wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our extensive experiments confirm that TPMiner always outperforms well-known existing algorithms, and in several cases the improvement with respect to a specific existing algorithm is significant.
Revised:  Our extensive experiments confirm that TPMiner always outperforms well-known existing algorithms, and in several cases the improvement with respect to existing algorithms is significant.
Edit intent: clarity
Original:  In one of the most natural generalizations of tolerance graphs with direct applications in the comparison of DNA sequences from different organisms, namely multitolerance graphs, two tolerances are allowed for each interval - one from the left and one from the right side.
Revised:  In one of the most natural generalizations of tolerance graphs with direct applications in the comparison of DNA sequences from different organisms, namely multitolerance graphs, two tolerances are allowed for each interval - one from the left and one from the right side.
Edit intent: fluency
Original:  In spite of this progress, the complexity status of some fundamental algorithmic problems on tolerance and multitolerance graphs, such as the dominating set problem, remained unresolved until now, three decades after the introduction of tolerance graphs.
Revised:  In spite of this progress, the complexity status of some fundamental algorithmic problems on tolerance and multitolerance graphs, such as the dominating set problem, remained unresolved until now, three decades after the introduction of tolerance graphs.
Edit intent: fluency
Original:  Moreover, the giant clusters of the metanetworks formed in genotype and phenotype spaces coincide up to 99%DIFDELCMD < \\%%% %DIF < .abstract
Revised:  %DIFDELCMD < \\%%% %DIF < .abstract
Edit intent: coherence
Original: A language is k-piecewise testable if it is a finite boolean combination of languages of the form \Sigma^* a_1 \Sigma^* \cdots \Sigma^* a_n \Sigma^* , where a_i\in\Sigma and 0\le n \le k.
Revised: A language is k-piecewise testable if it is a finite boolean combination of languages of the form \Sigma^* a_1 \Sigma^* \cdots \Sigma^* a_n \Sigma^* for a_i\in\Sigma and 0\le n \le k.
Edit intent: clarity
Original:  We investigate the problem, given a minimal DFA recognizing a piecewise testable language, what is the minimal k for which the language is k-piecewise testable?
Revised:  We study the following problem: Given a DFA recognizing a piecewise testable language, what is the minimal k for which the language is k-piecewise testable?
Edit intent: clarity
Original:  We provide a detailed complexity analysis for k%DIFDELCMD < \le %%% 2. Finally, we generalize a result valid for DFAs to NFAs and show that the upper bound  given by the depth of the minimal DFA can be exponentially far from the minimal k .
Revised:  We provide a detailed complexity analysis for k%DIFDELCMD < \le %%% 2. Finally, we generalize a result valid for DFAs to NFAs and show that the upper bound on k given by the depth of the minimal DFA can be exponentially far from the minimal k .
Edit intent: clarity
Original: Given a real-valued function f defined over a manifold M embedded in R^d, we are interested in recovering structural information about f from the sole information of its values on a finite sample P. Existing methods provide approximation to the persistence diagram of f when the noise is bounded in both the functional and geometric domains .
Revised: Given a real-valued function f defined over a manifold M embedded in R^d, we are interested in recovering structural information about f from the sole information of its values on a finite sample P. Existing methods provide approximation to the persistence diagram of f when geometric noise and functional noise are bounded .
Edit intent: clarity
Original:  We provide theoretical guarantees  on the quality of our approximation and some experimental results illustrating its behavior .
Revised:  We provide theoretical guarantees and experimental results on the quality of our approximation and some experimental results illustrating its behavior .
Edit intent: fluency
Original:  On the other hand, locality sensitive hashing has polynomial dependence in the dimension, sublinear query time with an exponent inversely proportional to the error factor \epsilon, and subquadratic space requirement.
Revised:  On the other hand, locality sensitive hashing has polynomial dependence in the dimension, sublinear query time , but subquadratic space requirement.
Edit intent: coherence
Original:  We generalize the Johnson-Lindenstrauss lemma to define "low-quality" mappings to a Euclidean space of significantly lower dimension, such that they satisfy a requirement weaker than approximately preserving all distances or even preserving the nearest neighbor.
Revised:  In this paper, we introduce a new definition of "low-quality" mappings to a Euclidean space of significantly lower dimension, such that they satisfy a requirement weaker than approximately preserving all distances or even preserving the nearest neighbor.
