wanyu/IteraTeR_v2 huggingface dataset:
Original:  We give the construction of a scale-free network in which a multi-objective algorithm and a greedy algorithm obtain optimal solutions, while the (1+1) EA obtains the worst possible solution with constant probability.
Revised:  We give the construction of a scale-free network in which the (1+1) EA obtains the worst possible solution with constant probability.
Edit intent: coherence
Original:  We prove that for the Dominating Set, Vertex Cover, Connected Dominating Set and Independent Set, the (1+1) EA obtains constant-factor approximation in expected run time O (n \log n) and O (n^4) respectively.
Revised:  We prove that for the Dominating Set, Vertex Cover, Connected Dominating Set and Independent Set, the (1+1) -EA obtains constant-factor approximation in expected run time O (n \log n) and O (n^4) respectively.
Edit intent: clarity
Original:  Whereas,  GSEMO gives even better approximation than (1+1) EA in expected run time O (n^3) for Dominating Set, Vertex Cover and Connected Dominating Set on such networks.
Revised:  Whereas, the GSEMO gives even better approximation than (1+1) EA in expected run time O (n^3) for Dominating Set, Vertex Cover and Connected Dominating Set on such networks.
Edit intent: fluency
Original: It has been experimentally observed that real-world networks follow certain topological properties, such as small-world, power-law etc.
Revised: It has been observed that many complex real-world networks follow certain topological properties, such as small-world, power-law etc.
Edit intent: clarity
Original: It has been experimentally observed that real-world networks follow certain topological properties, such as small-world, power-law etc.
Revised: It has been experimentally observed that real-world networks have certain properties, such as small-world, power-law etc.
Edit intent: clarity
Original:  To study these networks, many random graph models , such as Preferential Attachment, have been proposed .
Revised:  To study these networks, various random graph models , such as Preferential Attachment, have been proposed .
Edit intent: clarity
Original:  To study these networks, many random graph models , such as Preferential Attachment, have been proposed .
Revised:  To study these networks, many random graph models have been proposed .
Edit intent: coherence
Original:  We prove that for the Dominating Set , Vertex Cover, Connected Dominating Set and Independent Set, the (1+1)-EA obtains constant-factor approximation in expected run time \mathcal{O(n \log (n)) and O(n^4) respectively.
Revised:  We prove that for the Dominating Set , Vertex Cover, Connected Dominating Set (n \log (n)) and O(n^4) respectively.
Edit intent: coherence
Original:  Whereas, }  the GSEMO gives even better approximation than (1+1) -EA in the expected run time of O(n^3) for Dominating Set, Vertex Cover and Connected Dominating Set on such networks .
Revised:  Whereas, } the (1+1) -EA in the expected run time of O(n^3) for Dominating Set, Vertex Cover and Connected Dominating Set on such networks .
Edit intent: coherence
Original:  Compared to the known methods, our approach is fast, simple to present and to implement, and avoids any assumptions  Our construction explicitly yields those matrices for which particular lower and upper bounds are attained.
Revised:  Compared to the known methods, our approach is fast, simple to present and to implement, and avoids any assumptions . Our construction explicitly yields those matrices for which particular lower and upper bounds are attained.
Edit intent: fluency
Original:  A set automaton is a one-way finite automata with an additional storage - the set.
Revised:  The set automata are one-way finite automata with an additional storage - the set.
Edit intent: fluency
Original:  A set automaton is a one-way finite automata with an additional storage - the set.
Revised:  A set automaton is a one-way finite automata with an additional storage---the set.
Edit intent: fluency
Original:  There are two kind of set automata - the deterministic and the nondeterministic ones.
Revised:  There are two kinds of set automata---the deterministic and the nondeterministic ones.
Edit intent: fluency
Original:  DSA were presented by M. Kutrib, A. Malcher, M. Wendlandt in 2014 .
Revised:  The model was introduced by M. Kutrib, A. Malcher, M. Wendlandt in 2014 .
Edit intent: clarity
Original:  The main topic of this paper is computational complexity: we prove that  languages recognizable by DSA belongs to P and the word membership problem is P-complete for DSA without epsilon-loops, all the languages recognizable by NSA are in NP and there are NP-complete languages .
Revised:  The main topic of this paper is computational complexity: we prove that - languages recognizable by DSA belongs to P and the word membership problem is P-complete for DSA without epsilon-loops, all the languages recognizable by NSA are in NP and there are NP-complete languages .
Edit intent: fluency
Original:  The main topic of this paper is computational complexity: we prove that  languages recognizable by DSA belongs to P and the word membership problem is P-complete for DSA without epsilon-loops, all the languages recognizable by NSA are in NP and there are NP-complete languages .
