wanyu/IteraTeR_v2 huggingface dataset:
Original:  When the goals of evolution are modular, in the sense that specific groups of inputs affect specific groups of outputs, product-rule mutations  lead to modular structure;
Revised:  When the goals of evolution are modular, in the sense that specific groups of inputs affect specific groups of outputs, product-rule mutations also lead to modular structure;
Edit intent: clarity
Original: Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of the clones.
Revised: Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones.
Edit intent: fluency
Original:  This scenario differs qualitatively from the standard view of adaptation in that the speed of adaptation becomes independent of population size while the fitness variance does not , in apparent violation of Fisher's fundamental theorem .
Revised:  This scenario differs qualitatively from the standard view of adaptation in that the speed of adaptation becomes independent of population size while the fitness variance does not .
Edit intent: clarity
Original: Given oracle access to a Boolean function f:  0,1 ^n \mapsto 0,1 , we\eps\eps design a randomized tester that takes as input a parameter eps\eps >0, and  outputs {\sf Yes} if the function is monotone , and outputs {\sf No} with probability >2/3, if the function is \eps-far from monotone.
Revised: A Boolean function f: 0,1 ^n \mapsto 0,1 , we\eps\eps design a randomized tester that takes as input a parameter eps\eps >0, and outputs {\sf Yes} if the function is monotone , and outputs {\sf No} with probability >2/3, if the function is \eps-far from monotone.
Edit intent: clarity
Original: Given oracle access to a Boolean function f:  0,1 ^n \mapsto 0,1 , we\eps\eps design a randomized tester that takes as input a parameter eps\eps >0, and  outputs {\sf Yes} if the function is monotone , and outputs {\sf No} with probability >2/3, if the function is \eps-far from monotone.
Revised: Given oracle access to a Boolean function f: \{ 0,1 ^n \mapsto 0,1 , we\eps\eps design a randomized tester that takes as input a parameter eps\eps >0, and outputs {\sf Yes} if the function is monotone , and outputs {\sf No} with probability >2/3, if the function is \eps-far from monotone.
Edit intent: fluency
Original: Given oracle access to a Boolean function f:  0,1 ^n \mapsto 0,1 , we\eps\eps design a randomized tester that takes as input a parameter eps\eps >0, and  outputs {\sf Yes} if the function is monotone , and outputs {\sf No} with probability >2/3, if the function is \eps-far from monotone.
Revised: Given oracle access to a Boolean function f: 0,1 ^n \mapsto 0,1 , we\eps\eps design a randomized tester that is given oracle access to f and an input parameter\eps >0, and outputs {\sf Yes} if the function is monotone , and outputs {\sf No} with probability >2/3, if the function is \eps-far from monotone.
Edit intent: clarity
Original: Given oracle access to a Boolean function f:  0,1 ^n \mapsto 0,1 , we\eps\eps design a randomized tester that takes as input a parameter eps\eps >0, and  outputs {\sf Yes} if the function is monotone , and outputs {\sf No} with probability >2/3, if the function is \eps-far from monotone.
Revised: Given oracle access to a Boolean function f: 0,1 ^n \mapsto 0,1 , we\eps\eps design a randomized tester that takes as input a parameter eps\eps >0, and has the following guarantee: It outputs {\sf Yes} if the function is monotone , and outputs {\sf No} with probability >2/3, if the function is \eps-far from monotone.
Edit intent: coherence
Original:  That is, f needs to be modified at%DIFDELCMD < \eps%%% -fraction of the points to make it monotone.
Revised:  %DIFDELCMD < \eps%%% -fraction of the points to make it monotone.
Edit intent: coherence
Original:  Our non-adaptive, one-sided tester makes  (n^{7/8}\eps^{-3/2} \eps ) queries to the oracle.
Revised:  Our non-adaptive, one-sided tester makes (n^{7/8}\eps^{-3/2} \eps) ) queries to the oracle.
Edit intent: fluency
Original:  Our solution is based on a recursive space decomposition, combined with a fast algorithm to compute the union of two disjoint onion decompositions.
