wanyu/IteraTeR_v2 huggingface dataset:
Original:  We find that for classes known to be in P, such as 2SAT and \# XORSAT, the existence of appropriate rewrite rules allows for efficient simplification of the diagram, producing the solution in polynomial time.
Revised:  We find that for classes known to be in P, such as 2SAT and XORSAT, the existence of appropriate rewrite rules allows for efficient simplification of the diagram, producing the solution in polynomial time.
Edit intent: coherence
Original:  In contrast, for classes known to be NP-complete, such as 3SAT, or \# P-complete, such as \# 2SAT, the corresponding rewrite rules introduce hyperedges to the diagrams, in numbers which are not easily bounded above by a polynomial.
Revised:  In contrast, for classes known to be NP-complete, such as 3SAT, or P-complete, such as \# 2SAT, the corresponding rewrite rules introduce hyperedges to the diagrams, in numbers which are not easily bounded above by a polynomial.
Edit intent: fluency
Original:  In contrast, for classes known to be NP-complete, such as 3SAT, or \# P-complete, such as \# 2SAT, the corresponding rewrite rules introduce hyperedges to the diagrams, in numbers which are not easily bounded above by a polynomial.
Revised:  In contrast, for classes known to be NP-complete, such as 3SAT, or \# P-complete, such as 2SAT, the corresponding rewrite rules introduce hyperedges to the diagrams, in numbers which are not easily bounded above by a polynomial.
Edit intent: fluency
Original:  This diagrammatic approach unifies the diagnosis of the complexity of CSPs and \# CSPs and shows promise in aiding tensor network contraction-based algorithms.
Revised:  This diagrammatic approach unifies the diagnosis of the complexity of CSPs and CSPs and shows promise in aiding tensor network contraction-based algorithms.
Edit intent: fluency
Original:  We first show that, for any monadic second order formula over graphs that characterizes a given kind of subset of its vertices, the maximal number of such sets in a tree can be expressed as the \textit{growth rate  } of a bilinear system .
Revised:  We first show that, for any monadic second order formula over graphs that characterizes a given kind of subset of its vertices, the maximal number of such sets in a tree can be expressed as the \textit{growth rate of a bilinear system } of a bilinear system .
Edit intent: fluency
Original:  We first show that, for any monadic second order formula over graphs that characterizes a given kind of subset of its vertices, the maximal number of such sets in a tree can be expressed as the \textit{growth rate  } of a bilinear system .
Revised:  We first show that, for any monadic second order formula over graphs that characterizes a given kind of subset of its vertices, the maximal number of such sets in a tree can be expressed as the \textit{growth rate } .
Edit intent: clarity
Original:  Then we show that this ``growth rate'' of a bilinear system can be approximated from above.
Revised:  Then we show that this "growth rate" of a bilinear system can be approximated from above.
Edit intent: fluency
Original: We then use our implementation of this result to provide bounds (some sharp and some almost sharp) on the number of independent dominating sets, total perfect dominating sets, induced matchings, maximal induced matchings, minimal perfect dominating sets, perfect codes and maximal irredundant sets on trees.
Revised: We then use our implementation of this result to provide bounds on the number of independent dominating sets, total perfect dominating sets, induced matchings, maximal induced matchings, minimal perfect dominating sets, perfect codes and maximal irredundant sets on trees.
Edit intent: clarity
Original:  Our derivation is based on the analysis of an algorithm that achieves optimal performance on some model of communication within the system .
Revised:  Our derivation is based on the analysis of an algorithm that achieves optimal performance for a given model of replacements .
Edit intent: clarity
Original:  We obtain a generic bound that depends on the properties of such communication schemes , and instantiate that result for all-to-one and one-to-one communication models.
Revised:  We obtain a general bound that depends on the properties of such communication schemes , and instantiate that result for all-to-one and one-to-one communication models.
Edit intent: fluency
Original:  We obtain a generic bound that depends on the properties of such communication schemes , and instantiate that result for all-to-one and one-to-one communication models.
Revised:  We obtain a generic bound that depends on the properties of such communication schemes , and instantiate that result for all-to-one and one-to-one interaction models.
Edit intent: clarity
Original:  We provide lower bounds on the expected Mean Square Error of averaging algorithms in open systems of fixed size.
