wanyu/IteraTeR_v2 huggingface dataset:
Original:  Besides of this, we prove that the sizes of any two irredundant PC formulas for the same function differ at most by a polynomial factor in the number of the variables and present an example of a function demonstrating that a similar statement is not true for URC formulas.
Revised:  Besides of this, we prove that the sizes of any two irredundant PC formulas for the same function differ at most by a factor polynomial in the number of the variables and present an example of a function demonstrating that a similar statement is not true for URC formulas.
Edit intent: fluency
Original: In numerical integration, cubature methods are effective, in particular when the integrands can well be approximated by known test functions, such as polynomials.
Revised: In numerical integration, cubature methods are effective, especially when the integrands can well be approximated by known test functions, such as polynomials.
Edit intent: fluency
Original: In numerical integration, cubature methods are effective, in particular when the integrands can well be approximated by known test functions, such as polynomials.
Revised: In numerical integration, cubature methods are effective, in particular when the integrands can be well-approximated by known test functions, such as polynomials.
Edit intent: fluency
Original:  However, the construction of cubature formulas has not generally been known, and existing examples are only for particular domains of integrands such as hypercube and sphere .
Revised:  However, the construction of cubature formulas has not generally been known, and existing examples only represent the particular domains of integrands such as hypercube and sphere .
Edit intent: clarity
Original:  However, the construction of cubature formulas has not generally been known, and existing examples are only for particular domains of integrands such as hypercube and sphere .
Revised:  However, the construction of cubature formulas has not generally been known, and existing examples are only for particular domains of integrands , such as hypercubes and spheres .
Edit intent: fluency
Original:  In this study, we show that we can generally construct cubature formulas for probability measures provided that we have an i.i.d. sampler from the measure and  mean values of given test functions.
Revised:  In this study, we show that cubature formulas can be constructed for probability measures provided that we have an i.i.d. sampler from the measure and mean values of given test functions.
Edit intent: clarity
Original:  In this study, we show that we can generally construct cubature formulas for probability measures provided that we have an i.i.d. sampler from the measure and  mean values of given test functions.
Revised:  In this study, we show that we can generally construct cubature formulas for probability measures provided that we have an i.i.d. sampler from the measure and the mean values of given test functions.
Edit intent: fluency
Original:  We also see that our method work as a means of data compression, even if we do not have sufficient prior information of the measure  .
Revised:  Moreover, the proposed method also works as a means of data compression, even if we do not have sufficient prior information of the measure .
Edit intent: clarity
Original:  We also see that our method work as a means of data compression, even if we do not have sufficient prior information of the measure  .
Revised:  We also see that our method work as a means of data compression, even if sufficient prior information of the measure .
Edit intent: clarity
Original:  We obtain persistence and extinction results for the infected prey based on some assumptions on the bidimensional predator-prey subsystem that describes the dynamics in the absence of infected preys.
Revised:  We obtain persistence and extinction results for the infected prey based on assumptions on systems related to the dynamics in the absence of infected preys.
Edit intent: clarity
Original:  We apply our results to eco-epidemiological models constructed from several predator-prey models existent in the literature.
Revised:  We apply our results to eco-epidemiological models constructed from predator-prey models existent in the literature.
Edit intent: clarity
Original:  One consequence of this ill-conditioning is that the coefficients of  a frame approximation can grow large.
Revised:  One consequence of this ill-conditioning is that the coefficients of such a frame approximation can grow large.
Edit intent: clarity
Original:  As we show, these methods typically lead to little or no deterioration in the approximation accuracy, but successfully avoid the large coefficients inherent to previous approaches, thus making them attractive  where large coefficients are undesirable.
Revised:  As we show, these methods typically lead to little or no deterioration in the approximation accuracy, but successfully avoid the large coefficients inherent to previous approaches, thus making them attractive in situations where large coefficients are undesirable.
Edit intent: clarity
Original:  Utilizing data from five top neuroscience journals, we indeed find that reference lists tend to include more papers with men as first and last author than would be expected if gender was not a factor in referencing.
Revised:  Using data from five top neuroscience journals, we indeed find that reference lists tend to include more papers with men as first and last author than would be expected if gender was not a factor in referencing.
Edit intent: clarity
Original:  Utilizing data from five top neuroscience journals, we indeed find that reference lists tend to include more papers with men as first and last author than would be expected if gender was not a factor in referencing.
Revised:  Utilizing data from five top neuroscience journals, we find that reference lists tend to include more papers with men as first and last author than would be expected if gender was not a factor in referencing.
