wanyu/IteraTeR_v2 huggingface dataset:
Original:  We provide a counter-argument in this paper, and show that even though the solution profile develops singularities in the random space, which destroys the high accuracy of gPC, the physical quantities (such as the shock emergence time, the shock location, and the shock strength) are all smooth functions of the uncertainties coming from both initial data and the wave speed: with proper shifting, the solution's polynomial interpolation approximates with high accuracy .
Revised:  We provide a counter-argument in this paper, and show that even though the solution profile develops singularities in the random space, which destroys the spectral accuracy of gPC, the physical quantities (such as the shock emergence time, the shock location, and the shock strength) are all smooth functions of the uncertainties coming from both initial data and the wave speed: with proper shifting, the solution's polynomial interpolation approximates with high accuracy .
Edit intent: clarity
Original:  Therefore this work provides a new perspective to quantify uncertainties and significantly improves the accuracy of  gPC method with a slight reformulation.
Revised:  Therefore this work provides a new perspective to "quantify uncertainties" and significantly improves the accuracy of gPC method with a slight reformulation.
Edit intent: fluency
Original:  Therefore this work provides a new perspective to quantify uncertainties and significantly improves the accuracy of  gPC method with a slight reformulation.
Revised:  Therefore this work provides a new perspective to quantify uncertainties and significantly improves the accuracy of the gPC method with a slight reformulation.
Edit intent: fluency
Original:  We use the Burgers' equation as an example for  thorough analysis, and the analysis could be extended to general conservation laws with convex fluxes.
Revised:  We use the Burgers' equation as an example for the thorough analysis, and the analysis could be extended to general conservation laws with convex fluxes.
Edit intent: fluency
Original: Applying original and existing theoretical results, we propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the non-negative normalized B-basis of an arbitrary extended Chebyshev (EC)
Revised: We propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the non-negative normalized B-basis of an arbitrary extended Chebyshev (EC)
Edit intent: coherence
Original: Applying original and existing theoretical results, we propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the non-negative normalized B-basis of an arbitrary extended Chebyshev (EC)
Revised: Applying original and existing theoretical results, we propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the normalized B-basis of an arbitrary extended Chebyshev (EC)
Edit intent: clarity
Original: Applying original and existing theoretical results, we propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the non-negative normalized B-basis of an arbitrary extended Chebyshev (EC)
Revised: Applying original and existing theoretical results, we propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the non-negative normalized B-basis of a user-specified extended Chebyshev (EC)
Edit intent: clarity
Original:  space that comprises the constants and can be identified with the solution space of a user-defined constant-coefficient homogeneous linear differential equation  . Using the obtained non-negative normalized B-bases, our library can also generate, (partially) differentiate, modify and visualize a large family of so-called B-curves and tensor product B-surfaces.
Revised:  space that comprises the constants and can be identified with the solution space of a constant-coefficient homogeneous linear differential equation . Using the obtained non-negative normalized B-bases, our library can also generate, (partially) differentiate, modify and visualize a large family of so-called B-curves and tensor product B-surfaces.
Edit intent: clarity
Original:  space that comprises the constants and can be identified with the solution space of a user-defined constant-coefficient homogeneous linear differential equation  . Using the obtained non-negative normalized B-bases, our library can also generate, (partially) differentiate, modify and visualize a large family of so-called B-curves and tensor product B-surfaces.
Revised:  space that comprises the constants and can be identified with the solution space of a user-defined constant-coefficient homogeneous linear differential equation . Using the obtained normalized B-bases, our library can also generate, (partially) differentiate, modify and visualize a large family of so-called B-curves and tensor product B-surfaces.
Edit intent: clarity
Original:  Moreover, the library also implements methods that can be used to perform general order elevation, to subdivide B-curves and B-surfaces by means of general de Casteljau-like B-algorithms, and to generate general basis transformations for the control point based exact description of arbitrary integral curves and surfaces that are described in traditional parametric form by means of the ordinary bases of the underlying EC spaces.
Revised:  Moreover, the library also implements methods that can be used to perform general order elevation, to subdivide B-curves and B-surfaces by means of de Casteljau-like B-algorithms, and to generate general basis transformations for the control point based exact description of arbitrary integral curves and surfaces that are described in traditional parametric form by means of the ordinary bases of the underlying EC spaces.
Edit intent: clarity
Original:  Moreover, the library also implements methods that can be used to perform general order elevation, to subdivide B-curves and B-surfaces by means of general de Casteljau-like B-algorithms, and to generate general basis transformations for the control point based exact description of arbitrary integral curves and surfaces that are described in traditional parametric form by means of the ordinary bases of the underlying EC spaces.
