wanyu/IteraTeR_v2 huggingface dataset:
Original:  Also, a subset D of a graph G is a [ 1, 2 ] -set if, each vertex v \in V \setminus D is adjacent to either one or two vertices in D and  minimum cardinality of [ 1, 2 ] -dominating set of G, is denoted  [1,2](G).
Revised:  Also, a subset D of a graph G is a [ 1, 2 ] -set if, each vertex v \in V \setminus D is adjacent to either one or two vertices in D and the minimum cardinality of [ 1, 2 ] -dominating set of G, is denoted [1,2](G).
Edit intent: fluency
Original:  Also, a subset D of a graph G is a [ 1, 2 ] -set if, each vertex v \in V \setminus D is adjacent to either one or two vertices in D and  minimum cardinality of [ 1, 2 ] -dominating set of G, is denoted  [1,2](G).
Revised:  Also, a subset D of a graph G is a [ 1, 2 ] -set if, each vertex v \in V \setminus D is adjacent to either one or two vertices in D and minimum cardinality of [ 1, 2 ] -dominating set of G, is denoted by [1,2](G).
Edit intent: fluency
Original:  Chang's conjecture say that for every 16 \leq n \leq m, \gamma(G_{m,n})= \left \lfloor(n+2)(m+2){5}\right \rfloor-4 and his conjecture has been proven by Goncalves et al.
Revised:  Chang's conjecture say that for every 16 \leq n \leq m, \gamma(G_{m,n})= \left \lfloor(n+2)(m+2){5}\right \rfloor-4 and this conjecture has been proven by Goncalves et al.
Edit intent: clarity
Original:  This paper presents an explicit constructing method to find an optimal dominating set for grid graph G_{n,m} where m,n\geq 16 in O( \text{size of answer ).
Revised:  This paper presents an explicit constructing method to find an optimal dominating set for grid graph G_{n,m} where m,n\geq 16 in O( size of answer ).
Edit intent: fluency
Original:  Chang's conjecture say that for every 16 \leq n \leq m , \gamma(G_{m,n})= \left \lfloor(n+2)(m+2){5}\right \rfloor-4 and this conjecture has been proven by Goncalves et al.
Revised:  Chang's conjecture says that for every 16 \leq n \leq m , \gamma(G_{m,n})= \left \lfloor(n+2)(m+2){5}\right \rfloor-4 and this conjecture has been proven by Goncalves et al.
Edit intent: fluency
Original:  Chang's conjecture say that for every 16 \leq n \leq m , \gamma(G_{m,n})= \left \lfloor(n+2)(m+2){5}\right \rfloor-4 and this conjecture has been proven by Goncalves et al.
Revised:  Chang's conjecture say that for every 16 \leq m \leq n , \gamma(G_{m,n})= \left \lfloor(n+2)(m+2){5}\right \rfloor-4 and this conjecture has been proven by Goncalves et al.
Edit intent: fluency
Original:  This paper presents an explicit constructing method to find an optimal dominating set for grid graph G_{ n, m  } where m,n\geq 16 in O( size of answer ).
Revised:  This paper presents an explicit constructing method to find an optimal dominating set for grid graph G_{ m } where m,n\geq 16 in O( size of answer ).
Edit intent: fluency
Original:  In addition, we will show that \gamma(G_{ n, m  })=[1,2](G_{ n, m  })  holds in response to an open question posed by Chellali et al.
Revised:  In addition, we will show that \gamma(G_{ m })=[1,2](G_{ n, m }) holds in response to an open question posed by Chellali et al.
Edit intent: fluency
Original:  In addition, we will show that \gamma(G_{ n, m  })=[1,2](G_{ n, m  })  holds in response to an open question posed by Chellali et al.
Revised:  In addition, we will show that \gamma(G_{ n, m })=[1,2](G_{ m }) holds in response to an open question posed by Chellali et al.
Edit intent: fluency
Original: We propose a Learned Primal-Dual algorithm for tomographic reconstruction.
Revised: We propose the Learned Primal-Dual algorithm for tomographic reconstruction.
Edit intent: fluency
Original:  The algorithm includes the (possibly non-linear) forward operator in a deep neural network inspired by unrolled proximal primal-dual optimization methods , but where the proximal operators have been replaced with convolutional neural networks.
