wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our approach can be directly applied to the problem of finding a shortest rectilinear Steiner tree that interconnects the points of P . It provides a O\left(nh5^h\right) algorithm which improves significantly over the best known existing fixed-parameter algorithm for rectilinear Steiner tree .
Revised:  Our approach can be directly applied to the problem of finding a shortest rectilinear Steiner tree that interconnects the points of P . It provides a O\left(nh5^h\right) algorithm which improves significantly over the best time bounds known for these problems .
Edit intent: clarity
Original: In the k-SUM problem , we are given n real numbers as input, and we are asked whether there exists a zero-sum k-subset .
Revised: The k-SUM problem , we are given n real numbers as input, and we are asked whether there exists a zero-sum k-subset .
Edit intent: style
Original: In the k-SUM problem , we are given n real numbers as input, and we are asked whether there exists a zero-sum k-subset .
Revised: In the k-SUM problem is given n input real numbers to determine whether any k of them sum to zero .
Edit intent: clarity
Original:  Revisiting a known algorithm due to Meiser (1993), we show that there exist linear decision trees  of depth O(n^3\log^3 n) solving this problem .
Revised:  Inspired by an algorithm due to Meiser (1993), we show that there exist linear decision trees of depth O(n^3\log^3 n) solving this problem .
Edit intent: clarity
Original:  In particular, we prove that there exists o(n)-linear decision trees of depth O(n^c)for some constant c.
Revised:  In particular, we prove that there exist o(n)-linear decision trees of depth O(n^c)for some constant c.
Edit intent: fluency
Original:  Finally, a curious characterisation of log-concave distributions on the real line is derived, generalising the main optimisation-based representation.
Edit intent: coherence
Original:  We rigorously analyze the performance of the cooperative UCB algorithm and characterize the influence of communication graph structure on the decision-making performance of individual agents .
Revised:  We rigorously analyze the performance of the cooperative UCB algorithm and characterize the influence of communication graph structure on the decision-making performance of the group .
Edit intent: clarity
Original: We develop a new randomized iterative algorithm---%DIFDELCMD < {\em %%% stochastic dual ascent (SDA) ---for finding the projection of a given vector onto the solution space of a linear system.
Revised: We develop a new randomized iterative %DIFDELCMD < {\em %%% stochastic dual ascent (SDA) ---for finding the projection of a given vector onto the solution space of a linear system.
Edit intent: clarity
Original: We develop a new randomized iterative algorithm---%DIFDELCMD < {\em %%% stochastic dual ascent (SDA) ---for finding the projection of a given vector onto the solution space of a linear system.
Revised: We develop a new randomized iterative algorithm---%DIFDELCMD < {\em %%% algorithm---stochastic dual ascent (SDA) ---for finding the projection of a given vector onto the solution space of a linear system.
Edit intent: clarity
Original:  The notion of relative sign-stability is also introduced and a sufficient condition for the relative sign-stability of Metzler matrices is proposed .
Revised:  The concept of sign-stability is also introduced and a sufficient condition for the relative sign-stability of Metzler matrices is proposed .
Edit intent: clarity
Original: Several results on the sign properties of Metzler matrices are obtained.
Revised: Several results about sign properties of Metzler matrices are obtained.
Edit intent: fluency
Original:  The concept of sign-stability is then generalized to the concept of Ker_+(B)-sign-stability, a problem that arises in  analysis of certain jump Markov processes.
Revised:  The concept of sign-stability is then generalized to the concept of Ker_+(B)-sign-stability, a problem that arises in the analysis of certain jump Markov processes.
Edit intent: fluency
Original: For a polygonal domain with h holes and a total of n vertices, we present algorithms that compute the L_1 geodesic diameter in O(n^2+h^4) time and the L_1 geodesic center in O((n^4+n^2 h^4)\alpha(n)) time,  where \alpha(\cdot) denotes the inverse Ackermann function.
Revised: For a polygonal domain with h holes and a total of n vertices, we present algorithms that compute the L_1 geodesic diameter in O(n^2+h^4) time and the L_1 geodesic center in O((n^4+n^2 h^4)\alpha(n)) time, respectively, where \alpha(\cdot) denotes the inverse Ackermann function.
