wanyu/IteraTeR_v2 huggingface dataset:
Original:  We consider a set F(n,q) of all transformations \mathbb Z_2 ^n \to \mathbb Z_2 ^n that can be implemented by reversible circuits with (n+q) inputs.
Revised:  We consider a set F(n,q) of all transformations \mathbb Z_2 ^n \to \mathbb Z_2 ^n that can be realized by reversible circuits with (n+q) inputs.
Edit intent: clarity
Original:  An analogue of Lupanov's method for the synthesis of reversible logic circuits with additional memory is described.
Revised:  An analogue of Lupanov's method for the synthesis of reversible logic circuits with additional inputs is described.
Edit intent: clarity
Original:  Our results establish a clear relationships between attention, importance, and strength of social links, and could lead to improved algorithms to prioritize social media content 
Revised:  Our results establish a clear relationships between attention, importance, and strength of social links, and could lead to improved algorithms to prioritize social media content .
Edit intent: fluency
Original: We study a model for Darwinian evolution in an asexual population with a large but non-constant populations size .
Revised: We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size .
Edit intent: clarity
Original:  The model incorporates the basic evolutionary mechanisms, namely natural birth , density-depending logistic death due to age and competition and a probability u of mutation at each birth event.
Revised:  The model incorporates the basic evolutionary mechanisms, namely natural birth , density-depending logistic death due to age and competition and a probability of mutation at each birth event.
Edit intent: fluency
Original:  The difference between mothers and mutants trait will be random, but of order \sigma.
Edit intent: coherence
Original:  In the present paper, we study the long-term behavior of the systems in the limit of large population (K\to \infty) size, rare mutations (u\to 0), and small mutational effects (\sigma\to 0), proving convergence to the canonical equation of adaptive dynamics (CEAD).
Revised:  In the present paper, we study the long-term behavior of the system in the limit of large population (K\to \infty) size, rare mutations (u\to 0), and small mutational effects (\sigma\to 0), proving convergence to the canonical equation of adaptive dynamics (CEAD).
Edit intent: fluency
Original:  In contrast to  , e.g.  Champagnat and M\'el\'eard, 2011 , we study the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scales of birth and death events remains separated from that of successful mutational events.
Revised:  In contrast to earlier works , e.g. Champagnat and M\'el\'eard, 2011 , we study the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scales of birth and death events remains separated from that of successful mutational events.
Edit intent: clarity
Original:  In contrast to  , e.g.  Champagnat and M\'el\'eard, 2011 , we study the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scales of birth and death events remains separated from that of successful mutational events.
Revised:  In contrast to , e.g. by Champagnat and M\'el\'eard, 2011 , we study the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scales of birth and death events remains separated from that of successful mutational events.
Edit intent: clarity
Original:  In contrast to  , e.g.  Champagnat and M\'el\'eard, 2011 , we study the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scales of birth and death events remains separated from that of successful mutational events.
Revised:  In contrast to , e.g. Champagnat and M\'el\'eard, , we study the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scales of birth and death events remains separated from that of successful mutational events.
Edit intent: coherence
Original:  In contrast to  , e.g.  Champagnat and M\'el\'eard, 2011 , we study the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scales of birth and death events remains separated from that of successful mutational events.
Revised:  In contrast to , e.g. Champagnat and M\'el\'eard, 2011 we take the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scales of birth and death events remains separated from that of successful mutational events.
Edit intent: clarity
Original:  In contrast to  , e.g.  Champagnat and M\'el\'eard, 2011 , we study the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scales of birth and death events remains separated from that of successful mutational events.
Revised:  In contrast to , e.g. Champagnat and M\'el\'eard, 2011 , we study the three limits simultaneously, i.e. u=u_K and \sigma=\sigma_K, tend to zero with K, subject to conditions that ensure that the time-scale of birth and death events remains separated from that of successful mutational events.
Edit intent: fluency
Original:  The fact that \sigma_K tends to zero with K leads to a slows down the dynamics of the microscopic system and leads to serious technical difficulties that requires the use of completely different methods than those used in previous work .
Revised:  This slows down the dynamics of the microscopic system and leads to serious technical difficulties that requires the use of completely different methods than those used in previous work .
Edit intent: coherence
Original:  The fact that \sigma_K tends to zero with K leads to a slows down the dynamics of the microscopic system and leads to serious technical difficulties that requires the use of completely different methods than those used in previous work .
Revised:  The fact that \sigma_K tends to zero with K leads to a slows down the dynamics of the microscopic system and leads to serious technical difficulties that requires the use of completely different methods .
Edit intent: clarity
Original:  The corresponded optimal control problem may be reduced to a linear parabolic boundary problem under some assumptions on the underlying process and the utility function.
