wanyu/IteraTeR_v2 huggingface dataset:
Original:  However  when \sigma(y)=0 and since the price of the option depends on the second Brownian motion in which the volatility is defined, the (1 + 2) evolution is not reduced to the Black-Scholes-Merton equation , the model admits five Lie symmetries, plus the linear symmetry and the infinity number of solution symmetries.
Revised:  However when \sigma(y)=0 and since the price of the option depends on the second Brownian motion in which the volatility is defined, the (1 + 2) evolution is not reduced to the Black--Scholes--Merton Equation , the model admits five Lie symmetries, plus the linear symmetry and the infinity number of solution symmetries.
Edit intent: fluency
Original:  However  when \sigma(y)=0 and since the price of the option depends on the second Brownian motion in which the volatility is defined, the (1 + 2) evolution is not reduced to the Black-Scholes-Merton equation , the model admits five Lie symmetries, plus the linear symmetry and the infinity number of solution symmetries.
Revised:  However when \sigma(y)=0 and since the price of the option depends on the second Brownian motion in which the volatility is defined, the (1 + 2) evolution is not reduced to the Black-Scholes-Merton equation , the model admits five Lie symmetries, plus the linear symmetry and the infinite number of solution symmetries.
Edit intent: coherence
Original:  Furthermore we apply the zero-order invariants of the Lie symmetries and we reduce the (1 + 2) evolution equation to a linear second-order ordinary differential equation.
Revised:  We apply the zeroth-order invariants of the Lie symmetries and we reduce the (1 + 2) evolution equation to a linear second-order ordinary differential equation.
Edit intent: coherence
Original:  Finally  we study two models of special interest, the Heston model and the Stein-Stein model.
Revised:  Finally , we study two models of special interest, the Heston model and the Stein-Stein model.
Edit intent: fluency
Original:  Finally  we study two models of special interest, the Heston model and the Stein-Stein model.
Revised:  Finally we study two models of special interest, the Heston model and the Stein--Stein model.
Edit intent: clarity
Original: The computational task of continuous-time state estimation , nonlinear filtering and identification, i.e. ~parameter learning, poses a class of interesting problems, which mathematicians have been working on for over 50 years and which has received increasing attention in both machine-learning and neuroscience communities.
Revised: The computational task of continuous-time state estimation , i.e. ~parameter learning, poses a class of interesting problems, which mathematicians have been working on for over 50 years and which has received increasing attention in both machine-learning and neuroscience communities.
Edit intent: coherence
Original:  We show that the numerical performance of the model is adequate to account for both nonlinear filtering and identification problems.
Revised:  We show that the numerical performance of the model is adequate to account for both filtering and identification problems.
Edit intent: clarity
Original:  Recently proposed methodologies lack a satisfactory discussion of whether they actually produce the correct results according to their definition, especially in the context of Convolutional Neural Networks .
Revised:  Recently proposed methodologies lack a satisfactory analysis whether they actually produce the correct results according to their definition, especially in the context of Convolutional Neural Networks .
Edit intent: clarity
Original: We introduce and analyze a rigorous formulation of the dynamics of a signal processing scheme aimed at exact dense signal scanning  . Related methods proposed in the recent past lack a satisfactory analysis  whether they actually fulfill any exactness constraints.
Revised: A rigorous formulation of the dynamics of a signal processing scheme aimed at exact dense signal scanning . Related methods proposed in the recent past lack a satisfactory analysis whether they actually fulfill any exactness constraints.
Edit intent: coherence
Original: We introduce and analyze a rigorous formulation of the dynamics of a signal processing scheme aimed at exact dense signal scanning  . Related methods proposed in the recent past lack a satisfactory analysis  whether they actually fulfill any exactness constraints.
Revised: We introduce and analyze a rigorous formulation of the dynamics of a signal processing scheme aimed at dense signal scanning . Related methods proposed in the recent past lack a satisfactory analysis whether they actually fulfill any exactness constraints.
