wanyu/IteraTeR_v2 huggingface dataset:
Original:  This survey highlights the many insights from the wealth of empricial and theoretical studies that have been conducted, and the numerous unsolved problems that remain.
Revised:  This survey highlights the many insights from the wealth of empirical and theoretical studies that have been conducted, and the numerous unsolved problems that remain.
Edit intent: fluency
Original:  By examining existing models of limit order books , we identify some key unresolved questions and difficultes currently facing researchers of limit order trading .
Revised:  By examining existing models of limit order books , we identify several key unresolved questions and difficultes currently facing researchers of limit order trading .
Edit intent: clarity
Original:  By examining existing models of limit order books , we identify some key unresolved questions and difficultes currently facing researchers of limit order trading .
Revised:  By examining existing models of limit order books , we identify some key unresolved questions about LOBs .
Edit intent: clarity
Original: Many machine learning problems are solved by algorithms that involve eigenvalue decomposition (EVD) or singular value decomposition (SVD) in each iteration .
Revised: Many machine learning problems are solved by algorithms that involve eigenvalue decomposition (EVD) or singular value decomposition (SVD) .
Edit intent: clarity
Original:  Therefore, these algorithms suffer from the high computation cost of multiple EVD/ SVDs.
Revised:  Therefore, their solution suffers from the high computation cost of multiple EVD/ SVDs.
Edit intent: clarity
Original:  Therefore, these algorithms suffer from the high computation cost of multiple EVD/ SVDs.
Revised:  Therefore, these algorithms suffer from the high computation cost of multiple SVDs.
Edit intent: clarity
Original:  To relieve this issue, we introduce the block Lanczos method to replace the original exact EVD/SVD in each iteration by solving it approximately, yet still at a high precision.
Revised:  To relieve this issue, we propose using the block Lanczos method to replace the original exact EVD/SVD in each iteration by solving it approximately, yet still at a high precision.
Edit intent: clarity
Original:  We also propose to utilize the subspace obtained in the previous iteration  to start the block Lanczos procedure.
Revised:  We also propose to utilize the subspace obtained in the previous iteration are used to start the block Lanczos procedure.
Edit intent: clarity
Original:  Examples of three popular problems are presented to show how our block Lanczos with warm start (BLWS) technique can be adopted to accelerate its host algorithms . Experimental results show that our BLWS technique usually accelerates its host algorithms by at least two  times.
Revised:  Examples of three popular problems are presented to show how our block Lanczos with warm start (BLWS) technique can be adopted to accelerate its host algorithms . Experimental results show that our BLWS technique usually accelerates its host algorithm by at least two times.
Edit intent: fluency
Original:  Examples of three popular problems are presented to show how our block Lanczos with warm start (BLWS) technique can be adopted to accelerate its host algorithms . Experimental results show that our BLWS technique usually accelerates its host algorithms by at least two  times.
Revised:  Examples of three popular problems are presented to show how our block Lanczos with warm start (BLWS) technique can be adopted to accelerate its host algorithms . Experimental results show that our BLWS technique usually accelerates its host algorithms by at least two to three times.
Edit intent: clarity
Original:  The optimum function is found by minimizing the least square problem ( l2 \ell2 norm of the difference between the desired and the approximated filters) by means of the calculus of variation;
Revised:  The optimum function is found by minimizing the least square problem ( \ell2 norm of the difference between the desired and the approximated filters) by means of the calculus of variation;
Edit intent: clarity
Original:  Moreover, this decomposition of%DIFDELCMD < \psi %%% uses building blocksdefined mathematically in terms of purely diagrammatic laws .
Revised:  Moreover, this decomposition of%DIFDELCMD < \psi %%% of clearly defined building blocks .
Edit intent: clarity
Original: We generalize the notions of flippable and simultaneously-flippable edges in a triangulation of a set S of points in the plane , into so called pseudo simultaneously-flippable edges .
Revised: We generalize the notions of flippable and simultaneously flippable edges in a triangulation of a set S of points in the plane , into so called pseudo simultaneously-flippable edges .
