wanyu/IteraTeR_v2 huggingface dataset:
Original:  It has worst case running time n^{ 1/2%DIFDELCMD < \MBLOCKRIGHTBRACEm%%%   ^{ 1/2%DIFDELCMD < \MBLOCKRIGHTBRACEspoly%%% (log  (n), log (m), R, r, 1/ delta ), with n and s the dimension and sparsity of the input matrices, respectively, m the number of constraints, delta the accuracy of the solution, and R, r  upper bounds on the size of the optimal primal and dual solutions.
Revised:  It has worst case running time n^{ 1/2%DIFDELCMD < \MBLOCKRIGHTBRACEm%%% ^{ 1/2%DIFDELCMD < \MBLOCKRIGHTBRACEspoly%%% (log (n), log (m), R, r, 1/ delta ), with n and s the dimension and sparsity of the input matrices, respectively, m the number of constraints, \delta the accuracy of the solution, and R, r upper bounds on the size of the optimal primal and dual solutions.
Edit intent: clarity
Original:  It has worst case running time n^{ 1/2%DIFDELCMD < \MBLOCKRIGHTBRACEm%%%   ^{ 1/2%DIFDELCMD < \MBLOCKRIGHTBRACEspoly%%% (log  (n), log (m), R, r, 1/ delta ), with n and s the dimension and sparsity of the input matrices, respectively, m the number of constraints, delta the accuracy of the solution, and R, r  upper bounds on the size of the optimal primal and dual solutions.
Revised:  It has worst case running time n^{ 1/2%DIFDELCMD < \MBLOCKRIGHTBRACEm%%% ^{ 1/2%DIFDELCMD < \MBLOCKRIGHTBRACEspoly%%% (log (n), log (m), R, r, 1/ delta ), with n and s the dimension and sparsity of the input matrices, respectively, m the number of constraints, delta the accuracy of the solution, and R, r a upper bounds on the size of the optimal primal and dual solutions.
Edit intent: fluency
Original:  In particular it is based on an classical algorithm of Arora and Kale for approximately solving SDPs.
Revised:  In particular it is based on a classical algorithm of Arora and Kale for approximately solving SDPs.
Edit intent: fluency
Original:  We present a modification of their algorithm to eliminate the need of solving an inner linear program which may be of independent interest.
Revised:  We present a modification of their algorithm to eliminate the need for solving an inner linear program which may be of independent interest.
Edit intent: fluency
Original:  We examined whether evolution of the shared species acts as a coexistence mechanism and to what extent the answer depends on the genetic architecture underlying the evolving traits.
Revised:  We examine whether evolution of the shared species acts as a coexistence mechanism and to what extent the answer depends on the genetic architecture underlying the evolving traits.
Edit intent: fluency
Original:  The shared species evolves  defense or prey use in these modules .
Revised:  The shared species evolves its defense or prey use in these modules .
Edit intent: fluency
Original:  The shared species evolves  defense or prey use in these modules .
Revised:  The shared species evolves defense or prey use .
Edit intent: clarity
Original:  A single locus pleiotropically determines the nutritional quality of prey and the ability to capture prey .
Revised:  A single locus pleiotropically determines prey nutritional quality and predator attack rates .
Edit intent: clarity
Original:  When pleiotropy is sufficiently antagonistic (e.g. nutritional prey are harder to capture), community assembly culminates in one of two stable states supporting only two species.
Revised:  When pleiotropy is sufficiently antagonistic (e.g. nutritional prey are harder to capture), eco-evolutionary assembly culminates in one of two stable states supporting only two species.
Edit intent: clarity
Original:  When pleiotropy is weakly antagonistic or synergistic, the assembly dynamics are intransitive: species-genotype pairs are successively displaced in a cyclic fashion by rare invasions of the missing genotypes or species.
Revised:  When pleiotropy is weakly antagonistic or synergistic, assembly is intransitive: species-genotype pairs are successively displaced in a cyclic fashion by rare invasions of the missing genotypes or species.
