wanyu/IteraTeR_v2 huggingface dataset:
Original:  By use of the Grobner basis technique, the polynomial equations are transformed into other ones which have identical roots.
Revised:  By use of the Grobner bases technique, the polynomial equations are transformed into other ones which have identical roots.
Edit intent: fluency
Original:  It only considers long-range competition among trees and the effect of fire , and despite short-range facilitation is not taken into account, we recover the standard spatial patterns observed in realistic situations.
Revised:  It considers long-range competition among trees and the effect of fire , and despite short-range facilitation is not taken into account, we recover the standard spatial patterns observed in realistic situations.
Edit intent: coherence
Original:  We also study how fires affect the survival of trees in the long time limit as well as the maintenance of the patterns  .
Revised:  We also study how fires affect the survival of trees as well as the maintenance of the patterns .
Edit intent: clarity
Original: We propose a new projection matrix, based on which a  continuous-time, equality-constrained optimization approach is developed.
Revised: We propose a new projection matrix, based on which a continuous-time, equality-constrained optimization problem is developed.
Edit intent: clarity
Original:  A new projection matrix is then proposed to avoid singularity in the dynamical system.
Revised:  Then, the singularity is explained in detail and a new projection matrix is then proposed to avoid singularity in the dynamical system.
Edit intent: coherence
Original:  A new projection matrix is then proposed to avoid singularity in the dynamical system.
Revised:  A new projection matrix is proposed to avoid singularity in the dynamical system.
Edit intent: coherence
Original: We study a semi-random model for k-SAT involving an Achlioptas-process version of the random k-SAT process: a bounded number of k-CNF clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule.
Revised: We study an Achlioptas-process version of the random k-SAT process: a bounded number of k-CNF clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule.
Edit intent: clarity
Original: We study a semi-random model for k-SAT involving an Achlioptas-process version of the random k-SAT process: a bounded number of k-CNF clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule.
Revised: We study a semi-random model for k-SAT involving an Achlioptas-process version of the random k-SAT process: a bounded number of k-clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule.
Edit intent: clarity
Original:  We show the validity of the model by proving the existence of a rule that shifts the satisfiability threshold.
Revised:  We prove the existence of a rule that shifts the satisfiability threshold.
Edit intent: clarity
Original:  While the usual decision problem is trivial in some respects because of the sharp threshold, in this semi-random model, with an adversary who can shift the threshold, the problem becomes relevant.
Edit intent: coherence
Original:  Finally, we discuss connections to the study of Achlioptas random graphs .
Revised:  Finally, we discuss connections to the study of Achlioptas random graph processes .
Edit intent: clarity
Original:  We validated our technique by checking several safety properties on large open source projects.
Revised:  We validate our technique by checking several safety properties on large open source projects.
Edit intent: fluency
Original:  In this context, the copulaedas R package intends to provide a platform where EDAs based on copulas can be implemented and studied.
Revised:  In this context, the copulaedas package for R intends to provide a platform where EDAs based on copulas can be implemented and studied.
Edit intent: clarity
Original:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems,  utility functions to study the behavior of EDAs and the possibility of implementing new algorithms that can be  integrated into the package . EDAs are implemented using S4 classes with generic functions for its main parts: seeding, selection, learning, sampling, replacement, local optimization, termination, and reporting .
Revised:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems, and utility functions to study the behavior of EDAs and the possibility of implementing new algorithms that can be integrated into the package . EDAs are implemented using S4 classes with generic functions for its main parts: seeding, selection, learning, sampling, replacement, local optimization, termination, and reporting .
Edit intent: fluency
Original:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems,  utility functions to study the behavior of EDAs and the possibility of implementing new algorithms that can be  integrated into the package . EDAs are implemented using S4 classes with generic functions for its main parts: seeding, selection, learning, sampling, replacement, local optimization, termination, and reporting .
Revised:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems, utility functions to study the behavior of EDAs . It is also possible to implement new algorithms that can be integrated into the package . EDAs are implemented using S4 classes with generic functions for its main parts: seeding, selection, learning, sampling, replacement, local optimization, termination, and reporting .
Edit intent: coherence
Original:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems,  utility functions to study the behavior of EDAs and the possibility of implementing new algorithms that can be  integrated into the package . EDAs are implemented using S4 classes with generic functions for its main parts: seeding, selection, learning, sampling, replacement, local optimization, termination, and reporting .
Revised:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems, utility functions to study the behavior of EDAs and the possibility of implementing new algorithms that can be easily integrated into the package . EDAs are implemented using S4 classes with generic functions for its main parts: seeding, selection, learning, sampling, replacement, local optimization, termination, and reporting .