Edit intent: fluency
Original: We generalize the notions of flippable and simultaneously-flippable edges in a triangulation of a set S of points in the plane , into so called pseudo simultaneously-flippable edges .
Revised: We generalize the notions of flippable and simultaneously-flippable edges in a triangulation of a set S of points in the plane to so-called .
Edit intent: clarity
Original: We generalize the notions of flippable and simultaneously-flippable edges in a triangulation of a set S of points in the plane , into so called pseudo simultaneously-flippable edges .
Revised: We generalize the notions of flippable and simultaneously-flippable edges in a triangulation of a set S of points in the plane , into so called pseudo simultaneously-flippable edgespseudo-simultaneously flippable edges .
Edit intent: clarity
Original:  We derive a worst-case tight lower bound on the number of pseudo simultaneously-flippable edges in any triangulation , and use this bound to obtain upper bounds for the maximal number of several types of plane graphs that can be embedded (with crossing-free straight edges) on a fixed set of N points in the plane.
Revised:  We prove a worst-case tight lower bound on the number of pseudo simultaneously-flippable edges in any triangulation , and use this bound to obtain upper bounds for the maximal number of several types of plane graphs that can be embedded (with crossing-free straight edges) on a fixed set of N points in the plane.
Edit intent: clarity
Original:  We derive a worst-case tight lower bound on the number of pseudo simultaneously-flippable edges in any triangulation , and use this bound to obtain upper bounds for the maximal number of several types of plane graphs that can be embedded (with crossing-free straight edges) on a fixed set of N points in the plane.
Revised:  We derive a worst-case tight lower bound for the number of pseudo simultaneously-flippable edges in any triangulation , and use this bound to obtain upper bounds for the maximal number of several types of plane graphs that can be embedded (with crossing-free straight edges) on a fixed set of N points in the plane.
Edit intent: fluency
Original:  We derive a worst-case tight lower bound on the number of pseudo simultaneously-flippable edges in any triangulation , and use this bound to obtain upper bounds for the maximal number of several types of plane graphs that can be embedded (with crossing-free straight edges) on a fixed set of N points in the plane.
Revised:  We derive a worst-case tight lower bound on the number of pseudo simultaneously-flippable edges in any triangulation , and use this bound for deriving new upper bounds for the maximal number of several types of plane graphs that can be embedded (with crossing-free straight edges) on a fixed set of N points in the plane.
Edit intent: clarity
Original:  We derive a worst-case tight lower bound on the number of pseudo simultaneously-flippable edges in any triangulation , and use this bound to obtain upper bounds for the maximal number of several types of plane graphs that can be embedded (with crossing-free straight edges) on a fixed set of N points in the plane.
Revised:  We derive a worst-case tight lower bound on the number of pseudo simultaneously-flippable edges in any triangulation , and use this bound to obtain upper bounds for the maximal number of crossing-free straight-edge graphs that can be embedded (with crossing-free straight edges) on a fixed set of N points in the plane.
Edit intent: clarity
Original:  More specifically, denoting by tr(N) <30^N the maximum possible number of triangulations of a set of N points in the plane , we show that every set of N points in the plane can have at most 6.9283^N * tr(N) < 207.85^N plane graphs, O( 4.8895 ^N) * tr(N) = O( 146.69 ^N) spanning trees, and O( 5.4723 ^N) * tr(N) = O( 164.17 ^N) forests (that is, cycle-free graphs) .
Revised:  We obtain new upper bounds for the number of spanning trees and forests as well. Specifically, let tr(N) <30^N the maximum possible number of triangulations of a set of N points in the plane , we show that every set of N points in the plane can have at most 6.9283^N * tr(N) < 207.85^N plane graphs, O( 4.8895 ^N) * tr(N) = O( 146.69 ^N) spanning trees, and O( 5.4723 ^N) * tr(N) = O( 164.17 ^N) forests (that is, cycle-free graphs) .
