wanyu/IteraTeR_v2 huggingface dataset:
Original: We define a generic algorithmic framework to prove pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substitutions over a three-letter alphabet .
Revised: We define a generic algorithmic framework to prove pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substitutions .
Edit intent: clarity
Original:  We focus on the families obtained as the arbitrary finite products of the  substitutions associated with the Brun and the Jacobi-Perron continued fraction algorithms  .
Revised:  We focus on the families obtained as finite products of the substitutions associated with the Brun and the Jacobi-Perron continued fraction algorithms .
Edit intent: clarity
Original:  Our tools consist in a combinatorial reformulation of so-called coincidence conditions , in terms of qualitative properties of discrete plane generation , using a geometrical (dual) version of substitutions.
Revised:  Our tools consist in a reformulation of some combinatorial criteria (coincidence conditions) , in terms of qualitative properties of discrete plane generation , using a geometrical (dual) version of substitutions.
Edit intent: clarity
Original:  Our tools consist in a combinatorial reformulation of so-called coincidence conditions , in terms of qualitative properties of discrete plane generation , using a geometrical (dual) version of substitutions.
Revised:  Our tools consist in a combinatorial reformulation of so-called coincidence conditions , in terms of properties of discrete plane generation , using a geometrical (dual) version of substitutions.
Edit intent: clarity
Original:  Our tools consist in a combinatorial reformulation of so-called coincidence conditions , in terms of qualitative properties of discrete plane generation , using a geometrical (dual) version of substitutions.
Revised:  Our tools consist in a combinatorial reformulation of so-called coincidence conditions , in terms of qualitative properties of discrete plane generation , using a geometrical (dual) substitutions.
Edit intent: clarity
Original:  We also deduce some topological and dynamical properties of the associated Rauzy fractals,  as well as some number theoretical properties of the associated Pisot numbers.
Revised:  We also deduce some topological and dynamical properties of the Rauzy fractals, as well as some number theoretical properties of the associated Pisot numbers.
Edit intent: fluency
Original:  We also deduce some topological and dynamical properties of the associated Rauzy fractals,  as well as some number theoretical properties of the associated Pisot numbers.
Revised:  We also deduce some topological and dynamical properties of the associated Rauzy fractals, as well as some number-theoretical properties of the associated Pisot numbers.
Edit intent: fluency
Original:  This theory and its models, even simple ones, presents significant, geometrically fascinating challenges for automated reasoning tools are .
Revised:  This theory and its models, even simple ones, presents significant, geometrically fascinating challenges for automated reasoning tools .
Edit intent: clarity
Original: We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix by a system of Wiener-Hopf integral equations.
Revised: We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations.
Edit intent: clarity
Original:  The numerical inversion of the system of integral equations allows us to propose a fast and efficient method  ] to perform a non-parametric estimation of the Hawkes kernel matrix.
Revised:  The numerical inversion of this system of integral equations allows us to propose a fast and efficient method ] to perform a non-parametric estimation of the Hawkes kernel matrix.
Edit intent: clarity
Original:  The numerical inversion of the system of integral equations allows us to propose a fast and efficient method  ] to perform a non-parametric estimation of the Hawkes kernel matrix.
Revised:  The numerical inversion of the system of integral equations allows us to propose a fast and efficient method ], to perform a non-parametric estimation of the Hawkes kernel matrix.
Edit intent: fluency
Original:  We discuss the estimation error and provide some numerical examples . Applications to high frequency trading events in financial markets and to earthquakes occurrence dynamics are  considered.
Revised:  We discuss the estimation error and provide some numerical examples . Applications to high frequency trading events in financial markets and to earthquakes occurrence dynamics are finally considered.
Edit intent: coherence
Original: We study the close connection between rational functions that approximate some Boolean function, and quantum algorithms that compute the same function using postselection.
Revised: We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection.
Edit intent: clarity
Original:  We give optimal (up to constant factors) quantum algorithms with postselection for the majority function, slightly improving upon an earlier algorithm of Aaronson.
Revised:  We give optimal (up to constant factors) quantum algorithms with postselection for the Majority function, slightly improving upon an earlier algorithm of Aaronson.
Edit intent: fluency
Original:  Finally we show how Newman's classic theorem about low-degree rational approximation of the absolute-value function follows from our algorithm .
Revised:  Finally we show how Newman's classic theorem about low-degree rational approximation of the absolute-value function follows from these algorithms .
Edit intent: clarity
Original:  Indeed, many methods of communication suffer from such frictional losses.
Revised:  Indeed, many modes of communication suffer from such frictional losses.
