wanyu/IteraTeR_v2 huggingface dataset:
Original:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% /(f^e) (and \mu \Fzfe  is assumed greater than den \Pden .
Revised:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% \mu \Fzfe is assumed greater than den \Pden .
Edit intent: coherence
Original:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% /(f^e) (and \mu \Fzfe  is assumed greater than den \Pden .
Revised:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% /(f^e) (and \Fzfe is assumed greater than den \Pden .
Edit intent: fluency
Original:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% /(f^e) (and \mu \Fzfe  is assumed greater than den \Pden .
Revised:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% /(f^e) (and \mu \Fzfe (and \eta is assumed greater than den \Pden .
Edit intent: fluency
Original:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% /(f^e) (and \mu \Fzfe  is assumed greater than den \Pden .
Revised:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% /(f^e) (and \mu \Fzfe is assumed greater than \Pden .
Edit intent: fluency
Original:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% /(f^e) (and \mu \Fzfe  is assumed greater than den \Pden .
Revised:  For an n by n \nxn matrix A over the ring F z%DIFDELCMD < ]%%% /(f^e) \Fzfe , where f^e is a power of an irreducible polynomial f in F z\Fz of degree d, our algorithm requires O( \mu%DIFDELCMD < }%%% *de \bigO ^2n) operations in F \F , where our black box is assumed to require O( \mu \bigO ) operations in F \F to compute a matrix-vector product by a vector over F z%DIFDELCMD < ]%%% /(f^e) (and \mu \Fzfe is assumed greater than den \Pden) .
Edit intent: fluency
Original:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Revised:  The algorithm only requires additional storage for \bigO\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Edit intent: fluency
Original:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Revised:  The algorithm only requires additional storage for O(den \bigO(\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Edit intent: fluency
Original:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Revised:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Edit intent: fluency
Original:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Revised:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of F \F . In particular, if \mu = \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Edit intent: fluency
Original:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Revised:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in \F , which is an improvement on previous methods for small d and e.
Edit intent: fluency
Original:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on previous methods for small d and e.
Revised:  The algorithm only requires additional storage for O(den \bigO\Pden ) elements of F \F . In particular, if \mu = O(den \softO\Pden ), then our algorithm requires only O^{\sim \softO (n^2d^2e^3) operations in F \F , which is an improvement on known dense methods for small d and e.
Edit intent: clarity
Original:  For the ring Z \ZZ /p^e Z \ZZ , where p is a prime, we give an algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small.
Revised:  For the ring \ZZ /p^e Z \ZZ , where p is a prime, we give an algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small.
Edit intent: clarity
Original:  For the ring Z \ZZ /p^e Z \ZZ , where p is a prime, we give an algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small.
Revised:  For the ring Z \ZZ /p^e \ZZ , where p is a prime, we give an algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small.
Edit intent: clarity
Original:  The runtime is essentially linear in ne \mu%DIFDELCMD < } %%% log(p), where \mu%DIFDELCMD < } %%% is the cost of\ZZ\ZZ  black-box evaluation (assumed greater than n)  .
Revised:  The runtime is essentially linear in \mu%DIFDELCMD < } %%% log(p), where \mu%DIFDELCMD < } %%% is the cost of\ZZ\ZZ black-box evaluation (assumed greater than n) .
Edit intent: fluency
Original:  The runtime is essentially linear in ne \mu%DIFDELCMD < } %%% log(p), where \mu%DIFDELCMD < } %%% is the cost of\ZZ\ZZ  black-box evaluation (assumed greater than n)  .
Revised:  The runtime is essentially linear in ne %DIFDELCMD < } %%% log(p), where \mu%DIFDELCMD < } %%% is the cost of\ZZ\ZZ black-box evaluation (assumed greater than n) .
Edit intent: fluency
Original:  The runtime is essentially linear in ne \mu%DIFDELCMD < } %%% log(p), where \mu%DIFDELCMD < } %%% is the cost of\ZZ\ZZ  black-box evaluation (assumed greater than n)  .
Revised:  The runtime is essentially linear in ne \mu%DIFDELCMD < } %%% log(p), where %DIFDELCMD < } %%% is the cost of\ZZ\ZZ black-box evaluation (assumed greater than n) .
Edit intent: fluency
Original:  The runtime is essentially linear in ne \mu%DIFDELCMD < } %%% log(p), where \mu%DIFDELCMD < } %%% is the cost of\ZZ\ZZ  black-box evaluation (assumed greater than n)  .
Revised:  The runtime is essentially linear in ne \mu%DIFDELCMD < } %%% log(p), where \mu%DIFDELCMD < } %%% is the cost of\ZZ\ZZ to evaluate the black-box evaluation (assumed greater than n) .
Edit intent: clarity
Original:  The runtime is essentially linear in ne \mu%DIFDELCMD < } %%% log(p), where \mu%DIFDELCMD < } %%% is the cost of\ZZ\ZZ  black-box evaluation (assumed greater than n)  .
Revised:  The runtime is essentially linear in ne \mu%DIFDELCMD < } %%% log(p), where \mu%DIFDELCMD < } %%% is the cost of\ZZ\ZZ black-box (assumed greater than n) .
