wanyu/IteraTeR_v2 huggingface dataset:
Original:  The proposed framework does not assume uncorrelated observation or prior errors and can in principle be applied without expert knowledge about the model and the observations.
Revised:  The proposed framework does not assume uncorrelated observations or prior errors and can in principle be applied without expert knowledge about the model and the observations.
Edit intent: fluency
Original: Empirical risk minimization is the principal tool for prediction problems, but its extension to relational data remains unsolved.
Revised: Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved.
Edit intent: clarity
Original:  We solve this problem using recent advances in graph sampling theory .
Revised:  We solve this problem using recent ideas from graph sampling theory .
Edit intent: clarity
Original:  We (i) define an empirical risk for relational data and (ii) obtain stochastic gradients for this  risk that are automatically unbiased.
Revised:  We (i) define an empirical risk for relational data and (ii) obtain stochastic gradients for this empirical risk that are automatically unbiased.
Edit intent: fluency
Original:  The key ingredient is to consider the method by which data is sampled from a graph as an explicit component of model design.
Revised:  This is achieved by considering the method by which data is sampled from a graph as an explicit component of model design.
Edit intent: clarity
Original:  Theoretical results establish that the choice of sampling scheme is critical.
Edit intent: coherence
Original:  By integrating fast implementations of graph sampling schemes with standard automatic differentiation tools, we are able to solve the risk minimization in a plug-and-play fashion even on large datasets.
Revised:  By integrating fast implementations of graph sampling schemes with standard automatic differentiation tools, we provide an efficient turnkey solver for the risk minimization in a plug-and-play fashion even on large datasets.
Edit intent: clarity
Original:  A successfully regularized model strikes a balance between a perfect description of the training data and the ability to generalize to unseen data.
Edit intent: clarity
Original:  We incorporate the new measurement as a topological loss in training classifiers.
Revised:  We incorporate the new measurement as a topological penalty in training classifiers.
Edit intent: clarity
Original:  We also propose an efficient algorithm to compute the gradient  .
Revised:  We also pro- pose an efficient algorithm to compute the gradient .
Edit intent: fluency
Original:  Our method provides a novel way to topologically simplify the global structure of the model, without having to sacrifice too much of the flexibility of the model.
Revised:  Our method pro- vides a novel way to topologically simplify the global structure of the model, without having to sacrifice too much of the flexibility of the model.
Edit intent: clarity
Original:  This paper proposes an adaptation to  LRU strategy, called gLRU, where the file is sub-divided into equal-sized chunks.
Revised:  This paper proposes an adaptation to the LRU strategy, called gLRU, where the file is sub-divided into equal-sized chunks.
Edit intent: fluency
Original:  Further, gLRU outperforms  LRU strategy for  Zipf file popularity distribution and censored Pareto file size distribution for the file download times.
Revised:  Further, gLRU outperforms the LRU strategy for Zipf file popularity distribution and censored Pareto file size distribution for the file download times.
Edit intent: fluency
Original:  Further, gLRU outperforms  LRU strategy for  Zipf file popularity distribution and censored Pareto file size distribution for the file download times.
Revised:  Further, gLRU outperforms LRU strategy for a Zipf file popularity distribution and censored Pareto file size distribution for the file download times.
Edit intent: fluency
Original:  Video streaming applications can further use the partial cache contents to help the stall durations significantly, and the numerical results indicate significant improvements ( 29 \\%DIF < ) in stall durations using the gLRU strategy as compared to the LRU strategy %DIF > ) in stall duration using the gLRU strategy as compared to  .
Revised:  Video streaming applications can further use the partial cache contents to help the stall duration significantly, and the numerical results indicate significant improvements ( 29 \\%DIF < ) in stall durations using the gLRU strategy as compared to the LRU strategy %DIF > ) in stall duration using the gLRU strategy as compared to .
Edit intent: fluency
Original:  Video streaming applications can further use the partial cache contents to help the stall durations significantly, and the numerical results indicate significant improvements ( 29 \\%DIF < ) in stall durations using the gLRU strategy as compared to the LRU strategy %DIF > ) in stall duration using the gLRU strategy as compared to  .
Revised:  Video streaming applications can further use the partial cache contents to help the stall durations significantly, and the numerical results indicate significant improvements ( 29 \\%DIF < ) in stall durations using the gLRU strategy as compared to the LRU %DIF > ) in stall duration using the gLRU strategy as compared to .
Edit intent: fluency
Original: In semidefinite programming (SDP), some of the most commonly used pre-processing techniques for exploiting sparsity result in non-trivial numerical issues.
Revised: In semidefinite programming (SDP), a number of pre-processing techniques for exploiting sparsity result in non-trivial numerical issues.
