wanyu/IteraTeR_v2 huggingface dataset:
Original:  Contexts in which the appropriate integration of complex networks metrics can lead to improved classification rates with respect to classical data mining algorithms and, conversely, contexts in which data mining can be used to tackle important issues in complex network theory applications are illustrated.
Revised:  Contexts in which the appropriate integration of complex network metrics can lead to improved classification rates with respect to classical data mining algorithms and, conversely, contexts in which data mining can be used to tackle important issues in complex network theory applications are illustrated.
Edit intent: fluency
Original:  We make progress towards proving that this method is a strongly consistent estimator by proving a  strong law of large numbers for the vertices' weakly dependent colour values.
Revised:  We prove that this method is a strongly consistent estimator by proving a strong law of large numbers for the vertices' weakly dependent colour values.
Edit intent: clarity
Original:  We first identify necessary and sufficient conditions on the structure of the network for the uniqueness of these effort profiles .
Revised:  We identify necessary and sufficient conditions on the structure of the network for the uniqueness of these effort profiles .
Edit intent: coherence
Original:  All identified conditions are based only on the network structure, and therefore, are independent of the selected solution concept, or the mechanism/negotiations that lead to the effort profile.
Edit intent: coherence
Original:  In this case, the complete cure is not possible since the cancer cure state is no more stable, but tumor recurrence may be delayed if treatment is prolonged .
Revised:  In this case, the complete cure is not possible since the cancer cure state is no more stable, but tumor recurrence may be delayed if treatment is prolongued .
Edit intent: fluency
Original:  We review three indicators of the resilience of a stable equilibrium, related with size and shape of its basin of attraction: latitute , precariousness and resistance.
Revised:  We review three indicators of the resilience of a stable equilibrium, related with size and shape of its basin of attraction: latitude , precariousness and resistance.
Edit intent: fluency
Original:  2. Bayesian approaches offer a coherent framework for parameter inference that can account for multiple sources of uncertainty, while making use of prior information.
Revised:  2. The Bayesian approach offers a coherent framework for parameter inference that can account for multiple sources of uncertainty, while making use of prior information.
Edit intent: clarity
Original:  This approach offers a rigorous methodology for parameter inference  as well as modeling the link between unobservable model states and parameters, and observable quantities.
Revised:  This approach offers a rigorous methodology for parameter inference , as well as modeling the link between unobservable model states and parameters, and observable quantities.
Edit intent: fluency
Original:  This approach offers a rigorous methodology for parameter inference  as well as modeling the link between unobservable model states and parameters, and observable quantities.
Revised:  This approach offers a rigorous methodology for parameter inference as well as modelling the link between unobservable model states and parameters, and observable quantities.
Edit intent: fluency
Original:  Further functionality is provided to facilitate MCMC diagnostics and the visualisation of the posterior distributions of model parameters and trajectories  . 4. The templating approach makes deBInfer applicable to a wide range of DE models.
Revised:  Further functionality is provided to facilitate MCMC diagnostics , the visualisation of the posterior distributions of model parameters and trajectories . 4. The templating approach makes deBInfer applicable to a wide range of DE models.
Edit intent: fluency
Original: The problem of strongly refuting random constraint satisfaction problems (CSPs) is a well-studied algorithmic problem, in which we are asked, given a random CSP instance with m clauses and n variables , to algorithmically certify that no variable assignment satisfies more than the expected number of clauses (when m/n = \omega(1)).
Revised: Random constraint satisfaction problems (CSPs) is a well-studied algorithmic problem, in which we are asked, given a random CSP instance with m clauses and n variables , to algorithmically certify that no variable assignment satisfies more than the expected number of clauses (when m/n = \omega(1)).
