wanyu/IteraTeR_full_sent huggingface dataset:
Original:  When X is a semi-martingale with absolutely continuous characteristics, we derive necessary and sufficient conditions for the existence of the Laplace exponent of I\_t, and also the sufficient conditions of finiteness of the Mellin transform {\bf E}( I \_t^{\alpha \alpha\in\mathbb{R} . We give a recurrent integral equations for this Mellin transform .
Revised:  When X is a semi-martingale with absolutely continuous characteristics, we derive recurrent integral equations for Mellin transform {\bf E}( I \_t^{\alpha \alpha\in\mathbb{R} . We give a recurrent integral equations for this Mellin transform .
Edit intent: clarity
Original:  When X is a semi-martingale with absolutely continuous characteristics, we derive necessary and sufficient conditions for the existence of the Laplace exponent of I\_t, and also the sufficient conditions of finiteness of the Mellin transform {\bf E}( I \_t^{\alpha \alpha\in\mathbb{R} . We give a recurrent integral equations for this Mellin transform .
Revised:  When X is a semi-martingale with absolutely continuous characteristics, we derive necessary and sufficient conditions for the existence of the Laplace exponent of I\_t, and also the sufficient conditions of finiteness of the Mellin transform {\bf E}( I _t^{\alpha \alpha\in\mathbb{R} . We give a recurrent integral equations for this Mellin transform .
Edit intent: fluency
Original:  When X is a semi-martingale with absolutely continuous characteristics, we derive necessary and sufficient conditions for the existence of the Laplace exponent of I\_t, and also the sufficient conditions of finiteness of the Mellin transform {\bf E}( I \_t^{\alpha \alpha\in\mathbb{R} . We give a recurrent integral equations for this Mellin transform .
Revised:  When X is a semi-martingale with absolutely continuous characteristics, we derive necessary and sufficient conditions for the existence of the Laplace exponent of I\_t, and also the sufficient conditions of finiteness of the Mellin transform {\bf E}( I \_t^{\alpha \alpha\in\mathbb{R} , of the integral functional I_t .
Edit intent: clarity
Original:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD }  . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Revised:  We present also the corresponding results for the exponential functionals of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD } . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Edit intent: clarity
Original:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD }  . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Revised:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in }\hspace{0pt}%DIFAUXCMD } . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Edit intent: coherence
Original:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD }  . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Revised:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD } the paper of Bertoin, Yor (2005) . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Edit intent: meaning-changed
Original:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD }  . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Revised:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD } . In particular, we obtain an explicit formula for the moments of I \infty , and we precise the exact number of finite moments of I \_ \infty .
Edit intent: coherence
Original:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD }  . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Revised:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD } . In particular, we obtain an explicit formula for the moments of I \_t and I\_ _t and I_{\infty , and we precise the exact number of finite moments of I \_ \infty .
Edit intent: meaning-changed
Original:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD }  . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Revised:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD } . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \infty .
Edit intent: fluency
Original:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD }  . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ \infty .
Revised:  We present also the corresponding results for the exponentials of Levy processes, which hold under less restrictive conditions then in \mbox{%DIFAUXCMD \cite{BY}\hspace{0pt}%DIFAUXCMD } . In particular, we obtain an explicit formula for the moments of I \_t and I\_ \infty , and we precise the exact number of finite moments of I \_ _{\infty .
Edit intent: fluency
Original:  We use the probability density function (PDF) of turn angles, measured on tumbling E. coli wild-type {\it  , to build a Langevin equation for the deflection of the bacterial body swimming in isotropic media.
Revised:  We use the probability density function (PDF) of turn angles, measured on tumbling wild-type {\it , to build a Langevin equation for the deflection of the bacterial body swimming in isotropic media.
Edit intent: clarity
Original:  We use the probability density function (PDF) of turn angles, measured on tumbling E. coli wild-type {\it  , to build a Langevin equation for the deflection of the bacterial body swimming in isotropic media.
Revised:  We use the probability density function (PDF) of turn angles, measured on tumbling E. coli wild-type {\it E. coli , to build a Langevin equation for the deflection of the bacterial body swimming in isotropic media.
Edit intent: meaning-changed
Original:  This model is  also able to explain very satisfactory all available statistical experimental data, such as PDFs and average values of turning angles and times, of both run and tumble motions.
