wanyu/IteraTeR_v2 huggingface dataset:
Original:  ( 2) each peer consumes more content at a cooperative solution than at a non-cooperative solution;
Revised:  ( 2) a cooperative scheme allows peers to consume more content than non-cooperative solution;
Edit intent: clarity
Original:  In addition to providing the solutions of our model from different approaches , we discuss from a protocol designer's point of view the requirements of each solutionconcept in terms of the enforceability of peers' sharing decisions by the protocol designer and the level of knowledge needed for the protocol designer and peers .
Revised:  In addition to describing the solutions of our model from different approaches , we discuss from a protocol designer's point of view the requirements of each solutionconcept in terms of the enforceability of peers' sharing decisions by the protocol designer and the level of knowledge needed for the protocol designer and peers .
Edit intent: clarity
Original:  In addition to providing the solutions of our model from different approaches , we discuss from a protocol designer's point of view the requirements of each solutionconcept in terms of the enforceability of peers' sharing decisions by the protocol designer and the level of knowledge needed for the protocol designer and peers .
Revised:  In addition to providing the solutions of different formulations , we discuss from a protocol designer's point of view the requirements of each solutionconcept in terms of the enforceability of peers' sharing decisions by the protocol designer and the level of knowledge needed for the protocol designer and peers .
Edit intent: clarity
Original:  In addition to providing the solutions of our model from different approaches , we discuss from a protocol designer's point of view the requirements of each solutionconcept in terms of the enforceability of peers' sharing decisions by the protocol designer and the level of knowledge needed for the protocol designer and peers .
Revised:  In addition to providing the solutions of our model from different approaches , we discuss enforcement and informational requirements to implement each solution, aiming to offer a guideline for protocol designers when designing incentive schemes for P2P networks .
Edit intent: clarity
Original:  Let G be a 3-connected claw-free graph, x a vertex in G, e = xy is an edge in G, and P a 3-vertex path in G. Then (a1) if v(G) = 0 mod 3, then G has an L-factor containing (avoiding) e, (a2) if v(G) = 1 mod 3, then G -
Revised:  Let G be a 3-connected claw-free graph, x a vertex in G, e = xy an edge in G, and P a 3-vertex path in G. Then (a1) if v(G) = 0 mod 3, then G has an L-factor containing (avoiding) e, (a2) if v(G) = 1 mod 3, then G -
Edit intent: clarity
Original: In abstract interpretation , approximation is  encoded by abstract domains . Abstract domains provide a systematic guideline for defining abstract semantic functions as so-called best correct approximations of concrete semantic functions .
Revised: In abstract interpretation , approximation is typically encoded by abstract domains . Abstract domains provide a systematic guideline for defining abstract semantic functions as so-called best correct approximations of concrete semantic functions .
Edit intent: clarity
Original: In abstract interpretation , approximation is  encoded by abstract domains . Abstract domains provide a systematic guideline for defining abstract semantic functions as so-called best correct approximations of concrete semantic functions .
Revised: In abstract interpretation , approximation is encoded by abstract domains , providing systematic guidelines for specifying approximate semantic functions and precision assessments .
Edit intent: clarity
Original:  However, it may happen that an abstract domain is unnecessarily too accurate for the specific purpose of approximating a given set of semantic functions.
Revised:  However, it may happen that an abstract domain contains redundant information for the specific purpose of approximating a given set of semantic functions.
Edit intent: clarity
Original:  This work puts forward Abstraction-Guided Abstraction Simplification (AGAS) , a methodology that allows to simplify abstract domains, i.e. to remove abstract values from them, in a maximal way while retaining exactly the same best correct approximations of concrete semantic functions .
Revised:  This work puts forward Abstraction-Guided Abstraction Simplification (AGAS) , a methodology for simplifying abstract domains, i.e. to remove abstract values from them, in a maximal way while retaining exactly the same best correct approximations of concrete semantic functions .