Edit intent: coherence
Original:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde  ^{( D /2-1)(1-\delta)}  in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Revised:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n \ge \widetilde ^{( D /2-1)(1-\delta)} in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Edit intent: clarity
Original:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde  ^{( D /2-1)(1-\delta)}  in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Revised:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde O(n ^{( D /2-1)(1-\delta)} in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Edit intent: fluency
Original:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde  ^{( D /2-1)(1-\delta)}  in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Revised:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde ^{( k /2-1)(1-\delta)} in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Edit intent: fluency
Original:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde  ^{( D /2-1)(1-\delta)}  in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Revised:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde ^{( D /2-1)(1-\delta)} ) in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Edit intent: fluency
Original:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde  ^{( D /2-1)(1-\delta)}  in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Revised:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde ^{( D /2-1)(1-\delta)} in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) rounds of the sum-of-squares hierarchy , for any \delta \in [0,1) and any integer D \ge 3.
Edit intent: clarity
Original:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde  ^{( D /2-1)(1-\delta)}  in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer D \ge 3.
Revised:  } In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random D-LIN instances with clause density m/n =n \ge \widetilde ^{( D /2-1)(1-\delta)} in time \exp( %DIFDELCMD < \tilde %%% \widetilde O(n^{\delta})) or in \widetilde O(n^{\delta}) sum-of-squares rounds , for any \delta \in [0,1) and any integer k \ge 3.
Edit intent: clarity
Original:  For CSPs such as D-LIN, there is a long-standing gap between the clause density at which efficient strong refutation algorithms are known, m/n =%DIFDELCMD < \tilde %%% \Omega(n^{D/2), and the density at which instances become unsatisfiable with high probability, m/n=\omega(1).
Revised:  %DIFDELCMD < \tilde %%% \Omega(n^{D/2), and the density at which instances become unsatisfiable with high probability, m/n=\omega(1).
Edit intent: clarity
Original:  For CSPs such as D-LIN, there is a long-standing gap between the clause density at which efficient strong refutation algorithms are known, m/n =%DIFDELCMD < \tilde %%% \Omega(n^{D/2), and the density at which instances become unsatisfiable with high probability, m/n=\omega(1).
Revised:  For CSPs such as D-LIN, there is a long-standing gap between the clause density at which efficient strong refutation algorithms are known, m/n =%DIFDELCMD < \tilde %%% ), and the density at which instances become unsatisfiable with high probability, m/n=\omega(1).
Edit intent: coherence
Original:  We also leverage our D-LIN results to obtain strong refutation algorithms for SAT (or any other boolean CSP) at similar clause densities.
Revised:  We also leverage our D-LIN results to obtain strong refutation algorithms for SAT (or any other Boolean CSP) at similar clause densities.
Edit intent: fluency
Original:  in time \exp(}%DIFDELCMD < \tilde %%% O(n^{\delta)), for any \delta \in }%DIFDELCMD < [%%% 0,1/120), extending the best known poly-time algorithms which certify bounds of%DIFDELCMD < \tilde %%% O(n^{D/4) and approaching the tight bound of }%DIFDELCMD < \tilde %%% O(\sqrt{n .
Revised:  in time \exp(}%DIFDELCMD < \tilde %%% )), for any \delta \in }%DIFDELCMD < [%%% 0,1/120), extending the best known poly-time algorithms which certify bounds of%DIFDELCMD < \tilde %%% O(n^{D/4) and approaching the tight bound of }%DIFDELCMD < \tilde %%% O(\sqrt{n .
Edit intent: clarity
Original: Generally accepted depreciation methods do not factor in the Time Value of Money, despite the concept being a core principle of financial asset valuation .
Revised: Generally accepted depreciation methods do not factor in the Time Value of Money, a key principle within financial theory. This is disadvantageous, as knowing the intrinsic value of an asset can assist with making effective purchase and sale decisions .
Edit intent: clarity
Original:  While the Basic Depreciable Asset Value Model formulated withinhas its limitations, more complex models , which factor in a greater number of variables, can be formulated using its logic .
