wanyu/IteraTeR_v2 huggingface dataset:
Original:  In both missions,  robots were able to cooperate and carry out sequential operations in the correct order without having explicit knowledge about the mission's high-level goals or objectives.
Revised:  In both missions, robots were able to cooperate and carry out sequential operations without having explicit knowledge about the mission's high-level goals or objectives.
Edit intent: clarity
Original:  In both missions,  robots were able to cooperate and carry out sequential operations in the correct order without having explicit knowledge about the mission's high-level goals or objectives.
Revised:  In both missions, robots were able to cooperate and carry out sequential operations in the correct order without having explicit knowledge about the mission's high-level objectives.
Edit intent: clarity
Original:  Our methodology is category-theoretical in nature, where the definition of rule composition operations is encoding the non-deterministic sequential concurrent application of rules in Double-Pushout (DPO) and Sesqui-Pushout (SqPO) rewriting with application conditions based upon M-adhesive categories.
Revised:  Our methodology is category-theoretical in nature, where the definition of rule composition operations encodes the non-deterministic sequential concurrent application of rules in Double-Pushout (DPO) and Sesqui-Pushout (SqPO) rewriting with application conditions based upon M-adhesive categories.
Edit intent: fluency
Original:  We uncover an intricate interplay between the category-theoretical concepts of conditions on rules and morphisms, the compositionality and compatibility of certain shift and transport constructions for conditions, and thirdly the property of associativity of the composition of rules without conditions .
Revised:  We uncover an intricate interplay between the category-theoretical concepts of conditions on rules and morphisms, the compositionality and compatibility of certain shift and transport constructions for conditions, and thirdly the property of associativity of the composition of rules .
Edit intent: clarity
Original:  Lastly, we offer an open source computational jellyfish locomotion model to the science community that can be used as a starting place for future numerical experimentation.
Revised:  Lastly, we offer an open source computational model for jellyfish locomotion is offered to the science community that can be used as a starting place for future numerical experimentation.
Edit intent: clarity
Original: In this work, we examine to what extent the Internet's routing infrastructure needlessly exposes network traffic to nations geographically irrelevant to packet transmission.
Revised: We examine the extent of needless traffic exposure by the routing infrastructure to nations geographically irrelevant to packet transmission.
Edit intent: clarity
Original:  We quantify what countries are geographically logical to see on a network path traveling between two nations through the use of convex hulls circumscribing major population centers , and then compare that to the nation states observed in over 2.5 billion measured paths.
Revised:  We quantify what countries are geographically logical to observe on a network path traveling between two nations through the use of convex hulls circumscribing major population centers , and then compare that to the nation states observed in over 2.5 billion measured paths.
Edit intent: clarity
Original:  We quantify what countries are geographically logical to see on a network path traveling between two nations through the use of convex hulls circumscribing major population centers , and then compare that to the nation states observed in over 2.5 billion measured paths.
Revised:  We quantify what countries are geographically logical to see on a network path traveling between two nations through the use of convex hulls circumscribing major population centers . We then compare that to the nation states observed in over 2.5 billion measured paths.
Edit intent: coherence
Original:  Our results show that 44\% of paths concerning the entire geographic topology of the Internet unnecessarily expose traffic to at least one nation.
Revised:  Our results show that 44\% of paths across the entire geographic topology of the Internet unnecessarily expose traffic to at least one nation.
Edit intent: clarity
Original:  Furthermore, 33\% of  the user experience paths we have examined expose traffic to at least one nation.
Revised:  Furthermore, 33\% of paths in the user experience paths we have examined expose traffic to at least one nation.
Edit intent: clarity
Original:  Furthermore, 33\% of  the user experience paths we have examined expose traffic to at least one nation.
Revised:  Furthermore, 33\% of the user experience subset unnecessarily expose traffic to at least one nation.
Edit intent: clarity
Original:  Finally, we examine what happens when countries exercise both legal and physical control over ASes transiting traffic , gaining access to traffic outside of their geographic borders, but carried by organizations that fall under a particular country's legal jurisdiction.
