wanyu/IteraTeR_v2 huggingface dataset:
Original:   Our proofs rely on new techniques , based on stochastic calculus, and bypass the use of hypercontractivity common to previous proofs.
Revised:  Our proofs rely on techniques based on stochastic calculus, and bypass the use of hypercontractivity common to previous proofs.
Edit intent: clarity
Original:  Our third contribution is an O(N)-time approximation algorithm  to compute domain orderings, under which one can compute a box cover of size O(K^r), where K is the minimum box cover for Q under any domain ordering and r is the maximum arity of any relation.
Revised:  Our third contribution is a O(N)-time approximation algorithm to compute domain orderings, under which one can compute a box cover of size O(K^r), where K is the minimum box cover for Q under any domain ordering and r is the maximum arity of any relation.
Edit intent: fluency
Original: Traditionally, the theory of condition numbers assumes errors in the data that are constrained to be tangent to the input space.
Revised: The classic theory of condition numbers assumes errors in the data that are constrained to be tangent to the input space.
Edit intent: clarity
Original: Traditionally, the theory of condition numbers assumes errors in the data that are constrained to be tangent to the input space.
Revised: Traditionally, the theory of condition numbers assumes errors in the data is assumed to be tangent to the input space.
Edit intent: clarity
Original:  We extend this theory to unconstrained perturbations in the case when the input space is an embedded submanifold of an ambient Euclidean space.
Revised:  We extend this theory to unconstrained perturbations in the case where the input space is an embedded submanifold of an ambient Euclidean space.
Edit intent: fluency
Original:  We validate our main results through experiments with  n-camera triangulation  in computer vision.
Revised:  We validate our main results through experiments with the n-camera triangulation in computer vision.
Edit intent: fluency
Original: We consider the local sensitivity of least-squares problems for inverse problems.
Revised: We consider the local sensitivity of least-squares formulations of inverse problems.
Edit intent: clarity
Original:  We assume that the sets of inputs and outputs of the inverse problem have the structures of Riemannian manifolds.
Revised:  The sets of inputs and outputs of the inverse problem have the structures of Riemannian manifolds.
Edit intent: coherence
Original:  We assume that the sets of inputs and outputs of the inverse problem have the structures of Riemannian manifolds.
Revised:  We assume that the sets of inputs and outputs of these problems are assumed to have the structures of Riemannian manifolds.
Edit intent: clarity
Original:  The problems we consider include the approximation problem of finding the nearest point on a Riemannian embedded submanifold to a given point in the ambient space.
Revised:  The problems we consider include the approximation problem of finding the nearest point on a Riemannian embedded submanifold from a given point in the ambient space.
Edit intent: clarity
Original:  Recent work has proposed program synthesis techniques to automatically decompile triangle meshes to easier-to-edit Constructive Solid Geometry (CSG) designs.
Revised:  Recent work has proposed program synthesis techniques to automatically decompile triangle meshes to Constructive Solid Geometry (CSG) designs.
Edit intent: clarity
Original:  Numerical experiments demonstrate that the integration error for highly oscillatory problems is smaller than the one of some standard methods.
Revised:  Numerical experiments demonstrate that the integration error for highly oscillatory problems is smaller than that of some standard methods.
Edit intent: clarity
Original:  Classical encoding models use linear multivariate methods to predict brain activation (all the voxels) given the stimulus.
Revised:  State-of-the-art encoding models use linear multivariate methods to predict brain activation (all the voxels) given the stimulus.
Edit intent: clarity
Original:  Classical encoding models use linear multivariate methods to predict brain activation (all the voxels) given the stimulus.
Revised:  Classical encoding models use linear multivariate methods to predict brain activation given the stimulus.
Edit intent: clarity
Original:  This study also helps in understanding which of the brain regions get activated together , given a certain kind of stimulus .
Revised:  This study also helps in understanding the brain regions get activated together , given a certain kind of stimulus .
Edit intent: clarity
Original:  This study also helps in understanding which of the brain regions get activated together , given a certain kind of stimulus .
Revised:  This study also helps in understanding which of the brain regions that are activated together given different kinds of stimuli .
Edit intent: clarity
Original: Recently, the RIDL-SIT technology has been field-tested for control of Aedes aegypti .
Revised: Recently, the RIDL-SIT technology has been field-tested for control of Aedes aegypti .
Edit intent: fluency
Original:  The development of the model allow us to indicate some critical biological knowledge that is missing and could (should) be produced.
Revised:  The development of the model allows us to indicate some critical biological knowledge that is missing and could (should) be produced.
Edit intent: fluency
Original: Feedback of calcium signaling through calcium-activated potassium channels of a dendritic spine is investigated.
Revised: We investigate calcium signaling feedback through calcium-activated potassium channels of a dendritic spine is investigated.
