wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In this document , we focus on conversion of splines rather than going through the propertiesof them, i. e, converting the control points of a spline to the control points of another spline, which results in approximately the same curve, as the spline before conversion represents .
Revised:  In this document , we focus on conversion between cubic B\'ezier and Catmull-Rom curve segments, rather than going through the propertiesof them, i. e, converting the control points of a spline to the control points of another spline, which results in approximately the same curve, as the spline before conversion represents .
Edit intent: meaning-changed
Original:  In this document , we focus on conversion of splines rather than going through the propertiesof them, i. e, converting the control points of a spline to the control points of another spline, which results in approximately the same curve, as the spline before conversion represents .
Revised:  In this document , we focus on conversion of splines rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of a spline to the control points of another spline, which results in approximately the same curve, as the spline before conversion represents .
Edit intent: meaning-changed
Original:  In this document , we focus on conversion of splines rather than going through the propertiesof them, i. e, converting the control points of a spline to the control points of another spline, which results in approximately the same curve, as the spline before conversion represents .
Revised:  In this document , we focus on conversion of splines rather than going through the propertiesof them, i. e, converting the control points of either of the Catmull-Rom or B\'ezier cubic curves to a new set of control points, which corresponds to approximately the same curve, as the spline before conversion represents .
Edit intent: meaning-changed
Original:  In this document , we focus on conversion of splines rather than going through the propertiesof them, i. e, converting the control points of a spline to the control points of another spline, which results in approximately the same curve, as the spline before conversion represents .
Revised:  In this document , we focus on conversion of splines rather than going through the propertiesof them, i. e, converting the control points of a spline to the control points of another spline, which results in approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples .
Edit intent: meaning-changed
Original: Fat tails arise endogenously from modeling of price change based on  a quotient of arbitrarily correlated demand and supply (i.e., excess demand) whether or not jump discontinuities are present.
Revised: We show that the quotient of Levy processes of jump-diffusion type has a fat-tailed distribution. An application is to price theory in economics. We show that fat tails arise endogenously from modeling of price change based on a quotient of arbitrarily correlated demand and supply (i.e., excess demand) whether or not jump discontinuities are present.
Edit intent: meaning-changed
Original: Fat tails arise endogenously from modeling of price change based on  a quotient of arbitrarily correlated demand and supply (i.e., excess demand) whether or not jump discontinuities are present.
Revised: Fat tails arise endogenously from modeling of price change based on an excess demand analysis resulting in a quotient of arbitrarily correlated demand and supply (i.e., excess demand) whether or not jump discontinuities are present.
Edit intent: meaning-changed
Original:  If P^{-1}dP/dt (the relative price change in an interval dt) is given by a suitable function of  excess demand, \mathcal{D \left( \% -S}\right) /S -1 (where D and S are demand and supply), then the distribution has tail behavior F\left( x\right) \sim x^{-\zeta} for a power \zeta that depends on the function G in P^{-1}dP/dt=G\left( D/S\right) .
Revised:  If P^{-1}dP/dt (the relative price change in an interval dt) is given by a suitable function of relative excess demand, \mathcal{D \left( \% -S}\right) /S -1 (where D and S are demand and supply), then the distribution has tail behavior F\left( x\right) \sim x^{-\zeta} for a power \zeta that depends on the function G in P^{-1}dP/dt=G\left( D/S\right) .
Edit intent: fluency
Original:  If P^{-1}dP/dt (the relative price change in an interval dt) is given by a suitable function of  excess demand, \mathcal{D \left( \% -S}\right) /S -1 (where D and S are demand and supply), then the distribution has tail behavior F\left( x\right) \sim x^{-\zeta} for a power \zeta that depends on the function G in P^{-1}dP/dt=G\left( D/S\right) .
Revised:  If P^{-1}dP/dt (the relative price change in an interval dt) is given by a suitable function of excess demand, \left( \% -S}\right) /S -1 (where D and S are demand and supply), then the distribution has tail behavior F\left( x\right) \sim x^{-\zeta} for a power \zeta that depends on the function G in P^{-1}dP/dt=G\left( D/S\right) .