Revised:  Finally, we consider the scenario where countries exercise both legal and physical control over ASes transiting traffic , gaining access to traffic outside of their geographic borders, but carried by organizations that fall under a particular country's legal jurisdiction.
Edit intent: clarity
Original:  Finally, we examine what happens when countries exercise both legal and physical control over ASes transiting traffic , gaining access to traffic outside of their geographic borders, but carried by organizations that fall under a particular country's legal jurisdiction.
Revised:  Finally, we examine what happens when countries exercise both legal and physical control over ASes transiting traffic , gaining access to traffic outside of their geographic borders, but carried by organizations that fall under the AS's registered country's legal jurisdiction.
Edit intent: clarity
Original:  When considering both the physical and legal countries that a path traverses, our results show that at least 49\% of paths in both measurements expose traffic to a geographically irrelevant country  .
Revised:  At least 49\% of paths in both measurements expose traffic to a geographically irrelevant country .
Edit intent: coherence
Original:  When considering both the physical and legal countries that a path traverses, our results show that at least 49\% of paths in both measurements expose traffic to a geographically irrelevant country  .
Revised:  When considering both the physical and legal countries that a path traverses, our results show that at least 49\% of paths in both measurements expose traffic to a geographically irrelevant country when considering both the physical and legal countries that a path traverses .
Edit intent: coherence
Original: Persistence diagrams, a key descriptor from Topological Data Analysis, encode and summarize all sorts of topological features and have already proved pivotal in many different applications of data science.
Revised: Persistence diagrams, the most common descriptors of Topological Data Analysis, encode and summarize all sorts of topological features and have already proved pivotal in many different applications of data science.
Edit intent: clarity
Original: Persistence diagrams, a key descriptor from Topological Data Analysis, encode and summarize all sorts of topological features and have already proved pivotal in many different applications of data science.
Revised: Persistence diagrams, a key descriptor from Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science.
Edit intent: clarity
Original:  To address this concern  several vectorization methods have been put forward that embed persistence diagrams into either finite-dimensional Euclidean spaces or implicit Hilbert spaces with kernels.
Revised:  To address this concern , several vectorization methods have been put forward that embed persistence diagrams into either finite-dimensional Euclidean spaces or implicit Hilbert spaces with kernels.
Edit intent: fluency
Original:  This layer encompasses most of the vectorization methods of the literature.
Revised:  This layer encompasses most of the vectorization techniques used in the literature.
Edit intent: clarity
Original:  We illustrate its strengths on challenging classification problems on dynamical systems orbit or real-life graph data, with results improving or comparable to the state-of-the-art.
Revised:  We finally showcase the experimental strength of our setup by achieving competitive scores on classification tasks on real-life graph data, with results improving or comparable to the state-of-the-art.
Edit intent: clarity
Original:  A feed-forward neural network approximates the data set and automatic differentiation is used to construct this function libraryand perform regression within the neural network .
Revised:  A neural network approximates the data set and automatic differentiation is used to construct this function libraryand perform regression within the neural network .
Edit intent: clarity
Original:  A feed-forward neural network approximates the data set and automatic differentiation is used to construct this function libraryand perform regression within the neural network .
Revised:  A feed-forward neural network approximates the data and constructs the function library, but it also performs the sparse regression .
Edit intent: clarity
Original:  This construction makes it extremely robust to noise and applicable to small data sets  and, contrary to other deep learning methods, does not require a training set and is impervious to overfitting.
Revised:  This construction makes it extremely robust to noise , applicable to small data sets and, contrary to other deep learning methods, does not require a training set and is impervious to overfitting.
Edit intent: coherence
Original:  This construction makes it extremely robust to noise and applicable to small data sets  and, contrary to other deep learning methods, does not require a training set and is impervious to overfitting.
Revised:  This construction makes it extremely robust to noise and applicable to small data sets , and, contrary to other deep learning methods, does not require a training set and is impervious to overfitting.
