wanyu/IteraTeR_v2 huggingface dataset:
Original:  ] . We also investigate hitting distributions for disjointness predicate on k-element subsets of \{1, 2, \ldots, n\ Thickness Lemma, a combinatorial statement from the proof of Simulation Theorems of G\"{o\"{o}s et al and Chattopadhyaay et al. , and show that this Lemma can not be improved}  .
Revised:  ] . We also investigate hitting distributions for disjointness predicate on k-element subsets of \{1, 2, \ldots, n\ Thickness Lemma, \"{o}s et al and Chattopadhyaay et al. , and show that this Lemma can not be improved} .
Edit intent: coherence
Original: Recently, Chattopadhyay et al. chattopadhyay 2017 simulation proved that any gadget having so called hitting distributions admits deterministic "query-to-communication" simulation theorem.
Revised: Recently, Chattopadhyay et al. chattopadhyay 2017 simulation proved that any gadget having so called hitting distributions admits deterministic "query-to-communication" simulation theorem.
Edit intent: fluency
Original:  More specifically, when this gadget has k bits on input, it admits a simulation theorem for all outer function of arity roughly 2^{k/2} or less (the same was also known for k-bit Inner Product, chattopadhyay 2017 simulation ).
Revised:  More specifically, when this gadget has k bits on input, it admits a simulation theorem for all outer function of arity roughly 2^{k/2} or less (the same was also known for k-bit Inner Product, ).
Edit intent: clarity
Original: Given a web-scale graph that grows over time, how should its edges be stored and processed on multiple machines for rapid and accurate estimation of the count of triangles ?
Revised: Given a graph stream, how can we estimate the number of triangles in it using multiple machines with limited storage? Specifically, how should edges be processed and sampled across the machines for rapid and accurate estimation of the count of triangles ?
Edit intent: clarity
Original: Given a web-scale graph that grows over time, how should its edges be stored and processed on multiple machines for rapid and accurate estimation of the count of triangles ?
Revised: Given a web-scale graph that grows over time, how should its edges be stored and processed on multiple machines for rapid and accurate estimation ?
Edit intent: clarity
Original:  The count of triangles (i.e., cliques of size three) has proven useful in many applications, including anomaly detection, community detection, and link recommendation.
Revised:  The count of triangles (i.e., cliques of size three) has proven useful in numerous applications, including anomaly detection, community detection, and link recommendation.
Edit intent: clarity
Original:  To achieve the advantages of both approaches , we propose DiSLR, a distributed streaming algorithm that estimates the counts of global triangles  and local triangles associated with each node.
Revised:  To achieve the advantages of both approaches , we propose DiSLR, a distributed streaming algorithm for estimating the counts of global triangles and local triangles associated with each node.
Edit intent: clarity
Original:  To achieve the advantages of both approaches , we propose DiSLR, a distributed streaming algorithm that estimates the counts of global triangles  and local triangles associated with each node.
Revised:  To achieve the advantages of both approaches , we propose DiSLR, a distributed streaming algorithm that estimates the counts of global triangles and local triangles incident to each node.
Edit intent: clarity
Original:  Compared to its best competitors, DiSLR is (a) Accurate: giving up to 39X smaller estimation error, (b) Fast: up to 10.4X faster, scaling linearly with the number of edges in the input stream, and (c) Theoretically sound: yielding unbiased estimates with variances decreasing faster as the number of machines is scaled up.
Revised:  Compared to its best competitors, DiSLR is (a) Accurate: giving up to 39X smaller estimation error, (b) Fast: up to 10.4X faster, scaling linearly with the size of the input stream, and (c) Theoretically sound: yielding unbiased estimates with variances decreasing faster as the number of machines is scaled up.
Edit intent: clarity
Original:  Compared to its best competitors, DiSLR is (a) Accurate: giving up to 39X smaller estimation error, (b) Fast: up to 10.4X faster, scaling linearly with the number of edges in the input stream, and (c) Theoretically sound: yielding unbiased estimates with variances decreasing faster as the number of machines is scaled up.