Revised:  The algorithm accounts for a (possibly non-linear) forward operator in a deep neural network inspired by unrolled proximal primal-dual optimization methods , but where the proximal operators have been replaced with convolutional neural networks.
Edit intent: clarity
Original:  The algorithm includes the (possibly non-linear) forward operator in a deep neural network inspired by unrolled proximal primal-dual optimization methods , but where the proximal operators have been replaced with convolutional neural networks.
Revised:  The algorithm includes the (possibly non-linear) forward operator in a deep neural network by unrolling a proximal primal-dual optimization methods , but where the proximal operators have been replaced with convolutional neural networks.
Edit intent: clarity
Original:  The algorithm includes the (possibly non-linear) forward operator in a deep neural network inspired by unrolled proximal primal-dual optimization methods , but where the proximal operators have been replaced with convolutional neural networks.
Revised:  The algorithm includes the (possibly non-linear) forward operator in a deep neural network inspired by unrolled proximal primal-dual optimization method , but where the proximal operators have been replaced with convolutional neural networks.
Edit intent: fluency
Original:  The algorithm is trained end-to-end, working directly from raw measured data and  does not depend on any initial reconstruction such as FBP.
Revised:  The algorithm is trained end-to-end, working directly from raw measured data and it does not depend on any initial reconstruction such as FBP.
Edit intent: coherence
Original:  We evaluate the algorithm on low dose CT reconstruction using both analytic and human phantoms against classical reconstruction given by FBPand TVregularized reconstruction as well as deep learning based post-processing of a FBPreconstruction .
Revised:  We evaluate the algorithm on low dose CT reconstruction using both analytic and human phantoms against classical reconstruction given by FBPand TVregularized reconstruction as well as deep learning based post-processing of FBP .
Edit intent: clarity
Original:  For the human phantom we demonstrate a 6.6 dB improvement compared to TV and a 2.2 dB improvement as compared to learned post-processing .
Revised:  For the human phantom we demonstrate a 6.6 dB over TV and 2.2 dB improvement as compared to learned post-processing .
Edit intent: clarity
Original:  For the human phantom we demonstrate a 6.6 dB improvement compared to TV and a 2.2 dB improvement as compared to learned post-processing .
Revised:  For the human phantom we demonstrate a 6.6 dB improvement compared to TV and a 2.2 dB over learned post-processing .
Edit intent: clarity
Original:  The algorithm is trained end-to-end, working directly from raw measured data and it does not depend on any initial reconstruction such as filtered back-projection (FBP) .
Revised:  The algorithm is trained end-to-end, working directly from raw measured data and it does not depend on any initial reconstruction such as FBP .
Edit intent: clarity
Original:  We compare performance of the proposed method on low dose computed tomography reconstruction against FBP, total variation (TV) , and deep learning based post-processing of FBP.
Revised:  We compare performance of the proposed method on low dose CT reconstruction against FBP, total variation (TV) , and deep learning based post-processing of FBP.
Edit intent: clarity
Original:  We compare performance of the proposed method on low dose computed tomography reconstruction against FBP, total variation (TV) , and deep learning based post-processing of FBP.
Revised:  We compare performance of the proposed method on low dose computed tomography reconstruction against FBP, TV , and deep learning based post-processing of FBP.
Edit intent: clarity
Original:  For the Shepp-Logan phantom we obtain > 6 dB PSNR improvement against all compared methods.
Revised:  For the Shepp-Logan phantom we obtain > 6dB PSNR improvement against all compared methods.
Edit intent: fluency
Original:  For human phantoms the corresponding improvement is 6.6dB over TV and 2.2dB over learned post-processing along with a substantial improvement in the structural similarity index . Finally, our algorithm involves only ten forward-back-projection computations, making the method feasible for time critical clinical applications.
Revised:  For human phantoms the corresponding improvement is 6.6dB over TV and 2.2dB over learned post-processing along with a substantial improvement in the SSIM . Finally, our algorithm involves only ten forward-back-projection computations, making the method feasible for time critical clinical applications.
Edit intent: clarity
Original:  Typically , these applications are architected to utilize a data tier for persistence.
Revised:  Increasingly , these applications are architected to utilize a data tier for persistence.
Edit intent: clarity
Original:  We analyze current trends justifying the emergence of this abstraction and discuss a set of features for these new systems.
Revised:  We argue why the time is ripe today to examine the research opportunities afforded by this emerging system paradigm. Based on this discussion, we present design principles as well as candidate feature sets to help concretize the vision for such systems.
