wanyu/IteraTeR_full_sent huggingface dataset:
Original: We present a positivity preserving numerical scheme for the pathwise solution of nonlinear stochastic differential equations driven by a multi-dimensional Wiener process and governed by non-commutative linear and non-Lipschitz vector fields. This strong order one scheme uses: (i) Strang exponential splitting, an approximation that decomposes the stochastic flow separately into the drift flow, and the pure diffusion flow governed by the diffusion vector fields; (ii) an implicit Euler method to approximate the drift flow; and (iii) an implicit Milstein method to approximate the pure diffusion flow. The separate approximations for the drift and pure diffusion flows preserve positivity. Therefore the Strang exponential splitting approximation does also. We demonstrate the efficacy of our method by applying it to the Heston model and a variance curve model , and compare it against well-established positivity preserving schemes .
Revised: We present a positivity preserving numerical scheme for the pathwise solution of nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are implicit in the diffusion vector fields. They thus apply to a restricted class, namely those with sublinear form. This however, still includes most Langevin derived processes typical of volatility models in finance and molecular simulation in physics. When the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process. We thus consider the non-central chi-squared transition density with fractional degrees of freedom. We prove that we can sample from this density by simulating Poisson distributed sums of powers of generalized Gaussian random variables. Further we prove that Marsaglia's polar method extends to the generalized Gaussian distribution, providing an exact and efficient method for generalized Gaussian sampling. We apply our methods to a variance curve model , and compare it against well-established positivity preserving schemes .
Edit intent: meaning-changed
Original: For nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are implicit in the diffusion vector fields. They thus apply to a restricted class, namely those with sublinear form. This however, still includes most Langevin derived processes typical of volatility models in finance and molecular simulation in physics. When the  zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process.
Revised: In the Heston stochastic volatility model, the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process.
Edit intent: coherence
Original:  When the  zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process.
Revised:  When the transition probability of the variance process can be represented by a non-central chi-square density. We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process.
Edit intent: meaning-changed
Original:  When the  zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process. We thus consider the non-central chi-squared transition density with fractional degrees of freedom. We prove that we can sample from this density by simulating Poisson distributed sums of powers of generalized Gaussian random variables.
Revised:  When the zero boundary is attracting and attainable, typical in foreign exchange markets. We prove a new representation for this density based on sums of powers of generalized Gaussian random variables.
Edit intent: meaning-changed
Original:  Further we prove Marsaglia's polar method extends to this distribution, providing an exact method for generalized Gaussian sampling . The advantages are that for the mean-reverting square-root process in the Heston model and Cox-Ingersoll-Ross model, we can generate samples from the true transition density simply, efficiently and robustly .
Revised:  Further we prove Marsaglia's polar method extends to this distribution, providing an exact method for generalized Gaussian sampling and thus central chi-square sampling. Third we derive a simple, high-accuracy, robust and efficient direct inversion method for generalized Gaussian sampling based on the Beasley-Springer-Moro method. Indeed the accuracy of the approximation to the inverse cumulative distribution function is to the tenth decimal place. We then apply our methods to non-central chi-square variance sampling in the Heston model and Cox-Ingersoll-Ross model, we can generate samples from the true transition density simply, efficiently and robustly .
Edit intent: meaning-changed
Original:  The advantages are that for the mean-reverting square-root process in the Heston model and Cox-Ingersoll-Ross model, we can generate samples from the true transition density simply, efficiently and robustly .
Revised:  The advantages are that for the mean-reverting square-root process in the Heston model . We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. Using the additivity property of the chi-square distribution, our methods apply in all parameter regimes .
Edit intent: meaning-changed
Original:  Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece  grows with x and at q_{b x= 1. (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.
Revised:  Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece , which is very small at x = 0 (neutral channel) grows with x and at q_{b x= 1. (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.
Edit intent: meaning-changed
Original:  Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece  grows with x and at q_{b x= 1. (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.
Revised:  Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece grows with x and at x= 1. (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.
Edit intent: meaning-changed
Original:  Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece  grows with x and at q_{b x= 1. (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.
Revised:  Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece grows with x and at q_{b x= 1 reaches q_{b (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.
Edit intent: meaning-changed
Original: In the Kelly game (Kelly,  1956 ), a gambler is allowed to invest a part of the wealth in each turn.
Revised: Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game 1956 ), a gambler is allowed to invest a part of the wealth in each turn.