Edit intent: clarity
Original:  To simulate such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine , we apply\emph{the immersed boundary method with electrodiffusion .
Revised:  To simulate such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine \emph{the immersed boundary method with electrodiffusion .
Edit intent: coherence
Original:  To simulate such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine , we apply\emph{the immersed boundary method with electrodiffusion .
Revised:  To simulate such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine , we apply\emph{ .
Edit intent: coherence
Original:  In this simulation method , the permeability to ion flow across the membrane is regulated by the amplitude of chemical potential barriers along the membrane .
Revised:  In this simulation , the permeability to ion flow across the membrane is regulated by the amplitude of chemical potential barriers along the membrane .
Edit intent: clarity
Original:  In this simulation method , the permeability to ion flow across the membrane is regulated by the amplitude of chemical potential barriers along the membrane .
Revised:  In this simulation method , the permeability to ionic flow across the membrane is regulated by the amplitude of chemical potential barriers along the membrane .
Edit intent: clarity
Original:  In this simulation method , the permeability to ion flow across the membrane is regulated by the amplitude of chemical potential barriers along the membrane .
Revised:  In this simulation method , the permeability to ion flow across the membrane is regulated by the amplitude of chemical potential barriers .
Edit intent: fluency
Original:  This  represents the ion channel gating with multiple subunits, the open and closed states of which are governed by a continuous-time Markov process.
Revised:  This regulation represents the ion channel gating with multiple subunits, the open and closed states of which are governed by a continuous-time Markov process.
Edit intent: clarity
Original:  This  represents the ion channel gating with multiple subunits, the open and closed states of which are governed by a continuous-time Markov process.
Revised:  This represents the ion channel gating with multiple subunits, the open and closed states governed by a continuous-time Markov process.
Edit intent: clarity
Original:  The model simulation recapitulates an inhibitory action on voltage-sensitive calcium channels by  calcium-activated potassium channels in a stochastic manner with non-local feedback loop.
Revised:  The model simulation recapitulates an inhibitory action on voltage-sensitive calcium channels by the calcium-activated potassium channels in a stochastic manner with non-local feedback loop.
Edit intent: fluency
Original:  The model simulation recapitulates an inhibitory action on voltage-sensitive calcium channels by  calcium-activated potassium channels in a stochastic manner with non-local feedback loop.
Revised:  The model simulation recapitulates an inhibitory action on voltage-sensitive calcium channels by calcium-activated potassium channels in a stochastic manner as a non-local feedback loop.
Edit intent: clarity
Original:  The model also predicts higher calcium influx with more closely placed channel complexes, resolving a potential mechanism of differential calcium handling by locality of channel distribution .
Revised:  The model predicts amplified calcium influx with more closely placed channel complexes, resolving a potential mechanism of differential calcium handling by locality of channel distribution .
Edit intent: clarity
Original:  The model also predicts higher calcium influx with more closely placed channel complexes, resolving a potential mechanism of differential calcium handling by locality of channel distribution .
Revised:  The model also predicts higher calcium influx with more closely placed channel complexes, proposing a potential mechanism of differential calcium handling by locality of channel distribution .
Edit intent: clarity
Original:  The model also predicts higher calcium influx with more closely placed channel complexes, resolving a potential mechanism of differential calcium handling by locality of channel distribution .
Revised:  The model also predicts higher calcium influx with more closely placed channel complexes, resolving a potential mechanism of differential calcium handling by of channel distribution .
Edit intent: clarity
Original:  The model also predicts higher calcium influx with more closely placed channel complexes, resolving a potential mechanism of differential calcium handling by locality of channel distribution .
Revised:  The model also predicts higher calcium influx with more closely placed channel complexes, resolving a potential mechanism of differential calcium handling by locality channel distributions .
Edit intent: clarity
Original: The shared response model provides a simple but effective framework toanalyse fMRI data of subjects exposed to naturalistic stimuli.
Revised: The shared response model provides a simple but effective framework to analyse fMRI data of subjects exposed to naturalistic stimuli.
Edit intent: fluency
Original:  However whenthe number of subjects or runs is large, fitting the model requires a large amountof memory and computational power, which limits its use in practice.
Revised:  However when the number of subjects or runs is large, fitting the model requires a large amountof memory and computational power, which limits its use in practice.
Edit intent: fluency
Original:  However whenthe number of subjects or runs is large, fitting the model requires a large amountof memory and computational power, which limits its use in practice.
Revised:  However whenthe number of subjects or runs is large, fitting the model requires a large amount of memory and computational power, which limits its use in practice.
Edit intent: fluency
Original:  In thiswork , we introduce the FastSRM algorithm that relies on an intermediate atlas-based representation.