Edit intent: clarity
Original:  In computational experiments on SDP instances from the SDPLib, a benchmark, and structured instances from polynomial and binary quadratic optimisation, we show that combining the two-step pre-processing with a standard interior-point method outperforms the interior point method, with or without the traditional pre-processing , by a considerable margin .
Revised:  In computational experiments on SDP instances from the SDPLib, a benchmark, and structured instances from polynomial and binary quadratic optimisation, we show that such two-step pre-processing with a standard interior-point method outperforms the interior point method, with or without the traditional pre-processing , by a considerable margin .
Edit intent: clarity
Original:  In computational experiments on SDP instances from the SDPLib, a benchmark, and structured instances from polynomial and binary quadratic optimisation, we show that combining the two-step pre-processing with a standard interior-point method outperforms the interior point method, with or without the traditional pre-processing , by a considerable margin .
Revised:  In computational experiments on SDP instances from the SDPLib, a benchmark, and structured instances from polynomial and binary quadratic optimisation, we show that combining the two-step pre-processing with a standard interior-point method outperforms the interior point method, with or without the traditional pre-processing .
Edit intent: clarity
Original:  In this work  a novel approach for detecting port and net scan using Big Data Analytics frameworks is presented.
Revised:  In this work , a novel approach for detecting port and net scan using Big Data Analytics frameworks is presented.
Edit intent: fluency
Original:  In this work  a novel approach for detecting port and net scan using Big Data Analytics frameworks is presented.
Revised:  In this work a novel approach for detecting port and net scan using Big Data Analytics framework is presented.
Edit intent: fluency
Original:  The paper firstly describes the approach and the algorithm proposed and then presents an experimental analysis of its performance, containing also a comparison with Mawilab gold standard .
Revised:  The paper we describe the approach and the algorithm proposed and then presents an experimental analysis of its performance, containing also a comparison with Mawilab gold standard .
Edit intent: clarity
Original:  Results show that the algorithm is highly accurate in terms of Precision and Recall for port and net scan detection.
Revised:  Results show that the algorithm is highly efficient in terms of Precision and Recall for port and net scan detection.
Edit intent: clarity
Original:  Anomalies not detected by the gold standard are also detected by our approach . Moreover, the execution time of the algorithm on Apache Spark is very short, even on large traffic traces .
Revised:  Anomalies not detected by the gold standard are also detected by our approach .
Edit intent: coherence
Original:  The approach works at flow level and has been conceived to detect such anomalous events on high-speed networks in a short time.
Revised:  The approach works at flow-level and has been conceived to detect such anomalous events on high-speed networks in a short time.
Edit intent: fluency
Original:  The paper we describe the approach and the algorithm proposed and then presents an experimental analysis of its performance, containing also a comparison with Mawilab archieve .
Revised:  The paper describes the approach and the algorithm proposed and then presents an experimental analysis of its performance, containing also a comparison with Mawilab archieve .
Edit intent: clarity
Original:  The paper we describe the approach and the algorithm proposed and then presents an experimental analysis of its performance, containing also a comparison with Mawilab archieve .
Revised:  The paper we describe the approach and the algorithm proposed and then presents an experimental analysis of its performance, containing also a comparison with MAWILab archive .
Edit intent: fluency
Original:  Moreover,  results of this comparison show that the algorithm is highly efficient in terms of Precision and Recall for port and net scan detection.
Revised:  Moreover, the results of this comparison show that the algorithm is highly efficient in terms of Precision and Recall for port and net scan detection.
Edit intent: fluency
Original:  Anomalies not detected by the gold standard are also detected by our approach .
Revised:  Anomalies not detected by the gold standard are also detected by our approach 
Edit intent: fluency
Original:  The two most spread network anomalies related to network security are port and net scan , activities performed by a malicious host to find and examine potential victims .
Revised:  The two most spread network anomalies are port and net scan , activities performed by a malicious host to find and examine potential victims .
Edit intent: clarity
Original:  The two most spread network anomalies related to network security are port and net scan , activities performed by a malicious host to find and examine potential victims .
Revised:  The two most spread network anomalies related to network security are port and net scan .
