyte's lifetime. The novelty of this theory is to propose that long-lasting memory of the current mechanical stimulus gradually reset by bone remodelling.
Edit intent: meaning-changed
Original:  Our proposed cell-based mechanostat theory gives a cellular interpretation of the different phenomena and timescales occurring during the mechanical adaptation of bone tissues . The consideration of osteocyte desensitisation and osteocyte replacement enables to resolve several shortcomings of the standard mechanostat theory.
Revised:  Our proposed cell-based mechanostat theory gives a cellular interpretation of the different phenomena and timescales occurring during the mechanical adaptation of bone tissues , lending support to this theory.
Edit intent: coherence
Original:  With the bounded terminal condition as well as an additional local Lipschitz continuity, we give a simple and streamlined proof for the existence and the uniqueness of the solution . The universal bound and the stability result for the locally Lipschitz BSDEs with coefficients in the BMO space enable us to show the strong convergence of a sequence of globally Lipschitz BSDEs .
Revised:  With the bounded terminal condition as well as an additional local Lipschitz continuity, we give a simple and streamlined proof for the existence and the uniqueness of the solution without using the comparison principle. The properties of locally Lipschitz BSDEs with coefficients in the BMO space enable us to show the strong convergence of a sequence of globally Lipschitz BSDEs .
Edit intent: meaning-changed
Original:  The universal bound and the stability result for the locally Lipschitz BSDEs with coefficients in the BMO space enable us to show the strong convergence of a sequence of globally Lipschitz BSDEs .
Revised:  The universal bound and the stability result for the locally Lipschitz BSDEs with coefficients in BMO space enable us to show the strong convergence of a sequence of globally Lipschitz BSDEs .
Edit intent: clarity
Original:  The universal bound and the stability result for the locally Lipschitz BSDEs with coefficients in the BMO space enable us to show the strong convergence of a sequence of globally Lipschitz BSDEs . The result is then used to generalize the existing results on the Malliavin's differentiability of the quadratic BSDEs in the diffusion setup to the quadratic-exponential growth BSDEs with jumps .
Revised:  The universal bound and the stability result for the locally Lipschitz BSDEs with coefficients in the BMO space enable us to show the strong convergence of a sequence of globally Lipschitz BSDEs to the interested one, which is then used to generalize the existing results on the Malliavin's differentiability of the quadratic BSDEs in the diffusion setup to the quadratic-exponential growth BSDEs with jumps .
Edit intent: clarity
Original:  The result is then used to generalize the existing results on the Malliavin's differentiability of the quadratic BSDEs in the diffusion setup to the quadratic-exponential growth BSDEs with jumps .
Revised:  The result is then used to give sufficient conditions for the Malliavin's differentiability of the quadratic BSDEs in the diffusion setup to the quadratic-exponential growth BSDEs with jumps .
Edit intent: clarity
Original:  With a bounded terminal condition and local Lipschitz continuity , we give a simple and streamlined proof for the existence as well as the uniqueness of the solution without using the comparison principle. The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the  strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
Revised:  With a bounded terminal condition and local Lipschitz continuity and the strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
Edit intent: coherence
Original:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the  strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
Revised:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the so-called A_gamma-condition for the comparison principle to hold, we prove the existence of a unique solution under the general quadratic-exponential structure. We have also shown that the strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
Edit intent: meaning-changed
Original:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the  strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
Revised:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the strong convergence occurs under more general (not necessarily monotone) sequence of drivers , which is then used to give sufficient conditions for the Malliavin's differentiability.
Edit intent: meaning-changed
Original:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the  strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
Revised:  The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then applied to give the sufficient conditions for the Malliavin's differentiability.
Edit intent: clarity
Original: In this paper, we investigate the non-linear Black--Scholes equation: u_t+ax^2u_{xx}+bx^3u_{xx}^2+c(xu_x-u)=0,\quad a,b>0,\ c\geq0. and show that  one can be reduced to the equation u_t+(u_{xx}+u_x)^2=0 by an appropriate point transformation of variables.
Revised: In this paper, we investigate the non-linear Black--Scholes equation: u_t+ax^2u_{xx}+bx^3u_{xx}^2+c(xu_x-u)=0,\quad a,b>0,\ c\geq0. and show that the one can be reduced to the equation u_t+(u_{xx}+u_x)^2=0 by an appropriate point transformation of variables.
Edit intent: fluency
Original:  For the last equation, we study the group-theoretic properties, namely, we find the maximal algebra of invariance of its in Lie sense, carry out the symmetry reduction and seek for a number of exact group-invariant solutions of this equation.
Revised:  For the resulting equation, we study the group-theoretic properties, namely, we find the maximal algebra of invariance of its in Lie sense, carry out the symmetry reduction and seek for a number of exact group-invariant solutions of this equation.