Edit intent: clarity
Original:  We use this " information-friction " model to understand fundamental energy requirements on encoding and decoding in communication circuitry.
Revised:  We use this " information- friction " model to understand fundamental energy requirements on encoding and decoding in communication circuitry.
Edit intent: fluency
Original:  First, for communication across a binary input AWGN channel, we arrive at  limits on bit-meters (and thus energy consumption) for decoding implementations that have a predetermined input-independent lengths of messages.
Revised:  First, for communication across a binary input AWGN channel, we arrive at fundamental limits on bit-meters (and thus energy consumption) for decoding implementations that have a predetermined input-independent lengths of messages.
Edit intent: clarity
Original:  First, for communication across a binary input AWGN channel, we arrive at  limits on bit-meters (and thus energy consumption) for decoding implementations that have a predetermined input-independent lengths of messages.
Revised:  First, for communication across a binary input AWGN channel, we arrive at limits on bit-meters (and thus energy consumption) for decoding implementations that have a predetermined input-independent length of messages.
Edit intent: fluency
Original:  For encoding, we relax the fixed-length assumption and derive bounds for flexible-message-length implementations.
Revised:  For encoding, we relax the fixed-length assumption and derive bounds for flexible-message- length implementations.
Edit intent: fluency
Original: Although  differential evolution (DE) algorithms have shown great power in solving continuous optimization problems  , it is still a challenging task to design an efficient binary variant of DE algorithm.
Revised: Although differential evolution (DE) algorithms can perform well on continuous optimization problems , it is still a challenging task to design an efficient binary variant of DE algorithm.
Edit intent: clarity
Original: Although  differential evolution (DE) algorithms have shown great power in solving continuous optimization problems  , it is still a challenging task to design an efficient binary variant of DE algorithm.
Revised: Although differential evolution (DE) algorithms have shown great power in solving continuous optimization problems , it is still a challenging task to design an efficient binary-coded DE algorithm.
Edit intent: clarity
Original:  In this paper , we propose a binary learning differential evolution (BLDE) algorithm , which can efficiently search the feasible region by learning from the obtained solutions.
Revised:  In this paper , we propose a binary learning differential evolution (BLDE) algorithm that can efficiently locate the global optimal solutions by learning from the obtained solutions.
Edit intent: clarity
Original:  Availability and Implementation: The benchmarking scripts and the bwa-meth software are available at URL meth/ under the MIT License.
Revised:  Availability and Implementation: The benchmarking scripts and the bwa-meth software are available at URL under the MIT License.
Edit intent: clarity
Original:  By a Markov chain analysis, the average throughputs of the secondary users and average interference level among the secondary and primary users are evaluated .
Revised:  By a Markov chain analysis, the average throughputs of the secondary users and average interference level among the secondary and primary users are investigated .
Edit intent: clarity
Original: Developing an efficient spectrum access policy enables cognitive radios to dramatically increase spectrum utilization while ensuring predetermined quality of service levels for the primary users.
Revised: Developing an efficient spectrum access policy enables cognitive radios to dramatically increase spectrum utilization while ensuring predetermined quality of service levels for primary users.
Edit intent: fluency
Original:  Specifically, the secondary users create a random order of the available channels upon primary users return, and then find optimal transmission and handoff opportunities in a distributed manner.
Revised:  Specifically, the secondary users create a random order of available channels upon primary users return, and then find optimal transmission and handoff opportunities in a distributed manner.
Edit intent: fluency
Original:  A maximization of the secondary network performance in terms of  throughput while keeping under control the average interference is proposed.
Revised:  A maximization of the secondary network performance in terms of the throughput while keeping under control the average interference is proposed.
Edit intent: fluency
Original:  It is concluded that fully distributed sensing order algorithms can achieve substantial performance improvements in cognitive radio networks without the need of centralized management or message passing among the users.
Revised:  It is concluded that fully distributed sensing order algorithms can lead to substantial performance improvements in cognitive radio networks without the need of centralized management or message passing among the users.
Edit intent: clarity
Original: A graph H is t-apex if H-X is planar for some set X \subset V(H) of size t.
Revised: A graph H is t-apex if H-X is planar for some subset X of V(H) of size t.
Edit intent: clarity
Original: As architecture, systems, and data management communities pay greater attention to innovative big data systems and architecture , the pressure of benchmarking and evaluating these systems rises.
Revised: As architecture, systems, and data management communities pay greater attention to innovative big data systems and architectures , the pressure of benchmarking and evaluating these systems rises.
