wanyu/IteraTeR_v2 huggingface dataset:
Original:  Second, we show how Andreasen-Huge SABR can be combined with other well know analytic SABR formulae to allow consistent use in the non-arbitrage region .
Revised:  We test the analytic result in the application to the interest rate futures option market .
Edit intent: clarity
Original: The ongoing COVID-19 pandemic caused by SARS-CoV-2 virus, a highly contagious virus, affected most of the countries of Earth.
Revised: The ongoing COVID-19 pandemic has affected most of the countries of Earth.
Edit intent: coherence
Original:  It has become an epidemic outbreak with more than 22 million confirmed infections and above 750 thousand deaths worldwide.
Revised:  It has become a pandemic outbreak with more than 22 million confirmed infections and above 750 thousand deaths worldwide.
Edit intent: fluency
Original:  Mathematical models may help to explore the transmission dynamics and control of COVID-19 in the absence of an effective medicine or ready-to-use vaccine.
Edit intent: coherence
Original:  The system has an awareness free, disease-free equilibrium which is locally asymptotically stable.
Revised:  The local and global stability conditions for awareness free, disease-free equilibrium which is locally asymptotically stable.
Edit intent: clarity
Original:  Using Lyapunov function theory and LaSalle Invariance Principle, the DFE is shown globally asymptotically stable under some parametric conditions .
Revised:  Using Lyapunov function theory and LaSalle Invariance Principle, the DFE is shown globally asymptotically stable under some parametric constraints .
Edit intent: clarity
Original:  We have calibrated our proposed model parameters to fit daily cases and deaths from Colombia.
Revised:  We calibrate our proposed model parameters to fit daily cases and deaths from Colombia.
Edit intent: clarity
Original:  Yet, the very nature of frameworks used for generative modeling suggests that progress towards detecting deepfakes will enable more realistic deepfake generation.
Revised:  Yet, the adversarial nature of frameworks used for generative modeling suggests that progress towards detecting deepfakes will enable more realistic deepfake generation.
Edit intent: clarity
Original:  The second involves cryptography to maintain a tamper-proof and publicly-broadcasted record of all legitimate uses of the model.
Edit intent: coherence
Original:  We evaluate our approaches on the seminal example of face synthesis, demonstrating that our first approach achieves 97.62\% attribution accuracy, and is less sensitive to perturbations and adversarial examples.
Revised:  We evaluate our method on the seminal example of face synthesis, demonstrating that our first approach achieves 97.62\% attribution accuracy, and is less sensitive to perturbations and adversarial examples.
Edit intent: clarity
Original:  A key challenge in such networks is to provide predictable performance and adaptability in response to variations in link quality .
Revised:  A key challenge in such networks is to provide predictable performance and adaptability in response to link quality variations .
Edit intent: clarity
Original:  A salient feature of Recorp is that it provides predictable performance: a policy meets the end-to-end reliability and deadline of flows when  link quality exceeds a user-specified threshold.
Revised:  A salient feature of Recorp is that it provides predictable performance: a policy meets the end-to-end reliability and deadline of flows when the link quality exceeds a user-specified threshold.
Edit intent: fluency
Original:  conditional independence can be naturally expressed as a logical formula in this model.
Revised:  conditional independence can be directly captured as a logical formula in this model.
Edit intent: clarity
Original:  We consider the competitiveness of online algorithms in the random order input model (ROM) , when the offline vertices are weighted .
Revised:  We consider the competitiveness of online algorithms in the random order input model (ROM) .
Edit intent: clarity
Original:  If any one of the following three conditions is satisfied, then there is a conceptually simple deterministic greedy algorithm whose competitive ratio is 1-\frac{1{e}.
Revised:  {e}.
Edit intent: coherence
Original:  This implies that for population densities below a threshold , named Allee threshold, the population decreases instead of growing.
Revised:  This implies that for population densities below a threshold named Allee threshold, the population decreases instead of growing.
Edit intent: fluency
Original:  In a closed local population, this makes that environmental fluctuations always leads to extinction.
Revised:  In a closed local population, environmental fluctuations always leads to extinction.
Edit intent: coherence
Original:  In a closed local population, this makes that environmental fluctuations always leads to extinction.
Revised:  In a closed local population, this makes that environmental fluctuations always lead to extinction.
Edit intent: fluency
Original:  Our results show that close to global extinction patches where population density is high, low or extinct coexist (even for homogeneous habitats).
