wanyu/IteraTeR_v2 huggingface dataset:
Original:  For such A-algebras, we derive a relation between Krull dimension and combinatorial dimension  ] . An immediate application of this relation is that it gives a uniform method  to compute the dimension of A[x_1, \ldots, x_n]/a without having to consider individual properties of the ideal  .
Revised:  For such A-algebras, we derive a relation between Krull dimension and combinatorial dimension of A ] . An immediate application of this relation is that it gives a uniform method to compute the dimension of A[x_1, \ldots, x_n]/a without having to consider individual properties of the ideal .
Edit intent: clarity
Original:  For such A-algebras, we derive a relation between Krull dimension and combinatorial dimension  ] . An immediate application of this relation is that it gives a uniform method  to compute the dimension of A[x_1, \ldots, x_n]/a without having to consider individual properties of the ideal  .
Revised:  For such A-algebras, we derive a relation between Krull dimension and combinatorial dimension x_1, \ldots, x_n] . An immediate application of this relation is that it gives a uniform method to compute the dimension of A[x_1, \ldots, x_n]/a without having to consider individual properties of the ideal .
Edit intent: fluency
Original: Let \delta_0(P,k) denote the degree k dilation of a point set ~ P in the domain of plane geometric spanners.
Revised: Let \delta_0(P,k) denote the degree k dilation of a point set P in the domain of plane geometric spanners.
Edit intent: clarity
Original:  We also show that, in contrast with the case of generalized linear models, when used with deep networks with rectified linear units and the quadratic loss, the regularization penalty of dropout (a) is not only a function of the marginals on the independent variables, but also depends on the response variables, and (b) can be negative.
Revised:  We also show that, in contrast with the case of generalized linear models, when used with deep networks with rectified linear units and the quadratic loss, the regularization penalty of dropout (a) is not just a function of the marginals on the independent variables, but also depends on the response variables, and (b) can be negative.
Edit intent: fluency
Original:  We also show that, in contrast with the case of generalized linear models, when used with deep networks with rectified linear units and the quadratic loss, the regularization penalty of dropout (a) is not only a function of the marginals on the independent variables, but also depends on the response variables, and (b) can be negative.
Revised:  We also show that, in contrast with the case of generalized linear models, when used with deep networks with rectified linear units and the quadratic loss, the regularization penalty of dropout (a) is not only a function of the independent variables, but also depends on the response variables, and (b) can be negative.
Edit intent: clarity
Original: We study dropout and weight decay applied to deep networks with rectified linear units and the quadratic loss.
Revised: We analyze dropout in deep networks with rectified linear units and the quadratic loss.
Edit intent: clarity
Original: We study the computational complexity of several problems connected with the problems of finding a maximal distance-k matching of minimum cardinality or minimum weight  .
Revised: We study the computational complexity of several problems connected with finding a maximal distance-k matching of minimum cardinality or minimum weight .
Edit intent: fluency
Original:  We also prove that \ge  the problem of finding a minimum weight maximal distance-2l matching in chordal graphs is hard to approximate within a factor of \varepsilon \ln |V(G)| for a fixed \varepsilon unless P = NP, where \delta is a fixed constant} . Finally, we show NP-hardness of the minimum maximal induced matching problem in several restricted graph classes .
Revised:  We also prove that \ge the problem of finding a minimum weight maximal distance-2l matching in chordal graphs is hard to approximate within a factor of \delta \ln |V(G)| for a fixed \varepsilon unless P = NP, where \delta is a fixed constant} . Finally, we show NP-hardness of the minimum maximal induced matching problem in several restricted graph classes .
Edit intent: fluency
Original:  We also prove that \ge  the problem of finding a minimum weight maximal distance-2l matching in chordal graphs is hard to approximate within a factor of \varepsilon \ln |V(G)| for a fixed \varepsilon unless P = NP, where \delta is a fixed constant} . Finally, we show NP-hardness of the minimum maximal induced matching problem in several restricted graph classes .
