wanyu/IteraTeR_v2 huggingface dataset:
Original:  First, we prove an exponential separation between a drunk randomized CDCL SAT {\it   solver model with restarts and the same model without restarts using a family of satisfiable instances we call Ladder_n formulas .
Revised:  First, we prove an exponential separation between a drunk randomized CDCL SAT {\it solver model with restarts and the same model without restarts using a family of satisfiable instances .
Edit intent: coherence
Original:  Second, we show that the configuration of CDCL SAT solver with VSIDS branching and restarts (with activities erased after restarts) are exponentially more powerful than the same configuration without restarts for a family of unsatisfiable instances.
Revised:  Second, we show that the configuration of CDCL solver with VSIDS branching and restarts (with activities erased after restarts) are exponentially more powerful than the same configuration without restarts for a family of unsatisfiable instances.
Edit intent: clarity
Original:  Second, we show that the configuration of CDCL SAT solver with VSIDS branching and restarts (with activities erased after restarts) are exponentially more powerful than the same configuration without restarts for a family of unsatisfiable instances.
Revised:  Second, we show that the configuration of CDCL SAT solver with VSIDS branching and restarts (with activities erased after restarts) is exponentially more powerful than the same configuration without restarts for a family of unsatisfiable instances.
Edit intent: fluency
Original:  To the best of our knowledge, these are the first such set of separation results involving restarts in the context of SAT solvers.
Revised:  To the best of our knowledge, these are the first separation results involving restarts in the context of SAT solvers.
Edit intent: clarity
Original:  Third, we show that restarts do not add any proof complexity-theoretic power vis-a-vis a variety of models of CDCL and DPLL SAT solvers with non-deterministic static variable selection (branching) and value selection.
Revised:  Third, we show that restarts do not add any proof complexity-theoretic power vis-a-vis a number of models of CDCL and DPLL SAT solvers with non-deterministic static variable selection (branching) and value selection.
Edit intent: clarity
Original:  Third, we show that restarts do not add any proof complexity-theoretic power vis-a-vis a variety of models of CDCL and DPLL SAT solvers with non-deterministic static variable selection (branching) and value selection.
Revised:  Third, we show that restarts do not add any proof complexity-theoretic power vis-a-vis a variety of models of CDCL and DPLL SAT solvers with non-deterministic static variable and value selection.
Edit intent: clarity
Original: For two matroids M_1 and M_2 with the same ground set V and two cost functions w_1 and w_2 on 2^V, we consider the problem of finding bases X_1 of M_1 and X_2 of M_2 minimizing w_1(X_1)+w_2(X_2) subject to a certain cardinality constraint on their intersection X_1 \cap X_2.  Lendl, Peis, and Timmermans (2019) discussed modular cost functions: they reduced the problem to weighted matroid intersection for the case where the cardinality constraint is |X_1 \cap X_2|\le k or |X_1 \cap X_2|\ge k;
Revised: For two matroids M_1 and M_2 with the same ground set V and two cost functions w_1 and w_2 on 2^V, we consider the problem of finding bases X_1 of M_1 and X_2 of M_2 minimizing w_1(X_1)+w_2(X_2) subject to a certain cardinality constraint on their intersection X_1 \cap X_2. For this problem, Lendl, Peis, and Timmermans (2019) discussed modular cost functions: they reduced the problem to weighted matroid intersection for the case where the cardinality constraint is |X_1 \cap X_2|\le k or |X_1 \cap X_2|\ge k;
Edit intent: clarity
Original:  Finally, we present applications of our generalized problems in the recoverable robust matroid basis problem, matroid congestion games, and combinatorial optimization problems with interaction costs  .
Revised:  Finally, we present applications of our generalized problems in the recoverable robust matroid basis problem, combinatorial optimization problems with interaction costs .
Edit intent: clarity
Original: Groups, or communities, commonly overlap in real-world networks.
Revised: Communities commonly overlap in real-world networks.
Edit intent: clarity
Original:  Here, we analyze the performance of spectral clustering, which does not consider overlapping structures, by using the replica method from statistical physics.
Revised:  Here, we analyze an accuracy of spectral clustering, which does not consider overlapping structures, by using the replica method from statistical physics.
Edit intent: clarity
Original: Recommender systems (RS)  play a very important role in various aspects of people's online life .
Revised: Recommender systems (RS) now play a very important role in various aspects of people's online life .