Revised:  Our results show that patches where population density is high, low or extinct coexist (even for homogeneous habitats).
Edit intent: clarity
Original:  Our results show that close to global extinction patches where population density is high, low or extinct coexist (even for homogeneous habitats).
Revised:  Our results show that close to global extinction patches where population is high, low or extinct coexist (even for homogeneous habitats).
Edit intent: clarity
Original:  The extinction threshold increases proportionally to the squared root of the dispersal rate, decreases with the Allee threshold, and it is maximum for characteristic dispersal distances much larger than the spatial scale of synchrony of environmental fluctuations.
Revised:  The extinction threshold is maximum for characteristic dispersal distances much larger than the spatial scale of synchrony of environmental fluctuations.
Edit intent: clarity
Original:  The  low-density population solution can be particularly interesting for future applications, as to understand non-recovery events after harvesting.
Revised:  The low-density population solution can allow understanding difficulties in recovery after harvesting.
Edit intent: clarity
Original:  This theoretical framework allows novel approaches to address the impact of other factors,  as habitat fragmentation , on the population resilience to environmental fluctuations.
Revised:  This theoretical framework provides a novel approach to address other factors, as habitat fragmentation , on the population resilience to environmental fluctuations.
Edit intent: clarity
Original:  This theoretical framework allows novel approaches to address the impact of other factors,  as habitat fragmentation , on the population resilience to environmental fluctuations.
Revised:  This theoretical framework allows novel approaches to address the impact of other factors, such as habitat fragmentation , on the population resilience to environmental fluctuations.
Edit intent: coherence
Original: We give the first approximate-near-neighbor data structure for time series under the continuous Fr\'echet distance.
Revised: We give the first approximate-near-neighbor data structures for time series under the continuous Fr\'echet distance.
Edit intent: fluency
Original:  Both of our data structures make use of the concept of signatures, which were originally introduced for the problem of clustering time series under the Fr\'echet distance.
Revised:  All of our data structures make use of the concept of signatures, which were originally introduced for the problem of clustering time series under the Fr\'echet distance.
Edit intent: fluency
Original: We give the first approximate-near-neighbor data structures for time series under the continuous Fr\'echet distance.
Revised: We study approximate-near-neighbor data structures for time series under the continuous Fr\'echet distance.
Edit intent: clarity
Original:  As an indicator of hardness, we show that for any data structure which achieves an approximation factor less than 2 and which supports curves of arclength at most L, uses a word size bounded by O(L^{1-\epsilon) for some constant \epsilon>0, and answers the query using only a constant number of probes, the number of words used to store the data structure must be at least L^{\Omega(k)}.
Revised:  ) for some constant \epsilon>0, and answers the query using only a constant number of probes, the number of words used to store the data structure must be at least L^{\Omega(k)}.
Edit intent: coherence
Original:  We investigate the existence and the computation time of schematic representations of the structure of such a graph where the main component is drawn as a disk, the vertices that take part in separation pairs are points on the boundary of the disk, and the small components are placed outside the disk and are represented as non-intersecting lunes connecting their separation ~ pairs.
Revised:  We investigate the existence and the computation time of schematic representations of the structure of such a graph where the main component is drawn as a disk, the vertices that take part in separation pairs are points on the boundary of the disk, and the small components are placed outside the disk and are represented as non-intersecting lunes connecting their separation pairs.
Edit intent: fluency
Original:  We map the problem of testing for the existence of such representations to the one of testing for the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time and pseudo-polynomial-time algorithms.
Revised:  We map the problem of testing for the existence of such representations to the one of testing for the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time algorithms.
Edit intent: clarity
Original:  Here we address quantitatively this issue using  an agent-based model to simulate a workplace with extrovert and introvert agent stereotypes that differ solely on their propensities to initiate a social interaction.
Revised:  Here we address quantitatively this issue using an agent-based model for a workplace composed of extrovert and introvert agent stereotypes that differ solely on their propensities to initiate a social interaction.
Edit intent: clarity
Original:  We find that the effects of curtailing social interactions depend on the proportion of the stereotypes in the working group: while the social restriction measures always have a negative impact on the productivity of groups composed predominantly of introverts, they may actually improve the productivity of groups composed predominantly of extroverts , which offers then an explanation for the paradox of productivity during quarantine  .