Edit intent: clarity
Original:  For the last equation, we study the group-theoretic properties, namely, we find the maximal algebra of invariance of its in Lie sense, carry out the symmetry reduction and seek for a number of exact group-invariant solutions of this equation.
Revised:  For the last equation, we study the group-theoretic properties, namely, we find the maximal algebra of invariance of its in Lie sense, carry out the symmetry reduction and seek for a number of exact group-invariant solutions of the equation.
Edit intent: clarity
Original: In this paper, we investigate the implication of non-stationary market microstructure noise to integrated volatility estimation, provide statistical tools to test stationarity and non-stationarity in market microstructure noise , and discuss how to measure liquidity risk using high frequency financial data.
Revised: In this paper, we provide non-parametric statistical tools to test stationarity and non-stationarity in market microstructure noise , and discuss how to measure liquidity risk using high frequency financial data.
Edit intent: clarity
Original: In this paper, we investigate the implication of non-stationary market microstructure noise to integrated volatility estimation, provide statistical tools to test stationarity and non-stationarity in market microstructure noise , and discuss how to measure liquidity risk using high frequency financial data.
Revised: In this paper, we investigate the implication of non-stationary market microstructure noise to integrated volatility estimation, provide statistical tools to test stationarity of microstructure noise in general hidden Ito semimartingales , and discuss how to measure liquidity risk using high frequency financial data.
Edit intent: meaning-changed
Original:  In particular, we discuss the impact of non-stationary microstructure noise on TSRV (Two-Scale Realized Variance) estimator , and design three test statistics by exploiting the edge effectsand asymptotic approximation.
Revised:  In particular, we investigate the impact of non-stationary microstructure noise on TSRV (Two-Scale Realized Variance) estimator , and design three test statistics by exploiting the edge effectsand asymptotic approximation.
Edit intent: clarity
Original:  In particular, we discuss the impact of non-stationary microstructure noise on TSRV (Two-Scale Realized Variance) estimator , and design three test statistics by exploiting the edge effectsand asymptotic approximation.
Revised:  In particular, we discuss the impact of non-stationary microstructure noise on some volatility estimators , and design three test statistics by exploiting the edge effectsand asymptotic approximation.
Edit intent: clarity
Original:  In particular, we discuss the impact of non-stationary microstructure noise on TSRV (Two-Scale Realized Variance) estimator , and design three test statistics by exploiting the edge effectsand asymptotic approximation.
Revised:  In particular, we discuss the impact of non-stationary microstructure noise on TSRV (Two-Scale Realized Variance) estimator , and design three complementary tests by exploiting edge effects, information aggregation of local estimates and high-frequency asymptotic approximation.
Edit intent: meaning-changed
Original:  The asymptotic distributions of these test statistics are provided under both stationary and non-stationary noise assumptionsrespectively, and we empirically measure aggregate liquidity risks by these test statistics from 2006 to 2013.
Revised:  The asymptotic distributions of these tests are available under both stationary and non-stationary noise assumptionsrespectively, and we empirically measure aggregate liquidity risks by these test statistics from 2006 to 2013.
Edit intent: clarity
Original:  The asymptotic distributions of these test statistics are provided under both stationary and non-stationary noise assumptionsrespectively, and we empirically measure aggregate liquidity risks by these test statistics from 2006 to 2013.
Revised:  The asymptotic distributions of these test statistics are provided under both stationary and non-stationary assumptions, thereby enable us to conservatively control type-I errors and meanwhile ensure the proposed tests enjoy the asymptotically optimal statistical power. Besides it also enables us to empirically measure aggregate liquidity risks by these test statistics from 2006 to 2013.
Edit intent: meaning-changed
Original:  The asymptotic distributions of these test statistics are provided under both stationary and non-stationary noise assumptionsrespectively, and we empirically measure aggregate liquidity risks by these test statistics from 2006 to 2013.
Revised:  The asymptotic distributions of these test statistics are provided under both stationary and non-stationary noise assumptionsrespectively, and we empirically measure aggregate liquidity risks by these test statistics .
Edit intent: coherence
Original:  An auxiliary consequencereveals that the proliferation of networks as a now-common theoretical model for large-scale systems  in concert with the use of transfer-like entropies  has shoehorned dyadic relationships into our structural interpretation of URLanization and behavior of complex systems , despite the occurrence of polyadic dependencies.
Revised:  We also address an auxiliary consequence: The proliferation of networks as a now-common theoretical model for large-scale systems in concert with the use of transfer-like entropies has shoehorned dyadic relationships into our structural interpretation of URLanization and behavior of complex systems , despite the occurrence of polyadic dependencies.
