wanyu/IteraTeR_v2 huggingface dataset:
Original:  For the optimization task, we show that when the population size is large enough, the complete partition which contains only one sample in each component is always better, and utilize the correlation computation result obtained earlier to reduce finding optimal complete partition to a well-studied Max-r-Cut problem.
Revised:  For the optimization task, we show that when the population size is large enough, the complete partition which contains only one sample in each component is always better, and reduce finding the optimal simple partition to a well-studied Max-r-Cut problem.
Edit intent: clarity
Original:  We adopt the semidefinite programming algorithm for Max-r-Cut to solve our optimization problem, and further develop a greedy heuristic algorithm to improve the efficiency .
Revised:  We adopt the semi-definite programming algorithm for Max-r-Cut to solve our optimization problem, and further develop a greedy heuristic algorithm to improve the efficiency .
Edit intent: fluency
Original: Public opinion polling is typically done by random sampling from the entire population, treating the opinions of individuals as independent.
Revised: Public opinion polling is usually done by random sampling from the entire population, treating the opinions of individuals as independent.
Edit intent: fluency
Original: Public opinion polling is typically done by random sampling from the entire population, treating the opinions of individuals as independent.
Revised: Public opinion polling is typically done by random sampling from the entire population, treating individual opinions as independent.
Edit intent: clarity
Original:  In the real world, individuals' opinions are often correlated, especially among friends in a social network , due to the effect of both homophily and social influence .
Revised:  In the real world, individuals' opinions are often correlated, e.g., among friends in a social network , due to the effect of both homophily and social influence .
Edit intent: clarity
Original:  In the real world, individuals' opinions are often correlated, especially among friends in a social network , due to the effect of both homophily and social influence .
Revised:  In the real world, individuals' opinions are often correlated, especially among friends in a social network .
Edit intent: coherence
Original:  In this paper, we explore the idea of partitioned sampling, which partition individuals likely holding similar opinions into groups and sample every group separately to obtain an accurate estimate of the population opinion.
Revised:  In this paper, we explore the idea of partitioned sampling, which partitions individuals with high opinion similarities into groups and sample every group separately to obtain an accurate estimate of the population opinion.
Edit intent: clarity
Original:  In this paper, we explore the idea of partitioned sampling, which partition individuals likely holding similar opinions into groups and sample every group separately to obtain an accurate estimate of the population opinion.
Revised:  In this paper, we explore the idea of partitioned sampling, which partition individuals likely holding similar opinions into groups and then samples every group separately to obtain an accurate estimate of the population opinion.
Edit intent: clarity
Original:  We first rigorously formulate the above idea into an optimization problem.
Revised:  We rigorously formulate the above idea into an optimization problem.
Edit intent: coherence
Original:  We first rigorously formulate the above idea into an optimization problem.
Revised:  We first rigorously formulate the above idea as an optimization problem.
Edit intent: fluency
Original:  We show that the simple partitions that contain only one sample in each group are always better, and reduce finding the optimal simple partition to a well-studied Max-k-Cut problem.
Revised:  We show that the simple partitions which contain only one sample in each group are always better, and reduce finding the optimal simple partition to a well-studied Max-k-Cut problem.
Edit intent: fluency
Original:  We adopt the semi-definite programming algorithm for Max-k-Cut to solve our optimization problem, and further develop a greedy heuristic to improve efficiency .
Revised:  We adapt an approximation algorithm and a heuristic algorithm to solve the optimization problem .
Edit intent: clarity
Original:  Moreover, to address the issue of how to obtain opinion similarity efficiently, we propose an opinion evolution model based on reasonable user interaction patterns in social network , and provide efficient and exact computation of opinion similarity in the model.
Revised:  Moreover, to obtain opinion similarity efficiently, we propose an opinion evolution model based on reasonable user interaction patterns in social network , and provide efficient and exact computation of opinion similarity in the model.
Edit intent: clarity
Original:  Moreover, to address the issue of how to obtain opinion similarity efficiently, we propose an opinion evolution model based on reasonable user interaction patterns in social network , and provide efficient and exact computation of opinion similarity in the model.
Revised:  Moreover, to address the issue of how to obtain opinion similarity efficiently, we adapt a well-known opinion evolution model based on reasonable user interaction patterns in social network , and provide efficient and exact computation of opinion similarity in the model.
Edit intent: clarity
Original:  Moreover, to address the issue of how to obtain opinion similarity efficiently, we propose an opinion evolution model based on reasonable user interaction patterns in social network , and provide efficient and exact computation of opinion similarity in the model.
Revised:  Moreover, to address the issue of how to obtain opinion similarity efficiently, we propose an opinion evolution model to characterize social interactions , and provide efficient and exact computation of opinion similarity in the model.