Revised:  In this work , we introduce the FastSRM algorithm that relies on an intermediate atlas-based representation.
Edit intent: fluency
Original:  It provides considerable speed-up in time and memoryusage , hence it allows easy and fast large-scale analysis of naturalistic-stimulusfMRI data.
Revised:  It provides considerable speed-up in time and memory usage , hence it allows easy and fast large-scale analysis of naturalistic-stimulusfMRI data.
Edit intent: fluency
Original:  It provides considerable speed-up in time and memoryusage , hence it allows easy and fast large-scale analysis of naturalistic-stimulusfMRI data.
Revised:  It provides considerable speed-up in time and memoryusage , hence it allows easy and fast large-scale analysis of naturalistic-stimulus fMRI data.
Edit intent: fluency
Original:  Using four different datasets, we show that our method outperformsthe original SRM algorithm while being about 5x faster and 20x to 40x morememory efficient.
Revised:  Using four different datasets, we show that our method matches the performance of the original SRM algorithm while being about 5x faster and 20x to 40x morememory efficient.
Edit intent: clarity
Original:  Using four different datasets, we show that our method outperformsthe original SRM algorithm while being about 5x faster and 20x to 40x morememory efficient.
Revised:  Using four different datasets, we show that our method outperformsthe original SRM algorithm while being about 5x faster and 20x to 40x more memory efficient.
Edit intent: fluency
Original:  Based on this contribution, we use FastSRM to predict agefrom movie watching data on the CamCAN sample.
Revised:  Based on this contribution, we use FastSRM to predict age from movie watching data on the CamCAN sample.
Edit intent: fluency
Original:  Besides delivering accuratepredictions (mean absolute error of 7.5 years), FastSRM extracts topographicpatterns that are predictive of age, demonstrating that brain activity duringfree perception reflects age.
Revised:  Besides delivering accurate predictions (mean absolute error of 7.5 years), FastSRM extracts topographicpatterns that are predictive of age, demonstrating that brain activity duringfree perception reflects age.
Edit intent: fluency
Original:  Besides delivering accuratepredictions (mean absolute error of 7.5 years), FastSRM extracts topographicpatterns that are predictive of age, demonstrating that brain activity duringfree perception reflects age.
Revised:  Besides delivering accuratepredictions (mean absolute error of 7.5 years), FastSRM extracts topographic patterns that are predictive of age, demonstrating that brain activity duringfree perception reflects age.
Edit intent: fluency
Original:  Besides delivering accuratepredictions (mean absolute error of 7.5 years), FastSRM extracts topographicpatterns that are predictive of age, demonstrating that brain activity duringfree perception reflects age.
Revised:  Besides delivering accuratepredictions (mean absolute error of 7.5 years), FastSRM extracts topographicpatterns that are predictive of age, demonstrating that brain activity during free perception reflects age.
Edit intent: fluency
Original:  This corresponds to a local time term in the equation for the asset price.
Edit intent: coherence
Original:  Using white noise and Hida-Malliavin calculus we compute explicitly the optimal consumption rate and portfolio in this case and we show that the maximal value is finite as long as \theta> 0.
Revised:  Using white noise calculus we compute explicitly the optimal consumption rate and portfolio in this case and we show that the maximal value is finite as long as \theta> 0.
Edit intent: clarity
Original: This models a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier in order to prevent it from going below that barrier .
Revised: This can for example model a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier in order to prevent it from going below that barrier .
Edit intent: clarity
Original: This models a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier in order to prevent it from going below that barrier .
Revised: This models a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier .
Edit intent: clarity
Original:  See e.g. Jarrow \& Protter \mbox{ JP  for an explanation and discussion of this model  .
Revised:  See e.g. Jarrow Protter for an explanation and discussion of this model .
Edit intent: coherence
Original:  See e.g. Jarrow \& Protter \mbox{ JP  for an explanation and discussion of this model  .
Revised:  See e.g. Jarrow \& Protter \mbox{ JP JP for an explanation and discussion of this model .
Edit intent: fluency
Original:  As already pointed out by Karatzas \& Shreve \mbox{ KS0pt (see also Jarrow \& Protter \mbox{ JP }0pt )}  }  this allows for arbitrages in the market.
Revised:  As already pointed out by Karatzas 0pt (see also Jarrow \& Protter \mbox{ JP }0pt )} } this allows for arbitrages in the market.
Edit intent: clarity
Original:  See e.g. Lachapelleet al \mbox{ LLLL . In this paper we consider the case when there is a delay \theta> 0 in the information flow available for the trader.
Revised:  See e.g. Lachapelle \mbox{ LLLL . In this paper we consider the case when there is a delay \theta> 0 in the information flow available for the trader.
Edit intent: clarity
Original: We study a financial market where the risky asset is modelled by a geometric It\^o-L\'evy process, with a singular drift term.
