wanyu/IteraTeR_v2 huggingface dataset:
Original:  Given two random processes  f(x) and g(x) two generalized eigenvalues problems can be formulated and solved.
Revised:  Given two random processes , f(x) and g(x) two generalized eigenvalues problems can be formulated and solved.
Edit intent: fluency
Original:  Given two random processes  f(x) and g(x) two generalized eigenvalues problems can be formulated and solved.
Revised:  Given two random processes f(x) and g(x) , two generalized eigenvalue problems can be formulated and solved.
Edit intent: fluency
Original:  Besides obtaining two Lebesgue quadrature (for f and g) , projections of f-- and g-- eigenvectors on each other allow to build  joint distribution estimator.
Revised:  In addition to obtaining two Lebesgue quadrature (for f and g) , projections of f-- and g-- eigenvectors on each other allow to build joint distribution estimator.
Edit intent: coherence
Original:  Besides obtaining two Lebesgue quadrature (for f and g) , projections of f-- and g-- eigenvectors on each other allow to build  joint distribution estimator.
Revised:  Besides obtaining two Lebesgue quadratures (for f and g) , projections of f-- and g-- eigenvectors on each other allow to build joint distribution estimator.
Edit intent: fluency
Original:  Besides obtaining two Lebesgue quadrature (for f and g) , projections of f-- and g-- eigenvectors on each other allow to build  joint distribution estimator.
Revised:  Besides obtaining two Lebesgue quadrature (for f and g) , projections of f-- and g-- eigenvectors on each other allow to build a joint distribution estimator.
Edit intent: fluency
Original:  Two kind of estimators are obtained: value--correlation V_{f_i;g_j}, that is similar to regular correlation concept, and a new one, probability--correlation P_{f_i;g_j}.
Revised:  Two kinds of estimators are obtained: value--correlation V_{f_i;g_j}, that is similar to regular correlation concept, and a new one, probability--correlation P_{f_i;g_j}.
Edit intent: fluency
Original:  Two kind of estimators are obtained: value--correlation V_{f_i;g_j}, that is similar to regular correlation concept, and a new one, probability--correlation P_{f_i;g_j}.
Revised:  Two kind of estimators are obtained: value--correlation V_{f_i;g_j}, similar to the regular correlation concept, and a new one, probability--correlation P_{f_i;g_j}.
Edit intent: coherence
Original:  The theory is implemented numerically , the software is available under  GPLv3 license.
Revised:  The theory is implemented numerically ; the software is available under GPLv3 license.
Edit intent: fluency
Original:  The theory is implemented numerically , the software is available under  GPLv3 license.
Revised:  The theory is implemented numerically , the software is available under the GPLv3 license.
Edit intent: fluency
Original:  Two kinds of estimators are obtained: value--correlation V_{f_i;g_j}, similar to the regular correlation concept, and a new one,  probability--correlation P_{f_i;g_j}.
Revised:  Two kinds of estimators are obtained: value--correlation V_{f_i;g_j}, similar to the regular correlation concept, and a new one, the probability--correlation P_{f_i;g_j}.
Edit intent: fluency
Original:  In addition to obtaining two Lebesgue quadratures (for f and g) from two eigenproblems, the projections of f-- and g-- eigenvectors on each other allow to build a joint distribution estimator, the most general form of which is a density--matrix correlation.
Revised:  In addition to obtaining two Lebesgue quadratures (for f and g) from two eigenproblems, the projections of f- and g- eigenvectors on each other allow to build a joint distribution estimator, the most general form of which is a density--matrix correlation.
Edit intent: fluency
Original:  The examples of the density--matrix correlation can be the value--correlation V _{f _i ;g _j }, similar to the regular correlation concept, and a new one, the probability--correlation P _{f _i ;g _j }  . The theory is implemented numerically;
Revised:  The examples of the density--matrix correlation can be a value-correlation V _{f _i ;g _j }, similar to the regular correlation concept, and a new one, the probability--correlation P _{f _i ;g _j } . The theory is implemented numerically;
Edit intent: fluency
Original:  The examples of the density--matrix correlation can be the value--correlation V _{f _i ;g _j }, similar to the regular correlation concept, and a new one, the probability--correlation P _{f _i ;g _j }  . The theory is implemented numerically;
Revised:  The examples of the density--matrix correlation can be the value--correlation V _{f _i ;g _j }, similar to a regular correlation concept, and a new one, the probability--correlation P _{f _i ;g _j } . The theory is implemented numerically;
Edit intent: fluency
Original:  The examples of the density--matrix correlation can be the value--correlation V _{f _i ;g _j }, similar to the regular correlation concept, and a new one, the probability--correlation P _{f _i ;g _j }  . The theory is implemented numerically;
Revised:  The examples of the density--matrix correlation can be the value--correlation V _{f _i ;g _j }, similar to the regular correlation concept, and a new one, a probability-correlation P _{f _i ;g _j } . The theory is implemented numerically;
Edit intent: fluency
Original: Runtime verification is commonly used to detect and, if possible, react to the violation of desired properties in safety critical systems .
