wanyu/IteraTeR_v2 huggingface dataset:
Original:  Coarsening is then achieved by defining one "supernode" for each subgraph : the edges for this coarsened graph derives hence from connectivity between the subgraphs.
Revised:  Coarsening is achieved by defining one "supernode" for each subgraph : the edges for this coarsened graph derives hence from connectivity between the subgraphs.
Edit intent: coherence
Original:  Coarsening is then achieved by defining one "supernode" for each subgraph : the edges for this coarsened graph derives hence from connectivity between the subgraphs.
Revised:  Coarsening is then achieved by defining one "supernode" for each subgraph and the edges for this coarsened graph derives hence from connectivity between the subgraphs.
Edit intent: coherence
Original:  Coarsening is then achieved by defining one "supernode" for each subgraph : the edges for this coarsened graph derives hence from connectivity between the subgraphs.
Revised:  Coarsening is then achieved by defining one "supernode" for each subgraph : the edges for this coarsened graph derives from the connectivity between the subgraphs.
Edit intent: clarity
Original:  Unlike the "one every two nodes" downsampling operation on bipartite graphs, this coarsening operation does not have an exact formulation in the Fourier space of the graph . Instead, we rely on the local Fourier bases of each subgraph to define filtering operations.
Revised:  Unlike the "one every two nodes" downsampling on bipartite graphs, this coarsening operation does not have an exact formulation in the Fourier space of the graph . Instead, we rely on the local Fourier bases of each subgraph to define filtering operations.
Edit intent: fluency
Original:  Unlike the "one every two nodes" downsampling operation on bipartite graphs, this coarsening operation does not have an exact formulation in the Fourier space of the graph . Instead, we rely on the local Fourier bases of each subgraph to define filtering operations.
Revised:  Unlike the "one every two nodes" downsampling operation on bipartite graphs, this coarsening operation does not have an exact formulation in the graph Fourier domain . Instead, we rely on the local Fourier bases of each subgraph to define filtering operations.
Edit intent: clarity
Original:  We apply successfully this method to decompose graph signals, and show promising performance on compression and denoising experiments .
Revised:  We apply successfully this method to decompose graph signals, and show promising performance on compression and denoising .
Edit intent: clarity
Original:  To address this problem we present a  method, called metainference, that combines Bayesian inference, which is a powerful strategy to deal with errors in experimental measurements , with the maximum entropy principle, which represents a rigorous approach to deal with experimental measurements averaged over multiple states.
Revised:  To address this problem we present a Bayesian inference method, called metainference, that combines Bayesian inference, which is a powerful strategy to deal with errors in experimental measurements , with the maximum entropy principle, which represents a rigorous approach to deal with experimental measurements averaged over multiple states.
Edit intent: fluency
Original:  To address this problem we present a  method, called metainference, that combines Bayesian inference, which is a powerful strategy to deal with errors in experimental measurements , with the maximum entropy principle, which represents a rigorous approach to deal with experimental measurements averaged over multiple states.
Revised:  To address this problem we present a method, called metainference, that is able to deal with errors in experimental measurements , with the maximum entropy principle, which represents a rigorous approach to deal with experimental measurements averaged over multiple states.
Edit intent: clarity
Original: We study a system of N\gg 1 degrees of freedom individually relaxing with a rate \mu and coupled via a smooth stationary random Gaussian vector field with both gradient and divergence-free components.
Revised: We study a system of N\gg 1 degrees of freedom coupled via a smooth stationary random Gaussian vector field with both gradient and divergence-free components.
Edit intent: coherence
Original:   We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system experiences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterized by exponential in N number of equilibria,  vast majority of which is expected to be unstable.
Revised:  We show that generically with increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterized by exponential in N number of equilibria, vast majority of which is expected to be unstable.
Edit intent: clarity
Original:   We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system experiences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterized by exponential in N number of equilibria,  vast majority of which is expected to be unstable.
Revised:  We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically non-trivial regime characterized by exponential in N number of equilibria, vast majority of which is expected to be unstable.
Edit intent: clarity
Original:   We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system experiences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterized by exponential in N number of equilibria,  vast majority of which is expected to be unstable.
Revised:  We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system experiences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterised by an exponential number of equilibria, vast majority of which is expected to be unstable.
Edit intent: clarity
Original:   We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system experiences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterized by exponential in N number of equilibria,  vast majority of which is expected to be unstable.
Revised:  We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system experiences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterized by exponential in N number of equilibria, the vast majority of which is expected to be unstable.
Edit intent: fluency
Original:   We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system experiences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterized by exponential in N number of equilibria,  vast majority of which is expected to be unstable.
