wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our online scheme combines  the classical decentralized coded caching scheme maddah2013decentralized with ( i ) joint scheduling and power control for the fading broadcast channel, as well as ( ii ) congestion control for ensuring the optimal long-term average performance.
Revised:  Our online scheme combines the classical decentralized coded caching scheme maddah2013decentralized with ( ii ) joint scheduling and power control for the fading broadcast channel, as well as ( ii ) congestion control for ensuring the optimal long-term average performance.
Edit intent: fluency
Original:  By tuning the value of alpha, the proposed scheme enables to balance between different operating points on the average delivery rate region  .
Revised:  By tuning the value of alpha, the proposed scheme can achieve different operating points on the average delivery rate region .
Edit intent: clarity
Original:  We show that our proposed framework is effective with an average AUC improvement of 16:55 \% while requiring on average 853x less space than existing methods on a variety of graphs.
Revised:  We show that our proposed framework is effective with an average AUC improvement of 16.55 \% while requiring on average 853x less space than existing methods on a variety of graphs.
Edit intent: fluency
Original:  To demonstrate our logic , we verify a variant of a recent randomized concurrent counter algorithm  .
Revised:  To demonstrate Polaris , we verify a variant of a recent randomized concurrent counter algorithm .
Edit intent: clarity
Original:  To demonstrate our logic , we verify a variant of a recent randomized concurrent counter algorithm  .
Revised:  To demonstrate our logic , we verify a variant of a randomized concurrent counter algorithm .
Edit intent: clarity
Original:  Unfortunately, most compilers expose the browser's compromised execution model, so long-running programs freeze the browser tab, infinite loops crash IDEs, and so on.
Revised:  Unfortunately, most compilers inherit the browser's compromised execution model, so long-running programs freeze the browser tab, infinite loops crash IDEs, and so on.
Edit intent: clarity
Original:  In this paper, we propose the application of isogeometric analysis since it allows for the exact description of the geometrical domains with respect to common computer-aided design kernels and for a straightforward and convenient way of handling geometrical variations  .
Revised:  In this paper, we propose the application of isogeometric analysis since it allows for the exact description of the geometrical domains with respect to common computer-aided design kernels , for a straightforward and convenient way of handling geometrical variations .
Edit intent: coherence
Original:  That is,Y' is the solution of \Pi when the input is X', the vertex or edge set of some minor G' of G. Consider the set system (X, I), where I denotes the family of all sub-solutions of \Pi .
Revised:  That is,Y' is the solution of \Pi when the input is X', the vertex or edge set of some minor G' of G. Consider the set system (X, I), where I denotes the set of all the solutions and sub-solutions of \Pi .
Edit intent: clarity
Original:  We prove that the problem \Pi belongs to\not \hat  P if and only if  (X, I) satisfies  an extension of  the Exchange Axiom  of a greedoid (Augmentability) and the Partial\hat  Heredity Axiom of a greedoid (Accessibility) .
Revised:  We prove that the problem \Pi belongs to\not \hat P if and only if (X, I) satisfies an extension of both the Exchange Axiom of a greedoid (Augmentability) and the Partial\hat Heredity Axiom of a greedoid (Accessibility) .
Edit intent: clarity
Original:  We prove that the problem \Pi belongs to\not \hat  P if and only if  (X, I) satisfies  an extension of  the Exchange Axiom  of a greedoid (Augmentability) and the Partial\hat  Heredity Axiom of a greedoid (Accessibility) .
Revised:  We prove that the problem \Pi belongs to\not \hat P if and only if (X, I) satisfies an extension of the Exchange Axiom and the Accessibility Axiom of a greedoid (Augmentability) and the Partial\hat Heredity Axiom of a greedoid (Accessibility) .
Edit intent: fluency
Original:  A problem \hat \Pi is in NP if and only if , for all input X, (X, I) satisfies Axioms M2 '' , where M2 '' is an extension of the Augmentability Axiom.