Revised: Runtime monitoring is commonly used to detect and, if possible, react to the violation of desired properties in safety critical systems .
Edit intent: clarity
Original: Runtime verification is commonly used to detect and, if possible, react to the violation of desired properties in safety critical systems .
Revised: Runtime verification is commonly used to detect the violation of desired properties in safety critical systems .
Edit intent: coherence
Original: Runtime monitoring is commonly used to detect the violation of desired properties in safety critical  systems by observing run prefixes of the system . Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties , which is based on a three-valued semantics: the formula is already satisfied by the given prefix, it is already violated, or it is still undetermined, i.e., it can  be satisfied and violated  .
Revised: Runtime monitoring is commonly used to detect the violation of desired properties in safety critical systems by observing its executions . Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties , which is based on a three-valued semantics: the formula is already satisfied by the given prefix, it is already violated, or it is still undetermined, i.e., it can be satisfied and violated .
Edit intent: clarity
Original: Runtime monitoring is commonly used to detect the violation of desired properties in safety critical  systems by observing run prefixes of the system . Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties , which is based on a three-valued semantics: the formula is already satisfied by the given prefix, it is already violated, or it is still undetermined, i.e., it can  be satisfied and violated  .
Revised: Runtime monitoring is commonly used to detect the violation of desired properties in safety critical systems by observing run prefixes of the system . Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties based on a three-valued semantics: the formula is already satisfied by the given prefix, it is already violated, or it is still undetermined, i.e., it can be satisfied and violated .
Edit intent: coherence
Original: Runtime monitoring is commonly used to detect the violation of desired properties in safety critical  systems by observing run prefixes of the system . Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties , which is based on a three-valued semantics: the formula is already satisfied by the given prefix, it is already violated, or it is still undetermined, i.e., it can  be satisfied and violated  .
Revised: Runtime monitoring is commonly used to detect the violation of desired properties in safety critical systems by observing run prefixes of the system . Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties , which is based on a three-valued semantics: the formula is already satisfied by the given prefix, it is already violated, or it is still undetermined, i.e., it can still be satisfied and violated .
Edit intent: fluency
Original:  However, a wide range of formulas are not monitorable under this approach, meaning that every prefix is undetermined .
Revised:  However, a wide range of formulas are not monitorable under this approach, meaning that they have a prefix for which satisfaction and violation will always remain undetermined no matter how it is extended .
Edit intent: clarity
Original:  Recently,  robust semantics for LTL were introduced to capture degrees of violation of universal properties.
Revised:  Recently, a robust semantics for LTL were introduced to capture degrees of violation of universal properties.
Edit intent: fluency
Original:  Recently,  robust semantics for LTL were introduced to capture degrees of violation of universal properties.
Revised:  Recently, robust semantics for LTL was introduced to capture degrees of violation of universal properties.
Edit intent: fluency
Original: In this paper we present the attribute grammars as a formal approach for model checkers development.
Revised: In this paper we use attribute grammars as a formal approach for model checkers development.
Edit intent: coherence
Original:  An attribute grammar may be informally defined as a context-free grammar that has been extended with set of attributes and a collection of evaluation rules.
Revised:  An attribute grammar may be informally defined as a context-free grammar which is extended with a set of attributes and a collection of evaluation rules.
Edit intent: clarity
Original:  An attribute grammar may be informally defined as a context-free grammar that has been extended with set of attributes and a collection of evaluation rules.
Revised:  An attribute grammar may be informally defined as a context-free grammar that has been extended with set of attributes and a collection of semantic rules.
