wanyu/IteraTeR_v2 huggingface dataset:
Original:  we have considered in addition the influence of exclusion forces.
Revised:  we have considered , in addition, the influence of exclusion forces.
Edit intent: fluency
Original:  The order of the derivative at which the jump is observed is given by r(d+1), where r is the relative degree of the network transfer matrix, and d denotes the distance from the location of the failure to the observation point.
Revised:  The order of the derivative at which the jump is observed is given by r(d+1), where r is the relative degree of each system's transfer matrix, and d denotes the distance from the location of the failure to the observation point.
Edit intent: clarity
Original:  Furthermore, while written in Java, the toolkit can be used directly in MATLAB, GNU Octave and Python .
Revised:  Furthermore, while written in Java, the toolkit can be used directly in MATLAB, GNU Octave , Python and other environments .
Edit intent: clarity
Original:  We also show that every unit circular-arc graph admits\cal \cal \cal \cal \cal  a minimal circular-arc modeland provide a polynomial time algorithm that finds such a model.
Revised:  We also show that every unit circular-arc graph admits\cal \cal \cal \cal \cal a polynomial time algorithm that finds such a model.
Edit intent: clarity
Original:  We fix Mitas' algorithm but, unfortunately, the obtained algorithm runs in quadratic time and space .
Revised:  We fix this algorithm but, unfortunately, the obtained algorithm runs in quadratic time and space .
Edit intent: clarity
Original:  Finally, we discuss how the algorithms in this paper can be applied so as to find minimal powers of paths and cycles that contain a given proper interval graphs and unit circular-arc graph as induced subgraphs , respectively.
Revised:  Finally, we apply the minimal representation algorithms so as to find minimal powers of paths and cycles that contain a given proper interval graphs and unit circular-arc graph as induced subgraphs , respectively.
Edit intent: clarity
Original:  Finally, we discuss how the algorithms in this paper can be applied so as to find minimal powers of paths and cycles that contain a given proper interval graphs and unit circular-arc graph as induced subgraphs , respectively.
Revised:  Finally, we discuss how the algorithms in this paper can be applied so as to find the minimum powers of paths and cycles that contain a given proper interval graphs and unit circular-arc graph as induced subgraphs , respectively.
Edit intent: fluency
Original: We present a model of the cerebellum with two defining characteristics.
Revised: We present a cerebellar architecture with two main characteristics.
Edit intent: clarity
Original:  Although testing membership in \Lambda of a given arrival rate can be posed as a convex program, it is nonetheless of interest to understand the geometric properties of this set.
Revised:  Although testing membership in \Lambda of a given arrival rate can be posed as a convex program, it is nonetheless of interest to understand the properties of this set.
Edit intent: clarity
Original:  several equivalent descriptions of \Lambda , ii) a method to construct a vector of contention probabilities to stabilize any stabilizable arrival rate  , iii) the volume of \Lambda, iv) explicit polyhedral, spherical, and ellipsoid inner and outer bounds on \Lambda, and v) characterization of the generalized convexity properties of a natural "excess rate" function associated with \Lambda, including the convexity of the set of contention probabilities that stabilize a given arrival rate vector.
Revised:  several equivalent descriptions of \Lambda , ii) a method to construct a vector of contention probabilities to stabilize any stabilizable arrival rate vector , iii) the volume of \Lambda, iv) explicit polyhedral, spherical, and ellipsoid inner and outer bounds on \Lambda, and v) characterization of the generalized convexity properties of a natural "excess rate" function associated with \Lambda, including the convexity of the set of contention probabilities that stabilize a given arrival rate vector.
Edit intent: fluency
Original:  several equivalent descriptions of \Lambda , ii) a method to construct a vector of contention probabilities to stabilize any stabilizable arrival rate  , iii) the volume of \Lambda, iv) explicit polyhedral, spherical, and ellipsoid inner and outer bounds on \Lambda, and v) characterization of the generalized convexity properties of a natural "excess rate" function associated with \Lambda, including the convexity of the set of contention probabilities that stabilize a given arrival rate vector.