Edit intent: clarity
Original:  If P^{-1}dP/dt (the relative price change in an interval dt) is given by a suitable function of  excess demand, \mathcal{D \left( \% -S}\right) /S -1 (where D and S are demand and supply), then the distribution has tail behavior F\left( x\right) \sim x^{-\zeta} for a power \zeta that depends on the function G in P^{-1}dP/dt=G\left( D/S\right) .
Revised:  If P^{-1}dP/dt (the relative price change in an interval dt) is given by a suitable function of excess demand, \mathcal{D \left( \mathcal{D\% -S}\right) /S -1 (where D and S are demand and supply), then the distribution has tail behavior F\left( x\right) \sim x^{-\zeta} for a power \zeta that depends on the function G in P^{-1}dP/dt=G\left( D/S\right) .
Edit intent: fluency
Original:  If P^{-1}dP/dt (the relative price change in an interval dt) is given by a suitable function of  excess demand, \mathcal{D \left( \% -S}\right) /S -1 (where D and S are demand and supply), then the distribution has tail behavior F\left( x\right) \sim x^{-\zeta} for a power \zeta that depends on the function G in P^{-1}dP/dt=G\left( D/S\right) .
Revised:  If P^{-1}dP/dt (the relative price change in an interval dt) is given by a suitable function of excess demand, \mathcal{D \left( \% -S}\right) /S (where D and S are demand and supply), then the distribution has tail behavior F\left( x\right) \sim x^{-\zeta} for a power \zeta that depends on the function G in P^{-1}dP/dt=G\left( D/S\right) .
Edit intent: clarity
Original:  The value, q\tilde{=} \in\left[ 3,5\right] is in agreement with empirical data. While many theoretical explanations have been offered for the paradox of fat tails, we show that this issue never arises if one models price dynamics using basic economics methodology,  rather than the usual starting point for classical finance which assumes a normal distribution of price changes.
Revised:  The value, q\tilde{=} \in\left[ 3,5\right] for some markets. The discrepancy between the empirical result and theory never arises if one models price dynamics using basic economics methodology, rather than the usual starting point for classical finance which assumes a normal distribution of price changes.
Edit intent: clarity
Original:  While many theoretical explanations have been offered for the paradox of fat tails, we show that this issue never arises if one models price dynamics using basic economics methodology,  rather than the usual starting point for classical finance which assumes a normal distribution of price changes.
Revised:  While many theoretical explanations have been offered for the paradox of fat tails, we show that this issue never arises if one models price dynamics using basic economics methodology, i.e., generalized Walrasian adjustment, rather than the usual starting point for classical finance which assumes a normal distribution of price changes.
Edit intent: meaning-changed
Original:  The results establish a simple link between the decay exponent of the density function and the price adjustment function, a feature that can improve methodology for risk assessment  .
Revised:  The results establish a simple link between the decay exponent of the density function and the price adjustment function, a feature that can improve methodology for risk assessment . The mathematical results can be applied to other problems involving the relative difference or quotient of Levy processes of jump-diffusion type .
Edit intent: meaning-changed
Original:  We leveraged prior work regarding receptivity to JITAIs and deployed a chatbot-based digital coach  -- Walkie -- that provided physical-activity interventions and motivated participants to achieve their step goals.
Revised:  We leveraged prior work regarding receptivity to JITAIs and deployed a chatbot-based digital coach ~ -- Walkie -- that provided physical-activity interventions and motivated participants to achieve their step goals.
Edit intent: fluency
Original:  We leveraged prior work regarding receptivity to JITAIs and deployed a chatbot-based digital coach  -- Walkie -- that provided physical-activity interventions and motivated participants to achieve their step goals.
Revised:  We leveraged prior work regarding receptivity to JITAIs and deployed a chatbot-based digital coach -- Ally~ -- that provided physical-activity interventions and motivated participants to achieve their step goals.
Edit intent: meaning-changed
Original:  The Walkie app included two types of machine-learning model that used contextual information about a person to predict when a person is receptive: a static model that was built before the study started and remained constant for all participants and an adaptive model that continuously learned the receptivity of individual participants and updated itself as the study progressed.