Edit intent: clarity
Original:  This work puts forward Abstraction-Guided Abstraction Simplification (AGAS) , a methodology that allows to simplify abstract domains, i.e. to remove abstract values from them, in a maximal way while retaining exactly the same best correct approximations of concrete semantic functions .
Revised:  This work puts forward Abstraction-Guided Abstraction Simplification (AGAS) , a methodology that allows to simplify abstract domains, i.e. removing abstract values from them, in a maximal way while retaining exactly the same best correct approximations of concrete semantic functions .
Edit intent: fluency
Original:  This work puts forward Abstraction-Guided Abstraction Simplification (AGAS) , a methodology that allows to simplify abstract domains, i.e. to remove abstract values from them, in a maximal way while retaining exactly the same best correct approximations of concrete semantic functions .
Revised:  This work puts forward Abstraction-Guided Abstraction Simplification (AGAS) , a methodology that allows to simplify abstract domains, i.e. to remove abstract values from them, in a maximal way while retaining exactly the same approximate behavior of the system under analysis .
Edit intent: clarity
Original:  We show how AGAS can be applied in the context of abstract model checking by providing a simplification paradigm of abstract state spaces that can be viewed as a dual methodology to CounterExample-Guided Abstraction Refinement (CEGAR) .
Revised:  We show that, in abstract model checking by providing a simplification paradigm of abstract state spaces that can be viewed as a dual methodology to CounterExample-Guided Abstraction Refinement (CEGAR) .
Edit intent: coherence
Original:  We show how AGAS can be applied in the context of abstract model checking by providing a simplification paradigm of abstract state spaces that can be viewed as a dual methodology to CounterExample-Guided Abstraction Refinement (CEGAR) .
Revised:  We show how AGAS can be applied in the context of abstract model checking by providing a simplification paradigm of abstract state spaces that can be viewed as a dual methodology to CounterExample-Guided Abstraction Refinement ) methodology .
Edit intent: clarity
Original: In  static analysis, approximation is typically encoded by abstract domains , providing systematic guidelines for specifying approximate semantic functions and precision assessments.
Revised: In static analysis, approximation is encoded by abstract domains , providing systematic guidelines for specifying approximate semantic functions and precision assessments.
Edit intent: clarity
Original: In  static analysis, approximation is typically encoded by abstract domains , providing systematic guidelines for specifying approximate semantic functions and precision assessments.
Revised: In static analysis, approximation is typically encoded by abstract domains . They provide systematic guidelines for specifying approximate semantic functions and precision assessments.
Edit intent: clarity
Original:  However, it may happen that an abstract domain contains redundant information for the specific purpose of approximating a given semantic function modeling some behavior of a system .
Revised:  However, it may happen that an abstract domain contains redundant information for the specific purpose of approximating a given concrete semantic function .
Edit intent: clarity
Original:  This paper introduces correctness kernels of abstract interpretations, a methodology for simplifying abstract domains, i.e. removing abstract values from them, in a maximal way while retaining exactly the same approximate behavior of the system under analysis.
Revised:  This paper introduces the notion of correctness kernel of abstract interpretations, a methodology for simplifying abstract domains, i.e. removing abstract values from them, in a maximal way while retaining exactly the same approximate behavior of the system under analysis.
Edit intent: clarity
Original:  We show that , in abstract model checking and predicate abstraction, correctness kernels provide a simplification paradigm of the abstract state space that is guided by examples, meaning that it preserves spuriousness of examples (i.e., abstract paths).
Revised:  We show that in abstract model checking and predicate abstraction, correctness kernels provide a simplification paradigm of the abstract state space that is guided by examples, meaning that it preserves spuriousness of examples (i.e., abstract paths).
Edit intent: fluency
Original:  We show that , in abstract model checking and predicate abstraction, correctness kernels provide a simplification paradigm of the abstract state space that is guided by examples, meaning that it preserves spuriousness of examples (i.e., abstract paths).
