wanyu/IteraTeR_v2 huggingface dataset:
Original:  The mathematical technique relies on results for unbounded and possibly non-closed random sets in the Euclidean space.
Revised:  The mathematical technique relies on results for unbounded and possibly non-closed random sets in Euclidean space.
Edit intent: fluency
Original:  In this article, we design a CNN-based steganalyzer which is quite different from the previous study of {\em Quian et al.} and its successor, namely {\em Pibre et al.}
Revised:  In this article, we design a CNN-based steganalyzer which is quite different from the previous study of {\em Qian et al.} and its successor, namely {\em Pibre et al.}
Edit intent: fluency
Original: Edge deletion problems are those where given a graph G and a graph property \pi, the goal is to find a subset of edges such that after its removal the graph G will satisfy the property \pi.
Revised: Deletion problems are those where given a graph G and a graph property \pi, the goal is to find a subset of edges such that after its removal the graph G will satisfy the property \pi.
Edit intent: clarity
Original:  Typically, we want to minimize the number of edges removed.
Revised:  Typically, we want to minimize the number of elements removed.
Edit intent: clarity
Original:  In fair deletion problem we change the objective: we minimize the maximum number of edges incident to a single vertex.
Revised:  In fair deletion problems we change the objective: we minimize the maximum number of edges incident to a single vertex.
Edit intent: fluency
Original:  In fair deletion problem we change the objective: we minimize the maximum number of edges incident to a single vertex.
Revised:  In fair deletion problem we change the objective: we minimize the maximum number of deletions in a neighborhood of a single vertex.
Edit intent: clarity
Original:  Moreover, we show that there is no algorithm for fair MSO edge-deletion running in time n^{o( \sqrt k )}, where n is the size of the graph and k is the sum of the first three mentioned parameters, provided that the Exponential Time Hypothesis holds.
Revised:  Moreover, we show that there is no algorithm for fair FO vertex-deletion problem running in time n^{o( \sqrt k )}, where n is the size of the graph and k is the sum of the first three mentioned parameters, provided that the Exponential Time Hypothesis holds.
Edit intent: clarity
Original:  On the other hand, we provide an FPT algorithm for the fair MSO edge-deletion  parameterized by the size of minimum vertex cover and an FPT algorithm for the fair MSO vertex-deletion  parameterized by the neighborhood diversity .
Revised:  On the other hand, we provide an FPT algorithm for the fair MSO edge-deletion problem parameterized by the size of minimum vertex cover and an FPT algorithm for the fair MSO vertex-deletion parameterized by the neighborhood diversity .
Edit intent: clarity
Original:  On the other hand, we provide an FPT algorithm for the fair MSO edge-deletion  parameterized by the size of minimum vertex cover and an FPT algorithm for the fair MSO vertex-deletion  parameterized by the neighborhood diversity .
Revised:  On the other hand, we provide an FPT algorithm for the fair MSO edge-deletion parameterized by the size of minimum vertex cover and an FPT algorithm for the fair MSO vertex-deletion problem parameterized by the neighborhood diversity .
Edit intent: clarity
Original:  On the other hand, we provide an FPT algorithm for the fair MSO edge-deletion  parameterized by the size of minimum vertex cover and an FPT algorithm for the fair MSO vertex-deletion  parameterized by the neighborhood diversity .
Revised:  On the other hand, we provide an FPT algorithm for the fair MSO edge-deletion parameterized by the size of minimum vertex cover and an FPT algorithm for the fair MSO vertex-deletion parameterized by the neighborhood diversity 
Edit intent: fluency
Original:  SSA and D-SSA are up to 1200 times faster than the SIGMOD  15 best method, IMM, while providing the same ( 1- 1 /e-\epsilon) approximation guarantee.
Revised:  SSA and D-SSA are up to 1200 times faster than the SIGMOD ' 15 best method, IMM, while providing the same ( 1- 1 /e-\epsilon) approximation guarantee.
Edit intent: fluency
Original:  SSA and D-SSA are up to 1200 times faster than the SIGMOD  15 best method, IMM, while providing the same ( 1- 1 /e-\epsilon) approximation guarantee.
Revised:  SSA and D-SSA are up to 1200 times faster than the SIGMOD 15 best method, IMM, while providing the same ( 1-1 /e-\epsilon) approximation guarantee.
