wanyu/IteraTeR_v2 huggingface dataset:
Original:  The modeling approach combines Lattice Boltzmann method for simulating flow, hybrid cell membrane model to represent physiological elastic properties of a platelet and stochastic receptor-ligand binding model to describe biologically justified adhesion kinetics .
Revised:  The modeling approach combines Lattice Boltzmann method for simulating flow, hybrid cell membrane model to represent physiological elastic properties of a platelet , stochastic receptor-ligand binding model to describe biologically justified adhesion kinetics .
Edit intent: fluency
Original: We present an effect inference algorithm for Eff, an ML-style language with handlers of not only exceptions, but of any other algebraic effect such as input & output, mutable references , non-determinism and many others.
Revised: We present an effect inference algorithm for an ML-style language with handlers of not only exceptions, but of any other algebraic effect such as input & output, mutable references , non-determinism and many others.
Edit intent: clarity
Original: We present an effect inference algorithm for Eff, an ML-style language with handlers of not only exceptions, but of any other algebraic effect such as input & output, mutable references , non-determinism and many others.
Revised: We present an effect inference algorithm for Eff, an ML-style language with handlers of not only exceptions, but of any other algebraic effect such as input & output, mutable references and many others.
Edit intent: clarity
Original:  Since a detailed description of the dynamics is virtually unattainable , a more sensible goal is to recognize and mark the transition of a system between qualitatively different regimes of behavior.
Revised:  Since a detailed description of the dynamics is virtually unattainable , a more sensible goal is to recognize and mark transitions of a system between qualitatively different regimes of behavior.
Edit intent: fluency
Original:  The method uses trigraphs, introduced by Chudnovsky, and relies on the good behavior of both problems with respect to 2-join decomposition proved by Chudnovsky, Trotignon, Trunck and Vu\v{skovi\'c.
Revised:  The method uses trigraphs, introduced by Chudnovsky, and relies on the good behavior of 2-join with respect to 2-join decomposition proved by Chudnovsky, Trotignon, Trunck and Vu\v{skovi\'c.
Edit intent: clarity
Original:  The method uses trigraphs, introduced by Chudnovsky, and relies on the good behavior of both problems with respect to 2-join decomposition proved by Chudnovsky, Trotignon, Trunck and Vu\v{skovi\'c.
Revised:  The method uses trigraphs, introduced by Chudnovsky, and relies on the good behavior of both problems with respect to kovi\'c.
Edit intent: coherence
Original:  We address this question by implementing and evaluating efficient algorithms for accurately approximating the volume of H-polytopes in high dimensions (  one hundred).
Revised:  We address this question by implementing and evaluating efficient algorithms for accurately approximating the polytope's volume in high dimensions ( one hundred).
Edit intent: clarity
Original:  The Bayesian interpretation of inverse problem regularization is useful since it allows one to explore uncertainty in the solution of the inverse problem , as well as examine assumptions made in solving the problem -- namely  the subjective choice of regularization . Using a path-integral approach may be preferable to standard computational methods of inversion which typically involve the use of Markov-Chain-Monte-Carlo (MCMC) methods .
Revised:  The Bayesian interpretation of inverse problem regularization is useful since it allows one to explore uncertainty in the solution of inverse problems , as well as examine assumptions made in solving the problem -- namely the subjective choice of regularization . Using a path-integral approach may be preferable to standard computational methods of inversion which typically involve the use of Markov-Chain-Monte-Carlo (MCMC) methods .
Edit intent: fluency
Original:  The Bayesian interpretation of inverse problem regularization is useful since it allows one to explore uncertainty in the solution of the inverse problem , as well as examine assumptions made in solving the problem -- namely  the subjective choice of regularization . Using a path-integral approach may be preferable to standard computational methods of inversion which typically involve the use of Markov-Chain-Monte-Carlo (MCMC) methods .
Revised:  The Bayesian interpretation of inverse problem regularization is useful since it allows one to explore uncertainty in the solution of the inverse problem , as well as examine assumptions made in solving the problem -- namely whether the subjective choice of regularization . Using a path-integral approach may be preferable to standard computational methods of inversion which typically involve the use of Markov-Chain-Monte-Carlo (MCMC) methods .
