wanyu/IteraTeR_v2 huggingface dataset:
Original: We use computer algebra to determine explicitly the three fundamental invariants  of a 3 x 3 x 3 array over C as polynomials in the 27 variables x _ijk for 1 <= \le i, j, k <= \le 3.
Revised: We use computer algebra to determine explicitly the three fundamental invariants of a 3 x 3 x 3 array over C as polynomials in the 27 variables x _ijk for 1 \le i, j, k <= \le 3.
Edit intent: fluency
Original: We use computer algebra to determine explicitly the three fundamental invariants  of a 3 x 3 x 3 array over C as polynomials in the 27 variables x _ijk for 1 <= \le i, j, k <= \le 3.
Revised: We use computer algebra to determine explicitly the three fundamental invariants of a 3 x 3 x 3 array over C as polynomials in the 27 variables x _ijk for 1 <= \le i, j, k \le 3.
Edit intent: fluency
Original: The problem of path generation for the spherical 4R mechanism is solved using the Differential Evolution  (DE) algorithm .
Revised: The problem of path generation for the spherical 4R mechanism is solved using the Differential Evolution (DE) .
Edit intent: clarity
Original:  Formulas for the spherical geodesics are employed in order to obtain the parametric equation for the trajectory of the mechanism end-effector . Direct optimization of the objective function gives  solution to the path generation task without prescribed timing.
Revised:  Formulas for the spherical geodesics are employed in order to obtain the parametric equation for the generated trajectory . Direct optimization of the objective function gives solution to the path generation task without prescribed timing.
Edit intent: clarity
Original:  Formulas for the spherical geodesics are employed in order to obtain the parametric equation for the trajectory of the mechanism end-effector . Direct optimization of the objective function gives  solution to the path generation task without prescribed timing.
Revised:  Formulas for the spherical geodesics are employed in order to obtain the parametric equation for the trajectory of the mechanism end-effector . Direct optimization of the objective function gives the solution to the path generation task without prescribed timing.
Edit intent: fluency
Original:  Therefore, there is no need to separate this task into two stages and then proceed to the optimization.
Revised:  Therefore, there is no need to separate this task into two stages to make the optimization.
Edit intent: coherence
Original:  Two examples of optimum synthesis showing the simplicity and effectiveness of the approach are included.
Revised:  Two examples of optimum synthesis showing the simplicity and effectiveness of this approach are included.
Edit intent: clarity
Original:  The kernels allow local description of affine transformations and subsequent compact description of non-translational movement and of the entire non-rigid deformation.
Revised:  The kernels allow local description of affine transformations and subsequent compact description of non-translational movement in a globally non-rigid deformation.
Edit intent: clarity
Original:  This is obtained with a representation that contains directly interpretable information from both mathematical and modeling perspectives.
Revised:  The resulting representation contains directly interpretable information from both mathematical and modeling perspectives.
Edit intent: clarity
Original:  We develop the mathematical construction behind the higher order kernels , we show the implications for sparse image registration and deformation description, and we provide examples of how the capacity of the kernels enables registration with a very low number of parameters.
Revised:  We develop the mathematical construction behind the higher order kernels , we show the implications for sparse image registration and deformation description, and we provide examples of how the parametrization enables registration with a very low number of parameters.
Edit intent: clarity
Original:  The capacity and interpretability of the kernels lead to natural modeling of articulated movement, and the kernels promise to be useful for quantifying ventricle expansion and progressing atrophy during Alzheimer's disease.
Revised:  The capacity and interpretability of the kernels lead to natural modeling of articulated movement, and the method promises to be useful for quantifying ventricle expansion and progressing atrophy during Alzheimer's disease.
Edit intent: clarity
Original:  We compare the performance of this method to the independent-pair, naive mean- field, Thouless-Anderson-Palmer approximations, the Sessak-Monasson expansion, and susceptibility propagation in the Cayley tree, SK-model and random graph with fixed degree .
Revised:  We compare the performance of this method to the independent-pair, naive mean- field, Thouless-Anderson-Palmer approximations, the Sessak-Monasson expansion, and susceptibility propagation in the Cayley tree, SK-model and random graph with fixed connectivity .