Revised:  We extended the original Ally~app to include two types of machine-learning model that used contextual information about a person to predict when a person is receptive: a static model that was built before the study started and remained constant for all participants and an adaptive model that continuously learned the receptivity of individual participants and updated itself as the study progressed.
Edit intent: meaning-changed
Original:  The Walkie app included two types of machine-learning model that used contextual information about a person to predict when a person is receptive: a static model that was built before the study started and remained constant for all participants and an adaptive model that continuously learned the receptivity of individual participants and updated itself as the study progressed.
Revised:  The Walkie app included two types of machine-learning model that used contextual information about a person to predict when a person is receptive: a static model\/ that was built before the study started and remained constant for all participants and an adaptive model that continuously learned the receptivity of individual participants and updated itself as the study progressed.
Edit intent: clarity
Original:  The Walkie app included two types of machine-learning model that used contextual information about a person to predict when a person is receptive: a static model that was built before the study started and remained constant for all participants and an adaptive model that continuously learned the receptivity of individual participants and updated itself as the study progressed.
Revised:  The Walkie app included two types of machine-learning model that used contextual information about a person to predict when a person is receptive: a static model that was built before the study started and remained constant for all participants and an adaptive model\/ that continuously learned the receptivity of individual participants and updated itself as the study progressed.
Edit intent: clarity
Original:  We observed that the machine-learning models led up to a 40 \% improvement in receptivity as compared to the control model. Further, we evaluated the temporal dynamics of the different models and observed that receptivity to messages from the adaptive \\%DIF > improvement in receptivity as compared to the control model.
Revised:  We observed that the machine-learning models led up to a 40 \\%DIF > improvement in receptivity as compared to the control model.
Edit intent: coherence
Original:  To address this challenge, this paper proposes a Reachability-based Trajectory Safeguard (RTS), which leverages trajectory parameterization and reachability analysis to ensure safety while a policy is being learned.
Revised:  To address this challenge, this paper proposes a Reachability-based Trajectory Safeguard (RTS), which leverages reachability analysis to ensure safety while a policy is being learned.
Edit intent: clarity
Original:  To address this challenge, this paper proposes a Reachability-based Trajectory Safeguard (RTS), which leverages trajectory parameterization and reachability analysis to ensure safety while a policy is being learned. This method ensures a robot with continuous action space can be trained from scratch safely in real-time. Importantly, this safety layer can still be applied after a policy has been learned .
Revised:  To address this challenge, this paper proposes a Reachability-based Trajectory Safeguard (RTS), which leverages trajectory parameterization and reachability analysis to ensure safety during training and operation. Given a known (but uncertain) model of a robot, RTS precomputes a Forward Reachable Set of the robot tracking a continuum of parameterized trajectories. At runtime, the RL agent selects from this continuum in a receding-horizon way to control the robot; the FRS is used to identify if the agent's choice is safe or not, and to adjust unsafe choices .
Edit intent: meaning-changed
Original:  The efficacy of this method is illustrated on three nonlinear robot models, including a 12-D quadrotor drone, in simulation . By ensuring safety with RTS, this paper demonstrates that the proposed algorithm is not only safe , but can achieve a higher reward in a considerably shorter training time when compared to a non-safe counterpart .
Revised:  The efficacy of this method is illustrated on three nonlinear robot models, including a 12-D quadrotor drone, in simulation and in comparison with state-of-the-art safe motion planning methods .
Edit intent: clarity
Original:  Also, we are able to solve a special case of the DkSReg(n, k, d, \delta, \gamma) model introduced in [KL20], when the planted subgraph G S is a clique  .
Revised:  Also, we are able to solve special cases of the DkSReg(n, k, d, \delta, \gamma) model introduced in [KL20], when the planted subgraph G S is a clique .
Edit intent: fluency
Original:  Also, we are able to solve a special case of the DkSReg(n, k, d, \delta, \gamma) model introduced in [KL20], when the planted subgraph G S is a clique  .
