wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Finally, we also address in this work the problem of characterizing those curves whose position vector  , up to a translation, lies on a (moving ) plane spanned by the unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
Revised:  Finally, we also address in this work the problem of characterizing those curves whose position vector , up to a translation, on a moving plane spanned by the unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
Edit intent: clarity
Original:  Finally, we also address in this work the problem of characterizing those curves whose position vector  , up to a translation, lies on a (moving ) plane spanned by the unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
Revised:  Finally, we also address in this work the problem of characterizing those curves whose position vector , up to a translation, lies on a (moving ) plane spanned by their unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
Edit intent: clarity
Original:  Finally, we also address in this work the problem of characterizing those curves whose position vector  , up to a translation, lies on a (moving ) plane spanned by the unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
Revised:  Finally, we also address in this work the problem of characterizing those curves whose position vector , up to a translation, lies on a (moving ) plane spanned by the unit tangent and an RM vector field. Finally, as an application, we characterize Bertrand curves as curves whose so-called natural mates are spherical .
Edit intent: meaning-changed
Original:  We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as uniqueness of the  Hamilton--Jacobi--Bellman equation, and study  qualitative properties both analytically and numerically.
Revised:  We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as uniqueness of the solution to the Hamilton--Jacobi--Bellman equation, and study qualitative properties both analytically and numerically.
Edit intent: clarity
Original:  We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as uniqueness of the  Hamilton--Jacobi--Bellman equation, and study  qualitative properties both analytically and numerically.
Revised:  We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as uniqueness of the Hamilton--Jacobi--Bellman equation, and study its qualitative properties both analytically and numerically.
Edit intent: clarity
Original:  We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as uniqueness of the solution to the Hamilton--Jacobi--Bellman equation, and study its qualitative properties both analytically and numerically .
Revised:  We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as comparison between the sub- and supersolutions of the Hamilton--Jacobi--Bellman equation, and study its qualitative properties both analytically and numerically .
Edit intent: meaning-changed
Original:  We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as uniqueness of the solution to the Hamilton--Jacobi--Bellman equation, and study its qualitative properties both analytically and numerically .
Revised:  We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as uniqueness of the solution to the Hamilton--Jacobi--Bellman equation, and we provide an efficient and convergent numerical scheme for finding the solution .
Edit intent: meaning-changed
Original:  In this work we propose to use the eigenvector centrality metric distribution as a mean of post-processing molecular dynamics simulations to determine the principal correlation paths involved in the transfer of information which is essential for the normal performance of enzymatic activity.
Revised:  In this work , we establish the eigenvector centrality metric distribution as a mean of post-processing molecular dynamics simulations to determine the principal correlation paths involved in the transfer of information which is essential for the normal performance of enzymatic activity.
Edit intent: clarity
Original:  In this work we propose to use the eigenvector centrality metric distribution as a mean of post-processing molecular dynamics simulations to determine the principal correlation paths involved in the transfer of information which is essential for the normal performance of enzymatic activity.
Revised:  In this work we propose to use the eigenvector centrality metric in terms of the mutual information, as a mean of post-processing molecular dynamics simulations to determine the principal correlation paths involved in the transfer of information which is essential for the normal performance of enzymatic activity.
Edit intent: meaning-changed
Original:  In this work we propose to use the eigenvector centrality metric distribution as a mean of post-processing molecular dynamics simulations to determine the principal correlation paths involved in the transfer of information which is essential for the normal performance of enzymatic activity. We have chosen allosteric regulation as an example where these pathways can be clearly revealed. Essential amino-acids responsible for the energy transfer are clearly depicted .
Revised:  In this work we propose to use the eigenvector centrality metric distribution as a mean of elucidating the allosteric mechanism that regulates the enzymatic activity of proteins. Moreover, we propose a strategy to characterize the range of the physical interactions that underlie the allosteric process. In particular, the well known enzyme, imidazol glycerol phosphate synthase (IGPS), is utilized to test the proposed methodology. The eigenvector centrality measurement successfully describes the allosteric pathways of IGPS, and allows to pinpoint key amino acids in terms of their relevance in the momentum transfer process. The resulting insight can be utilized for refining the control of IGPS activity, widening the scope for its engineering. Furthermore, we propose a new centrality metric quantifying the relevance of the surroundings of each residue. In addition, the proposed technique is validated against experimental solution NMR measurements yielding fully consistent results. Overall, the methodologies proposed in the present work constitute a powerful and cost effective strategy to gain insight on the allosteric mechanism of proteins .
