wanyu/IteraTeR_v2 huggingface dataset:
Original: Natural languages can express some logical propositions that humans , with similar cultural traditions, are able to immediately and correctly compute .
Revised: Natural languages can express some logical propositions that humans , with similar cultural traditions, are able to understand .
Edit intent: clarity
Original:  We illustrate this fact with a famous text that Arthur Conan Doyle attributed to Sherlock Holmes: the 'old maxim' mentioned in 'The Adventure of the Beryl Coronet', where Holmes said: ' It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth'.
Revised:  We illustrate this fact with a famous text that Conan Doyle attributed to Sherlock Holmes: the 'old maxim' mentioned in 'The Adventure of the Beryl Coronet', where Holmes said: ' It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth'.
Edit intent: clarity
Original:  We illustrate this fact with a famous text that Arthur Conan Doyle attributed to Sherlock Holmes: the 'old maxim' mentioned in 'The Adventure of the Beryl Coronet', where Holmes said: ' It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth'.
Revised:  We illustrate this fact with a famous text that Arthur Conan Doyle attributed to Holmes: ' It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth'.
Edit intent: coherence
Original:  This maxim is a subtle logical statement and the astonishing point is that the reader feels that it is an evident true .
Revised:  This is a subtle logical statement and the astonishing point is that the reader feels that it is an evident true .
Edit intent: clarity
Original:  This maxim is a subtle logical statement and the astonishing point is that the reader feels that it is an evident true .
Revised:  This maxim is a subtle logical statement usually felt as an evident truth .
Edit intent: clarity
Original:  The problem we are trying to explain is the cognitive reason for such a feeling.
Revised:  The problem we are trying to solve is the cognitive reason for such a feeling.
Edit intent: clarity
Original:  We show how these theories converge in a class of neural network model, and we suggest that we accept as true Holmes' maxim  because our adult brains are equipped with neural modules that perform naturally modal logical computations.
Revised:  We show how these theories converge in a class of neural network model, and we suggest that we accept Holmes' maxim because our adult brains are equipped with neural modules that perform naturally modal logical computations.
Edit intent: clarity
Original:  We show how these theories converge in a class of neural network model, and we suggest that we accept as true Holmes' maxim  because our adult brains are equipped with neural modules that perform naturally modal logical computations.
Revised:  We show how these theories converge in a class of neural network model, and we suggest that we accept as true Holmes' maxim because our adult brains are equipped with neural modules that naturally perform modal logical computations.
Edit intent: fluency
Original:  We also show that the difference in terms of liquidity premiumbetween the constant participation rate case and the usual Almgren-Chriss-like case never exceeds 15\% .
Revised:  We also show that the difference in terms of risk-liquidity premium .
Edit intent: clarity
Original:  Considering the functional forms usually used by practitioners for market impact functions, we obtain a closed-form expression for the optimal participation rate.
Revised:  Considering the functional forms commonly used by practitioners for market impact functions, we obtain a closed-form expression for the optimal participation rate.
Edit intent: fluency
Original: Random hashing is a standard method to balance loads among nodes in P2P networks.
Revised: Random hashing is a standard method to balance loads among nodes in Peer-to-Peer networks.
Edit intent: fluency
Original:  However, their algorithm is not straight-forward to implement in real networks because it is recursive.
Revised:  However, their algorithm is not straightforward to implement in real networks because it is recursive.
Edit intent: clarity
Original:  By considering the lesser-known Beltrami hemisphere model of hyperbolic geometry, we overcome both the clipping and the arithmetic limitations of Klein construction .
Revised:  By considering the lesser-known Beltrami hemisphere model of hyperbolic geometry, we overcome the arithmetic limitations of Klein construction .
Edit intent: clarity
Original:  Here, we consider a generic two-dimensional  population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species , mutation, pair-exchange and individual hopping .
Revised:  Here, we consider a two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species , mutation, pair-exchange and individual hopping .
Edit intent: clarity
Original:  Here, we consider a generic two-dimensional  population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species , mutation, pair-exchange and individual hopping .
Revised:  Here, we consider a generic two-dimensional three-species population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species , mutation, pair-exchange and individual hopping .
Edit intent: fluency
Original:  Here, we consider a generic two-dimensional  population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species , mutation, pair-exchange and individual hopping .
Revised:  Here, we consider a generic two-dimensional population model and study the spiralling patterns arising from the combined effects of cyclic dominance of three species , mutation, pair-exchange and individual hopping .