Revised:  several equivalent descriptions of \Lambda , ii) a method to construct a vector of contention probabilities to stabilize any stabilizable arrival rate , iii) the volume of \Lambda, iv) explicit polyhedral, spherical, and ellipsoid inner and outer bounds on \Lambda, and v) characterization of the generalized convexity properties of a natural ``excess rate'' function associated with \Lambda, including the convexity of the set of contention probabilities that stabilize a given arrival rate vector.
Edit intent: fluency
Original:  On a global level , windows of immigration (in migration) map to the seasonal timing of epidemic spread, while windows of emigration (out migration) to epidemic decline.
Revised:  On a global level , windows of immigration (in migration) map to the seasonal timing of epidemic spread, while windows of increased emigration map to epidemic decline.
Edit intent: clarity
Original:  Seasonal patterns also affect the probability that local lineages go extinct and fail to contribute to long term viral evolution .
Revised:  Seasonal patterns also correlate with the probability that local lineages go extinct and fail to contribute to long term viral evolution .
Edit intent: clarity
Original:  This will better our understanding of seasonal drivers, improve predictions, and improve vaccine updating by identifying strains that not only escape immunity but also have the seasonal opportunity to establish and spread.
Revised:  This will better our understanding of the seasonal drivers of influenza,enhance epidemiological predictions, and improve vaccine updating by identifying strains that not only escape immunity but also have the seasonal opportunity to establish and spread.
Edit intent: clarity
Original:  This will better our understanding of seasonal drivers, improve predictions, and improve vaccine updating by identifying strains that not only escape immunity but also have the seasonal opportunity to establish and spread.
Revised:  This will better our understanding of seasonal drivers, improve predictions, and ameliorate vaccine updating by identifying strains that not only escape immunity but also have the seasonal opportunity to establish and spread.
Edit intent: clarity
Original:  Further work is also needed on additional conditions that contribute to the persistence and long term evolution of influenza within the human population,such as spatial heterogeneity with respect to climate and seasonality .
Revised:  Further work is also needed on additional conditions that contribute to the persistence and long term evolution of influenza within the human population,such as spatial heterogeneity with respect to climate and seasonality 
Edit intent: fluency
Original:  Its axiomatization, Koz, was introduced at the same time and is an extension of the minimal modal logic K with the so-called Park 's fixpoint induction principle.
Revised:  Its axiomatization, Koz, was introduced at the same time and is an extension of the minimal modal logic K with the so-called Park fixpoint induction principle.
Edit intent: fluency
Original:  Keywords: The modal mu-calculus, completeness, parity games, parity automata .
Revised:  Keywords: The modal mu-calculus, completeness, omega-automata .
Edit intent: clarity
Original:  Such nutrient balance within a food was quantified herein as nutritional fitness, using the food's frequency of occurrence in nutritionally-adequate food combinations.
Revised:  The nutrient balance of a food was quantified herein as nutritional fitness, using the food's frequency of occurrence in nutritionally-adequate food combinations.
Edit intent: clarity
Original:  Such nutrient balance within a food was quantified herein as nutritional fitness, using the food's frequency of occurrence in nutritionally-adequate food combinations.
Revised:  Such nutrient balance within a food was quantified herein as nutritional fitness, using the food's frequency of occurrence in nutritionally adequate food combinations.
Edit intent: fluency
Original:  Nutritional fitness offers prioritization of recommendable foods within a food network , in which foods are connected based on similarities of nutrient compositions.
Revised:  Nutritional fitness offers prioritization of recommendable foods within a global network of foods , in which foods are connected based on similarities of nutrient compositions.
Edit intent: clarity
Original:  Nutritional fitness offers prioritization of recommendable foods within a food network , in which foods are connected based on similarities of nutrient compositions.