Edit intent: clarity
Original:  Motivated by Solomon Asch's seminal experiments on  conformity and other related socio-psychological works, we propose a novel opinion dynamics model to study how such a discrepancy can arise in general social networks of interpersonal influence due to a pressure to conform to the group standard . Each individual in the network has both a private and an expressed opinion:
Revised:  Motivated by Solomon Asch's seminal experiments on social conformity and other related socio-psychological works, we propose a novel opinion dynamics model to study how such a discrepancy can arise in general social networks of interpersonal influence due to a pressure to conform to the group standard . Each individual in the network has both a private and an expressed opinion:
Edit intent: fluency
Original:  Motivated by Solomon Asch's seminal experiments on  conformity and other related socio-psychological works, we propose a novel opinion dynamics model to study how such a discrepancy can arise in general social networks of interpersonal influence due to a pressure to conform to the group standard . Each individual in the network has both a private and an expressed opinion:
Revised:  Motivated by Solomon Asch's seminal experiments on conformity and other related socio-psychological works, we propose a novel opinion dynamics model to study how such a discrepancy can arise in general social networks of interpersonal influence . Each individual in the network has both a private and an expressed opinion:
Edit intent: coherence
Original:  an individual's private opinion evolves under social influence from the expressed opinions of the individual's neighbours, while the individual determines his or her expressed opinion under a pressure to conform to the group average opinion, termed the public opinion . General conditions on the network that guarantee exponentially fast convergence of the opinions to a limit are obtained.
Revised:  an individual's private opinion evolves under social influence from the expressed opinions of the individual's neighbours, while the individual determines his or her expressed opinion under a pressure to conform to the group average opinion, termed the public opinion . General conditions on the network that guarantee exponentially fast convergence of the opinions to a limit are obtained.
Edit intent: fluency
Original:  Further analysis of the limit yields several semi-quantitative conclusions, which have insightful social interpretations, including the establishing of the conditions that ensure every individual in the network has such a discrepancy.
Revised:  Further analysis of the limit yields several semi-quantitative conclusions, which have insightful social interpretations, including the establishing of conditions that ensure every individual in the network has such a discrepancy.
Edit intent: fluency
Original:  Each individual in the network has both a private and an expressed opinion: an individual's private opinion evolves under social influence from the expressed opinions of the individual's neighbours, while the individual determines his or her expressed opinion under a pressure to conform to the group average opinion , termed the  public opinion.
Revised:  Each individual in the network has both a private and an expressed opinion: an individual's private opinion evolves under social influence from the expressed opinions of the individual's neighbours, while the individual determines his or her expressed opinion under a pressure to conform to the average expressed opinion of his or her neighbours , termed the public opinion.
Edit intent: clarity
Original:  We present an algorithm to produce connected random graphs using a Metropolis-Hastings framework.
Revised:  We present an algorithm to generate samples from an ensemble of connected random graphs using a Metropolis-Hastings framework.
Edit intent: clarity
Original:  This work investigates asymmetric modelling of the maternal-fetal anatomy in accordance with clinical observations and assesses its impacts for NI-FECG signal processing.
Revised:  This work investigates asymmetric modelling of the maternal-fetal tissues in accordance with clinical observations and assesses its impacts for NI-FECG signal processing.
Edit intent: clarity
Original:  This work investigates asymmetric modelling of the maternal-fetal anatomy in accordance with clinical observations and assesses its impacts for NI-FECG signal processing.
Revised:  This work investigates asymmetric modelling of the maternal-fetal anatomy in accordance with clinical observations and assesses their impacts for NI-FECG signal processing.
Edit intent: fluency
Original:  A graph G  is (k,p)-planar if its vertices can be partitioned into clusters of size at most k such that G admits a drawing where: (i) Each cluster is associated with a closed region in the plane (called cluster region) that is topologically equivalent to a disk ;
Revised:  A graph G is (k,p)-planar if V can be partitioned into clusters of size at most k such that G admits a drawing where: (i) Each cluster is associated with a closed region in the plane (called cluster region) that is topologically equivalent to a disk ;
Edit intent: clarity
Original:  A graph G  is (k,p)-planar if its vertices can be partitioned into clusters of size at most k such that G admits a drawing where: (i) Each cluster is associated with a closed region in the plane (called cluster region) that is topologically equivalent to a disk ;
Revised:  A graph G is (k,p)-planar if its vertices can be partitioned into clusters of size at most k such that G admits a drawing where: (i) each cluster is associated with a closed region in the plane (called cluster region) that is topologically equivalent to a disk ;
Edit intent: fluency
Original:  (ii) Cluster regions are pairwise disjoint ;
Revised:  (ii) cluster regions are pairwise disjoint ;
Edit intent: fluency
Original:  (ii) Cluster regions are pairwise disjoint ;
Revised:  (ii) Cluster regions are pairwise disjoint ,
Edit intent: fluency
Original:  (iii) Each vertex of a cluster is associated with at most p distinct points (called ports) on the boundary of its cluster region;
Revised:  (iii) each vertex v \in V is identified with at most p distinct points (called ports) on the boundary of its cluster region;
Edit intent: clarity
Original:  (iii) Each vertex of a cluster is associated with at most p distinct points (called ports) on the boundary of its cluster region;
Revised:  (iii) Each vertex of a cluster is associated with at most p distinct points , called on the boundary of its cluster region;
Edit intent: clarity
Original:  (iii) Each vertex of a cluster is associated with at most p distinct points (called ports) on the boundary of its cluster region;
Revised:  (iii) Each vertex of a cluster is associated with at most p distinct points (called ports), on the boundary of its cluster region;
Edit intent: fluency
Original:  (iv) Each edge (u,v) is a Jordan arc connecting a port of u with a port of v;
Revised:  (iv) Each edge (u,v) is a Jordan arc connecting a port of u to a port of v;
Edit intent: fluency
Original:  and (v) Edges connecting different clusters do not cross each other and do not intersect any cluster region, with the only exception for end-points .