Edit intent: fluency
Original:  Here, we consider a generic two-dimensional  population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species , mutation, pair-exchange and individual hopping .
Revised:  Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of generic cyclic dominance , mutation, pair-exchange and individual hopping .
Edit intent: clarity
Original:  Here, we consider a generic two-dimensional  population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species , mutation, pair-exchange and individual hopping .
Revised:  Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species , mutation, pair-exchange and hopping of the individuals .
Edit intent: clarity
Original:  The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion.
Revised:  The dynamics is characterised by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion.
Edit intent: fluency
Original:  The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion.
Revised:  The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's phase diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion.
Edit intent: clarity
Original:  The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion.
Revised:  The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from the underlying complex Ginzburg-Landau equation derived using a perturbative multiscale expansion.
Edit intent: clarity
Original:  While the dynamics is generally characterized by spiraling patterns, we show that spiral waves are stable in only one of the four phases.
Revised:  While the dynamics is generally characterised by spiralling patterns, we show that spiral waves are stable in only one of the four phases.
Edit intent: fluency
Original:  Furthermore, we characterize a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn.
Revised:  Furthermore, we characterise a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn.
Edit intent: fluency
Original:  Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion.
Revised:  Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiralling patterns are also affected by the nonlinear diffusion.
Edit intent: fluency
Original:  Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion.
Revised:  Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by nonlinear diffusion.
Edit intent: fluency
Original:  We show that with neurally plausible choices of parameters , the whole neural network is capable of representing any Boltzmann machine and performing a semi-stochastic Bayesian inference algorithm lying between Gibbs sampling and variational inference.
Revised:  We show that with neurally plausible settings , the whole neural network is capable of representing any Boltzmann machine and performing a semi-stochastic Bayesian inference algorithm lying between Gibbs sampling and variational inference.
Edit intent: clarity
Original:  We show that with neurally plausible choices of parameters , the whole neural network is capable of representing any Boltzmann machine and performing a semi-stochastic Bayesian inference algorithm lying between Gibbs sampling and variational inference.
Revised:  We show that with neurally plausible choices of parameters , the whole network is capable of representing any Boltzmann machine and performing a semi-stochastic Bayesian inference algorithm lying between Gibbs sampling and variational inference.
Edit intent: clarity
Original: We present a generic analytical scheme for the quantification of fluctuations due to bi-functionality induced signal transduction within the members of bacterial two-component system.
Revised: We present a generic analytical scheme for the quantification of fluctuations due to bifunctionality-induced signal transduction within the members of bacterial two-component system.
Edit intent: fluency
Original: Long-range migrations and the resulting admixture between populations have been an important force shaping human genetic diversity.
Revised: Long-range migrations and the resulting admixtures between populations have been an important force shaping human genetic diversity.
Edit intent: fluency
Original: Long-range migrations and the resulting admixture between populations have been an important force shaping human genetic diversity.
Revised: Long-range migrations and the resulting admixture between populations have been important forces shaping human genetic diversity.
Edit intent: fluency
Original:  We further show that we can discover phylogenetic relationships between populations by comparing weighted LD curves obtained using a suite of references.
Revised:  We further show that we can uncover phylogenetic relationships among populations by comparing weighted LD curves obtained using a suite of references.
Edit intent: clarity
Original:  Finally, we describe several improvements to the computation and fitting of weighted LD curves that greatly increase the robustness and speed of the computation .
Revised:  Finally, we describe several improvements to the computation and fitting of weighted LD curves that greatly increase the robustness and speed of the calculations .
Edit intent: clarity
Original:  We further show that the finite limit of (1-p)/p can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as \log 1/(1-\lambda), as \lambda \to 1.
Revised:  We further show that the finite limit of (1-p)/p can be achieved using only a finite lookahead window starting from the current time frame, whose length scales as \log 1/(1-\lambda), as \lambda \to 1.
Edit intent: fluency
Original:  It relates the homotopy invariant cat (G) , the minimal number of in G contractible graphs covering G, with crit(G), the minimal number of critical points which an injective function f on the vertex set V can have.
Revised:  It relates the minimal number tcat (G) , the minimal number of in G contractible graphs covering G, with crit(G), the minimal number of critical points which an injective function f on the vertex set V can have.
Edit intent: clarity
Original:  It relates the homotopy invariant cat (G) , the minimal number of in G contractible graphs covering G, with crit(G), the minimal number of critical points which an injective function f on the vertex set V can have.
Revised:  It relates the homotopy invariant cat (G) of in G contractible graphs covering G, with crit(G), the minimal number of critical points which an injective function f on the vertex set V can have.