Revised:  Nutritional fitness offers prioritization of recommendable foods within a food network , in which foods are connected based on the similarities of their nutrient compositions.
Edit intent: clarity
Original:  We found a number of key nutrients, such as choline and \alpha-linolenic acid, whose levels in foods can critically affect the foods' nutritional fitness.
Revised:  We identified a number of key nutrients, such as choline and \alpha-linolenic acid, whose levels in foods can critically affect the foods' nutritional fitness.
Edit intent: fluency
Original:  We found a number of key nutrients, such as choline and \alpha-linolenic acid, whose levels in foods can critically affect the foods' nutritional fitness.
Revised:  We found a number of key nutrients, such as choline and alpha-linolenic acid, whose levels in foods can critically affect the foods' nutritional fitness.
Edit intent: fluency
Original:  In fact, two nutrients can impact  nutritional fitness synergistically, although the individual nutrients alone may not.
Revised:  In fact, two nutrients can impact the nutritional fitness synergistically, although the individual nutrients alone may not.
Edit intent: fluency
Original:  This result, involving the tendency among nutrients to show correlations in their abundances across foods, implies a hidden layer of complexity when exploring for foods whose balance of nutrients within pairs holistically helps satisfy nutritional requirements.
Revised:  This result, involving the tendency among nutrients to show correlations in their abundances across foods, implies a hidden layer of complexity when exploring for foods whose balance of nutrients within pairs holistically helps meet nutritional requirements.
Edit intent: clarity
Original:  This effect expands our scope to a diverse repertoire of nutrient-nutrient correlations, integrated under a common network framework which yields unexpected yet coherent associations between nutrients.
Revised:  This effect expands our scope to a diverse repertoire of nutrient-nutrient correlations, integrated under a common network framework that yields unexpected yet coherent associations between nutrients.
Edit intent: fluency
Original:  Our nutrient-profiling approach combined with  network-based analysis provides a more unbiased, global view of  relationships between foods and nutrients, and can be extended towards nutritional policies, food marketing, and personalized nutrition.
Revised:  Our nutrient-profiling approach combined with a network-based analysis provides a more unbiased, global view of relationships between foods and nutrients, and can be extended towards nutritional policies, food marketing, and personalized nutrition.
Edit intent: fluency
Original:  Our nutrient-profiling approach combined with  network-based analysis provides a more unbiased, global view of  relationships between foods and nutrients, and can be extended towards nutritional policies, food marketing, and personalized nutrition.
Revised:  Our nutrient-profiling approach combined with network-based analysis provides a more unbiased, global view of the relationships between foods and nutrients, and can be extended towards nutritional policies, food marketing, and personalized nutrition.
Edit intent: fluency
Original:  We proof that this problem is NP-hard.
Revised:  We prove that this problem is NP-hard.
Edit intent: clarity
Original: Stochastic dynamical system models are often used to help understand the behavior of intracellular biochemical processes.
Revised: Stochastic models are often used to help understand the behavior of intracellular biochemical processes.
Edit intent: clarity
Original:  The methods are rather intuitive and utilize the multi-level Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.
Revised:  The methods are rather intuitive and utilize the multilevel Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.
Edit intent: clarity
Original:  Any cube is the unit length on each edge and its surface is colored so that what we call  Surface Color Condition is satisfied.
Revised:  Each cube has unit length on each edge and its surface is colored so that what we call Surface Color Condition is satisfied.
Edit intent: clarity
Original:  Any cube is the unit length on each edge and its surface is colored so that what we call  Surface Color Condition is satisfied.
Revised:  Any cube is the unit length on each edge and its surface is colored so that what we call the Surface Color Condition is satisfied.
Edit intent: fluency
Original:  Given a palette of 6 colors, the condition requires that each face should be assigned exactly one color and all faces should be assigned 6 different colors from each other.
Revised:  Given a palette of six colors, the condition requires that each face should be assigned exactly one color and all faces should be assigned 6 different colors from each other.