Revised:  The main topic of this paper is computational complexity: we prove that languages recognizable by DSA belong to P and the word membership problem is P-complete for DSA without epsilon-loops, all the languages recognizable by NSA are in NP and there are NP-complete languages .
Edit intent: fluency
Original:  The main topic of this paper is computational complexity: we prove that  languages recognizable by DSA belongs to P and the word membership problem is P-complete for DSA without epsilon-loops, all the languages recognizable by NSA are in NP and there are NP-complete languages .
Revised:  The main topic of this paper is computational complexity: we prove that languages recognizable by DSA belongs to P and there are P-complete for DSA without epsilon-loops, all the languages recognizable by NSA are in NP and there are NP-complete languages .
Edit intent: clarity
Original:  Yet, relying separately on data about scientific production on one side, through bibliometric indicators, and about technological advancements on the other side, through patents statistics, gives only a limited insight on the key interplay between science and technology which, as a matter of fact, move forward together within the innovation space.
Revised:  Relying separately on data about scientific production on one side, through bibliometric indicators, and about technological advancements on the other side, through patents statistics, gives only a limited insight on the key interplay between science and technology which, as a matter of fact, move forward together within the innovation space.
Edit intent: coherence
Original:  In this paper, using citation data of both scientific papers and patents, we quantify the direct impact of the scientific outputs of nations on further advancements in science and on the introduction of new technologies.
Revised:  In this paper, using citation data of both research papers and patents, we quantify the direct impact of the scientific outputs of nations on further advancements in science and on the introduction of new technologies.
Edit intent: clarity
Original:  In this paper, using citation data of both scientific papers and patents, we quantify the direct impact of the scientific outputs of nations on further advancements in science and on the introduction of new technologies.
Revised:  In this paper, using citation data of both scientific papers and patents, we quantify the direct influence of the scientific outputs of nations on further advancements in science and on the introduction of new technologies.
Edit intent: fluency
Original:  Our analysis highlights the presence of geo-cultural clusters of nations with similar innovation system features, and unveils the heterogeneous coupled dynamics of scientific and technological success .
Revised:  Our analysis highlights the presence of geo-cultural clusters of nations with similar innovation system features, and unveils the heterogeneous coupled dynamics of scientific and technological advancements .
Edit intent: clarity
Original:  This study represents a first step in the buildup of a comprehensive framework for knowledge creation and innovation.
Revised:  This study represents a step forward in the buildup of a comprehensive framework for knowledge creation and innovation.
Edit intent: clarity
Original:  This study represents a first step in the buildup of a comprehensive framework for knowledge creation and innovation.
Revised:  This study represents a first step in the buildup of an inclusive framework for knowledge creation and innovation.
Edit intent: clarity
Original:  Yet, most currently used MD force fields overstate non-bonded interactions between polysaccharide molecules, strongly limiting the usability of those simulations.
Revised:  Yet, currently used MD force fields overstate non-bonded interactions between polysaccharide molecules, strongly limiting the usability of those simulations.
Edit intent: clarity
Original: We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an expander, confirming a conjecture of Wigderson and Xiao up to logarithmic factors in the deviation parameter .
Revised: We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an expander, confirming a conjecture due to Wigderson and Xiao up to logarithmic factors in the deviation parameter .
Edit intent: clarity
Original: We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an expander, confirming a conjecture of Wigderson and Xiao up to logarithmic factors in the deviation parameter .
Revised: We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an expander, confirming a conjecture of Wigderson and Xiao .
Edit intent: clarity
Original:  Our proof is based on a recent multi-matrix extension of the Golden-Thompson inequality due to Sutteret al.
Revised:  Our proof is based on a new multi-matrix extension of the Golden-Thompson inequality due to Sutteret al.
Edit intent: clarity
Original:  \mbox{ Sutter2017 as well as an adaptation of an argument for the scalar case due to Healy \mbox{ healy08 . Secondarily, we also provide a generic reduction showing that any concentration inequality for vector-valued martingales implies a concentration inequality for the corresponding expander walk, with a weakening of parameters roughly proportional to the squared mixing time.
Revised:  \mbox{ Sutter2017 as well as an adaptation of an argument for the scalar case due to Healy . Secondarily, we also provide a generic reduction showing that any concentration inequality for vector-valued martingales implies a concentration inequality for the corresponding expander walk, with a weakening of parameters roughly proportional to the squared mixing time.