Edit intent: meaning-changed
Original: In the Kelly game (Kelly,  1956 ), a gambler is allowed to invest a part of the wealth in each turn. With a certain probability this investment is doubled, and otherwise it is lost. Motivated by the complexity of real investments, we propose several modifications of this game  to investigate the influence of diversification and limited information on investment performance.
Revised: In the Kelly game (Kelly, 1956 ) to investigate the influence of diversification and limited information on investment performance.
Edit intent: coherence
Original:  Motivated by the complexity of real investments, we propose several modifications of this game  to investigate the influence of diversification and limited information on investment performance. Analytical and numerical results obtained from these toy games are well related to their real-life counterparts .
Revised:  Motivated by the complexity of real investments, we propose several modifications of this game to investigate the influence of diversification and limited information on Kelly-optimal portfolios. In particular we present approximate formulas for optimizing diversified portfolios and exact results for optimal investment in unknown games where the only available information is past outcomes .
Edit intent: meaning-changed
Original: We introduce some new quantitative measures of fluctuations in the process of synthesis of proteins from a single messenger RNA (mRNA) template. We calculate the statistical distributions of these fluctuating quantities and extract the strength of the corresponding translational noise.
Revised: We introduce some new quantitative measures of fluctuations in the process of synthesis of proteins from a single messenger RNA (mRNA) track also as the corresponding template and the process is called translation. We explore, in depth and detail, the stochastic nature of the corresponding translational noise.
Edit intent: meaning-changed
Original:  We calculate the statistical distributions of these fluctuating quantities and extract the strength of the corresponding translational noise. For these calculations{\bf   we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions in ribosome traffic on the same mRNA track.
Revised:  We calculate the statistical distributions of these fluctuating quantities and extract the strength of the translation. We compute various distributions associated with the translation process; one of them, namely dwell time distribution, has been measured in recent single ribosome experiments (Wen et al. Nature{\bf we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions in ribosome traffic on the same mRNA track.
Edit intent: meaning-changed
Original:  For these calculations{\bf   we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions in ribosome traffic on the same mRNA track.
Revised:  For these calculations{\bf 452 we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions in ribosome traffic on the same mRNA track.
Edit intent: meaning-changed
Original:  For these calculations{\bf   we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions in ribosome traffic on the same mRNA track.
Revised:  For these calculations{\bf , 598 (2008)). The form of this distribution predicted by our theory is consistent with that extracted from the experimental data. For our quantitative calculations, we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions in ribosome traffic on the same mRNA track.
Edit intent: meaning-changed
Original:  For these calculations{\bf   we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions in ribosome traffic on the same mRNA track. By comparing our results for a specific gene of the%DIFDELCMD < {\it %%% Escherichia coli bacteria with those for the corresponding homogeneous mRNA template, we demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise .
Revised:  For these calculations{\bf we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions %DIFDELCMD < {\it %%% Escherichia coli bacteria with those for the corresponding homogeneous mRNA template, we demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise .
Edit intent: clarity
Original:  By comparing our results for a specific gene of the%DIFDELCMD < {\it %%% Escherichia coli bacteria with those for the corresponding homogeneous mRNA template, we demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise .
Revised:  By comparing our results for a specific gene of the%DIFDELCMD < {\it %%% bacteria with those for the corresponding homogeneous mRNA template, we demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise .
Edit intent: clarity
Original:  By comparing our results for a specific gene of the%DIFDELCMD < {\it %%% Escherichia coli bacteria with those for the corresponding homogeneous mRNA template, we demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise .
Revised:  By comparing our results for a specific gene of the%DIFDELCMD < {\it %%% Escherichia coli . We also demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise .
Edit intent: clarity
Original:  By comparing our results for a specific gene of the%DIFDELCMD < {\it %%% Escherichia coli bacteria with those for the corresponding homogeneous mRNA template, we demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise . We also suggest {\it in-vitro} laboratory experimentsfor testing our theoretical predictions .
Revised:  By comparing our results for a specific gene of the%DIFDELCMD < {\it %%% Escherichia coli bacteria with those for the corresponding homogeneous mRNA template, we demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise in translation. In principle, our new predictions can be tested by carrying out {\it in-vitro} laboratory experimentsfor testing our theoretical predictions .
Edit intent: meaning-changed
Original:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than equivalent martingale measures.
Revised:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition, we establish that asset-prices have be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than equivalent martingale measures.
Edit intent: clarity
Original:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than equivalent martingale measures.
Revised:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than equivalent martingale measures.