Revised:  Also, we are able to solve a special case of the DkSReg(n, k, d, \delta, \gamma) and DkSReg(n, k, d, \delta, d', \lambda) models introduced in [KL20], when the planted subgraph G S is a clique .
Edit intent: meaning-changed
Original:  Also, we are able to solve a special case of the DkSReg(n, k, d, \delta, \gamma) model introduced in [KL20], when the planted subgraph G S is a clique  .
Revised:  Also, we are able to solve a special case of the DkSReg(n, k, d, \delta, \gamma) model introduced in [KL20], when the planted subgraph S is a clique .
Edit intent: clarity
Original:  Also, we are able to solve a special case of the DkSReg(n, k, d, \delta, \gamma) model introduced in [KL20], when the planted subgraph G S is a clique  .
Revised:  Also, we are able to solve a special case of the DkSReg(n, k, d, \delta, \gamma) model introduced in [KL20], when the planted subgraph G \mathcal{G is a clique .
Edit intent: meaning-changed
Original:  Also, we are able to solve a special case of the DkSReg(n, k, d, \delta, \gamma) model introduced in [KL20], when the planted subgraph G S is a clique  .
Revised:  Also, we are able to solve a special case of the DkSReg(n, k, d, \delta, \gamma) model introduced in [KL20], when the planted subgraph G S is a clique instead of an arbitrary d-regular graph .
Edit intent: meaning-changed
Original:  Our model is inspired from the Feige-Kilian model [FK01] which has been studied in many other works [  Ste17, MMT20]  . Our algorithm and analysis is on similar lines to the one studied for the Densest k-subgraph problem in the recent work of Khanna and Louis [KL20].
Revised:  Our model is inspired from the Feige-Kilian model [FK01] which has been studied in many other works [ FK00, Ste17, MMT20] . Our algorithm and analysis is on similar lines to the one studied for the Densest k-subgraph problem in the recent work of Khanna and Louis [KL20].
Edit intent: meaning-changed
Original:  Our model is inspired from the Feige-Kilian model [FK01] which has been studied in many other works [  Ste17, MMT20]  . Our algorithm and analysis is on similar lines to the one studied for the Densest k-subgraph problem in the recent work of Khanna and Louis [KL20].
Revised:  Our model is inspired from the Feige-Kilian model [FK01] which has been studied in many other works [ Ste17, MMT20] for a variety of graph problems . Our algorithm and analysis is on similar lines to the one studied for the Densest k-subgraph problem in the recent work of Khanna and Louis [KL20].
Edit intent: meaning-changed
Original:  Also, we are able to solve special cases of the DkSReg(n, k, d, \delta, \gamma) and DkSReg(n, k, d, \delta, d', \lambda) models introduced in [KL20], when the planted subgraph \mathcal{G is a clique instead of an arbitrary d-regular graph.
Revised:  Also, we are able to solve special cases of the models introduced for the Densest k-subgraph problem in [KL20], when the planted subgraph \mathcal{G is a clique instead of an arbitrary d-regular graph.
Edit intent: meaning-changed
Original:  Also, we are able to solve special cases of the DkSReg(n, k, d, \delta, \gamma) and DkSReg(n, k, d, \delta, d', \lambda) models introduced in [KL20], when the planted subgraph \mathcal{G is a clique instead of an arbitrary d-regular graph.
Revised:  Also, we are able to solve special cases of the DkSReg(n, k, d, \delta, \gamma) and DkSReg(n, k, d, \delta, d', \lambda) models introduced in [KL20], when the planted subgraph is a clique instead of an arbitrary d-regular graph.
Edit intent: meaning-changed
Original:  In contrast to previous works that directly map from local appearance to 3D angles, we explore a progressive approach by extracting meaningful Intermediate Geometrical Representations (IGRs) for 3D pose estimation.
Revised:  In contrast to previous works that map from local appearance to 3D angles, we explore a progressive approach by extracting meaningful Intermediate Geometrical Representations (IGRs) for 3D pose estimation.
Edit intent: clarity
Original:  In contrast to previous works that directly map from local appearance to 3D angles, we explore a progressive approach by extracting meaningful Intermediate Geometrical Representations (IGRs) for 3D pose estimation.