Edit intent: clarity
Original:  Our algorithm, given n points in dimension d, achieves spaceusage in O(dn), preprocessing time in O(dn\log n), and query time in O(d n^{\rho} \log n), where%DIFDELCMD < \rhois %%% proportional to 1- 1 / \ln \ln n , for fixed \epsilon\in (0, 1 ).
Revised:  Our algorithm, given n points in dimension d, achieves spaceusage in O(dn), preprocessing time in O(dn\log n), and query time in O(d n^{\rho} %DIFDELCMD < \rhois %%% proportional to 1- 1 / \ln \ln n , for fixed \epsilon\in (0, 1 ).
Edit intent: fluency
Original:  Our algorithm, given n points in dimension d, achieves spaceusage in O(dn), preprocessing time in O(dn\log n), and query time in O(d n^{\rho} \log n), where%DIFDELCMD < \rhois %%% proportional to 1- 1 / \ln \ln n , for fixed \epsilon\in (0, 1 ).
Revised:  Our algorithm, given n points in dimension d, achieves spaceusage in O(dn), preprocessing time in O(dn\log n), and query time in O(d n^{\rho} \log n), where%DIFDELCMD < \rhois %%% ), for \rho\approx 1- 1 / \ln \ln n , for fixed \epsilon\in (0, 1 ).
Edit intent: clarity
Original:  Our algorithm, given n points in dimension d, achieves spaceusage in O(dn), preprocessing time in O(dn\log n), and query time in O(d n^{\rho} \log n), where%DIFDELCMD < \rhois %%% proportional to 1- 1 / \ln \ln n , for fixed \epsilon\in (0, 1 ).
Revised:  Our algorithm, given n points in dimension d, achieves spaceusage in O(dn), preprocessing time in O(dn\log n), and query time in O(d n^{\rho} \log n), where%DIFDELCMD < \rhois %%% proportional to 1- 1 / , for fixed \epsilon\in (0, 1 ).
Edit intent: fluency
Original:   We implement our method  and present experimental results in  up to 500 dimensions and 10 ^5 points, which show that the practical performance is better than predicted by the theoretical analysis.
Revised:  We implement our method and present experimental results in up to 500 and 10 ^5 points, which show that the practical performance is better than predicted by the theoretical analysis.
Edit intent: clarity
Original:   We implement our method  and present experimental results in  up to 500 dimensions and 10 ^5 points, which show that the practical performance is better than predicted by the theoretical analysis.
Revised:  We implement our method and present experimental results in up to 500 dimensions and 10 ^5 points, which show that performance is better than predicted by the theoretical analysis.
Edit intent: clarity
Original:   We implement our method  and present experimental results in  up to 500 dimensions and 10 ^5 points, which show that the practical performance is better than predicted by the theoretical analysis.
Revised:  We implement our method and present experimental results in up to 500 dimensions and 10 ^5 points, which show that the practical performance is better than predicted by the analysis.
Edit intent: clarity
Original:  We investigate the relationship between these two natural measures of convexity of S . We show that every set S\subseteqR^2 with simply connected components satisfies b(S)\leq\alphac(S) for an absolute constant \alpha, provided b(S) is defined.
Revised:  We investigate the relationship between these two natural measures of convexity . We show that every set S\subseteqR^2 with simply connected components satisfies b(S)\leq\alphac(S) for an absolute constant \alpha, provided b(S) is defined.
Edit intent: clarity
Original:  This implies an affirmative answer to the conjecture of Cabello et al. asserting that this estimate holds for simple polygons.
Revised:  This implies an affirmative answer to the conjecture of Cabello et al. that this estimate holds for simple polygons.
Edit intent: clarity
Original:  We provide an almost matching lower bound by showing that there is a constant \gamma(d)>0 such that for every \varepsilon \in(0,1 there is a set S\subseteq\mathbb{R}^d of Lebesgue measure one satisfying \operatorname{c}(S)\leq\varepsilon and \operatorname{b}_d(S)\geq\gamma\frac{\varepsilon}{\log_2{1/\varepsilon}}\geq\gamma\frac{\operatorname{c}(S)}{\log_2{1/\operatorname{c}(S)}}.