Edit intent: fluency
Original: We introduce and analyze a rigorous formulation of the dynamics of a signal processing scheme aimed at exact dense signal scanning  . Related methods proposed in the recent past lack a satisfactory analysis  whether they actually fulfill any exactness constraints.
Revised: We introduce and analyze a rigorous formulation of the dynamics of a signal processing scheme aimed at exact dense signal scanning . Related methods proposed in the recent past lack a satisfactory analysis of whether they actually fulfill any exactness constraints.
Edit intent: fluency
Original:  We improve on this through an exact characterization of the requirements for a sound sliding window approach.
Revised:  This is improved through an exact characterization of the requirements for a sound sliding window approach.
Edit intent: clarity
Original:  The contributed theory helps to eliminate redundant computations and renders special case treatment unnecessary, resulting in a dramatic boost in efficiency particularly on massively parallel processors.
Revised:  The proposed theory helps to eliminate redundant computations and renders special case treatment unnecessary, resulting in a dramatic boost in efficiency particularly on massively parallel processors.
Edit intent: clarity
Original: Collective sensing by many interacting cells is observed in a variety of biological systems, and yet a quantitative understanding of how sensory information is encoded by many cells is still lacking.
Revised: Collective sensing by interacting cells is observed in a variety of biological systems, and yet a quantitative understanding of how sensory information is encoded by many cells is still lacking.
Edit intent: clarity
Original:  In this study, we characterize the calcium dynamics of cocultured monolayers of fibroblast cells and breast cancer cells in response to external ATP stimuli.
Revised:  In this study, we characterize the calcium dynamics of monolayers of fibroblast cells and breast cancer cells in response to external ATP stimuli.
Edit intent: clarity
Original:  Instead, our results suggest that multicellular networks are organized near a dynamical critical point which allows cell-to-cell communications to significantly modulate the collective cellular dynamics .
Revised:  Instead, our results suggest that multicellular networks sit at a point in parameter space where cell-cell communication has a significant effect on the sensory response, allowing cells to simultaneously respond to a sensory input and to the presence of neighbors .
Edit intent: clarity
Original: The paper is devoted to the numerical solution of an elastoplastic constitutive initial value problems containing the Mohr-Coulomb yield criterion, a nonassociative plastic flow rule  and a nonlinear isotropic hardening.
Revised: The paper is devoted to the numerical solution of an elastoplastic constitutive initial value problem containing the Mohr-Coulomb yield criterion, a nonassociative plastic flow rule and a nonlinear isotropic hardening.
Edit intent: fluency
Original: The paper is devoted to the numerical solution of an elastoplastic constitutive initial value problems containing the Mohr-Coulomb yield criterion, a nonassociative plastic flow rule  and a nonlinear isotropic hardening.
Revised: The paper is devoted to the numerical solution of an elastoplastic constitutive initial value problems containing the Mohr-Coulomb yield criterion, a nonassociative plastic flow rule , and a nonlinear isotropic hardening.
Edit intent: fluency
Original:  The  plastic flow rule is formulated in a subdifferential form to keep just one plastic multiplier .
Revised:  The plastic flow rule using the subdifferential of the plastic potential to keep just one plastic multiplier .
Edit intent: clarity
Original: The current computer programmings encapsulate attributes and behaviours into objects, while without a mechanism to support connections between them.
Revised: The current computer programmings encapsulate attributes and behaviours into objects, but miss the mechanism to support connections between them.
Edit intent: clarity
Original:  A protocol programming paradigm is presented here, which builds an infrastructure (a connecting thread network) to connect all instantiated objects.
Revised:  A protocol programming paradigm is presented to connect all instantiated objects.
Edit intent: clarity
Original:  In this paper, an implementation is developed to show methodologies of protocol programming .
Revised:  In this paper, an implementation is also discussed to show the effectiveness of protocol programming .