Edit intent: fluency
Original:  In this manuscript, we develop a path-integral formulation for inverse problems and illustrate it on inverse problems in potential theory involving the Poisson equation.
Revised:  In this manuscript, we illustrate a path-integral formulation for inverse problems and illustrate it on inverse problems in potential theory involving the Poisson equation.
Edit intent: coherence
Original:  Perturbative path-integral approaches, while offering alternatives to computational approaches like Markov-Chain-Monte-Carlo (MCMC), also provide natural starting points for MCMC methods that can be used to refine perturbative approximations.
Revised:  Perturbative path-integral approaches, while offering alternatives to computational approaches like Markov-Chain-Monte-Carlo (MCMC), also provide natural starting points for MCMC methods that can be used to refine approximations.
Edit intent: fluency
Original:  In this manuscript, we illustrate a path-integral formulation for inverse problems and demonstrate it on an inverse problem in membrane biophysics as well as inverse problems in potential theory involving the Poisson equation.
Revised:  In this manuscript, we illustrate a path-integral formulation for inverse problems and demonstrate it on an inverse problem in membrane biophysics as well as inverse problems in potential theories involving the Poisson equation.
Edit intent: fluency
Original: The pairwise comparisons method is a convenient tool used when the relative order between different concepts (alternatives) need to be determined.
Revised: The pairwise comparisons method is a convenient tool used when the relative order among different concepts (alternatives) need to be determined.
Edit intent: fluency
Original: The pairwise comparisons method is a convenient tool used when the relative order between different concepts (alternatives) need to be determined.
Revised: The pairwise comparisons method is a convenient tool used when the relative order between different concepts (alternatives) needs to be determined.
Edit intent: fluency
Original:  One of the popular implementation of the method is based on solving  eigenvalue problem for the pairwise comparisons matrix.
Revised:  One popular implementation of the method is based on solving eigenvalue problem for the pairwise comparisons matrix.
Edit intent: clarity
Original:  One of the popular implementation of the method is based on solving  eigenvalue problem for the pairwise comparisons matrix.
Revised:  One of the popular implementation of the method is based on solving an eigenvalue problem for the pairwise comparisons matrix.
Edit intent: fluency
Original:  In such a case as the ranking result the principal eigenvector of the pairwise comparison matrix is adopted, whilst the eigenvalue is used to determine the index of inconsistency.
Revised:  In such cases the ranking result the principal eigenvector of the pairwise comparison matrix is adopted, whilst the eigenvalue is used to determine the index of inconsistency.
Edit intent: fluency
Original:  Abstract Studies on the eigenvalue based inconsistency index  led the author to propose the more general index of discrepancy.
Revised:  Studies on the eigenvalue based inconsistency index led the author to propose the more general index of discrepancy.
Edit intent: fluency
Original:  Abstract Studies on the eigenvalue based inconsistency index  led the author to propose the more general index of discrepancy.
Revised:  Abstract Studies on the eigenvalue based inconsistency index have led the author to propose the more general index of discrepancy.
Edit intent: fluency
Original:  Abstract Studies on the eigenvalue based inconsistency index  led the author to propose the more general index of discrepancy.
Revised:  Abstract Studies on the eigenvalue based inconsistency index led the author to propose a more general index of discrepancy.
Edit intent: fluency
Original:  It describes how far the input to the ranking procedure is from the ranking result.
Revised:  This describes how far the input to the ranking procedure is from the ranking result.
Edit intent: fluency
Original:  It may help to detect, localize and quantify possible problems related to the input data as well as the ranking procedure.
Revised:  It may help to detect, localize and quantify possible problems related to the input data and the ranking procedure.
Edit intent: clarity
Original:  Some of its properties  related to the eigenvalue based inconsistency index and the condition of order preservation  are presented as appropriate theorems.
Revised:  Some of its properties - those related to the eigenvalue based inconsistency index and the condition of order preservation are presented as appropriate theorems.
Edit intent: clarity
Original:  Some of its properties  related to the eigenvalue based inconsistency index and the condition of order preservation  are presented as appropriate theorems.
