wanyu/IteraTeR_v2 huggingface dataset:
Original: Allen-Zhu, Gelashvili, Micali, and Shavit constructed a sparse, sign-consistent Johnson Lindenstrauss distribution, and proved that this distribution yields an essentially optimal dimension for the correct choice of sparsity.
Revised: Allen-Zhu, Gelashvili, Micali, and Shavit constructed a sparse, sign-consistent Johnson-Lindenstrauss distribution, and proved that this distribution yields an essentially optimal dimension for the correct choice of sparsity.
Edit intent: fluency
Original: Allen-Zhu, Gelashvili, Micali, and Shavit constructed a sparse, sign-consistent Johnson Lindenstrauss distribution, and proved that this distribution yields an essentially optimal dimension for the correct choice of sparsity.
Revised: Allen-Zhu, Gelashvili, Micali, and Shavit constructed a sparse, sign-consistent Johnson Lindenstrauss distribution, and prove that this distribution yields an essentially optimal dimension for the correct choice of sparsity.
Edit intent: fluency
Original:  However, their analysis of the upper bound on the dimension and sparsity required a complicated combinatorial graph-based argument similar to Kane and Nelson's analysis of sparse JL. We present a simple, combinatorics-free analysis of sparse, sign-consistent JL that yields the same dimension and sparsity upper bounds as the original analysis.
Revised:  However, their analysis of the upper bound on the dimension and sparsity requires a complicated combinatorial graph-based argument similar to Kane and Nelson's analysis of sparse JL. We present a simple, combinatorics-free analysis of sparse, sign-consistent JL that yields the same dimension and sparsity upper bounds as the original analysis.
Edit intent: fluency
Original:  Our proof also yields dimension/sparsity tradeoffs, which were not previously known.
Revised:  Our analysis also yields dimension/sparsity tradeoffs, which were not previously known.
Edit intent: clarity
Original:  Here, we present a solution to this problem, reducing the computation time for  large systems from longer than the timespan of the universe to just several hours.
Revised:  Here, we present a solution to this problem, reducing the computation time for large systems from longer than the lifespan of the universe to just several hours.
Edit intent: clarity
Original:  We evaluate this solution in brain-like systems of coupled oscillators as well as in high-density electrocortigraphy data from two macaque monkeys, and show that the informational "weakest link" of the monkey cortex cleanly splits posterior sensory areas from anterior association areas.
Revised:  We evaluate this solution in brain-like systems of coupled oscillators as well as in high-density electrocortigraphy data from two macaque monkeys, and show that the informational "weakest link" of the monkey cortex splits posterior sensory areas from anterior association areas.
Edit intent: clarity
Original:  Finally, we use our solution to confirm the long-standing hypothesis that information integration is maximized by networks with a high global efficiency  .
Revised:  Finally, we use our solution to provide evidence in support of the long-standing hypothesis that information integration is maximized by networks with a high global efficiency .
Edit intent: clarity
Original:  We provide a rigorous formulation of this result in a fully general setting, only allowing for buy-and-hold positions and without imposing any semimartingale restriction .
Revised:  We provide a rigorous formulation of this result in a fully general setting, without imposing any semimartingale restriction .
Edit intent: clarity
Original:  We furthermore show that right-continuity is an indispensable requirement for any price process that does not admit sure profits.
Revised:  We furthermore show that any price process that does not admit sure profits.
Edit intent: clarity
Original:  We furthermore show that right-continuity is an indispensable requirement for any price process that does not admit sure profits.
Revised:  We furthermore show that right-continuity is an indispensable requirement for any price process is always right-continuous in the absence of sure profits.
Edit intent: clarity
Original:  Our results are robust with respect to small transaction costs or model mis-specifications and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.
Revised:  Our results are robust under small transaction costs or model mis-specifications and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.
Edit intent: clarity
Original:  Our results are robust with respect to small transaction costs or model mis-specifications and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.
Revised:  Our results are robust with respect to small transaction costs and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.
Edit intent: clarity
Original:  However the standard modeling of population dynamics would predict that these systems become less stable than communities with competitive or prey-predator interactionsas the number of species increases.
