wanyu/IteraTeR_v2 huggingface dataset:
Original:  The splinets exploit nearly orthogonalization featured by the B-splines themselves and through this gains are achieved at two levels: a locality that is exhibited through small size of the total support of a splinet and computational efficiency that follows from a small number of orthogonalization procedures needed to be performed on the B-splines to reach orthogonality.
Revised:  They efficiently exploit 'near-orthogonalization' featured by the B-splines themselves and through this gains are achieved at two levels: a locality that is exhibited through small size of the total support of a splinet and computational efficiency that follows from a small number of orthogonalization procedures needed to be performed on the B-splines to reach orthogonality.
Edit intent: clarity
Original:  The splinets exploit nearly orthogonalization featured by the B-splines themselves and through this gains are achieved at two levels: a locality that is exhibited through small size of the total support of a splinet and computational efficiency that follows from a small number of orthogonalization procedures needed to be performed on the B-splines to reach orthogonality.
Revised:  The splinets exploit nearly orthogonalization featured by the B-splines and gains are achieved at two levels: a locality that is exhibited through small size of the total support of a splinet and computational efficiency that follows from a small number of orthogonalization procedures needed to be performed on the B-splines to reach orthogonality.
Edit intent: clarity
Original:  The splinets exploit nearly orthogonalization featured by the B-splines themselves and through this gains are achieved at two levels: a locality that is exhibited through small size of the total support of a splinet and computational efficiency that follows from a small number of orthogonalization procedures needed to be performed on the B-splines to reach orthogonality.
Revised:  The splinets exploit nearly orthogonalization featured by the B-splines themselves and through this gains are achieved at two levels: locality that is exhibited through small size of the total support of a splinet and computational efficiency that follows from a small number of orthogonalization procedures needed to be performed on the B-splines to reach orthogonality.
Edit intent: fluency
Original:  In this paper, we consider a RIS-empowered downlink non-orthogonal multiple access (NOMA) network, where the beamforming vectors at the BS and the phase-shift matrix at the RIS are jointly optimized to minimize the total transmit power, taking into account the user ordering, the users' data rate requirements, and the reflecting elements' unit modulus constraints.
Revised:  In this paper, we consider an RIS-empowered downlink non-orthogonal multiple access (NOMA) network, where the beamforming vectors at the BS and the phase-shift matrix at the RIS are jointly optimized to minimize the total transmit power, taking into account the user ordering, the users' data rate requirements, and the reflecting elements' unit modulus constraints.
Edit intent: fluency
Original:  To this end, we present an alternating optimization framework to decouple the optimization variables and transform the quadratic programming problem in each alternation into a fixed-rank matrix optimization problem via matrix lifting.
Revised:  To this end, we present an alternating optimization framework to decouple the optimization variables and transform the quadratic programming problem in each alternating procedure into a fixed-rank matrix optimization problem via matrix lifting.
Edit intent: clarity
Original:  Simulation results demonstrate the effectiveness of deploying a RIS and the superiority of the proposed alternating DC algorithm in reducing the total transmit power.
Revised:  Simulation results demonstrate the effectiveness of deploying an RIS and the superiority of the proposed alternating DC algorithm in reducing the total transmit power.
Edit intent: fluency
Original:  By exploiting the difference between the nuclear norm and the spectral norm, we then propose a difference-of-convex (DC) function representation for the rank function to accurately detect the feasibility of the non-convex rank-one constraints .
Revised:  At the same time, to accurately detect the feasibility of the non-convex rank-one constraints .
Edit intent: coherence
Original:  To reduce the implementation complexity, we further propose a low-complexity user ordering scheme , where the ordering criterion is derived in closed-form  . Simulation results demonstrate the effectiveness of deploying an RIS and the superiority of the proposed alternating DC algorithm in reducing the total transmit power.
Revised:  To reduce the implementation complexity, we further propose a low-complexity user ordering scheme with closed-form . Simulation results demonstrate the effectiveness of deploying an RIS and the superiority of the proposed alternating DC algorithm in reducing the total transmit power.
Edit intent: coherence
Original:  To reduce the implementation complexity, we further propose a low-complexity user ordering scheme , where the ordering criterion is derived in closed-form  . Simulation results demonstrate the effectiveness of deploying an RIS and the superiority of the proposed alternating DC algorithm in reducing the total transmit power.