Edit intent: fluency
Original:  BigDataBench is publicly available from URL  Also, we comprehensively characterize 19 big data workloads included in BigDataBench with varying data inputs.
Revised:  BigDataBench is publicly available from URL . Also, we comprehensively characterize 19 big data workloads included in BigDataBench with varying data inputs.
Edit intent: fluency
Original: Given a set of n disjoint balls b_1,%DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data-structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( \log n + 1/ \varepsilon ^d) time, where k and \varepsilon are provided at query time.
Revised: Given a set of n disjoint balls %DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data-structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( \log n + 1/ \varepsilon ^d) time, where k and \varepsilon are provided at query time.
Edit intent: clarity
Original: Given a set of n disjoint balls b_1,%DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data-structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( \log n + 1/ \varepsilon ^d) time, where k and \varepsilon are provided at query time.
Revised: Given a set of n disjoint balls b_1,%DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( \log n + 1/ \varepsilon ^d) time, where k and \varepsilon are provided at query time.
Edit intent: fluency
Original: Given a set of n disjoint balls b_1,%DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data-structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( \log n + 1/ \varepsilon ^d) time, where k and \varepsilon are provided at query time.
Revised: Given a set of n disjoint balls b_1,%DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data-structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( log n + 1/ \varepsilon ^d) time, where k and \varepsilon are provided at query time.
Edit intent: fluency
Original: Given a set of n disjoint balls b_1,%DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data-structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( \log n + 1/ \varepsilon ^d) time, where k and \varepsilon are provided at query time.
Revised: Given a set of n disjoint balls b_1,%DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data-structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( \log n + 1/ \epsilon ^d) time, where k and \varepsilon are provided at query time.
Edit intent: fluency
Original: Given a set of n disjoint balls b_1,%DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data-structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( \log n + 1/ \varepsilon ^d) time, where k and \varepsilon are provided at query time.
Revised: Given a set of n disjoint balls b_1,%DIFDELCMD < \dots%%% , b_n in \mathbb{R , we provide a data-structure , of near linear size, that can answer (1 \pm \varepsilon )-approximate kth-nearest neighbor queries in O( \log n + 1/ \varepsilon ^d) time, where k and \epsilon are provided at query time.
Edit intent: fluency
Original:  If k and \varepsilon are provided in advance, we provide a data-structure to answer such queries, that requires (roughly) O(n/k) space;
Revised:  If k and \varepsilon are provided in advance, we provide a data structure to answer such queries, that requires (roughly) O(n/k) space;
Edit intent: fluency
Original:  that is, the data-structure has sublinear space requirement if k is sufficiently large.
Revised:  that is, the data structure has sublinear space requirement if k is sufficiently large.
Edit intent: fluency
Original:  Decision rules based on multiple comparisons can better accommodate class heterogeneity  and thereby increase accuracy, and might provide a link with biological mechanism.
Revised:  Decision rules based on multiple comparisons can better accommodate class heterogeneity , and thereby increase accuracy, and might provide a link with biological mechanism.
Edit intent: fluency
Original:  We consider a general framework ( " rank-in-context " ) for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support ("context").
Revised:  We consider a general framework ( `` rank-in-context " ) for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support ("context").
Edit intent: fluency
Original:  We consider a general framework ( " rank-in-context " ) for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support ("context").
Revised:  We consider a general framework ( " rank-in-context '' ) for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support ("context").
Edit intent: fluency
Original:  A notable example is phenotype prediction from gene expression data, for instance  detecting human cancers, differentiating subtypes , and predicting clinical outcomes.
Revised:  A notable example is phenotype prediction from gene expression data, for instance , detecting human cancers, differentiating subtypes , and predicting clinical outcomes.
Edit intent: fluency
Original:  A notable example is phenotype prediction from gene expression data, for instance  detecting human cancers, differentiating subtypes , and predicting clinical outcomes.
Revised:  A notable example is phenotype prediction from gene expression data, for instance detecting human cancers, differentiating subtypes and predicting clinical outcomes.
Edit intent: fluency
Original:  One reason is that the complexity of the decision rules that emerge from standard statistical learning impedes biological understanding, in particular  any mechanistic interpretation.
Revised:  One reason is that the complexity of the decision rules that emerge from standard statistical learning impedes biological understanding, in particular , any mechanistic interpretation.
Edit intent: fluency
Original:  We consider a general framework ( `` rank-in-context '' ) for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support ("context").
Revised:  We consider a general framework ( " rank-in-context '' ) for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support ("context").