Edit intent: meaning-changed
Original:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than equivalent martingale measures. Further, the utility maximization problem is considered and it is shown that using only buy-and-hold strategies, optimal utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well .
Revised:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Martingale Measures .
Edit intent: coherence
Original:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition ,  we establish that  asset-prices have to be semimartingales.
Revised:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition , namely, absence of arbitrages of the first kind, we establish that asset-prices have to be semimartingales.
Edit intent: meaning-changed
Original:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition ,  we establish that  asset-prices have to be semimartingales.
Revised:  Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition , we establish that discounted asset-prices have to be semimartingales.
Edit intent: meaning-changed
Original:  In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves  supermartingale deflators rather than Equivalent Martingale Measures.
Revised:  In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves strictly positive supermartingale deflators rather than Equivalent Martingale Measures.
Edit intent: meaning-changed
Original:  We introduce a new stochastic model of the proteasomal transport. We account for the protein translocation and the topology of the positioning of cleavage centers of a proteasome from first principles.
Revised:  We introduce a new stochastic model of the proteasomal digestion (cleavage) of proteins. In this model we account for the protein translocation and the topology of the positioning of cleavage centers of a proteasome from first principles.
Edit intent: meaning-changed
Original:  We show by test examples and by a comparison with experimental data that our model allows reconstruction of the translocation  rates from mass spectroscopy data on digestion patterns and can be used to investigate the properties of transport in different experimental set-ups.
Revised:  We show by test examples and by processing experimental data that our model allows reconstruction of the translocation rates from mass spectroscopy data on digestion patterns and can be used to investigate the properties of transport in different experimental set-ups.
Edit intent: clarity
Original:  We show by test examples and by a comparison with experimental data that our model allows reconstruction of the translocation  rates from mass spectroscopy data on digestion patterns and can be used to investigate the properties of transport in different experimental set-ups.
Revised:  We show by test examples and by a comparison with experimental data that our model allows reconstruction of the translocation and cleavage rates from mass spectroscopy data on digestion patterns and can be used to investigate the properties of transport in different experimental set-ups.
Edit intent: meaning-changed
Original:  Orientational control causes the switch to deviate from Poissonian behaviour: the distribution of times in the on state shows a peak and successive flip times are correlated . This model should provide a framework for understanding how DNA inversion switch architecture determines switch flipping statistics, with relevance to the role of such switches in microbial population dynamics .
Revised:  Orientational control causes the switch to deviate from Poissonian behaviour: the distribution of times in the on state shows a peak and successive flip times are correlated .
Edit intent: clarity
Original:  Recent {\it in-vivo} experiments with single cells have established that transcription takes place in ``bursts'' or ``pulses'' . In this letter we present a model that captures not only the mechano-chemistry of individual RNAPs and their steric interactions but also the switching of the gene between the ON and OFF states.
Revised:  Recent {\it in-vivo} experiments with single cells have established that transcription takes place in "bursts" or "pulses" . In this letter we present a model that captures not only the mechano-chemistry of individual RNAPs and their steric interactions but also the switching of the gene between the ON and OFF states.
Edit intent: fluency
Original:  The predictability of the model is also tested on bovine rhodopsin, the prototype of the G protein coupled receptor (GPCR) family also sensitive to the light, with results exhibiting the opposite behaviour of a decrease of conductance in the presence of light.
Revised:  The predictability of the model is further tested on bovine rhodopsin, the prototype of the G protein coupled receptor (GPCR) family also sensitive to the light, with results exhibiting the opposite behaviour of a decrease of conductance in the presence of light.
Edit intent: clarity
Original:  The predictability of the model is also tested on bovine rhodopsin, the prototype of the G protein coupled receptor (GPCR) family also sensitive to the light, with results exhibiting the opposite behaviour of a decrease of conductance in the presence of light.
Revised:  The predictability of the model is also tested on bovine rhodopsin, a G-protein coupled receptor (GPCR) family also sensitive to the light, with results exhibiting the opposite behaviour of a decrease of conductance in the presence of light.
Edit intent: clarity
Original:  The predictability of the model is also tested on bovine rhodopsin, the prototype of the G protein coupled receptor (GPCR) family also sensitive to the light, with results exhibiting the opposite behaviour of a decrease of conductance in the presence of light.
Revised:  The predictability of the model is also tested on bovine rhodopsin, the prototype of the G protein coupled receptor (GPCR) also sensitive to the light, with results exhibiting the opposite behaviour of a decrease of conductance in the presence of light.
Edit intent: clarity