Revised: We study a financial market where the risky asset is modelled by a geometric It\^o-L\'{e process, with a singular drift term.
Edit intent: fluency
Original:  See e.g. Jarrow & Protter JP for an explanation and discussion of this model in the Brownian motion case.
Revised:  See e.g. Jarrow & Protter for an explanation and discussion of this model in the Brownian motion case.
Edit intent: clarity
Original:  As already pointed out by Karatzas & Shreve KS (in the Brownian motion case ), this allows for arbitrages in the market.
Revised:  As already pointed out by Karatzas & Shreve (in the Brownian motion case ), this allows for arbitrages in the market.
Edit intent: clarity
Original:   See e.g. Lachapelle et al LLLL and the references therein.
Revised:  See e.g. Lachapelle et al and the references therein.
Edit intent: coherence
Original:  A boundary integral method together with a special quadrature scheme is applied to solve the Stokes equations to high accuracy, also for droplets in close interaction .
Revised:  A boundary integral method together with a special quadrature scheme is applied to solve the Stokes equations to high accuracy, also for closely interacting droplets .
Edit intent: clarity
Original:  The problem is considered in a periodic setting and an Ewald decomposition for the Stokeslet and stresslet is derivedto make the periodic sums convergent . Computations are sped up using the Spectral Ewald method.
Revised:  The problem is considered in a periodic setting and Ewald decompositions for the Stokeslet and stresslet is derivedto make the periodic sums convergent . Computations are sped up using the Spectral Ewald method.
Edit intent: fluency
Original:  The problem is considered in a periodic setting and an Ewald decomposition for the Stokeslet and stresslet is derivedto make the periodic sums convergent . Computations are sped up using the Spectral Ewald method.
Revised:  The problem is considered in a periodic setting and an Ewald decomposition for the Stokeslet and stresslet are derived . Computations are sped up using the Spectral Ewald method.
Edit intent: clarity
Original:  The problem is considered in a periodic setting and an Ewald decomposition for the Stokeslet and stresslet is derivedto make the periodic sums convergent . Computations are sped up using the Spectral Ewald method.
Revised:  The problem is considered in a periodic setting and an Ewald decomposition for the Stokeslet and stresslet is derivedto make the periodic sums convergent . Computations are accelerated using the spectral Ewald method.
Edit intent: fluency
Original:  The numerical method is tested through several convergence studies and other challenging examples and is shown to handle drops in close proximity both to other drops and solid objects to a high accuracy.
Revised:  The numerical method is tested through several convergence studies and other challenging examples and is shown to handle drops in close proximity both to other drops and solid objects to high accuracy.
Edit intent: fluency
Original:  The contribution of this paper is twofold: first, it formulates the trace completion as a reachability problem over data-aware models and second, it provides a rigorous mapping between our data-aware models and three important paradigms for reasoning about dynamic systems , namely Action Languages, Classical Planning, and Model-Checking.
Revised:  The contribution of this paper is twofold: first, it formulates the trace completion as a reachability problem over data-aware models and second, it provides a rigorous mapping between our data-aware models and three important paradigms for reasoning about dynamic systems : Action Languages, Classical Planning, and Model-Checking.
Edit intent: fluency
Original:  The rigorous encoding of our data-aware models, based on a common interpretation of the semantics of Action Languages, Classical Planning, and Model-Checking in terms of transition systems, paired with a first comprehensive assessment of the performances of their tools in computing reachability for data-aware workflow net languages, provide a solid contribution to advancing the state-of-the-art on the concrete exploitation of formal verification techniques on  business processes.
Revised:  The rigorous encoding of our data-aware models, based on a common interpretation of the semantics of Action Languages, Classical Planning, and Model-Checking in terms of transition systems, paired with a first comprehensive assessment of the performance of three popular tools supporting the above paradigms in solving reachability problems for imperative data-aware workflow net languages, provide a solid contribution to advancing the state-of-the-art on the concrete exploitation of formal verification techniques on business processes.
Edit intent: clarity
Original:  The rigorous encoding of our data-aware models, based on a common interpretation of the semantics of Action Languages, Classical Planning, and Model-Checking in terms of transition systems, paired with a first comprehensive assessment of the performances of their tools in computing reachability for data-aware workflow net languages, provide a solid contribution to advancing the state-of-the-art on the concrete exploitation of formal verification techniques on  business processes.
Revised:  The rigorous encoding of our data-aware models, based on a common interpretation of the semantics of Action Languages, Classical Planning, and Model-Checking in terms of transition systems, paired with a first comprehensive assessment of the performances of their tools in computing reachability for data-aware business processes, which paves the way for a theoretically well founded and practically viable exploitation of formal verification techniques on business processes.
Edit intent: clarity