Edit intent: clarity
Original:  When pleiotropy is weakly antagonistic or synergistic, the assembly dynamics are intransitive: species-genotype pairs are successively displaced in a cyclic fashion by rare invasions of the missing genotypes or species.
Revised:  When pleiotropy is weakly antagonistic or synergistic, the assembly dynamics are intransitive: species-genotype pairs are cyclically displaced by rare invasions of the missing genotypes or species.
Edit intent: clarity
Original:  This intransitive dynamic allows for coexistence if, along its equilibria, the geometric mean of recovery rates of rare genotypes or species exceeds the geometric mean of loss rates of  rare genotypes or species.
Revised:  This intransitivity allows for coexistence if, along its equilibria, the geometric mean of recovery rates of rare genotypes or species exceeds the geometric mean of loss rates of rare genotypes or species.
Edit intent: clarity
Original:  This intransitive dynamic allows for coexistence if, along its equilibria, the geometric mean of recovery rates of rare genotypes or species exceeds the geometric mean of loss rates of  rare genotypes or species.
Revised:  This intransitive dynamic allows for coexistence if, along its equilibria, the geometric mean of recovery rates exceeds the geometric mean of loss rates of rare genotypes or species.
Edit intent: fluency
Original:  This intransitive dynamic allows for coexistence if, along its equilibria, the geometric mean of recovery rates of rare genotypes or species exceeds the geometric mean of loss rates of  rare genotypes or species.
Revised:  This intransitive dynamic allows for coexistence if, along its equilibria, the geometric mean of recovery rates of rare genotypes or species exceeds the geometric mean of loss rates of the rare genotypes or species.
Edit intent: fluency
Original:  For diploid populations experiencing weak antagonistic pleiotropy, superadditive contributions of alleles to heterozygote fitness can mitigate coexistence via an eco-evolutionary storage effect.
Revised:  For diploid populations experiencing weak antagonistic pleiotropy, superadditive allelic contributions to fitness can mitigate coexistence via an eco-evolutionary storage effect.
Edit intent: clarity
Original:  Density-dependence and mutations also can mitigate coexistence.
Revised:  Density-dependence and mutations also promote coexistence.
Edit intent: clarity
Original:  These results suggest that eco-evolutionary feedbacks can maintain genetic and species diversity, but the strength of this coexistence mechanism depends on the underlying genetic architecture.
Revised:  These results highlight how the efficacy of evolution as a coexistence mechanism may depend on the underlying genetic architecture.
Edit intent: clarity
Original:  In addition, the complexity of the model is found to be linear in the size of the weight matrix.
Revised:  The complexity of the model is found to be linear in the size of the weight matrix.
Edit intent: coherence
Original:  While manufacturers struggle to perfect their screens it  also important to ensure high quality of displayed image.
Revised:  While manufacturers struggle to perfect their screens it is also important to ensure high quality of displayed image.
Edit intent: fluency
Original:  In this paper  we present a solution to calculate four distinct video quality metrics that can be applied to a real time video quality assessment system.
Revised:  In this paper , we present a solution to calculate four distinct video quality metrics that can be applied to a real time video quality assessment system.
Edit intent: fluency
Original:  Our assessment module is capable of processing 8K resolution in real time manner set at the level of 30 frames per second.
Revised:  Our assessment module is capable of processing 8K resolution in real time set at the level of 30 frames per second.
Edit intent: clarity
Original:  Throughput of 2.19 GB/s surpasses performance of puresoftware solutions.
Revised:  Throughput of 2.19 GB/s surpasses performance of pure software solutions.
Edit intent: clarity
Original:  To concentrate on architectural optimization  module was created using high level language.
Revised:  To concentrate on architectural optimization , the module was created using high level language.
Edit intent: coherence
Original:  We coin the term ' outlaw distributions' for such distributions since they ' defy' the Law of Large Numbers.
Revised:  We coin the term ` outlaw distributions' for such distributions since they ' defy' the Law of Large Numbers.
Edit intent: fluency
Original:  We coin the term ' outlaw distributions' for such distributions since they ' defy' the Law of Large Numbers.
Revised:  We coin the term ' outlaw distributions' for such distributions since they ` defy' the Law of Large Numbers.