Revised:  To reduce the implementation complexity, we further propose a low-complexity user ordering scheme , where the ordering criterion is derived in closed-form . Simulation results will validate the effectiveness of deploying an RIS and the superiority of the proposed alternating DC algorithm in reducing the total transmit power.
Edit intent: clarity
Original:  To reduce the implementation complexity, we further propose a low-complexity user ordering scheme , where the ordering criterion is derived in closed-form  . Simulation results demonstrate the effectiveness of deploying an RIS and the superiority of the proposed alternating DC algorithm in reducing the total transmit power.
Revised:  To reduce the implementation complexity, we further propose a low-complexity user ordering scheme , where the ordering criterion is derived in closed-form . Simulation results demonstrate the effectiveness of deploying an RIS and the superiority of the proposed DC-based alternating optimization method in reducing the total transmit power.
Edit intent: clarity
Original:  By rigorous error analysis, we show that the scheme provides  second order accuracy in H^\gamma for initial data in H^{\gamma+4} for any \gamma\geq0, which is the lowest possible regularity requirement so far .
Revised:  By rigorous error analysis, we show that the scheme provides the second order accuracy in H^\gamma for initial data in H^{\gamma+4} for any \gamma\geq0, which is the lowest possible regularity requirement so far .
Edit intent: fluency
Original:  To address this issue, we introduce a comprehensive audio-to-spiking conversion procedure and provide two novel spike-based classification datasets.
Revised:  To address this issue, we introduce a general audio-to-spiking conversion procedure and provide two novel spike-based classification datasets.
Edit intent: clarity
Original:  To address this issue, we introduce a general audio-to-spiking conversion procedure and provide two novel spike-based classification datasets .
Revised:  To address this issue, we introduce two spike-based classification datasets .
Edit intent: clarity
Original: We study an optimization problem for a portfolio with a risk-free, a liquid risky , and an illiquid asset which is sold in an exogenous random moment of time with a prescribed liquidation time distribution.
Revised: We study an optimization problem for a portfolio with a risk-free, a liquid , and an illiquid asset which is sold in an exogenous random moment of time with a prescribed liquidation time distribution.
Edit intent: clarity
Original: We study an optimization problem for a portfolio with a risk-free, a liquid risky , and an illiquid asset which is sold in an exogenous random moment of time with a prescribed liquidation time distribution.
Revised: We study an optimization problem for a portfolio with a risk-free, a liquid risky , and an illiquid asset which is sold in an exogenous random moment with a prescribed liquidation time distribution.
Edit intent: fluency
Original:  The complete set of nonequivalent group invariant reductions to two dimensional PDEs is provided for the three dimensional PDE with the EXPn utility function in accordance with an optimal system of sub algebras of the admitted Lie algebra.
Revised:  The complete set of nonequivalent group invariant reductions to two dimensional PDEs according to an optimal system of sub algebras of the admitted Lie algebra.
Edit intent: clarity
Original:  We can use the reduced two dimensional PDE to study the properties of the optimal solution and the investment - consumption strategies .
Revised:  This reduction represents a significant simplification of the original problem .
Edit intent: coherence
Original:  Second, we prove thatgiven a rational measure, an optimal transport to a set of measures can be computed in polynomial time .
Revised:  Second, we prove thatgiven a rational measure, an optimal transport to a set of measures can be verified in polynomial time .
Edit intent: clarity
Original:  We propose two novel unsupervised approaches to generate acoustic embeddings by modelling of acoustic context  .
Revised:  Two novel unsupervised approaches to generate acoustic embeddings by modelling of acoustic context .
Edit intent: clarity
Original:  To evaluate the effectiveness of our approaches compared to prior work, we chose two tasks - phone classification and speaker recognition - and test on different TIMIT data sets.
Revised:  To evaluate the effectiveness of our approaches compared to prior work, two tasks are conducted -- phone classification and speaker recognition - and test on different TIMIT data sets.
Edit intent: clarity
Original:  To evaluate the effectiveness of our approaches compared to prior work, we chose two tasks - phone classification and speaker recognition - and test on different TIMIT data sets.
Revised:  To evaluate the effectiveness of our approaches compared to prior work, we chose two tasks - phone classification and speaker recognition -- and test on different TIMIT data sets.