Edit intent: fluency
Original:  To achieve this goal, we seek to fit a weighted, nonnegative adjacency matrix among 100 \mu m \mum brain "voxels" using viral tracer data.
Revised:  To achieve this goal, we seek to fit a weighted, nonnegative adjacency matrix among 100 m \mum brain "voxels" using viral tracer data.
Edit intent: fluency
Original:  To achieve this goal, we seek to fit a weighted, nonnegative adjacency matrix among 100 \mu m \mum brain "voxels" using viral tracer data.
Revised:  To achieve this goal, we seek to fit a weighted, nonnegative adjacency matrix among 100 \mu \mum brain "voxels" using viral tracer data.
Edit intent: fluency
Original:  Despite a multi-year experimental effort, the problem remains severely underdetermined: Injection sites provide incomplete coverage, and the number of voxels  is orders of magnitude larger than the number of injections  .
Revised:  Despite a multi-year experimental effort, injections provide incomplete coverage, and the number of voxels is orders of magnitude larger than the number of injections .
Edit intent: clarity
Original:  Despite a multi-year experimental effort, the problem remains severely underdetermined: Injection sites provide incomplete coverage, and the number of voxels  is orders of magnitude larger than the number of injections  .
Revised:  Despite a multi-year experimental effort, the problem remains severely underdetermined: Injection sites provide incomplete coverage, and the number of voxels in our data is orders of magnitude larger than the number of injections .
Edit intent: clarity
Original:  Despite a multi-year experimental effort, the problem remains severely underdetermined: Injection sites provide incomplete coverage, and the number of voxels  is orders of magnitude larger than the number of injections  .
Revised:  Despite a multi-year experimental effort, the problem remains severely underdetermined: Injection sites provide incomplete coverage, and the number of voxels is orders of magnitude larger than the number of injections , making the problem severely underdetermined .
Edit intent: coherence
Original:  Our method combines three features: a matrix completion loss for missing data, a smoothing spline penalty term to regularize the problem, and (optionally) a low rank factorization.
Revised:  Our method combines three features: a matrix completion loss for missing data, a smoothing spline penalty to regularize the problem, and (optionally) a low rank factorization.
Edit intent: clarity
Original:  The first is computing dominance product: given a set of n points p_1,\ldots, p_n in R^d, compute a matrix D, such that D i,j%DIFDELCMD < ] %%% =%DIFDELCMD < \bigl| %%% \{k \mid p_i[k] \leq p_j[k]\}%DIFDELCMD < \bigr|%%% ;
Revised:  The first is computing dominance product: given a set of n points p_1,\ldots, p_n in R^d, i,j%DIFDELCMD < ] %%% =%DIFDELCMD < \bigl| %%% \{k \mid p_i[k] \leq p_j[k]\}%DIFDELCMD < \bigr|%%% ;
Edit intent: coherence
Original:  The first is computing dominance product: given a set of n points p_1,\ldots, p_n in R^d, compute a matrix D, such that D i,j%DIFDELCMD < ] %%% =%DIFDELCMD < \bigl| %%% \{k \mid p_i[k] \leq p_j[k]\}%DIFDELCMD < \bigr|%%% ;
Revised:  The first is computing dominance product: given a set of n points p_1,\ldots, p_n in R^d, compute a matrix D, such that D %DIFDELCMD < ] %%% =%DIFDELCMD < \bigl| %%% \{k \mid p_i[k] \leq p_j[k]\}%DIFDELCMD < \bigr|%%% ;
Edit intent: clarity
Original:  The first is computing dominance product: given a set of n points p_1,\ldots, p_n in R^d, compute a matrix D, such that D i,j%DIFDELCMD < ] %%% =%DIFDELCMD < \bigl| %%% \{k \mid p_i[k] \leq p_j[k]\}%DIFDELCMD < \bigr|%%% ;
Revised:  The first is computing dominance product: given a set of n points p_1,\ldots, p_n in R^d, compute a matrix D, such that D i,j%DIFDELCMD < ] %%% %DIFDELCMD < \bigl| %%% \{k \mid p_i[k] \leq p_j[k]\}%DIFDELCMD < \bigr|%%% ;
Edit intent: clarity
Original:  The second problem is the L_\infty Closest Pair in high dimensions: given a set S of n points in R^d, find a pair of distinct points in S at minimum distance under the L_\infty metric .
