wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We discuss applications of this model to problem of prediction of the native conformation of a protein from its primary structure and to description of dynamics of a protein  .
Revised:  We discuss applications of this model to problem of prediction of the native conformation of a protein from its primary structure and to description of dynamics of a protein . Modification of structural alignment taking into account statistical potentials for protein fragments is considered and application to threading procedure for proteins is discussed .
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Original: We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, which was invented by Elowitz and Leibler. We propose an alternative approach to model the dynamical behaviors  , that is, a type-dependent spin system, this class of stochastic models was introduced by Fern\'andez et. al (2009), and are useful since take account to inherent variability of gene expression.
Revised: We study an alternative approach to model the dynamical behaviors , that is, a type-dependent spin system, this class of stochastic models was introduced by Fern\'andez et. al (2009), and are useful since take account to inherent variability of gene expression.
Edit intent: clarity
Original:  We propose an alternative approach to model the dynamical behaviors  , that is, a type-dependent spin system, this class of stochastic models was introduced by Fern\'andez et. al (2009), and are useful since take account to inherent variability of gene expression.
Revised:  We propose an alternative approach to model the dynamical behaviors of biological feedback loop , that is, a type-dependent spin system, this class of stochastic models was introduced by Fern\'andez et. al (2009), and are useful since take account to inherent variability of gene expression.
Edit intent: meaning-changed
Original:  We  consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector in the thermodynamic limit .
Revised:  We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, invented by Elowitz and Leibler (2000). We consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector in the thermodynamic limit .
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Original: The main purpose of this work is to prove a theorem about the probability that a random mapping  possesses a unique highest tree in its underlying graph. However, we hope that some of auxiliary statements that we present here can be useful for proving results appealing to the theory of critical Galton-Watson branching processes.
Revised: The main purpose of this work is to prove a theorem about the probability that a random mapping possesses a unique highest tree . The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem as well as in the proof of the author's result about the probability of being synchronizable for a random automaton. Furthermore, some of auxiliary statements that we present here can be useful for proving results appealing to the theory of critical Galton-Watson branching processes.
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Original: We prove the exact asymptotic 1- \Theta(\frac{1 \left({{3}-827{288\pi}}}\right)  for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Revised: We prove the exact asymptotic 1- \left({{3}-827{288\pi}}}\right) for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Edit intent: meaning-changed
Original: We prove the exact asymptotic 1- \Theta(\frac{1 \left({{3}-827{288\pi}}}\right)  for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Revised: We prove the exact asymptotic 1- \Theta(\frac{1 \left({\frac{2\pi{3}-827{288\pi}}}\right) for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Edit intent: meaning-changed
Original: We prove the exact asymptotic 1- \Theta(\frac{1 \left({{3}-827{288\pi}}}\right)  for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Revised: We prove the exact asymptotic 1- \Theta(\frac{1 \left({{3}-827{288\pi}}}+o(1)\right) for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Edit intent: meaning-changed
Original: We prove the exact asymptotic 1- \Theta(\frac{1 \left({{3}-827{288\pi}}}\right)  for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Revised: We prove the exact asymptotic 1- \Theta(\frac{1 \left({{3}-827{288\pi}}}\right)/ for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Edit intent: clarity
Original: We prove the exact asymptotic 1- \Theta(\frac{1 \left({{3}-827{288\pi}}}\right)  for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Revised: We prove the exact asymptotic 1- \Theta(\frac{1 \left({{3}-827{288\pi}}}\right) \sqrt{n for the probability that the underlying graph of a random mapping of n elements possesses a unique highest tree.
Edit intent: meaning-changed
Original:  The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem \mbox{%DIFAUXCMD TRRCP08 as well as  in the proof of the author's result about the probability of being synchronizable for a random automaton \mbox{%DIFAUXCMD RandSynch .
Revised:  The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem as well as in the proof of the author's result about the probability of being synchronizable for a random automaton \mbox{%DIFAUXCMD RandSynch .
Edit intent: clarity
Original:  The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem \mbox{%DIFAUXCMD TRRCP08 as well as  in the proof of the author's result about the probability of being synchronizable for a random automaton \mbox{%DIFAUXCMD RandSynch .