Edit intent: clarity
Original:  Therefore, our algorithms are much faster than the algorithms for the Euclidean problems.
Revised:  Therefore, our algorithms are significantly faster than the algorithms for the Euclidean problems.
Edit intent: clarity
Original:  Building on Triple Helix research, we use entropy statistics to elaborate an indicator of mutual information among these dimensions that can provide indication of reduction of uncertainty.
Revised:  Building on triple helix research, we use entropy statistics to elaborate an indicator of mutual information among these dimensions that can provide indication of reduction of uncertainty.
Edit intent: fluency
Original:  The Medical Subject Headings (MeSH) of MEDLINE/PubMed provide us with publication records classified within the categories "Diseases" (C), "Drugs and Chemicals" (D), "Analytic, Diagnostic, and Therapeutic Techniques and Equipment" (E)  as knowledge representations of demand, supply, and technological capabilities, respectively.
Revised:  We use the Medical Subject Headings (MeSH) of MEDLINE/PubMed provide us with publication records classified within the categories "Diseases" (C), "Drugs and Chemicals" (D), "Analytic, Diagnostic, and Therapeutic Techniques and Equipment" (E) as knowledge representations of demand, supply, and technological capabilities, respectively.
Edit intent: coherence
Original:  The Medical Subject Headings (MeSH) of MEDLINE/PubMed provide us with publication records classified within the categories "Diseases" (C), "Drugs and Chemicals" (D), "Analytic, Diagnostic, and Therapeutic Techniques and Equipment" (E)  as knowledge representations of demand, supply, and technological capabilities, respectively.
Revised:  The Medical Subject Headings (MeSH) of MEDLINE/PubMed to identify publications classified within the categories "Diseases" (C), "Drugs and Chemicals" (D), "Analytic, Diagnostic, and Therapeutic Techniques and Equipment" (E) as knowledge representations of demand, supply, and technological capabilities, respectively.
Edit intent: clarity
Original:  The Medical Subject Headings (MeSH) of MEDLINE/PubMed provide us with publication records classified within the categories "Diseases" (C), "Drugs and Chemicals" (D), "Analytic, Diagnostic, and Therapeutic Techniques and Equipment" (E)  as knowledge representations of demand, supply, and technological capabilities, respectively.
Revised:  The Medical Subject Headings (MeSH) of MEDLINE/PubMed provide us with publication records classified within the categories "Diseases" (C), "Drugs and Chemicals" (D), "Analytic, Diagnostic, and Therapeutic Techniques and Equipment" (E) and use these as knowledge representations of demand, supply, and technological capabilities, respectively.
Edit intent: coherence
Original:  These are: (i) Human Papilloma Virus , (ii) RNA interference, and (iii) Magnetic Resonance Imaging .
Revised:  These are: (i) human papilloma virus , (ii) RNA interference, and (iii) Magnetic Resonance Imaging .
Edit intent: fluency
Original:  These are: (i) Human Papilloma Virus , (ii) RNA interference, and (iii) Magnetic Resonance Imaging .
Revised:  These are: (i) Human Papilloma Virus , (ii) RNA interference, and (iii) magnetic resonance imaging .
Edit intent: fluency
Original:  We find statistically significant periods of synergy among demand, supply, and technological capabilities (C-D-E) that points to three-dimensional interactions as a fundamental perspective for the understanding and governance of the uncertainty associated with medical innovation.
Revised:  We find statistically significant periods of synergy among demand, supply, and technological capabilities (C-D-E) that point to three-dimensional interactions as a fundamental perspective for the understanding and governance of the uncertainty associated with medical innovation.
Edit intent: fluency
Original:  This article extends the liability-side pricing theory with an exogenously determined initial margin profile or endogenously , delta approximated initial margin.
Revised:  This article extends the liability-side pricing theory with an exogenously determined initial margin profile or endogenously approximated initial margin.
Edit intent: fluency
Original:  An IM multiplier is applied to calibrate to historical data and CCP specific requirements to allow portfolio incremental pricing.