Revised:  We show that , in abstract model checking correctness kernels provide a simplification paradigm of the abstract state space that is guided by examples, meaning that it preserves spuriousness of examples (i.e., abstract paths).
Edit intent: coherence
Original:  We show that , in abstract model checking and predicate abstraction, correctness kernels provide a simplification paradigm of the abstract state space that is guided by examples, meaning that it preserves spuriousness of examples (i.e., abstract paths).
Revised:  We show that , in abstract model checking and predicate abstraction, correctness kernels provide a simplification paradigm of the abstract state space that is guided by examples, meaning that this simplification preserves spuriousness of examples (i.e., abstract paths).
Edit intent: clarity
Original: We study the SIG dimension of trees under L_{\infty} metric and answer an open problem posed by Michael and Quint (Discrete applied Mathematics: 127, pages 447-460, 2003).
Revised: We study the SIG dimension of trees under L_{\infty} metric and answer an open problem posed by Michael and Quint (Discrete Applied Mathematics: 127, pages 447-460, 2003).
Edit intent: fluency
Original:  We run simulations for complete and random graphs , as well as d-dimensional hypercubic lattices (for d=3,2,1).
Revised:  We run simulations for complete and random graphs as well as d-dimensional hypercubic lattices (for d=3,2,1).
Edit intent: fluency
Original:  For weak nonlinearity, a continuous nonequilibrium phase transition between an absorbing and an active phase is obtained, like in the usual stochastic SIRS model [Joo and Lebowitz, Phys.
Revised:  For weak nonlinearity, a continuous nonequilibrium phase transition between an absorbing and an active phase is obtained, such as in the usual stochastic SIRS model [Joo and Lebowitz, Phys.
Edit intent: fluency
Original:  The fourth case remains an interesting open problem.
Revised:  The fourth variant remains an intriguing open problem.
Edit intent: clarity
Original: Topological methods such as persistent homology are powerful tools for data analysis of high-dimensional data sets but these methods almost exclusively rely on thresholding techniques.
Revised: Topological methods , including persistent homology, are powerful tools for data analysis of high-dimensional data sets but these methods almost exclusively rely on thresholding techniques.
Edit intent: clarity
Original: Topological methods such as persistent homology are powerful tools for data analysis of high-dimensional data sets but these methods almost exclusively rely on thresholding techniques.
Revised: Topological methods such as persistent homology are powerful tools for analysis of high-dimensional data sets but these methods almost exclusively rely on thresholding techniques.
Edit intent: fluency
Original: Topological methods such as persistent homology are powerful tools for data analysis of high-dimensional data sets but these methods almost exclusively rely on thresholding techniques.
Revised: Topological methods such as persistent homology are powerful tools for data analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques.
Edit intent: fluency
Original:  However, in noisy data sets thesholding does not always allow for the recovery of topological information.
Revised:  In noisy data sets thesholding does not always allow for the recovery of topological information.
Edit intent: coherence
Original:  However, in noisy data sets thesholding does not always allow for the recovery of topological information.
Revised:  However, in noisy data sets , thresholding does not always allow for the recovery of topological information.
Edit intent: clarity
Original:  We present a computationally-efficient algorithm to allow for topological data analysis on noisy high-dimensional point cloud data sets  .
Revised:  We present an easy to implement, computationally efficient pre-processing algorithm to prepare noisy point cloud data sets .
Edit intent: clarity
Original:  In many cases, the algorithm returns data that has so few outliers that there is no need to threshold the data before performing topological analysis.
Edit intent: coherence
Original:  We apply the algorithm to synthetically-generated noisy data sets and show the recovery of topological information which is impossible to obtain via thresholding.
Revised:  We apply the algorithm to synthetically-generated noisy data sets and show the recovery of topological information which is impossible to obtain by thresholding.
Edit intent: fluency
Original:  We also apply the algorithm to natural image data in \mathbb{R ^8 and show a very clean recovery of topological information previously only available with significant amounts of thresholding.