Edit intent: coherence
Original:  \mbox{ Sutter2017 as well as an adaptation of an argument for the scalar case due to Healy \mbox{ healy08 . Secondarily, we also provide a generic reduction showing that any concentration inequality for vector-valued martingales implies a concentration inequality for the corresponding expander walk, with a weakening of parameters roughly proportional to the squared mixing time.
Revised:  \mbox{ Sutter2017 as well as an adaptation of an argument for the scalar case due to Healy \mbox{ healy08 . Secondarily, we also provide a generic reduction showing that any concentration inequality for vector-valued martingales implies a concentration inequality for the corresponding expander walk, with a weakening of parameters proportional to the squared mixing time.
Edit intent: clarity
Original:  However, higher-order structures beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order patterns is not well understood.
Revised:  However, higher-order cliques beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order patterns is not well understood.
Edit intent: clarity
Original:  However, higher-order structures beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order patterns is not well understood.
Revised:  However, higher-order structures beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order network structures is not well understood.
Edit intent: clarity
Original:  Here we introduce higher-order clustering coefficients that measure the closure probability of higher-order network structures and provide a more comprehensive view of how the edges of complex networks cluster.
Revised:  Here we introduce higher-order clustering coefficients that measure the closure probability of higher-order network cliques and provide a more comprehensive view of how the edges of complex networks cluster.
Edit intent: clarity
Original: In order to adopt deep learning for ad-hoc information retrieval, it is essential to establish suitable representations of query-document pairs and to design neural architectures that are able to digest such representations.
Revised: In order to adopt deep learning for information retrieval, it is essential to establish suitable representations of query-document pairs and to design neural architectures that are able to digest such representations.
Edit intent: clarity
Original:  In particular, they ought to capture all relevant information required to assess the relevance of a document for a given user query , including term overlap as well as positional information such as proximity and term dependencies .
Revised:  In particular, they ought to capture all relevant information required to assess the relevance of a document to a given user query , including term overlap as well as positional information such as proximity and term dependencies .
Edit intent: fluency
Original:  In particular, they ought to capture all relevant information required to assess the relevance of a document for a given user query , including term overlap as well as positional information such as proximity and term dependencies .
Revised:  In particular, they ought to capture all relevant information required to assess the relevance of a document for a given user query .
Edit intent: clarity
Original:  While previous work has successfully captured unigram term matches, none has successfully used position-dependent information on a standard benchmark test collection .
Revised:  While previous works have successfully captured unigram term matches, none has successfully used position-dependent information on a standard benchmark test collection .
Edit intent: fluency
Original:  While previous work has successfully captured unigram term matches, none has successfully used position-dependent information on a standard benchmark test collection .
Revised:  While previous work has successfully captured unigram term matches, how to fully employ position-dependent information on a standard benchmark test collection .
Edit intent: clarity
Original:  We present a novel model architecture consisting of convolutional layers to capture term dependencies and proximity among query term occurrences, followed by a recurrent layer to capture relevance over different query terms . Extensive experiments on  TREC Web Track data confirm that the proposed model with similarity matrix representations yields improved search results .
Revised:  We present a novel model architecture consisting of convolutional layers to capture term dependencies and proximity among query term occurrences, followed by a recurrent layer to capture relevance over different query terms . Extensive experiments on TREC Web Track data confirm that the proposed model yields better results under different benchmarks .
Edit intent: clarity
Original:  In this work, we propose a novel neural IR model named PACRR (Position-Aware Convolutional-Recurrent Relevance), aiming at better modeling position-dependent interactions between a query and a document via convolutional layers as well as recurrent layers . Extensive experiments on six years' TREC Web Track data confirm that the proposed model yields better results under different benchmarks.
Revised:  In this work, we propose a novel neural IR model named PACRR aiming at better modeling position-dependent interactions between a query and a document via convolutional layers as well as recurrent layers . Extensive experiments on six years' TREC Web Track data confirm that the proposed model yields better results under different benchmarks.
Edit intent: coherence
Original:  In this work, we propose a novel neural IR model named PACRR (Position-Aware Convolutional-Recurrent Relevance), aiming at better modeling position-dependent interactions between a query and a document via convolutional layers as well as recurrent layers . Extensive experiments on six years' TREC Web Track data confirm that the proposed model yields better results under different benchmarks.
Revised:  In this work, we propose a novel neural IR model named PACRR (Position-Aware Convolutional-Recurrent Relevance), aiming at better modeling position-dependent interactions between a query and a document . Extensive experiments on six years' TREC Web Track data confirm that the proposed model yields better results under different benchmarks.
Edit intent: coherence
Original:  In this work, we propose a novel neural IR model named PACRR (Position-Aware Convolutional-Recurrent Relevance), aiming at better modeling position-dependent interactions between a query and a document via convolutional layers as well as recurrent layers . Extensive experiments on six years' TREC Web Track data confirm that the proposed model yields better results under different benchmarks.
