wanyu/IteraTeR_v2 huggingface dataset:
Original: Let A(x)=A _0 +x _1A_1 + \cdots +x _nA_n be a linear matrix, or pencil, generated by given symmetric matrices A _0,A_1,\ldots,A_n of size m with rational entries.
Revised: Let A(x)=A \_0 +x _1A_1 + \cdots +x _nA_n be a linear matrix, or pencil, generated by given symmetric matrices A _0,A_1,\ldots,A_n of size m with rational entries.
Edit intent: fluency
Original: Learning novel and interesting concepts and relations from relational databases is an important problem with many applications in database systems and machine learning.
Revised: Learning novel concepts and relations from relational databases is an important problem with many applications in database systems and machine learning.
Edit intent: clarity
Original:  Relational learning algorithms generally leverage the properties of the database schema to find the definition of the target concept in terms of the existing relations in the database.
Revised:  Relational learning algorithms learn the definition of a new relation in terms of the existing relations in the database.
Edit intent: clarity
Original:  Relational learning algorithms generally leverage the properties of the database schema to find the definition of the target concept in terms of the existing relations in the database.
Revised:  Relational learning algorithms generally leverage the properties of the database schema to find the definition of the target concept in terms of existing relations in the database.
Edit intent: fluency
Original:  Nevertheless, it is well established that the same data set may be represented under different schemas for various reasons, such as efficiency, data quality, and usability.
Revised:  Nevertheless, the same data set may be represented under different schemas for various reasons, such as efficiency, data quality, and usability.
Edit intent: coherence
Original:  Unfortunately, many current learning algorithms tend to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency , which complicates their off-the-shelf application.
Revised:  Unfortunately, the output of current relational learning algorithms tends to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency , which complicates their off-the-shelf application.
Edit intent: clarity
Original:  Unfortunately, many current learning algorithms tend to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency , which complicates their off-the-shelf application.
Revised:  Unfortunately, many current learning algorithms tend to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency . This variation complicates their off-the-shelf application.
Edit intent: clarity
Original:  In this paper, we  formalize the property of schema independence of relational learning algorithms, and study both the theoretical and empirical dependence of existing algorithms on the common class of vertical (de) composition schema transformations.
Revised:  In this paper, we formalize the property of schema independence of relational learning algorithms, and study both the theoretical and empirical dependence of existing algorithms on the common class of (de) composition schema transformations.
Edit intent: clarity
Original:  We prove that practical top-down algorithms are generally not schema independent , while, in contrast, two bottom-up algorithms Golem and ProGolem are schema independent with some modifications .
Revised:  We prove that practical top-down algorithms are generally not schema independent .
Edit intent: coherence
Original: Deep convolutional neural networks ( DCNN ) have attracted much attention recently, and have been shown able to recognize thousands of object categories in natural image databases.
Revised: Deep convolutional neural networks ( DCNNs ) have attracted much attention recently, and have been shown able to recognize thousands of object categories in natural image databases.
Edit intent: clarity
Original: Deep convolutional neural networks ( DCNN ) have attracted much attention recently, and have been shown able to recognize thousands of object categories in natural image databases.
Revised: Deep convolutional neural networks ( DCNN ) have attracted much attention recently, and have shown to be able to recognize thousands of object categories in natural image databases.
Edit intent: fluency
Original: To investigate this issue , we benchmarked 8 state-of-the-art DCNNs, the HMAX model, and a baseline  model and compared the results to humans with backward masking.
Revised: To investigate this issue , we benchmarked eight state-of-the-art DCNNs, the HMAX model, and a baseline model and compared the results to humans with backward masking.
Edit intent: fluency
Original: To investigate this issue , we benchmarked 8 state-of-the-art DCNNs, the HMAX model, and a baseline  model and compared the results to humans with backward masking.
Revised: To investigate this issue , we benchmarked 8 state-of-the-art DCNNs, the HMAX model, and a baseline model and compared their results to those of humans with backward masking.
Edit intent: clarity
Original: Network techniques have been used to visualize bibliometric data for many years.
Edit intent: clarity
Original:  This gives the proportion of highly cited papers from an institution, and is considered generally as a robust indicator for measuring impact  .
Revised:  This gives the proportion of highly cited papers from an institution, and is considered generally as an indicator for measuring impact .
Edit intent: clarity
Original:  Within single subject areas, we have investigated and visualized how successfully overall an institution (reference institution) has collaborated (compared to all the other institutions in a subject area), and with which other institutions (network institutions) an institution (reference institution ) has collaborated particularly successfully.