Revised:  We also apply the algorithm to natural image data in R ^8 and show a very clean recovery of topological information previously only available with significant amounts of thresholding.
Edit intent: coherence
Original:  Their algorithm invokes the ellipsoid algorithm at each iteration for determining the next comparison, making it unpractical .
Revised:  Their algorithm invokes the ellipsoid algorithm at each iteration for determining the next comparison, making it impractical .
Edit intent: fluency
Original:  Furthermore, we approximate the entropy at most once, and compute the entropy at most once.
Edit intent: coherence
Original:  - an O(n ^{2.5 ) algorithm performing at most (1+ eps ) log e(P) + O_e ps (n) comparisons;
Revised:  - an O(n ^2.5 ) algorithm performing at most (1+ eps ) log e(P) + O_e ps (n) comparisons;
Edit intent: fluency
Original:  - an O(n ^{2.5 ) algorithm performing O(log e(P)) comparisons.
Revised:  - an O(n ^2.5 ) algorithm performing O(log e(P)) comparisons.
Edit intent: fluency
Original: Families of exact solutions are found for a nonlinear modification of the Black-Scholes equation.
Revised: Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation.
Edit intent: fluency
Original:  On this way we can describe  complete set of possible reductions of the nonlinear RAPM model.
Revised:  In this way we can describe complete set of possible reductions of the nonlinear RAPM model.
Edit intent: fluency
Original:  On this way we can describe  complete set of possible reductions of the nonlinear RAPM model.
Revised:  On this way we can describe the complete set of possible reductions of the nonlinear RAPM model.
Edit intent: fluency
Original:  Reductions are given in  form of different second order ordinary differential equations.
Revised:  Reductions are given in the form of different second order ordinary differential equations.
Edit intent: fluency
Original:  In some cases they can be reduced as well to first oder equations .
Revised:  In all cases we provide solutions to these equations in an exact or parametric form .
Edit intent: coherence
Original:  We discuss the property of these reductions and  corresponding invariant solutions.
Revised:  We discuss the properties of these reductions and corresponding invariant solutions.
Edit intent: fluency
Original:  We discuss the property of these reductions and  corresponding invariant solutions.
Revised:  We discuss the property of these reductions and the corresponding invariant solutions.
Edit intent: fluency
Original: We show that a recent algorithm of A. Salagean which computes a minimal polynomial for a finite sequence over a field can be obtained as a straightforward rewrite of a published algorithm .
Revised: Let s be a finite sequence over a field. A recent article by A. Salagean which computes a minimal polynomial for a finite sequence over a field can be obtained as a straightforward rewrite of a published algorithm .
Edit intent: clarity
Original: The key challenge in cooperative control for multi-agent systems could be how to design the local interaction rules and coordination principles among agents so as to achieve certain desired global behaviors.
Revised: The key challenge in cooperative control for multi-agent systems could be how to design these local interactions among agents so as to achieve certain desired global behaviors.
Edit intent: clarity
Original:  In this paper , we try to tackle this challenge from the angle of hierarchical control, and propose a divide-and-conquer approach  .
Revised:  In this paper , we try to tackle this challenge and proposes a divide-and-conquer approach .
Edit intent: coherence
Original:  The basic idea is to decompose the requested global specification into subtasks for individual agents or small clusters of agents .
Revised:  The basic idea is to decompose the requested global specification into subtasks for each individual agent .
Edit intent: clarity
Original:  Then, a natural follow-up question is what the necessary and sufficient condition should be for the proposed decomposability of a task automaton .
Revised:  Then, a natural follow-up question is what the necessary and sufficient condition should be for the proposed decomposability of a global specification .
Edit intent: clarity
Original:  The main part of the paper is  to answer this question , and it is found that the automaton A is decomposable if it has some symmetric properties.
Revised:  The main part of the paper is set to answer this question , and it is found that the automaton A is decomposable if it has some symmetric properties.