Edit intent: fluency
Original:  We show that the existence of outlaw distributions over sufficiently ' smooth' functions implies the existence of constant query LDCs and vice versa.
Revised:  We show that the existence of outlaw distributions over sufficiently ` smooth' functions implies the existence of constant query LDCs and vice versa.
Edit intent: fluency
Original:  We also give several candidates for outlaw distributions over smooth functions coming from finite field incidence geometry  and from hypergraph (non)expanders.
Revised:  We give several candidates for outlaw distributions over smooth functions coming from finite field incidence geometry and from hypergraph (non)expanders.
Edit intent: clarity
Original:  In this paper, we study the game over interdependent networks, investigating how the rational behaviors of entities impact the whole system .
Revised:  In this paper, we study the game investigating how the rational behaviors of entities impact the whole system .
Edit intent: clarity
Original:  In this paper, we study the game over interdependent networks, investigating how the rational behaviors of entities impact the whole system .
Revised:  In this paper, we study the game over interdependent networks, investigating how the rational behaviors of entities impact the system robustness .
Edit intent: clarity
Original:  Then we study the Nash equilibrium  and compare it with the optimal social welfare.
Revised:  Then we study the Nash equilibrium of the game and compare it with the optimal social welfare.
Edit intent: clarity
Original:  We reveal that the cooperation between different entities can be reached to maximize the social welfare  only when the average degree of each network is constant.
Revised:  We reveal that the cooperation among different entities can be reached to maximize the social welfare only when the average degree of each network is constant.
Edit intent: fluency
Original:  Otherwise, there may be a huge gap between the Nash equilibrium and optimal social welfare .
Revised:  Therefore, the huge gap between the Nash equilibrium and optimal social welfare .
Edit intent: coherence
Original:  Otherwise, there may be a huge gap between the Nash equilibrium and optimal social welfare .
Revised:  Otherwise, there may be a huge gap between Nash equilibrium and optimal social welfare .
Edit intent: clarity
Original:  Therefore, the rationality of different entities that operates these networks makes the system inherently deficient and even  extremely vulnerable in some cases.
Revised:  Therefore, the rationality of different entities that operates these networks makes the system inherently deficient and even renders it extremely vulnerable in some cases.
Edit intent: clarity
Original:   Furthermore, we uncover some factors (such as weakening coupled strength of interdependent networks, designing suitable topology dependency of the system) that help reduce the gap and improve the system vulnerability.
Revised:  Furthermore, we uncover some factors (such as weakening coupled strength of interdependent networks, designing suitable topology dependency of the system) that help reduce the gap and the system vulnerability.
Edit intent: clarity
Original: In this paper, we prove the counting problem of numerical semigroup gaps to be #NP-complete under relaxed subtractive reductions.
Revised: In this paper, we prove that the numerical-semigroup-gap counting problem is #NP-complete under relaxed subtractive reductions.
Edit intent: clarity
Original:  In 2005, Ramirez-Alfonsin proposed a question whether the numerical semigroup gap counting problem is #P-complete.
Revised:  In 2005, Ramirez-Alfonsin proposed a question whether or not the numerical-semigroup-gap counting problem is #P-complete.
Edit intent: clarity
Original:  Moreover, we prove the #NP-completenesses of other two variants of the numerical semigroup gap counting problemunder parsimonious reductions .
Revised:  Moreover, we prove the #NP-completenesses of other two variants of the numerical-semigroup-gap counting problem .
Edit intent: clarity
Original: Data exchange is the problem of transforming data that is structured under the source schema into data structured under another schema, called the target schema, so that both  source and target data satisfy the relationship between the schemas.
Revised: Data exchange is the problem of transforming data that is structured under a source schema into data structured under another schema, called the target schema, so that both source and target data satisfy the relationship between the schemas.
Edit intent: fluency
Original: Data exchange is the problem of transforming data that is structured under the source schema into data structured under another schema, called the target schema, so that both  source and target data satisfy the relationship between the schemas.