Revised:  In this work, we propose a novel neural IR model named PACRR (Position-Aware Convolutional-Recurrent Relevance), aiming at better modeling position-dependent interactions between a query and a document via convolutional layers as well as recurrent layers . Extensive experiments on six years' TREC Web Track data confirm that the proposed model yields better results under multiple benchmarks.
Edit intent: clarity
Original: Motivated by the Babai conjecture and the \v{Cern\'{y} }  conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set.
Revised: Motivated by the Babai conjecture and the ern\'{y} } conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set.
Edit intent: coherence
Original:  If U is any semigroup, and A be a subset of U, then we denote by \langle A\rangle the least subsemigroup of U containing A.
Revised:  If U is any semigroup, and A is a subset of U, then we denote by \langle A\rangle the least subsemigroup of U containing A.
Edit intent: clarity
Original:  If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about \langle A\rangle, that has been found using the Froidure-Pin Algorithm, to compute the semigroup \langle A , B\rangle.
Revised:  If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about \langle A\rangle, that has been found using the Froidure-Pin Algorithm, to compute the semigroup \langle A \cup B\rangle.
Edit intent: clarity
Original: We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry-adapted coordinates system where the given SDE has notable invariant properties.
Revised: We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties.
Edit intent: fluency
Original: To increase the scalability of software defined networks (SDNs), flow aggregation schemes have been proposed to merge multiple mice flows into an elephant aggregated flow for traffic engineering.
Revised: To increase the scalability of Software Defined Networks (SDNs), flow aggregation schemes have been proposed to merge multiple mice flows into an elephant aggregated flow for traffic engineering.
Edit intent: fluency
Original: To increase the scalability of software defined networks (SDNs), flow aggregation schemes have been proposed to merge multiple mice flows into an elephant aggregated flow for traffic engineering.
Revised: To increase the scalability of software defined networks (SDNs), flow aggregation schemes have been proposed to merge multiple mouse flows into an elephant aggregated flow for traffic engineering.
Edit intent: fluency
Original:  In this paper, we first notice that the user bit-rate requirements of mice flows are no longer guaranteed in the aggregated flow since the flow rate decided by TCP fair allocation is usually different from the desired bit-rate of each user.
Revised:  In this paper, we first notice that the user bit-rate requirements of mouse flows are no longer guaranteed in the aggregated flow since the flow rate decided by TCP fair allocation is usually different from the desired bit-rate of each user.
Edit intent: fluency
Original:  In this paper, we first notice that the user bit-rate requirements of mice flows are no longer guaranteed in the aggregated flow since the flow rate decided by TCP fair allocation is usually different from the desired bit-rate of each user.
Revised:  In this paper, we first notice that the user bit-rate requirements of mice flows are no longer guaranteed in the aggregated flow since the flow rate decided by the TCP allocation is usually different from the desired bit-rate of each user.
Edit intent: clarity
Original:  To address the above issue, we present a novel architecture, named Flexible Flow And Rate Management ( F2ARM ), to control the rates of only a few flows in order to increase the scalability of SDN, while leaving the uncontrolled flows managed by TCP.
Revised:  To address the above issue, we present a novel architecture, named Flexible Flow And Rate Management ( F^2ARM ), to control the rates of only a few flows in order to increase the scalability of SDN, while leaving the uncontrolled flows managed by TCP.
Edit intent: clarity
Original:  We formulate a new optimization problem, named Scalable Per-Flow Rate Control for SDN (SPFRCS), which aims to find a minimum subset of flows as controlled flows but ensure that the flow rates of all uncontrolled flows can still satisfy  minimum required rates by TCP fair allocation .
Revised:  We formulate a new optimization problem, named Scalable Per-Flow Rate Control for SDN (SPFRCS), which aims to find a minimum subset of flows as controlled flows but ensure that the flow rates of all uncontrolled flows can still satisfy the minimum required rates by TCP fair allocation .
Edit intent: fluency
Original:  We formulate a new optimization problem, named Scalable Per-Flow Rate Control for SDN (SPFRCS), which aims to find a minimum subset of flows as controlled flows but ensure that the flow rates of all uncontrolled flows can still satisfy  minimum required rates by TCP fair allocation .
Revised:  We formulate a new optimization problem, named Scalable Per-Flow Rate Control for SDN (SPFRCS), which aims to find a minimum subset of flows as controlled flows but ensure that the flow rates of all uncontrolled flows can still satisfy minimum required rates by TCP .
Edit intent: clarity