Revised:  We also prove that \ge the problem of finding a minimum weight maximal distance-2l matching in chordal graphs is hard to approximate within a factor of \varepsilon \ln |V(G)| unless \mathrm{P = NP, where \delta is a fixed constant} . Finally, we show NP-hardness of the minimum maximal induced matching problem in several restricted graph classes .
Edit intent: clarity
Original:  We also prove that \ge  the problem of finding a minimum weight maximal distance-2l matching in chordal graphs is hard to approximate within a factor of \varepsilon \ln |V(G)| for a fixed \varepsilon unless P = NP, where \delta is a fixed constant} . Finally, we show NP-hardness of the minimum maximal induced matching problem in several restricted graph classes .
Revised:  We also prove that \ge the problem of finding a minimum weight maximal distance-2l matching in chordal graphs is hard to approximate within a factor of \varepsilon \ln |V(G)| for a fixed \varepsilon unless P = NP, where \delta is a fixed constant} . Finally, we show NP-hardness of the minimum maximal induced matching problem in large-girth planar graphs .
Edit intent: clarity
Original:  We also prove that for any fixed integer \ell \ge 1 the problem of finding a minimum weight maximal distance-2\ell matching in chordal graphs cannot be approximated in polynomial time  within a factor of \delta \ln |V(G)| unless P = NP, where \delta is a fixed constant  .
Revised:  We also prove that for any fixed integer \ell \ge 1 the problem of finding a minimum weight maximal distance-2\ell matching in chordal graphs cannot be approximated in polynomial time in chordal graphs within a factor of \delta \ln |V(G)| unless P = NP, where \delta is a fixed constant .
Edit intent: fluency
Original:  Finally, we show  NP-hardness of the minimum maximal induced matching problem in large-girth planar graphs.
Revised:  Finally, we show the NP-hardness of the minimum maximal induced matching problem in large-girth planar graphs.
Edit intent: fluency
Original:  Finally, we show the NP-hardness of the minimum maximal induced matching and k-independent dominating set problems in large-girth planar graphs.
Revised:  Finally, we show the NP-hardness of the minimum maximal induced matching and independent dominating set problems in large-girth planar graphs.
Edit intent: clarity
Original: Cliques (or quasi-cliques) are frequently used to model communities: a  set of nodes where each pair is (equally ) likely to be connected.
Revised: Cliques are frequently used to model communities: a set of nodes where each pair is (equally ) likely to be connected.
Edit intent: clarity
Original: Cliques (or quasi-cliques) are frequently used to model communities: a  set of nodes where each pair is (equally ) likely to be connected.
Revised: Cliques (or quasi-cliques) are frequently used to model communities: a community is a set of nodes where each pair is (equally ) likely to be connected.
Edit intent: clarity
Original: Cliques (or quasi-cliques) are frequently used to model communities: a  set of nodes where each pair is (equally ) likely to be connected.
Revised: Cliques (or quasi-cliques) are frequently used to model communities: a set of nodes where each pair is equally likely to be connected.
Edit intent: fluency
Original:  However, when observing real-world communities , we see that most communities have more structure than that.
Revised:  But studying real-world communities , we see that most communities have more structure than that.
Edit intent: clarity
Original:  However, when observing real-world communities , we see that most communities have more structure than that.
Revised:  However, when observing real-world communities reveals that they have more structure than that.
Edit intent: clarity
Original: We investigate the influence of a contact network structure over the spread of epidemics in an heterogeneous population.
Revised: We investigate the influence of the contact network structure over the spread of epidemics in an heterogeneous population.
Edit intent: fluency
Original: We investigate the influence of a contact network structure over the spread of epidemics in an heterogeneous population.
Revised: We investigate the influence of a contact network structure on the spread of epidemics in an heterogeneous population.
Edit intent: fluency
Original: We investigate the influence of a contact network structure over the spread of epidemics in an heterogeneous population.
Revised: We investigate the influence of a contact network structure over the spread of epidemics over an heterogeneous population.
Edit intent: fluency
Original:  Basically the epidemics spreads over a directed weighted graph.
Revised:  In our model, the epidemic process spreads over a directed weighted graph.