Revised:  Our solution is based on a recursive space decomposition, combined with a fast algorithm to compute the union of two disjoint onion 
Edit intent: coherence
Original:  This IWCEA uses a new decoding method and incorporates a heuristic method in initialization.
Revised:  This RWCEA uses a new decoding method and incorporates a heuristic method in initialization.
Edit intent: clarity
Original:  Computational results show that the IWCEA runs faster and performs better than a weight-coded evolutionary algorithm proposed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.
Revised:  Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm proposed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.
Edit intent: clarity
Original:  We extend pathlet routing by introducing a new control plane for internal routing that has the following qualities: it is designed to operate on the internal routing of an ISP;
Revised:  We extend pathlet routing by introducing a new control plane for internal routing that has the following qualities: it is designed to operate in the internal network of an ISP;
Edit intent: clarity
Original:  it can be incrementally deployed and  nicely coexist with other control planes.
Revised:  it can be incrementally deployed and it can nicely coexist with other control planes.
Edit intent: fluency
Original:  Besides formally introducing the algorithms and messages of our control plane, we propose an experimental validation in the simulation framework OMNeT++ that we use to assess scalability and robustness .
Revised:  Besides formally introducing the algorithms and messages of our control plane, we propose an experimental validation in the simulation framework OMNeT++ that we use to assess the effectiveness and scalability of our approach .
Edit intent: clarity
Original:  By homogeneous we mean homogeneous with respect to a \ZZ -grading on the first (q-)Weyl algebra%DIFDELCMD < } %%% which will be introduced in this article.
Revised:  By homogeneous we mean homogeneous with respect to a \ZZ (q-)Weyl algebra%DIFDELCMD < } %%% which will be introduced in this article.
Edit intent: clarity
Original:  It turns out that the factorization can be almost completely reduced to commutative univariate factorization  with some additional easy combinatorial steps.
Revised:  It turns out that the factorization can be almost completely reduced to commutative univariate factorization with some additional uncomplicated combinatorial steps.
Edit intent: clarity
Original:  The implementation beats }  currently available implementations dealing with factorization in the first Weyl algebra  in speed and elegancy of the results .
Revised:  The implementation beats } currently available implementations dealing with factorization in the first Weyl algebra both in speed and elegancy of the results .
Edit intent: clarity
Original: In this paper, we describe a novel algorithm for the extraction of iso-valued hypersurfaces that may be implicitly contained in four-dimensional (4D) data sets, e.g., like time-varying computed tomographic three-dimensional images .
Revised: In this paper, we describe a novel algorithm for the extraction of iso-valued hypersurfaces that may be implicitly contained in four-dimensional (4D) data sets, such as temporal sequences of three-dimensional images .
Edit intent: clarity
Original:  This so-called STEVE (Space-Time-Enclosing Volume Extraction) algorithm is based on its three main ingredients: (i) an indexing scheme for 4D points specifically located within the tesseract-like 2x2x2x2-neighborhood of toxels (i.e., - without loss of generality - time-varying voxels), (ii) a vector path table that provides proper links for contributing volume segments, and (iii) a connectivity diagram that helps to resolve topological ambiguities .
Revised:  This so-called STEVE (Space-Time-Enclosing Volume Extraction) algorithm is based on its three main ingredients: (i) an indexing scheme for 4D points specifically located within the tesseract-like 2x2x2x2-neighborhood of toxels (i.e., - without loss of generality - time-varying computed tomography .
Edit intent: clarity
Original:  Furthermore, the information of the interior/exterior of the enclosed regions is propagated to each  of the tetrahedrons, which are embedded into 4D and which in their union represent the final, iso-valued hypersurface(s). 
Revised:  Furthermore, the information of the interior/exterior of the enclosed regions is propagated to each one of the tetrahedrons, which are embedded into 4D and which in their union represent the final, iso-valued hypersurface(s). 
Edit intent: clarity
Original:  While this limiting procedure plays a pivotal role in elucidating the mechanisms of some very important effects such as chimera states, multistability, synchronization, and the coherence-incoherence transition, its mathematical basis remains little understood.