Revised:  Compared to its best competitors, DiSLR is (a) Accurate: giving up to 39X smaller estimation error, (b) Fast: up to 10.4X faster, scaling linearly with the number of edges in the input stream, and (c) Theoretically sound: yielding unbiased estimates with variances dropping faster as the number of machines is scaled up.
Edit intent: fluency
Original: The method of moments has been proposed as a potential means to reduce the dimensionality of the chemical master equation (CME) appearing in stochastic chemical kinetics .
Revised: Applying the method of moments has been proposed as a potential means to reduce the dimensionality of the chemical master equation (CME) appearing in stochastic chemical kinetics .
Edit intent: clarity
Original: The method of moments has been proposed as a potential means to reduce the dimensionality of the chemical master equation (CME) appearing in stochastic chemical kinetics .
Revised: The method of moments to the chemical master equation (CME) appearing in stochastic chemical kinetics .
Edit intent: clarity
Original:  Recently, a method was proposed for calculating rigorous bounds on quantities of interest for stochastic chemical kinetic systems at steady state.
Revised:  Recently, a method was proposed for calculating rigorous bounds on various descriptions of the stochastic chemical kinetic systems at steady state.
Edit intent: clarity
Original:  In particular, the method used semidefinite programming to calculate bounds on mean molecular counts, variances in these counts, and probability histograms .
Revised:  In particular, the method used semidefinite programming to calculate bounds on mean molecular counts, variances in these counts, and so on .
Edit intent: clarity
Original:  In this paper, we extend that idea to the associated dynamic problem-- calculating rigorous time-varying bounds on means and variances .
Revised:  In this paper, we show that these ideas can be extended to the corresponding dynamic problem, calculating time-varying bounds on means and variances .
Edit intent: clarity
Original:  In this paper, we extend that idea to the associated dynamic problem-- calculating rigorous time-varying bounds on means and variances .
Revised:  In this paper, we extend that idea to the associated dynamic problem-- calculating rigorous time-varying bounds on the same descriptions .
Edit intent: clarity
Original: Large-scale networks are widely used to represent object relationships in many real world applications.
Revised: Large-scale graphs are widely used to represent object relationships in many real world applications.
Edit intent: clarity
Original:  In this paper , we introduce a novel perspective regarding the network summarization problem based on concepts from spectral graph theory.
Revised:  In this work , we introduce a novel perspective regarding the network summarization problem based on concepts from spectral graph theory.
Edit intent: clarity
Original:  In this paper , we introduce a novel perspective regarding the network summarization problem based on concepts from spectral graph theory.
Revised:  In this paper , we introduce a new perspective regarding the network summarization problem based on concepts from spectral graph theory.
Edit intent: clarity
Original:  We show that our proposed algorithms consistently perform better results in terms of the spectral measurements and running time compared to previous network summarization algorithms .
Revised:  We show that our proposed algorithms consistently achieve better results compared to previous network summarization algorithms .
Edit intent: clarity
Original:  Among others, methods based on statistical inference are of particular interest: such algorithms are mathematically sound and were shown to provide partitions of  good quality.
Revised:  Among others, methods based on statistical inference are of particular interest: such algorithms are mathematically sound and were shown to provide partitions of a good quality.
Edit intent: fluency
Original:  The choice of this underlying model (a.k.a. null model) is very important for such methods and this choice is the  focus of the current study.
Revised:  The choice of a suitable underlying model (a.k.a. null model) is very important for such methods and this choice is the focus of the current study.
Edit intent: clarity
Original:  The choice of this underlying model (a.k.a. null model) is very important for such methods and this choice is the  focus of the current study.
Revised:  The choice of this underlying model (a.k.a. null model) is very important for such methods and this choice is the main focus of the current study.
Edit intent: clarity
Original:  recently proposed degree-corrected modification of this model, and a new one-parametric null model which has some desirable statistical properties.
Revised:  recently proposed degree-corrected modification of this model, and new one-parametric null model which has some desirable statistical properties.
Edit intent: fluency
Original: Community detection has recently became one of the most important problems in network analysis and many algorithms have been proposed to solve this problem.