Edit intent: clarity
Original:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems,  utility functions to study the behavior of EDAs and the possibility of implementing new algorithms that can be  integrated into the package . EDAs are implemented using S4 classes with generic functions for its main parts: seeding, selection, learning, sampling, replacement, local optimization, termination, and reporting .
Revised:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems, utility functions to study the behavior of EDAs and the possibility of implementing new algorithms that can be integrated into the package , since EDAs are defined using S4 classes with generic functions for its main parts: seeding, selection, learning, sampling, replacement, local optimization, termination, and reporting .
Edit intent: clarity
Original:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems,  utility functions to study the behavior of EDAs and the possibility of implementing new algorithms that can be  integrated into the package . EDAs are implemented using S4 classes with generic functions for its main parts: seeding, selection, learning, sampling, replacement, local optimization, termination, and reporting .
Revised:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems, utility functions to study the behavior of EDAs and the possibility of implementing new algorithms that can be integrated into the package . EDAs are implemented using S4 classes with generic functions for its main components .
Edit intent: coherence
Original:  This paper provides an overview of EDAs based on copulas, describes the implementation of copulaedas and illustrates its use with examples.
Revised:  This paper presents copulaedas by providing an overview of EDAs based on copulas, describes the implementation of copulaedas and illustrates its use with examples.
Edit intent: clarity
Original:  This paper provides an overview of EDAs based on copulas, describes the implementation of copulaedas and illustrates its use with examples.
Revised:  This paper provides an overview of EDAs based on copulas, a description of the implementation of copulaedas and illustrates its use with examples.
Edit intent: fluency
Original:  This paper provides an overview of EDAs based on copulas, describes the implementation of copulaedas and illustrates its use with examples.
Revised:  This paper provides an overview of EDAs based on copulas, describes the implementation of the package, and an illustration of its use with examples.
Edit intent: clarity
Original:  The examples include running the EDAs implemented in the package, implementing new algorithms  and performing an empirical study to compare the behavior of a group of EDAs .
Revised:  The examples include running the EDAs implemented in the package, implementing new algorithms , and performing an empirical study to compare the behavior of a group of EDAs .
Edit intent: fluency
Original: The use of probabilistic models based on copulas in EDAs ( Estimation of Distribution Algorithms ) is currently an active area of research.
Revised: The use of copula-based models in EDAs ( Estimation of Distribution Algorithms ) is currently an active area of research.
Edit intent: clarity
Original: The use of probabilistic models based on copulas in EDAs ( Estimation of Distribution Algorithms ) is currently an active area of research.
Revised: The use of probabilistic models based on copulas in EDAs ( estimation of distribution algorithms ) is currently an active area of research.
Edit intent: fluency
Original:  In this context, the copulaedas package for R intends to provide a platform where EDAs based on copulas can be implemented and studied.
Revised:  In this context, the copulaedas package for R provides a platform where EDAs based on copulas can be implemented and studied.
Edit intent: clarity
Original:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known benchmark problems, and utility functions to study the behavior of EDAs.
Revised:  The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known optimization problems, and utility functions to study the behavior of EDAs.
Edit intent: clarity
Original:  It is also possible to implement new algorithmsthat can be easily integrated into the package , since EDAs are defined using S4 classes with generic functions for its main components.
Revised:  It is also possible to implement new algorithmsthat can be easily integrated into the package by extending an S4 classes with generic functions for its main components.
Edit intent: clarity
Original:  It is also possible to implement new algorithmsthat can be easily integrated into the package , since EDAs are defined using S4 classes with generic functions for its main components.
Revised:  It is also possible to implement new algorithmsthat can be easily integrated into the package , since EDAs are defined using S4 class with generic functions for its main components.
Edit intent: fluency
Original:  It is also possible to implement new algorithmsthat can be easily integrated into the package , since EDAs are defined using S4 classes with generic functions for its main components.
Revised:  It is also possible to implement new algorithmsthat can be easily integrated into the package , since EDAs are defined using S4 classes with generic functions for their main components.
Edit intent: fluency
Original:  This paper presents copulaedas by providing an overview of EDAs based on copulas, a description of the implementation of the package, and an illustration of its use with examples.
Revised:  This paper presents copulaedas by providing an overview of EDAs based on copulas, a description of the implementation of the package, and an illustration of its use through examples.
Edit intent: fluency
Original:  The examples include running the EDAs implemented in the package, implementing new algorithms, and performing an empirical study to compare the behavior of a group of algorithms on benchmark functions and a real-world problem.