Revised:  We find that the effects of curtailing social interactions depend on the proportion of the stereotypes in the working group: while the social restriction measures always have a negative impact on the productivity of groups composed predominantly of introverts, they may actually improve the productivity of groups composed predominantly of extroverts . Our results offer a proof of concept that the paradox of productivity during quarantine .
Edit intent: coherence
Original: We consider a problem of optimal placement of concentrated masses along a weightless elastic column (rod) that is clamped at one end and loaded by a nonconservative follower force at the free end.
Revised: We consider the problem of optimal placement of concentrated masses along a weightless elastic column (rod) that is clamped at one end and loaded by a nonconservative follower force at the free end.
Edit intent: fluency
Original: We consider a problem of optimal placement of concentrated masses along a weightless elastic column (rod) that is clamped at one end and loaded by a nonconservative follower force at the free end.
Revised: We consider a problem of optimal placement of concentrated masses along a massless elastic column that is clamped at one end and loaded by a nonconservative follower force at the free end.
Edit intent: clarity
Original:  By definition, the measures possess useful properties and can often be computed fast .
Revised:  By definition, the measures possess useful properties and can often be computed quickly .
Edit intent: clarity
Original:  The discrepancy theory, which deals with finding a bi-coloring of a set system such that the coloring of each set is balanced, has a huge number of applications in approximation algorithm design.
Revised:  Discrepancy theory, which deals with finding a bi-coloring of a set system such that the coloring of each set is balanced, has a huge number of applications in approximation algorithm design.
Edit intent: coherence
Original:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Revised:  A classical theorem of Spencer [ Che52 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Edit intent: fluency
Original:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Revised:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements will have discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Edit intent: clarity
Original:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Revised:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n \log n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Edit intent: fluency
Original:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Revised:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomials dates back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Edit intent: fluency
Original:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Revised:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century when used to solve PDEs by G{\aa}rding [G{\aa}r59] for solving PDEs .
Edit intent: coherence
Original:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] for solving PDEs .
Revised:  A classical theorem of Spencer [ Spe85 ] shows that any set system with n sets and n elements has discrepancy O( \sqrt{n [ Che52 ] only gives O(\sqrt{n \log n . The study of hyperbolic polynomial is dating back to the early 20th century , due to G{\aa}rding [G{\aa}r59] .
Edit intent: coherence
Original:  In particular, the breakthrough result by Marcus, Spielman, and Srivastava [MSS15] uses the theory of hyperbolic polynomial to prove the Kadison-Singer conjecture [KS59], which is closely related to the discrepancy theory.
Revised:  In particular, the breakthrough result by Marcus, Spielman, and Srivastava [MSS15] uses the theory of hyperbolic polynomials to prove the Kadison-Singer conjecture [KS59], which is closely related to the discrepancy theory.
Edit intent: fluency
Original:  In particular, the breakthrough result by Marcus, Spielman, and Srivastava [MSS15] uses the theory of hyperbolic polynomial to prove the Kadison-Singer conjecture [KS59], which is closely related to the discrepancy theory.
Revised:  In particular, the breakthrough result by Marcus, Spielman, and Srivastava [MSS15] uses the theory of hyperbolic polynomial to prove the Kadison-Singer conjecture [KS59], which is closely related to discrepancy theory.
Edit intent: fluency
Original:  The classical matrix Chernoff and discrepancy results are based on determinant polynomial which is a special case of hyperbolic polynomial .
Revised:  The classical matrix Chernoff and discrepancy results are based on determinant polynomial .
Edit intent: clarity
Original:  We also provide an approximate solution, for arbitrary programs.
Revised:  We also provide a kind of approximate solution, for arbitrary programs.
Edit intent: clarity
Original:  We demonstrate our approach on the challenging Replica environments of real-world 3D scenes  .
Revised:  We demonstrate our approach on two challenging datasets of real-world 3D scenes .
Edit intent: clarity
Original:  In this paper, we propose GraphReach, a position-aware GNN framework that captures the global positioning of nodes with respect to a set of fixed nodes , referred to as anchors.
Revised:  In this paper, we propose GraphReach, a position-aware , inductive GNN. GraphReach captures the global positioning of nodes with respect to a set of fixed nodes , referred to as anchors.
Edit intent: clarity
Original:  In this paper, we propose GraphReach, a position-aware GNN framework that captures the global positioning of nodes with respect to a set of fixed nodes , referred to as anchors.