Revised:  While this method has been widely used in the analysis of pattern formation in nonlocally coupled networks, its mathematical basis remains little understood.
Edit intent: clarity
Original:  While this limiting procedure plays a pivotal role in elucidating the mechanisms of some very important effects such as chimera states, multistability, synchronization, and the coherence-incoherence transition, its mathematical basis remains little understood.
Revised:  While this limiting procedure plays a pivotal role in elucidating the mechanisms of some very important effects such as chimera states, multistability, synchronization, and the coherence-incoherence transition, its mathematical basis remained little understood.
Edit intent: fluency
Original:  In this paper, we use the combination of the ideas and results of the theory of graph limits and techniques for nonlinear evolution equations to provide a rigorous mathematical justification for taking the continuum limit and to extend this method to cover many complex networks, for which it has not been applied before.
Revised:  In this paper, we use the combination of ideas and results of the theory of graph limits and techniques for nonlinear evolution equations to provide a rigorous mathematical justification for taking the continuum limit and to extend this method to cover many complex networks, for which it has not been applied before.
Edit intent: fluency
Original:  In this paper, we use the combination of the ideas and results of the theory of graph limits and techniques for nonlinear evolution equations to provide a rigorous mathematical justification for taking the continuum limit and to extend this method to cover many complex networks, for which it has not been applied before.
Revised:  In this paper, we use the combination of the ideas and results from the theory of graph limits and techniques for nonlinear evolution equations to provide a rigorous mathematical justification for taking the continuum limit and to extend this method to cover many complex networks, for which it has not been applied before.
Edit intent: fluency
Original:  In this paper, we use the combination of the ideas and results of the theory of graph limits and techniques for nonlinear evolution equations to provide a rigorous mathematical justification for taking the continuum limit and to extend this method to cover many complex networks, for which it has not been applied before.
Revised:  In this paper, we use the combination of the ideas and results of the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking the continuum limit and to extend this method to cover many complex networks, for which it has not been applied before.
Edit intent: clarity
Original:  In addition, for sequences of simple graphs that converge to {0, 1}-valued graphons, we show that the rate of convergence depends on the fractal dimension of the boundary of the support of the graph limit.
Revised:  For sequences of simple graphs that converge to {0, 1}-valued graphons, we show that the rate of convergence depends on the fractal dimension of the boundary of the support of the graph limit.
Edit intent: coherence
Original:  In addition, for sequences of simple graphs that converge to {0, 1}-valued graphons, we show that the rate of convergence depends on the fractal dimension of the boundary of the support of the graph limit.
Revised:  In addition, for sequences of simple graphs converging to {0, 1}-valued graphons, we show that the rate of convergence depends on the fractal dimension of the boundary of the support of the graph limit.
Edit intent: clarity
Original:  In addition, for sequences of simple graphs that converge to {0, 1}-valued graphons, we show that the rate of convergence depends on the fractal dimension of the boundary of the support of the graph limit.
Revised:  In addition, for sequences of simple graphs that converge to {0, 1}-valued graphons, it is shown that the convergence rate depends on the fractal dimension of the boundary of the support of the graph limit.
Edit intent: clarity
Original:  The results of this paper are used to study the regions of continuity of chimera states and the attractors of the nonlocal Kuramoto equation on certain bipartite graphs.
Revised:  These results are then used to study the regions of continuity of chimera states and the attractors of the nonlocal Kuramoto equation on certain bipartite graphs.
Edit intent: clarity
Original:  For sequences of simple graphs converging to {0, 1}-valued graphons, it is shown that the convergence rate depends on the fractal dimension of the boundary of the support of the graph limit.
Revised:  In addition, for sequences of simple graphs converging to {0, 1}-valued graphons, it is shown that the convergence rate depends on the fractal dimension of the boundary of the support of the graph limit.
Edit intent: coherence
Original:  Finally we address a geometric problem of representing planar graphswith unit cubes and using the results of the threshold coloring problem , we obtain unit-cube contact representation for some subclasses of planar graphs  .