Revised:  Within single subject areas, we have investigated and visualized how successfully overall an institution (reference institution) has collaborated (compared to all the other institutions in a subject area), and with which other institutions (network institutions) a reference institution has collaborated particularly successfully.
Edit intent: fluency
Original: We study diffusion on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential.
Revised: We study spreading on networks where the contact dynamics between the nodes is governed by a random process and where the inter-contact time distribution may differ from the exponential.
Edit intent: clarity
Original:  We consider a process of imperfect diffusion , where transmission is successful with a determined probability at each contact.
Revised:  We consider a process of imperfect spreading , where transmission is successful with a determined probability at each contact.
Edit intent: clarity
Original:  The possibility of effective classical computations of average particle numbers in single-mode measurement for bosonic linear optical networks is shown using the analogy.
Revised:  The possibility of effective classical computations of average particle numbers in single-mode measurement for bosonic linear optical networks is treated using the analogy.
Edit intent: clarity
Original:  A difference between couple relevant models is discussed in presented work.
Revised:  A difference between a pair of relevant models is discussed in presented work.
Edit intent: fluency
Original: Expressions with permanents in quantum processes with bosons deserved recently certain attention  .
Revised: Particular complexity of quantum processes with bosons deserved recently certain attention .
Edit intent: clarity
Original:  A difference between a pair of relevant models is discussed in presented work.
Revised:  A difference between two relevant models is discussed in presented work.
Edit intent: fluency
Original:  The second model has certain resemblance with matchgate circuits also known as "fermionic linear optics" and effectively simulated on classical computer.
Revised:  The second model has certain resemblance with "fermionic linear optics" and effectively simulated on classical computer.
Edit intent: clarity
Original:  The second model has certain resemblance with matchgate circuits also known as "fermionic linear optics" and effectively simulated on classical computer.
Revised:  The second model has certain resemblance with matchgate circuits also known as "fermionic linear optics" effectively simulated on classical computer.
Edit intent: coherence
Original:  The possibility of effective classical computations of average particle numbers in single-mode measurement for bosonic linear optical networks is treated using the analogy  .
Revised:  Simplicity of average particle number evaluation for single-mode measurement for bosonic linear optical networks is treated using the analogy .
Edit intent: clarity
Original:  More elaborated modelhas certain resemblance with "fermionic linear optics"  effectively simulated on classical computer.
Revised:  More elaborated modelhas certain resemblance with "fermionic linear optics" is effectively simulated on classical computer.
Edit intent: clarity
Original:  Simplicity of average particle number evaluation for single-mode measurements in both bosonic and fermionic case is treated using the analogy.
Revised:  The comparison of bosonic and fermionic case is treated using the analogy.
Edit intent: clarity
Original:  In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other  double stranded DNA is taken to have an intrinsic rigidity for bending.
Revised:  In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other the double stranded DNA is taken to have an intrinsic rigidity for bending.
Edit intent: coherence
Original:  The change in the elastic constant for the flexible case is shown to be due to the thermally generated bubbles  .
Revised:  The change in the elastic constant for the flexible case due to the thermally generated bubbles .
Edit intent: clarity
Original: The temperature dependence of the DNA flexibility is studied in the presence of stretching and unzipping forces.
Revised: The temperature dependence of DNA flexibility is studied in the presence of stretching and unzipping forces.
Edit intent: fluency
Original:  In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other the double stranded DNA is taken to have an intrinsic rigidity for bending.
Revised:  In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other the double-stranded DNA is taken to have an intrinsic rigidity for bending.
Edit intent: fluency
Original:  The change in the elastic constant for the flexible case due to the thermally generated bubbles has been obtained exactly.
Revised:  The change in the elastic constant for the flexible case due to thermally generated bubbles has been obtained exactly.
Edit intent: fluency
Original:  The change in the elastic constant for the flexible case due to the thermally generated bubbles has been obtained exactly.
Revised:  The change in the elastic constant for the flexible case due to the thermally generated bubbles is obtained exactly.
Edit intent: clarity
Original:  As depicted in the teaser above, we demonstrate the applicability of such extensions in two application problems;
Revised:  We demonstrate the applicability of such extensions in two application problems;
Edit intent: coherence
Original:  Using the ecological examplethat led us to discover this problem , we show how these estimation problems can affect ecological inference.
Revised:  Using an animal movement example , we show how these estimation problems can affect ecological inference.
Edit intent: clarity
Original:  This  enables us to capture market dynamics at various timescalesand shed light on mechanisms underlying certain market behaviors  such as transitions between bull- and bear markets and the self-similar behavior of price changes.
Revised:  This enables us to capture market dynamics at various timescalesand shed light on mechanisms underlying certain market behaviors , such as transitions between bull- and bear markets and the self-similar behavior of price changes.