Revised:  While the Basic Depreciable Asset Value Model formulated withinhas its limitations, more complex formulas , which factor in a greater number of variables, can be formulated using its logic .
Edit intent: clarity
Original:  While the Basic Depreciable Asset Value Model formulated withinhas its limitations, more complex models , which factor in a greater number of variables, can be formulated using its logic .
Revised:  While the Basic Depreciable Asset Value Model formulated withinhas its limitations, more complex models , which factor for a greater number of variables, can be formulated using its logic .
Edit intent: fluency
Original: The discriminator of an integer sequence s = (s(i))_{i >= 1 }, introduced by Arnold, Benkoski, and McCabe in 1985, is the map D_s(n) that sends n  to the least  integer m such that the  numbers s(0), s(1), ..., s(n-1) are pairwise incongruent modulo m.
Revised: The discriminator of an integer sequence s = (s(i))_{i >= 0 }, introduced by Arnold, Benkoski, and McCabe in 1985, is the map D_s(n) that sends n to the least integer m such that the numbers s(0), s(1), ..., s(n-1) are pairwise incongruent modulo m.
Edit intent: fluency
Original: The discriminator of an integer sequence s = (s(i))_{i >= 1 }, introduced by Arnold, Benkoski, and McCabe in 1985, is the map D_s(n) that sends n  to the least  integer m such that the  numbers s(0), s(1), ..., s(n-1) are pairwise incongruent modulo m.
Revised: The discriminator of an integer sequence s = (s(i))_{i >= 1 }, introduced by Arnold, Benkoski, and McCabe in 1985, is the map D_s(n) that sends n to the least integer m such that the n numbers s(0), s(1), ..., s(n-1) are pairwise incongruent modulo m.
Edit intent: fluency
Original: We introduce a general class of distances (metrics) over Markov chains, which are based on linear behaviour.
Revised: We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour.
Edit intent: clarity
Original: A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. \ involving algebraic, smooth, or even continuous functions) is presented.
Revised: A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented.
Edit intent: fluency
Original:  The technique is to first plot each function as a pixel matrix, and to then perform a sequence of elementary matrix operations, as dictated by how variables are shared by the relations in the system.
Revised:  The technique is to first plot each function as a pixel matrix, and to then perform a sequence of basic matrix operations, as dictated by how variables are shared by the relations in the system.
Edit intent: fluency
Original: We present  an expressive framework , called PrivInfer, for writing and verifying differentially private  machine learning algorithms.
Revised: We present an expressive framework for writing and verifying differentially private machine learning algorithms.
Edit intent: clarity
Original:  Programs in PrivInfer are written in a rich functional probabilistic  language with constructs for performing Bayesian inference.
Revised:  Programs in PrivInfer are written in a rich functional probabilistic programming language with constructs for performing Bayesian inference.
Edit intent: clarity
Original:  Our framework leverages recent developments in Bayesian inference, probabilistic program- ming languages, and in relational refinement types.
Revised:  Our framework leverages recent developments in Bayesian inference, probabilistic programming languages, and in relational refinement types.
Edit intent: fluency
Original: Apples, porcupines, and the most obscure Bob Dylan song--is every topic a few clicks from Philosophy?
Revised: Apples, porcupines, and the most obscure Bob Dylan song---is every topic a few clicks from Philosophy?
Edit intent: fluency
Original:  Far from dispersed, first links disproportionately accumulate at a few articles--flowing from specific to general and culminating around fundamental notions such as Community, State, and Science.
Revised:  Far from dispersed, first links disproportionately accumulate at a few articles---flowing from specific to general and culminating around fundamental notions such as Community, State, and Science.
Edit intent: fluency
Original: Computational complexity is studied for the problem of stabbing set of straight line segments with the smallest cardinality set of disks of fixed radii r > 0 where the set of segments forms  straight line drawing of planar graph .
Revised: Computational complexity is studied for the problem of stabbing set of straight line segments with the smallest cardinality set of disks of fixed radii r > 0 where the set of segments forms a straight line drawing of planar graph .