Revised:  In contrast to previous works that directly map from local appearance to observation angles, we explore a progressive approach by extracting meaningful Intermediate Geometrical Representations (IGRs) for 3D pose estimation.
Edit intent: clarity
Original:  In contrast to previous works that directly map from local appearance to 3D angles, we explore a progressive approach by extracting meaningful Intermediate Geometrical Representations (IGRs) for 3D pose estimation. We design a deep model that transforms perceived intensities to IGRs, which are mapped to a 3D representation encoding object orientation in the camera coordinate system.
Revised:  In contrast to previous works that directly map from local appearance to 3D angles, we explore a progressive approach by extracting meaningful Intermediate Geometrical Representations (IGRs) to estimate egocentric vehicle orientation. This approach features a deep model that transforms perceived intensities to IGRs, which are mapped to a 3D representation encoding object orientation in the camera coordinate system.
Edit intent: meaning-changed
Original:  However,  the limited storage and computing resources of mobile devices cannot meet the real-time requirements of deep neural network computing.
Revised:  However, pandemics like covid-19 require deep learning capabilities at mobile devices (detect respiratory rate using mobile robotics or conduct CT scan using a mobile scanner), which are severely constrained by the limited storage and computing resources of mobile devices cannot meet the real-time requirements of deep neural network computing.
Edit intent: meaning-changed
Original:  However,  the limited storage and computing resources of mobile devices cannot meet the real-time requirements of deep neural network computing. In this paper , we propose a safer respiratory rate monitoring system using a three-tier architecture : robot layers, edge layers, and cloud layers.
Revised:  However, the limited storage and computation resources at the device level. To solve this problem , we propose a safer respiratory rate monitoring system using a three-tier architecture : robot layers, edge layers, and cloud layers.
Edit intent: clarity
Original:  In this paper , we propose a safer respiratory rate monitoring system using a three-tier architecture : robot layers, edge layers, and cloud layers. We decompose the task into a three-tier architecture of a lightweight network according to the computing resources of different devices, including mobile robots, edges, and clouds. We deploy feature extraction tasks, Spatio-temporal feature tracking tasks, and signal extraction and preprocessing tasks to robot layers, edge layers, and cloud layers , respectively.
Revised:  In this paper , we propose a safer respiratory rate monitoring system using a three-tier architecture , including robot layers, edge layers, and cloud layers , respectively.
Edit intent: coherence
Original:  We deploy feature extraction tasks, Spatio-temporal feature tracking tasks, and signal extraction and preprocessing tasks to robot layers, edge layers, and cloud layers , respectively. We have deployed this non-contact respiratory monitoring system in the Second Affiliated Hospital of the Anhui Medical University of China . Experimental results  show that the proposed approach in this paper significantly outperforms other approaches.
Revised:  We deploy feature extraction tasks, Spatio-temporal feature tracking tasks, and signal extraction and preprocessing tasks to robot layers, edge layers, and cloud layers . We adopt this architecture to design a non-contact respiratory monitoring system in the Second Affiliated Hospital of the Anhui Medical University of China . Experimental results show that the proposed approach in this paper significantly outperforms other approaches.
Edit intent: meaning-changed
Original:  We have deployed this non-contact respiratory monitoring system in the Second Affiliated Hospital of the Anhui Medical University of China . Experimental results  show that the proposed approach in this paper significantly outperforms other approaches.
Revised:  We have deployed this non-contact respiratory monitoring system in the Second Affiliated Hospital of the Anhui Medical University of China . Experimental results of respiratory rate monitoring show that the proposed approach in this paper significantly outperforms other approaches.
Edit intent: meaning-changed
Original:  It is supported by the computation time cost of robot+edge+cloud architecture, which are 2.26 ms per frame, 27.48 ms per frame, 0.78 seconds for  processing one-minute length respiratory signals, respectively.
Revised:  It is supported by computation time costs with 2.26 ms per frame, 27.48 ms per frame, 0.78 seconds for processing one-minute length respiratory signals, respectively.
Edit intent: clarity