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Original:  Further, in a more specific linear-quadratic model where two interacting Principals hire one common Agent , we are able to calculate the optimal effort by the Agent for both Principals .
Revised:  We provide conditions ensuring that for risk-neutral Principals, the system of coupled HJB equations admits a solution. Further, we apply our study in a more specific linear-quadratic model where two interacting Principals hire one common Agent , we are able to calculate the optimal effort by the Agent for both Principals .
Edit intent: meaning-changed
Original:  In this continuous time model, we extend the result of Bernheim and Whinston (1986) in which the authors compare the optimal effort of the Agent in a non-cooperative Principals model and that in the aggregate model, and give the condition under which these two optimisations coincide  .
Revised:  In this continuous time model, we extend the result of Bernheim and Whinston (1986) in which the authors compare the optimal effort of the Agent in a non-cooperative Principals model and that in the aggregate model, by showing that these two optimisations coincide .
Edit intent: coherence
Original:  In this continuous time model, we extend the result of Bernheim and Whinston (1986) in which the authors compare the optimal effort of the Agent in a non-cooperative Principals model and that in the aggregate model, and give the condition under which these two optimisations coincide  .
Revised:  In this continuous time model, we extend the result of Bernheim and Whinston (1986) in which the authors compare the optimal effort of the Agent in a non-cooperative Principals model and that in the aggregate model, and give the condition under which these two optimisations coincide only in the first best case. We also study the sensibility of the optimal effort and the optimal remunerations with respect to appetence parameters and the correlation between the projects .
Edit intent: meaning-changed
Original:  It is shown that, similarly to the case of the stock market crash investigated by Lillo and Mantegna Phys. Rev. E 68, 016119 (2003) , the relaxation is characterized by a power law, which is in analogy with the Omori-Utsu law for earthquake aftershocks.
Revised:  It is shown that, similarly to the case of the stock market crash investigated by Lillo and Mantegna , the relaxation is characterized by a power law, which is in analogy with the Omori-Utsu law for earthquake aftershocks.
Edit intent: coherence
Original:  In this article, we use the Sliced Wasserstein approximation SW of the Wasserstein distance to define a new kernel for PDs, which is not only provably stable but also provably discriminative (depending on the number of points in the PDs) w.r.t. the Wasserstein distance W^1_\infty between PDs.
Revised:  In this article, we use the Sliced Wasserstein approximation SW of the Wasserstein distance to define a new kernel for PDs, which is not only provably stable but also provably discriminative (depending on the number of points in the PDs) w.r.t. the Wasserstein distance d_1 between PDs.
Edit intent: meaning-changed
Original: We consider the problem of selecting a portfolio of items of fixed cardinality where the goal is to have at least one item achieve a high return , which we refer to as winning.
Revised: We consider the problem of evaluating the quality of startup companies. This can be quite challenging due to the rarity of successful startup companies and the complexity of factors which impact such success. In this work we collect data on tens of thousands of startup companies, their performance, the backgrounds of their founders, and their investors. We develop a novel model for the success of a startup company based on the first passage time of a Brownian motion. The drift and diffusion of the Brownian motion associated with a startup company are a function of features based its sector, founders, and initial investors. All features are calculated using our massive dataset. Using a Bayesian approach, we are able to obtain quantitative insights about the features of successful startup companies from our model. To test the performance of our model, we use it to build a portfolio of companies where the goal is to have at least one item achieve a high return , which we refer to as winning.
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Original:  This  framework is very general and can be used to model a variety of problems , such as pharmaceutical companies choosing drugs to develop , studios selecting movies to produce , or our focus in this work, which is venture capital firms picking startup companies in which to invest.
Revised:  This picking winners framework is very general and can be used to model a variety of problems , such as pharmaceutical companies choosing drugs to develop , studios selecting movies to produce , or our focus in this work, which is venture capital firms picking startup companies in which to invest.
Edit intent: meaning-changed
Original:  This  framework is very general and can be used to model a variety of problems , such as pharmaceutical companies choosing drugs to develop , studios selecting movies to produce , or our focus in this work, which is venture capital firms picking startup companies in which to invest.