Edit intent: clarity
Original:  We consider in detail the BSDE (backward stochastic differential equations ) characterising the value  function.
Revised:  We consider in detail the BSDE (backward stochastic differential equation ) characterising the value function.
Edit intent: fluency
Original: Point cloud is the most fundamental representation of 3D geometric objects as it provides the most exact information of them .
Revised: Point cloud is the most fundamental representation of 3D geometric objects .
Edit intent: clarity
Original:  While empirical studies have been done to infer network growth processes in these sites, few studies have characterized social interaction behavior and the role of social interaction in network growth.
Revised:  While empirical studies have been done to learn about the network growth processes in these sites, few studies have characterized social interaction behavior and the role of social interaction in network growth.
Edit intent: clarity
Original:  While empirical studies have been done to infer network growth processes in these sites, few studies have characterized social interaction behavior and the role of social interaction in network growth.
Revised:  While empirical studies have been done to infer network growth processes in these sites, few studies have focused on social interaction behaviour and the effect of social interaction in network growth.
Edit intent: clarity
Original:  While empirical studies have been done to infer network growth processes in these sites, few studies have characterized social interaction behavior and the role of social interaction in network growth.
Revised:  While empirical studies have been done to infer network growth processes in these sites, few studies have characterized social interaction behavior and the role of social interaction on network growth.
Edit intent: clarity
Original:  In this paper, we analyze large-scale data collected from the Flickr social network to understand favoriting behavior and study the effect of a favorite on network growth .
Revised:  In this paper, we analyze large-scale data collected from the Flickr social network to learn about individual favoriting behaviour and examine the occurrence of link formation after a favorite is created .
Edit intent: clarity
Original:  Our investigation reveals that (a) favoriting is well-described by preferential attachment, (b) over 50\% of favorites are reciprocated within 10 days if at all they are reciprocated, (c) different kinds of favorites differ in how fast they are reciprocated, and (d) favoriting leads to link formation in the follow layer through multiplex triadic closure .
Revised:  Our investigation reveals that (a) favoriting is well-described by preferential attachment, (b) over 50\% of favorites are reciprocated within 10 days if at all they are reciprocated, (c) different kinds of favorites differ in how fast they are reciprocated, and (d) after a favorite is created, multiplex triangles are closed by the creation of follow links by the favoriter's followers to the favorite receiver .
Edit intent: clarity
Original:  Our algorithm uses rook strategy during its active pursuit phase, rather than the well-known lion  strategy.
Revised:  Our algorithm uses rook strategy during its pursuit phase, rather than the well-known lion strategy.
Edit intent: clarity
Original:  Our algorithm uses rook strategy during its active pursuit phase, rather than the well-known lion  strategy.
Revised:  Our algorithm uses rook strategy during its active pursuit phase, rather than the well-known lion 's strategy.
Edit intent: clarity
Original:  The rook  strategy is crucial for obtaining a capture time that is linear in the area of Q. For  monotone and scallop polygons, our algorithm has a capture time of O(n(Q) + area(Q)), where n(Q) is the number of polygon vertices .
Revised:  The rook 's strategy is crucial for obtaining a capture time that is linear in the area of Q. For monotone and scallop polygons, our algorithm has a capture time of O(n(Q) + area(Q)), where n(Q) is the number of polygon vertices .
Edit intent: fluency
Original:  The rook  strategy is crucial for obtaining a capture time that is linear in the area of Q. For  monotone and scallop polygons, our algorithm has a capture time of O(n(Q) + area(Q)), where n(Q) is the number of polygon vertices .
Revised:  The rook strategy is crucial for obtaining a capture time that is linear in the area of Q. For both monotone and scallop polygons, our algorithm has a capture time of O(n(Q) + area(Q)), where n(Q) is the number of polygon vertices .