Revised: Community detection is one of the most important problems in network analysis and many algorithms have been proposed to solve this problem.
Edit intent: clarity
Original:  Among others , methods based on statistical inference are of particular interest: such algorithms are mathematically sound and were shown to provide partitions of a good quality.
Revised:  Among others , methods based on statistical inference are of particular interest: they are mathematically sound and were shown to provide partitions of a good quality.
Edit intent: clarity
Original:  Among others , methods based on statistical inference are of particular interest: such algorithms are mathematically sound and were shown to provide partitions of a good quality.
Revised:  Among others , methods based on statistical inference are of particular interest: such algorithms are mathematically sound and were shown to provide partitions of good quality.
Edit intent: fluency
Original:  The main ingredient of statistical inference methods is to assume some underlying random graph model and then fit this model to the observed graph by maximizing the likelihood.
Revised:  Statistical inference methods are based on fitting some random graph model and then fit this model to the observed graph by maximizing the likelihood.
Edit intent: clarity
Original:  The main ingredient of statistical inference methods is to assume some underlying random graph model and then fit this model to the observed graph by maximizing the likelihood.
Revised:  The main ingredient of statistical inference methods is to assume some underlying random graph model and then fit this model to the observed network by maximizing the likelihood.
Edit intent: clarity
Original:  The choice of a suitable underlying model (a.k.a. null model) is very important for such methods and this choice is  the main focus of the current study.
Revised:  The choice of this model is the main focus of the current study.
Edit intent: clarity
Original:  recently proposed degree-corrected modification of this model, and new one-parametric null model which has some desirable statistical properties.
Revised:  recently proposed degree-corrected modification of this model, and a new null model having some desirable statistical properties.
Edit intent: clarity
Original:  We also develop and compare two likelihood optimization algorithms suitable for the null models under consideration.
Revised:  We also develop and compare two likelihood optimization algorithms suitable for the models under consideration.
Edit intent: clarity
Original:  An extensive empirical analysis on a variety of datasets shows, in particular, that the new model is the best one for describing most of the considered real-world complex networks according to the likelihood of the observed graph structures.
Revised:  An extensive empirical analysis on a variety of datasets shows, in particular, that the new model is the best one for describing most of the considered real-world complex networks according to the likelihood of observed graph structures.
Edit intent: fluency
Original:  To illustrate potential applications of our method , we show how the reconstructed couplings can be used to investigate the chromosome organizationby Brownian Dynamics .
Revised:  To illustrate potential applications of our method , we show how the reconstructed couplings can be used to study chromatin organization, and possibly give some clue about its dynamics .
Edit intent: clarity
Original: In the context of Fifth Generation (5G) mobile networks, the concept of " slice as a service " ( SaaS ) promotes mobile network operators to flexibly share infrastructures with mobile service providers and stakeholders.
Revised: In the context of Fifth Generation (5G) mobile networks, the concept of " Slice as a Service " ( SaaS ) promotes mobile network operators to flexibly share infrastructures with mobile service providers and stakeholders.
Edit intent: fluency
Original: In the context of Fifth Generation (5G) mobile networks, the concept of " slice as a service " ( SaaS ) promotes mobile network operators to flexibly share infrastructures with mobile service providers and stakeholders.
Revised: In the context of Fifth Generation (5G) mobile networks, the concept of " slice as a service " ( SlaaS ) promotes mobile network operators to flexibly share infrastructures with mobile service providers and stakeholders.
Edit intent: fluency
Original:  We propose a novel performance tournament graph with papers as nodes, where edges encode noisy performance comparison information extracted from  papers.
Revised:  We propose a novel performance improvement graph with papers as nodes, where edges encode noisy performance comparison information extracted from papers.
Edit intent: clarity
Original:  These extractions resemble (noisy) outcomes of matches in an incomplete tournament.
Revised:  These extractions resemble (noisy) outcomes of 'matches' in an incomplete tournament.