Edit intent: coherence
Original:  Utilizing data from five top neuroscience journals, we indeed find that reference lists tend to include more papers with men as first and last author than would be expected if gender was not a factor in referencing.
Revised:  Utilizing data from five top neuroscience journals, we indeed find that reference lists tend to include more papers with men as first and last author than would be expected if gender were not a factor in referencing.
Edit intent: fluency
Original:  Importantly, we show that this overcitation of men and undercitation of women is driven largely by the citation practices of men, and is increasing with time despite greater diversity in the academy .
Revised:  Importantly, we show that this overcitation of men and undercitation of women is driven largely by the citation practices of men, and is increasing over time as the field becomes more diverse .
Edit intent: clarity
Original:  We discuss possible mechanisms and consider how individual researchers might incorporate these findings into their own referencing practices.
Revised:  We discuss possible mechanisms and consider how individual researchers might address these findings in their own practices.
Edit intent: clarity
Original:  Artists paint using unique combinations of brushes, strokes, colors, and layers .
Revised:  Artists paint using unique combinations of brushes, strokes, and colors .
Edit intent: clarity
Original:  We implement this model as a convolutional neural network, and introduce a  training scheme to facilitate learning from a limited dataset of painting time lapses.
Revised:  We implement this model as a convolutional neural network, and introduce a novel training scheme to facilitate learning from a limited dataset of painting time lapses.
Edit intent: clarity
Original:  We implement this model as a convolutional neural network, and introduce a  training scheme to facilitate learning from a limited dataset of painting time lapses.
Revised:  We implement this model as a convolutional neural network, and introduce a training scheme to enable learning from a limited dataset of painting time lapses.
Edit intent: clarity
Original:  We evaluate our method on digital and watercolor paintings collected from video websites, and show that human raters find our synthesized videos to be similar to time lapses produced by real artists. 
Revised:  We evaluate our method on digital and watercolor paintings collected from video websites, and show that human raters find our synthetic videos to be similar to time lapses produced by real artists. 
Edit intent: fluency
Original:  We evaluate our method on digital and watercolor paintings collected from video websites, and show that human raters find our synthesized videos to be similar to time lapses produced by real artists. 
Revised:  We evaluate our method on digital and watercolor paintings collected from video websites, and show that human raters find our synthesized videos to be similar to time lapse videos produced by real artists. 
Edit intent: fluency
Original: Adaptive optics (AO) corrected flood imaging of the retina is a popular technique for studying the retinal structure and function in the living eye.
Revised: Adaptive optics (AO) corrected ood imaging of the retina is a popular technique for studying the retinal structure and function in the living eye.
Edit intent: fluency
Original: We present here two logical systems - intuitionistic paraconsistent weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL)  as examples of logics with some rules of inference that have variable sharing restrictions imposed on them.
Revised: We present here two logical systems - Intuitionistic Paraconsistent Weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL) as examples of logics with some rules of inference that have variable sharing restrictions imposed on them.
Edit intent: fluency
Original: We present here two logical systems - intuitionistic paraconsistent weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL)  as examples of logics with some rules of inference that have variable sharing restrictions imposed on them.
Revised: We present here two logical systems - intuitionistic paraconsistent weak Kleene logic (IPWK) and Paraconsistent Pre-Rough logic (PPRL) as examples of logics with some rules of inference that have variable sharing restrictions imposed on them.
Edit intent: fluency
Original: We present here two logical systems - intuitionistic paraconsistent weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL)  as examples of logics with some rules of inference that have variable sharing restrictions imposed on them.
Revised: We present here two logical systems - intuitionistic paraconsistent weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL) - are presented here as examples of logics with some rules of inference that have variable sharing restrictions imposed on them.
Edit intent: coherence
Original:  We prove that  peak age of information (AoI) at the receiver is minimized by a threshold-based stopping rule that accepts only young packets to the transmission server.
Revised:  We prove that average peak age of information (AoI) at the receiver is minimized by a threshold-based stopping rule that accepts only young packets to the transmission server.
Edit intent: fluency
Original: Diversity is a concept relevant to numerous domains of research as diverse as ecology, information theory, and  economics, to cite a few.
Revised: Diversity is a concept relevant to numerous domains of research varying from ecology, to information theory, and economics, to cite a few.
Edit intent: clarity
Original: Diversity is a concept relevant to numerous domains of research as diverse as ecology, information theory, and  economics, to cite a few.