Revised:  This framework is very general and can be used to model many problems with low probability, high reward outcomes, such as pharmaceutical companies choosing drugs to develop , studios selecting movies to produce , or our focus in this work, which is venture capital firms picking startup companies in which to invest.
Edit intent: meaning-changed
Original:  This  framework is very general and can be used to model a variety of problems , such as pharmaceutical companies choosing drugs to develop , studios selecting movies to produce , or our focus in this work, which is venture capital firms picking startup companies in which to invest.
Revised:  This framework is very general and can be used to model a variety of problems , such as pharmaceutical companies choosing drugs to develop or studios selecting movies to produce , or our focus in this work, which is venture capital firms picking startup companies in which to invest.
Edit intent: fluency
Original:  This  framework is very general and can be used to model a variety of problems , such as pharmaceutical companies choosing drugs to develop , studios selecting movies to produce , or our focus in this work, which is venture capital firms picking startup companies in which to invest. We first frame the construction of a  portfolio as a combinatorial optimization problem with objective function given by the probability of having at least one item in the selected portfolio win.
Revised:  This framework is very general and can be used to model a variety of problems , such as pharmaceutical companies choosing drugs to develop , studios selecting movies to produce . We frame the construction of a portfolio as a combinatorial optimization problem with objective function given by the probability of having at least one item in the selected portfolio win.
Edit intent: coherence
Original:  We first frame the construction of a  portfolio as a combinatorial optimization problem with objective function given by the probability of having at least one item in the selected portfolio win. We show that a greedy solution to this problem has strong performance guarantees , even under arbitrary correlations between the items .
Revised:  We first frame the construction of a portfolio as a combinatorial optimization problem and show that a greedy solution to this problem has strong performance guarantees , even under arbitrary correlations between the items .
Edit intent: clarity
Original:  We apply the picking winners framework to the problem of choosing a portfolio of startups to invest in. This is a relevant problem due to recent policy changes in the United States which have greatly expanded the market for startup investment. We develop a novel model for the success of a startup company based on Brownian motion first passage times. We fit this model to a large amount of data on startup company founders, investors, and performance. Our model provides some qualitative insights to the features of successful startup companies.
Revised:  We apply the picking winners framework to the problem of choosing a portfolio of startup companies.
Edit intent: meaning-changed
Original: This paper documents a new stylized fact about the leverage cycle and proposes a model of risk preference heterogeneity to explain this fact. In particular, leverage cyclicality depends on the preferences of the marginal agent in the economy, as this determines financial variables. I propose a model of risk preference heterogeneity to explain this fact and prove existence of a new, low dimensional Markovian equilibrium which may exist in other heterogeneous agent models. This equilibrium is studied in an application to margin constraints  .
Revised: This paper solves an open problem in financial mathematics by characterizing the equilibrium in a continuous time financial market populated by heterogeneous agents who differ in their rate of relative risk aversion and face convex portfolio constraints. The model is studied in an application to margin constraints .
Edit intent: clarity
Original:  In addition, heterogeneity and margin constraints are shown to produce both pro- and counter-cyclical leverage cycles as seen in the data. Finally , more preference types causes a reduction in the severity of crisis and a lower relative deviation from complete markets in  all variables.
Revised:  In addition, heterogeneity and margin constraints are shown to produce both pro- and counter-cyclical leverage cycles . Beyond two types , more preference types causes a reduction in the severity of crisis and a lower relative deviation from complete markets in all variables.
Edit intent: meaning-changed
Original:  At the same time expected returns on the stock must remain high to compensate risk averse agents to hold a larger share  .
Revised:  At the same time expected returns on the stock must remain high to compensate risk averse agents to hold a larger share and leverage is mechanically low as agents are limited in their borrowing. Finally, empirical results are given, documenting a novel stylized fact which is predicted by the model, namely that the leverage cycle is both pro- and counter-cyclical .
Edit intent: meaning-changed
Original:  Beyond two types, more preference types causes a reduction in the severity of crisis and a lower relative deviation from complete markets in almost all variables. At the same time expected returns on the stock must remain high to compensate risk averse agents to hold a larger share and leverage is mechanically low as agents are limited in their borrowing .
Revised:  Beyond two types, it is shown how constraints can cascade and how leverage can exhibit highly non-linear dynamics .
Edit intent: clarity
Original:  As an application, we employ the default contagion model to price synthetic CDOs. The calculation time is reduced dramatically comparing with related literatures, especially, when the number of reference obligors is large ]{ [ }  .