Edit intent: clarity
Original:  Very recently , Lokshtanov, Pilipczuk and van Leeuwen showed that weighted ED is solvable in polynomial time for P_6-free graphs, based on their sub-exponential algorithm for the Maximum Weight Independent Set problem for P_6-free graphs.
Revised:  Recently , Lokshtanov, Pilipczuk and van Leeuwen showed that weighted ED is solvable in polynomial time for P_6-free graphs, based on their sub-exponential algorithm for the Maximum Weight Independent Set problem for P_6-free graphs.
Edit intent: coherence
Original: The use of Liouvillian forms to construct symplectic and Hamiltonian maps is a natural generalization to the method of generating functions, which gives us a deeper unsderstanding of the underlying geometry .
Revised: The use of Liouvillian forms to construct symplectic and Hamiltonian maps is a natural generalization of the method of generating functions, which gives us a deeper unsderstanding of the underlying geometry .
Edit intent: fluency
Original: The use of Liouvillian forms to construct symplectic and Hamiltonian maps is a natural generalization to the method of generating functions, which gives us a deeper unsderstanding of the underlying geometry .
Revised: The use of Liouvillian forms to construct symplectic and Hamiltonian maps is a natural generalization to the method of generating functions, which gives us a deeper unsderstanding of the geometry of this procedure .
Edit intent: clarity
Original:  We give an interpretation of this result based on the original framework constructed by Poincar\'e.
Revised:  We give an interpretation of this result based in the original framework constructed by Poincar\'e.
Edit intent: fluency
Original: The use of Liouvillian forms to construct symplectic and Hamiltonian maps is a natural generalization of the method of generating functions, which gives us a deeper unsderstanding of the geometry of this procedure.
Revised: The use of Liouvillian forms to construct symplectic and Hamiltonian maps is a natural alternative to the method of generating functions, which gives us a deeper unsderstanding of the geometry of this procedure.
Edit intent: clarity
Original: The use of Liouvillian forms to construct symplectic and Hamiltonian maps is a natural generalization of the method of generating functions, which gives us a deeper unsderstanding of the geometry of this procedure.
Revised: The use of Liouvillian forms to construct symplectic and Hamiltonian maps is a natural generalization of the method of generating functions, and provides a deeper understanding of the geometry of this procedure.
Edit intent: clarity
Original:  We show that under this method , Poincar\'e's generating function does not corresponds to the symplectic mid-point rule, but to the identity map.
Revised:  We show that in this framework , Poincar\'e's generating function does not corresponds to the symplectic mid-point rule, but to the identity map.
Edit intent: clarity
Original:  We show that under this method , Poincar\'e's generating function does not corresponds to the symplectic mid-point rule, but to the identity map.
Revised:  We show that under this method , Poincar\'e's generating function does not correspond to the symplectic mid-point rule, but to the identity map.
Edit intent: fluency
Original:  We give an interpretation of this result based in the original framework constructed by Poincar\'e.
Revised:  We give an interpretation of this result based on the original framework constructed by Poincar\'e.
Edit intent: fluency
Original:  Additionally, we construct families of Liouvillian forms generating, as a particular case, the mid-point rule, showing that their structure is different to the differential of the generating function used by Poincar\'e for studying periodic orbits.
Revised:  Additionally, we construct families of Liouvillian forms generating, as a particular case, the mid-point rule, showing that their structure is different from the differential of the generating function used by Poincar\'e for studying periodic orbits.
Edit intent: fluency
Original:  Additionally, we construct families of Liouvillian forms generating, as a particular case, the mid-point rule, showing that their structure is different from the differential of the generating function used by Poincar\'e for studying periodic orbits.
Edit intent: coherence
Original:  On the one hand, the new framework captures very closely the true, micro-level, mechanics of an auction-style exchange.
Revised:  The new framework captures very closely the true, micro-level, mechanics of an auction-style exchange.
Edit intent: coherence
Original:  On the other hand , it uses the standard abstractions of games with continuum of players (in particular, the mean field game theory) to obtain a tractable macro-level description of the LOB.
