wanyu/IteraTeR_v2 huggingface dataset:
Original:  This is achieved through the formulation of the transform in terms of circular harmonic expansion satisfying the consistency condition in Cormack's sense.
Revised:  This is achieved through the formulation of the transform in terms of circular harmonic expansion satisfying the consistency conditions in Cormack's sense.
Edit intent: fluency
Original:  From a practical point of view, a collimator-free system considerably increases the amount of  data, which is particularly significant in a scatter imaging system.
Revised:  From a practical point of view, an uncollimated detector system considerably increases the amount of data, which is particularly significant in a scatter imaging system.
Edit intent: clarity
Original:  From a practical point of view, a collimator-free system considerably increases the amount of  data, which is particularly significant in a scatter imaging system.
Revised:  From a practical point of view, a collimator-free system considerably increases the amount of collected data, which is particularly significant in a scatter imaging system.
Edit intent: clarity
Original:  Many single-dataset algorithms and one multi-dataset algorithm were compared to test the performance of the algorithm.
Revised:  Many single-dataset and multi-dataset algorithm were compared to test the performance of the algorithm.
Edit intent: clarity
Original:  Many single-dataset algorithms and one multi-dataset algorithm were compared to test the performance of the algorithm.
Revised:  Many single-dataset algorithms and one multi-dataset algorithms were compared to test the performance of the algorithm.
Edit intent: fluency
Original:  Let A be an arbitrary subset of the Boolean cube, and be the metric complement of A --- the set of all vectors of the Boolean cube at the maximal possible distance from A.
Revised:  Let A be an arbitrary subset of the Boolean cube, and be the metric complement of A -- the set of all vectors of the Boolean cube at the maximal possible distance from A.
Edit intent: fluency
Original:  In this work we describe metric complements and establish  metric regularity of the codes RM(0,m) and RM(k,m) for k \geqslant m-3.
Revised:  In this work we describe metric complements and establish the metric regularity of the codes RM(0,m) and RM(k,m) for k \geqslant m-3.
Edit intent: fluency
Original:  Additionally,  metric regularity of the \mathcal{RM is proved.
Revised:  Additionally, the metric regularity of the \mathcal{RM is proved.
Edit intent: fluency
Original:  Additionally,  metric regularity of the \mathcal{RM is proved.
Revised:  Additionally, metric regularity of the codes \mathcal{RM is proved.
Edit intent: clarity
Original:  Combined with previous results by Tokareva N. (2012) concerning duality of affine and bent functions, this proves metric regularity of most Reed-Muller codes with known covering radius.
Revised:  Combined with previous results by Tokareva N. (2012) concerning duality of affine and bent functions, this establishes the metric regularity of most Reed-Muller codes with known covering radius.
Edit intent: clarity
Original: In this paper, we propose a virtual gang based parallel real-time task scheduling approach for multicore platforms.
Revised: We propose a virtual-gang based parallel real-time task scheduling approach for multicore platforms.
Edit intent: clarity
Original:  Our approach is based on the notion of virtual gang , which is a group of parallel real-time tasks that are statically linked and scheduled together by a gang scheduler.
Revised:  Our approach is based on the notion of a virtual-gang , which is a group of parallel real-time tasks that are statically linked and scheduled together by a gang scheduler.
Edit intent: fluency
Original:  We present an intra-gang synchronization framework  and virtual gang formation algorithms that provide strong temporal isolation and high real-time schedulability in scheduling parallel real-time tasks on multicore.
Revised:  We present an intra-gang synchronization framework and virtual gang formation algorithms that provide strong temporal isolation and high real-time schedulability in scheduling real-time tasks on multicore.
Edit intent: clarity
Original:  We implement our system in a real embedded multicore platform and evaluate our approach both analytically  with generated tasksets  and empirically with a case-study involving real-world workloads , demonstrating the effectiveness of our approach .
Revised:  We evaluate our approach both analytically with generated tasksets and empirically with a case-study involving real-world workloads , demonstrating the effectiveness of our approach .
Edit intent: clarity
Original:  We implement our system in a real embedded multicore platform and evaluate our approach both analytically  with generated tasksets  and empirically with a case-study involving real-world workloads , demonstrating the effectiveness of our approach .
Revised:  We implement our system in a real embedded multicore platform and evaluate our approach both analytically , with generated tasksets and empirically with a case-study involving real-world workloads , demonstrating the effectiveness of our approach .
Edit intent: fluency
Original:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in  O^*(  3^{cc ' }) time when an edge clique cover of size cc' is given .