Edit intent: clarity
Original:  Overall, our results show that multivariate threshold dependencies are emergent and common features of the investigated models that can have therapeutic relevance.
Revised:  Overall, our results show that the threshold dependencies are emergent and common features of the investigated models that can have therapeutic relevance.
Edit intent: clarity
Original:  Overall, our results show that multivariate threshold dependencies are emergent and common features of the investigated models that can have therapeutic relevance.
Revised:  Overall, our results show that multivariate threshold dependencies are emergent features of the investigated models that can have therapeutic relevance.
Edit intent: clarity
Original:  Overall, our results show that multivariate threshold dependencies are emergent and common features of the investigated models that can have therapeutic relevance.
Revised:  Overall, our results show that multivariate threshold dependencies are emergent and common features of the investigated model with eventual therapeutic relevance.
Edit intent: clarity
Original:  Presented examples demonstrate importance of  cell to cell heterogeneity within a system of clones with different reversibility potentials, quantified by appropriately chosen genetic and epigenetic entropy measures.
Revised:  Presented examples demonstrate importance of taking into account cell to cell heterogeneity within a system of clones with different reversibility potentials, quantified by appropriately chosen genetic and epigenetic entropy measures.
Edit intent: clarity
Original:  Presented examples demonstrate importance of  cell to cell heterogeneity within a system of clones with different reversibility potentials, quantified by appropriately chosen genetic and epigenetic entropy measures.
Revised:  Presented examples demonstrate importance of cell to cell heterogeneity within a system of clones with different reversibility quantified by appropriately chosen genetic and epigenetic entropy measures.
Edit intent: clarity
Original:  In this work, we study whether users tend to be in contact with people interested in similar topics, i.e., topical homophily .
Revised:  In this work, we study whether users tend to be in contact with people interested in similar topics, i.e., if they are topically aligned .
Edit intent: clarity
Original:  Our results show that, on average, users are connected with other users similar to them and stronger relationships are due to a higher topical similarity .
Revised:  Our results show that, on average, users are connected with other users similar to them .
Edit intent: clarity
Original:  Our work, besides providing a way to assess the topical similarity of users, quantifies topical homophily among individuals, contributing to a better understanding of how complex social systems are structured.
Revised:  Our work, besides providing a way to assess the topical similarity of users, quantifies topical alignment among individuals, contributing to a better understanding of how complex social systems are structured.
Edit intent: clarity
Original:  In this paper, we propose a novel method using persistent homology to quantify the perturbation of features that occur in time-varying graphs.
Revised:  In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs.
Edit intent: clarity
Original:  Specifically, we slice the graph data into temporal snapshots, transform the snapshots into metric spaces, extract topological features using persistent homology, and compare those features over time.
Revised:  Specifically, we transform each instance of the time-varying graph into metric spaces, extract topological features using persistent homology, and compare those features over time.
Edit intent: clarity
Original:  We provide a visualization that assists in time-varying graph exploration , and helps to identify patterns of behavior within the graph .
Revised:  We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the graph .
Edit intent: fluency
Original:  We provide a visualization that assists in time-varying graph exploration , and helps to identify patterns of behavior within the graph .
Revised:  We provide a visualization that assists in time-varying graph exploration , and helps to identify patterns of behavior within the data .
Edit intent: clarity
Original: In the token jumping problem for a vertex subset problem Q on graphs we are given a graph G and two feasible solutions S_s, S_t\subseteq V(G) of Q with |S_s|=|S_t| , and imagine that a token is placed on each vertex of S_s . The problem is to determine whether there exists a sequence S_1,\ldots,S_n of feasible solutions, where S_1=S_s, S_n=S_t \pm  and each S_{i+1} results from S_i, 1\leq i<n, by moving exactly one token to another vertex.
Revised: Let \mathcal{Q a vertex subset problem Q on graphs we are given a graph G and two feasible solutions S_s, S_t\subseteq V(G) of Q with |S_s|=|S_t| , and imagine that a token is placed on each vertex of S_s . The problem is to determine whether there exists a sequence S_1,\ldots,S_n of feasible solutions, where S_1=S_s, S_n=S_t \pm and each S_{i+1} results from S_i, 1\leq i<n, by moving exactly one token to another vertex.