Revised:  The second problem is the L_\infty Closest Pair in high dimensions: given a set S of n points in R^d, find a pair of distinct points in S at minimum distance .
Edit intent: clarity
Original:  When d is constant, there are efficient algorithms that solve this problem, and fast approximate solutions are known for general d.
Revised:  When d is constant, there are efficient algorithms that solve this problem, and fast approximate solutions for general d.
Edit intent: clarity
Original:  We significantly simplify and improve previous results , showing that the problem can be solved by a deterministic strongly-polynomial algorithm that runs in O(DP(n,d)\log n)
Revised:  We significantly simplify and improve previous results , showing that it can be solved by a deterministic strongly-polynomial algorithm that runs in O(DP(n,d)\log n)
Edit intent: clarity
Original:  time,  where DP(n,d) is the time bound for computing the dominance product {\em  for n points in R^d.  ] \bigl| \bigr| For integer coordinates from some interval [-M, M], and for d=n^r for some r > 0 , we obtain an algorithm that runs in \tilde{O}\left(\min\{Mn^{\omega(1,r,1)},\, DP(n,d)\}\right) time, where \omega(1,r,1) is the exponent of multiplying an n \times n^r matrix by an n^r \times n matrix  .
Revised:  time, where DP(n,d) is the time bound for computing the {\em for n points in R^d. ] \bigl| \bigr| For integer coordinates from some interval [-M, M], and for d=n^r for some r > 0 , we obtain an algorithm that runs in \tilde{O}\left(\min\{Mn^{\omega(1,r,1)},\, DP(n,d)\}\right) time, where \omega(1,r,1) is the exponent of multiplying an n \times n^r matrix by an n^r \times n matrix .
Edit intent: clarity
Original:  time,  where DP(n,d) is the time bound for computing the dominance product {\em  for n points in R^d.  ] \bigl| \bigr| For integer coordinates from some interval [-M, M], and for d=n^r for some r > 0 , we obtain an algorithm that runs in \tilde{O}\left(\min\{Mn^{\omega(1,r,1)},\, DP(n,d)\}\right) time, where \omega(1,r,1) is the exponent of multiplying an n \times n^r matrix by an n^r \times n matrix  .
Revised:  time, where DP(n,d) is the time bound for computing the dominance product {\em dominance product for n points in R^d. ] \bigl| \bigr| For integer coordinates from some interval [-M, M], and for d=n^r for some r > 0 , we obtain an algorithm that runs in \tilde{O}\left(\min\{Mn^{\omega(1,r,1)},\, DP(n,d)\}\right) time, where \omega(1,r,1) is the exponent of multiplying an n \times n^r matrix by an n^r \times n matrix .
Edit intent: fluency
Original:  time,  where DP(n,d) is the time bound for computing the dominance product {\em  for n points in R^d.  ] \bigl| \bigr| For integer coordinates from some interval [-M, M], and for d=n^r for some r > 0 , we obtain an algorithm that runs in \tilde{O}\left(\min\{Mn^{\omega(1,r,1)},\, DP(n,d)\}\right) time, where \omega(1,r,1) is the exponent of multiplying an n \times n^r matrix by an n^r \times n matrix  .
Revised:  time, where DP(n,d) is the time bound for computing the dominance product {\em for n points in R^d. ] =\bigl| \bigr| For integer coordinates from some interval [-M, M], and for d=n^r for some r > 0 , we obtain an algorithm that runs in \tilde{O}\left(\min\{Mn^{\omega(1,r,1)},\, DP(n,d)\}\right) time, where \omega(1,r,1) is the exponent of multiplying an n \times n^r matrix by an n^r \times n matrix .
Edit intent: clarity
Original:  time,  where DP(n,d) is the time bound for computing the dominance product {\em  for n points in R^d.  ] \bigl| \bigr| For integer coordinates from some interval [-M, M], and for d=n^r for some r > 0 , we obtain an algorithm that runs in \tilde{O}\left(\min\{Mn^{\omega(1,r,1)},\, DP(n,d)\}\right) time, where \omega(1,r,1) is the exponent of multiplying an n \times n^r matrix by an n^r \times n matrix  .
Revised:  time, where DP(n,d) is the time bound for computing the dominance product {\em for n points in R^d. ] \bigl| \bigr| For integer coordinates from some interval [-M, M], we obtain an algorithm that runs in \tilde{O}\left(\min\{Mn^{\omega(1,r,1)},\, DP(n,d)\}\right) time, where \omega(1,r,1) is the exponent of multiplying an n \times n^r matrix by an n^r \times n matrix .