Revised:  Moreover, the library also implements methods that can be used to perform general order elevation, to subdivide B-curves and B-surfaces by means of general de Casteljau-like B-algorithms, and to generate basis transformations for the control point based exact description of arbitrary integral curves and surfaces that are described in traditional parametric form by means of the ordinary bases of the underlying EC spaces.
Edit intent: fluency
Original:  Moreover, the library also implements methods that can be used to perform general order elevation, to subdivide B-curves and B-surfaces by means of general de Casteljau-like B-algorithms, and to generate general basis transformations for the control point based exact description of arbitrary integral curves and surfaces that are described in traditional parametric form by means of the ordinary bases of the underlying EC spaces.
Revised:  Moreover, the library also implements methods that can be used to perform general order elevation, to subdivide B-curves and B-surfaces by means of general de Casteljau-like B-algorithms, and to generate general basis transformations for the B-representation of arbitrary integral curves and surfaces that are described in traditional parametric form by means of the ordinary bases of the underlying EC spaces.
Edit intent: clarity
Original: Reaction-diffusion systems are used to model many biological and physical phenomena.
Revised: Reaction-diffusion systems are used to represent many biological and physical phenomena.
Edit intent: clarity
Original:  Spatial hybrid methods couple two or more of these representations in order to improve the efficiency of a model without compromising accuracy.
Revised:  Spatial hybrid methods couple two or more of these representations in order to improve efficiency without compromising accuracy.
Edit intent: clarity
Original:  In this paper, we present a novel spatial hybrid method, which we call the auxiliary region method (ARM), which couples PDE and Brownian representations of reaction-diffusion systems.
Revised:  In this paper, we present a novel spatial hybrid method, which we call the auxiliary region method (ARM), which couples PDE and Brownian-based representations of reaction-diffusion systems.
Edit intent: clarity
Original:  Numerical PDE solutions on one side of the interface are coupled to Brownian dynamics on the other side using compartment-based "auxiliary regions".
Revised:  Numerical PDE solutions on one side of an interface are coupled to Brownian dynamics on the other side using compartment-based "auxiliary regions".
Edit intent: fluency
Original:  Numerical PDE solutions on one side of the interface are coupled to Brownian dynamics on the other side using compartment-based "auxiliary regions".
Revised:  Numerical PDE solutions on one side of the interface are coupled to Brownian-based dynamics on the other side using compartment-based "auxiliary regions".
Edit intent: fluency
Original: Modern society depends on the flow of information over online social networks, and popular social platforms now generate significant behavioral data .
Revised: Modern society depends on the flow of information over online social networks, and users of popular platforms generate significant behavioral data .
Edit intent: clarity
Original:  Yet it remains unclear what fundamental limits may exist when using these data to predict the activities and interests of individuals  .
Revised:  Yet it remains unclear what fundamental limits exist when using these data to predict the activities and interests of individuals .
Edit intent: clarity
Original:  Here we apply tools from information theory to estimate the predictive information content of the writings of Twitter users and to what extent that information flows between users . Distinct temporal and social effects are visible in the information flow , and these estimates provide a fundamental bound on the predictive accuracy achievable with these data.
Revised:  Here we apply tools from information theory to estimate the predictive information within the writings of Twitter users and to what extent that information flows between users . Distinct temporal and social effects are visible in the information flow , and these estimates provide a fundamental bound on the predictive accuracy achievable with these data.
Edit intent: clarity
Original:  We propose a method for generating hypotheses in the field of physics using the massive publications of physics journals .
Revised:  We propose an automatic method that is helpful for generating research hypotheses in the field of physics using the massive publications of physics journals .
Edit intent: clarity
Original:  We propose a method for generating hypotheses in the field of physics using the massive publications of physics journals .
Revised:  We propose a method for generating hypotheses in the field of physics using the massive number of physics journal publications .
Edit intent: clarity
Original:  We convert the text data of titles and abstracts in publications to a bipartite graph  extracting words of matter and keywords and suggest methods for predicting links between matter and keywords node.
Revised:  We convert the text data of titles and abstract sections in publications to a bipartite graph extracting words of matter and keywords and suggest methods for predicting links between matter and keywords node.
Edit intent: clarity
Original:  We convert the text data of titles and abstracts in publications to a bipartite graph  extracting words of matter and keywords and suggest methods for predicting links between matter and keywords node.
Revised:  We convert the text data of titles and abstracts in publications to a bipartite graph , extracting words of matter and keywords and suggest methods for predicting links between matter and keywords node.
Edit intent: fluency
Original:  Those links generate hypotheses for research by suggesting the new possible relationship between some matter and phenomena or properties . Suggested methods have better performance than existed methods for link prediction in the bipartite graph.