Revised:  Some of its properties related to the eigenvalue based inconsistency index and the condition of order preservation - are presented as appropriate theorems.
Edit intent: fluency
Original: Given a large database, we want to compute lineage for sum database queries, i. e., appropriately select a small piece of the data for Aggregate Lineage that is useful to explain answers of SUM aggregate queries.
Revised: AI systems typically make decisions and find patterns in data based on the computation of aggregate and specifically sum functions, expressed as queries, on data's attributes. This computation can become costly or even inefficient when these queries concern the whole or big parts of the data for Aggregate Lineage that is useful to explain answers of SUM aggregate queries.
Edit intent: clarity
Original: We describe efficient algorithms to check if the Galois group of a polynomial p with integer coefficients is "generic" (which, for arbitrary polynomials of degree n means the full symmetric group S_n, while for reciprocal polynomials of degree 2n it means the hyperoctahedral group C_2 \wr S_n.).
Revised: We describe efficient algorithms to check if the Galois group of a polynomial p with integer coefficients is ``generic'' (which, for arbitrary polynomials of degree n means the full symmetric group S_n, while for reciprocal polynomials of degree 2n it means the hyperoctahedral group C_2 \wr S_n.).
Edit intent: fluency
Original:  We  show how these algorithms give efficient algorithms to check if a set of matrices in \mathrm{SL (n, Z) or \mathrm{Sp( 2n, Z) generate a Zariski dense subgroup.
Revised:  We show how these algorithms give efficient algorithms to check if a set of matrices in \mathrm{SL (n, Z) or \mathop{Sp 2n, Z) generate a Zariski dense subgroup.
Edit intent: fluency
Original:  is of order O(n^4 \log n ) and in \mathrm{Sp\|)\log \epsilon and in Sp} (2n, \mathbb{Z}) the complexity is of order O(n^8 \log n \|)\log \epsilon In general semisimple groups we show that Zariski density can be confirmed or denied in time of order O(n^14 \log \|\mathcal{G}\|\log \epsilon), where \epsilon is the probability of a wrong "NO" answer, while \|\mathcal{G}\| is the measure of complexity of the input (the maximum of the Frobenius norms of the generating matrices} ).
Revised:  is of order O(n^4 \log n \log \|\mathcal{G\|)\log \epsilon and in Sp} (2n, \mathbb{Z}) the complexity is of order O(n^8 \log n \|)\log \epsilon In general semisimple groups we show that Zariski density can be confirmed or denied in time of order O(n^14 \log \|\mathcal{G}\|\log \epsilon), where \epsilon is the probability of a wrong "NO" answer, while \|\mathcal{G}\| is the measure of complexity of the input (the maximum of the Frobenius norms of the generating matrices} ).
Edit intent: clarity
Original:  is of order O(n^4 \log n ) and in \mathrm{Sp\|)\log \epsilon and in Sp} (2n, \mathbb{Z}) the complexity is of order O(n^8 \log n \|)\log \epsilon In general semisimple groups we show that Zariski density can be confirmed or denied in time of order O(n^14 \log \|\mathcal{G}\|\log \epsilon), where \epsilon is the probability of a wrong "NO" answer, while \|\mathcal{G}\| is the measure of complexity of the input (the maximum of the Frobenius norms of the generating matrices} ).
Revised:  is of order O(n^4 \log n ) and in \mathrm{Sp\|)\log \epsilon and in Sp} (2n, \mathbb{Z}) the complexity is of order O(n^8 \log n \log \|\mathcal{G\|)\log \epsilon In general semisimple groups we show that Zariski density can be confirmed or denied in time of order O(n^14 \log \|\mathcal{G}\|\log \epsilon), where \epsilon is the probability of a wrong "NO" answer, while \|\mathcal{G}\| is the measure of complexity of the input (the maximum of the Frobenius norms of the generating matrices} ).
Edit intent: fluency
Original: We describe efficient algorithms to check if the Galois group of a polynomial p with integer coefficients is ``generic'' (which, for arbitrary polynomials of degree n means the full symmetric group S_n, while for reciprocal polynomials of degree 2n it means the hyperoctahedral group C_2 \wr S_n.).