Edit intent: fluency
Original:  Encrypted computing is the emerging science and technology of processors that take encrypted inputs to encrypted outputs via encrypted intermediates (at nearly conventional speeds).
Revised:  Encrypted computing is the emerging science and technology of processors that take encrypted inputs to encrypted outputs via encrypted intermediate values (at nearly conventional speeds).
Edit intent: clarity
Original:  A stumbling block has always been that memory addresses are data and good encryption means the encrypted value varies randomly, and that makes hitting any target in memory problematic without address decryption, but decryption anywhere on the memory path would open up many easily exploitable vulnerabilities.
Revised:  A stumbling block has always been that memory addresses are data and good encryption means the encrypted value varies randomly, and that makes hitting any target in memory problematic without address decryption, yet decryption anywhere on the memory path would open up many easily exploitable vulnerabilities.
Edit intent: fluency
Original:  This paper `solves  compilation' for processors without address decryption, covering all of ANSI C while satisfying the required security properties and opening up encrypted computing for the standard software toolchain and infrastructure.
Revised:  This paper `solves compilation' for processors without address decryption, covering all of ANSI C while satisfying the required security properties and opening up the field for the standard software toolchain and infrastructure.
Edit intent: clarity
Original:  This paper `solves  compilation' for processors without address decryption, covering all of ANSI C while satisfying the required security properties and opening up encrypted computing for the standard software toolchain and infrastructure.
Revised:  This paper `solves compilation' for processors without address decryption, covering all of ANSI C while satisfying the required security properties and opening up encrypted computing for the standard software tool-chain and infrastructure.
Edit intent: fluency
Original:  An `obfuscation' for this context is quantified exactly, leading to an argument that security against polynomial-time attacks has been achieved for user data, with or without encryption.
Revised:  That produces the argument referred to above, which may also hold without encryption.
Edit intent: coherence
Original:  Machine learning based solutions have been already used as a tool to supersede signature based anti-malware systems.
Revised:  Machine learning-based solutions have been already used as a tool to supersede signature based anti-malware systems.
Edit intent: fluency
Original:  Machine learning based solutions have been already used as a tool to supersede signature based anti-malware systems.
Revised:  Machine learning based solutions have been already used as a tool to supersede signature-based anti-malware systems.
Edit intent: fluency
Original:  However, malware authors leverage attributes from malicious and legitimate samples to estimate statistical difference in-order to create adversarial examples.
Revised:  However, malware authors leverage features from malicious and legitimate samples to estimate statistical difference in-order to create adversarial examples.
Edit intent: clarity
Original:  By doing this, the classification algorithm inappropriately fits  discriminant function on the set of data points, eventually yielding a higher misclassification rate.
Revised:  By doing this, the classification algorithm inappropriately fits the discriminant function on the set of data points, eventually yielding a higher misclassification rate.
Edit intent: fluency
Original:  Additionally, evasive variants generated by our attacks models when used to harden the developed anti-malware system improves the detection rate  .
Revised:  Additionally, evasive variants generated by our attack models when used to harden the developed anti-malware system improves the detection rate .
Edit intent: fluency
Original: In this paper, we consider the problem of the approximation of the solution of a one-dimensional stochastic differential equation with non-globally Lipschitz drift and diffusion coefficients of form x^\alpha, with \alpha>1.
Revised: We consider the problem of the approximation of the solution of a one-dimensional stochastic differential equation with non-globally Lipschitz drift and diffusion coefficients of form x^\alpha, with \alpha>1.
Edit intent: clarity
Original: In this paper, we consider the problem of the approximation of the solution of a one-dimensional stochastic differential equation with non-globally Lipschitz drift and diffusion coefficients of form x^\alpha, with \alpha>1.
Revised: In this paper, we consider the problem of the approximation of the solution of a one-dimensional SDE with non-globally Lipschitz drift and diffusion coefficients of form x^\alpha, with \alpha>1.
Edit intent: clarity
Original: In this paper, we consider the problem of the approximation of the solution of a one-dimensional stochastic differential equation with non-globally Lipschitz drift and diffusion coefficients of form x^\alpha, with \alpha>1.
