wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Looking at the ChAS of these epigenomic features in the interaction networks, we find Polycomb Group proteins and associated histone marks to be the most assortative factors . Remarkably,  we observe higher ChAS of the actively elongating form of RNA Polymerase 2 compared to the inactive forms in interactions between promoters and other distal elements, suggesting an important role for active elongation in promoter-enhancer contacts. CONCLUSIONS: Our method can be used to compare the association of epigenomic features to different type of genomic contacts. Furthermore, it facilitates the comparison of any number of chromatin interaction datasets in the context of the corresponding epigenomic landscape .
Revised:  Looking at the ChAS of these epigenomic features in the interaction networks, we find Polycomb Group proteins and associated histone marks to be the most assortative factors . Remarkably, we observe higher ChAS of the actively elongating form of RNA Polymerase 2 compared to the inactive forms in interactions between promoters and other elements. Conclusions: Contacts amongst promoters and between promoters and other elements have different characteristic epigenomic features. Using ChAs we identify a possible role of the elongating form of RNAPII in enhancer activity. Our approach facilitates the study of multiple genome-wide epigenomic profiles, considering network topology and allowing for the comparison of any number of chromatin interaction datasets in the context of the corresponding epigenomic landscape .
Edit intent: meaning-changed
Original:  Experimental results show that no individual algorithm outperforms all others in all cases, and that the challenging and non-trivial nature of network inference is evident in the struggle of some of the algorithms to turn in a performance that is better than random guesswork.
Revised:  Experimental results show that no individual algorithm outperforms all others in all cases, and that the challenging and non-trivial nature of network inference is evident in the struggle of some of the algorithms to turn in a performance that is superior to random guesswork.
Edit intent: clarity
Original: Culture impacts every aspect of society. This paper studies the impact of one of the most important dimensions of culture -- the tension between individualism and collectivism -- on some of the most important aspects of society -- size and wealth. We present a mathematical model of the consequences of individualism and collectivism and derive implications of the model for the size and wealth of the society and for the wealth distribution within the society. Our model provides a useful lens for examining some empirical data; simple regressions suggest that our model explains a significant portion of the data .
Revised: This paper presents a dynamic model to study the impact on the economic outcomes in different societies during the Malthusian Era of individualism (time spent working alone) and collectivism (complementary time spent working with others). The model is driven by opposing forces: a greater degree of collectivism provides a higher safety net for low quality workers but a greater degree of individualism allows high quality workers to leave larger bequests. The model suggests that more individualistic societies display smaller populations, greater per capita income and greater income inequality. Some (limited) historical evidence is consistent with these predictions .
Edit intent: meaning-changed
Original: This note gives a simple construction of the pathwise stochastic integral \int_0^t\phi d\omega for a continuous integrand \phi and continuous price path \omega  .
Revised: This note gives a simple construction of the pathwise stochastic integral \int_0^t\phi d\omega for a continuous integrand \phi and continuous price path \omega as integrator. A basic version of It\^o's lemma shows that this definition agrees with F\"ollmer's .
Edit intent: meaning-changed
Original: This note gives a simple construction of the pathwise stochastic integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator.
Revised: This note gives a simple construction of the pathwise It\^o integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator.
Edit intent: meaning-changed
Original:  A basic version of It\^o's lemma shows that this definition agrees with F\"ollmer's  .
Revised:  A basic version of It\^o's lemma shows that this definition agrees with F\"ollmer's . Finally, we show the existence of \int_0^t\phi d\omega for a c\`adl\`ag \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded by 1 in absolute value .
Edit intent: meaning-changed
Original: This note gives a simple construction of the pathwise It\^o integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator.
Revised: This paper gives a simple construction of the pathwise It\^o integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator.
Edit intent: clarity
Original:   A basic version of It\^o's lemma shows that this definition agrees with F\"ollmer's.
Revised:  The definition is pathwise in that neither \phi nor \omega are assumed to be paths of stochastic processes, and the It\^o integral exists almost surely in a non-probabilistic financial sense. A basic version of It\^o's lemma shows that this definition agrees with F\"ollmer's.
Edit intent: meaning-changed
Original:  Finally, we  show the existence of \int_0^t\phi d\omega for a c\`adl\`ag  \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded by 1 in absolute value .