Revised: Data exchange is the problem of transforming data that is structured under the source schema into data structured under another schema, called the target schema, so that both the source and target data satisfy the relationship between the schemas.
Edit intent: fluency
Original:  Many applications such as planning, scheduling, medical and fraud detection systems, require data exchange in the context of temporal data.
Edit intent: coherence
Original:  Even though the formal framework of data exchange for relational database systems is well-established, it does not immediately carry over to the setting of temporal data, which necessitates reasoning over unbounded periods of time.
Revised:  Even though the formal framework of data exchange for relational database systems is well-established, it does not immediately carry over to the settings of temporal data, which necessitates reasoning over unbounded periods of time.
Edit intent: fluency
Original:  We first motivate the need for two views of temporal data: the concrete view, which depicts how temporal data is compactly represented and on which  implementations are based, and the abstract view, which defines the semantics of temporal data .
Revised:  We first motivate the need for two views of temporal data: the concrete view, which depicts how temporal data is compactly represented and on which the implementations are based, and the abstract view, which defines the semantics of temporal data .
Edit intent: fluency
Original:  To obtain the semantic alignment, the nulls (which are introduced by data exchange and model incompleteness) in both the concrete view and the abstract view are annotated with temporal information.
Revised:  To obtain the semantic alignment, the nulls in the concrete view and the abstract view are annotated with temporal information.
Edit intent: clarity
Original:  To obtain the semantic alignment, the nulls (which are introduced by data exchange and model incompleteness) in both the concrete view and the abstract view are annotated with temporal information.
Revised:  To obtain the semantic alignment, the nulls (which are introduced by data exchange and model incompleteness) in both the concrete view are annotated with temporal information.
Edit intent: clarity
Original:  We define na\"ive evaluation on the result of the concrete chase and show it produces certain answers.
Revised:  We define naive evaluation on the result of the concrete chase and show it produces certain answers.
Edit intent: fluency
Original: We present a deep learning technique for facial performance capture , i.e., the transfer of video footage into a motion sequence of a 3D mesh representing an actor's face . Specifically, we build on a conventional capture pipeline based on computer vision and multi-view video, and use its results to train a deep neural network to produce similar output from a monocular video sequence .
Revised: We present a real-time deep learning framework for video-based facial performance capture , i.e., the transfer of video footage into a motion sequence of a 3D mesh representing an actor's face . Specifically, we build on a conventional capture pipeline based on computer vision and multi-view video, and use its results to train a deep neural network to produce similar output from a monocular video sequence .
Edit intent: clarity
Original: We present a deep learning technique for facial performance capture , i.e., the transfer of video footage into a motion sequence of a 3D mesh representing an actor's face . Specifically, we build on a conventional capture pipeline based on computer vision and multi-view video, and use its results to train a deep neural network to produce similar output from a monocular video sequence .
Revised: We present a deep learning technique for facial performance capture -- the dense 3D mesh representing an actor's face . Specifically, we build on a conventional capture pipeline based on computer vision and multi-view video, and use its results to train a deep neural network to produce similar output from a monocular video sequence .
Edit intent: clarity
Original: We present a deep learning technique for facial performance capture , i.e., the transfer of video footage into a motion sequence of a 3D mesh representing an actor's face . Specifically, we build on a conventional capture pipeline based on computer vision and multi-view video, and use its results to train a deep neural network to produce similar output from a monocular video sequence .
Revised: We present a deep learning technique for facial performance capture , i.e., the transfer of video footage into a motion sequence of a 3D tracking of an actor's face . Specifically, we build on a conventional capture pipeline based on computer vision and multi-view video, and use its results to train a deep neural network to produce similar output from a monocular video sequence .
Edit intent: clarity
Original: We present a deep learning technique for facial performance capture , i.e., the transfer of video footage into a motion sequence of a 3D mesh representing an actor's face . Specifically, we build on a conventional capture pipeline based on computer vision and multi-view video, and use its results to train a deep neural network to produce similar output from a monocular video sequence .
Revised: We present a deep learning technique for facial performance capture , i.e., the transfer of video footage into a motion sequence of a 3D mesh representing an actor's face . Specifically, we build on a conventional capture pipeline based on multi-view video, and use its results to train a deep neural network to produce similar output from a monocular video sequence .