Edit intent: clarity
Original:  We are using an ATL attribute grammar for specifying an operational semantics of the language of the ATL formulas by defining a translation into the language which describes the set of states from the ATL model where the corresponding ATL formulas are satisfied.
Revised:  We use an ATL attribute grammar for specifying an operational semantics of the language of the ATL formulas by defining a translation into the language which describes the set of states from the ATL model where the corresponding ATL formulas are satisfied.
Edit intent: coherence
Original:  Also, is presented the technique of implementing the semantic actions in ANTLR  , which is the concept of connection between attribute evaluation in the grammar that generates the language of ATL formulas and algebraic compiler implementation that represents the ATL model checker.
Revised:  Also, the technique of implementing the semantic actions in ANTLR , which is the concept of connection between attribute evaluation in the grammar that generates the language of ATL formulas and algebraic compiler implementation that represents the ATL model checker.
Edit intent: coherence
Original:  First we prove that the maximum possible number of edges in a graph of diameter D and edge metric dimension k is at most (\lfloor 2D{3}\rfloor +1)^{k}+k \sum_{i = 1}^{\lceil D{3}\rceil } ( 2i-1 )^{k-1}, sharpening the bound of k{2}+k D^{k-1}+D^{k} from Zubrilina (2018).
Revised:  We show that the maximum possible number of edges in a graph of diameter D and edge metric dimension k is at most (\lfloor 2D{3}\rfloor +1)^{k}+k \sum_{i = 1}^{\lceil D{3}\rceil } ( 2i-1 )^{k-1}, sharpening the bound of k{2}+k D^{k-1}+D^{k} from Zubrilina (2018).
Edit intent: coherence
Original:  First we prove that the maximum possible number of edges in a graph of diameter D and edge metric dimension k is at most (\lfloor 2D{3}\rfloor +1)^{k}+k \sum_{i = 1}^{\lceil D{3}\rceil } ( 2i-1 )^{k-1}, sharpening the bound of k{2}+k D^{k-1}+D^{k} from Zubrilina (2018).
Revised:  First we prove that the maximum possible number of edges in a graph of diameter D and edge metric dimension k is at most (\lfloor 2D{3}\rfloor +1)^{k}+k \sum_{i = 1}^{\lceil D{3}\rceil } ( 2i )^{k-1}, sharpening the bound of k{2}+k D^{k-1}+D^{k} from Zubrilina (2018).
Edit intent: fluency
Original:  Moreover, we prove that the maximum value of n such that a graph of metric dimension \leq k can contain the complete graph K_{n} as a subgraph is n = 2^{k}.
Revised:  We also show that the maximum value of n such that a graph of metric dimension \leq k can contain the complete graph K_{n} as a subgraph is n = 2^{k}.
Edit intent: coherence
Original:  Moreover, we prove that the maximum value of n such that a graph of metric dimension \leq k can contain the complete graph K_{n} as a subgraph is n = 2^{k}.
Revised:  Moreover, we prove that the maximum value of n for which some graph of metric dimension \leq k can contain the complete graph K_{n} as a subgraph is n = 2^{k}.
Edit intent: clarity
Original:  Moreover, we prove that the maximum value of n such that a graph of metric dimension \leq k can contain the complete graph K_{n} as a subgraph is n = 2^{k}.
Revised:  Moreover, we prove that the maximum value of n such that a graph of metric dimension \leq k contains the complete graph K_{n} as a subgraph is n = 2^{k}.
Edit intent: clarity
Original:  We also prove that the maximum value of n such that a graph of metric dimension or edge metric dimension \leq k can contain the complete bipartite graph K_{n,n} as a subgraph is 2^{ \theta (k)}.
Revised:  We prove that the maximum value of n such that a graph of metric dimension or edge metric dimension \leq k can contain the complete bipartite graph K_{n,n} as a subgraph is 2^{ \theta (k)}.
Edit intent: clarity
Original:  We also prove that the maximum value of n such that a graph of metric dimension or edge metric dimension \leq k can contain the complete bipartite graph K_{n,n} as a subgraph is 2^{ \theta (k)}.
Revised:  We also prove that the maximum value of n for which some graph of metric dimension or edge metric dimension \leq k can contain the complete bipartite graph K_{n,n} as a subgraph is 2^{ \theta (k)}.
Edit intent: clarity
Original:  We also prove that the maximum value of n such that a graph of metric dimension or edge metric dimension \leq k can contain the complete bipartite graph K_{n,n} as a subgraph is 2^{ \theta (k)}.