Revised:  In this paper, we propose GraphReach, a position-aware GNN framework that captures the global positioning of nodes with respect to a set of nodes called anchors.
Edit intent: clarity
Original: Learning feature space node embeddings that encode the position of a node within the context of a graph is useful in several graph prediction tasks.
Edit intent: coherence
Original:  Consequently, two nodes that are vastly distant but located in similar local neighborhoods would map to similar embeddings  .
Revised:  Consequently, two nodes that are vastly distant but located in similar local neighborhoods map to similar embeddings .
Edit intent: clarity
Original:  This limitation may prevent accurate performance in predictive tasks that rely on position information.
Revised:  This limitation prevents accurate performance in predictive tasks that rely on position information.
Edit intent: clarity
Original:  The anchors are strategically selected so that the reachability estimations across all  nodes are maximized.
Revised:  The anchors are strategically selected so that reachability estimations across all nodes are maximized.
Edit intent: fluency
Original:  The anchors are strategically selected so that the reachability estimations across all  nodes are maximized.
Revised:  The anchors are strategically selected so that the reachability estimations across all the nodes are maximized.
Edit intent: fluency
Original:  We show that this combinatorial anchor selection problem is NP-hard and  consequently, develop a greedy (1-1/e) approximation .
Revised:  We show that this combinatorial anchor selection problem is NP-hard and , consequently, develop a greedy (1-1/e) approximation .
Edit intent: fluency
Original:  In addition, GraphReach is more robust against adversarial attacks.
Revised:  In addition, it is more robust against adversarial attacks.
Edit intent: clarity
Original:  In addition, GraphReach is more robust against adversarial attacks.
Revised:  In addition, GraphReach is more robust to adversarial attacks.
Edit intent: fluency
Original: The probabilistic Boolean network plays a remarkable role in the modelling and control of gene regulatory networks.
Revised: Probabilistic Boolean Networks play a remarkable role in the modelling and control of gene regulatory networks.
Edit intent: fluency
Original:  There are several works aiming to give a scalable and exact method for the decomposition .
Revised:  There are several works aiming to design a scalable algorithm to compute exact treedepth decompositions .
Edit intent: clarity
Original:  For optimal functioning, particularly as sensors, the length of a specific protrusion must not cross a narrow band bounded by two thresholds.
Revised:  For proper functioning, particularly as sensors, the length of a specific protrusion must not cross a narrow band bounded by two thresholds.
Edit intent: clarity
Original: The functional consequences of convenient size of subcellular structures have been analysed in the past and currently the questions regarding the underlying physical mechanisms for their genesis, the sensing of their size by the cell and maintenance of their convenient size in the steady state are receiving much attention.
Edit intent: coherence
Original:  Long cell protrusions, which are effectively one-dimensional, are highly dynamic subcellular structures and their length keep fluctuating about the mean length even in the the steady state.
Revised:  Long cell protrusions, which are effectively one-dimensional, are highly dynamic subcellular structures . Length of many such protrusions keep fluctuating about the mean length even in the the steady state.
Edit intent: clarity
Original:  Long cell protrusions, which are effectively one-dimensional, are highly dynamic subcellular structures and their length keep fluctuating about the mean length even in the the steady state.
Revised:  Long cell protrusions, which are effectively one-dimensional, are highly dynamic subcellular structures and their length keep fluctuating about the mean value even in the the steady state.
Edit intent: clarity
Original: To overcome these problems, we present FastORB-SLAM which is light-weight and efficient as it tracks keypoints between adjacent frames without computing descriptors.
Revised: To overcome these problems, we present FastORB-SLAM which is lightweight and efficient as it tracks keypoints between adjacent frames without computing descriptors.
Edit intent: fluency
Original:  To achieve this, a two-stage coarse-to-fine descriptor independent keypoint matching method is proposed based on sparse optical flow.
Revised:  To achieve this, a two stage coarse-to-fine descriptor independent keypoint matching method is proposed based on sparse optical flow.
Edit intent: fluency
Original:  In the first stage, we first predict initial keypoint correspondences via a uniform acceleration motion model and then robustly establish the correspondences via a pyramid-based sparse optical flow tracking method .
Revised:  In the first stage, we predict initial keypoint correspondences via a uniform acceleration motion model and then robustly establish the correspondences via a pyramid-based sparse optical flow tracking method .
Edit intent: coherence