Revised:  We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system experiences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterized by exponential in N number of equilibria, vast majority of which are expected to be unstable.
Edit intent: fluency
Original:  This picture is suggested to provide a nonlinear analogue of May-Wigner instability transition .
Revised:  It is suggested that this picture provides a global view on the nature of the May-Wigner instability transition .
Edit intent: clarity
Original:  We show that, even by the stronger definition, greater assortment favours the evolution of cooperation for many cooperative dilemmasof interest, including prisoners' dilemmas, snowdrift games, and stag-hunt games  .
Revised:  We show that, by the stronger definition, greater assortment favours the evolution of cooperation for many cooperative dilemmasof interest, including prisoners' dilemmas, snowdrift games, and stag-hunt games .
Edit intent: clarity
Original:  We show that, even by the stronger definition, greater assortment favours the evolution of cooperation for many cooperative dilemmasof interest, including prisoners' dilemmas, snowdrift games, and stag-hunt games  .
Revised:  We show that, even by the stronger definition, greater assortment favours the evolution of cooperation for many cooperative dilemmasof interest, including prisoners' dilemmas, snowdrift games, stag-hunt games .
Edit intent: fluency
Original:  First, given a set of n complex algebraic plane curves of degree at most D , we show that there are O(n^{3/2}) points where two or more curves are tangent.
Revised:  First, given a set of n complex algebraic plane curves , we show that there are O(n^{3/2}) points where two or more curves are tangent.
Edit intent: clarity
Original:  For the case of orthogonal curve intersections, we employ Guth and Zahl's bound for two-rich points in space curve arrangements.
Revised:  For the case of orthogonal curve intersections, we employ a bound of Guth and the third author to control the number of two-rich points in space curve arrangements.
Edit intent: clarity
Original:  The proposed methodsin particular draw upon the structural relevance  and principles of orthogonalization and biorthogonalization and are presented from the perspectives of signal processing, convex programming, continuation methods and nonlinear projection operators.
Revised:  These methods, in particular, draw upon the structural relevance and principles of orthogonalization and biorthogonalization and are presented from the perspectives of signal processing, convex programming, continuation methods and nonlinear projection operators.
Edit intent: clarity
Original:  The proposed methodsin particular draw upon the structural relevance  and principles of orthogonalization and biorthogonalization and are presented from the perspectives of signal processing, convex programming, continuation methods and nonlinear projection operators.
Revised:  The proposed methodsin particular draw upon the structural relevance and are presented from the perspectives of signal processing, convex programming, continuation methods and nonlinear projection operators.
Edit intent: coherence
Original:  Each method is specifically endowed with either a homotopy or tuning parameter in order to facilitate tradeoff analysis between accuracy and numerical stability.
Revised:  Each method is specifically endowed with either a homotopy or tuning parameter to facilitate tradeoff analysis between accuracy and numerical stability.
Edit intent: coherence
Original:  An example involving a basis comprised of real exponential signals illustrates the utility of these methods on an ill-conditioned inverse problem and the results are compared with standard regularization techniques from the  literature.
Revised:  An example involving a basis comprised of real exponential signals illustrates the utility of the proposed methods on an ill-conditioned inverse problem and the results are compared with standard regularization techniques from the literature.
Edit intent: clarity
Original:  An example involving a basis comprised of real exponential signals illustrates the utility of these methods on an ill-conditioned inverse problem and the results are compared with standard regularization techniques from the  literature.
Revised:  An example involving a basis comprised of real exponential signals illustrates the utility of these methods on an ill-conditioned inverse problem and the results are compared to standard regularization techniques from the literature.
Edit intent: fluency
Original:  An example involving a basis comprised of real exponential signals illustrates the utility of these methods on an ill-conditioned inverse problem and the results are compared with standard regularization techniques from the  literature.
Revised:  An example involving a basis comprised of real exponential signals illustrates the utility of these methods on an ill-conditioned inverse problem and the results are compared with standard regularization techniques from the signal processing literature.
Edit intent: clarity
Original: We introduce a predictive objective function for the rate aspect of spike-timing dependent plasticity (STDP) , i.e., ignoring the effects of synchrony of spikes but looking at spiking%DIFDELCMD < {\em %%% rate changes .
Revised: We introduce a predictive objective function for the rate aspect of spike-timing dependent plasticity (STDP) %DIFDELCMD < {\em %%% rate changes .
Edit intent: coherence
Original: We introduce a predictive objective function for the rate aspect of spike-timing dependent plasticity (STDP) , i.e., ignoring the effects of synchrony of spikes but looking at spiking%DIFDELCMD < {\em %%% rate changes .