Edit intent: clarity
Original: In the token jumping problem for a vertex subset problem Q on graphs we are given a graph G and two feasible solutions S_s, S_t\subseteq V(G) of Q with |S_s|=|S_t| , and imagine that a token is placed on each vertex of S_s . The problem is to determine whether there exists a sequence S_1,\ldots,S_n of feasible solutions, where S_1=S_s, S_n=S_t \pm  and each S_{i+1} results from S_i, 1\leq i<n, by moving exactly one token to another vertex.
Revised: In the token jumping problem for a vertex subset problem Q on graphs we are given a graph G and two feasible solutions S_s, S_t\subseteq V(G) of Q with |S_s|=|S_t| , and imagine that a token is placed on each vertex of S_s . The problem is to determine whether there exists a sequence S_1,\ldots,S_n of feasible solutions, where S_1=S_s, S_n=S_t \pm 1, and each S_{i+1} results from S_i, 1\leq i<n, by moving exactly one token to another vertex.
Edit intent: clarity
Original: In the token jumping problem for a vertex subset problem Q on graphs we are given a graph G and two feasible solutions S_s, S_t\subseteq V(G) of Q with |S_s|=|S_t| , and imagine that a token is placed on each vertex of S_s . The problem is to determine whether there exists a sequence S_1,\ldots,S_n of feasible solutions, where S_1=S_s, S_n=S_t \pm  and each S_{i+1} results from S_i, 1\leq i<n, by moving exactly one token to another vertex.
Revised: In the token jumping problem for a vertex subset problem Q on graphs we are given a graph G and two feasible solutions S_s, S_t\subseteq V(G) of Q with |S_s|=|S_t| , and imagine that a token is placed on each vertex of S_s . The problem is to determine whether there exists a sequence S_1,\ldots,S_n of feasible solutions, where S_1=S_s, S_n=S_t \pm and each S_{i+1} results from S_i, 1\leq i<n, by the addition or removal of a single vertex.
Edit intent: clarity
Original:  We prove that for every nowhere dense class of graphs and for every  r\geq 1 there exists a polynomial p_r such that the token jumping problem for the distance-r independent set problem and for the distance-r dominating set problem admit kernels of size p_r(k) , where k is the number of used tokens . If k is equal to the size of a minimum distance-r dominating set, then  we even obtain a kernel of almost linear size O (k^{1+\epsilon}) for any fixed \epsilon>0.
Revised:  We prove that for every nowhere dense class of graphs and for every integer r\geq 1 there exists a polynomial p_r such that the token jumping problem for the distance-r independent set problem and for the distance-r dominating set problem admit kernels of size p_r(k) , where k is the number of used tokens . If k is equal to the size of a minimum distance-r dominating set, then we even obtain a kernel of almost linear size O (k^{1+\epsilon}) for any fixed \epsilon>0.
Edit intent: clarity
Original:  We prove that for every nowhere dense class of graphs and for every  r\geq 1 there exists a polynomial p_r such that the token jumping problem for the distance-r independent set problem and for the distance-r dominating set problem admit kernels of size p_r(k) , where k is the number of used tokens . If k is equal to the size of a minimum distance-r dominating set, then  we even obtain a kernel of almost linear size O (k^{1+\epsilon}) for any fixed \epsilon>0.
Revised:  We prove that for every nowhere dense class of graphs and for every r\geq 1 there exists a polynomial p_r such that the token jumping problem for the distance-r independent set problem and the distance-r dominating set problem admit kernels of size p_r(k) , where k is the number of used tokens . If k is equal to the size of a minimum distance-r dominating set, then we even obtain a kernel of almost linear size O (k^{1+\epsilon}) for any fixed \epsilon>0.
Edit intent: fluency
Original:  We prove that for every nowhere dense class of graphs and for every  r\geq 1 there exists a polynomial p_r such that the token jumping problem for the distance-r independent set problem and for the distance-r dominating set problem admit kernels of size p_r(k) , where k is the number of used tokens . If k is equal to the size of a minimum distance-r dominating set, then  we even obtain a kernel of almost linear size O (k^{1+\epsilon}) for any fixed \epsilon>0.
Revised:  We prove that for every nowhere dense class of graphs and for every r\geq 1 there exists a polynomial p_r such that the token jumping problem for the distance-r independent set problem and for the distance-r dominating set problem admit kernels of size p_r(k) . If k is equal to the size of a minimum distance-r dominating set, then we even obtain a kernel of almost linear size O (k^{1+\epsilon}) for any fixed \epsilon>0.