Edit intent: clarity
Original: Background: Combining computational toxicology with ExpoCast exposure data and ToxCast assay data gives us access to predictions of human health risks stemming from realistic exposures to chemical mixtures.
Revised: Background: Combining computational toxicology with ExpoCast exposure estimates and ToxCast assay data gives us access to predictions of human health risks stemming from realistic exposures to chemical mixtures.
Edit intent: clarity
Original: Background: Combining computational toxicology with ExpoCast exposure data and ToxCast assay data gives us access to predictions of human health risks stemming from realistic exposures to chemical mixtures.
Revised: Background: Combining computational toxicology with ExpoCast exposure data and ToxCast assay data gives us access to predictions of human health risks stemming from exposures to chemical mixtures.
Edit intent: clarity
Original:  Objectives: To quantify , through mathematical modeling and simulations, the size of potential effects of random mixtures of aromatase inhibitors on the dynamics of women's menstrual cycle .
Revised:  Objectives: To explore , through mathematical modeling and simulations, the size of potential effects of random mixtures of aromatase inhibitors on the dynamics of women's menstrual cycle .
Edit intent: clarity
Original:  Objectives: To quantify , through mathematical modeling and simulations, the size of potential effects of random mixtures of aromatase inhibitors on the dynamics of women's menstrual cycle .
Revised:  Objectives: To quantify , through mathematical modeling and simulations, the size of potential effects of random mixtures of aromatase inhibitors on the dynamics of women's menstrual cycles .
Edit intent: fluency
Original:  Conclusions: Those results demonstrate the possibility to predict large scale mixture effects for endocrine disrupters with a predictive toxicology approach, suitable for high throughput ranking and risk assessment.
Revised:  Conclusions: Those results demonstrate the possibility to predict large-scale mixture effects for endocrine disrupters with a predictive toxicology approach, suitable for high throughput ranking and risk assessment.
Edit intent: fluency
Original:  Conclusions: Those results demonstrate the possibility to predict large scale mixture effects for endocrine disrupters with a predictive toxicology approach, suitable for high throughput ranking and risk assessment.
Revised:  Conclusions: Those results demonstrate the possibility to predict large scale mixture effects for endocrine disrupters with a predictive toxicology approach, suitable for high-throughput ranking and risk assessment.
Edit intent: fluency
Original:  The size of the effects predicted is consistent with an increased risk of infertility in women from daily life exposures to our chemical environment.
Revised:  The size of the effects predicted is consistent with an increased risk of infertility in women from everyday exposures to our chemical environment.
Edit intent: clarity
Original:  We are extending this to create a  comprehensive legal semantic map.
Revised:  We are extending this to create a more comprehensive legal semantic map.
Edit intent: clarity
Original: This paper reports the results of the first survey of introductory programming courses ( \mathrm{N =80) taught at UK universities as part of their first year computer science (or similar ) degree programmes, conducted in the first half of 2016.
Revised: This paper reports the results of the first survey of introductory programming courses ( N =80) taught at UK universities as part of their first year computer science (or similar ) degree programmes, conducted in the first half of 2016.
Edit intent: fluency
Original: This paper reports the results of the first survey of introductory programming courses ( \mathrm{N =80) taught at UK universities as part of their first year computer science (or similar ) degree programmes, conducted in the first half of 2016.
Revised: This paper reports the results of the first survey of introductory programming courses ( \mathrm{N =80) taught at UK universities as part of their first year computer science (or related ) degree programmes, conducted in the first half of 2016.
Edit intent: clarity
Original:  Results of this survey are compared with a related survey conducted since 2010 (as well as earlier surveys from 2001 and 2003) in Australia and New Zealand.
Edit intent: coherence
Original:  We report on student numbers, programming paradigm, programming languages and environment/tools used, as well as the reasons for choice of such.
Revised:  We report on student numbers, programming paradigm, programming languages and environment/tools used, as well as the underpinning rationale for these choices. Knowledge:
Edit intent: clarity