Revised: We describe efficient algorithms to check if the Galois group of a polynomial p with integer coefficients is "generic" (which, for arbitrary polynomials of degree n means the full symmetric group S_n, while for reciprocal polynomials of degree 2n it means the hyperoctahedral group C_2 \wr S_n.).
Edit intent: fluency
Original: Let k be a positive integer and let \mathcal{X a k-fold packing of infinitely many simply connected compact setsin the plane, that is, assume that every point belongs to at most k sets.
Revised: Suppose k is a positive integer and let \mathcal{X a k-fold packing of infinitely many simply connected compact setsin the plane, that is, assume that every point belongs to at most k sets.
Edit intent: clarity
Original: Let k be a positive integer and let \mathcal{X a k-fold packing of infinitely many simply connected compact setsin the plane, that is, assume that every point belongs to at most k sets.
Revised: Let k be a positive integer and \mathcal{X a k-fold packing of infinitely many simply connected compact setsin the plane, that is, assume that every point belongs to at most k sets.
Edit intent: fluency
Original:  Suppose that there is a function f(n)=o(n^2) with the property that any n members of X surround at most f(n) holes, which means that the complement of their union has at most f(n) bounded connected components.
Revised:  Suppose there is a function f(n)=o(n^2) with the property that any n members of X surround at most f(n) holes, which means that the complement of their union has at most f(n) bounded connected components.
Edit intent: fluency
Original:  Suppose that there is a function f(n)=o(n^2) with the property that any n members of X surround at most f(n) holes, which means that the complement of their union has at most f(n) bounded connected components.
Revised:  Suppose that there is a function f(n)=o(n^2) with the property that any n members of X determine at most f(n) holes, which means that the complement of their union has at most f(n) bounded connected components.
Edit intent: clarity
Original: The effect of disturbance on a model ecosystem of sessile and mutually competitive species [ Math- iesen et al.
Revised: The effect of disturbance on a model ecosystem of sessile and mutually competitive species [ Mathiesen et al.
Edit intent: fluency
Original:  Thus low latency networking , not well supported by current network design, is becoming a major concern of both industry and academia.
Revised:  Thus low latency networking is becoming a major concern of both industry and academia.
Edit intent: clarity
Original:  We also present our perspective of the research challenges and opportunities, hoping to aspire more future work in this space.
Revised:  We also present our perspectives of the research challenges and opportunities, hoping to aspire more future work in this space.
Edit intent: fluency
Original:  Here we fill this gap by using first, a short time scale for data collection of scanning micro X-ray diffraction microscopy and second, methods of statistical physics for the analysis of time evolution of this non-invasive local structure experimental approach .
Revised:  Here we report the feasibility of the application of an innovative non-invasive local structure experimental approach .
Edit intent: clarity
Original: In the Hausdorff Voronoi diagram of a set of point-clusters in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P while the diagram is defined in a nearest sense .
Revised: In the Hausdorff Voronoi diagram of a family of clusters of points in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P while the diagram is defined in a nearest sense .
Edit intent: clarity
Original: In the Hausdorff Voronoi diagram of a set of point-clusters in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P while the diagram is defined in a nearest sense .
Revised: In the Hausdorff Voronoi diagram of a set of point-clusters in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P , and the diagram is defined in a nearest sense .
Edit intent: coherence
Original:  In this paper , we consider non-crossing clusters  , for which the combinatorial complexity of the  diagram is linear in the total number n of points on the convex hulls of all clusters.
Revised:  In this paper we consider non-crossing clusters , for which the combinatorial complexity of the diagram is linear in the total number n of points on the convex hulls of all clusters.
Edit intent: fluency
Original:  In this paper , we consider non-crossing clusters  , for which the combinatorial complexity of the  diagram is linear in the total number n of points on the convex hulls of all clusters.
Revised:  In this paper , we consider non-crossing clusters , for which the combinatorial complexity of the diagram is linear in the total number of points, n, on the convex hulls of all clusters.
Edit intent: clarity
Original:  We present a randomized incremental construction, based on point-location, to compute the diagram in expected O(n\log ^2{n ) time and expected O(n) space , which considerably improves previous results.