Revised:  This model is the bacterium during the run or tumble movements, through a control parameter that can be tuned also able to explain very satisfactory all available statistical experimental data, such as PDFs and average values of turning angles and times, of both run and tumble motions.
Edit intent: meaning-changed
Original:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{ tasks such as assignments where the same problem sets are solved by many students.
Revised:  The technique supports the detection of plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{ tasks such as assignments where the same problem sets are solved by many students.
Edit intent: fluency
Original:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{ tasks such as assignments where the same problem sets are solved by many students.
Revised:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{unique \emph{ tasks such as assignments where the same problem sets are solved by many students.
Edit intent: meaning-changed
Original:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{ tasks such as assignments where the same problem sets are solved by many students.
Revised:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ tasks, such as theses and\emph{ tasks such as assignments where the same problem sets are solved by many students.
Edit intent: coherence
Original:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{ tasks such as assignments where the same problem sets are solved by many students.
Revised:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{equal tasks such as assignments where the same problem sets are solved by many students.
Edit intent: clarity
Original:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{ tasks such as assignments where the same problem sets are solved by many students.
Revised:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{ tasks such as assignments for which the same problem sets are solved by many students.
Edit intent: clarity
Original:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{ tasks such as assignments where the same problem sets are solved by many students. Evaluation focuses on the latter case using collected logs by an interactive development environment (IDE) from more than 60 students for three programming assignments.
Revised:  The technique supports detecting plagiarism for digital outcomes stemming from unique taskssuch as thesis as well as equal\emph{ \emph{ tasks such as assignments where the same problem sets are solved by multiple students. Focusing on the latter case using collected logs by an interactive development environment (IDE) from more than 60 students for three programming assignments.
Edit intent: coherence
Original:  Combining this finding with the knowledge of protein folding, we derive a correspondence between protein fitness and folding free energy, i.e., 4N_e m (1 - 1/(2N)) and -\Delta G_{ND}/k_B T_s  , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is the effective temperatureof natural selection.
Revised:  On the other hand, the probability distribution of sequences with maximum entropy that satisfies a given amino acid composition at each site and a given pairwise amino acid frequency at each site pair is a Boltzmann distribution with \exp( - 1/(2N)) and -\Delta G_{ND}/k_B T_s , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is the effective temperatureof natural selection.
Edit intent: meaning-changed
Original:  Combining this finding with the knowledge of protein folding, we derive a correspondence between protein fitness and folding free energy, i.e., 4N_e m (1 - 1/(2N)) and -\Delta G_{ND}/k_B T_s  , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is the effective temperatureof natural selection.
Revised:  Combining this finding with the knowledge of protein folding, we derive a correspondence between protein fitness and folding free energy, i.e., 4N_e m (1 - \psi_N), where \psi_N is represented as the sum of one body and pairwise potentials. A protein folding theory indicates that homologous sequences obey a canonical ensemble characterized by \exp( -\Delta G_{ND}/k_B T_s , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is the effective temperatureof natural selection.
Edit intent: meaning-changed
Original:  Combining this finding with the knowledge of protein folding, we derive a correspondence between protein fitness and folding free energy, i.e., 4N_e m (1 - 1/(2N)) and -\Delta G_{ND}/k_B T_s  , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is the effective temperatureof natural selection.
Revised:  Combining this finding with the knowledge of protein folding, we derive a correspondence between protein fitness and folding free energy, i.e., 4N_e m (1 - 1/(2N)) and -\Delta G_{ND}/k_B T_s ) or by \exp(- G_{N , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is the effective temperatureof natural selection.
Edit intent: meaning-changed
Original:  Combining this finding with the knowledge of protein folding, we derive a correspondence between protein fitness and folding free energy, i.e., 4N_e m (1 - 1/(2N)) and -\Delta G_{ND}/k_B T_s  , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is the effective temperatureof natural selection. In the preceding manuscript, we analyzed dimensionless free energy changes, \Delta \psi_N (= \Delta G_N /  k_B T_s ), due to single nucleotide mutations, for which the total interaction \psi_N of a sequence was estimated from a multiple sequence alignment . Based on this analyis, we study the equilibrium state of protein stability in a monoclonal approximation, in which protein evolution proceeds with single amino acid substitutions fixed at a time in a population.