Edit intent: fluency
Original:  Using the model, we design the prototypes of algorithmic strategies that utilize news flow, quantified and measured, as the only input to trade on market return forecasts over multiple horizons, from days to months.
Revised:  Using the model, we design algorithmic strategies that utilize news flow, quantified and measured, as the only input to trade on market return forecasts over multiple horizons, from days to months.
Edit intent: clarity
Original:  Namely, the comparison of different community detection methods, and the study of the the consistency, robustness and temporal evolution of the hierarchical modular structure of networks.
Revised:  Namely, the comparison of different community detection methods, and the study of the consistency, robustness and temporal evolution of the hierarchical modular structure of networks.
Edit intent: fluency
Original:  The resulting eigenvectors encode the embedding coordinates for the training samples only, preventing the transformation of novel data samples without recomputation .
Revised:  The resulting eigenvectors encode the embedding coordinates for the training samples only, and so the embedding of novel data samples without recomputation .
Edit intent: clarity
Original:  In this paper, we present a method for out-of sample extension of graph embeddings that uses deep neural networks (DNN) to parametrically approximate these nonlinear maps.
Revised:  In this paper, we present a method for the out-of-sample extension of graph embeddings that uses deep neural networks (DNN) to parametrically approximate these nonlinear maps.
Edit intent: fluency
Original:  In this paper, we present a method for out-of sample extension of graph embeddings that uses deep neural networks (DNN) to parametrically approximate these nonlinear maps.
Revised:  In this paper, we present a method for out-of sample extension of graph embeddings using deep neural networks (DNN) to parametrically approximate these nonlinear maps.
Edit intent: coherence
Original: This paper studies the synchronization problem of a dynamical network with event-based communication , where each node communicates to its neighbours only when an event-triggering condition is fulfilled .
Revised: This paper studies synchronization of dynamical networks with event-based communication , where each node communicates to its neighbours only when an event-triggering condition is fulfilled .
Edit intent: clarity
Original: This paper studies the synchronization problem of a dynamical network with event-based communication , where each node communicates to its neighbours only when an event-triggering condition is fulfilled .
Revised: This paper studies the synchronization problem of a dynamical network with event-based communication .
Edit intent: clarity
Original:  Then, with the assistance of the two estimators, a distributed event-triggering rule  with a dwell-time is designed such that the network achieves synchronization asymptotically , and meanwhile no Zeno behaviour occurs .
Revised:  Then, with these two estimators, a distributed event-triggering rule with a dwell-time is designed such that the network achieves synchronization asymptotically , and meanwhile no Zeno behaviour occurs .
Edit intent: clarity
Original:  Then, with the assistance of the two estimators, a distributed event-triggering rule  with a dwell-time is designed such that the network achieves synchronization asymptotically , and meanwhile no Zeno behaviour occurs .
Revised:  Then, with the assistance of the two estimators, a distributed event-triggering rule with a dwell-time is designed such that the network achieves synchronization asymptotically with no Zeno behaviours .
Edit intent: coherence
Original:  The designed event-triggering rule only depends on the information that each node can obtain, and thus can be implemented in a decentralized way .
Revised:  The designed ETR only depends on the information that each node can obtain, and thus can be implemented in a decentralized way .
Edit intent: clarity
Original:  Then, with these two estimators, a distributed event-triggering rule (ETR) with a dwell-time is designed such that the network achieves synchronization asymptotically with no Zeno behaviours.
Revised:  Then, with these two estimators, a distributed event-triggering rule (ETR) with a dwell time is designed such that the network achieves synchronization asymptotically with no Zeno behaviours.
Edit intent: fluency
Original: Dzhafarov, Zhang, and Kujala ( arXiv:1504.07422 ) reviewed several behavioral data sets imitating the formal design of the quantum-mechanical contextuality experiments (such as EPR-Bell or Leggett-Garg ones), the conclusion was that contextuality was not present in any of these data sets .
Revised: Dzhafarov, Zhang, and Kujala ( arXiv:1504.07422 ) reviewed several behavioral data sets imitating the formal design of the quantum-mechanical contextuality experiments . The conclusion was that contextuality was not present in any of these data sets .
Edit intent: coherence
Original: Dzhafarov, Zhang, and Kujala ( arXiv:1504.07422 ) reviewed several behavioral data sets imitating the formal design of the quantum-mechanical contextuality experiments (such as EPR-Bell or Leggett-Garg ones), the conclusion was that contextuality was not present in any of these data sets .