Edit intent: fluency
Original:  Given a palette of 6 colors, the condition requires that each face should be assigned exactly one color and all faces should be assigned 6 different colors from each other.
Revised:  Given a palette of 6 colors, the condition requires that each face should have exactly one color and all faces should be assigned 6 different colors from each other.
Edit intent: clarity
Original:  Given a palette of 6 colors, the condition requires that each face should be assigned exactly one color and all faces should be assigned 6 different colors from each other.
Revised:  Given a palette of 6 colors, the condition requires that each face should be assigned exactly one color and all faces should have different colors from each other.
Edit intent: clarity
Original:  The puzzle asks to compose a 2x2x2 cube that satisfies  Surface Color Condition from 8 suitable cubes in the instance.
Revised:  The puzzle asks to compose a 2x2x2 cube that satisfies the Surface Color Condition from 8 suitable cubes in the instance.
Edit intent: fluency
Original:  The puzzle asks to compose a 2x2x2 cube that satisfies  Surface Color Condition from 8 suitable cubes in the instance.
Revised:  The puzzle asks to compose a 2x2x2 cube that satisfies Surface Color Condition from eight suitable cubes in the instance.
Edit intent: fluency
Original:  Next we create two extreme instances: a universal instance (i.e., one having all 30 solutions)and an infeasible instance (i.e., one having no solution ).
Revised:  Next we create two extreme instances: a universal instance (i.e., one having all 30 solutions)and an infeasible instance (i.e., one having all 30 solutions ).
Edit intent: clarity
Original:  The latter result affirmatively solves one of the open problems that were raised in [E.Berkove et al., "An Analysis of the (Colored Cubes)^3 Puzzle," Discrete Mathematics, Vol. 308 (2008) pp. 1033--1045 ].
Revised:  The latter result affirmatively solves one of the open problems that were raised in [E.Berkove et al., "An Analysis of the (Colored Cubes)^3 Puzzle," Discrete Mathematics, 308 (2008) pp. 1033--1045 ].
Edit intent: clarity
Original:  The latter result affirmatively solves one of the open problems that were raised in [E.Berkove et al., "An Analysis of the (Colored Cubes)^3 Puzzle," Discrete Mathematics, Vol. 308 (2008) pp. 1033--1045 ].
Revised:  The latter result affirmatively solves one of the open problems that were raised in [E.Berkove et al., "An Analysis of the (Colored Cubes)^3 Puzzle," Discrete Mathematics, Vol. 308 (2008) pp. 1033-1045 ].
Edit intent: fluency
Original: Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain new results that are of interest from both quantum theory and the  complexity theory point of view.
Revised: Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the complexity theory point of view.
Edit intent: clarity
Original: Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain new results that are of interest from both quantum theory and the  complexity theory point of view.
Revised: Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain new results that are of interest from both quantum theory and the computational complexity theory point of view.
Edit intent: clarity
Original:  On the other hand, considering input squeezed-vacuum states , we show the output probabilities are proportional to a quantity which is, for at least a specific configuration, #P-hard to approximate .
Revised:  We further consider input squeezed-vacuum states , we show the output probabilities are proportional to a quantity which is, for at least a specific configuration, #P-hard to approximate .
Edit intent: clarity
Original:  On the other hand, considering input squeezed-vacuum states , we show the output probabilities are proportional to a quantity which is, for at least a specific configuration, #P-hard to approximate .
Revised:  On the other hand, considering input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output .
Edit intent: clarity
Original:  Furthermore, the trading strategy is given by a dynamical programming algorithm .
Revised:  Furthermore, we use binomial models in order to provide numerical schemes for the calculation of the shortfall risk and the corresponding optimal portfolio in the BS model .
Edit intent: coherence
Original:  To outline what is achievable in principle and in practic , we recall how some limits were circumvented, compare loose and tight limits.
Revised:  To outline what is achievable in principle and in practice , we recall how some limits were circumvented, compare loose and tight limits.