Edit intent: clarity
Original:  Moreover, to address the issue of how to obtain opinion similarity efficiently, we propose an opinion evolution model based on reasonable user interaction patterns in social network , and provide efficient and exact computation of opinion similarity in the model.
Revised:  Moreover, to address the issue of how to obtain opinion similarity efficiently, we propose an opinion evolution model based on reasonable user interaction patterns in social network , and provide an exact computation of opinion similarity in the model.
Edit intent: clarity
Original:  Moreover, to address the issue of how to obtain opinion similarity efficiently, we propose an opinion evolution model based on reasonable user interaction patterns in social network , and provide efficient and exact computation of opinion similarity in the model.
Revised:  Moreover, to address the issue of how to obtain opinion similarity efficiently, we propose an opinion evolution model based on reasonable user interaction patterns in social network , and provide efficient and exact computation of opinion similarities based on the model.
Edit intent: clarity
Original:  We use both synthetic and real-world datasets to demonstrate that our partitioned sampling method results in significant improvement in sampling quality  .
Revised:  We use both synthetic and real-world datasets to demonstrate that the partitioned sampling method results in significant improvement in sampling quality .
Edit intent: fluency
Original:  Our study relies on a set of rosebushes flowering data, and Gaussian mixture models are mainly used to quantify the reblooming behavior of each one.
Revised:  Our study relies on a set of rosebushes flowering data, and Gaussian mixture models are mainly used to quantify the reblooming properties of each one.
Edit intent: clarity
Original:  Three classes are created on the basis of the reblooming indicators, and a subclassification is made using a longitudinal k--means algorithm which  highlights the role also played by the precocity of the flowering.
Revised:  Three classes are created on the basis of the reblooming indicators, and a subclassification is made using a longitudinal k--means algorithm which also highlights the role also played by the precocity of the flowering.
Edit intent: fluency
Original:  Three classes are created on the basis of the reblooming indicators, and a subclassification is made using a longitudinal k--means algorithm which  highlights the role also played by the precocity of the flowering.
Revised:  Three classes are created on the basis of the reblooming indicators, and a subclassification is made using a longitudinal k--means algorithm which highlights the role played by the precocity of the flowering.
Edit intent: clarity
Original:  A principal component analysis is finally conducted on a set of indicators derived from our statistical approach to get an overview of the correlations between the features that we have decided to retain on each curve.
Revised:  In this way, we obtain an overview of the correlations between the features that we have decided to retain on each curve.
Edit intent: clarity
Original:  A principal component analysis is finally conducted on a set of indicators derived from our statistical approach to get an overview of the correlations between the features that we have decided to retain on each curve.
Revised:  A principal component analysis is finally conducted on a set of indicators derived from our statistical approach to get an overview of the correlations between the features we decided to retain on each curve.
Edit intent: fluency
Original:  Results suggest the lack of correlation between reblooming and flowering precocity.
Revised:  In particular, results suggest the lack of correlation between reblooming and flowering precocity.
Edit intent: coherence
Original:  We show that , contrarily to what was previously thought, adversarial images do not appear isolated in the pixel space.
Revised:  We show that adversarial images appear in large regions in the pixel space.
Edit intent: clarity
Original:  We probe the pixel space of adversarial images using random Gaussian noise with varying standard deviation, and a heavy-tailed noise given by a non-parametric model of the empirical distribution of the adversarial distortion pixels .
Revised:  We probe the pixel space of adversarial images using noise of varying intensity and statistic. We bring novel visualizations that showcase the phenomenon and its high variability .
Edit intent: clarity
Original: We probe the pixel space of adversarial images using noise of varying intensity and statistic .
Revised: We probe the pixel space of adversarial images using noise of varying intensity and distribution .
Edit intent: clarity
Original:  In order to facilitate Bayesian inference on the true value of the estimator, we derive the asymptotic posterior distribution of the estimate.
Revised:  In order to facilitate Bayesian inference on the true value of the estimator, we derive the approximate posterior distribution of the estimate.
Edit intent: clarity
Original:  Weaker bounds have previously appeared in the literature , and our result offers an improvement .
Revised:  Weaker bounds have previously appeared in the literature ) .
Edit intent: clarity
Original: We analyze the locus generation algorithm of the dynamic geometry software Cinderella, and examine how it uses complex detours to resolve singularities.
Revised: We discuss the locus generation algorithm of the dynamic geometry software Cinderella, and examine how it uses complex detours to resolve singularities.
Edit intent: clarity
Original: We analyze the locus generation algorithm of the dynamic geometry software Cinderella, and examine how it uses complex detours to resolve singularities.