Revised: Dzhafarov, Zhang, and Kujala ( arXiv:1504.07422 ) reviewed several behavioral data sets imitating the formal design of the quantum-mechanical contextuality experiments (such as EPR-Bell or Leggett-Garg ones), the conclusion was that none of these data sets .
Edit intent: clarity
Original:  We show that their experimental data exhibit no contextuality in the sense of the general definition of contextuality proposed in Dzhafarov, Kujala, and Larsson ( Foundation of Physics 7, 762-782, 2015), while the traditional , narrow definition of contextuality does not apply to their data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signaling condition, no-disturbance principle, etc.).
Revised:  We show that their experimental data exhibit no contextuality in the sense of the general definition of contextuality proposed in Dzhafarov, Kujala, and Larsson ( Found. Phys. 7, 762-782, 2015), while the traditional , narrow definition of contextuality does not apply to their data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signaling condition, no-disturbance principle, etc.).
Edit intent: clarity
Original:  We show that their experimental data exhibit no contextuality in the sense of the general definition of contextuality proposed in Dzhafarov, Kujala, and Larsson ( Foundation of Physics 7, 762-782, 2015), while the traditional , narrow definition of contextuality does not apply to their data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signaling condition, no-disturbance principle, etc.).
Revised:  We show that their experimental data exhibit no contextuality in the sense of the general definition of contextuality proposed in Dzhafarov, Kujala, and Larsson ( Foundation of Physics 7, 762-782, 2015), while the traditional definition of contextuality does not apply to their data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signaling condition, no-disturbance principle, etc.).
Edit intent: clarity
Original:  We show that their experimental data exhibit no contextuality in the sense of the general definition of contextuality proposed in Dzhafarov, Kujala, and Larsson ( Foundation of Physics 7, 762-782, 2015), while the traditional , narrow definition of contextuality does not apply to their data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signaling condition, no-disturbance principle, etc.).
Revised:  We show that their experimental data exhibit no contextuality in the sense of the general definition of contextuality proposed in Dzhafarov, Kujala, and Larsson ( Foundation of Physics 7, 762-782, 2015), while the traditional , narrow definition of contextuality does not apply to these data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signaling condition, no-disturbance principle, etc.).
Edit intent: fluency
Original:  Matroid Intersection: Our runtimes are O( (nr\log ^2 nT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} n)\log nM) and O( ( n^2\log n T_{ind}+n^3 \log^{O(1)} n)\log nM ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Revised:  Matroid Intersection: Our runtimes are O( nrT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} n)\log nM) and O( ( n^2\log n T_{ind}+n^3 \log^{O(1)} n)\log nM ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Edit intent: coherence
Original:  Matroid Intersection: Our runtimes are O( (nr\log ^2 nT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} n)\log nM) and O( ( n^2\log n T_{ind}+n^3 \log^{O(1)} n)\log nM ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Revised:  Matroid Intersection: Our runtimes are O( (nr\log ^2 nT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} (nM)) and O( ( n^2\log n T_{ind}+n^3 \log^{O(1)} n)\log nM ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Edit intent: clarity
Original:  Matroid Intersection: Our runtimes are O( (nr\log ^2 nT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} n)\log nM) and O( ( n^2\log n T_{ind}+n^3 \log^{O(1)} n)\log nM ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Revised:  Matroid Intersection: Our runtimes are O( (nr\log ^2 nT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} n)\log nM) and O( n^2\log n T_{ind}+n^3 \log^{O(1)} n)\log nM ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Edit intent: fluency
Original:  Matroid Intersection: Our runtimes are O( (nr\log ^2 nT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} n)\log nM) and O( ( n^2\log n T_{ind}+n^3 \log^{O(1)} n)\log nM ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Revised:  Matroid Intersection: Our runtimes are O( (nr\log ^2 nT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} n)\log nM) and O( ( n^2\log (nM) T_{ind}+n^3 \log^{O(1)} n)\log nM ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Edit intent: fluency
Original:  Matroid Intersection: Our runtimes are O( (nr\log ^2 nT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} n)\log nM) and O( ( n^2\log n T_{ind}+n^3 \log^{O(1)} n)\log nM ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Revised:  Matroid Intersection: Our runtimes are O( (nr\log ^2 nT_{\text{rank}\log n\log (nM) } +n^3\log^{O(1)} n)\log nM) and O( ( n^2\log n T_{ind}+n^3 \log^{O(1)} (nM) ), achieving the first quadratic bound on the query complexity for the independence and rank oracles.
Edit intent: clarity
Original: We propose a method combining relational-logic representations with deep neural network learning.
Revised: We propose a method combining relational-logic representations with neural network learning.
Edit intent: clarity