Revised: Diversity is a concept relevant to numerous domains of research as diverse as ecology, information theory, and to economics, to cite a few.
Edit intent: fluency
Original:  It is a notion that is continuously gaining attention in the information retrieval, network analysis, and artificial neural networks communities.
Revised:  It is a notion that is steadily gaining attention in the information retrieval, network analysis, and artificial neural networks communities.
Edit intent: clarity
Original:  While the use of diversity measures in network-structured data finds a growing number of applications, no clear and comprehensive description is available for the different ways in which diversities can be measured in data described by these structures .
Revised:  While the use of diversity measures in network-structured data counts a growing number of applications, no clear and comprehensive description is available for the different ways in which diversities can be measured in data described by these structures .
Edit intent: fluency
Original:  While the use of diversity measures in network-structured data finds a growing number of applications, no clear and comprehensive description is available for the different ways in which diversities can be measured in data described by these structures .
Revised:  While the use of diversity measures in network-structured data finds a growing number of applications, no clear and comprehensive description is available for the different ways in which diversities can be measured .
Edit intent: clarity
Original:  In this article, we develop a formal framework for the application of a large family of diversity measures to heterogeneous information networks (HINs), a flexible, widely used, network data formalism.
Revised:  In this article, we develop a formal framework for the application of a large family of diversity measures to heterogeneous information networks (HINs), a flexible, widely-used network data formalism.
Edit intent: fluency
Original:  This allows for an extension of the application of diversity measures, from systems of classifications and apportionments, to more complex relations that can be better modeled by networks.
Revised:  This extends the application of diversity measures, from systems of classifications and apportionments, to more complex relations that can be better modeled by networks.
Edit intent: clarity
Original:  In doing so, we do not only provide an effective organization of multiple practices from different domains, but we also unearth new observables in systems modeled by heterogeneous information networks.
Revised:  In doing so, we not only provide an effective organization of multiple practices from different domains, but we also unearth new observables in systems modeled by heterogeneous information networks.
Edit intent: fluency
Original:  In doing so, we do not only provide an effective organization of multiple practices from different domains, but we also unearth new observables in systems modeled by heterogeneous information networks.
Revised:  In doing so, we do not only provide an effective organization of multiple practices from different domains, but also unearth new observables in systems modeled by heterogeneous information networks.
Edit intent: fluency
Original:  The pertinence of the approach is illustrated by the development of different applications related to various domains concerned by both diversity and networks.
Revised:  We illustrate the pertinence of our approach by developing different applications related to various domains concerned by both diversity and networks.
Edit intent: clarity
Original:  In particular, we illustrate the usefulness of these new proposed observables in the domains of recommender systems and social media studies  among other fields.
Revised:  In particular, we illustrate the usefulness of these new proposed observables in the domains of recommender systems and social media studies , among other fields.
Edit intent: fluency
Original: We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form \mathsf{A x=\lambda \mathsf{B x, where the matrices \mathsf{A and/or \mathsf{B may depend on a scalar parameter.
Revised: We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form x=\lambda \mathsf{B x, where the matrices \mathsf{A and/or \mathsf{B may depend on a scalar parameter.
Edit intent: fluency
Original: We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form \mathsf{A x=\lambda \mathsf{B x, where the matrices \mathsf{A and/or \mathsf{B may depend on a scalar parameter.
Revised: We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form \mathsf{A x=\lambda x, where the matrices \mathsf{A and/or \mathsf{B may depend on a scalar parameter.
Edit intent: fluency
Original: We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form \mathsf{A x=\lambda \mathsf{B x, where the matrices \mathsf{A and/or \mathsf{B may depend on a scalar parameter.
Revised: We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form \mathsf{A x=\lambda \mathsf{B x, where the matrices and/or \mathsf{B may depend on a scalar parameter.
Edit intent: fluency
Original: We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form \mathsf{A x=\lambda \mathsf{B x, where the matrices \mathsf{A and/or \mathsf{B may depend on a scalar parameter.
Revised: We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form \mathsf{A x=\lambda \mathsf{B x, where the matrices \mathsf{A and/or may depend on a scalar parameter.
Edit intent: fluency
Original: We introduce a new , diagrammatic notation for representing the result of algebraic effectful computations.
Revised: We introduce a new diagrammatic notation for representing the result of algebraic effectful computations.
Edit intent: fluency
Original: We introduce a new , diagrammatic notation for representing the result of algebraic effectful computations.