Revised: We analyze the locus generation algorithm used by the dynamic geometry software Cinderella, and examine how it uses complex detours to resolve singularities.
Edit intent: clarity
Original: We analyze the locus generation algorithm of the dynamic geometry software Cinderella, and examine how it uses complex detours to resolve singularities.
Revised: We analyze the locus generation algorithm of the dynamic geometry software Cinderella, and how it uses complex detours to resolve singularities.
Edit intent: clarity
Original:  We introduce a variation of the algorithm that  generates entire real connected components of real algebraic loci.
Revised:  We introduce a variation of the algorithm that possibly generates entire real connected components of real algebraic loci.
Edit intent: clarity
Original:  The first class significantly generalizes monotone read-k-times NBPs {\sc   and the second class generalizes oblivious read k times branching programs .
Revised:  The first class significantly generalizes monotone read-k-times {\sc and the second class generalizes oblivious read k times branching programs .
Edit intent: clarity
Original:  The first class significantly generalizes monotone read-k-times NBPs {\sc   and the second class generalizes oblivious read k times branching programs .
Revised:  The first class significantly generalizes monotone read-k-times NBPs {\sc s and the second class generalizes oblivious read k times branching programs .
Edit intent: fluency
Original: The goal of this work is to study homomorphism problems ( from a computational point of view ) on two superclasses of graphs: 2-edge-coloured graphs and signed graphs .
Revised: We study homomorphism problems ( from a computational point of view ) on two superclasses of graphs: 2-edge-coloured graphs and signed graphs .
Edit intent: clarity
Original: The goal of this work is to study homomorphism problems ( from a computational point of view ) on two superclasses of graphs: 2-edge-coloured graphs and signed graphs .
Revised: The goal of this work is to study homomorphism problems of signed graphs from a computational point of view ) on two superclasses of graphs: 2-edge-coloured graphs and signed graphs .
Edit intent: clarity
Original:  Specifically, as long as (H,\Pi) does not contain a negative (respectively a positive) loop, the problem is polynomial-time solvable if the core of (H,\Pi) has at most two edges  and is NP-complete otherwise.
Revised:  Specifically, as long as (H,\Pi) does not contain a negative (respectively a positive) loop, the problem is polynomial-time solvable if the core of (H,\Pi) has at most two edges , and is NP-complete otherwise.
Edit intent: fluency
Original: In this paper we consider a market model where there are two levels of information , the public information generated by the financial assets  and a larger flow of information that contains additional knowledge about a death time  of an insured.
Revised: This paper considers a market model where there are two levels of information , the public information generated by the financial assets and a larger flow of information that contains additional knowledge about a death time of an insured.
Edit intent: coherence
Original: In this paper we consider a market model where there are two levels of information , the public information generated by the financial assets  and a larger flow of information that contains additional knowledge about a death time  of an insured.
Revised: In this paper we consider a market model with two levels of information , the public information generated by the financial assets and a larger flow of information that contains additional knowledge about a death time of an insured.
Edit intent: coherence
Original: In this paper we consider a market model where there are two levels of information , the public information generated by the financial assets  and a larger flow of information that contains additional knowledge about a death time  of an insured.
Revised: In this paper we consider a market model where there are two levels of information . The public information generated by the financial assets and a larger flow of information that contains additional knowledge about a death time of an insured.
Edit intent: fluency
Original: In this paper we consider a market model where there are two levels of information , the public information generated by the financial assets  and a larger flow of information that contains additional knowledge about a death time  of an insured.
Revised: In this paper we consider a market model where there are two levels of information , the public information generated by the financial assets and a larger flow of information containing additional knowledge about a death time of an insured.
Edit intent: fluency
Original:  By using the expansion of filtration, the death uncertainty and its entailed risk are fully considered without any mathematical restriction.
Revised:  By expanding the filtration, the death uncertainty and its entailed risk are fully considered without any mathematical restriction.
Edit intent: clarity
Original:  In this context, which catches real features such as correlation between  market model and  time of death, we address the risk-minimisation problem for a large class of equity-linked mortality and/or mortality contracts.
Revised:  In this context, which catches real features such as correlation between market model and time of death, we address the risk-minimisation problem for a large class of equity-linked mortality contracts.
Edit intent: coherence
Original:  The three orthogonal martingale classes are vital pillars for establishing our optional martingale representation theorem, when (local ) martingales of the large filtration are stopped at the death time  .
Revised:  The three orthogonal martingale classes are vital pillars for establishing our optional martingale representation results, which state that any local martingale in the large filtration are stopped at the death time .
Edit intent: clarity
Original:  The three orthogonal martingale classes are vital pillars for establishing our optional martingale representation theorem, when (local ) martingales of the large filtration are stopped at the death time  .