Revised: In this paper, we consider the problem of the approximation of the solution of a one-dimensional stochastic differential equation with non-globally Lipschitz drift and diffusion coefficients behaving as x^\alpha, with \alpha>1.
Edit intent: clarity
Original:  We propose an  exponential-Euler scheme and study its convergence of the weak approximation error.
Revised:  We propose an exponential-Euler scheme and study its convergence through its weak approximation error.
Edit intent: clarity
Original:  We analyze the regularity of the solution of the associated backward Kolmogorov partial differential equation through a Feynman-Kac representation  .
Revised:  We analyze the regularity of the solution of the associated backward Kolmogorov PDE using its Feynman-Kac representation .
Edit intent: clarity
Original:  Finally, numerical experiments are shown in order to support and complement our theoretical results .
Revised:  Finally, numerical experiments are shown in order to support and complement our theoretical result .
Edit intent: coherence
Original:  We solve the FISH-Hi-C paradox  using a theory based on a Generalized Rouse Model for Chromosomes (GRMC).
Revised:  Here, we show that the FISH-Hi-C paradox using a theory based on a Generalized Rouse Model for Chromosomes (GRMC).
Edit intent: clarity
Original:  The FISH-Hi-C paradox arises because the cell population is highly heterogeneous, which means that a given contact is present in only a fraction , \eta, of cells.
Revised:  The FISH-Hi-C paradox arises because the cell population is highly heterogeneous, which means that a given contact is present in only a fraction of cells.
Edit intent: clarity
Original:  Heterogeneity is pervasive in genome organization at all length scales, reflecting large cell-to-cell variations.
Revised:  Our results show that heterogeneity is pervasive in genome organization at all length scales, reflecting large cell-to-cell variations.
Edit intent: clarity
Original:  The algorithm runs in O(n^{3/2+ \varepsilon }) time, which is a considerable improvement over  previously known algorithms.
Revised:  The algorithm runs in O(n^{3/2+ \epsilon }) time, which is a considerable improvement over previously known algorithms.
Edit intent: fluency
Original:  The algorithm runs in O(n^{3/2+ \varepsilon }) time, which is a considerable improvement over  previously known algorithms.
Revised:  The algorithm runs in O(n^{3/2+ \varepsilon }) time, which is a considerable improvement over the previously known algorithms.
Edit intent: fluency
Original:  A user can define a model and customize the fitting process, making it as simple or complex as desired, and as application-targeted or general-purpose as desired.
Revised:  A user can define a model and customize the calibration process, making it as simple or complex as desired, and as application-targeted or general-purpose as desired.
Edit intent: clarity
Original:  As application examples of our approach, we demonstrate both linear and nonlinear models;
Revised:  To evaluate our approach, we demonstrate both linear and nonlinear models;
Edit intent: clarity
Original:  A user can define a model and customize the calibration process, making it as simple or complex as desired, and as application-targeted or general-purpose as desired.
Revised:  A user can define a model and customize the calibration process, making it as simple or complex as desired, and as application-targeted or general as desired.
Edit intent: clarity
Original: Given an affine space of matrices L and a matrix \theta \in L , consider the problem of finding the closest rank deficient matrix to \theta on L with respect to the Frobenius norm.
Revised: Given an affine space of matrices L and a matrix \Theta\in L , consider the problem of finding the closest rank deficient matrix to \theta on L with respect to the Frobenius norm.
Edit intent: fluency
Original: Given an affine space of matrices L and a matrix \theta \in L , consider the problem of finding the closest rank deficient matrix to \theta on L with respect to the Frobenius norm.
Revised: Given an affine space of matrices L and a matrix \theta \in L , consider the problem of computing the closest rank deficient matrix to \theta on L with respect to the Frobenius norm.
Edit intent: clarity
Original:  We introduce a novel semidefinite programming (SDP) relaxation, and we show that the SDP solves the problem exactly in the low noise regime, i.e., when \theta is close to be rank deficient.