Revised:  Finally, we propose a tentative definition and show the existence of \int_0^t\phi d\omega for a c\`adl\`ag \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded by 1 in absolute value .
Edit intent: meaning-changed
Original:  Finally, we  show the existence of \int_0^t\phi d\omega for a c\`adl\`ag  \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded by 1 in absolute value .
Revised:  Finally, we show the existence of \int_0^t\phi d\omega for a c\`adl\`ag integrand \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded by 1 in absolute value .
Edit intent: meaning-changed
Original:  Finally, we  show the existence of \int_0^t\phi d\omega for a c\`adl\`ag  \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded by 1 in absolute value .
Revised:  Finally, we show the existence of \int_0^t\phi d\omega for a c\`adl\`ag \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded in a predictable manner .
Edit intent: meaning-changed
Original: This paper gives a simple construction of the pathwise It\^o integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator .
Revised: This paper gives several simple constructions of the pathwise It\^o integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator .
Edit intent: meaning-changed
Original: This paper gives a simple construction of the pathwise It\^o integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator .
Revised: This paper gives a simple construction of the pathwise Ito integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator .
Edit intent: fluency
Original: This paper gives a simple construction of the pathwise It\^o integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator .
Revised: This paper gives a simple construction of the pathwise It\^o integral \int_0^t\phi d\omega for an integrand \phi and a price path \omega as integrator .
Edit intent: clarity
Original: This paper gives a simple construction of the pathwise It\^o integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator . The definition is pathwise in that neither \phi nor \omega are assumed to be paths of stochastic processes, and the It\^o integral exists almost surely in a non-probabilistic financial sense.
Revised: This paper gives a simple construction of the pathwise It\^o integral \int_0^t\phi d\omega for a continuous integrand \phi whose variation index is finite and a continuous price path \omega as integrator , with \phi and \omega satisfying various topological and analytical conditions. The definitions are purely pathwise in that neither \phi nor \omega are assumed to be paths of stochastic processes, and the It\^o integral exists almost surely in a non-probabilistic financial sense.
Edit intent: meaning-changed
Original:  A basic version of It\^o's lemma shows that our definition of the It\^o integral agrees with F\"ollmer's. Finally, we propose a tentative definition and show the existence of \int_0^t\phi d\omega for a c\`adl\`ag integrand \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded in a predictable manner.
Revised:  For example, one of the results shows the existence of \int_0^t\phi d\omega for a c\`adl\`ag integrand \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded in a predictable manner.
Edit intent: clarity
Original:  Finally, we propose a tentative definition and show the existence of \int_0^t\phi d\omega for a c\`adl\`ag integrand \phi with a finite variation index and a c\`adl\`ag integrator \omega with jumps bounded in a predictable manner.
Revised:  Finally, we propose a tentative definition and show the existence of \int_0^t\phi d\omega for a cadlag integrand \phi and a cadlag integrator \omega with jumps bounded in a predictable manner.
Edit intent: clarity
Original:  Transfer RNA (tRNA) molecules, each species of which is "charged" with a specific amino acid, enters the ribosome and participates in the reading of the codon by the ribosome. Both mis-reading of mRNA codon and prior mis-charging of a tRNA can lead to "mis-sense" error, i. e,. erroneous substitution of a correct amino acid monomer by an incorrect one during the synthesis of a protein.
Revised:  We develop a stochastic kinetic model that captures the possibilities of mis-reading of mRNA codon and prior mis-charging of a tRNA can lead to "mis-sense" error, i. e,. erroneous substitution of a correct amino acid monomer by an incorrect one during the synthesis of a protein.
Edit intent: clarity
Original:  Both mis-reading of mRNA codon and prior mis-charging of a tRNA can lead to "mis-sense" error, i. e,. erroneous substitution of a correct amino acid monomer by an incorrect one during the synthesis of a protein. We develop a theoretical model of protein synthesis that allows for both types of contributions to the "mis-sense" error. We report exact analytical formulae for several quantities that characterize the interplay of mis-charging of tRNA and mis-reading of mRNA. The average rate of elongation of a protein is given by a generalized Michaelis-Menten-like formula.