Edit intent: clarity
Original: Recommender systems (RS)  play a very important role in various aspects of people's online life .
Revised: Recommender systems (RS) play a very important role in people's online life .
Edit intent: clarity
Original:  Many companies leverage RS to help users discover new and favored items . Despite their empirical success, these systems still suffer from two main problems : data noise and data sparsity.
Revised:  Many companies leverage RS to help users discover new and favored items . Despite their empirical success, however, these systems are still confronted with two limitations : data noise and data sparsity.
Edit intent: clarity
Original:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distribution, and they also provide new means to mitigate the aforementioned problems of RS. Particularly, owing to adversarial learning, the problem of data noise can be handled by adding adversarial perturbations or forcing discriminators to tell the informative and uninformative data examples apart.
Revised:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS. Particularly, owing to adversarial learning, the problem of data noise can be handled by adding adversarial perturbations or forcing discriminators to tell the informative and uninformative data examples apart.
Edit intent: clarity
Original:  As for the mitigation of data sparsity issue, the GAN-based models are able to replicate the real distribution of the user-item interactions and augment the available data .
Revised:  As for the mitigation of data sparsity issue, data augmentation implemented by capturing the distribution of real data under the Mini-max framework is the primary coping strategy .
Edit intent: clarity
Original:  To gain a comprehensive understanding of these GAN-based recommendation models , we provide a retrospective of these studies and organize them from a problem-driven perspective.
Revised:  To gain a comprehensive understanding of these research efforts , we provide a retrospective of these studies and organize them from a problem-driven perspective.
Edit intent: clarity
Original:  To gain a comprehensive understanding of these GAN-based recommendation models , we provide a retrospective of these studies and organize them from a problem-driven perspective.
Revised:  To gain a comprehensive understanding of these GAN-based recommendation models , we provide a retrospective of the corresponding studies and models and organize them from a problem-driven perspective.
Edit intent: clarity
Original: Recommender systems ( RS ) now play a very important role in people's online life as they serve as personalized filters for users to discover relevant items from a sea of options.
Revised: Recommender systems ( RSs ) now play a very important role in people's online life as they serve as personalized filters for users to discover relevant items from a sea of options.
Edit intent: clarity
Original: Recommender systems ( RS ) now play a very important role in people's online life as they serve as personalized filters for users to discover relevant items from a sea of options.
Revised: Recommender systems ( RS ) now play a very important role in the online lives of people as they serve as personalized filters for users to discover relevant items from a sea of options.
Edit intent: clarity
Original: Recommender systems ( RS ) now play a very important role in people's online life as they serve as personalized filters for users to discover relevant items from a sea of options.
Revised: Recommender systems ( RS ) now play a very important role in people's online life as they serve as personalized filters for users to find relevant items from a sea of options.
Edit intent: fluency
Original: Recommender systems ( RS ) now play a very important role in people's online life as they serve as personalized filters for users to discover relevant items from a sea of options.
Revised: Recommender systems ( RS ) now play a very important role in people's online life as they serve as personalized filters for users to discover relevant items from an array of options.
Edit intent: clarity
Original:  Due to their effectiveness, RS have been widely employed in consumer-oriented e-commerce platforms.
Revised:  Owing to their effectiveness, RS have been widely employed in consumer-oriented e-commerce platforms.
Edit intent: fluency
Original:  Due to their effectiveness, RS have been widely employed in consumer-oriented e-commerce platforms.
Revised:  Due to their effectiveness, RSs have been widely employed in consumer-oriented e-commerce platforms.
Edit intent: fluency
Original:  Despite their empirical success, however, these systems are still confronted with two limitations: data noise and data sparsity.
Revised:  However, despite their empirical successes, these systems still suffer from two limitations: data noise and data sparsity.