Revised:  We provide lower bounds on the expected Mean Squared Error achievable by any averaging algorithms in open systems of fixed size.
Edit intent: clarity
Original:  Our derivation is based on the analysis of an algorithm that achieves optimal performance for a given model of replacements.
Revised:  Our derivation is based on the analysis of a conceptual algorithm that would achieve optimal performance for a given model of replacements.
Edit intent: clarity
Original: The heavy-tailed mutation operator proposed in Doerr et al. (GECCO 2017), called fast mutation to agree with the previously used language, so far was successfully used only in purely mutation-based algorithms.
Revised: The heavy-tailed mutation operator proposed in Doerr et al. (GECCO 2017), called fast mutation to agree with the previously used language, so far was successfully used only in purely mutation-based algorithms.
Edit intent: fluency
Original: The heavy-tailed mutation operator proposed in Doerr et al. (GECCO 2017), called fast mutation to agree with the previously used language, so far was successfully used only in purely mutation-based algorithms.
Revised: The heavy-tailed mutation operator proposed in Doerr et al. (GECCO 2017), called fast mutation to agree with the previously used language, so far was proven to be advantageous only in mutation-based algorithms.
Edit intent: clarity
Original:  With a heavy-tailed mutation rate, the runtime of the (1+(\lambda,\lambda)) genetic algorithm on the OneMax benchmark function becomes linear in the problem size .
Revised:  For the (1+(\lambda,\lambda)) genetic algorithm on the OneMax benchmark function becomes linear in the problem size .
Edit intent: clarity
Original:  With a heavy-tailed mutation rate, the runtime of the (1+(\lambda,\lambda)) genetic algorithm on the OneMax benchmark function becomes linear in the problem size .
Revised:  With a heavy-tailed mutation rate, the runtime of the (1+(\lambda,\lambda)) genetic algorithm optimizing the OneMax benchmark function becomes linear in the problem size .
Edit intent: clarity
Original:  With a heavy-tailed mutation rate, the runtime of the (1+(\lambda,\lambda)) genetic algorithm on the OneMax benchmark function becomes linear in the problem size .
Revised:  With a heavy-tailed mutation rate, the runtime of the (1+(\lambda,\lambda)) genetic algorithm on the OneMax benchmark function , we show that with a heavy-tailed mutation rate a linear runtime can be achieved .
Edit intent: clarity
Original:  This is asymptotically faster than  with any static mutation rate and is the same asymptotic runtime that can be obtained with a self-adjusting  choice of the mutation rate .
Revised:  This is asymptotically faster than what can be obtained with any static mutation rate and is the same asymptotic runtime that can be obtained with a self-adjusting choice of the mutation rate .
Edit intent: clarity
Original:  This is asymptotically faster than  with any static mutation rate and is the same asymptotic runtime that can be obtained with a self-adjusting  choice of the mutation rate .
Revised:  This is asymptotically faster than with any static mutation rate , and is asymptotically equivalent to the runtime of the self-adjusting choice of the mutation rate .
Edit intent: clarity
Original:  This is asymptotically faster than  with any static mutation rate and is the same asymptotic runtime that can be obtained with a self-adjusting  choice of the mutation rate .
Revised:  This is asymptotically faster than with any static mutation rate and is the same asymptotic runtime that can be obtained with a self-adjusting version of the choice of the mutation rate .
Edit intent: clarity
Original:  This result is complemented by an empirical study which shows the effectiveness of the fast mutation also on random MAX-3SAT instances.
Revised:  This result is complemented by an empirical study which shows the effectiveness of the fast mutation also on random satisfiable Max-3SAT instances.
Edit intent: clarity
Original: Migration of talent is a major driver of innovation . Large-scale bibliometric data have been used to measure international mobility of scholars.
Revised: Migration of scholars is a major driver of innovation . Large-scale bibliometric data have been used to measure international mobility of scholars.
Edit intent: clarity
Original:  Yet , our understanding of internal migration among researchers is quite limited partly due to lack of data aggregated at a suitable sub-national level.
Revised:  Yet , our understanding of internal migration among researchers is very limited. This is partly due to lack of data aggregated at a suitable sub-national level.