Revised:  Applying the new framework, we give analytical pricing formulaes for synthetic collateralized debt obligations (CDOs). The numerical studies validate our theory and its practical applications. Our empirical studies give the evidence that systematic default risk coupling with default contagion could have the leading component of the total default risk as Das, Duffie, Kapadia and Saita ]{ [ } .
Edit intent: meaning-changed
Original:  The calculation time is reduced dramatically comparing with related literatures, especially, when the number of reference obligors is large ]{ [ }  .
Revised:  The calculation time is reduced dramatically comparing with related literatures, especially, when the number of reference obligors is large ]{ [ } demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
Edit intent: meaning-changed
Original:  Thereby, we derive analytically the dynamics of the default process by set-valued Markov chain approach. Applying the new framework, we give analytical pricing formulaes for synthetic collateralized debt obligations (CDOs).
Revised:  Thereby, we derive analytically the dynamics of the default process by set-valued Markov chain to model the default process, which is the set of all defaulted obligors in the group. We obtain analytic characterizations for the default process, and use them to derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs).
Edit intent: meaning-changed
Original:  The numerical studies validate our theory and its practical applications. Our empirical studies give the evidence that systematic default risk coupling with default contagion could have the leading component of the total default risk as Das,
Revised:  Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupling with default contagion could have the leading component of the total default risk as Das,
Edit intent: meaning-changed
Original:  Our empirical studies give the evidence that systematic default risk coupling with default contagion could have the leading component of the total default risk as Das, Duffie, Kapadia and Saita The Journal of Finance, 2007%DIFDELCMD < ]{%%% DasDuffie2007 and Duffie, Eckner, Horel and Saita%DIFDELCMD < [%%% The Journal of Finance, 2009 duffieEHS2009%DIFDELCMD < } %%% demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
Revised:  Our empirical studies give the evidence that systematic default risk coupling with default contagion could have the leading component of the total default risk The Journal of Finance, 2007%DIFDELCMD < ]{%%% DasDuffie2007 and Duffie, Eckner, Horel and Saita%DIFDELCMD < [%%% The Journal of Finance, 2009 duffieEHS2009%DIFDELCMD < } %%% demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
Edit intent: clarity
Original:  Duffie, Kapadia and Saita The Journal of Finance, 2007%DIFDELCMD < ]{%%% DasDuffie2007 and Duffie, Eckner, Horel and Saita%DIFDELCMD < [%%% The Journal of Finance, 2009 duffieEHS2009%DIFDELCMD < } %%% demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
Revised:  Duffie, Kapadia and Saita %DIFDELCMD < ]{%%% DasDuffie2007 and Duffie, Eckner, Horel and Saita%DIFDELCMD < [%%% The Journal of Finance, 2009 duffieEHS2009%DIFDELCMD < } %%% demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
Edit intent: fluency
Original:  Duffie, Kapadia and Saita The Journal of Finance, 2007%DIFDELCMD < ]{%%% DasDuffie2007 and Duffie, Eckner, Horel and Saita%DIFDELCMD < [%%% The Journal of Finance, 2009 duffieEHS2009%DIFDELCMD < } %%% demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
Revised:  Duffie, Kapadia and Saita The Journal of Finance, 2007%DIFDELCMD < ]{%%% and Duffie, Eckner, Horel and Saita%DIFDELCMD < [%%% The Journal of Finance, 2009 duffieEHS2009%DIFDELCMD < } %%% demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
Edit intent: coherence
Original:  Duffie, Kapadia and Saita The Journal of Finance, 2007%DIFDELCMD < ]{%%% DasDuffie2007 and Duffie, Eckner, Horel and Saita%DIFDELCMD < [%%% The Journal of Finance, 2009 duffieEHS2009%DIFDELCMD < } %%% demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
Revised:  Duffie, Kapadia and Saita The Journal of Finance, 2007%DIFDELCMD < ]{%%% DasDuffie2007 %DIFDELCMD < [%%% The Journal of Finance, 2009 duffieEHS2009%DIFDELCMD < } %%% demonstrate the presence of frailty correlated default and the incapability of doubly stochastic assumption to capture default contagion or frailty (unobservable explanatory variables that are correlated across firms) .
Edit intent: coherence