Edit intent: clarity
Original:  We describe the epidemic process as a continuous-time individual-based susceptible-infected-susceptible (SIS) model using a first-order mean-field approximation.
Revised:  A continuous-time individual-based susceptible-infected-susceptible (SIS) model using a first-order mean-field approximation.
Edit intent: clarity
Original:  We describe the epidemic process as a continuous-time individual-based susceptible-infected-susceptible (SIS) model using a first-order mean-field approximation.
Revised:  We describe the epidemic process as a continuous-time individual-based susceptible-infected-susceptible (SIS) is analyzed using a first-order mean-field approximation.
Edit intent: clarity
Original:  First  we consider a network without a specific topology , investigating the epidemic threshold and the stability properties of the system.
Revised:  First , we consider a network without a specific topology , investigating the epidemic threshold and the stability properties of the system.
Edit intent: fluency
Original:  Then  we analyze the case of a community network , relying on the graph-theoretical notion of equitable partition , and using a lower-dimensional dynamical system in order to individuate the epidemic threshold .
Revised:  Then , we analyze the case of a community network , relying on the graph-theoretical notion of equitable partition , and using a lower-dimensional dynamical system in order to individuate the epidemic threshold .
Edit intent: fluency
Original:  Then  we analyze the case of a community network , relying on the graph-theoretical notion of equitable partition , and using a lower-dimensional dynamical system in order to individuate the epidemic threshold .
Revised:  Then we analyze the case of a community network relying on the graph-theoretical notion of equitable partition , and using a lower-dimensional dynamical system in order to individuate the epidemic threshold .
Edit intent: fluency
Original:  Then  we analyze the case of a community network , relying on the graph-theoretical notion of equitable partition , and using a lower-dimensional dynamical system in order to individuate the epidemic threshold .
Revised:  Then we analyze the case of a community network , relying on the graph-theoretical notion of equitable partition , and using a lower-dimensional dynamical system .
Edit intent: coherence
Original:  Moreover we prove that the positive steady-state of the original system, that appears above the threshold, can be computed by this lower-dimensional system.
Revised:  Moreover we prove that the positive steady-state of the original system, that appears above the threshold, can be computed using this lower-dimensional system.
Edit intent: clarity
Original:  Taking into account the connectivity of the network, we provide a cost-optimal distribution of resources to prevent the disease from persisting indefinitely in the population;
Revised:  Taking into account the connectivity of the network, we provide a cost-optimal curing policy, in order to prevent the disease from persisting indefinitely in the population;
Edit intent: clarity
Original:  for a particular case of two-level immunization problem we report on the construction of a polynomial time complexity algorithm
Revised:  for a particular case of two-level optimal curing problem, an algorithm is designed with a polynomial time complexity algorithm
Edit intent: clarity
Original:  Then, we analyze the case of a community network relying on the graph-theoretical notion of equitable partition .
Revised:  Then, we analyze the case of a community network , our investigation relies on the graph-theoretical notion of equitable partition .
Edit intent: clarity
Original:  Finally, in the case of a  two-level optimal curing problem,  an algorithm is designed with a polynomial time complexity in the network size.
Revised:  Finally, in the case of a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.
Edit intent: clarity
Original:  This raised the interest of numerous researchers for studying the constraints induced by the genetic code on the various overlapping frames, mostly based on information theory.
Revised:  This motivated numerous researchers to study the constraints induced by the genetic code on the various overlapping frames, mostly based on information theory.
Edit intent: clarity
Original:  Our interest here is on the constraints induced on two overlapping genes in terms of amino acids, as well as polypeptides.
Revised:  Our focus in this paper is on the constraints induced on two overlapping genes in terms of amino acids, as well as polypeptides.
Edit intent: clarity
Original:  Importantly, considering polypeptides , and not just single amino acids , reveals novel constraints .
Revised:  Novel constraints are revealed when polypeptides are considered , and not just single amino acids , reveals novel constraints .
Edit intent: clarity
Original:  Importantly, considering polypeptides , and not just single amino acids , reveals novel constraints .
Revised:  Importantly, considering polypeptides , and not just single amino acids .