Revised:  The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem \mbox{%DIFAUXCMD TRRCP08 as well as the generalization of this property in the proof of the author's result about the probability of being synchronizable for a random automaton \mbox{%DIFAUXCMD RandSynch .
Edit intent: meaning-changed
Original:  The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem \mbox{%DIFAUXCMD TRRCP08 as well as  in the proof of the author's result about the probability of being synchronizable for a random automaton \mbox{%DIFAUXCMD RandSynch .
Revised:  The property of having a unique highest tree turned out to be crucial in the solution of the famous Road Coloring Problem \mbox{%DIFAUXCMD TRRCP08 as well as in the proof of the author's result about the probability of being synchronizable for a random automaton .
Edit intent: meaning-changed
Original:  Despite its importance, the physical principles that underpin the primary steps of photosynthesis , from photon absorption to electronic charge separation, remain to be understood in full. Previously, electronic coherence within tightly-packed light-harvesting (LH) units or within individual reaction centers (RCs) has been recognized as an important ingredient for a complete understanding of the excitation energy transfer dynamics.
Revised:  Despite its importance, the physical principles that underpin the primary steps of photosynthesis involve the photo-excitation of reaction centres (RCs) has been recognized as an important ingredient for a complete understanding of the excitation energy transfer dynamics.
Edit intent: clarity
Original:  Previously, electronic coherence within tightly-packed light-harvesting (LH) units or within individual reaction centers (RCs) has been recognized as an important ingredient for a complete understanding of the excitation energy transfer dynamics. However, the electronic coherence across RC and LH units has been consistently neglected as it does not play a significant role during these relatively slow transfer processes .
Revised:  Previously, electronic coherence within tightly-packed light-harvesting (LH) units or within individual reaction centers (RCs) and light-harvesting (LH) units .
Edit intent: clarity
Original:  Here, we turn our attention to the absorption process, which occurs on much shorter timescales. We demonstrate that the - often overlooked - spatially extended but short-lived excitonic delocalization across RC and LH units plays a relevant role in general photosynthetic systems, as it causes a redistribution of direct absorption towards the charge separation unit.
Revised:  Here, we show that the --historically overlooked-- excitonic delocalisation across RC and LH units plays a relevant role in general photosynthetic systems, as it causes a redistribution of direct absorption towards the charge separation unit.
Edit intent: clarity
Original:  We demonstrate that the - often overlooked - spatially extended but short-lived excitonic delocalization across RC and LH units plays a relevant role in general photosynthetic systems, as it causes a redistribution of direct absorption towards the charge separation unit.
Revised:  We demonstrate that the - often overlooked - spatially extended but short-lived excitonic delocalization across RC and LH pigments results in a redistribution of direct absorption towards the charge separation unit.
Edit intent: clarity
Original:  We demonstrate that the - often overlooked - spatially extended but short-lived excitonic delocalization across RC and LH units plays a relevant role in general photosynthetic systems, as it causes a redistribution of direct absorption towards the charge separation unit. Using the complete core complex of Rhodospirillum rubrum, we verify experimentally an 80 \% increase in the direct optical absorption of the RC in situ as compared to isolated RCs. Numerical calculations reveal that similar enhancements can be expected for a wide variety of photosynthetic units in both plant and bacterial systems, suggesting that this mechanism is conserved across species and providing a clear new design principle for light-harvesting nanostructures
Revised:  We demonstrate that the - often overlooked - spatially extended but short-lived excitonic delocalization across RC and LH units plays a relevant role in general photosynthetic systems, as it causes a redistribution of dipole strengths that benefits the absorption cross section of the optical bands associated with the RC of several species. While we prove that this redistribution is robust to the microscopic details of the dephasing between these units in the purple bacterium Rhodospirillum rubrum, we are able to show that the redistribution witnesses a more fragile, but persistent, coherent population dynamics which directs excitations from the LH towards the RC units under incoherent illumination and physiological conditions. Stochastic optimisation allows us to delineate clear guidelines and develop simple analytic expressions, in order to achieve directed coherent population dynamics in artificial nano-structures.