Edit intent: clarity
Original:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS . In general, two lines of research have been conducted, and the common ideas can be summarized as follows:
Revised:  In recent years, generative adversarial networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS . In general, two lines of research have been conducted, and the common ideas can be summarized as follows:
Edit intent: fluency
Original:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS . In general, two lines of research have been conducted, and the common ideas can be summarized as follows:
Revised:  In recent years, Generative Adversarial Networks (GANs) have garnered increased interest in many fields because of their great potential to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS . In general, two lines of research have been conducted, and the common ideas can be summarized as follows:
Edit intent: clarity
Original:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS . In general, two lines of research have been conducted, and the common ideas can be summarized as follows:
Revised:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields , owing to their strong capacity to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS . In general, two lines of research have been conducted, and the common ideas can be summarized as follows:
Edit intent: clarity
Original:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS . In general, two lines of research have been conducted, and the common ideas can be summarized as follows:
Revised:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distributions; their abilities to enhance RSs by tackling the challenges these systems exhibit have also been demonstrated in numerous studies . In general, two lines of research have been conducted, and the common ideas can be summarized as follows:
Edit intent: clarity
Original:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS . In general, two lines of research have been conducted, and the common ideas can be summarized as follows:
Revised:  In recent years, Generative Adversarial Networks (GANs) have received a surge of interests in many fields because of their great potential to learn complex real data distribution, and a mass of research efforts also have demonstrated the capability of GANs to enhance RS by dealing with the challenging problems of RS . In general, two lines of research have been conducted, and their common ideas can be summarized as follows:
Edit intent: fluency
Original:  (1) for the data noise issue, adversarial perturbations and adversarial sampling-based adversarial training often work as the antidote ;
Revised:  (1) for the data noise issue, adversarial perturbations and adversarial sampling-based training often serve as a solution ;
Edit intent: clarity
Original:  (2) for the data sparsity issue, data augmentation implemented by capturing the distribution of real data under the Mini-max framework is the primary coping strategy.
Revised:  (2) for the data sparsity issue, data augmentation--implemented by capturing the distribution of real data under the Mini-max framework is the primary coping strategy.
Edit intent: fluency
Original:  (2) for the data sparsity issue, data augmentation implemented by capturing the distribution of real data under the Mini-max framework is the primary coping strategy.
Revised:  (2) for the data sparsity issue, data augmentation implemented by capturing the distribution of real data under the minimax framework--is the primary coping strategy.
Edit intent: fluency
Original:  To gain a comprehensive understanding of these research efforts, we provide a retrospective of the corresponding studies and models and organize them from a problem-driven perspective.
Revised:  To gain a comprehensive understanding of these research efforts, we review the corresponding studies and models and organize them from a problem-driven perspective.
Edit intent: clarity
Original:  To gain a comprehensive understanding of these research efforts, we provide a retrospective of the corresponding studies and models and organize them from a problem-driven perspective.
Revised:  To gain a comprehensive understanding of these research efforts, we provide a retrospective of the corresponding studies and models , organizing them from a problem-driven perspective.
Edit intent: coherence
Original:  Specifically , we propose a taxonomy of these models, along with a detailed description of them and their advantages.
Revised:  More specifically , we propose a taxonomy of these models, along with a detailed description of them and their advantages.
Edit intent: coherence
Original:  Specifically , we propose a taxonomy of these models, along with a detailed description of them and their advantages.
Revised:  Specifically , we propose a taxonomy of these models, along with their detailed descriptions and advantages.
Edit intent: fluency
Original:  Finally, we elaborate on several open issues and expand on current trends in the GAN-based RS .
Revised:  Finally, we elaborate on several open issues and current trends in the GAN-based RS .
Edit intent: clarity
Original:  Finally, we elaborate on several open issues and expand on current trends in the GAN-based RS .
Revised:  Finally, we elaborate on several open issues and expand on current trends in GAN-based RS .
Edit intent: fluency
Original:  Finally, we elaborate on several open issues and expand on current trends in the GAN-based RS .
Revised:  Finally, we elaborate on several open issues and expand on current trends in the GAN-based RSs .
Edit intent: fluency
Original:  We analyze the algorithm in two different models,  stochastic input model and  random permutation model, with minimal assumptions on the input of the LP.
Revised:  We analyze the algorithm in two different models, the stochastic input model and random permutation model, with minimal assumptions on the input of the LP.
Edit intent: fluency
Original:  We analyze the algorithm in two different models,  stochastic input model and  random permutation model, with minimal assumptions on the input of the LP.
Revised:  We analyze the algorithm in two different models, stochastic input model and the random permutation model, with minimal assumptions on the input of the LP.
Edit intent: fluency
Original:  Furthermore, the algorithm is generalized to a multi-dimensional LP setting which covers a wider range of applications and features for the same performance guarantee .
Revised:  The algorithm enjoys the same performance guarantee when generalized to a multi-dimensional LP setting which covers a wider range of applications and features for the same performance guarantee .