Edit intent: clarity
Original:  These results yield support for understanding the mechanism of overlapping genes  and for developing novel overlapping gene detection methods .
Revised:  These results yield support for understanding the mechanism of overlapping genes , and for developing novel overlapping gene detection methods .
Edit intent: fluency
Original:  For k=3, we improve their bound from 6n-12  to 11{2}n-11 and we also show that this is tight for multi-graphs with no homotopic edges .
Revised:  For k=3, the bound of 6n-12 to 11{2}n-11 and we also show that this is tight for multi-graphs with no homotopic edges .
Edit intent: clarity
Original: A k-planar graph is one  that can be drawn in the plane such that every edge is crossed at most k times.
Revised: A k-planar graph that can be drawn in the plane such that every edge is crossed at most k times.
Edit intent: clarity
Original:  In particular, unbounded lookahead might be necessary.
Revised:  In particular, unbounded lookahead is in general necessary.
Edit intent: clarity
Original:  Here, we study delay games with winning conditions given by PROMPT-LTL , Linear Temporal Logic equipped with a parameterized eventually operator whose scope is bounded.
Revised:  Here, we study delay games with winning conditions given by Prompt-LTL , Linear Temporal Logic equipped with a parameterized eventually operator whose scope is bounded.
Edit intent: fluency
Original:  Our main result shows that solving PROMPT-LTL delay games is complete for triply-exponential time.
Revised:  Our main result shows that solving Prompt-LTL delay games is complete for triply-exponential time.
Edit intent: fluency
Original:  Thus, we identify PROMPT-LTL as the first known class of well-behaved quantitative winning conditions for delay games  .
Revised:  Thus, we identify Prompt-LTL as the first known class of well-behaved quantitative winning conditions for delay games .
Edit intent: fluency
Original:  Our redundancy measure is easy to compute, and Matlab code implementing the measure , together with all considered examples , is provided .
Revised:  Our redundancy measure is easy to compute, and Matlab code implementing the measure , together with all considered examples .
Edit intent: clarity
Original: The aim is to highlight and elaborate the structural result for branching bisimilarity on normed BPA (Basic Process Algebra) processes that was the crux of a conference paper by Czerwinski and Jancar (arxiv 7/2014 and LiCS 2015 CJ-2014,2015 ).
Revised: The aim is to highlight and elaborate the structural result for branching bisimilarity on normed BPA (Basic Process Algebra) processes that was the crux of a conference paper by Czerwinski and Jancar (arxiv 7/2014 and LiCS 2015 ).
Edit intent: coherence
Original:  He and Huang indirectly acknowledge the decomposition ideas in CJ-2014 on which they also built, but it is difficult for the reader to understand what was their starting point and what are the crucial new ideas.
Revised:  He and Huang indirectly acknowledge the decomposition ideas CJ-2014 on which they also built, but it is difficult for the reader to understand what was their starting point and what are the crucial new ideas.
Edit intent: fluency
Original:  He and Huang indirectly acknowledge the decomposition ideas in CJ-2014 on which they also built, but it is difficult for the reader to understand what was their starting point and what are the crucial new ideas.
Revised:  He and Huang indirectly acknowledge the decomposition ideas in CJ-2014 on which they also built, but it is difficult to separate their starting point and what are the crucial new ideas.
Edit intent: clarity
Original:  He and Huang indirectly acknowledge the decomposition ideas in CJ-2014 on which they also built, but it is difficult for the reader to understand what was their starting point and what are the crucial new ideas.
Revised:  He and Huang indirectly acknowledge the decomposition ideas in CJ-2014 on which they also built, but it is difficult for the reader to understand what was their starting point from their new ideas.
Edit intent: clarity
Original:  Another aim is to provide a complete description, including an informal overview  that should also make clear how Fu's ideas were used, and to give all proofs in a form that should be both rigorous and readable .
Revised:  Another aim is to provide a complete description, including an informal overview , that should also make clear how Fu's ideas were used, and to give all proofs in a form that should be both rigorous and readable .