Revised:  A problem \hat \Pi is in NP if and only if , for all input X, (X, I) satisfies Axioms M2 " , where M2 '' is an extension of the Augmentability Axiom.
Edit intent: fluency
Original:  A problem \hat \Pi is in NP if and only if , for all input X, (X, I) satisfies Axioms M2 '' , where M2 '' is an extension of the Augmentability Axiom.
Revised:  A problem \hat \Pi is in NP if and only if , for all input X, (X, I) satisfies Axioms M2 '' , where M2 " is an extension of the Augmentability Axiom.
Edit intent: fluency
Original:  Finally, the problem \hat \Pi is in NP-complete if and only if, for all input X, (X, I) satisfies Axiom M1. Using the fact that Hamiltonicity is an accessible property that satisfies M2 '' , but does not satisfies Axiom M2', in Corollary 1 we get that \mathcal{P} \not = \mathcal{NP}.
Revised:  Finally, the problem \hat \Pi is in NP-complete if and only if, for all input X, (X, I) satisfies Axiom M1. Using the fact that Hamiltonicity is an accessible property that satisfies M2 " , but does not satisfies Axiom M2', in Corollary 1 we get that \mathcal{P} \not = \mathcal{NP}.
Edit intent: fluency
Original: One of the classic ways to measure the success of a scientific facility is the publication return, which is defined as the  refereed papers produced per unit of allocated resources (for example, telescope time or proposals).
Revised: One of the classic ways to measure the success of a scientific facility is the publication return, which is defined as the number of refereed papers produced per unit of allocated resources (for example, telescope time or proposals).
Edit intent: clarity
Original:  For this purpose, ESO conducted a Survey of Non-Publishing Programmes (SNPP) within the activities of the Time Allocation Working Group , a , similar to the monitoring campaign that was recently implemented at ALMA (Stoehr et al. 2016).
Revised:  For this purpose, ESO conducted a Survey of Non-Publishing Programmes (SNPP) within the activities of the Time Allocation Working Group , similar to the monitoring campaign that was recently implemented at ALMA (Stoehr et al. 2016).
Edit intent: fluency
Original:  Furthermore  the network size can be reduced by taking only the most relevant components of the network.
Revised:  Furthermore , the network size can be reduced by taking only the most relevant components of the network.
Edit intent: fluency
Original:  We show that already linearly activated recurrent neural networks can approximate any time-dependent function f(t) given by a number of function values.
Revised:  We show how a type of linearly activated recurrent neural networks can approximate any time-dependent function f(t) given by a number of function values.
Edit intent: clarity
Original:  The networks have interesting properties: In the stationary case they end up in ellipse trajectories in the long run , and they allow the prediction of further values and compact representations of functions.
Revised:  The networks have interesting properties: They end up in ellipse trajectories in the long run , and they allow the prediction of further values and compact representations of functions.
Edit intent: coherence
Original:  The networks have interesting properties: In the stationary case they end up in ellipse trajectories in the long run , and they allow the prediction of further values and compact representations of functions.
Revised:  The networks have interesting properties: In the stationary case they end up in ellipse trajectories in the long run and allow the prediction of further values and compact representations of functions.
Edit intent: coherence
Original:  Furthermore, the network size can be reduced by taking only the most relevant components of the network .
Revised:  Furthermore, the network size can be reduced by taking only most relevant components of the network .
Edit intent: fluency
Original:  Furthermore, the network size can be reduced by taking only the most relevant components of the network .
Revised:  Furthermore, the network size can be reduced by taking only the most relevant components .
Edit intent: clarity
Original:  We show how a type of linearly activated recurrent neural networks , which we call predictive neural networks, can approximate any time-dependent function f(t) given by a number of function values.
Revised:  We show how linear, i.e., linearly activated recurrent neural networks , which we call predictive neural networks, can approximate any time-dependent function f(t) given by a number of function values.