Revised:  We also prove that the maximum value of n such that a graph of metric dimension \leq k contains the complete bipartite graph K_{n,n} as a subgraph is 2^{ \theta (k)}.
Edit intent: clarity
Original:  We also prove that the maximum value of n such that a graph of metric dimension or edge metric dimension \leq k can contain the complete bipartite graph K_{n,n} as a subgraph is 2^{ \theta (k)}.
Revised:  We also prove that the maximum value of n such that a graph of metric dimension or edge metric dimension \leq k can contain the complete bipartite graph K_{n,n} as a subgraph is 2^{ \Theta (k)}.
Edit intent: fluency
Original:  Furthermore, we show that the maximum value of n such that a graph of edge metric dimension \leq k can contain K_{1,n} as a subgraph is n = 2^{k}.
Revised:  Furthermore, we show that the maximum value of n for which some graph of edge metric dimension \leq k can contain K_{1,n} as a subgraph is n = 2^{k}.
Edit intent: clarity
Original:  Furthermore, we show that the maximum value of n such that a graph of edge metric dimension \leq k can contain K_{1,n} as a subgraph is n = 2^{k}.
Revised:  Furthermore, we show that the maximum value of n such that a graph of edge metric dimension \leq k contains K_{1,n} as a subgraph is n = 2^{k}.
Edit intent: clarity
Original:  We also show that the maximum value of n such that a graph of metric dimension \leq k can contain K_{1,n} as a subgraph is 3^{k}-O(k).
Revised:  We also show that the maximum value of n for which some graph of metric dimension \leq k can contain K_{1,n} as a subgraph is 3^{k}-O(k).
Edit intent: clarity
Original:  We also show that the maximum value of n such that a graph of metric dimension \leq k can contain K_{1,n} as a subgraph is 3^{k}-O(k).
Revised:  We also show that the maximum value of n such that a graph of metric dimension \leq k contains K_{1,n} as a subgraph is 3^{k}-O(k).
Edit intent: clarity
Original:  In addition, we prove that the d-dimensional grid \prod_{i = 1}^{d} P_{r_{i}} has edge metric dimension at most d.
Revised:  In addition, we prove that the d-dimensional grids \prod_{i = 1}^{d} P_{r_{i}} has edge metric dimension at most d.
Edit intent: fluency
Original:  In addition, we prove that the d-dimensional grid \prod_{i = 1}^{d} P_{r_{i}} has edge metric dimension at most d.
Revised:  In addition, we prove that the d-dimensional grid \prod_{i = 1}^{d} P_{r_{i}} have edge metric dimension at most d.
Edit intent: fluency
Original:  This generalizes two results of Kelenc et al  (2016), that non-path grids have edge metric dimension 2 and that d-dimensional hypercubes have edge metric dimension at most d.
Revised:  This generalizes two results of Kelenc et al . (2016), that non-path grids have edge metric dimension 2 and that d-dimensional hypercubes have edge metric dimension at most d.
Edit intent: fluency
Original: Our eyes sample a disproportionately large amount of information at the centre of gaze with increasingly sparse sampling into the periphery.
Revised: Our vision is sharpest at the center of our gaze and becomes progressively blurry into the periphery.
Edit intent: clarity
Original:  This sampling scheme is widely believed to be a wiring constraint whereby high resolution at the centre is achieved by sacrificing spatial acuityin the periphery.
Revised:  It is widely believed to be a wiring constraint whereby high resolution at the centre is achieved by sacrificing spatial acuityin the periphery.
Edit intent: clarity
Original:  Here we propose that this sampling scheme may be optimal for object recognition because the relevant spatial content is dense near an object and sparse in the surrounding vicinity.
Revised:  Here we propose that this sampling scheme is actually optimal for object recognition because the relevant spatial content is dense near an object and sparse in the surrounding vicinity.
Edit intent: clarity
Original:  Taken together our results suggest that, peripheral blurring in our eyes may have evolved for optimal object recognition , rather than merely to satisfy wiring constraints.
Revised:  Taken together our results suggest that, peripheral blurring in our eyes may have evolved to optimize object recognition rather than merely to satisfy wiring constraints.
Edit intent: fluency
Original:  Taken together our results suggest that, peripheral blurring in our eyes may have evolved for optimal object recognition , rather than merely to satisfy wiring constraints.