Edit intent: clarity
Original:  It also improves an earlier result by Bollob\'{a Our algorithm is asymptotically optimal, under the Exponential Time Hypothesis, and is strengthened by a polynomial-time computable kernel of polynomial size.
Revised:  Our algorithm is asymptotically optimal, under the Exponential Time Hypothesis, and is strengthened by a polynomial-time computable kernel of polynomial size.
Edit intent: coherence
Original:  We introduce a pricing scheme based on the transmission energy requirements and compute the symmetric Nash equilibrium of the game in closed form.
Revised:  We introduce a pricing scheme based on the transmission energy requirements and compute the symmetric Nash equilibria of the game in closed form.
Edit intent: fluency
Original:  The Price of anarchy is then analyzed for these games.
Revised:  The Price of Anarchy is then analyzed for these games.
Edit intent: fluency
Original:  With delay based utility, we bound the price of anarchy and study the effect of the price factor.
Revised:  For the game with delay based utility, we bound the price of anarchy and study the effect of the price factor.
Edit intent: clarity
Original:  With goodput based utility, it is shown that price of anarchy is infinite at the price factor that achieves the global optima.
Revised:  For the game with goodput based utility, it is shown that price of anarchy is infinite at the price factor that achieves the global optima.
Edit intent: clarity
Original:  If L is regular, then we prove that only finitely many distinct languages result.
Revised:  If L is regular, it is easy to see that only finitely many distinct languages result.
Edit intent: clarity
Original:  We use our technique to prove a similar result for the operation diag, which extracts the diagonal of words of square length  .
Revised:  We use our technique to show that the operation diag, which extracts the diagonal of words of square length .
Edit intent: clarity
Original:  These distributions are shown to be well described in the continuous approximation, which is then used to discuss the qualitative features of the protein equilibrium distributions as a function of the biological parameters in the fast mRNA regime  .
Revised:  These distributions are generally well described in the continuous approximation, which is then used to discuss the qualitative features of the protein equilibrium distributions as a function of the biological parameters in the fast mRNA regime .
Edit intent: clarity
Original: The expectation monad is introduced abstractly via two composable adjunctions, but concretely cap- tures measures.
Revised: The expectation monad is introduced abstractly via two composable adjunctions, but concretely captures measures.
Edit intent: fluency
Original:  These structures capture states and effects in quantum founda- tions , and also the duality between them.
Revised:  These structures capture states and effects in quantum foundations , and also the duality between them.
Edit intent: fluency
Original:  Resource detection or feeding patterns in space and time are not commonly studied, yet they are tightly coupled to landscape properties and add relevant information on foraging behavior.
Revised:  Resource detection patterns in space and time are not commonly studied, yet they are tightly coupled to landscape properties and add relevant information on foraging behavior.
Edit intent: clarity
Original:  For instance, detections are Poissonian in uniform random environments for markedly different foraging movements (e.g. L\'evy and ballistic).
Revised:  Detections are expected to be Poissonian in uniform random environments for markedly different foraging movements (e.g. L\'evy and ballistic).
Edit intent: clarity
Original:  In the context of long-range foraging seabirds, we find that the specific shape of the detection time distribution is mainly driven by meso and submeso-scale  structures and depends little on the forager strategy or behavioral responses .
Revised:  In the context of long-range foraging seabirds, we find that the specific shape of the distribution of time intervals between prey detection is mainly driven by meso and submeso-scale structures and depends little on the forager strategy or behavioral responses .
Edit intent: clarity
Original:  the separate power consumption of the processor cores and caches;
Revised:  the power consumption of the processor cores and caches;
Edit intent: clarity
Original:  We use this platform to generate realistic video decoding traces with which we simulate the proposed on-line scheduling algorithm in Matlab.
Revised:  We use this platform to generate realistic video decoding traces with which we evaluate the proposed on-line scheduling algorithm in Matlab.
Edit intent: clarity
Original: Changes in population size influence genetic diversity of the population and, as a result, leave imprints in individual genomes in the population.
Revised: Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population.