Edit intent: clarity
Original:  An auxiliary consequencereveals that the proliferation of networks as a now-common theoretical model for large-scale systems  in concert with the use of transfer-like entropies  has shoehorned dyadic relationships into our structural interpretation of URLanization and behavior of complex systems , despite the occurrence of polyadic dependencies.
Revised:  An auxiliary consequencereveals that the proliferation of networks as a now-common theoretical model for large-scale systems , in concert with the use of transfer-like entropies has shoehorned dyadic relationships into our structural interpretation of URLanization and behavior of complex systems , despite the occurrence of polyadic dependencies.
Edit intent: fluency
Original:  An auxiliary consequencereveals that the proliferation of networks as a now-common theoretical model for large-scale systems  in concert with the use of transfer-like entropies  has shoehorned dyadic relationships into our structural interpretation of URLanization and behavior of complex systems , despite the occurrence of polyadic dependencies.
Revised:  An auxiliary consequencereveals that the proliferation of networks as a now-common theoretical model for large-scale systems in concert with the use of transfer-like entropies , has shoehorned dyadic relationships into our structural interpretation of URLanization and behavior of complex systems , despite the occurrence of polyadic dependencies.
Edit intent: fluency
Original:  An auxiliary consequencereveals that the proliferation of networks as a now-common theoretical model for large-scale systems  in concert with the use of transfer-like entropies  has shoehorned dyadic relationships into our structural interpretation of URLanization and behavior of complex systems , despite the occurrence of polyadic dependencies.
Revised:  An auxiliary consequencereveals that the proliferation of networks as a now-common theoretical model for large-scale systems in concert with the use of transfer-like entropies has shoehorned dyadic relationships into our structural interpretation of URLanization and behavior of complex systems . This interpretation thus fails to include the effects of polyadic dependencies.
Edit intent: clarity
Original:  It is first established that checking the sign-stability of a Metzler sign-matrix can be either characterized in terms of the Hurwitz stability of the unit sign-matrix in the corresponding qualitative class, or in terms of the acyclicity of the graph associated with the sign-pattern . Similar results are obtained for the case of  block-matrices and  mixed-matrices, the latter containing both sign patterns and fixed real entries.
Revised:  It is first established that checking the sign-stability of a Metzler sign-matrix can be either characterized in terms of the Hurwitz stability of the unit sign-matrix in the corresponding qualitative class, or in terms the negativity of the diagonal elements of the Metzler sign-matrix and the acyclicity of the graph associated with the sign-pattern . Similar results are obtained for the case of block-matrices and mixed-matrices, the latter containing both sign patterns and fixed real entries.
Edit intent: meaning-changed
Original:  It is first established that checking the sign-stability of a Metzler sign-matrix can be either characterized in terms of the Hurwitz stability of the unit sign-matrix in the corresponding qualitative class, or in terms of the acyclicity of the graph associated with the sign-pattern . Similar results are obtained for the case of  block-matrices and  mixed-matrices, the latter containing both sign patterns and fixed real entries.
Revised:  It is first established that checking the sign-stability of a Metzler sign-matrix can be either characterized in terms of the Hurwitz stability of the unit sign-matrix in the corresponding qualitative class, or in terms of the acyclicity of the associated directed graph . Similar results are obtained for the case of block-matrices and mixed-matrices, the latter containing both sign patterns and fixed real entries.
Edit intent: clarity
Original:  It is first established that checking the sign-stability of a Metzler sign-matrix can be either characterized in terms of the Hurwitz stability of the unit sign-matrix in the corresponding qualitative class, or in terms of the acyclicity of the graph associated with the sign-pattern . Similar results are obtained for the case of  block-matrices and  mixed-matrices, the latter containing both sign patterns and fixed real entries.
Revised:  It is first established that checking the sign-stability of a Metzler sign-matrix can be either characterized in terms of the Hurwitz stability of the unit sign-matrix in the corresponding qualitative class, or in terms of the acyclicity of the graph associated with the sign-pattern . Similar results are obtained for the case of Metzler block-matrices and mixed-matrices, the latter containing both sign patterns and fixed real entries.
Edit intent: fluency
Original:  It is first established that checking the sign-stability of a Metzler sign-matrix can be either characterized in terms of the Hurwitz stability of the unit sign-matrix in the corresponding qualitative class, or in terms of the acyclicity of the graph associated with the sign-pattern . Similar results are obtained for the case of  block-matrices and  mixed-matrices, the latter containing both sign patterns and fixed real entries.
Revised:  It is first established that checking the sign-stability of a Metzler sign-matrix can be either characterized in terms of the Hurwitz stability of the unit sign-matrix in the corresponding qualitative class, or in terms of the acyclicity of the graph associated with the sign-pattern . Similar results are obtained for the case of block-matrices and Metzler mixed-matrices, the latter containing both sign patterns and fixed real entries.
Edit intent: fluency