Revised: We introduce a predictive objective function for the rate aspect of spike-timing dependent plasticity (STDP) , i.e., ignoring the effects of synchrony of spikes but looking at spiking%DIFDELCMD < {\em %%% .
Edit intent: clarity
Original:  The proposed weight update is proportional to the presynaptic spiking (or firing ) rate times the%DIFDELCMD < {\em %%% temporal change of the integrated postsynaptic activity.
Revised:  The proposed weight update is proportional to the presynaptic spiking (or firing ) rate times the%DIFDELCMD < {\em %%% of the integrated postsynaptic activity.
Edit intent: clarity
Original:  Telugu script is a complex abugida and the language is agglutinative, making the problem hard.
Revised:  Telugu script is a complex alphasyllabary and the language is agglutinative, making the problem hard.
Edit intent: fluency
Original:  For specific classes of reaction networks, we show that these conditions  are equivalent to one another and, thus, necessary and sufficient for persistence .
Revised:  For specific classes of reaction networks, we show that these conditions for persistence are equivalent to one another and, thus, necessary and sufficient for persistence .
Edit intent: clarity
Original:  For specific classes of reaction networks, we show that these conditions  are equivalent to one another and, thus, necessary and sufficient for persistence .
Revised:  For specific classes of reaction networks, we show that these conditions are equivalent to one another .
Edit intent: clarity
Original:  Furthermore, they can also be characterized by easily checkable strong connectivity properties of the underlying graph.
Revised:  Furthermore, they can also be characterized by easily checkable strong connectivity properties of a related graph.
Edit intent: clarity
Original:  Since  the aforementioned sufficient conditions for persistence preclude the existence of boundary steady states, our method also provides a graphical tool to check for that.
Revised:  Since one of the aforementioned sufficient conditions for persistence preclude the existence of boundary steady states, our method also provides a graphical tool to check for that.
Edit intent: clarity
Original:  Since  the aforementioned sufficient conditions for persistence preclude the existence of boundary steady states, our method also provides a graphical tool to check for that.
Revised:  Since the aforementioned sufficient conditions for persistence precludes the existence of boundary steady states, our method also provides a graphical tool to check for that.
Edit intent: fluency
Original:  During this process, they can cause mutations, chromosomal rearrangements and lead to an increase in genome size.
Revised:  During this process, they can cause mutations, and lead to an increase in genome size.
Edit intent: clarity
Original:  Despite representing a large genomic fraction, transposable elements have no clear biological function , and have therefore been labelled as "junk DNA" . This work builds upon a previous model, to propose a new concept of natural selection which combines Lamarckian and Darwinian elements.
Revised:  Despite representing a large genomic fraction, transposable elements have no clear biological function . This work builds upon a previous model, to propose a new concept of natural selection which combines Lamarckian and Darwinian elements.
Edit intent: coherence
Original:  Let X ^{(1)}, \ldots, X ^{(\ell) , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)})  be random vectors such that for every coordinatei \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Revised:  Let X ^{(1)}, \ldots, X ^{(\ell) , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) be random vectors such that for every coordinatei \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Edit intent: fluency
Original:  Let X ^{(1)}, \ldots, X ^{(\ell) , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)})  be random vectors such that for every coordinatei \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Revised:  Let X ^{(1)}, \ldots, ^{(\ell) , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) be random vectors such that for every coordinatei \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Edit intent: fluency
Original:  Let X ^{(1)}, \ldots, X ^{(\ell) , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)})  be random vectors such that for every coordinatei \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Revised:  Let X ^{(1)}, \ldots, X , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) be random vectors such that for every coordinatei \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Edit intent: fluency
Original:  Let X ^{(1)}, \ldots, X ^{(\ell) , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)})  be random vectors such that for every coordinatei \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Revised:  Let X ^{(1)}, \ldots, X ^{(\ell) , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) , be random vectors such that for every coordinatei \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Edit intent: fluency
Original:  Let X ^{(1)}, \ldots, X ^{(\ell) , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)})  be random vectors such that for every coordinatei \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Revised:  Let X ^{(1)}, \ldots, X ^{(\ell) , }X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) be random vectors such that for every coordinate i \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. according to P.