Revised:  An IM multiplier is applied to calibrate to external IM models to allow portfolio incremental pricing.
Edit intent: clarity
Original:  The model illustrates that recent CME-LCH basis spread widening is related to elevated MVA accompanying dealers' hedging of customer flows.
Revised:  The model illustrates that recent CME-LCH basis spread widening to elevated MVA accompanying dealers' hedging of customer flows.
Edit intent: clarity
Original:  However, the majority of applications require computation of a large number K _{\max of eigenpairs, where K_{\max} is an upper bound on the number K of clusters, called the order of }  the clustering algorithms.
Revised:  However, the majority of applications require computation of a large number K of eigenpairs, where K_{\max} is an upper bound on the number K of clusters, called the order of } the clustering algorithms.
Edit intent: fluency
Original:  This method leverages the eigenstructure of graph Laplacian matrix to obtain the k-th eigenpairs of the Laplacian matrix given a collection of all the k-1 smallest eigenpairs.
Revised:  This method leverages the eigenstructure of graph Laplacian matrix to obtain the K-th eigenpairs of the Laplacian matrix given a collection of all the k-1 smallest eigenpairs.
Edit intent: fluency
Original:  This method leverages the eigenstructure of graph Laplacian matrix to obtain the k-th eigenpairs of the Laplacian matrix given a collection of all the k-1 smallest eigenpairs.
Revised:  This method leverages the eigenstructure of graph Laplacian matrix to obtain the k-th eigenpairs of the Laplacian matrix given a collection of all the K-1 smallest eigenpairs.
Edit intent: fluency
Original:  As a practical application of our proposed method , we consider user-guided spectral clustering.
Revised:  As a practical application , we consider user-guided spectral clustering.
Edit intent: clarity
Original:  The first option, more often, yield suboptimal result, while the second option is computationally expensive.
Revised:  The first option, more often, yields suboptimal result, while the second option is computationally expensive.
Edit intent: fluency
Original: In the face of increasing size of sequence databases caused by the development of high throughput sequencing,  multiple alignment algorithms  face one of the greatest challenges yet.
Revised: Increasing size of sequence databases caused by the development of high throughput sequencing, multiple alignment algorithms face one of the greatest challenges yet.
Edit intent: clarity
Original: In the face of increasing size of sequence databases caused by the development of high throughput sequencing,  multiple alignment algorithms  face one of the greatest challenges yet.
Revised: In the face of increasing size of sequence databases caused by the development of high throughput sequencing, poses multiple alignment algorithms face one of the greatest challenges yet.
Edit intent: fluency
Original: In the face of increasing size of sequence databases caused by the development of high throughput sequencing,  multiple alignment algorithms  face one of the greatest challenges yet.
Revised: In the face of increasing size of sequence databases caused by the development of high throughput sequencing, multiple alignment algorithms to face one of the greatest challenges yet.
Edit intent: fluency
Original:  In this paper we showthat well-established techniques , refinement and consistency, are ineffective when large protein families are of interest.
Revised:  As we show, well-established techniques , refinement and consistency, are ineffective when large protein families are of interest.
Edit intent: clarity
Original:  When analysing hundreds of sequences, QuickProbs 2 properly aligns up to 20\% more columns than ClustalOmega , the previous leader for processing numerous protein families.
Revised:  When analysing hundreds of sequences, QuickProbs 2 is significantly better than Clustal Omega , the previous leader for processing numerous protein families.
Edit intent: clarity
Original:  Due to computational scalability of selective consistency and utilisation of massively parallel architectures, presented algorithm is comparable to ClustalOmega in terms of execution time, and orders of magnitude faster than full consistency approaches, like MSAProbs or PixAA . All these make QuickProbs 2 a useful tool for aligning families ranging from few, to hundreds of proteins. 
Revised:  Due to computational scalability of selective consistency and utilisation of massively parallel architectures, presented algorithm is comparable to Clustal Omega in terms of execution time, and orders of magnitude faster than full consistency approaches, like MSAProbs or PixAA . All these make QuickProbs 2 a useful tool for aligning families ranging from few, to hundreds of proteins. 