Revised:  We show that the number of minimal separators of graphs is at most 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in O^*( 3^{cc ' }) time when an edge clique cover of size cc' is given .
Edit intent: clarity
Original:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in  O^*(  3^{cc ' }) time when an edge clique cover of size cc' is given .
Revised:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in O^*( 3^{cc ' }) time when an edge clique cover of size cc' is given .
Edit intent: fluency
Original:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in  O^*(  3^{cc ' }) time when an edge clique cover of size cc' is given .
Revised:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is at most 3^{cc} ) . Furthermore, potential maximal cliques can be listed in O^*( 3^{cc ' }) time when an edge clique cover of size cc' is given .
Edit intent: clarity
Original:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in  O^*(  3^{cc ' }) time when an edge clique cover of size cc' is given .
Revised:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} . Furthermore, potential maximal cliques can be listed in O^*( 3^{cc ' }) time when an edge clique cover of size cc' is given .
Edit intent: fluency
Original:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in  O^*(  3^{cc ' }) time when an edge clique cover of size cc' is given .
Revised:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, these objects can be listed in O^*( 3^{cc ' }) time when an edge clique cover of size cc' is given .
Edit intent: clarity
Original:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in  O^*(  3^{cc ' }) time when an edge clique cover of size cc' is given .
Revised:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in times O^*( 3^{cc ' }) time when an edge clique cover of size cc' is given .
Edit intent: clarity
Original:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in  O^*(  3^{cc ' }) time when an edge clique cover of size cc' is given .
Revised:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in O^*( 3^{cc }) time when an edge clique cover of size cc' is given .
Edit intent: fluency
Original:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in  O^*(  3^{cc ' }) time when an edge clique cover of size cc' is given .
Revised:  We show that the number of minimal separators on graphs with edge clique cover of size cc is O( 2^{cc} ) and the number of potential maximal cliques is O( 3^{cc} ) . Furthermore, potential maximal cliques can be listed in O^*( 3^{cc ' }) , respectively, even when no edge clique cover of size cc' is given .
Edit intent: clarity
Original:  This yields O^*(3^{cc ' }) time algorithms for all problems in the framework of potential maximal cliques, for example Treewidth, Minimum Fill-In and Maximum Independent Set.
Revised:  This yields O^*(3^{cc }) time algorithms for all problems in the framework of potential maximal cliques, for example Treewidth, Minimum Fill-In and Maximum Independent Set.
Edit intent: fluency
Original:  This yields O^*(3^{cc ' }) time algorithms for all problems in the framework of potential maximal cliques, for example Treewidth, Minimum Fill-In and Maximum Independent Set.
Revised:  This yields O^*(3^{cc ' }) time algorithms for problems in the framework of potential maximal cliques, for example Treewidth, Minimum Fill-In and Maximum Independent Set.
Edit intent: clarity
Original:  What is the structure of scientific collaboration when considering works investigating criminal issues using machine learning, deep learning  and AI in general?
Revised:  What is the structure of scientific collaboration when considering works investigating criminal issues using machine learning, deep learning , and AI in general?
Edit intent: fluency
Original:  Using data retrieved from  Scopus database, this work quantitatively analyzes  published works at the intersection between AI and crime employing network science to respond to these questions.
Revised:  Using data retrieved from the Scopus database, this work quantitatively analyzes published works at the intersection between AI and crime employing network science to respond to these questions.
Edit intent: fluency
Original:  This means that scholars working in highly productive countries (e.g. the United States, China) tend to collaborate with researchers based in their same countries .
Revised:  This means that scholars working in highly productive countries (e.g. the United States, China) tend to mostly collaborate domestically .
Edit intent: clarity
Original: In the paper, we study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics.
Revised: We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics.
Edit intent: clarity
Original:  A standard approach to this estimation problem is to employ the Fluctuation-Dissipation Theory, which , in turn, requires the knowledge of the functional form of the underlying unperturbed density that is not available in general.
Revised:  A standard approach to this estimation problem is to employ the Fluctuation-Dissipation Theory, which requires the knowledge of the functional form of the underlying unperturbed density that is not available in general.
Edit intent: coherence
Original:  To overcome this issue, we consider a nonparametric density estimator formulated by the kernel embedding of distribution .
Revised:  To overcome this issue, we consider a nonparametric density estimator formulated by the kernel embedding of distributions .
Edit intent: fluency
Original:  To avoid the computational expense arises using radial type kernels, we consider the "Mercer-type" kernels constructed based on the classical orthogonal bases defined on non-compact domains , such as the Hermite and Laguerre polynomials.