Edit intent: fluency
Original:  The question we address is : does there exist a function c _{\mathcal{P independent of n such that for every f: \Omega^n \to [0, 1] with \mathop{\mathrm{E  = \mu > 0: %DIFDELCMD < \begin{align*} %DIFDELCMD < \mathop{\mathrm{E}} \left[ \prod_{j=1}^\ell f(\underline{X}^{(j)}) \right] %DIFDELCMD < \ge c_{\mathcal{P}}(\mu) > 0 \;
Revised:  The question we address is : does there exist a function c () independent of n such that for every f: \Omega^n \to [0, 1] with \mathop{\mathrm{E = \mu > 0: %DIFDELCMD < \begin{align*} %DIFDELCMD < \mathop{\mathrm{E}} \left[ \prod_{j=1}^\ell f(\underline{X}^{(j)}) \right] %DIFDELCMD < \ge c_{\mathcal{P}}(\mu) > 0 \;
Edit intent: clarity
Original:  The question we address is : does there exist a function c _{\mathcal{P independent of n such that for every f: \Omega^n \to [0, 1] with \mathop{\mathrm{E  = \mu > 0: %DIFDELCMD < \begin{align*} %DIFDELCMD < \mathop{\mathrm{E}} \left[ \prod_{j=1}^\ell f(\underline{X}^{(j)}) \right] %DIFDELCMD < \ge c_{\mathcal{P}}(\mu) > 0 \;
Revised:  The question we address is : does there exist a function c _{\mathcal{P independent of n such that for every f: \Omega^n \to [0, 1] with E = \mu > 0: %DIFDELCMD < \begin{align*} %DIFDELCMD < \mathop{\mathrm{E}} \left[ \prod_{j=1}^\ell f(\underline{X}^{(j)}) \right] %DIFDELCMD < \ge c_{\mathcal{P}}(\mu) > 0 \;
Edit intent: fluency
Original:  ? \end{align*} We settle the question for \ell = 2 and when \ell > 2 and \mathcal{P has bounded correlation \rho( \mathcal{P ) < 1. {\em  
Revised:  ? \end{align*} We settle the question for \ell = 2 and when \ell > 2 and P has bounded correlation \rho( \mathcal{P ) < 1. {\em 
Edit intent: fluency
Original:  ? \end{align*} We settle the question for \ell = 2 and when \ell > 2 and \mathcal{P has bounded correlation \rho( \mathcal{P ) < 1. {\em  
Revised:  ? \end{align*} We settle the question for \ell = 2 and when \ell > 2 and \mathcal{P has bounded correlation \rho( P ) < 1. {\em 
Edit intent: fluency
Original:  ? \end{align*} We settle the question for \ell = 2 and when \ell > 2 and \mathcal{P has bounded correlation \rho( \mathcal{P ) < 1. {\em  
Revised:  ? \end{align*} We settle the question for \ell = 2 and when \ell > 2 and \mathcal{P has bounded correlation \rho( \mathcal{P ) < 1. {\em obstructions 
Edit intent: coherence
Original: There is a common theme to  research questions in additive combinatorics and noise stability.
Revised: There is a common theme to some research questions in additive combinatorics and noise stability.
Edit intent: fluency
Original:  Let X ^{(1)}, \ldots, X^{(\ell)  ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) , be random vectors such that for every coordinate i \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. ~according to P . A central question that is addressed in both areas is:
Revised:  Let X ^{(1)}, \ldots, X^{(\ell) ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) , be random vectors such that for every coordinate i \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. ~according to P . A central question that is addressed in both areas is:
Edit intent: fluency
Original:  Let X ^{(1)}, \ldots, X^{(\ell)  ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) , be random vectors such that for every coordinate i \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. ~according to P . A central question that is addressed in both areas is:
Revised:  Let X ^{(1)}, \ldots, X ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) , be random vectors such that for every coordinate i \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. ~according to P . A central question that is addressed in both areas is:
Edit intent: fluency
Original:  Let X ^{(1)}, \ldots, X^{(\ell)  ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) , be random vectors such that for every coordinate i \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. ~according to P . A central question that is addressed in both areas is:
Revised:  Let X ^{(1)}, \ldots, X^{(\ell)^{(\ell) ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) , be random vectors such that for every coordinate i \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. ~according to P . A central question that is addressed in both areas is:
Edit intent: fluency
Original:  Let X ^{(1)}, \ldots, X^{(\ell)  ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) , be random vectors such that for every coordinate i \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. ~according to P . A central question that is addressed in both areas is:
Revised:  Let X ^{(1)}, \ldots, X^{(\ell) ^{(j)} = (X_1^{(j)}, \ldots, X_n^{(j)}) be random vectors such that for every coordinate i \in [n] the tuples (X_i^{(1)}, \ldots, X_i^{(\ell)}) are i.i.d. ~according to P . A central question that is addressed in both areas is:
Edit intent: fluency