Edit intent: clarity
Original:  It turns out that the times where genealogical lineages coalesce contain all information about population size dynamics.
Revised:  It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics.
Edit intent: clarity
Original:  Viewing these coalescent times as a point process, estimation of population size trajectories is equivalent to estimating a conditional intensity of this point process.
Revised:  Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process.
Edit intent: fluency
Original:  We compare our Gaussian process (GP) approach to one of the state of the art Gaussian Markov random field (GMRF) methods for estimating population size dynamics . Using simulated data, we demonstrate that our method has better accuracy and precision.
Revised:  We compare our Gaussian process (GP) approach to one of the state of the art Gaussian Markov random field (GMRF) methods for estimating population trajectories . Using simulated data, we demonstrate that our method has better accuracy and precision.
Edit intent: clarity
Original:  Next, we analyze two genealogies reconstructed from real sequences of hepatitis C virus in Egypt and human Influenza A virus sampled in New York . In both cases, we recover more known aspects of the viral demographic histories than the GMRF approach.
Revised:  Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A virus sampled in New York . In both cases, we recover more known aspects of the viral demographic histories than the GMRF approach.
Edit intent: clarity
Original:  Next, we analyze two genealogies reconstructed from real sequences of hepatitis C virus in Egypt and human Influenza A virus sampled in New York . In both cases, we recover more known aspects of the viral demographic histories than the GMRF approach.
Revised:  Next, we analyze two genealogies reconstructed from real sequences of hepatitis C virus in Egypt and human Influenza A viruses . In both cases, we recover more known aspects of the viral demographic histories than the GMRF approach.
Edit intent: clarity
Original:  Next, we analyze two genealogies reconstructed from real sequences of hepatitis C virus in Egypt and human Influenza A virus sampled in New York . In both cases, we recover more known aspects of the viral demographic histories than the GMRF approach.
Revised:  Next, we analyze two genealogies reconstructed from real sequences of hepatitis C virus in Egypt and human Influenza A virus sampled in New York . In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach.
Edit intent: clarity
Original:  Looking at the optimization process as a "system" of interconnected parts, in this paper are collected some ideas about how to tackle an optimization problem using a class of tools from evolutionary computations called Genetic Algorithms.
Revised:  Looking at the optimization process as a "system" of intercon- nected parts, in this paper are collected some ideas about how to tackle an optimization problem using a class of tools from evolutionary computations called Genetic Algorithms.
Edit intent: fluency
Original:  Despite the number of optimization techniques available nowadays the author of this paper thinks that Genetic Algorithm still play a central role for their versatility, robustness, theoretical framework and simplicity of use.
Revised:  Despite the number of optimization techniques available nowadays the author of this paper thinks that Genetic Algorithms still play a central role for their versatility, robustness, theoretical framework and simplicity of use.
Edit intent: fluency
Original:  Using these two results, we provide new results on polynomially-solvable problems and hence refine the boundary between P and NP for these problems.
Revised:  Using these two results, we provide new results on polynomially solvable problems and hence refine the boundary between P and NP for these problems.
Edit intent: fluency
Original:  However, at shorter evolutionary times an apparent acceleration of the rate of molecular evolution has been noted.
Revised:  However, at shorter time scales a number of recent studies have observed an apparent acceleration of the rate of molecular evolution has been noted.
Edit intent: clarity
Original:  However, at shorter evolutionary times an apparent acceleration of the rate of molecular evolution has been noted.
Revised:  However, at shorter evolutionary times an apparent acceleration in the rate of molecular evolution has been noted.
Edit intent: clarity
Original:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at  t=0.
Revised:  We demonstrate that this apparent increase is a consequence of ignoring short term effects due to existing diversity within the population. The acceleration can be accounted for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at t=0.
Edit intent: clarity
Original:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at  t=0.
Revised:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at t=0.
Edit intent: fluency
Original:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at  t=0.
Revised:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 %DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at t=0.
Edit intent: fluency
Original:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at  t=0.
Revised:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at t=0.
Edit intent: fluency
Original:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at  t=0.
Revised:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 %DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at t=0.