Revised:  Those links generate hypotheses for research by suggesting the new possible relationship between some matter and phenomena or properties . Suggested methods have better performance than existing methods for link prediction in the bipartite graph.
Edit intent: fluency
Original:  Over the years, the research effort in Computational Intelligence area resulted in algorithms able to achieve good results by solving problems with more than one conflicting objective.
Revised:  Over the years, the research effort in the Computational Intelligence field resulted in algorithms able to achieve good results by solving problems with more than one conflicting objective.
Edit intent: clarity
Original:  For this, we used concepts and ideas often found in the literature and applied in state-of-the-art algorithms, namely: (i) reference points and lines in the objectives space;
Revised:  For this, we used concepts and ideas often employed by state-of-the-art algorithms, namely: (i) reference points and lines in the objectives space;
Edit intent: clarity
Original:  Results have shown competitiveness, as well as the necessity of improving the performance of the proposed technique on multi-modal many-objective problems .
Revised:  Moreover, a version of the proposed technique tailored to solve multi-modal many-objective problems .
Edit intent: clarity
Original:  This adaptation is based on the division of the school in clusters that are specialized in solving a single-objective problem generated by the decomposition of the original problem.
Revised:  This adaptation is based on the division of the candidate solutions in clusters that are specialized in solving a single-objective problem generated by the decomposition of the original problem.
Edit intent: clarity
Original:  The "thickness ' of a graph G is the minimum integer k such that in some drawing of G, the edges can be partitioned into k noncrossing subgraphs.
Revised:  The "thickness " of a graph G is the minimum integer k such that in some drawing of G, the edges can be partitioned into k noncrossing subgraphs.
Edit intent: fluency
Original:  We first propose a general framework and show that eight different optical component design problems amount to solving a Light Energy Conservation equation that involves the computation of Visibility diagrams.
Revised:  We first propose a general framework and show that eight different optical component design problems amount to solving a light energy conservation equation that involves the computation of Visibility diagrams.
Edit intent: fluency
Original:  We first propose a general framework and show that eight different optical component design problems amount to solving a Light Energy Conservation equation that involves the computation of Visibility diagrams.
Revised:  We first propose a general framework and show that eight different optical component design problems amount to solving a Light Energy Conservation equation that involves the computation of visibility diagrams.
Edit intent: fluency
Original:  We  show that these diagrams all have the same structure and can be obtained by intersecting a 3D Power Diagram with a planar or spherical domain.
Revised:  We show that these diagrams all have the same structure and can be obtained by intersecting a 3D Power diagram with a planar or spherical domain.
Edit intent: fluency
Original:  This allows us to propose an efficient and fully generic algorithm capable to solve the eight optical component design problems.
Revised:  This allows us to propose an efficient and fully generic algorithm capable to solve these eight optical component design problems.
Edit intent: fluency
Original:  Our solutions can satisfy design constraints such as convexity or concavity and are always graphs over the plane or the sphere .
Revised:  Our solutions can satisfy design constraints such as convexity or concavity .
Edit intent: coherence
Original:  We show the effectiveness of our algorithm on numerous simulated examples.
Revised:  We show the effectiveness of our algorithm on simulated and fabricated examples.
Edit intent: clarity
Original:  Firstly, quantum teleportation technology is used for coin transaction, which prevents an owner of a coin from keeping the original coin data  after sending the coin to another.
Revised:  Firstly, quantum teleportation technology is used for coin transaction, which prevents from the owner of the coin keeping the original coin data after sending the coin to another.
Edit intent: clarity
Original:  Firstly, quantum teleportation technology is used for coin transaction, which prevents an owner of a coin from keeping the original coin data  after sending the coin to another.
Revised:  Firstly, quantum teleportation technology is used for coin transaction, which prevents an owner of a coin from keeping the original coin data even after sending the coin to another.
Edit intent: clarity
Original:  This was a main problem in systems using classical information and a blockchain was introduced to solve this issue.
Revised:  This was a main problem in a classical circuit and a blockchain was introduced to solve this issue.
Edit intent: clarity
Original:  Making a bock is time consuming and the system of qBitcoin is based on a quantum chain, instead of blocks.
Revised:  Making a block is time consuming and the system of qBitcoin is based on a quantum chain, instead of blocks.
Edit intent: fluency
Original:  At the same time, we also show that the prospect theoretic distortions at both the transmitter and the receiver are both smaller than the expected distortion, thus making behavioral agents more contended than unbiased agents.
Revised:  At the same time, we also show that the prospect-theoretic distortions at both the transmitter and the receiver are both smaller than the expected distortion, thus making behavioral agents more contended than unbiased agents.
Edit intent: fluency
Original:  At the same time, we also show that the prospect theoretic distortions at both the transmitter and the receiver are both smaller than the expected distortion, thus making behavioral agents more contended than unbiased agents.