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Original: This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, where bio-nanomachines, or biological cells, communicate  each other using  cell-to-cell communication mechanism mediated by a diffusible signaling molecule  .
Revised: This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular communication networks, bio-nanomachines, or biological cells, communicate each other using cell-to-cell communication mechanism mediated by a diffusible signaling molecule .
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Original: This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, where bio-nanomachines, or biological cells, communicate  each other using  cell-to-cell communication mechanism mediated by a diffusible signaling molecule  .
Revised: This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, where bio-nanomachines, or biological cells, communicate with each other using cell-to-cell communication mechanism mediated by a diffusible signaling molecule .
Edit intent: fluency
Original: This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, where bio-nanomachines, or biological cells, communicate  each other using  cell-to-cell communication mechanism mediated by a diffusible signaling molecule  .
Revised: This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, where bio-nanomachines, or biological cells, communicate each other using a cell-to-cell communication mechanism mediated by a diffusible signaling molecule .
Edit intent: fluency
Original: This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, where bio-nanomachines, or biological cells, communicate  each other using  cell-to-cell communication mechanism mediated by a diffusible signaling molecule  .
Revised: This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, where bio-nanomachines, or biological cells, communicate each other using cell-to-cell communication mechanism mediated by a diffusible signaling molecule , thereby the dynamics of molecular concentrations are approximately modeled as a reaction-diffusion system with a single diffuser .
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Original:  The theoretical results are demonstrated on a novel biochemical circuit called activator-repressor-diffuser system , and the Turing pattern formation is numerically confirmed. Finally, we show that the activator-repressor-diffuser system is a minimum biochemical circuit that admits URLanized patterns in biomolecular communication networks .
Revised:  The theoretical results are demonstrated on a novel biochemical circuit called activator-repressor-diffuser system and show that it is one of the minimum biomolecular circuits that admit URLanized patterns over cell population .
Edit intent: clarity
Original:  In biomolecular communication networks, bio-nanomachines , or biological cells, communicate with each other using a cell-to-cell communication mechanism mediated by a diffusible signaling molecule, thereby the dynamics of molecular concentrations are approximately modeled as a reaction-diffusion system with a single diffuser.
Revised:  In biomolecular communication networks, bionanomachines , or biological cells, communicate with each other using a cell-to-cell communication mechanism mediated by a diffusible signaling molecule, thereby the dynamics of molecular concentrations are approximately modeled as a reaction-diffusion system with a single diffuser.
Edit intent: fluency
Original:  We calculate the probability that a complex made up of a given number of molecules is completely formed, as well as the distribution of completion times, upon the binding of a seed molecule at a target site on the filament  .
Revised:  We calculate the probability that a complex made up of a given number of molecules is completely formed, as well as the distribution of completion times, upon the binding of a seed molecule at a target site on the filament (without explicitly modeling the three-dimensional diffusion that precedes binding) .
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Original:  We apply the powerful theory of characteristic functions and Hilbert transforms , which have not been used in this combination before .
Revised:  We apply the powerful theory of characteristic functions and Hilbert transforms . The latter concept is used to express the characteristic function (c.f.) of the random variable (r.v.) \max(Y, 0) in terms of the c.f. of the r.v. Y. The present paper applies this concept for the first time in mathematical finance .
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Original:  Super-resolved imaging of single molecules has revolutionized our view of quasi-static nanostructures . A wide-field approach based on localizing individual fluorophores has emerged as a versatile method to surpass the standard resolution limit. In those techniques, the super-resolution is realized by sparse photoactivation and localization together with the statistical analysis based on point spread functions. Nevertheless, the slow temporal resolution of super-resolved imaging severely restricts the utility to the study of live-cell phenomena. Clearly, a major breakthrough to observe fast, nanoscale dynamics needs to be made. Here we present a super-resolved imaging method that achieves the theoretical-limit time resolution . By invoking information theory, we can achieve the robust localization of overlapped light emitters at an order of magnitude faster speed than the conventional super-resolution microscopy . Our method thus provides a general way to uncover hidden structures below the diffraction limit and should have a wide range of applications in all disciplines of science and technology .