Edit intent: clarity
Original:  Over the past two decades, the migration network has become more dense, but also more diverse, including greater exchange between states along the Gulf and the Pacific Coast.
Revised:  Over the past two decades, the migration network has become more dense, and more diverse, including greater exchange between states along the Gulf and the Pacific Coast.
Edit intent: coherence
Original:  Our analysis of mobility events as a temporal network suggests that Mexican scholarly migration is experiencing a mobility transition in which migration between urban centers is increasing in particular to and from a single metropolitan region .
Revised:  Our analysis , which is mostly empirical in nature, sets the foundations for testing and developing theories that can rely on the analytical framework developed by migration scholars and the richness of appropriately processed bibliometric data .
Edit intent: coherence
Original: Migration of scholars is a major driver of innovation and  diffusion of knowledge.
Revised: The migration of scholars is a major driver of innovation and diffusion of knowledge.
Edit intent: fluency
Original: Migration of scholars is a major driver of innovation and  diffusion of knowledge.
Revised: Migration of scholars is a major driver of innovation and of diffusion of knowledge.
Edit intent: fluency
Original:  This is partly due to  lack of data aggregated at a suitable sub-national level.
Revised:  This is partly due to a lack of data aggregated at a suitable sub-national level.
Edit intent: fluency
Original:  Substantively, we combine demographic and network science techniques to improve our understanding of internal migration patterns  country boundaries.
Revised:  Substantively, we combine demographic and network science techniques to improve our understanding of internal migration patterns within country boundaries.
Edit intent: clarity
Original:  Migration patterns between states in Mexico appear to be heterogeneous in size and direction across regions.
Revised:  The migration patterns between states in Mexico appear to be heterogeneous in size and direction across regions.
Edit intent: clarity
Original:  Over the past two decades, we observed a general decreasing trend in the crude migration intensity.
Revised:  Over the past two decades, there has been a general decreasing trend in the crude migration intensity.
Edit intent: clarity
Original:  However, the migration network has become more dense , and more diverse, including greater exchange between states along the Gulf and the Pacific Coast.
Revised:  However, the migration network has become more dense and more diverse, including greater exchange between states along the Gulf and the Pacific Coast.
Edit intent: fluency
Original:  However, the migration network has become more dense , and more diverse, including greater exchange between states along the Gulf and the Pacific Coast.
Revised:  However, the migration network has become more dense , and more diverse, and has included greater exchanges between states along the Gulf and the Pacific Coast.
Edit intent: coherence
Original:  Our analysis, which is mostly empirical in nature, sets the foundations for testing and developing theories that can rely on the analytical framework developed by migration scholars  and the richness of appropriately processed bibliometric data.
Revised:  Our analysis, which is mostly empirical in nature, lays the foundations for testing and developing theories that can rely on the analytical framework developed by migration scholars and the richness of appropriately processed bibliometric data.
Edit intent: fluency
Original:  Our analysis, which is mostly empirical in nature, sets the foundations for testing and developing theories that can rely on the analytical framework developed by migration scholars  and the richness of appropriately processed bibliometric data.
Revised:  Our analysis, which is mostly empirical in nature, sets the foundations for testing and developing theories that can rely on the analytical framework developed by migration scholars , and the richness of appropriately processed bibliometric data.
Edit intent: fluency
Original:  In this paper, we study a joint user and power scheduling problem in downlink NOMA over fading channels.
Revised:  In this paper, we study the joint user and power scheduling problem in downlink NOMA over fading channels.
Edit intent: fluency
Original:  In this paper, we study a joint user and power scheduling problem in downlink NOMA over fading channels.
Revised:  In this paper, we study a joint user and power scheduling for downlink NOMA over fading channels.
Edit intent: clarity
Original:  Specifically, we focus on a stochastic optimization problem to maximize the average weighted sum rate while ensuring given minimum average data rates of users.
Revised:  Specifically, we focus on a stochastic optimization problem to maximize the weighted average sum rate while ensuring given minimum average data rates of users.
Edit intent: fluency
Original:  To address this challenging problem, we first develop an opportunistic user and power scheduling algorithm (OUPS) based on the duality and stochastic optimization theory , which transforms our stochastic problem into a series of deterministic ones to maximize the instantaneous weighted sum rate for each time slot.