Revised:  It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under some assumptions on the underlying process and the utility function.
Edit intent: coherence
Original:  Our main result is the exact solution to the optimal control problem within the framework of the Heston model.
Revised:  Our main result is the exact solution for optimal investment in Heston model.
Edit intent: clarity
Original: We present a scalable Boltzmann machine (BM) architecture based on theoretical analysis on the representation power of deep BMs (DBMs) . Application of DBMs is limited due to its poor scalability where deep stacking of layers does not largely help the performance.
Revised: We present a scalable Boltzmann machine (BM) architecture based on theoretical analysis on the representation power of deep BMs (DBMs) is limited due to its poor scalability where deep stacking of layers does not largely help the performance.
Edit intent: clarity
Original: We present a scalable Boltzmann machine (BM) architecture based on theoretical analysis on the representation power of deep BMs (DBMs) . Application of DBMs is limited due to its poor scalability where deep stacking of layers does not largely help the performance.
Revised: We present a scalable Boltzmann machine (BM) architecture based on theoretical analysis on the representation power of deep BMs (DBMs) . Application of DBMs is limited due to its poor scalability where deep stacking of layers does not largely improve the performance.
Edit intent: clarity
Original:  It is widely believed that DBMs have huge representation power  and its poor  scalability is mainly due to inefficiency of optimization algorithms.
Revised:  It is widely believed that DBMs have huge representation power , and its poor scalability is mainly due to inefficiency of optimization algorithms.
Edit intent: fluency
Original:  In this paper, we provide both theoretical and empirical evidences that the representation power of DBMs is actually rather limited  and the inefficiency of the model can result in the poor scalability.
Revised:  In this paper, we theoretically show that that the representation power of DBMs is actually rather limited and the inefficiency of the model can result in the poor scalability.
Edit intent: coherence
Original:  In this paper, we provide both theoretical and empirical evidences that the representation power of DBMs is actually rather limited  and the inefficiency of the model can result in the poor scalability.
Revised:  In this paper, we provide both theoretical and empirical evidences that the representation power of DBMs is actually rather limited , and the inefficiency of the model can result in the poor scalability.
Edit intent: fluency
Original:  Based on these observations, we propose an alternative BM architecture with improved representation power , which we dub soft-deep BMs (sDBMs).
Revised:  Based on these observations, we propose an alternative BM architecture , which we dub soft-deep BMs (sDBMs).
Edit intent: clarity
Original:   Experiments demonstrate that we are able to train sDBMs with up to 6 layers without pretraining  and sDBMs nicely compare state-of-the-art models on binarized MNIST and Caltech-101 silhouettes.
Revised:  Experiments demonstrate that we are able to train sDBMs with up to 6 layers without pretraining , and sDBMs nicely compare state-of-the-art models on binarized MNIST and Caltech-101 silhouettes.
Edit intent: fluency
Original:  In this paper, we theoretically show that that the representation power of DBMs is actually rather limited , and the inefficiency of the model can result in the poor scalability .
Revised:  In this paper, we theoretically show that that the representation power of DBMs can be actually rather limited , and the inefficiency of the model can result in the poor scalability .
Edit intent: fluency
Original:  We theoretically show that sDBMs possess much greater representation power than DBMs . Experiments demonstrate that we are able to train sDBMs with up to 6 layers without pretraining, and sDBMs nicely compare state-of-the-art models  on binarized MNIST and Caltech-101 silhouettes.
Revised:  We show that sDBMs possess much greater representation power than DBMs . Experiments demonstrate that we are able to train sDBMs with up to 6 layers without pretraining, and sDBMs nicely compare state-of-the-art models on binarized MNIST and Caltech-101 silhouettes.
Edit intent: coherence
Original:  We theoretically show that sDBMs possess much greater representation power than DBMs . Experiments demonstrate that we are able to train sDBMs with up to 6 layers without pretraining, and sDBMs nicely compare state-of-the-art models  on binarized MNIST and Caltech-101 silhouettes.
Revised:  We theoretically show that sDBMs possess much greater representation power than DBMs . Experiments demonstrate that sDBMs outperform several state-of-the-art models on binarized MNIST and Caltech-101 silhouettes.
Edit intent: clarity
Original:  We theoretically show that sDBMs possess much greater representation power than DBMs . Experiments demonstrate that we are able to train sDBMs with up to 6 layers without pretraining, and sDBMs nicely compare state-of-the-art models  on binarized MNIST and Caltech-101 silhouettes.