Edit intent: fluency
Original:  We consider a general framework ( `` rank-in-context '' ) for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support ("context").
Revised:  We consider a general framework ( `` rank-in-context " ) for designing discriminant functions, including a data-driven selection of the number and identity of the genes in the support ("context").
Edit intent: fluency
Original: Circle graphs are intersection graphs of chords in a circle and k-polygon graphs are the intersection graphs of chords in a convex k-sided polygon where each chord has its endpoints on distinct sides.
Revised: Circle graphs are intersection graphs of chords in a circle and k-polygon graphs are intersection graphs of chords in a convex k-sided polygon where each chord has its endpoints on distinct sides.
Edit intent: coherence
Original:  Every k-polygon graph is a circle graph and every circle graph is a k-polygon graph for some k\ge  .
Revised:  The k-polygon graph is a circle graph and every circle graph is a k-polygon graph for some k\ge .
Edit intent: fluency
Original:  Every k-polygon graph is a circle graph and every circle graph is a k-polygon graph for some k\ge  .
Revised:  Every k-polygon graphs, for k\ge .
Edit intent: clarity
Original:  of a circle graph G is the minimum k such that G is a k-polygon graph and the polygon number of a circle representation is the minimum number of corners that must be added to the circle to produce a polygon representation . Given a circle graph G and an integer k, determining whether \psi \gp (G) \le k is NP-complete, while the problem is solvable in polynomial time for fixed k , and the polygon number of a circle representation can be computed in polynomial time .
Revised:  of a circle graph G is the minimum k such that G is a k-polygon graph . Given a circle graph G and an integer k, determining whether \psi \gp (G) \le k is NP-complete, while the problem is solvable in polynomial time for fixed k , and the polygon number of a circle representation can be computed in polynomial time .
Edit intent: clarity
Original:  of a circle graph G is the minimum k such that G is a k-polygon graph and the polygon number of a circle representation is the minimum number of corners that must be added to the circle to produce a polygon representation . Given a circle graph G and an integer k, determining whether \psi \gp (G) \le k is NP-complete, while the problem is solvable in polynomial time for fixed k , and the polygon number of a circle representation can be computed in polynomial time .
Revised:  of a circle graph G is the minimum k such that G is a k-polygon graph and the polygon number of a circle representation is the minimum number of corners that must be added to the circle to produce a polygon representation . Given a circle graph G and an integer k, determining whether \gp (G) \le k is NP-complete, while the problem is solvable in polynomial time for fixed k , and the polygon number of a circle representation can be computed in polynomial time .
Edit intent: clarity
Original:  of a circle graph G is the minimum k such that G is a k-polygon graph and the polygon number of a circle representation is the minimum number of corners that must be added to the circle to produce a polygon representation . Given a circle graph G and an integer k, determining whether \psi \gp (G) \le k is NP-complete, while the problem is solvable in polynomial time for fixed k , and the polygon number of a circle representation can be computed in polynomial time .
Revised:  of a circle graph G is the minimum k such that G is a k-polygon graph and the polygon number of a circle representation is the minimum number of corners that must be added to the circle to produce a polygon representation . Given a circle graph G and an integer k, determining whether \psi \gp (G) \le k is NP-complete, while the problem is solvable in polynomial time for fixed k .
Edit intent: clarity
Original:  In this paper, we give bounds on \psi\gp (G) when G is an arbitrary circle graph -- upper bounds in terms of the independence number , the clique cover number, and the number of vertices of G, and a lower bound in terms of the asteroidal number of G -- and show that \psi(G) is equal to the asteroidal number of G when G is a connected nonclique distance hereditary graph .
Revised:  In this paper, we show that\gp (G) when G is an arbitrary circle graph -- upper bounds in terms of the independence number , the clique cover number, and the number of vertices of G, and a lower bound in terms of the asteroidal number of G -- and show that \psi(G) is equal to the asteroidal number of G when G is a connected nonclique distance hereditary graph .
Edit intent: clarity
Original:  In this paper, we give bounds on \psi\gp (G) when G is an arbitrary circle graph -- upper bounds in terms of the independence number , the clique cover number, and the number of vertices of G, and a lower bound in terms of the asteroidal number of G -- and show that \psi(G) is equal to the asteroidal number of G when G is a connected nonclique distance hereditary graph .
Revised:  In this paper, we give bounds on \psi\gp (G) when G is an arbitrary circle graph -- upper bounds in terms of the independence number , the clique cover number, and the number of vertices of G, and equal to the asteroidal number of G when G is a connected nonclique distance hereditary graph .
Edit intent: clarity