Revised:  At the same time, we also show that the prospect theoretic distortions at both the transmitter and the receiver are both larger than the expected distortion, thus making behavioral agents more contended than unbiased agents.
Edit intent: clarity
Original:  At the same time, we also show that the prospect theoretic distortions at both the transmitter and the receiver are both smaller than the expected distortion, thus making behavioral agents more contended than unbiased agents.
Revised:  At the same time, we also show that the prospect theoretic distortions at both the transmitter and the receiver are both smaller than the expected distortion, thus making behavioral agents less contended than unbiased agents.
Edit intent: clarity
Original: The problem of determining Herbrand equivalence of terms at each program point in a data flow framework is a central problem in program analysis and compiler optimizations.
Revised: The problem of determining Herbrand equivalence of terms at each program point in a data flow framework is a central and well studied question in program analysis and compiler optimizations.
Edit intent: clarity
Original:  Whereas the algorithmic computation of Herbrand equivalence in data flow frameworks proceeds via iterative fix-point computation on an abstract lattice framework, a fix-point characterization for Herbrand equivalence for data flow frameworks does not seem to appear so far in the literature.
Revised:  Whereas the algorithmic computation of Herbrand equivalence in data flow frameworks proceed via iterative fix-point computation on an abstract lattice framework, a fix-point characterization for Herbrand equivalence for data flow frameworks does not seem to appear so far in the literature.
Edit intent: fluency
Original: We study the structure learning problem for graph homomorphisms, commonly referred to as H-colorings, including the weighted case which corresponds to spin systems with hard constraints .
Revised: We study the structure learning problem for H-colorings, including the weighted case which corresponds to spin systems with hard constraints .
Edit intent: clarity
Original:  We prove that  when q>d  the problem is identifiable and we can learn G in \mathrm{poly {\rm  (d,q) \times O(n^2n) time.
Revised:  We prove that when q>d ) the problem is identifiable and we can learn G in \mathrm{poly {\rm (d,q) \times O(n^2n) time.
Edit intent: fluency
Original:  We prove that  when q>d  the problem is identifiable and we can learn G in \mathrm{poly {\rm  (d,q) \times O(n^2n) time.
Revised:  We prove that when q>d the problem is identifiable and we can learn G in {\rm (d,q) \times O(n^2n) time.
Edit intent: coherence
Original:  We prove that  when q>d  the problem is identifiable and we can learn G in \mathrm{poly {\rm  (d,q) \times O(n^2n) time.
Revised:  We prove that when q>d the problem is identifiable and we can learn G in \mathrm{poly {\rm poly (d,q) \times O(n^2n) time.
Edit intent: fluency
Original:  When q\leq d  we prove that the problem is not identifiable , and we cannot hope to learn G . When q<d-d + \Theta(1) we prove that even learning an equivalent graph (any graph with the same set of H-colorings) is computationally hard---sample complexity is exponential in n in the worst-case.
Revised:  When q\leq d ) we prove that the problem is not identifiable , and we cannot hope to learn G . When q<d-d + \Theta(1) we prove that even learning an equivalent graph (any graph with the same set of H-colorings) is computationally hard---sample complexity is exponential in n in the worst-case.
Edit intent: fluency
Original:  When q\leq d  we prove that the problem is not identifiable , and we cannot hope to learn G . When q<d-d + \Theta(1) we prove that even learning an equivalent graph (any graph with the same set of H-colorings) is computationally hard---sample complexity is exponential in n in the worst-case.
Revised:  When q\leq d we prove that the problem is not identifiable and thus G cannot be learned. Moreover, when q<d-d + \Theta(1) we prove that even learning an equivalent graph (any graph with the same set of H-colorings) is computationally hard---sample complexity is exponential in n in the worst-case.
Edit intent: clarity
Original:  We explore this connection for general H-colorings and prove that under a well-known condition in statistical physics, known as Dobrushin uniqueness condition, we can learn G in \mathrm{poly {\rm  (d,q)\times O(n^2n) time.
Revised:  We explore this connection for general H-colorings and prove that under the well-known condition in statistical physics, known as Dobrushin uniqueness condition, we can learn G in \mathrm{poly {\rm (d,q)\times O(n^2n) time.
Edit intent: fluency
Original:  We explore this connection for general H-colorings and prove that under a well-known condition in statistical physics, known as Dobrushin uniqueness condition, we can learn G in \mathrm{poly {\rm  (d,q)\times O(n^2n) time.
Revised:  We explore this connection for general H-colorings and prove that under a well-known Dobrushin uniqueness condition, we can learn G in \mathrm{poly {\rm (d,q)\times O(n^2n) time.
Edit intent: clarity