Edit intent: fluency
Original:  Due to computational scalability of selective consistency and utilisation of massively parallel architectures, presented algorithm is comparable to ClustalOmega in terms of execution time, and orders of magnitude faster than full consistency approaches, like MSAProbs or PixAA . All these make QuickProbs 2 a useful tool for aligning families ranging from few, to hundreds of proteins. 
Revised:  Due to computational scalability of selective consistency and utilisation of massively parallel architectures, presented algorithm is comparable to ClustalOmega in terms of execution time, and orders of magnitude faster than full consistency approaches, like MSAProbs or PicXAA . All these make QuickProbs 2 a useful tool for aligning families ranging from few, to hundreds of proteins. 
Edit intent: fluency
Original:  Here, by studying the eigenvalue bounds of the community matrix, we show that under a conservation of interaction strengths, ecosystems will favor mutual relationships with symmetrical dependencies and predatory-prey relationships with asymmetrical dependencies, in agreement with real-world observations.
Revised:  Here, by studying the eigenvalue bounds of the community matrix, we show that under a conservation of interaction strengths, ecosystems will favor mutual relationships with asymmetrical dependencies and predatory-prey relationships with asymmetrical dependencies, in agreement with real-world observations.
Edit intent: fluency
Original:  Here, by studying the eigenvalue bounds of the community matrix, we show that under a conservation of interaction strengths, ecosystems will favor mutual relationships with symmetrical dependencies and predatory-prey relationships with asymmetrical dependencies, in agreement with real-world observations.
Revised:  Here, by studying the eigenvalue bounds of the community matrix, we show that under a conservation of interaction strengths, ecosystems will favor mutual relationships with symmetrical dependencies and predatory-prey relationships with symmetrical dependencies, in agreement with real-world observations.
Edit intent: fluency
Original:  We determine that this effect is more pronounced in mutualistic networks than trophic networks which is also in agreement with real-world observations.
Revised:  We determine that this effect is more pronounced in trophic networks than mutualistic networks which is also in agreement with real-world observations.
Edit intent: fluency
Original:  Here, by studying the eigenvalue bounds of the community matrix , we show that under a conservation of interaction strengths, ecosystems will favor mutual relationships with asymmetrical dependencies and predatory-prey relationships with symmetrical dependencies, in agreement with real-world observations.
Revised:  Here, by obtaining eigenvalue bounds of the community matrix , we show that under a conservation of interaction strengths, ecosystems will favor mutual relationships with asymmetrical dependencies and predatory-prey relationships with symmetrical dependencies, in agreement with real-world observations.
Edit intent: clarity
Original:  Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor cooperative relationships that are asymmetrical (non-reciprocative) and competitive relationships that are symmetrical (reciprocative).
Revised:  Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-reciprocative) and competitive relationships that are symmetrical (reciprocative).
Edit intent: clarity
Original:  Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor cooperative relationships that are asymmetrical (non-reciprocative) and competitive relationships that are symmetrical (reciprocative).
Revised:  Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor cooperative relationships that are asymmetrical (non-reciprocative) and trophic relationships that are symmetrical (reciprocative).
Edit intent: clarity
Original: In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piece-wise linear functions.
Revised: In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions.
Edit intent: fluency
Original:  The algorithm transforms a discrete piece-wise linear into a fi?ltered simplicial complex that is analyzed with persistent homology and persistent entropy.
Revised:  The algorithm transforms a discrete piecewise linear function into a filtered simplicial complex that is analyzed with persistent homology and persistent entropy.
Edit intent: clarity
Original:  The algorithm is successfully applied for solving the supervised classi?cation problem of real long length noisy signals of DC electrical motors.
Revised:  The algorithm is successfully applied for solving the supervised classification problem of real long length noisy signals of DC electrical motors.
Edit intent: fluency
Original:  The quality of classi?cation is stated in terms of the area under receiver operating characteristic curve (AUC=94.52\%).
Revised:  The quality of classification is stated in terms of the area under receiver operating characteristic curve (AUC=94.52\%).