Revised:  Combining this finding with the knowledge of protein folding, we derive a correspondence between protein fitness and folding free energy, i.e., 4N_e m (1 - 1/(2N)) and -\Delta G_{ND}/k_B T_s , where \Delta G_{ND} \equiv G_N - G_D, G_N and G_D are the native and denatured free energies, and T_s is selective temperature. Thus, 4N_e m (1 - 1 / k_B T_s ), due to single nucleotide mutations, for which the total interaction \psi_N of a sequence was estimated from a multiple sequence alignment . Based on this analyis, we study the equilibrium state of protein stability in a monoclonal approximation, in which protein evolution proceeds with single amino acid substitutions fixed at a time in a population.
Edit intent: meaning-changed
Original:  In the preceding manuscript, we analyzed dimensionless free energy changes, \Delta \psi_N (= \Delta G_N /  k_B T_s ), due to single nucleotide mutations, for which the total interaction \psi_N of a sequence was estimated from a multiple sequence alignment . Based on this analyis, we study the equilibrium state of protein stability in a monoclonal approximation, in which protein evolution proceeds with single amino acid substitutions fixed at a time in a population.
Revised:  In the preceding manuscript, we analyzed dimensionless free energy changes, \Delta \psi_N (= \Delta G_N / (2N)), -\Delta G_{ND k_B T_s ), due to single nucleotide mutations, for which the total interaction \psi_N of a sequence was estimated from a multiple sequence alignment . Based on this analyis, we study the equilibrium state of protein stability in a monoclonal approximation, in which protein evolution proceeds with single amino acid substitutions fixed at a time in a population.
Edit intent: meaning-changed
Original:  In the preceding manuscript, we analyzed dimensionless free energy changes, \Delta \psi_N (= \Delta G_N /  k_B T_s ), due to single nucleotide mutations, for which the total interaction \psi_N of a sequence was estimated from a multiple sequence alignment . Based on this analyis, we study the equilibrium state of protein stability in a monoclonal approximation, in which protein evolution proceeds with single amino acid substitutions fixed at a time in a population.
Revised:  In the preceding manuscript, we analyzed dimensionless free energy changes, \Delta \psi_N (= \Delta G_N / k_B T_s , and -\Delta \psi_{ND . Based on this analyis, we study the equilibrium state of protein stability in a monoclonal approximation, in which protein evolution proceeds with single amino acid substitutions fixed at a time in a population.
Edit intent: coherence
Original:  In the preceding manuscript, we analyzed dimensionless free energy changes, \Delta \psi_N (= \Delta G_N /  k_B T_s ), due to single nucleotide mutations, for which the total interaction \psi_N of a sequence was estimated from a multiple sequence alignment . Based on this analyis, we study the equilibrium state of protein stability in a monoclonal approximation, in which protein evolution proceeds with single amino acid substitutions fixed at a time in a population. The ensemble of proteins attains the equilibrium, \psi_N= \psi_N ^{eq, where the average of \Delta \psi}  _{ N } over fixed mutants is equal to zero.
Revised:  In the preceding manuscript, we analyzed dimensionless free energy changes, \Delta \psi_N (= \Delta G_N / k_B T_s ), due to single nucleotide mutations, for which the total interaction \psi_N of a sequence was estimated from a multiple sequence alignment . Based on , where the average of \Delta \psi} _{ N } over fixed mutants is equal to zero.
Edit intent: meaning-changed
Original:  The ensemble of proteins attains the equilibrium, \psi_N= \psi_N ^{eq, where the average of \Delta \psi}  _{ N } over fixed mutants is equal to zero.
Revised:  The ensemble of proteins attains the equilibrium, \psi_N= \psi_N ^{eq, where the average of \Delta \psi} the analysis of the changes (\Delta \psi_N) of \psi_N due to single nucleotide nonsynonymous substitutions, T_s, and then glass transition temperature T_g, and \Delta G _{ N } over fixed mutants is equal to zero.
Edit intent: meaning-changed
Original:  The ensemble of proteins attains the equilibrium, \psi_N= \psi_N ^{eq, where the average of \Delta \psi}  _{ N } over fixed mutants is equal to zero.
Revised:  The ensemble of proteins attains the equilibrium, \psi_N= \psi_N ^{eq, where the average of \Delta \psi} _{ ND } over fixed mutants is equal to zero.