Edit intent: clarity
Original:  The quest for a time and memory efficient solution without the restriction on number of nontrivial invariant factors remains open.
Revised:  The quest for a time- and memory-efficient solution without restrictions on the number of nontrivial invariant factors remains open.
Edit intent: fluency
Original: Use of the Hirsch-index ( H ) as measure of an author's visibility in the scientific literature has become popular as an alternative to a gross measure like total citations (c).
Revised: Use of the Hirsch-index ( h ) as measure of an author's visibility in the scientific literature has become popular as an alternative to a gross measure like total citations (c).
Edit intent: fluency
Original:  I show that, at least in astrophysics, H correlates tightly with overall citations.
Revised:  I show that, at least in astrophysics, h correlates tightly with overall citations.
Edit intent: fluency
Original:  The mean relation is H =0.5(\sqrt c+1).
Revised:  The mean relation is h =0.5(\sqrt c+1).
Edit intent: fluency
Original:  Outliers are few and not too far from the mean, especially if `normalized' ADS citations are used for c and H . Whatever the theoretical reasoning behind it, the Hirsch index in practice does not appear to measure something significantly new.
Revised:  Outliers are few and not too far from the mean, especially if `normalized' ADS citations are used for c and h . Whatever the theoretical reasoning behind it, the Hirsch index in practice does not appear to measure something significantly new.
Edit intent: fluency
Original: Known results on the moments of the distribution generated by  two-locus two-allele Wright-Fisher diffusion model and a duality between the diffusion  and the ancestral recombination graph is briefly summalized .
Revised: Known results on the moments of the distribution generated by the two-locus two-allele Wright-Fisher diffusion model and a duality between the diffusion and the ancestral recombination graph is briefly summalized .
Edit intent: fluency
Original: Known results on the moments of the distribution generated by  two-locus two-allele Wright-Fisher diffusion model and a duality between the diffusion  and the ancestral recombination graph is briefly summalized .
Revised: Known results on the moments of the distribution generated by two-locus Wright-Fisher diffusion model and a duality between the diffusion and the ancestral recombination graph is briefly summalized .
Edit intent: clarity
Original: Known results on the moments of the distribution generated by  two-locus two-allele Wright-Fisher diffusion model and a duality between the diffusion  and the ancestral recombination graph is briefly summalized .
Revised: Known results on the moments of the distribution generated by two-locus two-allele Wright-Fisher diffusion model and a duality between the diffusion process and the ancestral recombination graph is briefly summalized .
Edit intent: clarity
Original: Known results on the moments of the distribution generated by  two-locus two-allele Wright-Fisher diffusion model and a duality between the diffusion  and the ancestral recombination graph is briefly summalized .
Revised: Known results on the moments of the distribution generated by two-locus two-allele Wright-Fisher diffusion model and a duality between the diffusion and the ancestral process with recombination are briefly summarized .
Edit intent: clarity
Original:  A numerical method for computing moments by a Markov chain Monte Carlo and an intuitive method to obtain closed-form expressions of the moments is presented.
Revised:  A numerical methods for computing moments by a Markov chain Monte Carlo and an intuitive method to obtain closed-form expressions of the moments is presented.
Edit intent: fluency
Original:  A numerical method for computing moments by a Markov chain Monte Carlo and an intuitive method to obtain closed-form expressions of the moments is presented.
Revised:  A numerical method for computing moments by a Markov chain Monte Carlo and a method to compute closed-form expressions of the moments is presented.
Edit intent: clarity
Original:  A numerical method for computing moments by a Markov chain Monte Carlo and an intuitive method to obtain closed-form expressions of the moments is presented.
Revised:  A numerical method for computing moments by a Markov chain Monte Carlo and an intuitive method to obtain closed-form expressions of the moments are presented.
Edit intent: fluency
Original:  By using the duality argument , properties of the ancestral recombination graph is studied in terms of the moments.
Revised:  By using the duality argument properties of the ancestral recombination graph is studied in terms of the moments.
Edit intent: fluency
Original:  By using the duality argument , properties of the ancestral recombination graph is studied in terms of the moments.
Revised:  By using the duality argument , properties of the ancestral recombination graph are studied in terms of the moments.
Edit intent: fluency
Original:  For this purpose several modeling strategies such as the Gillespie algorithm and chemical master equations have been efficiently used .
Revised:  For this purpose several modeling strategies such as the Gillespie algorithm have been used successfully .
Edit intent: clarity
Original:  This manuscript contributes with an alternative approach from these classical settings.
Revised:  This manuscript contributes an alternative approach from these classical settings.
Edit intent: fluency
Original:  This manuscript contributes an alternative approach from these classical settings.
Revised:  This paper contributes an approach as an alternative to these classical settings.
Edit intent: clarity
Original:  This approach allows a finer analysis of discrete models and provide a natural set up for cell population simulations  .
Revised:  This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations .
Edit intent: fluency
Original:  We applied our methods to two of the best studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.
Revised:  We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.
Edit intent: clarity
Original: A number of representation schemes have been presented for use within Learning Classifier Systems , ranging from binary encodings to neural networks.