Edit intent: coherence
Original:  We conclude that when time-locking is a crucial step in the analysis of neuronal activity patterns, both the emergence and the timing of the classification accuracy are affected by structural properties of the network that generates the signal.
Revised:  We conclude that when time-locking is a crucial step in the analysis of neural activity patterns, both the emergence and the timing of the classification accuracy are affected by structural properties of the network that generates the signal.
Edit intent: fluency
Original:  Moreover, it shows that the the recently proposed batch normalization and weight normalization re-parametrizations enjoy good generalization properties, and leads to a novel network regularizer based on the network's Jacobian matrix.
Revised:  Moreover, it shows that the recently proposed batch normalization and weight normalization re-parametrizations enjoy good generalization properties, and leads to a novel network regularizer based on the network's Jacobian matrix.
Edit intent: fluency
Original:  The analysis is supported with experimental results on the MNIST and CIFAR-10  datasets.
Revised:  The analysis is supported with experimental results on the MNIST , CIFAR-10 datasets.
Edit intent: fluency
Original:  Our counterexample of a regular event domain  with bounded \natural-cliques , and not admitting a regular nice labeling is based on (i) the bijection between event domains, median graphs, and CAT(0) cube complexes and is derived from (ii) an example by Wise (1996 and 2007) of a nonpositively curved square complex {\bf X} with six squares, whose edges are colored in five colors, and whose universal cover \bf X is a CAT(0) square complex containing a particular plane with an aperiodic tiling.
Revised:  Our counterexample of a regular event domain ( with bounded \natural-cliques , and not admitting a regular nice labeling is based on (i) the bijection between event domains, median graphs, and CAT(0) cube complexes and is derived from (ii) an example by Wise (1996 and 2007) of a nonpositively curved square complex {\bf X} with six squares, whose edges are colored in five colors, and whose universal cover \bf X is a CAT(0) square complex containing a particular plane with an aperiodic tiling.
Edit intent: fluency
Original:  Our counterexample of a regular event domain  with bounded \natural-cliques , and not admitting a regular nice labeling is based on (i) the bijection between event domains, median graphs, and CAT(0) cube complexes and is derived from (ii) an example by Wise (1996 and 2007) of a nonpositively curved square complex {\bf X} with six squares, whose edges are colored in five colors, and whose universal cover \bf X is a CAT(0) square complex containing a particular plane with an aperiodic tiling.
Revised:  Our counterexample of a regular event domain with bounded \natural-cliques ) that does not admit a regular nice labeling is based on (i) the bijection between event domains, median graphs, and CAT(0) cube complexes and is derived from (ii) an example by Wise (1996 and 2007) of a nonpositively curved square complex {\bf X} with six squares, whose edges are colored in five colors, and whose universal cover \bf X is a CAT(0) square complex containing a particular plane with an aperiodic tiling.
Edit intent: coherence
Original:  Our counterexample of a regular event domain  with bounded \natural-cliques , and not admitting a regular nice labeling is based on (i) the bijection between event domains, median graphs, and CAT(0) cube complexes and is derived from (ii) an example by Wise (1996 and 2007) of a nonpositively curved square complex {\bf X} with six squares, whose edges are colored in five colors, and whose universal cover \bf X is a CAT(0) square complex containing a particular plane with an aperiodic tiling.
Revised:  Our counterexample of a regular event domain with bounded \natural-cliques , and not admitting a regular nice labeling . Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex {\bf X} with six squares, whose edges are colored in five colors, and whose universal cover \bf X is a CAT(0) square complex containing a particular plane with an aperiodic tiling.
Edit intent: clarity
Original:  There exist nice interpretations of these structures as combinatorial and geometric objects and both conjectures can be reformulated in this framework . Namely, from a graph theoretical point of view, the domains of prime event structures correspond exactly to median graphs;
Revised:  There exist nice interpretations of these structures as combinatorial and geometric objects . Namely, from a graph theoretical point of view, the domains of prime event structures correspond exactly to median graphs;
Edit intent: coherence
Original:  A necessary condition for both conjectures to be true is that domains of respective regular event structures  admit a regular nice labeling (which corresponds to a special coloring of the hyperplanes of the associated CAT(0) cube complex) .