Revised:  The three orthogonal martingale classes are vital pillars for establishing our optional martingale representation theorem, when (local ) martingales of the large filtration stopped at the death time .
Edit intent: clarity
Original: This paper considers a market model with two levels of information.
Revised: We consider a market model with two levels of information.
Edit intent: clarity
Original: This paper considers a market model with two levels of information.
Revised: This paper considers a market model where there are two levels of information.
Edit intent: clarity
Original:  The public information generated by the financial assets, and a larger flow of information containing additional knowledge about a death time(random time /horizon) of an insured.
Revised:  The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a death time(random time /horizon) of an insured.
Edit intent: fluency
Original:  Thanks to this optional representation, we succeed to decompose the risk in some popular mortality and/or longevity securities into the sum of orthogonal risks using a risk basis.
Revised:  Thanks to this optional representation, we decompose any defaultable or mortality and/or longevity securities into the sum of orthogonal risks using a risk basis.
Edit intent: clarity
Original:  Thanks to this optional representation, we succeed to decompose the risk in some popular mortality and/or longevity securities into the sum of orthogonal risks using a risk basis.
Revised:  Thanks to this optional representation, we succeed to decompose the risk in some popular mortality and/or longevity liability into the sum of orthogonal risks using a risk basis.
Edit intent: clarity
Original: Our goal here is to study American options in discrete time without using probability and stochastic process . Using the binomial model we compute the fair price of European and American options.
Revised: Our goal here is to discuss the pricing problem of European and American options in discrete time without using probability and stochastic process . Using the binomial model we compute the fair price of European and American options.
Edit intent: clarity
Original:  Finally, we give a criterion that the holder can use to decide when it is appropriate to exercise the option  .
Revised:  We give a criterion that the holder can use to decide when it is appropriate to exercise the option .
Edit intent: coherence
Original:  In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) is the maximum number of value changes from greater to smaller one over all increasing chains of tuples of variables values).
Revised:  In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that \lceil2(d(f)+1)\rceil NOT gates are necessary and sufficient to compute any Boolean function f (where d(f) is the maximum number of value changes from greater to smaller over all increasing chains of tuples of variables values).
Edit intent: clarity
Original:  This result is extended on k-valued functions computing in the paper.
Revised:  This result is extended to k-valued functions computing in the paper.
Edit intent: fluency
Original:  This result is extended on k-valued functions computing in the paper.
Revised:  This result is extended on k-valued functions computing in this paper.
Edit intent: fluency
Original:  Thereupon one can use monotone functions "for free" like in  Boolean case.
Revised:  Thereupon one can use monotone functions "for free" like in the Boolean case.
Edit intent: fluency
Original:  It is shown that the minimal sufficient for a realization of the arbitrary k-valued logic function f number of non-monotone gates is equal to \lceil2(d(f)+1)\rceil if Post negation (function x+1 k) is used in NOT nodes and is also equal to \lceilk(d(f)+1)\rceil, if {\L}ukasiewicz negation (function k-1-x) is used in NOT nodes.
Revised:  It is shown that the minimum sufficient number of non-monotone gates for the realization of the arbitrary k-valued logic function f number of non-monotone gates is equal to \lceil2(d(f)+1)\rceil if Post negation (function x+1 k) is used in NOT nodes and is also equal to \lceilk(d(f)+1)\rceil, if {\L}ukasiewicz negation (function k-1-x) is used in NOT nodes.
Edit intent: fluency
Original:  It is shown that the minimal sufficient for a realization of the arbitrary k-valued logic function f number of non-monotone gates is equal to \lceil2(d(f)+1)\rceil if Post negation (function x+1 k) is used in NOT nodes and is also equal to \lceilk(d(f)+1)\rceil, if {\L}ukasiewicz negation (function k-1-x) is used in NOT nodes.
Revised:  It is shown that the minimal sufficient for a realization of the arbitrary k-valued logic function f is equal to \lceil2(d(f)+1)\rceil if Post negation (function x+1 k) is used in NOT nodes and is also equal to \lceilk(d(f)+1)\rceil, if {\L}ukasiewicz negation (function k-1-x) is used in NOT nodes.
Edit intent: clarity
Original:  Similar extension for another classical result of A. A. Markov for the inversion complexity of  system of Boolean functions to k-valued logic functions has been obtained.
Revised:  Similar extension for another classical result of A. A. Markov for the inversion complexity of a system of Boolean functions to k-valued logic functions has been obtained.
Edit intent: fluency
Original:  To alleviate this problem, we develop here two distinct methods to compute the sampling probability for variable population size functions that are piecewise constant.
Revised:  To alleviate this problem, we develop here new methods to compute the sampling probability for variable population size functions that are piecewise constant.
Edit intent: clarity