Edit intent: fluency
Original:  In this paper we claim strong NP-hardness of the problem over the classes of 4-connected (i.e. Hamiltonian) plane triangulations of bounded vertex degree ,d_{\max}}]  ,\eta d_{\max}}]  as well as  of 4-connected plane half-\theta_6 graphs for small r.
Revised:  In this paper we claim strong NP-hardness of the problem over the classes of 4-connected (i.e. Hamiltonian) plane triangulations of bounded vertex degree ,d_{\max}}] ,\eta d_{\max}}] as well as within the class of 4-connected plane half-\theta_6 graphs for small r.
Edit intent: clarity
Original: Computational complexity and approximability are studied for a problem of intersecting a set of straight line segments with the smallest cardinality set of disks of fixed radii r \geq 0 where the set of segments forms a straight line drawing G=(V,E ,F ) of a planar graph without edge crossings.
Revised: Computational complexity and approximation algorithms are reported for a problem of intersecting a set of straight line segments with the smallest cardinality set of disks of fixed radii r \geq 0 where the set of segments forms a straight line drawing G=(V,E ,F ) of a planar graph without edge crossings.
Edit intent: clarity
Original: Computational complexity and approximability are studied for a problem of intersecting a set of straight line segments with the smallest cardinality set of disks of fixed radii r \geq 0 where the set of segments forms a straight line drawing G=(V,E ,F ) of a planar graph without edge crossings.
Revised: Computational complexity and approximability are studied for a problem of stabbing a set of straight line segments with the smallest cardinality set of disks of fixed radii r \geq 0 where the set of segments forms a straight line drawing G=(V,E ,F ) of a planar graph without edge crossings.
Edit intent: clarity
Original: Computational complexity and approximability are studied for a problem of intersecting a set of straight line segments with the smallest cardinality set of disks of fixed radii r \geq 0 where the set of segments forms a straight line drawing G=(V,E ,F ) of a planar graph without edge crossings.
Revised: Computational complexity and approximability are studied for a problem of intersecting a set of straight line segments with the least cardinality set of disks of fixed radii r \geq 0 where the set of segments forms a straight line drawing G=(V,E ,F ) of a planar graph without edge crossings.
Edit intent: clarity
Original:  We claim strong NP-hardness of the problem within the class of ( edge sets of ) Delaunay , TD-Delaunay triangulationsand their subgraphs for r\in [d_{\min}, d_{\max and r\in%DIFDELCMD < [%%% d_{\max \eta d_{\max}] for some large constant \eta as well as within the class of 4-connected TD-Delaunay triangulations for r=0 where d_{\max} and d_{\min} are Euclidean lengths of the longest and shortest graph edges respectively.
Revised:  We claim strong NP-hardness of the problem for edge sets of ) Delaunay , TD-Delaunay triangulationsand their subgraphs for r\in [d_{\min}, d_{\max and r\in%DIFDELCMD < [%%% d_{\max \eta d_{\max}] for some large constant \eta as well as within the class of 4-connected TD-Delaunay triangulations for r=0 where d_{\max} and d_{\min} are Euclidean lengths of the longest and shortest graph edges respectively.
Edit intent: fluency
Original:  We claim strong NP-hardness of the problem within the class of ( edge sets of ) Delaunay , TD-Delaunay triangulationsand their subgraphs for r\in [d_{\min}, d_{\max and r\in%DIFDELCMD < [%%% d_{\max \eta d_{\max}] for some large constant \eta as well as within the class of 4-connected TD-Delaunay triangulations for r=0 where d_{\max} and d_{\min} are Euclidean lengths of the longest and shortest graph edges respectively.