Revised:  We provide an almost matching lower bound by showing that there is a constant \gamma(d)>0 such that for every \varepsilon \in(0,1) there is a set S\subseteq\mathbb{R}^d of Lebesgue measure one satisfying \operatorname{c}(S)\leq\varepsilon and \operatorname{b}_d(S)\geq\gamma\frac{\varepsilon}{\log_2{1/\varepsilon}}\geq\gamma\frac{\operatorname{c}(S)}{\log_2{1/\operatorname{c}(S)}}.
Edit intent: fluency
Original:  We provide an almost matching lower bound by showing that there is a constant \gamma(d)>0 such that for every \varepsilon \in(0,1 there is a set S\subseteq\mathbb{R}^d of Lebesgue measure one satisfying \operatorname{c}(S)\leq\varepsilon and \operatorname{b}_d(S)\geq\gamma\frac{\varepsilon}{\log_2{1/\varepsilon}}\geq\gamma\frac{\operatorname{c}(S)}{\log_2{1/\operatorname{c}(S)}}.
Revised:  We provide an almost matching lower bound by showing that there is a constant \gamma(d)>0 such that for every \varepsilon \in(0,1 there is a set S\subseteq\mathbb{R}^d of Lebesgue measure 1 satisfying \operatorname{c}(S)\leq\varepsilon and \operatorname{b}_d(S)\geq\gamma\frac{\varepsilon}{\log_2{1/\varepsilon}}\geq\gamma\frac{\operatorname{c}(S)}{\log_2{1/\operatorname{c}(S)}}.
Edit intent: clarity
Original:  This paper attempts to improve the scalability of tensor decompositions and provides two major contributions: A flexible and fast algorithm for the CP decomposition (FFCP) of tensors based on their Tucker compression;
Revised:  This paper attempts to improve the scalability of tensor decompositions and provides two contributions: A flexible and fast algorithm for the CP decomposition (FFCP) of tensors based on their Tucker compression;
Edit intent: clarity
Original:  We analyse a large dataset with more than six million get-tagged tweets posted in Australia, and  demonstrate that Twitter can be a reliable source for studying human mobility patterns.
Revised:  We analyse a Twitter dataset with more than six million get-tagged tweets posted in Australia, and demonstrate that Twitter can be a reliable source for studying human mobility patterns.
Edit intent: clarity
Original:  We analyse a large dataset with more than six million get-tagged tweets posted in Australia, and  demonstrate that Twitter can be a reliable source for studying human mobility patterns.
Revised:  We analyse a large dataset with more than six million get-tagged tweets posted in Australia, and we demonstrate that Twitter can be a reliable source for studying human mobility patterns.
Edit intent: fluency
Original:  We find that crucial information of human mobility, such as its multi-scale and multi-modal nature, returning tendency and regularity, as well as the heterogeneous moving scale among individuals , can be extracted from geo-tagged tweets using various statistical indicators.
Revised:  Our analysis shows that geotagged tweets can capture rich features of human mobility, such as its multi-scale and multi-modal nature, returning tendency and regularity, as well as the heterogeneous moving scale among individuals , can be extracted from geo-tagged tweets using various statistical indicators.
Edit intent: clarity
Original:  Our analysis of the spatial-temporal patterns for people with different moving scales shows that long-distance travellers have highly concentrated urban movements .
Revised:  Our analysis of the diversity of movement orbits among individuals and of movements within and between cities. We also find that short and long-distance travellers have highly concentrated urban movements .
Edit intent: clarity
Original:  We further showed active interactions among social sensors by constructing retweet networks during a baseball game.
Revised:  We further show active interactions among social sensors by constructing retweet networks during a baseball game.
Edit intent: fluency
Original:  More specifically, our  tweet analysis of Japanese professional baseball games in 2013 revealed that social sensors can immediately show reactions to positive and negative events through bursts of tweets, but that positive events are more likely to induce a subsequent burst of retweets.
Revised:  More specifically, our tweet analysis of Japanese professional baseball games in 2013 revealed that social sensors can immediately react to positive and negative events through bursts of tweets, but that positive events are more likely to induce a subsequent burst of retweets.
Edit intent: clarity
Original:  While previous studies have mainly focused on either bursts of tweets or retweets as a simple indicator of a real-world event, the temporal correlation between these two imply unique aspects to social sensors, offering new insights into human behavior in a highly connected world.