Revised:  Both mis-reading of mRNA codon and prior mis-charging of a tRNA . By a combination of analytical and numerical methods we obtain the distribution of the times taken for incorporation of the successive amino acids in the growing protein in this mathematical model. The corresponding exact analytical expression for the average rate of elongation of a protein is given by a generalized Michaelis-Menten-like formula.
Edit intent: clarity
Original:  These formulae will be very useful in future in analyzing the data collected during experimental investigations of this phenomenon{\it   .
Revised:  These formulae will be very useful in future in analyzing the data collected during experimental investigations of this phenomenon{\it for the average rate of enzymatic reactions. This generalized Michaelis-Menten-like formula (and the exact analytical expressions for a few other quantities) that we report here display the interplay of four different branched pathways corresponding to selection of four different types of tRNA .
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Original:   The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat , but hyperbolic .
Revised:  Trade distances, which are based on a gravity model predicting the existence of significant trade channels, are such that the closer countries are in trade space, the greater their chance of becoming connected. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat , but hyperbolic .
Edit intent: meaning-changed
Original:  In this situation, ordinary macroscopic-level fluctuations can be overwhelmed by non-negligible large fluctuations, which results in drastic changes in chemical-reaction dynamics and the resulting statistics compared to those observed under a large system size with a large number of molecules.
Revised:  In this situation, ordinary macroscopic-level fluctuations can be overwhelmed by non-negligible large fluctuations, which results in drastic changes in chemical-reaction dynamics and statistics compared to those observed under a large system size with a large number of molecules.
Edit intent: clarity
Original:  In this situation, ordinary macroscopic-level fluctuations can be overwhelmed by non-negligible large fluctuations, which results in drastic changes in chemical-reaction dynamics and the resulting statistics compared to those observed under a large system size with a large number of molecules. Thus, analyses based on the average behavior of molecules valid at a macroscopic level (i.e., with a large-number limit) will not necessarily hold when considering a small size system containing a much smaller number of molecules  .
Revised:  In this situation, ordinary macroscopic-level fluctuations can be overwhelmed by non-negligible large fluctuations, which results in drastic changes in chemical-reaction dynamics and the resulting statistics compared to those observed under a macroscopic system (i.e., with a large-number limit) will not necessarily hold when considering a small size system containing a much smaller number of molecules .
Edit intent: coherence
Original:  Thus, analyses based on the average behavior of molecules valid at a macroscopic level (i.e., with a large-number limit) will not necessarily hold when considering a small size system containing a much smaller number of molecules  .
Revised:  Thus, analyses based on the average behavior of molecules valid at a macroscopic level (i.e., with a large-number limit) will not necessarily hold when considering a small size system containing a much smaller number of molecules ) .
Edit intent: fluency
Original:  In order to understand how salient changes emerge from fluctuations in molecular number, we here quantitatively define small-number effect by focusing on a "mesoscopic" level, in which the concentration distribution is distinguishable both from micro- and macroscopic ones, and propose a criterion for determining whether or not such an effect can emerge in a given chemical reaction network.
Revised:  In order to understand how salient changes emerge from fluctuations in molecular number, we here quantitatively define small-number effect by focusing on a `mesoscopic' level, in which the concentration distribution is distinguishable both from micro- and macroscopic ones, and propose a criterion for determining whether or not such an effect can emerge in a given chemical reaction network.
Edit intent: fluency
Original:  Using the proposed criterion, we systematically derive a list of motifs of chemical reaction networks that can show small-number effects, which includes motifs showing emergence of the power law and the bimodal distribution observable in a mesoscopic regime with respect to molecule number . Motif analysis revealed that autocatalytic reactions are essential for the emergence of the small-number effect .
Revised:  Using the proposed criterion, we systematically derive a list of motifs of chemical reaction networks that can show small-number effects, which includes motifs showing emergence of the power law and the bimodal distribution observable in a mesoscopic regime with respect to molecule number .
Edit intent: coherence
Original:  We investigate whether the model is able to consistently reproduce the implied volatility of FX cross rates , once the single components are calibrated to univariate shifted lognormal mixture dynamics models  .
Revised:  We investigate whether the model is able to consistently reproduce the implied volatility of FX cross rates , once the single components are calibrated to univariate shifted lognormal mixture dynamics models . We consider in particular the case of the Chinese renminbi FX rate, showing that the shifted MVMD model correctly recovers the CNY/EUR smile given the EUR/USD smile and the USD/CNY smile, thus highlighting that the model can also work as an arbitrage free volatility smile extrapolation tool for cross currencies that may not be liquid or fully observable .