Edit intent: fluency
Original:  We also prove  the cup length estimate cup(G) is less or equal to cat (G) which is valid also for any finite simple graph.
Revised:  We also prove that the cup length estimate cup(G) is less or equal to cat (G) which is valid also for any finite simple graph.
Edit intent: fluency
Original:  We also prove  the cup length estimate cup(G) is less or equal to cat (G) which is valid also for any finite simple graph.
Revised:  We also prove the cup length cup(G) is less or equal to cat (G) which is valid also for any finite simple graph.
Edit intent: clarity
Original:  We therefore have a relation between an algebraic (cup), a topological  (cat) and  analytic quantity ( crit).
Revised:  We therefore have a relation between an algebraic (cup), a topological quantity (cat) and analytic quantity ( crit).
Edit intent: fluency
Original:  We therefore have a relation between an algebraic (cup), a topological  (cat) and  analytic quantity ( crit).
Revised:  We therefore have a relation between an algebraic (cup), a topological (cat) and an analytic quantity ( crit).
Edit intent: fluency
Original:  Here, we describe extensions and improvements of previous models, new families of models, and --- perhaps most importantly --- a much more thorough treatment of algorithm parameters as model inputs.
Revised:  Here, we describe extensions and improvements of existing models, new families of models, and --- perhaps most importantly --- a much more thorough treatment of algorithm parameters as model inputs.
Edit intent: clarity
Original:  Here, we describe extensions and improvements of previous models, new families of models, and --- perhaps most importantly --- a much more thorough treatment of algorithm parameters as model inputs.
Revised:  Here, we describe extensions and improvements of previous models, new families of models, and -- perhaps most importantly --- a much more thorough treatment of algorithm parameters as model inputs.
Edit intent: fluency
Original:  Here, we describe extensions and improvements of previous models, new families of models, and --- perhaps most importantly --- a much more thorough treatment of algorithm parameters as model inputs.
Revised:  Here, we describe extensions and improvements of previous models, new families of models, and --- perhaps most importantly -- a much more thorough treatment of algorithm parameters as model inputs.
Edit intent: fluency
Original:  We also describe novel features for predicting algorithm runtime for the propositional satisfiability (SAT),  mixed integer programming (MIP) , and travelling salesperson (TSP) problems.
Revised:  We also describe novel features for predicting algorithm runtime for propositional satisfiability (SAT), mixed integer programming (MIP) , and travelling salesperson (TSP) problems.
Edit intent: clarity
Original:  We also describe novel features for predicting algorithm runtime for the propositional satisfiability (SAT),  mixed integer programming (MIP) , and travelling salesperson (TSP) problems.
Revised:  We also describe novel features for predicting algorithm runtime for the propositional satisfiability (SAT), mixed integer programming (MIP) problems.
Edit intent: clarity
Original: Computing the coordinate-wise maxima and  convex hull of a planar point set are probably the most classic problems in computational geometry.
Revised: Finding the coordinate-wise maxima and convex hull of a planar point set are probably the most classic problems in computational geometry.
Edit intent: clarity
Original: Computing the coordinate-wise maxima and  convex hull of a planar point set are probably the most classic problems in computational geometry.
Revised: Computing the coordinate-wise maxima and the convex hull of a planar point set are probably the most classic problems in computational geometry.
Edit intent: fluency
Original:  We give an algorithm for these problems in the self-improving setting.
Revised:  We consider these problems in the self-improving setting.
Edit intent: clarity
Original:  An input set of points (p1, p2, ..., pn ) is generated by taking an independent sample pi from each Di , so the input distribution D is the product D1 x D2 x . .. x Dn. A self-improving algorithm repeatedly gets inputs from the distribution D (which is a priori unknown) and tries to optimize its running time for D.
Revised:  An input point set (p_1, \ldots, p_n ) is generated by taking an independent sample pi from each Di , so the input distribution D is the product D1 x D2 x . .. x Dn. A self-improving algorithm repeatedly gets inputs from the distribution D (which is a priori unknown) and tries to optimize its running time for D.
Edit intent: clarity
Original:  An input set of points (p1, p2, ..., pn ) is generated by taking an independent sample pi from each Di , so the input distribution D is the product D1 x D2 x . .. x Dn. A self-improving algorithm repeatedly gets inputs from the distribution D (which is a priori unknown) and tries to optimize its running time for D.