Revised:  While previous studies have mainly focused on bursts of tweets or retweets as a simple indicator of a real-world event, the temporal correlation between these two imply unique aspects to social sensors, offering new insights into human behavior in a highly connected world.
Edit intent: clarity
Original:  While previous studies have mainly focused on either bursts of tweets or retweets as a simple indicator of a real-world event, the temporal correlation between these two imply unique aspects to social sensors, offering new insights into human behavior in a highly connected world.
Revised:  While previous studies have mainly focused on either bursts of tweets as a simple indicator of a real-world event, the temporal correlation between these two imply unique aspects to social sensors, offering new insights into human behavior in a highly connected world.
Edit intent: clarity
Original:  While previous studies have mainly focused on either bursts of tweets or retweets as a simple indicator of a real-world event, the temporal correlation between these two imply unique aspects to social sensors, offering new insights into human behavior in a highly connected world.
Revised:  While previous studies have mainly focused on either bursts of tweets or retweets as a simple indicator of a real-world event, the temporal correlation between tweets and retweets implies unique aspects of social sensors, offering new insights into human behavior in a highly connected world.
Edit intent: clarity
Original:  %DIFDELCMD < + 1{2}||\X-\B||_{F}^{2}, equation*%%% equation* {Prox}_{g}^{{\sigma}}(B)=\arg\minXi=1^{m}g(i(X)) + 1{2}||X-B||_{F}^{2}, \end{equation*} associated with a nonconvex function g defined on the singular values of %DIFDELCMD < \X%%%  . We prove that GSVT can be obtained by performing the proximal operator of g (denoted as %DIFDELCMD < \Prox%%%  _g(\cdot)) on the singular values since %DIFDELCMD < \Prox%%%  _g(\cdot) is monotone when g is lower bounded.
Revised:  %DIFDELCMD < + 1{2}||\X-\B||_{F}^{2}, equation*%%% equation* {Prox}_{g}^{{\sigma}}(B)=\arg\minXi=1^{m}g(i(X)) + 1{2}||X-B||_{F}^{2}, \end{equation*} associated with a nonconvex function g defined on the singular values of %DIFDELCMD < \X%%% X . We prove that GSVT can be obtained by performing the proximal operator of g (denoted as %DIFDELCMD < \Prox%%% _g(\cdot)) on the singular values since %DIFDELCMD < \Prox%%% _g(\cdot) is monotone when g is lower bounded.
Edit intent: clarity
Original:  Finally, we prove that the transition semigroup of a minimal deterministic automaton accepting such a witness language is unique for each n %DIFDELCMD < \ge %%% 7.
Revised:  Finally, we prove that the transition semigroup of a minimal deterministic automaton accepting a witness language is unique for each n %DIFDELCMD < \ge %%% 7.
Edit intent: clarity
Original: Multi-versioned database systems have the potential to significantly increase the amount of concurrency in transaction processing systems because they can avoid read-write conflicts.
Revised: Multi-versioned database systems have the potential to significantly increase the amount of concurrency in transaction processing because they can avoid read-write conflicts.
Edit intent: fluency
Original:  Unfortunately, these increases in concurrency usually come at the cost of transaction serializability.
Revised:  Unfortunately, the increase in concurrency usually come at the cost of transaction serializability.
Edit intent: coherence
Original:  Unfortunately, these increases in concurrency usually come at the cost of transaction serializability.
Revised:  Unfortunately, these increases in concurrency usually comes at the cost of transaction serializability.
Edit intent: fluency
Original:  If a database user requests full serializability, modern multi-versioned systems significantly constrain their read-write concurrency  .
Revised:  If a database user requests full serializability, modern multi-versioned systems significantly constrain read-write concurrency .
Edit intent: clarity
Original:  In main-memory , multi-core settings  these additional constraints are so significant, that multi-versioned systems are often  outperformed by single-version systems.
Revised:  In main-memory multi-core settings these additional constraints are so significant, that multi-versioned systems are often outperformed by single-version systems.
Edit intent: fluency
Original:  In main-memory , multi-core settings  these additional constraints are so significant, that multi-versioned systems are often  outperformed by single-version systems.
Revised:  In main-memory , multi-core settings , these additional constraints are so significant, that multi-versioned systems are often outperformed by single-version systems.