Edit intent: meaning-changed
Original:  These dynamical systems closely resemble a Hamiltonian system in \Bbb R^{2n}, but with the canonical equation for one of the variables in each conjugate pair rescaled by a ratio of the diffusion coefficients. The ratio therefore measures the obstruction preventing a two-component feedback loop from being Hamiltonian (where the ratio equals one) .
Revised:  These dynamical systems closely resemble a Hamiltonian system in \Bbb 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. The Turing instability parameter therefore measures the obstruction preventing a two-component feedback loop from being Hamiltonian (where the ratio equals one) .
Edit intent: clarity
Original:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their biological interpretation motivates new problems in Floer theory, mirror symmetry, and the study of \Bbb D-K\"{a}hler manifolds  .
Revised:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their biological interpretation motivates new problems in Floer theory, mirror symmetry, and the study of \Bbb D-K\"{a}hler manifolds . Since many questions in complex network theory can be translated into the topological setting, this paper therefore serves to bring a selection of ideas from biology to pure mathematics .
Edit intent: meaning-changed
Original: Two-component feedback loops (TCFLs) are dynamical systems arising in mathematical biology that describe the time evolution of pairs of interacting molecules using complex network theory. These dynamical systems closely resemble a Hamiltonian system in %DIFDELCMD < \Bbb %%% 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 a Hamiltonian system in %DIFDELCMD < \Bbb %%% 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: clarity
Original:  These dynamical systems closely resemble a Hamiltonian system in %DIFDELCMD < \Bbb %%% 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:  These dynamical systems closely resemble Hamiltonian system in %DIFDELCMD < \Bbb %%% 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:  These dynamical systems closely resemble a Hamiltonian system in %DIFDELCMD < \Bbb %%% 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:  These dynamical systems closely resemble a Hamiltonian system in %DIFDELCMD < \Bbb %%% \mathbb{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:  The Turing instability parameter therefore measures the obstruction preventing a TCFL from being Hamiltonian where the Turing instability parameter equals one. To generalise TCFLs to symplectic manifolds in this paper we introduce and study the properties of deformed Hamiltonian vector fields on Lagrangian fibrations.
Revised:  To generalise these dynamical systems to symplectic manifolds in this paper we introduce and study the properties of deformed Hamiltonian vector fields on Lagrangian fibrations.
Edit intent: clarity
Original:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their biological interpretation motivates new problems in Floer theory, mirror symmetry, and the study of %DIFDELCMD < \Bbb %%% D-K \"{a}hler manifolds . Since many questions in complex network theory can be translated into the topological setting, this paper therefore serves to bring a selection of ideas from biology to pure mathematics .
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 %DIFDELCMD < \Bbb %%% D-K \"{a}hler manifolds . Since many questions in complex network theory can be translated into the topological setting, this paper therefore serves to bring a selection of ideas from biology to pure mathematics .
Edit intent: clarity
Original:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their biological interpretation motivates new problems in Floer theory, mirror symmetry, and the study of %DIFDELCMD < \Bbb %%% D-K \"{a}hler manifolds . Since many questions in complex network theory can be translated into the topological setting, this paper therefore serves to bring a selection of ideas from biology to pure mathematics .
Revised:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their biological interpretation motivates new problems in Floer theory, mirror symmetry, and the study of %DIFDELCMD < \Bbb %%% \mathbb{D \"{a}hler manifolds . Since many questions in complex network theory can be translated into the topological setting, this paper therefore serves to bring a selection of ideas from biology to pure mathematics .
Edit intent: clarity
Original:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their biological interpretation motivates new problems in Floer theory, mirror symmetry, and the study of %DIFDELCMD < \Bbb %%% D-K \"{a}hler manifolds . Since many questions in complex network theory can be translated into the topological setting, this paper therefore serves to bring a selection of ideas from biology to pure mathematics .
Revised:  We describe why these objects have some interesting applications to symplectic geometry and discuss how their biological interpretation motivates new problems in Floer theory, mirror symmetry, and the study of %DIFDELCMD < \Bbb %%% D-K \"{a}hler manifolds .
Edit intent: coherence