Revised:  Taken together our results suggest that, peripheral blurring in our eyes may have evolved for optimal object recognition , rather than merely due to wiring constraints.
Edit intent: clarity
Original: Most existing knowledge graphs (KGs) in academic domains suffer from problems of insufficient multi-relational information, name ambiguity and improper data format for large-scale machine pro- cessing .
Revised: Most existing knowledge graphs (KGs) in academic domains suffer from problems of insufficient multi-relational information, name ambiguity and improper data format for large-scale machine processing .
Edit intent: clarity
Original:  We present the problem of online set cover with delay (SCD) . A family of sets with costs and a universe of elements are known in advance.
Revised:  We present the problem of online set cover with delay (SCD) . A family of sets with costs are known in advance.
Edit intent: clarity
Original:  Requests then arrive over time on the elements, and each request accumulates delay cost until served by the algorithm through buying a containing set.
Revised:  Requests arrive over time on the elements, and each request accumulates delay cost until served by the algorithm through buying a containing set.
Edit intent: coherence
Original:  The O(\log k\cdot\log n)-competitive algorithm is based on exponential weights combined with the max operator (in contrast to most algorithms employing exponential weights, which use summation).
Revised:  The O(\log k\cdot\log n)-competitive algorithm is based on exponential weights combined with the max operator (in contrast to summation).
Edit intent: clarity
Original:  The lower bound is described by a recursive construction  .
Revised:  The lower bounds are described by a recursive construction .
Edit intent: fluency
Original:  We also show lower bounds of \Omega( \sqrt{\log k ) and \Omega( \sqrt{\log n) on the competitiveness of any algorithm for SCD , improving exponentially over their lower bound for known sets.
Revised:  We also show lower bounds of \Omega( \sqrt{\log n ) and \Omega( \sqrt{\log n) on the competitiveness of any algorithm for SCD , improving exponentially over their lower bound for known sets.
Edit intent: clarity
Original:  We also show lower bounds of \Omega( \sqrt{\log k ) and \Omega( \sqrt{\log n) on the competitiveness of any algorithm for SCD , improving exponentially over their lower bound for known sets.
Revised:  We also show lower bounds of \Omega( \sqrt{\log k ) and \Omega( ) on the competitiveness of any algorithm for SCD , improving exponentially over their lower bound for known sets.
Edit intent: clarity
Original: Queueing networks are systems of theoretical interest that give rise to complex families of stochastic processes, and find widespread use in the performance evaluation of interconnected resources.
Revised: Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources.
Edit intent: clarity
Original:  Yet, despite their importance within applications, and in comparison to their counterpart stochastic models in genetics or mathematical biology, there exist few relevant approaches for transient inference and uncertainty quantification tasks in these systems.
Revised:  In comparison to counterpart models in genetics or mathematical biology, there exist few relevant approaches for transient inference and uncertainty quantification tasks in these systems.
Edit intent: clarity
Original: The Congested Clique model , proposed by Lotker et al.[ SPAA'03, SICOMP'05] , was introduced in order to provide a simple abstraction for overlay networks.
Revised: The Congested Clique model proposed by Lotker et al.[ SPAA'03, SICOMP'05] , was introduced in order to provide a simple abstraction for overlay networks.
Edit intent: fluency
Original: The Congested Clique model , proposed by Lotker et al.[ SPAA'03, SICOMP'05] , was introduced in order to provide a simple abstraction for overlay networks.
Revised: The Congested Clique model , proposed by Lotker et al.[ SICOMP'05] , was introduced in order to provide a simple abstraction for overlay networks.
Edit intent: coherence
Original: The Congested Clique model , proposed by Lotker et al.[ SPAA'03, SICOMP'05] , was introduced in order to provide a simple abstraction for overlay networks.
Revised: The Congested Clique model , proposed by Lotker et al.[ SPAA'03, SICOMP'05] was introduced in order to provide a simple abstraction for overlay networks.
Edit intent: fluency
Original:  Congested Clique is a model of distributed (or parallel) computing, in which there are n players (nodes) with unique identifiers from set 1, ..., n , which perform computations in synchronous rounds.
Revised:  Congested Clique is a model of distributed (or parallel) computing, in which there are n players with unique identifiers from set 1, ..., n , which perform computations in synchronous rounds.
Edit intent: clarity