Revised:  To avoid the computational expense associated with using radial type kernels, we consider the "Mercer-type" kernels constructed based on the classical orthogonal bases defined on non-compact domains , such as the Hermite and Laguerre polynomials.
Edit intent: clarity
Original:  We establish the uniform convergence of the estimator , which justifies the use of the estimator for interpolation.
Revised:  We establish the uniform convergence of the estimator . More importantly, the estimator for interpolation.
Edit intent: coherence
Original:  For the linear response estimation, our study provides practical conditions for the well-posedness of both the estimator and the underlying response statistics.
Revised:  For the linear response estimation, our study provides practical conditions for the well-posedness of not only the estimator but also the well-posedness of the underlying response statistics.
Edit intent: clarity
Original:  We offer a theoretical guarantee for the convergence of the estimator to the underlying actual linear response statistics.
Revised:  We provide a theoretical guarantee for the convergence of the estimator to the underlying actual linear response statistics.
Edit intent: fluency
Original:  We offer a theoretical guarantee for the convergence of the estimator to the underlying actual linear response statistics.
Revised:  We offer a theoretical guarantee for the convergence of the estimator to the underlying linear response statistics.
Edit intent: clarity
Original:  Finally, we provide a statistical error bound for the density estimation that accounts for the Monte-Carlo averaging over non-i.i.d time series and  biases due to finite basis truncation.
Revised:  Finally, we offer an error bound for the density estimation that accounts for the Monte-Carlo averaging over non-i.i.d time series and biases due to finite basis truncation.
Edit intent: clarity
Original:  Finally, we provide a statistical error bound for the density estimation that accounts for the Monte-Carlo averaging over non-i.i.d time series and  biases due to finite basis truncation.
Revised:  Finally, we provide a statistical error bound for the density estimation that accounts for the Monte-Carlo averaging over non-i.i.d time series and the biases due to finite basis truncation.
Edit intent: fluency
Original:  Finally, we provide a statistical error bound for the density estimation that accounts for the Monte-Carlo averaging over non-i.i.d time series and  biases due to finite basis truncation.
Revised:  Finally, we provide a statistical error bound for the density estimation that accounts for the Monte-Carlo averaging over non-i.i.d time series and biases due to truncation.
Edit intent: clarity
Original:  This error bound provides a mean to understand the feasibility as well as limitation of the kernel embedding with Mercer-type kernel . Numerically, we verify the effectiveness of the kernel embedding linear response estimator on two stochastic dynamics with known, yet, non-trivial equilibrium densities.
Revised:  This error bound helps understand the feasibility as well as limitation of the kernel embedding with Mercer-type kernel . Numerically, we verify the effectiveness of the kernel embedding linear response estimator on two stochastic dynamics with known, yet, non-trivial equilibrium densities.
Edit intent: clarity
Original:  This error bound provides a mean to understand the feasibility as well as limitation of the kernel embedding with Mercer-type kernel . Numerically, we verify the effectiveness of the kernel embedding linear response estimator on two stochastic dynamics with known, yet, non-trivial equilibrium densities.
Revised:  This error bound provides a mean to understand the feasibility as well as limitation of the kernel embedding with Mercer-type kernels . Numerically, we verify the effectiveness of the kernel embedding linear response estimator on two stochastic dynamics with known, yet, non-trivial equilibrium densities.
Edit intent: fluency
Original:  To avoid the computational expense associated with using radial type kernels, we consider the "Mercer-type" kernels  constructed based on the classical orthogonal bases defined on non-compact domains.
Revised:  To avoid the computational expense associated with using radial type kernels, we consider the "Mercer-type" kernels , constructed based on the classical orthogonal bases defined on non-compact domains.
Edit intent: fluency
Original:  While the resulting representation is analogous to Polynomial Chaos Expansion (PCE), by studying in the reproducing kernel Hilbert space (RKHS) setting, we establish the uniform convergence of the estimator .
Revised:  While the resulting representation is analogous to Polynomial Chaos Expansion (PCE), the connection to the reproducing kernel Hilbert space (RKHS) setting, we establish the uniform convergence of the estimator .
Edit intent: clarity
Original:  While the resulting representation is analogous to Polynomial Chaos Expansion (PCE), by studying in the reproducing kernel Hilbert space (RKHS) setting, we establish the uniform convergence of the estimator .
Revised:  While the resulting representation is analogous to Polynomial Chaos Expansion (PCE), by studying in the reproducing kernel Hilbert space (RKHS) theory allows one to establish the uniform convergence of the estimator .