Revised:  Finally we address a geometric problem of representing planar graphswith unit cubes and using the results of the threshold coloring problem , we obtain unit-cube contact representation for several classes of planar graphs .
Edit intent: clarity
Original:  Finally we considered several natural variants of this problem and show the relation of these variants to several well-known graph coloring and graph theoretic problems.
Revised:  Variants of the threshold coloring problem are related to well-known graph coloring and graph theoretic problems.
Edit intent: clarity
Original: We propose a fast, parallel , maximum clique algorithm for large , sparse graphs that is designed to exploit characteristics of social and information networks.
Revised: We propose a fast, parallel maximum clique algorithm for large , sparse graphs that is designed to exploit characteristics of social and information networks.
Edit intent: fluency
Original: We propose a fast, parallel , maximum clique algorithm for large , sparse graphs that is designed to exploit characteristics of social and information networks.
Revised: We propose a fast, parallel , maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks.
Edit intent: fluency
Original:  We observe roughly linear runtime scaling over graphs between 1000 vertices and 100M vertices .
Revised:  The method exhibits a roughly linear runtime scaling over graphs between 1000 vertices and 100M vertices .
Edit intent: clarity
Original:  We observe roughly linear runtime scaling over graphs between 1000 vertices and 100M vertices .
Revised:  We observe roughly linear runtime scaling over real-world networks ranging from 1000 vertices and 100M vertices .
Edit intent: clarity
Original:  We observe roughly linear runtime scaling over graphs between 1000 vertices and 100M vertices .
Revised:  We observe roughly linear runtime scaling over graphs between 1000 to 100 million nodes .
Edit intent: clarity
Original:  In a test with a 1.8 billion-edge social network , the algorithm finds the largest clique in about 20 minutes.
Revised:  In a test on a social network with 1.8 billion-edge social network , the algorithm finds the largest clique in about 20 minutes.
Edit intent: clarity
Original:  In a test with a 1.8 billion-edge social network , the algorithm finds the largest clique in about 20 minutes.
Revised:  In a test with a 1.8 billion edges , the algorithm finds the largest clique in about 20 minutes.
Edit intent: clarity
Original:  For social networks, in particular, we found that using the core number of a vertex in combination with a good heuristic clique finder efficiently removes the vast majority of the search space.
Revised:  For social networks, in particular, we found that using the core number of a vertex in combination with a good heuristic clique finder to efficiently remove the vast majority of the search space.
Edit intent: clarity
Original:  In the algorithm , processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with especially large search spaces can be pruned by other processes.
Revised:  During the search , processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with especially large search spaces can be pruned by other processes.
Edit intent: clarity
Original:  In the algorithm , processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with especially large search spaces can be pruned by other processes.
Revised:  In the algorithm , processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with large search spaces can be pruned by other processes.
Edit intent: clarity
Original:  We use this clique finder to investigate the size of the largest temporal strong components in dynamic networks, which requires finding the largest clique in a particular temporal reachability graph .
Revised:  We apply the algorithm to two problems: to compute temporal strong components in dynamic networks, which requires finding the largest clique in a particular temporal reachability graph .
Edit intent: clarity
Original:  We use this clique finder to investigate the size of the largest temporal strong components in dynamic networks, which requires finding the largest clique in a particular temporal reachability graph .
Revised:  We use this clique finder to investigate the size of the largest temporal strong components and to compress graphs .
Edit intent: clarity
Original: We are interested in fixed points in Boolean networks, i.e. functions f from \{0,1\}^n to itself.
Revised: We are interested in fixed points in Boolean networks, i.e. functions f from \{0,1\}^n to itself.
Edit intent: fluency
Original:  and for the class of non-expansive networks we get a ``dichotomization'' of the previous forbidden subnetwork theorem: every subnetwork of f (and f itself in particular) has at most (resp. at least) one fixed point if and only if f has no subnetworks in \C^+ (resp.
Revised:  and for the class of non-expansive networks we get a "dichotomization" of the previous forbidden subnetwork theorem: every subnetwork of f (and f itself in particular) has at most (resp. at least) one fixed point if and only if f has no subnetworks in \C^+ (resp.