Edit intent: clarity
Original:  More specifically, denoting by tr(N) <30^N the maximum possible number of triangulations of a set of N points in the plane , we show that every set of N points in the plane can have at most 6.9283^N * tr(N) < 207.85^N plane graphs, O( 4.8895 ^N) * tr(N) = O( 146.69 ^N) spanning trees, and O( 5.4723 ^N) * tr(N) = O( 164.17 ^N) forests (that is, cycle-free graphs) .
Revised:  More specifically, denoting by tr(N) denote the maximum number of triangulations of a set of N points in the plane , we show that every set of N points in the plane can have at most 6.9283^N * tr(N) < 207.85^N plane graphs, O( 4.8895 ^N) * tr(N) = O( 146.69 ^N) spanning trees, and O( 5.4723 ^N) * tr(N) = O( 164.17 ^N) forests (that is, cycle-free graphs) .
Edit intent: clarity
Original:  More specifically, denoting by tr(N) <30^N the maximum possible number of triangulations of a set of N points in the plane , we show that every set of N points in the plane can have at most 6.9283^N * tr(N) < 207.85^N plane graphs, O( 4.8895 ^N) * tr(N) = O( 146.69 ^N) spanning trees, and O( 5.4723 ^N) * tr(N) = O( 164.17 ^N) forests (that is, cycle-free graphs) .
Revised:  More specifically, denoting by tr(N) <30^N the maximum possible number of triangulations on a set of N points in the plane , we show that every set of N points in the plane can have at most 6.9283^N * tr(N) < 207.85^N plane graphs, O( 4.8895 ^N) * tr(N) = O( 146.69 ^N) spanning trees, and O( 5.4723 ^N) * tr(N) = O( 164.17 ^N) forests (that is, cycle-free graphs) .
Edit intent: clarity
Original:  More specifically, denoting by tr(N) <30^N the maximum possible number of triangulations of a set of N points in the plane , we show that every set of N points in the plane can have at most 6.9283^N * tr(N) < 207.85^N plane graphs, O( 4.8895 ^N) * tr(N) = O( 146.69 ^N) spanning trees, and O( 5.4723 ^N) * tr(N) = O( 164.17 ^N) forests (that is, cycle-free graphs) .
Revised:  More specifically, denoting by tr(N) <30^N the maximum possible number of triangulations of a set of N points in the plane , we show that every set of N points in the plane can have at most 6.9283^N * tr(N) < 207.85^N plane graphs, O( 4.8895 ^N) * tr(N) = O( 146.69 ^N) spanning trees, and O( 5.4723 ^N) * tr(N) = O( 164.17 ^N) forests .
Edit intent: clarity
Original: We propose a general class of models for the simultaneous treatment of equity, corporate bonds, government bonds and derivatives.
Revised: We propose a general framework for the simultaneous treatment of equity, corporate bonds, government bonds and derivatives.
Edit intent: clarity
Original: We propose a general class of models for the simultaneous treatment of equity, corporate bonds, government bonds and derivatives.
Revised: We propose a general class of models for the simultaneous modeling of equity, corporate bonds, government bonds and derivatives.
Edit intent: clarity
Original: We propose a general class of models for the simultaneous treatment of equity, corporate bonds, government bonds and derivatives.
Revised: We propose a general class of models for the simultaneous treatment of equity, government bonds, corporate bonds and derivatives.
Edit intent: fluency
Original:  The noise is generated by a general affine Markov process.
Revised:  Uncertainty is generated by a general affine Markov process.
Edit intent: clarity
Original:  The framework allows for stochastic volatility, jumps, the possibility of default and correlations between different assets.
Revised:  The setting allows for stochastic volatility, jumps, the possibility of default and correlations between different assets.
Edit intent: clarity
Original:  The framework allows for stochastic volatility, jumps, the possibility of default and correlations between different assets.
Revised:  The framework allows for stochastic volatility, jumps, the possibility of default and correlation between different assets.
Edit intent: fluency
Original:  We extend the notion of a discounted moment generation function of the log stock price to the case where the underlying can default and show how to calculate it in terms of a coupled system of generalized Riccati equations.