Edit intent: clarity
Original:  In terms of the linear response estimation, our study provides practical conditions for the well-posedness of not only the estimator but also the well-posedness of the underlying response statistics.
Revised:  In terms of the linear response estimation, our study provides practical conditions for the well-posedness of not only the estimator but also of the underlying response statistics.
Edit intent: fluency
Original:  We provide a theoretical guarantee for the convergence of the estimator to the underlying linear response statistics.
Edit intent: coherence
Original:  Finally, we offer an error bound for the density estimation that accounts for the Monte-Carlo averaging over non-i.i.d time series and the biases due to  truncation.
Revised:  Finally, we provide a statistical error bound for the density estimation that accounts for the Monte-Carlo averaging over non-i.i.d time series and the biases due to truncation.
Edit intent: clarity
Original:  This error bound helps understand the feasibility as well as limitation of the kernel embedding with Mercer-type kernels.
Revised:  This error bound provides a means to understand the feasibility as well as limitation of the kernel embedding with Mercer-type kernels.
Edit intent: clarity
Original:  Numerically, we verify the effectiveness of the kernel embedding linear response estimator on two stochastic dynamics with known, yet, non-trivial equilibrium densities.
Revised:  Numerically, we verify the effectiveness of the estimator on two stochastic dynamics with known, yet, non-trivial equilibrium densities.
Edit intent: clarity
Original: We study the spread of an SIRS-type epidemics with vaccination on network.
Revised: We study the spread of an SIRS-type epidemic with vaccination on network.
Edit intent: fluency
Original:  Starting from an exact Markov description of the model  we investigate the mean epidemic lifetime by providing a sufficient condition for the fast extinction , depending on the topology of the network.
Revised:  Starting from an exact Markov description of the model , we investigate the mean epidemic lifetime by providing a sufficient condition for the fast extinction , depending on the topology of the network.
Edit intent: fluency
Original:  Starting from an exact Markov description of the model  we investigate the mean epidemic lifetime by providing a sufficient condition for the fast extinction , depending on the topology of the network.
Revised:  Starting from an exact Markov description of the model we investigate the mean epidemic lifetime by providing a sufficient condition for fast extinction that depends on the model parameters and the topology of the network.
Edit intent: clarity
Original:  Then, we pass to consider a first-order mean-field approximation of the exact model .
Revised:  Then, we pass to consider a firstorder mean-field approximation of the exact model .
Edit intent: fluency
Original:  In the case of graphs possessing this kind of partition, we find a positively invariant set which contain the endemic equilibrium , that can be computed by using a lower-dimensional dynamical system.
Revised:  In the case of graphs possessing this kind of partition, we prove that the endemic equilibrium , that can be computed by using a lower-dimensional dynamical system.
Edit intent: clarity
Original:  In the case of graphs possessing this kind of partition, we find a positively invariant set which contain the endemic equilibrium , that can be computed by using a lower-dimensional dynamical system.
Revised:  In the case of graphs possessing this kind of partition, we find a positively invariant set which contain the endemic equilibrium can be computed by using a lower-dimensional dynamical system.
Edit intent: coherence
Original:  Finally, in the special case of regular graphs, we show that when the recovery rate is higher than the vaccination rate, the aforementioned invariant set is contained in the domain of attraction of the endemic equilibrium.
Revised:  Finally, in the special case of regular graphs, we investigate the domain of attraction of the endemic equilibrium.
Edit intent: clarity
Original: We develop a computational framework for simulating thin fluid flow in narrow interfaces between contacting solids, which is relevant for a range  engineering, biological and geophysical applications.
Revised: We developed a computational framework for simulating thin fluid flow in narrow interfaces between contacting solids, which is relevant for a range engineering, biological and geophysical applications.
Edit intent: fluency
Original: We develop a computational framework for simulating thin fluid flow in narrow interfaces between contacting solids, which is relevant for a range  engineering, biological and geophysical applications.
Revised: We develop a computational framework for simulating thin fluid flow in narrow interfaces between contacting solids, which is relevant for a range of engineering, biological and geophysical applications.
Edit intent: fluency
Original:  We develop a monolithic finite-element framework for handling  contact, thin incompressible viscous flow and fluid-induced tractions on the surface of the solid, suitable for both one- and two-way coupling approaches.
Revised:  We developed a monolithic finite-element framework for handling contact, thin incompressible viscous flow and fluid-induced tractions on the surface of the solid, suitable for both one- and two-way coupling approaches.
Edit intent: fluency