Revised:  We introduce a novel semidefinite programming (SDP) relaxation, and we show that the SDP solves the problem exactly in the low noise regime, i.e., when \Theta is close to be rank deficient.
Edit intent: fluency
Original:   We evaluate the performance of the SDP relaxation in applications from control theory, computer algebra, and computer vision .
Revised:  We evaluate the performance of our SDP relaxation in applications from control theory, computer algebra, and computer vision .
Edit intent: clarity
Original:  Our relaxation reliably obtains the global minimizer in all cases for non-adversarial noise  .
Revised:  Our relaxation reliably obtains the global minimizer under non-adversarial noise .
Edit intent: clarity
Original: Metapopulations is a multi-patch habitat system, where populations live and interact in  habitat patches, and individuals disperse from one patch to  other via dispersal connections.
Revised: A metapopulations network is a multi-patch habitat system, where populations live and interact in habitat patches, and individuals disperse from one patch to other via dispersal connections.
Edit intent: clarity
Original: Metapopulations is a multi-patch habitat system, where populations live and interact in  habitat patches, and individuals disperse from one patch to  other via dispersal connections.
Revised: Metapopulations is a multi-patch habitat system, where populations live and interact in the habitat patches, and individuals disperse from one patch to other via dispersal connections.
Edit intent: fluency
Original: Metapopulations is a multi-patch habitat system, where populations live and interact in  habitat patches, and individuals disperse from one patch to  other via dispersal connections.
Revised: Metapopulations is a multi-patch habitat system, where populations live and interact in habitat patches, and individuals disperse from one patch to the other via dispersal connections.
Edit intent: fluency
Original:  The loss of dispersal connections among  habitat patches can impact negatively on the stability of the system.
Revised:  The loss of dispersal connections among the habitat patches can impact negatively on the stability of the system.
Edit intent: fluency
Original:  The loss of dispersal connections among  habitat patches can impact negatively on the stability of the system.
Revised:  The loss of dispersal connections among habitat patches can impact the stability of the system.
Edit intent: clarity
Original:  In addition, we perform extensive simulations by sampling and averaging over a large number of possible payoff matrices to compare with and demonstrate analytical results.
Revised:  In addition, we perform extensive simulations by sampling and averaging over a large number of possible payoff matrices to compare with and illustrate analytical results.
Edit intent: clarity
Original: In  low-rank approximation with missing entries , given A \in R^{n \times n} and binary W \in \{0,1\}^{n \times n}, the goal is to find a rank-k matrix L for which: cost(L)=i=1^{n} j=1^{n}W_{i,j}\cdot (A_{i,j} - L_{i,j})^2\le OPT+\epsilon \|A\|_F^2, where OPT=\min_{rank-k\ L}cost(\hat L).
Revised: In masked low-rank approximation with missing entries , given A \in R^{n \times n} and binary W \in \{0,1\}^{n \times n}, the goal is to find a rank-k matrix L for which: cost(L)=i=1^{n} j=1^{n}W_{i,j}\cdot (A_{i,j} - L_{i,j})^2\le OPT+\epsilon \|A\|_F^2, where OPT=\min_{rank-k\ L}cost(\hat L).
Edit intent: fluency
Original: In  low-rank approximation with missing entries , given A \in R^{n \times n} and binary W \in \{0,1\}^{n \times n}, the goal is to find a rank-k matrix L for which: cost(L)=i=1^{n} j=1^{n}W_{i,j}\cdot (A_{i,j} - L_{i,j})^2\le OPT+\epsilon \|A\|_F^2, where OPT=\min_{rank-k\ L}cost(\hat L).
Revised: In low-rank approximation , given A \in R^{n \times n} and binary W \in \{0,1\}^{n \times n}, the goal is to find a rank-k matrix L for which: cost(L)=i=1^{n} j=1^{n}W_{i,j}\cdot (A_{i,j} - L_{i,j})^2\le OPT+\epsilon \|A\|_F^2, where OPT=\min_{rank-k\ L}cost(\hat L).
Edit intent: clarity