Edit intent: clarity
Original:  Furthermore, the network size can be reduced  by taking only  most relevant components.
Revised:  Furthermore, the network size can be reduced by taking only the most relevant components.
Edit intent: fluency
Original:  Thus , in contrast to others, our approach not only learns network weights but also the network architecture.
Revised:  Therefore , in contrast to others, our approach not only learns network weights but also the network architecture.
Edit intent: fluency
Original:  Thus , in contrast to others, our approach not only learns network weights but also the network architecture.
Revised:  Thus , in contrast to others, we do not only learn network weights but also the network architecture.
Edit intent: clarity
Original:  The networks have interesting properties: They end up in ellipse trajectories in the long run and allow the prediction of further values and compact representations of functions.
Revised:  LRNNs have interesting properties: They end up in ellipse trajectories in the long run and allow the prediction of further values and compact representations of functions.
Edit intent: clarity
Original:  Predictive neural networks outperform the previous state-of-the-art for the MSO task with a minimal number of units.
Revised:  LRNNs outperform the previous state-of-the-art for the MSO task with a minimal number of units.
Edit intent: clarity
Original: Differential equations with distributional sources---in particular, involving delta distributions and/or derivatives thereof---have become increasingly ubiquitous in numerous areas of physics and applied mathematics.
Revised: Partial differential equations with distributional sources---in particular, involving delta distributions and/or derivatives thereof---have become increasingly ubiquitous in numerous areas of physics and applied mathematics.
Edit intent: fluency
Original: Differential equations with distributional sources---in particular, involving delta distributions and/or derivatives thereof---have become increasingly ubiquitous in numerous areas of physics and applied mathematics.
Revised: Differential equations with distributional sources---in particular, involving (derivatives of) delta distributions---have become increasingly ubiquitous in numerous areas of physics and applied mathematics.
Edit intent: clarity
Original:  It is often of considerable interest to obtain numerical solutions for such equations, but the singular (" point-like " ) modeling of the sources in these problems typically introduces nontrivial obstacles for devising a satisfactory numerical implementation .
Revised:  It is often of considerable interest to obtain numerical solutions for such equations, but the singular (" point-like " -like) source modeling invariably introduces nontrivial computational obstacles .
Edit intent: clarity
Original:  A common method to circumvent these is through some form of delta function approximation procedure on the computational grid , yet this strategy often carries significant limitations  .
Revised:  A common method to circumvent these is through some form of delta function approximation procedure on the computational grid ; however, this often carries significant limitations .
Edit intent: clarity
Original:  in this way , one only needs to solve homogeneous equations in each domain, with the source effectively replaced by jump (boundary) conditions thereon.
Revised:  thus , one only needs to solve homogeneous equations in each domain, with the source effectively replaced by jump (boundary) conditions thereon.
Edit intent: coherence
Original:  We prove here that this method is applicable to any linear PDE (of arbitrary order) the source of which is a linear combination of one-dimensional delta distributions and derivatives thereof supported at an arbitrary number of particles.
Revised:  We prove here that this method yields solutions to any linear PDE (of arbitrary order) the source of which is a linear combination of one-dimensional delta distributions and derivatives thereof supported at an arbitrary number of particles.
Edit intent: clarity
Original:  We prove here that this method is applicable to any linear PDE (of arbitrary order) the source of which is a linear combination of one-dimensional delta distributions and derivatives thereof supported at an arbitrary number of particles.
Revised:  We prove here that this method is applicable to any linear PDE the source of which is a linear combination of one-dimensional delta distributions and derivatives thereof supported at an arbitrary number of particles.
Edit intent: clarity
Original:  We prove here that this method is applicable to any linear PDE (of arbitrary order) the source of which is a linear combination of one-dimensional delta distributions and derivatives thereof supported at an arbitrary number of particles.
Revised:  We prove here that this method is applicable to any linear PDE (of arbitrary order) the source of which is any linear combination of one-dimensional delta distributions and derivatives thereof supported at an arbitrary number of particles.