Revised:  However standard models in population dynamics predict that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with competitive or prey-predator interactionsas the number of species increases.
Edit intent: clarity
Original: Empirical observations show that natural communities of species with mutualistic interactions such microbes, can have a  number of coexisting species of the order of hundreds.
Revised: Empirical observations show that ecological communities can have a number of coexisting species of the order of hundreds.
Edit intent: clarity
Original: Empirical observations show that natural communities of species with mutualistic interactions such microbes, can have a  number of coexisting species of the order of hundreds.
Revised: Empirical observations show that natural communities of species with mutualistic interactions such microbes, can have a huge number of coexisting species of the order of hundreds.
Edit intent: clarity
Original:  We also find that, in the large system size limit, any number of species can coexist for a very general class of interaction networks  .
Revised:  In the large system size limit, any number of species can coexist for a very general class of interaction networks .
Edit intent: coherence
Original:  For pure mutualistic/commensalistic interactions we analytically find the topological properties of the network that guarantee species coexistence.
Revised:  For pure mutualistic/commensalistic interactions we determine the topological properties of the network that guarantee species coexistence.
Edit intent: clarity
Original:  In order to make this process more effective, search engines provide related queries to help users to specify the information need in their search process.
Revised:  To make this process more effective, search engines provide related queries to help users to specify the information need in their search process.
Edit intent: coherence
Original:  In order to make this process more effective, search engines provide related queries to help users to specify the information need in their search process.
Revised:  In order to make this process more effective, search engines provide related queries to help users in specifying the information need in their search process.
Edit intent: clarity
Original:  This enables us to control the scope of the session from which we infer the suggested next query, which helps not only handle the noisy data but also automatically detect session boundaries.
Revised:  is enables us to control the scope of the session from which we infer the suggested next query, which helps not only handle the noisy data but also automatically detect session boundaries.
Edit intent: fluency
Original:  Furthermore, we observe that based on user query reformulation behavior, a large portion of terms of a query in a session is retained from the previously submitted queries in the same session and consists of mostly infrequent or unseen terms that are usually not included in the vocabulary.
Revised:  Furthermore, we observe that , based on the user query reformulation behavior, a large portion of terms of a query in a session is retained from the previously submitted queries in the same session and consists of mostly infrequent or unseen terms that are usually not included in the vocabulary.
Edit intent: fluency
Original:  Furthermore, we observe that based on user query reformulation behavior, a large portion of terms of a query in a session is retained from the previously submitted queries in the same session and consists of mostly infrequent or unseen terms that are usually not included in the vocabulary.
Revised:  Furthermore, we observe that based on user query reformulation behavior, within a single session a large portion of terms of a query in a session is retained from the previously submitted queries in the same session and consists of mostly infrequent or unseen terms that are usually not included in the vocabulary.
Edit intent: clarity
Original:  Furthermore, we observe that based on user query reformulation behavior, a large portion of terms of a query in a session is retained from the previously submitted queries in the same session and consists of mostly infrequent or unseen terms that are usually not included in the vocabulary.
Revised:  Furthermore, we observe that based on user query reformulation behavior, a large portion of query terms is retained from the previously submitted queries in the same session and consists of mostly infrequent or unseen terms that are usually not included in the vocabulary.
Edit intent: clarity
Original:  Furthermore, we observe that based on user query reformulation behavior, a large portion of terms of a query in a session is retained from the previously submitted queries in the same session and consists of mostly infrequent or unseen terms that are usually not included in the vocabulary.
Revised:  Furthermore, we observe that based on user query reformulation behavior, a large portion of terms of a query in a session is retained from the previously submitted queries and consists of mostly infrequent or unseen terms that are usually not included in the vocabulary.
Edit intent: clarity
Original:  The results suggest that our model outperforms the baselines both in terms of the generating queries and scoring candidate queries for the task of query suggestion.
Revised:  e results suggest that our model outperforms the baselines both in terms of the generating queries and scoring candidate queries for the task of query suggestion.
Edit intent: fluency
Original: This paper summarizes the development of  an object-oriented C++ library for the virtual element method (VEM) named Veamy , whose modular design is focused on its extensibility.