Revised:  The examples include running the EDAs defined in the package, implementing new algorithms, and performing an empirical study to compare the behavior of a group of algorithms on benchmark functions and a real-world problem.
Edit intent: clarity
Original:  The examples include running the EDAs implemented in the package, implementing new algorithms, and performing an empirical study to compare the behavior of a group of algorithms on benchmark functions and a real-world problem.
Revised:  The examples include running the EDAs implemented in the package, implementing new algorithms, and performing an empirical study to compare the behavior of different algorithms on benchmark functions and a real-world problem.
Edit intent: clarity
Original:  However, these two measures may not be enough to describe the strongness of rules .
Revised:  However, these two measures may not be enough to describe the strength of a rule .
Edit intent: fluency
Original:  In this paper, we introduce granular association rules with four measures to reveal connections between concepts in two universes, and propose three algorithms for rule mining.
Revised:  In this paper, we introduce granular association rules with four measures to reveal connections between granules in two universes, and propose three algorithms for rule mining.
Edit intent: clarity
Original:  Two examples of such associations might be " men like alcohol" and "young men like France alcohol."
Revised:  An example of such a rule might be " men like alcohol" and "young men like France alcohol."
Edit intent: clarity
Original:  With four measures, namely source coverage,  target coverage, source confidence and target confidence,  our rules are semantically richer than existing ones.
Revised:  With four measures, namely source coverage, target coverage, the source confidence, and the target confidence, our rules are semantically richer than existing ones.
Edit intent: coherence
Original:  With four measures, namely source coverage,  target coverage, source confidence and target confidence,  our rules are semantically richer than existing ones.
Revised:  With four measures, namely source coverage, target coverage, source confidence and target confidence, respectively. With these measures, our rules are semantically richer than existing ones.
Edit intent: clarity
Original:  Three subtypes of rules are obtained through considering special requirements on the source confidence and the target confidence.
Revised:  Three subtypes of rules are obtained through considering special requirements on the source / target confidence.
Edit intent: coherence
Original:  Moreover, a forward algorithm and a backward algorithm for one particular subtype can speed up the mining process further.
Revised:  A forward algorithm and a backward algorithm for one particular subtype can speed up the mining process further.
Edit intent: coherence
Original:  We investigate  the notion of ambiguity for recursive \omega-languages with regard to acceptance by B\"uchi Turing machines.
Revised:  We investigate here the notion of ambiguity for recursive \omega-languages with regard to acceptance by B\"uchi Turing machines.
Edit intent: clarity
Original:  this provides an effective analogue to a theorem of Arnold on B\"uchi transition systems Arnold83%DIFDELCMD < ]%%% . Moreover, using some effective descriptive set theory, we prove that recursive \omega-languages satisfy the following dichotomy property.
Revised:  this provides an effective analogue to a theorem of Arnold on B\"uchi transition systems %DIFDELCMD < ]%%% . Moreover, using some effective descriptive set theory, we prove that recursive \omega-languages satisfy the following dichotomy property.
Edit intent: coherence
Original:  A recursive \omega-language L\subseteq X^\omega is either unambiguous or has a great degree of ambiguity in the following sense: for every B\"uchi Turing machine T accepting L, there exist infinitely many \omega-words which have 2^{\aleph_0 accepting runs by T.
Revised:  A recursive \omega-language L\subseteq X^\omega is either unambiguous or has a great degree of ambiguity in the following sense: for every B\"uchi Turing accepting runs by T.
Edit intent: clarity
Original:  We also show that if L \subseteq X^\omega is accepted by a B\"uchi Turing machine T and L is an analytic but non Borel set, then the set of }  \omega -words, which have 2^{\aleph_0 accepting runs by T, has cardinality 2^{\aleph_0}.
Revised:  We also show that if L \subseteq X^\omega is accepted by a B\"uchi Turing machine T and L is an analytic but non Borel set, then the set of } \omega accepting runs by T, has cardinality 2^{\aleph_0}.
Edit intent: clarity
Original: An \omega -language is a set of infinite words over a finite alphabet X.
Revised: An \omega -language is a set of infinite words over a finite alphabet X.
Edit intent: fluency
Original:  We consider the class of recursive \omega -languages, i.e. the class of \omega -languages accepted by Turing machines with a B\"uchi acceptance condition, which is also the class \Sigma_1^1  of (effective) analytic subsets of X ^\omega for some finite alphabet X.
Revised:  We consider the class of recursive \omega -languages, i.e. the class of \omega -languages accepted by Turing machines with a B\"uchi acceptance condition, which is also the class \Sigma_1^1 of (effective) analytic subsets of X ^\omega for some finite alphabet X.