Edit intent: fluency
Original:  We prove here that this method is applicable to any linear PDE (of arbitrary order) the source of which is a linear combination of one-dimensional delta distributions and derivatives thereof supported at an arbitrary number of particles.
Revised:  We prove here that this method is applicable to any linear PDE (of arbitrary order) the source of which is a linear combination of delta distributions and derivatives thereof supported at an arbitrary number of particles.
Edit intent: clarity
Original:  Furthermore, UMAP as described has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.
Revised:  Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.
Edit intent: coherence
Original:  Towards this goal we also give an algorithm for computing formal power series associated to the variants of the Hammersley's process , that have the formal languages studies in this paper as their support .
Revised:  Towards this goal we also give an algorithm for computing formal power series associated to the variants of Hammersley's process , that have the formal languages studies in this paper as their support .
Edit intent: fluency
Original:  Towards this goal we also give an algorithm for computing formal power series associated to the variants of the Hammersley's process , that have the formal languages studies in this paper as their support .
Revised:  Towards this goal we also give an algorithm for computing formal power series associated to the variants of the Hammersley's process .
Edit intent: clarity
Original:  While sometimes external information can be used to infer the strength of social ties, access to such information may be restricted or impractical.
Revised:  While sometimes external information can be used to infer the strength of social ties, access to such information may be restricted or impractical.
Edit intent: fluency
Original:  Sintos and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by leveraging the Strong Triadic Closure (STC) property.
Revised:  Sintos and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by leveraging the property.
Edit intent: clarity
Original:  In particular, we define a sibling partition in a cograph and show that the network is controllable if all nodes of any cell of this partition except one are chosen as the control nodes.
Revised:  In particular, we define a sibling partition in a cograph and show that the network is controllable if all nodes of any cell of this partition except one are chosen as control nodes.
Edit intent: fluency
Original: We prove that deep ReLU neural networks with conventional fully-connected architectures with W weights can approximate continuous \nu-variate functions f with uniform error not exceeding a_\nu\omega_f(c_\nu W^{-2/\nu), where \omega_f is }  the modulus of continuity of f and a_\nu, c_\nu are some \nu-dependent constants.
Revised: We prove that deep ReLU neural networks ), where \omega_f is } the modulus of continuity of f and a_\nu, c_\nu are some \nu-dependent constants.
Edit intent: clarity
Original: Time series produced by dynamical systems as frequently the case in neuroscience  are rarely stationary  but often exhibit quite abrupt changes due to bifurcations or other dynamical phenomena .
Revised: Time series , as frequently the case in neuroscience are rarely stationary but often exhibit quite abrupt changes due to bifurcations or other dynamical phenomena .
Edit intent: clarity
Original: Time series produced by dynamical systems as frequently the case in neuroscience  are rarely stationary  but often exhibit quite abrupt changes due to bifurcations or other dynamical phenomena .
Revised: Time series produced by dynamical systems as frequently the case in neuroscience , are rarely stationary but often exhibit quite abrupt changes due to bifurcations or other dynamical phenomena .
Edit intent: fluency
Original: Time series produced by dynamical systems as frequently the case in neuroscience  are rarely stationary  but often exhibit quite abrupt changes due to bifurcations or other dynamical phenomena .
Revised: Time series produced by dynamical systems as frequently the case in neuroscience are rarely stationary , but often exhibit quite abrupt changes due to bifurcations or other dynamical phenomena .
Edit intent: fluency
Original: Time series produced by dynamical systems as frequently the case in neuroscience  are rarely stationary  but often exhibit quite abrupt changes due to bifurcations or other dynamical phenomena .
Revised: Time series produced by dynamical systems as frequently the case in neuroscience are rarely stationary but often exhibit abrupt changes due to bifurcations or other dynamical phenomena .