Revised:  To address this problem, we first develop an opportunistic user and power scheduling algorithm (OUPS) based on the duality and stochastic optimization theory , which transforms our stochastic problem into a series of deterministic ones to maximize the instantaneous weighted sum rate for each time slot.
Edit intent: clarity
Original:  To address this challenging problem, we first develop an opportunistic user and power scheduling algorithm (OUPS) based on the duality and stochastic optimization theory , which transforms our stochastic problem into a series of deterministic ones to maximize the instantaneous weighted sum rate for each time slot.
Revised:  To address this challenging problem, we first develop an opportunistic user and power scheduling algorithm (OUPS) based on the duality and stochastic optimization theory . By OUPS, the stochastic problem is transformed into a series of deterministic ones to maximize the instantaneous weighted sum rate for each time slot.
Edit intent: clarity
Original:  To address this challenging problem, we first develop an opportunistic user and power scheduling algorithm (OUPS) based on the duality and stochastic optimization theory , which transforms our stochastic problem into a series of deterministic ones to maximize the instantaneous weighted sum rate for each time slot.
Revised:  To address this challenging problem, we first develop an opportunistic user and power scheduling algorithm (OUPS) based on the duality and stochastic optimization theory , which transforms our stochastic problem into a series of deterministic ones for the instantaneous weighted sum rate for each time slot.
Edit intent: clarity
Original:  Through the numerical results, we demonstrate that USPA provides near-optimal performance despite very low computational complexity and OUPS ensures given minimum average data rates of users .
Revised:  Through the numerical results, we demonstrate that USPA provides near-optimal performance with very low computational complexity and OUPS ensures given minimum average data rates of users .
Edit intent: clarity
Original:  Through the numerical results, we demonstrate that USPA provides near-optimal performance despite very low computational complexity and OUPS ensures given minimum average data rates of users .
Revised:  Through the numerical results, we demonstrate that USPA provides near-optimal performance despite very low computational complexity , and OUPS well guarantees given minimum average data rates of users .
Edit intent: clarity
Original:  Through the numerical results, we demonstrate that USPA provides near-optimal performance despite very low computational complexity and OUPS ensures given minimum average data rates of users .
Revised:  Through the numerical results, we demonstrate that USPA provides near-optimal performance despite very low computational complexity and OUPS ensures given minimum average data rates .
Edit intent: clarity
Original: Network method of moments arXiv:1202.5101 is an important tool for nonparametric network inferences .
Revised: Network method of moments arXiv:1202.5101 is an important tool for nonparametric network inference .
Edit intent: fluency
Original:  These were demonstrated by comprehensive simulation studies.
Revised:  We demonstrate the clear advantage of our method by comprehensive simulation studies.
Edit intent: clarity
Original:  We proved , to our knowledge, for the first time that some network bootstraps enjoy higher-order accuracy , and provided theoretical guidance for tuning network sub-sampling.
Revised:  We prove , to our knowledge, for the first time that some network bootstraps enjoy higher-order accuracy , and provided theoretical guidance for tuning network sub-sampling.
Edit intent: fluency
Original:  We proved , to our knowledge, for the first time that some network bootstraps enjoy higher-order accuracy , and provided theoretical guidance for tuning network sub-sampling.
Revised:  We proved , to our knowledge, the first theoretical guarantee of higher-order accuracy , and provided theoretical guidance for tuning network sub-sampling.
Edit intent: clarity
Original:  We proved , to our knowledge, for the first time that some network bootstraps enjoy higher-order accuracy , and provided theoretical guidance for tuning network sub-sampling.
Revised:  We proved , to our knowledge, for the first time that some network bootstraps enjoy higher-order accuracy for some network bootstrap schemes, and moreover, the first theoretical guidance for tuning network sub-sampling.
Edit intent: clarity
Original:  We proved , to our knowledge, for the first time that some network bootstraps enjoy higher-order accuracy , and provided theoretical guidance for tuning network sub-sampling.
Revised:  We proved , to our knowledge, for the first time that some network bootstraps enjoy higher-order accuracy , and provided theoretical guidance for selecting the sub-sample size for network sub-sampling.