Edit intent: fluency
Original:  While these results are interesting from a physics point of view, they are also relevant for social, economic, and biological systems, as they allow one to understand conditions for (1) the breakdown of cooperation, (2) the coexistence of different behaviors ("subcultures"), (2) the evolution of commonly shared behaviors ("norms"), and (4) the occurence of polarization or conflict.
Revised:  While these results are interesting from a physics point of view, they are also relevant for social, economic, and biological systems, as they allow one to understand conditions for (1) the breakdown of cooperation, (2) the coexistence of different behaviors ("subcultures"), (2) the evolution of commonly shared behaviors ("norms"), and (4) the occurrence of polarization or conflict.
Edit intent: fluency
Original:  Using the Wiener-Hopf factorization, we derive expressions for the analytically extended characteristic function of the supremum and the infimum of a L\'evy process.
Revised:  Using the Wiener--Hopf factorization, we derive expressions for the analytically extended characteristic function of the supremum and the infimum of a L\'evy process.
Edit intent: fluency
Original: We give a rigorous proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility.
Revised: We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility.
Edit intent: clarity
Original:  With this proof we fix the problem of a circular definition in the original derivation of Gatheral, who introduced this implied volatility representation in his book 'The Volatility Surface'.
Revised:  With this proof we fix the problem of a circular definition in the original derivation of Gatheral, who introduced this representation in his book 'The Volatility Surface'.
Edit intent: clarity
Original: A quantitative model of concurrent interaction in introduced.
Revised: A quantitative model of concurrent interaction is introduced.
Edit intent: fluency
Original: As observed in Holder et al 2008, the popular consensus tree has a natural interpretation as the Bayes estimator which minimizes the expected Robinson--Foulds distance to the unknown true tree.
Revised: Tree reconstruction methods are often judged by their accuracy, measured by how close they get to the true tree.
Edit intent: clarity
Original:  In both cases, the archival resources have URIs that are protocol-wise disconnected from the URI of the resource of which they represent a prior state.
Revised:  In both cases, the archival copies have URIs that are protocol-wise disconnected from the URI of the resource of which they represent a prior state.
Edit intent: clarity
Original: In live streaming systems (IPTV, life-stream services, etc.), an attractive service consists in allowing users to access past portions of the stream.
Revised: An attractive new feature of connected TV systems consists in allowing users to access past portions of the stream.
Edit intent: clarity
Original: In "spot-sensing" applications of sensor networks , each node makes measurements ( such as temperature or humidity ) at the precise location of the node and there is no concept of a sensing radius as in "area-sensing" applications such as surveillance or target tracking.
Revised: In "spot-sensing" applications of sensor networks in which each sensor node makes measurements ( such as temperature or humidity ) at the precise location of the node and there is no concept of a sensing radius as in "area-sensing" applications such as surveillance or target tracking.
Edit intent: clarity
Original: In "spot-sensing" applications of sensor networks , each node makes measurements ( such as temperature or humidity ) at the precise location of the node and there is no concept of a sensing radius as in "area-sensing" applications such as surveillance or target tracking.
Revised: In "spot-sensing" applications of sensor networks , each node makes measurements , such as temperature or humidity ) at the precise location of the node and there is no concept of a sensing radius as in "area-sensing" applications such as surveillance or target tracking.
Edit intent: fluency
Original: In "spot-sensing" applications of sensor networks , each node makes measurements ( such as temperature or humidity ) at the precise location of the node and there is no concept of a sensing radius as in "area-sensing" applications such as surveillance or target tracking.
Revised: In "spot-sensing" applications of sensor networks , each node makes measurements ( such as temperature or humidity , at the precise location of the node and there is no concept of a sensing radius as in "area-sensing" applications such as surveillance or target tracking.
Edit intent: fluency
Original:  A new distributed algorithm is presented for each node to determine if and when it should sense or sleep to conserve energy while also preserving quality of coverage .
Revised:  A new distributed algorithm is presented for each node to determine if and when it should sense or sleep to conserve energy while also preserving the quality of representation .
Edit intent: clarity