Revised: This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) named Veamy , whose modular design is focused on its extensibility.
Edit intent: fluency
Original:  In contrast to the standard finite element method, the VEM in two dimensions uses polygonal finite element meshes.
Edit intent: coherence
Original:  The theory of the VEM in which Veamy is based upon is presented using a notation and a terminology that resemble the language of the finite element method  in engineering analysis.
Revised:  The theory of the VEM in which Veamy is based upon is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis.
Edit intent: clarity
Original:  The theory of the VEM in which Veamy is based upon is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis.
Revised:  The theory of the VEM , upon which Veamy is based upon is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis.
Edit intent: coherence
Original:  The theory of the VEM in which Veamy is based upon is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis.
Revised:  The theory of the VEM in which Veamy is built, is presented using a notation and a terminology that resemble the language of the finite element method (FEM) in engineering analysis.
Edit intent: clarity
Original: Ecosystems display a complex spatial organization , and ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales.
Revised: Ecosystems display a complex spatial organization . Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales.
Edit intent: coherence
Original:  However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several theoretical challenges , limiting the quantitative characterization of these patterns in real ecosystems .
Revised:  However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems , limiting the quantitative characterization of these patterns in real ecosystems .
Edit intent: clarity
Original:  However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several theoretical challenges , limiting the quantitative characterization of these patterns in real ecosystems .
Revised:  However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several theoretical challenges , limiting the quantitative understanding of spatial biodiversity .
Edit intent: clarity
Original:  In this review, we discuss the main results obtained for spatial neutral models and related open problems .
Revised:  In this review, we discuss the state of the art in spatial neutral theory .
Edit intent: clarity
Original:  We emphasize the connection with the physics of non-equilibrium phase transitions -- in particular, with the voter model, stepping-stone model, and contact process -- and on how concepts developed in statistical physics translate in population dynamics, and vice versa.
Revised:  We emphasize the connection with the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa.
Edit intent: coherence
Original:  We conclude by discussing simple near-neutral models incorporating spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.
Revised:  We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.
Edit intent: clarity
Original:  Applications of our results ranges from multivariate cryptography, group isomorphism, to polynomial identity testing.
Revised:  Applications of our results range from multivariate cryptography, group isomorphism, to polynomial identity testing.
Edit intent: fluency
Original:  We evaluate our method on the (sequential) perceptual grouping task and find that it is accurately able to recover the constituent objects.
Revised:  We evaluate our method on the (sequential) perceptual grouping task and find that it is able to accurately recover the constituent objects.
Edit intent: fluency
Original: We search an autocatalytic structure in networks of technological fields and evaluate its significance for technological change .
Revised: We analyse the autocatalytic structure of technological networks and evaluate its significance for technological change .
Edit intent: clarity
Original:  To this aim  we define a technology network based on the International Patents Classification  , and we study if autocatalytic structures in the network foster innovation as measured by the rate of production of patents.
Revised:  To this aim , we define a technology network based on the International Patents Classification , and we study if autocatalytic structures in the network foster innovation as measured by the rate of production of patents.
Edit intent: fluency
Original:  Technology classes in the core of the autocatalytic structure perform better in terms of their innovativeness, as measured by the rate of growth of the number of patents .
Revised:  Technology classes in the core of the autocatalytic set display greater fitness, i.e. they tend to appear in a greater number of patents, thus suggesting the presence of positive spillovers as well as positive reinforcement .
Edit intent: clarity
Original:  Finally, the links between classes that define the autocatalytic structure of the technology network break the hierarchical structure of the database, and indicate that recombinant innovation and its autocatalytic patterns are an important stylised fact of technological change .
Revised:  Finally, the links between classes that define the autocatalytic structure ; the latter observation instead points to the importance of recombinant innovation taking place between close as well as distant fields of the hierarchical classification of technological fields .
Edit intent: clarity
Original:  To this aim, we define a directed network of technological fields (defined accordingly to the International Patents Classification ) , in which a node (source ) is connected to another node (receiver ) via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random.