Edit intent: clarity
Original:  We also derived a one-sample test and Cornish-Fisher confidence interval for any given moment , both with analytical formulation and explicit errorrates .
Revised:  We also derive one-sample test and Cornish-Fisher confidence interval for any given moment , both with analytical formulation and explicit errorrates .
Edit intent: fluency
Original:  This also yields a lower bound on the quality of the Nearest Neighbor heuristic for the traveling salesperson problem on trees.
Edit intent: coherence
Original:  The best-known lower bound for these two graph classes is 2.
Revised:  The best known lower bound for these two graph classes is 2.
Edit intent: fluency
Original:  We show that with the right parameters, the (1 + (\lambda,\lambda)) GA \ollga optimizes any jump function with jump size 2 \le k \le n/ 16 in expected time O(n^{(k+1)/2} e^{O(k)} k^{-k/2}), which significantly and already for constant  k outperforms standard mutation-based algorithms with their \Theta(n^k) runtime and standard crossover-based algorithms with their O(n^{k-1}) runtime .
Revised:  We show that with the right parameters, the \ollga optimizes any jump function with jump size 2 \le k \le n/ 16 in expected time O(n^{(k+1)/2} e^{O(k)} k^{-k/2}), which significantly and already for constant k outperforms standard mutation-based algorithms with their \Theta(n^k) runtime and standard crossover-based algorithms with their O(n^{k-1}) runtime .
Edit intent: clarity
Original:  We show that with the right parameters, the (1 + (\lambda,\lambda)) GA \ollga optimizes any jump function with jump size 2 \le k \le n/ 16 in expected time O(n^{(k+1)/2} e^{O(k)} k^{-k/2}), which significantly and already for constant  k outperforms standard mutation-based algorithms with their \Theta(n^k) runtime and standard crossover-based algorithms with their O(n^{k-1}) runtime .
Revised:  We show that with the right parameters, the (1 + (\lambda,\lambda)) GA \ollga optimizes any jump function with jump size 2 \le k \le n/ 16 in expected time O(n^{(k+1)/2} e^{O(k)} k^{-k/2}), which significantly and already for constant ~ k outperforms standard mutation-based algorithms with their \Theta(n^k) runtime and standard crossover-based algorithms with their O(n^{k-1}) runtime .
Edit intent: fluency
Original:  For the isolated problem of leaving the local optimum of jump functions, we determine provably optimal parameters that lead to a runtime of is (n/k)^{k/2} e^{ O (k)}.
Revised:  For the isolated problem of leaving the local optimum of jump functions, we determine provably optimal parameters that lead to a runtime of (n/k)^{k/2} e^{ O (k)}.
Edit intent: clarity
Original:  We show that with the right parameters, the \ollga optimizes any jump function with jump size 2 \le k \le n/4 in expected time O(n^{(k+1)/2} e^{O(k)} k^{-k/2}), which significantly and already for constant~k outperforms standard mutation-based algorithms with their \Theta(n^k) runtime and standard crossover-based algorithms with their O (n^{k-1}) runtime guarantee.
Revised:  We show that with the right parameters, the \ollga optimizes any jump function with jump size 2 \le k \le n/4 in expected time O(n^{(k+1)/2} e^{O(k)} k^{-k/2}), which significantly and already for constant~k outperforms standard mutation-based algorithms with their \Theta(n^k) runtime and standard crossover-based algorithms with their (n^{k-1}) runtime guarantee.
Edit intent: clarity
Original: Automatic animation line art colorization is a challenging computer vision problem since line art is a highly sparse and abstracted information and there exists a strict requirement for the color and style consistency between frames.
Revised: Automatic animation line art colorization is a challenging computer vision problem , since the information of the line art is a highly sparse and abstracted information and there exists a strict requirement for the color and style consistency between frames.
Edit intent: clarity
Original: Automatic animation line art colorization is a challenging computer vision problem since line art is a highly sparse and abstracted information and there exists a strict requirement for the color and style consistency between frames.
Revised: Automatic animation line art colorization is a challenging computer vision problem since line art is highly sparse and abstracted information and there exists a strict requirement for the color and style consistency between frames.
Edit intent: fluency