Edit intent: fluency
Original:  As a result, tissues are made up of different ``patches'' , i.e., adjacent tissue regions of different ages and different material properties, within evolving boundaries.
Revised:  As a result, tissues are made up of different "patches" , i.e., adjacent tissue regions of different ages and different material properties, within evolving boundaries.
Edit intent: fluency
Original:  Recommender systems, industrial plants and language models are only some of the many real-world tasks involving large numbers of discrete actions for which current methods can be difficult or even  impossible to apply.
Revised:  Recommender systems, industrial plants and language models are only some of the many real-world tasks involving large numbers of discrete actions for which current methods are difficult or even impossible to apply.
Edit intent: clarity
Original:  Recommender systems, industrial plants and language models are only some of the many real-world tasks involving large numbers of discrete actions for which current methods can be difficult or even  impossible to apply.
Revised:  Recommender systems, industrial plants and language models are only some of the many real-world tasks involving large numbers of discrete actions for which current methods can be difficult or even often impossible to apply.
Edit intent: clarity
Original:  z(t)= T\_c(t + \phi), where a,b,care integers, T\_n(t) is the Chebyshev polynomialof degree n and \phi \in %DIFDELCMD < \RR%%% . When%DIFDELCMD < \cC%%%  (a,b,c,\phi) is nonsingular,it defines a polynomial knot.
Revised:  z(t)= T\_c(t + \phi), where a,b,care integers, T\_n(t) is the Chebyshev polynomialof degree n and \phi \in %DIFDELCMD < \RR%%% %DIFDELCMD < \cC%%% (a,b,c,\phi) is nonsingular,it defines a polynomial knot.
Edit intent: coherence
Original:  Belief propagation (BP) and mean field (MF) message passing are employed for, respectively, the motion-related and measurement-related parts of the underlying factor graph.
Revised:  Belief propagation and mean field (MF) message passing are employed for, respectively, the motion-related and measurement-related parts of the underlying factor graph.
Edit intent: clarity
Original:  Belief propagation (BP) and mean field (MF) message passing are employed for, respectively, the motion-related and measurement-related parts of the underlying factor graph.
Revised:  Belief propagation (BP) and mean field message passing are employed for, respectively, the motion-related and measurement-related parts of the underlying factor graph.
Edit intent: clarity
Original:  Belief propagation (BP) and mean field (MF) message passing are employed for, respectively, the motion-related and measurement-related parts of the underlying factor graph.
Revised:  Belief propagation (BP) and mean field (MF) message passing are employed for, respectively, the motion-related and measurement-related part of the factor graph.
Edit intent: clarity
Original:  Using a Gaussian belief approximation, closed-form expressions of all messages are obtained, and only three real values per message passing iteration have to be broadcast to neighboring agents.
Revised:  Using a Gaussian belief approximation, only three real values per message passing iteration have to be broadcast to neighboring agents.
Edit intent: clarity
Original:  Despite these very low communication requirements, the estimation accuracy can be comparable to that of particle-based BP .
Revised:  Despite these very low communication requirements, the estimation accuracy can be comparable to that of particle-based belief propagation .
Edit intent: clarity
Original:  Our new results are based on the exploitation of a common technique , which aims to reduce the graph under consideration to a k-partite graph that can be decomposed in a certain way which, as we prove, ensures boundedness of their clique-width .
Revised:  Our technique for handling this case is to reduce the graph under consideration to a k-partite graph that can be decomposed in a certain way which, as we prove, ensures boundedness of their clique-width .
Edit intent: clarity
Original:  While some combinations of ingredients lead to efficiently classically simulable circuits, other combinations that might just be slightly different, lead to circuits which are likely not.
Revised:  While some combinations of ingredients lead to efficiently classically simulable circuits, other combinations , which might just be slightly different, lead to circuits which are likely not.
Edit intent: fluency
Original:  Firstly , we consider how the classical simulation complexity changes when we allow for more general measurements.
Revised:  First , we consider how the classical simulation complexity changes when we allow for more general measurements.
Edit intent: fluency