Revised: A number of representation schemes have been presented for use within learning classifier systems , ranging from binary encodings to neural networks.
Edit intent: fluency
Original:  This paper presents results from an investigation into using discrete and fuzzy dynamical system representations within the XCSF Learning Classifier System .
Revised:  This paper presents results from an investigation into using discrete and fuzzy dynamical system representations within the XCSF learning classifier system .
Edit intent: fluency
Original:  In particular, asynchronous Random Boolean Networks are used to represent the traditional condition-action production system rules in the discrete case and asynchronous Fuzzy Logic Networks in the continuous-valued case.
Revised:  In particular, asynchronous random Boolean networks are used to represent the traditional condition-action production system rules in the discrete case and asynchronous Fuzzy Logic Networks in the continuous-valued case.
Edit intent: fluency
Original:  In particular, asynchronous Random Boolean Networks are used to represent the traditional condition-action production system rules in the discrete case and asynchronous Fuzzy Logic Networks in the continuous-valued case.
Revised:  In particular, asynchronous Random Boolean Networks are used to represent the traditional condition-action production system rules in the discrete case and asynchronous fuzzy logic networks in the continuous-valued case.
Edit intent: fluency
Original: We studied the formation of exploratory patterns by Argentine ants  . Using a novel imaging and analysis technique on experimental data we estimated pheromone concentrations at all spatial positions in the experimental arena and at different times.
Revised: We studied the formation of trail patterns by Argentine ants . Using a novel imaging and analysis technique on experimental data we estimated pheromone concentrations at all spatial positions in the experimental arena and at different times.
Edit intent: clarity
Original: We studied the formation of exploratory patterns by Argentine ants  . Using a novel imaging and analysis technique on experimental data we estimated pheromone concentrations at all spatial positions in the experimental arena and at different times.
Revised: We studied the formation of exploratory patterns by Argentine ants . Using a novel imaging and analysis technique we estimated pheromone concentrations at all spatial positions in the experimental arena and at different times.
Edit intent: clarity
Original:  However, agent based simulations based on the Weber's Law response function determined experimentally produced results compatible with those reported in the literature and reproduced the formation of trails .
Revised:  However, agent based simulations implementing the Weber's Law response function determined experimentally produced results compatible with those reported in the literature and reproduced the formation of trails .
Edit intent: clarity
Original:  However, agent based simulations based on the Weber's Law response function determined experimentally produced results compatible with those reported in the literature and reproduced the formation of trails .
Revised:  However, agent based simulations based on the Weber's Law response function led to the formation of trails and reproduced results reported in the literature and reproduced the formation of trails .
Edit intent: clarity
Original:  However, agent based simulations based on the Weber's Law response function determined experimentally produced results compatible with those reported in the literature and reproduced the formation of trails .
Revised:  However, agent based simulations based on the Weber's Law response function determined experimentally produced results compatible with those reported in the literature .
Edit intent: clarity
Original:  We show analytically that  the classical Deneubourg model for collective decision making  can be derived from the individual Weber-type response to pheromone concentrations that we have established in our experiments when directional noise around the preferred direction of movement of the ants is assumed.
Revised:  We show analytically that the classical Deneubourg model for collective decision making , can be derived from the individual Weber-type response to pheromone concentrations that we have established in our experiments when directional noise around the preferred direction of movement of the ants is assumed.
Edit intent: fluency
Original: We consider an illiquid financial market where a risk-averse investor has to liquidate a large portfolio within a finite time horizon [0,T] and can trade continuously at a traditional exchange (the "primary venue") and in a dark pool.
Revised: We consider an illiquid financial market where a risk averse investor has to liquidate a large portfolio within a finite time horizon [0,T] and can trade continuously at a traditional exchange (the "primary venue") and in a dark pool.
Edit intent: fluency
Original: We consider an illiquid financial market where a risk-averse investor has to liquidate a large portfolio within a finite time horizon [0,T] and can trade continuously at a traditional exchange (the "primary venue") and in a dark pool.
Revised: We consider an illiquid financial market where a risk-averse investor has to liquidate a portfolio within a finite time horizon [0,T] and can trade continuously at a traditional exchange (the "primary venue") and in a dark pool.
Edit intent: clarity
Original:  Although the differential equation is not a Riccati equation, we are able to show that this limit exists by using an appropriate matrix inequality and a comparison result for Riccati  equations.
Revised:  We show that this limit exists by using an appropriate matrix inequality and a comparison result for Riccati equations.
Edit intent: coherence
Original:  According to the proposed decomposition, the h-index is the product of two indicators, the first of which measures the impact of the scientist on the research community and the second measures the level of concentration of the citations in correspondence of a reduced number of papers.
Revised:  According to the proposed decomposition, the h-index is the product of two indicators, the first of which measures the impact of the scientist on the research community and the second may be seen as a measure of concentration of the citations in correspondence of a reduced number of papers.
Edit intent: clarity
Original:  The paper has two contributions: a conceptual  and an algorithmical one.
Revised:  The paper has two contributions: a conceptual one and an algorithmical one.
Edit intent: fluency