Revised:  We show how to calculate it in terms of a coupled system of generalized Riccati equations.
Edit intent: coherence
Original:  Other European payoffs can be approximated by a linear combination of  power payoffs and vanilla options.
Revised:  Other European payoffs can be approximated with a linear combination of power payoffs and vanilla options.
Edit intent: fluency
Original: Motivation : Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, bounded Petri nets, and agent-based models . Simulation is a common practice for analyzing discrete models, but many systems are far too large to capture all the relevant dynamical features through simulation alone.
Revised: Background : Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, bounded Petri nets, and agent-based models . Simulation is a common practice for analyzing discrete models, but many systems are far too large to capture all the relevant dynamical features through simulation alone.
Edit intent: coherence
Original: Motivation : Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, bounded Petri nets, and agent-based models . Simulation is a common practice for analyzing discrete models, but many systems are far too large to capture all the relevant dynamical features through simulation alone.
Revised: Motivation : Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models . Simulation is a common practice for analyzing discrete models, but many systems are far too large to capture all the relevant dynamical features through simulation alone.
Edit intent: clarity
Original:  Results: We convert discrete models into algebraic models and apply tools from computational algebra  to analyze their dynamics.
Revised:  Results: We convert discrete models into algebraic models , tools from computational algebra to analyze their dynamics.
Edit intent: coherence
Original:  The key feature of biological systems that is exploited by our algorithms is their sparsity: while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes .
Revised:  Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Results: A method for efficiently identifying attractors, and the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness, i.e., while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes .
Edit intent: clarity
Original: This paper studies neighbor discovery problem in wireless networks.
Revised: This paper studies the problem of neighbor discovery in wireless networks.
Edit intent: fluency
Original:  A novel scheme , called compressed neighbor discovery is proposed, which assigns each node a unique  signature and let  nodes simultaneously transmit their signatures during the discovery period.
Revised:  A novel paradigm , called compressed neighbor discovery is proposed, which assigns each node a unique signature and let nodes simultaneously transmit their signatures during the discovery period.
Edit intent: clarity
Original:  A novel scheme , called compressed neighbor discovery is proposed, which assigns each node a unique  signature and let  nodes simultaneously transmit their signatures during the discovery period.
Revised:  A novel scheme , called compressed neighbor discovery is proposed, which assigns each node a unique signature and let all nodes simultaneously transmit their signatures during the discovery period.
Edit intent: clarity
Original:  The query node then determines, based on the superposition of the signatures , a small number of nodes as its neighbors , out of a large number of nodes in the network .
Revised:  The query node then determines, based on the superposition of the signatures , a small number of ) neighbors out of a large number of nodes in the network .
Edit intent: clarity
Original:  The first scheme assigns sparse pseudo-random on-off signatures to the nodes, so that each node can listen to the channel during its own off-slots.
Revised:  The first scheme employs sparse pseudo-random on-off signatures to the nodes, so that each node can listen to the channel during its own off-slots.
Edit intent: clarity
Original:  Decoding using the chirp algorithm entails only sub-linear complexity, so the scheme is feasible for networks with 2^32 nodes or more.
Revised:  Decoding using the chirp algorithm is sub-linear complexity, so the scheme is feasible for networks with 2^32 nodes or more.
Edit intent: clarity
Original: This paper studies the problem of neighbor discovery in wireless networks  .
Revised: This paper studies neighbor discovery problem in wireless networks .
Edit intent: fluency
Original:  A novel paradigm, called compressed neighbor discovery is proposed, which enables all nodes to simultaneously discover their respective neighborhoods within a single frame of transmission.
Revised:  A novel paradigm, called compressed neighbor discovery is proposed, which enables all nodes to simultaneously discover their respective neighborhoods with a single frame of transmission.
Edit intent: clarity
Original:  To identify its (small number of) neighbors out of a large network address space, each node solves a sparse recovery problem.
Revised:  To identify its neighbors out of a large network address space, each node solves a sparse recovery problem.
Edit intent: clarity
Original:  The first scheme employs sparse pseudo-random on-off signatures, and each node discovers its neighbors by carrying out a simple noncoherent detection algorithm based on group testing.