Revised:  To this aim, we define a directed network of technological fields based on the International Patents Classification ) , in which a node (source ) is connected to another node (receiver ) via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random.
Edit intent: clarity
Original:  To this aim, we define a directed network of technological fields (defined accordingly to the International Patents Classification ) , in which a node (source ) is connected to another node (receiver ) via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random.
Revised:  To this aim, we define a directed network of technological fields (defined accordingly to the International Patents Classification , in which a node (source ) is connected to another node (receiver ) via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random.
Edit intent: fluency
Original:  To this aim, we define a directed network of technological fields (defined accordingly to the International Patents Classification ) , in which a node (source ) is connected to another node (receiver ) via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random.
Revised:  To this aim, we define a directed network of technological fields (defined accordingly to the International Patents Classification ) , in which a source node is connected to another node (receiver ) via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random.
Edit intent: fluency
Original:  To this aim, we define a directed network of technological fields (defined accordingly to the International Patents Classification ) , in which a node (source ) is connected to another node (receiver ) via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random.
Revised:  To this aim, we define a directed network of technological fields (defined accordingly to the International Patents Classification ) , in which a node (source ) is connected to a receiver node via a link if patenting activity in the source field anticipates patents in the receiver field in the same region more frequently than we would expect at random.
Edit intent: clarity
Original:  the latter observation instead points to the importance of recombinant innovation taking place between close as well as distant fields of the hierarchical classification of technological fields.
Revised:  this points to the importance of recombinant innovation taking place between close as well as distant fields of the hierarchical classification of technological fields.
Edit intent: clarity
Original:  To provide a tractable proof method for it, we define a property of distribution confluence which is shown to imply the desired unicity (even for infinite sequences of reduction) and further properties.
Revised:  To provide a tractable proof method for it, we define a property of distribution confluence which is shown to imply the desired uniqueness (even for infinite sequences of reduction) and further properties.
Edit intent: fluency
Original:  Using these criteria, we obtain simple proofs of confluence for \lambda_1, an affine probabilistic lambda-calculus , and for Q^*, a quantum programming language for which a related property has already been proven in the literature.
Revised:  Using these criteria, we obtain simple proofs of confluence for \lambda_1, an affine probabilistic \lambda-calculus , and for Q^*, a quantum programming language for which a related property has already been proven in the literature.
Edit intent: fluency
Original:  When one specific column is considered, the problem is equivalent to synchronization on the (d-1)-dimensional unit sphere and when all the columns are considered  the problem is equivalent to synchronization on SO(d).
Revised:  When one specific column is considered, the problem is equivalent to synchronization on the (d-1)-dimensional unit sphere and when all the columns are considered , the problem is equivalent to synchronization on SO(d).
Edit intent: fluency
Original:  We design dynamic control laws that solve these synchronization problems.
Revised:  We design dynamic control laws for these synchronization problems.
Edit intent: clarity
Original:  The benefit of this QR-factorization approach is that we can decouple the dynamics of the k columns from the remaining d-k ones.
Revised:  The benefit of this QR-factorization approach is that we can decouple the dynamics for the k columns from the remaining d-k ones.
Edit intent: fluency
Original:  Under the control scheme, the closed loop system achieves almost global convergence to synchronization for quasi-strong graph interaction topologies.
Revised:  Under the control scheme, the closed loop system achieves almost global convergence to synchronization for quasi-strong interaction graph topologies.
Edit intent: fluency
Original: Receptor mediated endocytosis is an ubiquitous process through which cells internalize biological or synthetic nanoscale objects, including viruses, unicellular parasites, and nanomedical vectors for drug or gene delivery.
Revised: Receptor-mediated endocytosis is an ubiquitous process through which cells internalize biological or synthetic nanoscale objects, including viruses, unicellular parasites, and nanomedical vectors for drug or gene delivery.
Edit intent: fluency
Original: In recent years  consumer-level depth sensors have been adopted in various applications.
Revised: In recent years , consumer-level depth sensors have been adopted in various applications.
Edit intent: fluency
Original: In recent years  consumer-level depth sensors have been adopted in various applications.
Revised: In recent years consumer-level depth cameras have been adopted in various applications.
Edit intent: clarity