Edit intent: fluency
Original:  As a consequence , we show that in both cases the probability to see the maximal possible number of equilibria tends to zero when d or n respectively goes to infinity  .
Revised:  As a consequence , we show that in both cases the probability of seeing the maximal possible number of equilibria tends to zero when d or n respectively goes to infinity .
Edit intent: fluency
Original: We evaluate a version of the recently-proposed  Optimized Dissimilarity Space Embedding (ODSE) classification system that operates in the input space of sequences of generic objects.
Revised: We evaluate a version of the recently-proposed Optimized Dissimilarity Space Embedding (ODSE) that operates in the input space of sequences of generic objects.
Edit intent: clarity
Original:  The ODSE system has been originally presented as a labeled graph classification system .
Revised:  The ODSE system has been originally presented as a classification system for patterns represented as labeled graphs .
Edit intent: clarity
Original:  We demonstrate the effectiveness of the ODSE classifier for sequences  considering an application dealing with  recognition of the solubility degree of the Escherichia coli proteome.
Revised:  Here we demonstrate the effectiveness of the ODSE classifier for sequences considering an application dealing with recognition of the solubility degree of the Escherichia coli proteome.
Edit intent: fluency
Original:  We demonstrate the effectiveness of the ODSE classifier for sequences  considering an application dealing with  recognition of the solubility degree of the Escherichia coli proteome.
Revised:  We demonstrate the effectiveness of the ODSE classifier for sequences by considering an application dealing with recognition of the solubility degree of the Escherichia coli proteome.
Edit intent: coherence
Original:  We demonstrate the effectiveness of the ODSE classifier for sequences  considering an application dealing with  recognition of the solubility degree of the Escherichia coli proteome.
Revised:  We demonstrate the effectiveness of the ODSE classifier for sequences considering an application dealing with the recognition of the solubility degree of the Escherichia coli proteome.
Edit intent: fluency
Original:  However, when combined with the mutation trajectory, these observables place strong constraints on the set of possible models of epistasis, ruling out most existing explanations of the data.
Revised:  However, when combined with the mutation trajectory, these observables place strong constraints on the set of possible models of epistasis, ruling out many existing explanations of the data.
Edit intent: clarity
Original:  Instead, we find the strongest support for a "two-epoch" model of adaptation, in which an initial burst of diminishing returns epistasis is followed by a steady accumulation of mutations under a constant distribution of fitness effects.
Revised:  Instead, we find that the data are consistent with "two-epoch" model of adaptation, in which an initial burst of diminishing returns epistasis is followed by a steady accumulation of mutations under a constant distribution of fitness effects.
Edit intent: clarity
Original: An integro-differential model for evolutionary dynamics with muta- tions is investigated by improving the understanding of its behavior using numerical simulations.
Revised: An integro-differential model for evolutionary dynamics with mutations is investigated by improving the understanding of its behavior using numerical simulations.
Edit intent: fluency
Original:  We find  sparse and heterogeneous connectivity patterns to emerge, which show qualitative agreement with real transcriptional regulatory networks and metabolic networks.
Revised:  We find that sparse and heterogeneous connectivity patterns to emerge, which show qualitative agreement with real transcriptional regulatory networks and metabolic networks.
Edit intent: fluency
Original:  We find  sparse and heterogeneous connectivity patterns to emerge, which show qualitative agreement with real transcriptional regulatory networks and metabolic networks.
Revised:  We find sparse and heterogeneous connectivity patterns emerge, which show qualitative agreement with real transcriptional regulatory networks and metabolic networks.
Edit intent: clarity
Original:  However, many real life systems involve multiple kinds of objects .
Revised:  However, many real-life systems involve multiple kinds of objects .
Edit intent: coherence
Original:  The general approach is illustrated by examples and theoretical findings are compared with numerical calculations.
Revised:  The general approach is illustrated by examples ; theoretical findings are compared with numerical calculations.
Edit intent: coherence