Edit intent: fluency
Original:  The IM-GMS problem is to find the best strategy mix x^* that maximize the influence spread due to influence propagation from the activated seeds, subject to the budget constraint that j\in [d] x_j%DIFDELCMD < \le %%% k . We adapt the scalable reverse influence sampling (RIS) approach and design a scalable algorithm that provides a (1-1/e -\varepsilon) approximate solution (for any \varepsilon > 0), with running time near-linear in the network size.
Revised:  %DIFDELCMD < \le %%% k . We adapt the scalable reverse influence sampling (RIS) approach and design a scalable algorithm that provides a (1-1/e -\varepsilon) approximate solution (for any \varepsilon > 0), with running time near-linear in the network size.
Edit intent: coherence
Original:  The IM-GMS problem is to find the best strategy mix x^* that maximize the influence spread due to influence propagation from the activated seeds, subject to the budget constraint that j\in [d] x_j%DIFDELCMD < \le %%% k . We adapt the scalable reverse influence sampling (RIS) approach and design a scalable algorithm that provides a (1-1/e -\varepsilon) approximate solution (for any \varepsilon > 0), with running time near-linear in the network size.
Revised:  The IM-GMS problem is to find the best strategy mix x^* that maximize the influence spread due to influence propagation from the activated seeds, subject to the budget constraint that j\in [d] x_j%DIFDELCMD < \le %%% We adapt the scalable reverse influence sampling (RIS) approach and design a scalable algorithm that provides a (1-1/e -\varepsilon) approximate solution (for any \varepsilon > 0), with running time near-linear in the network size.
Edit intent: clarity
Original:  The IM-GMS problem is to find the best strategy mix x^* that maximize the influence spread due to influence propagation from the activated seeds, subject to the budget constraint that j\in [d] x_j%DIFDELCMD < \le %%% k . We adapt the scalable reverse influence sampling (RIS) approach and design a scalable algorithm that provides a (1-1/e -\varepsilon) approximate solution (for any \varepsilon > 0), with running time near-linear in the network size.
Revised:  The IM-GMS problem is to find the best strategy mix x^* that maximize the influence spread due to influence propagation from the activated seeds, subject to the budget constraint that j\in [d] x_j%DIFDELCMD < \le %%% k . We adapt the reverse influence sampling (RIS) approach and design a scalable algorithm that provides a (1-1/e -\varepsilon) approximate solution (for any \varepsilon > 0), with running time near-linear in the network size.
Edit intent: fluency
Original:  We further extend IM-GMS to allow partitioned budget constraint, and show that our scalable algorithm provides a ( 1/ 2-\varepsilon) solution in this case.
Revised:  We further extend IM-GMS to allow partitioned budget constraint, and show that a minor variation of our algorithms would achieve 1/ 2-\varepsilon) solution in this case.
Edit intent: clarity
Original: For the last two decades , matrix factorization has  become one of the fundamental methods for tackling recommendation problems.
Revised: In the past decade , matrix factorization has become one of the fundamental methods for tackling recommendation problems.
Edit intent: clarity
Original:  In this work , we propose modelling user-item interaction patterns in an alternative way by considering positions and distances of users and items{\em  .
Revised:  To overcome this problem , we propose modelling user-item interaction patterns in an alternative way by considering positions and distances of users and items{\em .
Edit intent: clarity
Original:  We assume that users and items can be positioned in a low dimensional space and their explicit closeness can be measured using Euclidean distance metric.
Revised:  We assume that users and items can be placed in a low dimensional space and their explicit closeness can be measured using Euclidean distance metric.
Edit intent: clarity
Original:  Comprehensive experiments on multiple real-world datasets demonstrate superior performances of our model over state-of-the-art competing methods including conventional matrix factorization based approaches and recent metric learning based approaches .
Revised:  Comprehensive experiments on multiple real-world datasets show that our approach outperforms existing state-of-the-art competing methods including conventional matrix factorization based approaches and recent metric learning based approaches .
Edit intent: clarity
Original: Network slicing is the key to providing flexible, scalable and on-demand solutions for the vast array of applications in 5G networks.