Edit intent: fluency
Original:  The present note corrects this terminology and introduces the more adequate term  similarity-adapted publication vectors  .
Revised:  The present note corrects this terminology and introduces the more adequate term ' similarity-adapted publication vectors .
Edit intent: fluency
Original:  The present note corrects this terminology and introduces the more adequate term  similarity-adapted publication vectors  .
Revised:  The present note corrects this terminology and introduces the more adequate term similarity-adapted publication vectors ' .
Edit intent: fluency
Original:   Overall, we find rather strong correlations between cognitive distances obtained by the 2-dimensional (barycenters) and the N-dimensional ( similarity-adapted publication vectors ) approaches .
Revised:  Overall, we find that the three approaches (distance between barycenters, distance between similarity-adapted publication vectors ) approaches .
Edit intent: clarity
Original:  First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which allows us to characterized the class of exclusive stochastic languages.
Revised:  First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which allows us to characterize the class of exclusive stochastic languages.
Edit intent: fluency
Original: Inverse reinforcement learning (IRL) is the problem of recovering a system's latent reward function from observed system behavior.
Revised: Inverse reinforcement learning (IRL) has become a useful tool for learning behavioral models from demonstration data. However, IRL remains mostly unexplored for multi-agent systems.
Edit intent: clarity
Original:  In this paper, we concentrate on IRL in homogeneous large-scale systems, which we refer to as swarms.
Revised:  In this paper, we show how the principle of IRL can be extended to homogeneous large-scale systems, which we refer to as swarms.
Edit intent: clarity
Original:  Based on this finding, we reformulate the corresponding optimal control problemas a fix-point problem pointing towards a symmetric Nash equilibrium, which we solve using a novel heterogeneous learning scheme  particularly tailored to the swarm setting.
Revised:  Based on this finding, we reformulate the corresponding optimal control problemas a fix-point problem pointing towards a symmetric Nash equilibrium, which we solve using a novel heterogeneous learning scheme that is particularly tailored to the swarm setting.
Edit intent: coherence
Original:  Results on the Vicsek model and the Ising model demonstrate that the proposed framework is able to produce meaningful  reward models from which we can learn near-optimal local controllers that replicate the observed  system dynamics.
Revised:  Results on two example systems demonstrate that our framework is able to produce meaningful reward models from which we can learn near-optimal local controllers that replicate the observed system dynamics.
Edit intent: clarity
Original:  Results on the Vicsek model and the Ising model demonstrate that the proposed framework is able to produce meaningful  reward models from which we can learn near-optimal local controllers that replicate the observed  system dynamics.
Revised:  Results on the Vicsek model and the Ising model demonstrate that the proposed framework is able to produce meaningful local reward models from which we can learn near-optimal local controllers that replicate the observed system dynamics.
Edit intent: fluency
Original:  Results on the Vicsek model and the Ising model demonstrate that the proposed framework is able to produce meaningful  reward models from which we can learn near-optimal local controllers that replicate the observed  system dynamics.
Revised:  Results on the Vicsek model and the Ising model demonstrate that the proposed framework is able to produce meaningful reward models from which we can replicate the observed system dynamics.
Edit intent: clarity
Original: In this work we consider the nonlinear graph p-Laplacian and the set of eigenvalues and associated eigenvectors of this operator defined by a variational principle.
Revised: We consider the nonlinear graph p-Laplacian and the set of eigenvalues and associated eigenvectors of this operator defined by a variational principle.
Edit intent: clarity
Original: In this work we consider the nonlinear graph p-Laplacian and the set of eigenvalues and associated eigenvectors of this operator defined by a variational principle.
Revised: In this work we consider the nonlinear graph p-Laplacian and its set of eigenvalues and associated eigenvectors of this operator defined by a variational principle.
Edit intent: clarity
Original: In this work we consider the nonlinear graph p-Laplacian and the set of eigenvalues and associated eigenvectors of this operator defined by a variational principle.
Revised: In this work we consider the nonlinear graph p-Laplacian and the set of eigenvalues and associated eigenfunctions of this operator defined by a variational principle.
Edit intent: clarity