Revised:  We claim strong NP-hardness of the problem within the class of ( edge sets of ) Delaunay , TD-Delaunay triangulationsand their subgraphs for r\in [d_{\min}, and r\in%DIFDELCMD < [%%% d_{\max \eta d_{\max}] for some large constant \eta as well as within the class of 4-connected TD-Delaunay triangulations for r=0 where d_{\max} and d_{\min} are Euclidean lengths of the longest and shortest graph edges respectively.
Edit intent: fluency
Original:  We claim strong NP-hardness of the problem within the class of ( edge sets of ) Delaunay , TD-Delaunay triangulationsand their subgraphs for r\in [d_{\min}, d_{\max and r\in%DIFDELCMD < [%%% d_{\max \eta d_{\max}] for some large constant \eta as well as within the class of 4-connected TD-Delaunay triangulations for r=0 where d_{\max} and d_{\min} are Euclidean lengths of the longest and shortest graph edges respectively.
Revised:  We claim strong NP-hardness of the problem within the class of ( edge sets of ) Delaunay , TD-Delaunay triangulationsand their subgraphs for r\in [d_{\min}, d_{\max %DIFDELCMD < [%%% d_{\max \eta d_{\max}] for some large constant \eta as well as within the class of 4-connected TD-Delaunay triangulations for r=0 where d_{\max} and d_{\min} are Euclidean lengths of the longest and shortest graph edges respectively.
Edit intent: coherence
Original:  We claim strong NP-hardness of the problem within the class of ( edge sets of ) Delaunay , TD-Delaunay triangulationsand their subgraphs for r\in [d_{\min}, d_{\max and r\in%DIFDELCMD < [%%% d_{\max \eta d_{\max}] for some large constant \eta as well as within the class of 4-connected TD-Delaunay triangulations for r=0 where d_{\max} and d_{\min} are Euclidean lengths of the longest and shortest graph edges respectively.
Revised:  We claim strong NP-hardness of the problem within the class of ( edge sets of ) Delaunay , TD-Delaunay triangulationsand their subgraphs for r\in [d_{\min}, d_{\max and r\in%DIFDELCMD < [%%% \eta d_{\max}] for some large constant \eta as well as within the class of 4-connected TD-Delaunay triangulations for r=0 where d_{\max} and d_{\min} are Euclidean lengths of the longest and shortest graph edges respectively.
Edit intent: fluency
Original: Let \mathcal{G_{m,\sigma} } \Ga be the collection of all weighted bipartite graphs each having \sigma and m, as the size of a vertex partition and the total weight, respectively.
Revised: Let _{m,\sigma} } \Ga be the collection of all weighted bipartite graphs each having \sigma and m, as the size of a vertex partition and the total weight, respectively.
Edit intent: clarity
Original:  We give a tight lower bound \lceil m-\sigma{\sigma} \rceil+1 for the set \{Wt(mwm(G))~|~G \in \mathcal{G_{m,\sigma}} \Ga \} which denotes the collection of weights of maximum weight bipartite matchings of all graphs in \mathcal{G_{m,\sigma}} \Ga .
Revised:  We give a tight lower bound \lceil m-\sigma{\sigma} \rceil+1 for the set \{Wt(mwm(G))~|~G \in _{m,\sigma}} \Ga \} which denotes the collection of weights of maximum weight bipartite matchings of all graphs in \mathcal{G_{m,\sigma}} \Ga .
Edit intent: clarity
Original:  We give a tight lower bound \lceil m-\sigma{\sigma} \rceil+1 for the set \{Wt(mwm(G))~|~G \in \mathcal{G_{m,\sigma}} \Ga \} which denotes the collection of weights of maximum weight bipartite matchings of all graphs in \mathcal{G_{m,\sigma}} \Ga .
Revised:  We give a tight lower bound \lceil m-\sigma{\sigma} \rceil+1 for the set \{Wt(mwm(G))~|~G \in \mathcal{G_{m,\sigma}} \Ga \} which denotes the collection of weights of maximum weight bipartite matchings of all graphs in _{m,\sigma}} \Ga .
Edit intent: fluency