Revised: 5G network slicing is essential to providing flexible, scalable and on-demand solutions for the vast array of applications in 5G networks.
Edit intent: clarity
Original:  In this paper , we address the question of optimal allocation of a slice in 5G core networks  .
Revised:  In this letter , we address the question of optimal allocation of a slice in 5G core networks .
Edit intent: clarity
Original:  We adopt and extend the work by D. Dietrich et al.
Revised:  We adopt and extend the work by D. Dietrich 
Edit intent: clarity
Original:  In this letter , we address the question of optimal allocation of a slice in 5G core networks by addressing these two challenges.
Revised:  In this paper , we address the question of optimal allocation of a slice in 5G core networks by addressing these two challenges.
Edit intent: clarity
Original:  In this paper, we address the question of optimal allocation of a slice in 5G core networks by addressing these two challenges.
Revised:  In this paper, we address the question of optimal allocation of a slice in 5G core networks by tackling these two challenges.
Edit intent: fluency
Original: Luks'  algorithm (JCSS 1982) to test isomorphism of bounded degree graphs in polynomial time is one of  most important results in the context of the Graph Isomorphism Problem and has been repeatedly used as a basic building block for many other algorithms.
Revised: Luks' s algorithm (JCSS 1982) to test isomorphism of bounded degree graphs in polynomial time is one of most important results in the context of the Graph Isomorphism Problem and has been repeatedly used as a basic building block for many other algorithms.
Edit intent: fluency
Original: Luks'  algorithm (JCSS 1982) to test isomorphism of bounded degree graphs in polynomial time is one of  most important results in the context of the Graph Isomorphism Problem and has been repeatedly used as a basic building block for many other algorithms.
Revised: Luks' algorithm (JCSS 1982) to test isomorphism of bounded degree graphs in polynomial time is one of the most important results in the context of the Graph Isomorphism Problem and has been repeatedly used as a basic building block for many other algorithms.
Edit intent: fluency
Original:  In this work, we obtain such an improvement: we give an algorithm that solves the Graph Isomorphism Problem in time n^{ \mathcal{O ((\log d)^{c})}, where n is the number of vertices of the input graphs, d is the maximum degree of the input graphs, and c is an absolute constant.
Revised:  In this work, we obtain such an improvement: we give an algorithm that solves the Graph Isomorphism Problem in time n^{ O ((\log d)^{c})}, where n is the number of vertices of the input graphs, d is the maximum degree of the input graphs, and c is an absolute constant.
Edit intent: coherence
Original:  The best previous isomorphism test for graphs of maximum degree d due to Babai, Kantor and Luks (FOCS 1983) runs in time n^{ \mathcal{O (d/ \log d)} . Our result generalizes the quasipolynomial-time algorithm for the general isomorphism problem due to Babai .
Revised:  The best previous isomorphism test for graphs of maximum degree d due to Babai, Kantor and Luks (FOCS 1983) runs in time n^{ O (d/ \log d)} . Our result generalizes the quasipolynomial-time algorithm for the general isomorphism problem due to Babai .
Edit intent: coherence
Original:  The best previous isomorphism test for graphs of maximum degree d due to Babai, Kantor and Luks (FOCS 1983) runs in time n^{ \mathcal{O (d/ \log d)} . Our result generalizes the quasipolynomial-time algorithm for the general isomorphism problem due to Babai .
Revised:  The best previous isomorphism test for graphs of maximum degree d due to Babai, Kantor and Luks (FOCS 1983) runs in time n^{ \mathcal{O (d/ \log d)} .
Edit intent: coherence
Original:  Due to the lack of a closed-form expression for this probability when the distribution of birthdays is not uniform, the resulting computation is not feasible in some applications;
Revised:  Due to the lack of a closed-form expression for this probability when the distribution of birthdays is not uniform, the resulting expression is not simple to analyze; in
Edit intent: clarity
Original:  the information-theoretic formulation, however, can be analyzed for all distributions.
Revised:  the information-theoretic formulation, however, the asymptotic behavior of this probability can be characterized exactly for all distributions.
Edit intent: clarity