Edit intent: clarity
Original:  A plethora of methods for detecting such changes in time series statistics , commonly called change point analysis, have been developed over the years, in addition to test criteria to evaluate change point significance.
Revised:  A plethora of methods for detecting such change points in time series statistics , commonly called change point analysis, have been developed over the years, in addition to test criteria to evaluate change point significance.
Edit intent: fluency
Original:  A plethora of methods for detecting such changes in time series statistics , commonly called change point analysis, have been developed over the years, in addition to test criteria to evaluate change point significance.
Revised:  A plethora of methods for detecting such changes in time series statistics have been developed over the years, in addition to test criteria to evaluate change point significance.
Edit intent: clarity
Original:  A plethora of methods for detecting such changes in time series statistics , commonly called change point analysis, have been developed over the years, in addition to test criteria to evaluate change point significance.
Revised:  A plethora of methods for detecting such changes in time series statistics , commonly called change point analysis, have been developed over the years, in addition to test criteria to evaluate their significance.
Edit intent: clarity
Original:  Here, a general method called Paired Adaptive Regressors for Cumulative Sum (PARCS) is developed for detecting multiple change points in  multivariate time series.
Revised:  Here, a general method called Paired Adaptive Regressors for Cumulative Sum is developed for detecting multiple change points in multivariate time series.
Edit intent: clarity
Original:  A plethora of methods for detecting such change points in time series statistics have been developed over the years, in addition to test criteria to evaluate their significance.
Revised:  A plethora of methods for detecting such change points in time series statistics have been developed over the years, in addition to test criteria to evaluate their significance.
Edit intent: fluency
Original:  The method's flexibility to incorporate useful features from state-of-the-art change point detection techniques is highlighted, and its advantages over alternative approaches are demonstrated through a series of simulation experiments , along with potential drawbacks and suggestions to remedy them .
Revised:  The method's advantages over alternative approaches are demonstrated through a series of simulation experiments , along with potential drawbacks and suggestions to remedy them .
Edit intent: clarity
Original:  The method's flexibility to incorporate useful features from state-of-the-art change point detection techniques is highlighted, and its advantages over alternative approaches are demonstrated through a series of simulation experiments , along with potential drawbacks and suggestions to remedy them .
Revised:  The method's flexibility to incorporate useful features from state-of-the-art change point detection techniques is highlighted, and its advantages over alternative approaches are demonstrated through a series of simulation experiments .
Edit intent: clarity
Original:  Additional astronomical research questions and challenges would be better addressed with integrated data and computational resources that fall outside the scope of existing observatory and space mission projects.
Revised:  Astronomical research questions and challenges would be better addressed with integrated data and computational resources that fall outside the scope of existing observatory and space mission projects.
Edit intent: clarity
Original: We present low-rank methods for event detection  .
Revised: Monitoring of streamed data to detect abnormal behavior (variously known as event detection, anomaly detection, change detection, or outlier detection) underlies many applications of the Internet of Things. Here, we propose a novel framework for event detection .
Edit intent: clarity
Original:  We assume that normal observation come from a low-rank subspace, prior to being corrupted by a uniformly distributed noise.
Revised:  We assume that normal observations come from a low-rank subspace, prior to being corrupted by a uniformly distributed noise.
Edit intent: fluency
Original:  Correspondingly, we aim at recovering a representation of the subspace , and perform event detection by running point-to-subspace distance query in \ell^\infty, for each incoming observation .
Revised:  Correspondingly, we aim to recover a representation of the subspace , and perform event detection by running point-to-subspace distance query in \ell^\infty, for each incoming observation .
Edit intent: fluency
Original:  Correspondingly, we aim at recovering a representation of the subspace , and perform event detection by running point-to-subspace distance query in \ell^\infty, for each incoming observation .
Revised:  Correspondingly, we aim at recovering a representation of the subspace and perform event detection by running point-to-subspace distance query in \ell^\infty, for each incoming observation .
Edit intent: fluency