Revised:  An input set of points (p1, p2, ..., pn ) is generated by taking an independent sample pi from each Di , so the input is distributed according to the product D = \prod_i D_i. A self-improving algorithm repeatedly gets inputs from the distribution D (which is a priori unknown) and tries to optimize its running time for D.
Edit intent: clarity
Original:  An input set of points (p1, p2, ..., pn ) is generated by taking an independent sample pi from each Di , so the input distribution D is the product D1 x D2 x . .. x Dn. A self-improving algorithm repeatedly gets inputs from the distribution D (which is a priori unknown) and tries to optimize its running time for D.
Revised:  An input set of points (p1, p2, ..., pn ) is generated by taking an independent sample pi from each Di , so the input distribution D is the product D1 x D2 x . .. x Dn. A self-improving algorithm repeatedly gets inputs from the distribution D (which is a priori unknown) , and it tries to optimize its running time for D.
Edit intent: coherence
Original:  \text{OPTCH}_\mathcal{D}) be } the expected depth of an optimal \emph{ linear comparison tree computing the maxima (resp. convex hull) for distribution D . Our maxima algorithm eventually has an expected running time of O(OPTMAX(D)_\mathcal{D} } + n) , even though it did not know D to begin with.
Revised:  \text{OPTCH}_\mathcal{D}) be } the expected depth of an \emph{ linear comparison tree computing the maxima (resp. convex hull) for distribution D . Our maxima algorithm eventually has an expected running time of O(OPTMAX(D)_\mathcal{D} } + n) , even though it did not know D to begin with.
Edit intent: clarity
Original:  \text{OPTCH}_\mathcal{D}) be } the expected depth of an optimal \emph{ linear comparison tree computing the maxima (resp. convex hull) for distribution D . Our maxima algorithm eventually has an expected running time of O(OPTMAX(D)_\mathcal{D} } + n) , even though it did not know D to begin with.
Revised:  \text{OPTCH}_\mathcal{D}) be } the expected depth of an optimal \emph{ linear comparison tree computing the maxima (resp. convex hull) for \mathcal{D . Our maxima algorithm eventually has an expected running time of O(OPTMAX(D)_\mathcal{D} } + n) , even though it did not know D to begin with.
Edit intent: clarity
Original:  \text{OPTCH}_\mathcal{D}) be } the expected depth of an optimal \emph{ linear comparison tree computing the maxima (resp. convex hull) for distribution D . Our maxima algorithm eventually has an expected running time of O(OPTMAX(D)_\mathcal{D} } + n) , even though it did not know D to begin with.
Revised:  \text{OPTCH}_\mathcal{D}) be } the expected depth of an optimal \emph{ linear comparison tree computing the maxima (resp. convex hull) for distribution D . Our maxima algorithm eventually achieves expected running time of O(OPTMAX(D)_\mathcal{D} } + n) , even though it did not know D to begin with.
Edit intent: clarity
Original:  Analogously, we have a self-improving algorithm for convex hull computation with expected running time O( OPTCH(D)_\mathcal{D} } + n log log n).
Revised:  Analogously, we have a self-improving algorithm for convex hulls with expected running time O( OPTCH(D)_\mathcal{D} } + n log log n).
Edit intent: clarity
Original:  Our results require new tools for manipulating linear comparison trees.
Revised:  Our results require new tools for understanding linear comparison trees.
Edit intent: clarity
Original:  In particular, we show how to convert a general linear comparison tree to a very restricted version , which can then berelated to the running time of our algorithms.
Revised:  In particular, we convert a general linear comparison tree to a very restricted version , which can then berelated to the running time of our algorithms.
Edit intent: clarity
Original:  In particular, we show how to convert a general linear comparison tree to a very restricted version , which can then berelated to the running time of our algorithms.
Revised:  In particular, we show how to convert a general linear comparison tree to a restricted version that can then be related to the running time of our algorithms.
Edit intent: clarity
Original:  Another interesting feature of our approach is an interleaved search , where we try to determine the likeliest point to be extremal with minimal computation.
Revised:  Another interesting feature is an interleaved search , where we try to determine the likeliest point to be extremal with minimal computation.
Edit intent: clarity
Original:  Another interesting feature of our approach is an interleaved search , where we try to determine the likeliest point to be extremal with minimal computation.
Revised:  Another interesting feature of our approach is an interleaved search procedure to determine the likeliest point to be extremal with minimal computation.
Edit intent: clarity
Original:  This allows the running time to be competitive with the optimal algorithm for the distribution D .
Revised:  This allows our algorithms to be competitive with the optimal algorithm for the distribution D .
Edit intent: clarity