Edit intent: clarity
Original: In this paper, we develop a simple and fast online algorithm for solving a general class of binary integer linear programs (LPs)  .
Revised: In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) .
Edit intent: clarity
Original:  To complete the discussion , we employ the notion of permutational Rademacher complexity and analyze the regret of two online LP algorithms in the literature under the random permutation model .
Revised:  In addition , we employ the notion of permutational Rademacher complexity and analyze the regret of two online LP algorithms in the literature under the random permutation model .
Edit intent: coherence
Original:  Numerical experiments illustrate the general applicability and the performance of the algorithms.
Revised:  Numerical experiments illustrate the general applicability and effectiveness of the algorithms.
Edit intent: clarity
Original:  However, rendering volumetric content requires high amounts of processing power and is still a very demanding tasks for today's mobile devices.
Revised:  However, processing volumetric content requires high amounts of processing power and is still a very demanding tasks for today's mobile devices.
Edit intent: clarity
Original:  However, rendering volumetric content requires high amounts of processing power and is still a very demanding tasks for today's mobile devices.
Revised:  However, rendering volumetric content requires high amounts of processing power and is still a very demanding task for today's mobile devices.
Edit intent: fluency
Original:  We demonstrate our system using both a browser-based client and a Microsoft Hololens client.
Revised:  We demonstrate our system using both a browser-based client and a Microsoft HoloLens client.
Edit intent: fluency
Original:  Our application contains generic interfaces that allow  easy deployment of different augmented/mixed reality clients using the same server implementation.
Revised:  Our application contains generic interfaces that allow for easy deployment of different augmented/mixed reality clients using the same server implementation.
Edit intent: fluency
Original:  Our application contains generic interfaces that allow  easy deployment of different augmented/mixed reality clients using the same server implementation.
Revised:  Our application contains generic interfaces that allow easy deployment of various augmented/mixed reality clients using the same server implementation.
Edit intent: fluency
Original:  The implementation will be publicly available.
Revised:  The implementation is publicly available.
Edit intent: clarity
Original:  The diagonal sweeping DDM uses 2^n sweeps of diagonal directions on the checkerboard domain decomposition based on the source transfer method , it is sequential in nature yet suitable for parallel computing , since the number of sequential steps is quite small compared to the number of subdomains.
Revised:  The diagonal sweeping DDM uses 2^n sweeps along respective diagonal directions with checkerboard domain decomposition based on the source transfer method , it is sequential in nature yet suitable for parallel computing , since the number of sequential steps is quite small compared to the number of subdomains.
Edit intent: clarity
Original:  The diagonal sweeping DDM uses 2^n sweeps of diagonal directions on the checkerboard domain decomposition based on the source transfer method , it is sequential in nature yet suitable for parallel computing , since the number of sequential steps is quite small compared to the number of subdomains.
Revised:  The diagonal sweeping DDM uses 2^n sweeps of diagonal directions on the checkerboard domain decomposition based on the source transfer method , it is highly suitable for parallel computing , since the number of sequential steps is quite small compared to the number of subdomains.
Edit intent: clarity
Original:  The diagonal sweeping DDM uses 2^n sweeps of diagonal directions on the checkerboard domain decomposition based on the source transfer method , it is sequential in nature yet suitable for parallel computing , since the number of sequential steps is quite small compared to the number of subdomains.
Revised:  The diagonal sweeping DDM uses 2^n sweeps of diagonal directions on the checkerboard domain decomposition based on the source transfer method , it is sequential in nature yet suitable for parallel computing , since the number of sequential steps in each sweep is much smaller than the number of subdomains.
Edit intent: clarity
Original:  second, the sweeping algorithm becomes simpler since the transferred traces have only n cardinal directions , whereas the transferred sources have all 3^n-1  directions.
Revised:  second, the sweeping algorithm becomes simpler since the transferred traces have only n cardinal directions , whereas the transferred sources come from a total of 3^n-1 directions.
Edit intent: clarity
Original:  The efficiency of the proposed method is demonstrated using numerical experiments in two and three dimensions , and it is found that numerical differences of the diagonal sweeping DDM with the two transfer methods are very small using second-order finite difference discretization .
Revised:  The efficiency of the proposed method is demonstrated using numerical experiments in two and three dimensions .
Edit intent: coherence