Revised:  Super-resolved imaging of single molecules has revolutionized our view of quasi-static nanostructures We present a method that can simultaneously locate positions of overlapped multi-emitters at the theoretical-limit precision. We derive a set of simple equations whose solution gives the maximum likelihood estimator of multi-emitter positions. We compare the performance of our simultaneous localization analysis with the conventional single-molecule analysis for simulated images and show that our method can improve the time-resolution of superresolution microscopy an order of magnitude. In particular, we derive the information-theoretical bound on time resolution of localization-based superresolution microscopy and demonstrate that the bound can be closely attained by our analysis .
Edit intent: clarity
Original:  On the other hand, the number of records of a discrete-time random walk in a given time-interval follows a Gaussian distribution provided that its increment distribution has finite variance. As as consequence, record statistics of uncorrelated, biased, random walks provide an attractive new estimator of Sharpe ratios  .
Revised:  On the other hand, the number of records of a discrete-time random walk in a given time-interval follows a Gaussian distribution that depends on its true Sharpe ratio. Reversely, this suggests an estimator of Sharpe ratios .
Edit intent: clarity
Original:  As as consequence, record statistics of uncorrelated, biased, random walks provide an attractive new estimator of Sharpe ratios  .
Revised:  As as consequence, record statistics of uncorrelated, biased, random walks provide an attractive new estimator of Sharpe ratios based the total duration of drawdowns. Its efficiency is several times larger than moment-based estimators for symmetric heavy-tailed price returns. Such type of data also leads mechanically to a larger number of expected price records, hence, to a smaller duration of drawdowns. Thus, for a given number of records, the absolute value of the estimated Sharpe ratios is smaller when price returns are heavy tailed. This means that moment-based estimators are prone to overestimate true Sharpe ratios in difficult market conditions, which implies that using them for investment decisions may amplify large price returns .
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Original:  First, I derive an approximate expression of the expected number of price records in a given time interval when the increments follow Student's t distribution with tail exponent equal to 4 in the limit of vanishing Sharpe ratios . Remarkably, this expression explicitly links the expected record numbers to Sharpe ratios and and suggests to estimate the average Sharpe ratio from record statistics. Numerically, the asymptotic efficiency of a permutation estimator of Sharpe ratios based on record statistics is several times larger than that of the t-statistics for uncorrelated returnswith a Student's t distribution with tail exponent of 4.
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Original: Estimating Sharpe ratios requires the computation of the moments of price returns, which is problematic because the latter are heavy-tailed. On the other hand, the total duration of drawdowns of a time series, or equivalently the number of its upper price records, follows a Gaussian distribution that depends on its true Sharpe ratio.
Revised: The total duration of drawdowns of a time series, or equivalently the number of its upper price records, follows a Gaussian distribution that depends on its true Sharpe ratio.
Edit intent: clarity
Original:  On the other hand, the total duration of drawdowns of a time series, or equivalently the number of its upper price records, follows a Gaussian distribution that depends on its true Sharpe ratio. Reversely, this suggests an estimator of Sharpe ratios based the total duration of drawdowns.
Revised:  On the other hand, the total duration of drawdowns is shown to be an efficient and robust estimator of Sharpe ratios based the total duration of drawdowns.
Edit intent: clarity
Original:  Such type of data also leads mechanically to a larger number of expected price records, hence, to a smaller duration of drawdowns. Thus, for a given number of records, the absolute value of the estimated Sharpe ratios is smaller when price returnsare heavy tailed. This means that moment-based estimators are prone to overestimate true Sharpe ratios in difficult market conditions , which implies that using them for investment decisions may amplify large price returns  .
Revised:  Such type of data mechanically reduces the expected total drawdown duration with respect to Gaussian price returns, moment-based estimators are prone to overestimate true Sharpe ratios in difficult market conditions , which implies that using them for investment decisions may amplify large price returns .
Edit intent: clarity
Original:  This means that moment-based estimators are prone to overestimate true Sharpe ratios in difficult market conditions , which implies that using them for investment decisions may amplify large price returns  .
Revised:  This means that moment-based estimators are prone to overestimate true Sharpe ratios in difficult market conditions , which implies that using them for investment decisions may amplify large price returns when they are used by trend-followers .
Edit intent: meaning-changed