Edit intent: fluency
Original:  We consider the class of recursive \omega -languages, i.e. the class of \omega -languages accepted by Turing machines with a B\"uchi acceptance condition, which is also the class \Sigma_1^1  of (effective) analytic subsets of X ^\omega for some finite alphabet X.
Revised:  We consider the class of recursive \omega -languages, i.e. the class of \omega -languages accepted by Turing machines with a B\"uchi acceptance condition, which is also the class \Sigma_1^1 of (effective) analytic subsets of X \omega for some finite alphabet X.
Edit intent: fluency
Original:  We investigate here the notion of ambiguity for recursive \omega -languages with regard to acceptance by B\"uchi Turing machines.
Revised:  We investigate here the notion of ambiguity for recursive \omega -languages with regard to acceptance by B\"uchi Turing machines.
Edit intent: fluency
Original:  We first present in detail essentials on the literature on \omega -languages accepted by Turing Machines.
Revised:  We first present in detail essentials on the literature on \omega -languages accepted by Turing Machines.
Edit intent: fluency
Original:  Then we give a complete and broad view on the notion of ambiguity and unambiguity of B\"uchi Turing machines and of the \omega -languages they accept.
Revised:  Then we give a complete and broad view on the notion of ambiguity and unambiguity of B\"uchi Turing machines and of the \omega -languages they accept.
Edit intent: fluency
Original:  First, we investigate the problem of generic data multicast in femtocell networks.
Revised:  We investigate the problem of generic data multicast in femtocell networks.
Edit intent: coherence
Original:  We then consider three typical connection scenarios in the femtocell network, and develop optimal and near-optimal algorithms for the three scenarios.
Revised:  Then we consider three typical connection scenarios in the femtocell network, and develop optimal and near-optimal algorithms for the three scenarios.
Edit intent: coherence
Original:  VNTRS are overrepresented in encoding sequence of particular functional groups where their presence could influence protein interactions.
Revised:  VNTRs are overrepresented in encoding sequence of particular functional groups where their presence could influence protein interactions.
Edit intent: clarity
Original:  The focus is on providing a model, alternative to coalgebras, where interaction is built-in, instead of relying on a (possibly difficult) understanding of the side effects of a component in isolation.
Revised:  In this model, interaction is built-in, instead of relying on a (possibly difficult) understanding of the side effects of a component in isolation.
Edit intent: coherence
Original:  Kernel equivalence in dialgebras can be used as a standard notion of behavioural equivalence, determined by how a given process interacts with the others, and the obtained observations.
Revised:  Behavioural equivalence in dialgebras can be used as a standard notion of behavioural equivalence, determined by how a given process interacts with the others, and the obtained observations.
Edit intent: fluency
Original:  Kernel equivalence in dialgebras can be used as a standard notion of behavioural equivalence, determined by how a given process interacts with the others, and the obtained observations.
Revised:  Kernel equivalence in dialgebras is determined by how a given process interacts with the others, and the obtained observations.
Edit intent: clarity
Original:  We develop a technique to compare equivalences of different categories of dialgebras .
Revised:  We develop a technique to inter-define categories of dialgebras .
Edit intent: clarity
Original: Efficient construction of arbitrary Dicke state remains elusive for quite some time and we solve this problem in this letter .
Revised: We present an efficient construction of arbitrary Dicke state remains elusive for quite some time and we solve this problem in this letter .
Edit intent: clarity
Original: Efficient construction of arbitrary Dicke state remains elusive for quite some time and we solve this problem in this letter .
Revised: Efficient construction of arbitrary Dicke state .
Edit intent: coherence
Original:  Our work improve the results of Childs et al (2002).
Revised:  Our work improves the results of Childs et al (2002).
Edit intent: fluency
Original:  Our work improves the results of Childs et al (2002).
Revised:  Our work compares fairly with the results of Childs et al (2002).
Edit intent: clarity
Original:  Furthermore, it is shown that in characteristic zero black-box derandomization of the symbolic trace or determinant identity testing (STIT or equivalently SDIT) brings the problem of derandomizing Noether's Normalization Lemma  for the ring of invariants of the adjoint action of the general linear group on a tuple of matrices  from EXPSPACE (where it is currently) to P.
Revised:  Furthermore, it is shown that in characteristic zero black-box derandomization of the symbolic trace or determinant identity testing (STIT or equivalently SDIT) brings the problem of derandomizing Noether's Normalization Lemma for the ring of invariants of the adjoint action of the general linear group on a tuple of matrices can be brought down from EXPSPACE (where it is currently) to P.
Edit intent: clarity