Edit intent: fluency
Original:  In main-memory , multi-core settings  these additional constraints are so significant, that multi-versioned systems are often  outperformed by single-version systems.
Revised:  In main-memory , multi-core settings these additional constraints are so burdensome that multi-versioned systems are often outperformed by single-version systems.
Edit intent: clarity
Original: Online social networks (OSNs) are increasingly used to help users make trust and access control decisions , e.g., based on the existence and the strength of social relationships.
Revised: Social relationships are a natural basis on which humans make trust decisions. Online Social Networks (OSNs) are increasingly used to help users make trust and access control decisions , e.g., based on the existence and the strength of social relationships.
Edit intent: coherence
Original: Online social networks (OSNs) are increasingly used to help users make trust and access control decisions , e.g., based on the existence and the strength of social relationships.
Revised: Online social networks (OSNs) are increasingly often used to let users base trust decisions on the existence and the strength of social relationships.
Edit intent: clarity
Original:  Discovering the length of the social path between two usersis often supported by popular social networks, however, in a centralized way .
Revised:  Discovering the length of the social path to other users, they do so in a centralized way .
Edit intent: clarity
Original:  This requires users to always rely on the provider and, worse yet, to reveal their interest in each other.
Revised:  This requires users to always rely on the service provider and reveal their interest in each other.
Edit intent: clarity
Original:  In this paper , we introduce Social Pal, the first system supporting the ubiquitous privacy-preserving discovery of the social path length between any two social network users.
Revised:  This paper presents Social PaL, a system supporting the ubiquitous privacy-preserving discovery of the social path length between any two social network users.
Edit intent: clarity
Original:  In this paper , we introduce Social Pal, the first system supporting the ubiquitous privacy-preserving discovery of the social path length between any two social network users.
Revised:  In this paper , we introduce Social Pal, the first system supporting the privacy-preserving discovery of the social path length between any two social network users.
Edit intent: clarity
Original:  In this paper , we introduce Social Pal, the first system supporting the ubiquitous privacy-preserving discovery of the social path length between any two social network users.
Revised:  In this paper , we introduce Social Pal, the first system supporting the ubiquitous privacy-preserving discovery of arbitrary-length social paths between any two social network users.
Edit intent: clarity
Original:  We prove that Social Pal allows users to find all paths of length two and demonstrate, via extensive simulation, that it discovers a significant fraction of longer paths, even with a small percentage of users in the system, e.g.  70\% of all paths with only 40\% of the users.
Revised:  We prove that Social Pal allows users to find all paths of length two and to discover a significant fraction of longer paths, even with a small percentage of users in the system, e.g. 70\% of all paths with only 40\% of the users.
Edit intent: clarity
Original:  We prove that Social Pal allows users to find all paths of length two and demonstrate, via extensive simulation, that it discovers a significant fraction of longer paths, even with a small percentage of users in the system, e.g.  70\% of all paths with only 40\% of the users.
Revised:  We prove that Social Pal allows users to find all paths of length two and demonstrate, via extensive simulation, that it discovers a significant fraction of longer paths, even with a small percentage of users in the system, e.g. , discovering 70\% of all paths with only 40\% of the users.
Edit intent: coherence
Original:  Then, we implement Social Pal by means of a scalable server-side architecture and a modular Android client library, and design two mobile apps on top of it that allow nearby users to interact and share their Internet connection based on their social relationship .
Revised:  We implement Social PaL using a scalable server-side architecture and a modular Android client library, and design two mobile apps on top of it that allow nearby users to interact and share their Internet connection based on their social relationship .
Edit intent: clarity
Original:  Then, we implement Social Pal by means of a scalable server-side architecture and a modular Android client library, and design two mobile apps on top of it that allow nearby users to interact and share their Internet connection based on their social relationship .
Revised:  Then, we implement Social Pal by means of a scalable server-side architecture and a modular Android client library, allowing developers to seamlessly integrate it into their apps .
Edit intent: clarity
Original: Minkowski sums are of theoretical interest and have applications in fields related to industrial back-grounds .
Revised: Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds .
Edit intent: fluency
Original:  The algorithm we developped can be implemented and parallelized in a very easy way.
Revised:  The algorithm we developed can be implemented and parallelized in a very easy way.
Edit intent: fluency