Edit intent: meaning-changed
Original:  The ensemble of proteins attains the equilibrium, \psi_N= \psi_N ^{eq, where the average of \Delta \psi}  _{ N } over fixed mutants is equal to zero. Approximating the probability density function (PDF) of \Delta \psi_N by a log-normal distribution, the PDF of \Delta \psi _{N (\simeq \Delta\Delta \psi_{ND}) in fixed mutants is estimated.
Revised:  The ensemble of proteins attains the equilibrium, \psi_N= \psi_N ^{eq, where the average of \Delta \psi} _{ N } are estimated with reasonable values for 14 protein domains. In addition, approximating the probability density function (PDF) of \Delta \psi_N by a log-normal distribution, the PDF of \Delta \psi _{N (\simeq \Delta\Delta \psi_{ND}) in fixed mutants is estimated.
Edit intent: meaning-changed
Original:  Approximating the probability density function (PDF) of \Delta \psi_N by a log-normal distribution, the PDF of \Delta \psi _{N (\simeq \Delta\Delta \psi_{ND}) in fixed mutants is estimated.
Revised:  Approximating the probability density function (PDF) of \Delta \psi_N by a log-normal distribution, PDFs of \Delta \psi _{N (\simeq \Delta\Delta \psi_{ND}) in fixed mutants is estimated.
Edit intent: fluency
Original:  Approximating the probability density function (PDF) of \Delta \psi_N by a log-normal distribution, the PDF of \Delta \psi _{N (\simeq \Delta\Delta \psi_{ND}) in fixed mutants is estimated.
Revised:  Approximating the probability density function (PDF) of \Delta \psi_N by a log-normal distribution, the PDF of \Delta \psi (\simeq \Delta\Delta \psi_{ND}) in fixed mutants is estimated.
Edit intent: fluency
Original:  The PDFs of }  K_a/K_s, which is the ratio of nonsynonymous to synonymous substitution rate per site, at equilibrium confirm that T_s negatively correlates with the amino acid substitution rate.
Revised:  The PDFs of } _N and K_a/K_s, which is the ratio of nonsynonymous to synonymous substitution rate per site, at equilibrium confirm that T_s negatively correlates with the amino acid substitution rate.
Edit intent: meaning-changed
Original:  The PDFs of }  K_a/K_s, which is the ratio of nonsynonymous to synonymous substitution rate per site, at equilibrium confirm that T_s negatively correlates with the amino acid substitution rate.
Revised:  The PDFs of } K_a/K_s, which is the ratio of nonsynonymous to synonymous substitution rate per site, in all and in fixed mutants are estimated. It is confirmed that T_s negatively correlates with the amino acid substitution rate.
Edit intent: meaning-changed
Original:  The PDFs of }  K_a/K_s, which is the ratio of nonsynonymous to synonymous substitution rate per site, at equilibrium confirm that T_s negatively correlates with the amino acid substitution rate.
Revised:  The PDFs of } K_a/K_s, which is the ratio of nonsynonymous to synonymous substitution rate per site, at equilibrium confirm that T_s negatively correlates with the average of K_a/K_s. Stabilizing mutations are significantly fixed by positive selection, and balance with destabilizing mutations fixed by random drift.
Edit intent: meaning-changed
Original:  However, due to increasing amounts of heterogeneous real-world network data with nodes and edges of different types, we extend three recent state-of-the-art homogeneous NA methods, WAVE, MAGNA++, and SANA, to allow for heterogeneous NA for the first time.
Revised:  Due to increasing amounts of heterogeneous real-world network data with nodes and edges of different types, we extend three recent state-of-the-art homogeneous NA methods, WAVE, MAGNA++, and SANA, to allow for heterogeneous NA for the first time.
Edit intent: coherence
Original:  However, due to increasing amounts of heterogeneous real-world network data with nodes and edges of different types, we extend three recent state-of-the-art homogeneous NA methods, WAVE, MAGNA++, and SANA, to allow for heterogeneous NA for the first time.
Revised:  However, due to increasing amounts of heterogeneous network data with nodes and edges of different types, we extend three recent state-of-the-art homogeneous NA methods, WAVE, MAGNA++, and SANA, to allow for heterogeneous NA for the first time.
Edit intent: clarity