Revised:  We theoretically show that sDBMs possess much greater representation power than DBMs . Experiments demonstrate that we are able to train sDBMs with up to 6 layers without pretraining, and sDBMs nicely compare state-of-the-art models , including DBMs, in generative tasks on binarized MNIST and Caltech-101 silhouettes.
Edit intent: clarity
Original:  In this paper, by viewing the k-shell value of each node as its mass and the shortest path distance between any two nodes as their distance, then inspired by the idea of the gravity formula, we propose a gravity centrality index to identify the influential spreaders in complex networks.
Revised:  In this paper, by viewing the k-shell value of each node as its mass and the shortest path distance between two nodes as their distance, then inspired by the idea of the gravity formula, we propose a gravity centrality index to identify the influential spreaders in complex networks.
Edit intent: clarity
Original:  The comparison between the gravity centrality index with some well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as artificial networks.
Revised:  The comparison between the gravity centrality index and some well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as artificial networks.
Edit intent: fluency
Original:  The comparison between the gravity centrality index with some well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as artificial networks.
Revised:  The comparison between the gravity centrality index with some well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as synthetic networks.
Edit intent: clarity
Original:  This latter fractional order recovery model is shown to be consistent with an age-structured Kermack-McKendrick SIR model.
Revised:  This latter fractional order recovery model is shown to be consistent with the Kermack-McKendrick SIR model.
Edit intent: clarity
Original:  The algorithm is designed to work with first-principles methods, facilitated by the incorporation of local optimization and blacklisting conformers that prevents repeated evaluations of very similar solutions.
Revised:  The algorithm is designed to work with first-principles methods, facilitated by the incorporation of local optimization and blacklisting conformers to prevent repeated evaluations of very similar solutions.
Edit intent: coherence
Original:  Thus optimal 2-separable codes behave neither like 2-frameproof nor 1-frameproof codes.
Revised:  So optimal 2-separable codes behave neither like 2-frameproof nor 1-frameproof codes.
Edit intent: fluency
Original:  Also, the bound of Gao and Ge is strengthened to show that a q-ary \overline{2}-separable code of length n can have at most \[ q^{\lceil 2n/3\rceil}+\tfrac{1}{2}q^{\lfloor n/3\rfloor}(q^{\lfloor n/3\rfloor}-1) \] codewords.
Revised:  Also, the Gao--Ge bound is strengthened to show that a q-ary \overline{2}-separable code of length n can have at most \[ q^{\lceil 2n/3\rceil}+\tfrac{1}{2}q^{\lfloor n/3\rfloor}(q^{\lfloor n/3\rfloor}-1) \] codewords.
Edit intent: clarity
Original: We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture  market's important features.
Revised: We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features.
Edit intent: fluency
Original:  In particular, transaction costs can be approximately compensated  applying the Leland adjusting volatility principle and  asymptotic property of the hedging error due to discrete readjustments is characterized.
Revised:  In particular, transaction costs can be approximately compensated by applying the Leland adjusting volatility principle and asymptotic property of the hedging error due to discrete readjustments is characterized.
Edit intent: fluency
Original:  In particular, transaction costs can be approximately compensated  applying the Leland adjusting volatility principle and  asymptotic property of the hedging error due to discrete readjustments is characterized.
Revised:  In particular, transaction costs can be approximately compensated applying the Leland adjusting volatility principle and the asymptotic property of the hedging error due to discrete readjustments is characterized.
Edit intent: fluency
Original:  We show that jump risk is approximately eliminated and the results established in continuous diffusion models are recovered.
Revised:  In particular, the jump risk can be approximately eliminated and the results established in continuous diffusion models are recovered.
Edit intent: clarity
Original: One of the problems faced by a firm that sells certain goods is to determine which is the number of products that must supply to maximize profits .
Revised: One of the problems faced by a firm that sells certain commodities is to determine which is the number of products that must supply to maximize profits .
Edit intent: clarity
Original: One of the problems faced by a firm that sells certain goods is to determine which is the number of products that must supply to maximize profits .
Revised: One of the problems faced by a firm that sells certain goods is to determine the number of products that must supply to maximize profits .
Edit intent: clarity
Original: One of the problems faced by a firm that sells certain goods is to determine which is the number of products that must supply to maximize profits .
Revised: One of the problems faced by a firm that sells certain goods is to determine which is the number of products that it must supply in order to maximize its profit .
Edit intent: clarity
Original:  In this article, we give an answer to this problem of economic interest.
Revised:  In this article, the authors give an answer to this problem of economic interest.
Edit intent: clarity
Original:  To solve it we use the theorem "unconscious statistician".
Edit intent: coherence
Original:  In addition, the described procedure is simple and can be successfully applied to any number of goods .
Revised:  In addition, the described procedure is simple and can be successfully applied to any number of commodities .