Edit intent: fluency
Original:  We define the subnetworks of f as the restrictions of f to the sub-cubes of \{0,1\}^n, and we characterizes a class %DIFDELCMD < \F %%%  of Boolean networks satisfying the following property:
Revised:  We define the subnetworks of f as the restrictions of f to the subcubes of \{0,1\}^n, and we characterizes a class %DIFDELCMD < \F %%% of Boolean networks satisfying the following property:
Edit intent: fluency
Original:  every subnetwork of f (and f itself in particular) has a unique fixed point if and only if f has no subnetwork in %DIFDELCMD < \F%%%  . This characterization generalizes the fixed point theorem of Shih and Dong, which asserts that if for every x in \{0,1\}^n there is no directed cycle in the directed graph whose the adjacency matrix is the discrete Jacobian matrix of f evaluated at point x, then f has a unique fixed point.
Revised:  Every subnetwork of f (and f itself in particular) has a unique fixed point if and only if f has no subnetwork in %DIFDELCMD < \F%%% . This characterization generalizes the fixed point theorem of Shih and Dong, which asserts that if for every x in \{0,1\}^n there is no directed cycle in the directed graph whose the adjacency matrix is the discrete Jacobian matrix of f evaluated at point x, then f has a unique fixed point.
Edit intent: fluency
Original:  every subnetwork of f (and f itself in particular) has a unique fixed point if and only if f has no subnetwork in %DIFDELCMD < \F%%%  . This characterization generalizes the fixed point theorem of Shih and Dong, which asserts that if for every x in \{0,1\}^n there is no directed cycle in the directed graph whose the adjacency matrix is the discrete Jacobian matrix of f evaluated at point x, then f has a unique fixed point.
Revised:  every subnetwork of f has a unique fixed point if and only if f has no subnetwork in %DIFDELCMD < \F%%% . This characterization generalizes the fixed point theorem of Shih and Dong, which asserts that if for every x in \{0,1\}^n there is no directed cycle in the directed graph whose the adjacency matrix is the discrete Jacobian matrix of f evaluated at point x, then f has a unique fixed point.
Edit intent: clarity
Original:  and for the class of non-expansive networks we get a "dichotomization" of the previous forbidden subnetwork theorem: every subnetwork of f (and f itself in particular) has at most (resp. at least) one fixed point if and only if f has no subnetworks in %DIFDELCMD < \C%%%  ^+ (resp. %DIFDELCMD < \C%%%  ^-) subnetwork.
Revised:  and for the class of non-expansive networks we get a "dichotomization" of the previous forbidden subnetwork theorem: Every subnetwork of f (and f itself in particular) has at most (resp. at least) one fixed point if and only if f has no subnetworks in %DIFDELCMD < \C%%% ^+ (resp. %DIFDELCMD < \C%%% ^-) subnetwork.
Edit intent: fluency
Original:  and for the class of non-expansive networks we get a "dichotomization" of the previous forbidden subnetwork theorem: every subnetwork of f (and f itself in particular) has at most (resp. at least) one fixed point if and only if f has no subnetworks in %DIFDELCMD < \C%%%  ^+ (resp. %DIFDELCMD < \C%%%  ^-) subnetwork.
Revised:  and for the class of non-expansive networks we get a "dichotomization" of the previous forbidden subnetwork theorem: every subnetwork of f has at most (resp. at least) one fixed point if and only if f has no subnetworks in %DIFDELCMD < \C%%% ^+ (resp. %DIFDELCMD < \C%%% ^-) subnetwork.
Edit intent: clarity
Original:  Finally, we prove that if f is a conjunctive network then every subnetwork of f (and f itself in particular) has at most one fixed point if and only if f has no subnetworks in%DIFDELCMD < \C%%% ^+.
Revised:  Finally, we prove that if f is a conjunctive network then every subnetwork of f has at most one fixed point if and only if f has no subnetworks in%DIFDELCMD < \C%%% ^+.
Edit intent: clarity