Edit intent: clarity
Original:  We prove that for every nowhere dense class of graphs and for every  r\geq 1 there exists a polynomial p_r such that the token jumping problem for the distance-r independent set problem and for the distance-r dominating set problem admit kernels of size p_r(k) , where k is the number of used tokens . If k is equal to the size of a minimum distance-r dominating set, then  we even obtain a kernel of almost linear size O (k^{1+\epsilon}) for any fixed \epsilon>0.
Revised:  We prove that for every nowhere dense class of graphs and for every r\geq 1 there exists a polynomial p_r such that the token jumping problem for the distance-r independent set problem and for the distance-r dominating set problem admit kernels of size p_r(k) , where k is the number of used tokens . If k is equal to the size of a minimum distance-r dominating set, then for any fixed \epsilon>0 we even obtain a kernel of almost linear size O (k^{1+\epsilon}) for any fixed \epsilon>0.
Edit intent: fluency
Original:  We then prove that if a class ~C is somewhere dense and closed under taking subgraphs, then for some value of r\geq 1 the reconfiguration problem for the above problems on C is W 1 are \mathsf{W}[1]} -hard (and in particular we cannot expect the existence of kernelization algorithms).
Revised:  We then prove that if a class ~C is somewhere dense and closed under taking subgraphs, then for some value of r\geq 1 the reconfiguration variants of the above problems on C is W 1 are \mathsf{W}[1]} -hard (and in particular we cannot expect the existence of kernelization algorithms).
Edit intent: clarity
Original:  We then prove that if a class ~C is somewhere dense and closed under taking subgraphs, then for some value of r\geq 1 the reconfiguration problem for the above problems on C is W 1 are \mathsf{W}[1]} -hard (and in particular we cannot expect the existence of kernelization algorithms).
Revised:  We then prove that if a class ~C is somewhere dense and closed under taking subgraphs, then for some value of r\geq 1 the reconfiguration problem for the above problems on 1 are \mathsf{W}[1]} -hard (and in particular we cannot expect the existence of kernelization algorithms).
Edit intent: clarity
Original:  It is usually studied in the exact setting where the goal is to compute all pairs of sets that exceed a given level of similarity (measured e.g. ~ as Jaccard similarity).
Revised:  It is usually studied in the exact setting where the goal is to compute all pairs of sets that exceed a given similarity threshold (measured e.g. ~ as Jaccard similarity).
Edit intent: clarity
Original:  It is usually studied in the exact setting where the goal is to compute all pairs of sets that exceed a given level of similarity (measured e.g. ~ as Jaccard similarity).
Revised:  It is usually studied in the exact setting where the goal is to compute all pairs of sets that exceed a given level of similarity (measured e.g. as Jaccard similarity).
Edit intent: fluency
Original:  We present a new randomized algorithm for set similarity join that can achieve any desired recall up to 100\%, and show theoretically and empirically that it significantly outperforms state-of-the-art implementations of exact methods , and improves on existing approximate methods .
Revised:  We present a new randomized algorithm for set similarity join that can achieve any desired recall up to 100\%, and show theoretically and empirically that it significantly improves on existing methods. The present state-of-the-art implementations of exact methods , and improves on existing approximate methods .
Edit intent: clarity
Original:  Our experiments on benchmark data sets show the method is several times faster than comparable approximate methods , at 90\% recall the algorithm is often more than 2 orders of magnitude faster than exact methods .
Revised:  Our experiments on benchmark data sets also show that the method is several times faster than comparable approximate methods , at 90\% recall the algorithm is often more than 2 orders of magnitude faster than exact methods .
Edit intent: clarity
Original:  Our experiments on benchmark data sets show the method is several times faster than comparable approximate methods , at 90\% recall the algorithm is often more than 2 orders of magnitude faster than exact methods .
Revised:  Our experiments on benchmark data sets show the method is several times faster than comparable approximate methods .
Edit intent: clarity
Original:  Our algorithm makes use of recent theoretical advances in high-dimensional sketching and indexing that we believe to be of wider relevance to the database community.
Revised:  Our algorithm makes use of recent theoretical advances in high-dimensional sketching and indexing that we believe to be of wider relevance to the data engineering community.
Edit intent: clarity