Revised:  At the same time , it uses the standard abstractions of games with continuum of players (in particular, the mean field game theory) to obtain a tractable macro-level description of the LOB.
Edit intent: coherence
Original:  On the other hand , it uses the standard abstractions of games with continuum of players (in particular, the mean field game theory) to obtain a tractable macro-level description of the LOB.
Revised:  On the other hand , it uses the standard abstractions of a continuum-player game to obtain a tractable macro-level description of the LOB.
Edit intent: coherence
Original:  We use the proposed modeling framework to analyze the effects of trading frequency on the liquidity of the market in a very general setting.
Revised:  We use the proposed modeling framework to analyze the effects of trading frequency on the market liquidity in a very general setting.
Edit intent: clarity
Original:  In particular, we show that the higher trading frequency increases market efficiency  if the agents choose to provide liquidity in equilibrium.
Revised:  In particular, we show that the higher trading frequency increases market efficiency , if the agents choose to provide liquidity in equilibrium.
Edit intent: fluency
Original: We use the proposed modeling framework to analyze the effects of trading frequency on the market liquidity in a very general setting.
Revised: We use the proposed modeling framework to analyze the effects of trading frequency on market liquidity in a very general setting.
Edit intent: fluency
Original:  This framework allows us to provide more insight into how such a liquidity crises unfolds, connecting it to the so-called adverse selection effect.
Revised:  This framework allows us to provide more insight into how such a liquidity crisis unfolds, connecting it to the so-called adverse selection effect.
Edit intent: fluency
Original: In this work , we present a discrete time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents).
Revised: In this article , we present a discrete time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents).
Edit intent: clarity
Original:  This framework allows us to provide more insight into how such a liquidity crisis unfolds, connecting it to the so-called adverse selection effect.
Revised:  This framework enables us to provide more insight into how such a liquidity crisis unfolds, connecting it to the so-called adverse selection effect.
Edit intent: fluency
Original:  In Twitter there are different types of users, but most utility lies in finding the most influential ones.
Revised:  Twitter has different types of users, but most utility lies in finding the most influential ones.
Edit intent: clarity
Original:  In Twitter there are different types of users, but most utility lies in finding the most influential ones.
Revised:  In Twitter there are different types of users, but the greatest utility lies in finding the most influential ones.
Edit intent: clarity
Original:  The purpose of this article is to collect and classify the different measures of influence of Twitter that exist so far in literature.
Revised:  The purpose of this article is to collect and classify the different Twitter influence measures that exist so far in literature.
Edit intent: clarity
Original:  The diversity of these measures is very high . Some are based on simple metrics , and others are based on complex mathematical models.
Revised:  These measures are very diverse . Some are based on simple metrics , and others are based on complex mathematical models.
Edit intent: clarity
Original:  Some measures consider the timeline of publication, others the content of the messages, some are focused on specific topics, and others try to make predictions.
Revised:  Some others consider the timeline of publication, others the content of the messages, some are focused on specific topics, and others try to make predictions.
Edit intent: clarity
Original:  We consider all these aspects, and some additional others .
Revised:  We consider all these aspects, and some additional ones .
Edit intent: clarity
Original:  Furthermore, we mention measures of activity and popularity, the traditional mechanisms to correlate measures, and some simple but important aspects of computational complexity for this particular context.
Revised:  Furthermore, we include measures of activity and popularity, the traditional mechanisms to correlate measures, and some simple but important aspects of computational complexity for this particular context.
Edit intent: coherence
Original:  Furthermore, we mention measures of activity and popularity, the traditional mechanisms to correlate measures, and some simple but important aspects of computational complexity for this particular context.
Revised:  Furthermore, we mention measures of activity and popularity, the traditional mechanisms to correlate measures, and some important aspects of computational complexity for this particular context.
Edit intent: coherence