Revised:  We present a randomized incremental construction, based on point location, that computes this diagram in expected O(n\log ^2{n ) time and expected O(n) space , which considerably improves previous results.
Edit intent: clarity
Original: In the Hausdorff Voronoi diagram of a family of clusters of points in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P, and the diagram is defined in a nearest-neighbor sense for the input clusters.
Revised: In the Hausdorff Voronoi diagram of a family of clusters of points in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P, and the diagram is defined in a nearest-neighbor sense for the input clusters.
Edit intent: fluency
Original:  In this paper we consider  non-crossing  clusters in the plane, for which the combinatorial complexity of the Hausdorff Voronoi diagram is linear in the total number of points, n, on the convex hulls of all clusters.
Revised:  In this paper we consider non-crossing " clusters in the plane, for which the combinatorial complexity of the Hausdorff Voronoi diagram is linear in the total number of points, n, on the convex hulls of all clusters.
Edit intent: fluency
Original:  It is known that RNDB and WSDB are equivalent , in the sense that they require an identical set of conditions on the rate constants .
Revised:  It is known that RNDB and WSDB are equivalent .
Edit intent: clarity
Original:  We prove that WSDB and MCDB are also intimately related but are not equivalent , although they are sometimes confused for each other .
Revised:  We prove that WSDB and MCDB are also intimately related but are not equivalent .
Edit intent: coherence
Original:  Using the fact that RNDB implies MCDB, we give a new algorithm to find conditions on the rate constants that are required for MCDB and we obtain an explicit formula for the stationary distribution of networks with RNDB .
Revised:  Using the fact that RNDB implies MCDB, we give a new algorithm to find conditions on the rate constants that are required for MCDB .
Edit intent: coherence
Original:   We demonstrated state-of-the-art classification performances with NIN on CIFAR-10 /100, SVHN and MINST datasets.
Revised:  We demonstrated state-of-the-art classification performances with NIN on CIFAR-10 , CIFAR-100 and SVHN datasets.
Edit intent: clarity
Original: We propose a novel  network structure called "Network In Network" (NIN) to enhance the model discriminability for local receptive fields .
Revised: We propose a novel network structure called "Network In Network" (NIN) to enhance model discriminability for local receptive fields .
Edit intent: fluency
Original:  Instead, we build micro neural networks with more complex structures to handle the variance of the local receptive fields .
Revised:  Instead, we build micro neural networks with more complex structures to abstract the data within the receptive field .
Edit intent: clarity
Original:  We instantiate the micro neural network with a nonlinear multiple layer structure which is a potent function approximator.
Revised:  We instantiate the micro neural network with a multilayer perceptron, which is a potent function approximator.
Edit intent: clarity
Original:  The feature maps are obtained by sliding the micro networks over the input in a similar manner of CNNand then fed into the next layer.
Revised:  The feature maps are obtained by sliding the micro networks over the input in a similar manner as CNN; they are then fed into the next layer.
Edit intent: clarity
Original:  With the enhanced local modeling via  micro network, we are able to utilize global average pooling over feature maps in the classification layer, which is more interpretable and less prone to overfitting than traditional fully connected layers.
Revised:  With the enhanced local modeling via the micro network, we are able to utilize global average pooling over feature maps in the classification layer, which is more interpretable and less prone to overfitting than traditional fully connected layers.
Edit intent: fluency
Original:  With the enhanced local modeling via  micro network, we are able to utilize global average pooling over feature maps in the classification layer, which is more interpretable and less prone to overfitting than traditional fully connected layers.
Revised:  With the enhanced local modeling via micro network, we are able to utilize global average pooling over feature maps in the classification layer, which is easier to interpret and less prone to overfitting than traditional fully connected layers.
Edit intent: clarity
Original:  We demonstrated  state-of-the-art classification performances with NIN on CIFAR-10 , CIFAR-100 and SVHN datasets.
Revised:  We demonstrated the state-of-the-art classification performances with NIN on CIFAR-10 , CIFAR-100 and SVHN datasets.
Edit intent: fluency