Edit intent: fluency
Original:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at  t=0.
Revised:  We demonstrate that this apparent increase is a consequence of ignoring short term effects and show that for a Jukes-Cantor process it can be corrected for by adding the correction term h_0e^{ -4 \mu%DIFDELCMD < }%%% t /3} to the usual Jukes-Cantor formula p(t)=(3/4)(1-e^{ -4 \mu%DIFDELCMD < }%%% t /3}), where h_0 is the expected heterozygosity in the population at time t=0.
Edit intent: clarity
Original:  Given a geographic map and values associated with each country in the map, the cartogram is a new map in which the areas of the countries represent the corresponding values.
Revised:  Given a political map and values associated with each country in the map, the cartogram is a new map in which the areas of the countries represent the corresponding values.
Edit intent: style
Original:  Given a geographic map and values associated with each country in the map, the cartogram is a new map in which the areas of the countries represent the corresponding values.
Revised:  Given a geographic map and values associated with each country in the map, a cartogram is a new map in which the areas of the countries represent the corresponding values.
Edit intent: fluency
Original:  Given a geographic map and values associated with each country in the map, the cartogram is a new map in which the areas of the countries represent the corresponding values.
Revised:  Given a geographic map and values associated with each country in the map, the cartogram is a distorted map in which the areas of the countries represent the corresponding values.
Edit intent: clarity
Original:  Given a geographic map and values associated with each country in the map, the cartogram is a new map in which the areas of the countries represent the corresponding values.
Revised:  Given a geographic map and values associated with each country in the map, the cartogram is a new map in which the areas of the countries are proportional to the corresponding values.
Edit intent: clarity
Original:  In the circular-arc cartogram model straight-line segments can be replaced with circular arcs in order to achieve the desired areas , while the corners of the polygons defining each country remain fixed.
Revised:  In the circular-arc cartogram model straight-line segments can be replaced by circular arcs in order to achieve the desired areas , while the corners of the polygons defining each country remain fixed.
Edit intent: fluency
Original:  In the circular-arc cartogram model straight-line segments can be replaced with circular arcs in order to achieve the desired areas , while the corners of the polygons defining each country remain fixed.
Revised:  In the circular-arc cartogram model straight-line segments can be replaced with circular arcs in order to modify the areas of the polygons , while the corners of the polygons defining each country remain fixed.
Edit intent: clarity
Original:  In the circular-arc cartogram model straight-line segments can be replaced with circular arcs in order to achieve the desired areas , while the corners of the polygons defining each country remain fixed.
Revised:  In the circular-arc cartogram model straight-line segments can be replaced with circular arcs in order to achieve the desired areas , while the corners of the polygons remain fixed.
Edit intent: clarity
Original:  This makes is easy to determine whether a country has grown or shrunk, just by its overall shape.
Revised:  This makes it easy to determine whether a country has grown or shrunk, just by its overall shape.
Edit intent: fluency
Original:  We show that determining whether a given map and  area-values can be realized with a circular-arc cartogram is an NP-hard problem.
Revised:  We show that determining whether a given map and given area-values can be realized with a circular-arc cartogram is an NP-hard problem.
Edit intent: fluency
Original:  We show that determining whether a given map and  area-values can be realized with a circular-arc cartogram is an NP-hard problem.
Revised:  We show that determining whether a given map and area-values can be realized as a circular-arc cartogram is an NP-hard problem.
Edit intent: clarity
Original:  Next we describe a heuristic method for constructing circular-arc cartograms, which uses a max-flow computation on the dual  of the map, along with a computation of the straight skeleton of the underlying polygonal decomposition.
Revised:  Next we describe a heuristic method for constructing circular-arc cartograms, which uses a max-flow computation on the dual graph of the map, along with a computation of the straight skeleton of the underlying polygonal decomposition.
Edit intent: clarity
Original:  Our method is implemented and produces cartograms that, while not  perfectly accurate, achieve  the desired areas for many real-world examples.
Revised:  Our method is implemented and produces cartograms that, while not yet perfectly accurate, achieve the desired areas for many real-world examples.
Edit intent: clarity