Revised:  A necessary condition for both conjectures to be true is that domains of regular event structures admit a regular nice labeling (which corresponds to a special coloring of the hyperplanes of the associated CAT(0) cube complex) .
Edit intent: clarity
Original:  A necessary condition for both conjectures to be true is that domains of respective regular event structures  admit a regular nice labeling (which corresponds to a special coloring of the hyperplanes of the associated CAT(0) cube complex) .
Revised:  A necessary condition for both conjectures to be true is that domains of respective regular event structures admit a regular nice labeling .
Edit intent: coherence
Original:  Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex %DIFDELCMD < {\bf %%% X with six squares, whose edges are colored in five colors, and whose universal cover%DIFDELCMD < \bf X %DIFDELCMD < %%%  is a CAT(0) square complex containing a particular plane with an aperiodic tiling  .
Revised:  Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex %DIFDELCMD < {\bf %%% with six squares, whose edges are colored in five colors, and whose universal cover%DIFDELCMD < \bf X %DIFDELCMD < %%% is a CAT(0) square complex containing a particular plane with an aperiodic tiling .
Edit intent: fluency
Original:  Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex %DIFDELCMD < {\bf %%% X with six squares, whose edges are colored in five colors, and whose universal cover%DIFDELCMD < \bf X %DIFDELCMD < %%%  is a CAT(0) square complex containing a particular plane with an aperiodic tiling  .
Revised:  Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex %DIFDELCMD < {\bf %%% X %DIFDELCMD < \bf X %DIFDELCMD < %%% is a CAT(0) square complex containing a particular plane with an aperiodic tiling .
Edit intent: coherence
Original:  Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex %DIFDELCMD < {\bf %%% X with six squares, whose edges are colored in five colors, and whose universal cover%DIFDELCMD < \bf X %DIFDELCMD < %%%  is a CAT(0) square complex containing a particular plane with an aperiodic tiling  .
Revised:  Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex %DIFDELCMD < {\bf %%% X with six squares, whose edges are colored in five colors, and whose universal cover%DIFDELCMD < \bf X %DIFDELCMD < %%% whose universal cover is a CAT(0) square complex containing a particular plane with an aperiodic tiling .
Edit intent: fluency
Original: Traditional intra prediction usually utilizes the nearest reference line to generate the prediction block when only considering the strong spatial correlation.
Revised: Traditional intra prediction usually utilizes the nearest reference line to generate the predicted block when considering strong spatial correlation.
Edit intent: clarity
Original:  However, this kind of single line-based method is not always a good solution because of two reasons .
Revised:  However, this kind of single line-based method does not always work well due to at least two issues .
Edit intent: clarity
Original:  Because of the two reasons , this paper proposes to utilize multiple reference lines to improve the intra prediction .
Revised:  Because of the two reasons , this paper proposes an efficient multiple line-based intra prediction scheme to improve coding efficiency .
Edit intent: clarity
Original:  In addition , this paper also designs several optional acceleration algorithmswhen considering the encoding complexity .
Revised:  In addition , this paper designs several fast algorithms .
Edit intent: clarity
Original:  Experimental results show that for all intra configuration, the bit saving of the proposed fast scheme is 1.9\% on average ,  and up to 3.2 \%, with increasing the encoding time 115 \%.
Revised:  Experimental results show that , and up to 3.2 \%, with increasing the encoding time 115 \%.
Edit intent: coherence
Original: Given the network of interactions underlying a complex system, what can we learn about controlling such a system solely from its structure?
Revised: What can we learn about controlling such a system solely from its structure?
Edit intent: clarity
Original: Given the network of interactions underlying a complex system, what can we learn about controlling such a system solely from its structure?
Revised: Given the network of interactions underlying a complex system, what can we learn about controlling a system solely from its structure?
Edit intent: clarity
Original:  Here we use a new mathematical framework for structure-based control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes.
Revised:  Here we use a framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes.
Edit intent: clarity
Original:  This  framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors and which are guaranteed to be effective regardless of the dynamic details and parameters of the underlying system .
Revised:  This framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors , regardless of the dynamic details and parameters of the underlying system .
Edit intent: clarity
Original:  This  framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors and which are guaranteed to be effective regardless of the dynamic details and parameters of the underlying system .
Revised:  This framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors and which are guaranteed to be effective regardless of the dynamic details and system parameters .
Edit intent: clarity