Revised:  (v) Edges connecting different clusters do not cross each other and do not intersect any cluster region, with the only exception for end-points .
Edit intent: coherence
Original:  and (v) Edges connecting different clusters do not cross each other and do not intersect any cluster region, with the only exception for end-points .
Revised:  and (v) inter-cluster edges do not cross each other and do not intersect any cluster region, with the only exception for end-points .
Edit intent: clarity
Original:  and (v) Edges connecting different clusters do not cross each other and do not intersect any cluster region, with the only exception for end-points .
Revised:  and (v) Edges connecting different clusters do not cross or intersect cluster regions except at their endpoints .
Edit intent: clarity
Original:  We first ask a Tur\'{a the number of edges of (k,p)-planar graphs .
Revised:  We first ask a Tur\'{a the number of edges in a (k,p)-planar graphs .
Edit intent: clarity
Original:  We then study the complexity of the (k,p)-planarity testing problem and prove that (4,1)-planarity testing and (2,2)-planarity testing are both NP-complete problems.
Revised:  We then prove that (4,1)-planarity testing and (2,2)-planarity testing are both NP-complete problems.
Edit intent: coherence
Original:  We then study the complexity of the (k,p)-planarity testing problem and prove that (4,1)-planarity testing and (2,2)-planarity testing are both NP-complete problems.
Revised:  We then study the complexity of the (k,p)-planarity testing problem and prove that (4,1)-planarity testing and (2,2)-planarity testing are NP-complete problems.
Edit intent: clarity
Original:  Finally, motivated by the NP-completeness of (2,2)-planarity testing, we investigate the combinatorial properties of (2,2)-planar graphs and study their relationship with 1-planar graphs, describing families of 1-planar graphs that are (2,2 )-planar as well as families that are not .
Revised:  Finally, motivated by the NP-completeness of (2,2)-planarity testing, we investigate the combinatorial properties of (2,2)-planar graphs nor the class of 1-planar graphs that are (2,2 )-planar as well as families that are not .
Edit intent: clarity
Original: We provide a Galois theoretical framework which allows to produce good polynomials for the Tamo and Barg construction of optimal locally recoverable codes (LRC).
Revised: We provide a Galois theoretical framework that allows to produce good polynomials for the Tamo and Barg construction of optimal locally recoverable codes (LRC).
Edit intent: fluency
Original:  Our approach allows to prove existence results and to construct new good polynomials , which in turn allows to build new LRCs . The existing theory of good polynomials fits  in our new framework  .
Revised:  Using our approach we construct new good polynomials , which in turn allows to build new LRCs . The existing theory of good polynomials fits in our new framework .
Edit intent: coherence
Original:  Our approach allows to prove existence results and to construct new good polynomials , which in turn allows to build new LRCs . The existing theory of good polynomials fits  in our new framework  .
Revised:  Our approach allows to prove existence results and to construct new good polynomials , which in turn allows to build new LRCs . The existing theory of good polynomials fits entirely in our new framework .
Edit intent: clarity
Original: We study an NP-hard uncapacitated discrete facility location problem : The task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids.
Revised: We study an NP-hard uncapacitated discrete facility location problem , where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids.
Edit intent: coherence
Original:  Combining the color coding technique with representative sets of matroid intersections, we show that the problem is fixed-parameter tractable parameterized by the number of matroids and the minimum rank among the client-side matroids.
Revised:  We show that the problem is fixed-parameter tractable parameterized by the number of matroids and the minimum rank among the client-side matroids.
Edit intent: clarity
Original:  We apply this algorithm to obtain fixed-parameter algorithms for social network analysis , line planning in public transport, and team management .
Revised:  We apply this algorithm to obtain fixed-parameter algorithms for social network analysis .
Edit intent: clarity
Original: We introduce a new ] uncapacitated discrete facility location problem , where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids.
Revised: We introduce a new ]: an uncapacitated discrete facility location problem , where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids.
Edit intent: fluency