Revised: We introduce a new , diagrammatic notation for representing the result of (algebraic) effectful computations.
Edit intent: fluency
Original:   We give a formal foundation for our notation in terms of Lawvere theories and generic effects.
Revised:  We give a formal foundation for such a calculus in terms of Lawvere theories and generic effects.
Edit intent: clarity
Original: When training the sequence-to-sequence voice conversion model, we need to handle an issue of insufficient data about the number of speech tuples which consist of the same utterance.
Revised: For training the sequence-to-sequence voice conversion model, we need to handle an issue of insufficient data about the number of speech tuples which consist of the same utterance.
Edit intent: clarity
Original: When training the sequence-to-sequence voice conversion model, we need to handle an issue of insufficient data about the number of speech tuples which consist of the same utterance.
Revised: When training the sequence-to-sequence voice conversion model, we need to handle an issue of insufficient data about the number of speech pairs which consist of the same utterance.
Edit intent: clarity
Original:  This study experimentally investigated the effects of Mel-spectrogram augmentation on  the sequence-to-sequence voice conversion model .
Revised:  This study experimentally investigated the effects of Mel-spectrogram augmentation on training the sequence-to-sequence voice conversion model .
Edit intent: clarity
Original:  To find the optimal hyperparameters of augmentation policies for voice conversion, we experimented based on the new metric  , namely deformation per deteriorating ratio.
Revised:  Moreover, to find the appropriate hyperparameters of augmentation policies for voice conversion, we experimented based on the new metric , namely deformation per deteriorating ratio.
Edit intent: clarity
Original:  We observed the effect of these through experiments based on various sizes of training set and combinations of augmentation policy .
Revised:  We compared the effect of these through experiments based on various sizes of training set and combinations of augmentation policy .
Edit intent: clarity
Original:  We observed the effect of these through experiments based on various sizes of training set and combinations of augmentation policy .
Revised:  We observed the effect of these Mel-spectrogram augmentation methods based on various sizes of training set and combinations of augmentation policy .
Edit intent: clarity
Original:  We observed the effect of these through experiments based on various sizes of training set and combinations of augmentation policy .
Revised:  We observed the effect of these through experiments based on various sizes of training set and augmentation policies .
Edit intent: clarity
Original: The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs \varepsilon \subseteq E or vertices \nu \subseteq V whose removal G\setminus \varepsilon, G\setminus \nu makes a given multi-digraph G=(V,E) acyclic, respectively.
Revised: The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs \varepsilon \subseteq E or vertices \nu \subseteq V whose removal G\setminus \varepsilon, G\setminus \nu makes a given multi-digraph G=(V,E) acyclic, respectively.
Edit intent: fluency
Original:  The corresponding decision problems are part of the 21 NP-complete problems of R. M. Karp's famous list.
Edit intent: coherence
Original:  While  r \approx 1.3606 is known to be a lower bound for the APX-hardness, at least by validation, we show that r \leq 2. Applying the approximation preserving L-reduction from the directed FVSP to the FASP thereby allows computing feedback vertex sets with the same accuracy.
Revised:  While r \approx 1.3606 is known to be a lower bound for the APX-hardness, at least by empirical validation we achieve an approximation of r \leq 2. Applying the approximation preserving L-reduction from the directed FVSP to the FASP thereby allows computing feedback vertex sets with the same accuracy.
Edit intent: clarity
Original:  Benchmarking the algorithm with state of the art alternatives yields that, for the first time, the most relevant instance class of large sparse graphs can be solved efficiently within tight error bounds .
Revised:  Benchmarking the algorithm with state of the art alternatives yields that, for the first time, the most relevant instance class of large sparse graphs , which can be done efficiently within tight error bounds .
Edit intent: clarity
Original:  In particular, the impact of back-propagating waves on the Dirichlet-to-Neumann map will be analyzed.
Revised:  In particular, the impact of back-propagating waves on the Dirichlet-to-Neumann map is analyzed.
Edit intent: clarity
Original:  Afterwards, the performance of the well-established optimized 0th-order, evanescent modes damping, optimized 2nd-order and Pad\'e-localized square-root transmission conditions will be discussed.
Revised:  Afterwards, the performance of the well-established optimized 0th-order, evanescent modes damping, optimized 2nd-order and Pad\'e-localized square-root transmission conditions is discussed.
Edit intent: clarity
Original: Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination for programs operating on integers.
Revised: Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers.
Edit intent: fluency