Edit intent: clarity
Original: Classical reconstruction methods for phase-contrast tomography consist of two stages , namely phase retrieval followed by tomographic reconstruction.
Revised: Classical reconstruction methods for phase-contrast tomography consist of two stages : phase retrieval and tomographic reconstruction.
Edit intent: clarity
Original:  We compare the combined method with standard two-stage method in simulated free-space propagation experiments with phantoms inspired by materials science.
Revised:  We compare the combined method with standard two-stage method given. Using simulated free-space propagation experiments with phantoms inspired by materials science.
Edit intent: clarity
Original:  In reconstructions produced by the novel method it is easier to distinguish between similar materials, than in the two-stage methods.
Revised:  In reconstructions produced by the novel method with the two-stage methods.
Edit intent: clarity
Original: In this work the  problem of inferring interactions and fields for an Ising neural network from given patterns under a local stability hypothesis (Gardner problem) is addressed under a dual perspective.
Revised: In this work the Gardner problem of inferring interactions and fields for an Ising neural network from given patterns under a local stability hypothesis (Gardner problem) is addressed under a dual perspective.
Edit intent: fluency
Original: In this work the  problem of inferring interactions and fields for an Ising neural network from given patterns under a local stability hypothesis (Gardner problem) is addressed under a dual perspective.
Revised: In this work the problem of inferring interactions and fields for an Ising neural network from given patterns under a local stability hypothesis is addressed under a dual perspective.
Edit intent: coherence
Original:  By means of duality arguments an integer linear system is defined whose solution space is the dual of the space of interactions and whose solutions represent mutually unstable patterns.
Revised:  By means of duality arguments an integer linear system is defined whose solution space is the dual of the Gardner space and whose solutions represent mutually unstable patterns.
Edit intent: clarity
Original:  We illustrate the problem on a set of real data and perform ensemble calculation that shows how the emergence of phase dominated by unstable pattern can be triggered in a non-linear discontinuous way.
Revised:  We illustrate the problem on a set of real data and perform ensemble calculation that shows how the emergence of phase dominated by unstable patterns can be triggered in a non-linear discontinuous way.
Edit intent: fluency
Original:  These methods are important in many planning and optimization tasks in wireless networks.
Revised:  These methods are particularly important in planning and optimization tasks in wireless networks.
Edit intent: clarity
Original:  To address this and more general problems,  we show two alternative but equivalent ways to construct a matrix that is guaranteed to have spectral radius strictly smaller than one if the corresponding mapping has a fixed point.
Revised:  To address this and more general problems, we show two alternative but equivalent ways to construct a matrix that is guaranteed to have spectral radius strictly smaller than one if the mapping has a fixed point.
Edit intent: clarity
Original: Extended Chebyshev spaces that also comprise the constants represent large families of functions that can be used in real-life modeling or engineering applications that also involve important (e.g. \ transcendental) integral or rational curves and surfaces.
Revised: Extended Chebyshev spaces that also comprise the constants represent large families of functions that can be used in real-life modeling or engineering applications that also involve important (e.g. transcendental) integral or rational curves and surfaces.
Edit intent: fluency
Original: Let A be an (m \times n) integral matrix of the rank n and let P=\{ x : A x \leq b\} be  n-dimensional polytope.
Revised: Let A be an (m \times n) integral matrix , and let P=\{ x : A x \leq b\} be n-dimensional polytope.
Edit intent: clarity
Original: Let A be an (m \times n) integral matrix of the rank n and let P=\{ x : A x \leq b\} be  n-dimensional polytope.
Revised: Let A be an (m \times n) integral matrix of the rank n and let P=\{ x : A x \leq b\} be an n-dimensional polytope.
Edit intent: fluency
Original:  Let \Delta denote the smallest absolute value of the determinant among basis matrices of A . We prove that if every basis matrix of A has  determinant equal to \pm \Delta  and w(P)\ge (\Delta  -1)(n+1), then P contains a lattice n - dimensional simplex.
Revised:  Let \Delta denote the smallest absolute value of the determinant among basis matrices of A . We prove that if every basis matrix of A has a determinant equal to \pm \Delta and w(P)\ge (\Delta -1)(n+1), then P contains a lattice n - dimensional simplex.
Edit intent: fluency
Original:   \pm  \}. } When P is a simplex and w(P)\ge \Delta -1 we describe the polynomial time algorithm for finding an integer point in P \emph{ ^n \} can be solved in polynomial time.
Revised:  \pm \}. } When P is a simplex and w(P)\ge \Delta -1 , we describe a polynomial time algorithm for finding an integer point in P \emph{ ^n \} can be solved in polynomial time.
Edit intent: fluency