Revised:  The first employs random on-off signatures, and each node discovers its neighbors by carrying out a simple noncoherent detection algorithm based on group testing.
Edit intent: clarity
Original:  The first scheme employs sparse pseudo-random on-off signatures, and each node discovers its neighbors by carrying out a simple noncoherent detection algorithm based on group testing.
Revised:  The first scheme employs sparse pseudo-random on-off signatures, and each node discovers its neighbors using a noncoherent detection algorithm based on group testing.
Edit intent: clarity
Original:  The second scheme uses deterministic signatures from a second order Reed-Muller code, which are converted to on-off signatures using random erasures, and applies a chirp algorithm for decoding .
Revised:  The second scheme uses on-off signatures based on a deterministic second-order Reed-Muller code, which are converted to on-off signatures using random erasures, and applies a chirp algorithm for decoding .
Edit intent: clarity
Original:  The second scheme uses deterministic signatures from a second order Reed-Muller code, which are converted to on-off signatures using random erasures, and applies a chirp algorithm for decoding .
Revised:  The second scheme uses deterministic signatures from a second order Reed-Muller code, and applies a chirp algorithm for decoding .
Edit intent: clarity
Original:  It is found that the latter scheme requires much lower signal-to-noise ratio (SNR) and  shorter frame to achieve the same error performance.
Revised:  It is found that the latter scheme requires much lower signal-to-noise ratio (SNR) and a shorter frame to achieve the same error performance.
Edit intent: fluency
Original:  Within a single frame of 4,096 symbols, nodes can discover their respective neighbors with on average 99.9 \% accuracy at 16 dB SNR. The complexity of the chirp  algorithm is sub-linear, so that it is  scalable to networks with billions of nodes with 48-bit  MAC addresses.
Revised:  Within a single frame of 4,096 symbols, nodes can discover their respective neighbors with on average 99.9 \% accuracy at 16 dB SNR. The complexity of the chirp algorithm is sub-linear, so that it is in principle scalable to networks with billions of nodes with 48-bit MAC addresses.
Edit intent: clarity
Original:  Within a single frame of 4,096 symbols, nodes can discover their respective neighbors with on average 99.9 \% accuracy at 16 dB SNR. The complexity of the chirp  algorithm is sub-linear, so that it is  scalable to networks with billions of nodes with 48-bit  MAC addresses.
Revised:  Within a single frame of 4,096 symbols, nodes can discover their respective neighbors with on average 99.9 \% accuracy at 16 dB SNR. The complexity of the chirp algorithm is sub-linear, so that it is scalable to networks with 48-bit MAC addresses.
Edit intent: clarity
Original:  The compressed neighbor discovery schemes are much more efficient than conventional random access discovery, where nodes transmit their respective NIAs over many frames with random delays to be discovered at least once without collision .
Revised:  The compressed neighbor discovery schemes are much more efficient than conventional random access discovery, where nodes have to retransmit over many frames with random delays to be discovered at least once without collision .
Edit intent: clarity
Original:  The compressed neighbor discovery schemes are much more efficient than conventional random access discovery, where nodes transmit their respective NIAs over many frames with random delays to be discovered at least once without collision .
Revised:  The compressed neighbor discovery schemes are much more efficient than conventional random access discovery, where nodes transmit their respective NIAs over many frames with random delays to be successfully discovered due to collisions .
Edit intent: clarity
Original: This paper studies neighbor discovery problem in wireless networks, namely, each node wishes to discover and identify the network interface addresses (NIAs) of those nodes within a single hop.
Revised: This paper studies the problem of neighbor discovery in wireless networks, namely, each node wishes to discover and identify the network interface addresses (NIAs) of those nodes within a single hop.
Edit intent: fluency
Original:  The second scheme needs much lower signal-to-noise ratio (SNR) and a shorter frame to achieve the same error performance.
Revised:  The second scheme needs much lower signal-to-noise ratio (SNR) to achieve the same error performance.
Edit intent: clarity