Edit intent: fluency
Original:  Experimental results show that one of our proposed approaches outperforms phone classification baselines, yielding a classification accuracy of 74.1\%.
Revised:  Experimental results show that one of the proposed approaches outperforms phone classification baselines, yielding a classification accuracy of 74.1\%.
Edit intent: fluency
Original:  When using additional out-of-domain data for training, an additional 2-3 \% improvements can be obtained, for both for phone classification and speaker recognition tasks.
Revised:  When using additional out-of-domain data for training, an additional 3 \% improvements can be obtained, for both for phone classification and speaker recognition tasks.
Edit intent: clarity
Original:  A great deal of attention has been devoted to the community detection problem in multiplex networks, that is, revealing meaningful patterns of node groupings into communities by considering different types of interactions among them.
Edit intent: coherence
Original:  In this article , we provide the reader with a taxonomy on the community detection algorithms in multiplex networks.
Revised:  In this article we provide a taxonomy of community detection algorithms in multiplex networks.
Edit intent: coherence
Original:  We then provide an extensive  evaluation of the reviewed methods according to different criteria trying to answer three main questions , to what extent the evaluated methods are able to detect ground truth communities, to what extent different methods produce similar community structures and to what extent the evaluated methods are scalable.
Revised:  We then provide an extensive evaluation of the reviewed methods to answer three main questions , to what extent the evaluated methods are able to detect ground truth communities, to what extent different methods produce similar community structures and to what extent the evaluated methods are scalable.
Edit intent: coherence
Original:  We then provide an extensive  evaluation of the reviewed methods according to different criteria trying to answer three main questions , to what extent the evaluated methods are able to detect ground truth communities, to what extent different methods produce similar community structures and to what extent the evaluated methods are scalable.
Revised:  We then provide an extensive evaluation of the reviewed methods according to different criteria trying to answer three main questions : to what extent the evaluated methods are able to detect ground truth communities, to what extent different methods produce similar community structures and to what extent the evaluated methods are scalable.
Edit intent: fluency
Original:  We then provide an extensive  evaluation of the reviewed methods according to different criteria trying to answer three main questions , to what extent the evaluated methods are able to detect ground truth communities, to what extent different methods produce similar community structures and to what extent the evaluated methods are scalable.
Revised:  We then provide an extensive evaluation of the reviewed methods according to different criteria trying to answer three main questions , to what extent the evaluated methods are able to detect ground-truth communities, to what extent different methods produce similar community structures and to what extent the evaluated methods are scalable.
Edit intent: fluency
Original:  The ultimate goal of this survey is to drive scholars and practitioners in choosing the right method for the data and the task at hand  .
Revised:  One goal of this survey is to drive scholars and practitioners in choosing the right method for the data and the task at hand .
Edit intent: clarity
Original:  The ultimate goal of this survey is to drive scholars and practitioners in choosing the right method for the data and the task at hand  .
Revised:  The ultimate goal of this survey is to help scholars and practitioners in choosing the right method for the data and the task at hand .
Edit intent: clarity
Original:  The ultimate goal of this survey is to drive scholars and practitioners in choosing the right method for the data and the task at hand  .
Revised:  The ultimate goal of this survey is to drive scholars and practitioners to choose the right methods for the data and the task at hand .
Edit intent: fluency
Original: We consider a one-spatial dimensional tumour growth model  that consists of three variables;
Revised: We consider a one--spatial dimensional tumour growth model that consists of three variables;
Edit intent: fluency
Original:  The model variables form a coupled system of semi-linear advection equation (hyperbolic), simplified stationary Stokes equation (elliptic), and linear diffusion equation (parabolic) with appropriate conditions on the time-dependent boundary  which is governed by an ordinary differential equation.
Revised:  The model variables satisfy a coupled system of semi-linear advection equation (hyperbolic), simplified stationary Stokes equation (elliptic), and linear diffusion equation (parabolic) with appropriate conditions on the time-dependent boundary which is governed by an ordinary differential equation.
Edit intent: clarity
Original:  The model variables form a coupled system of semi-linear advection equation (hyperbolic), simplified stationary Stokes equation (elliptic), and linear diffusion equation (parabolic) with appropriate conditions on the time-dependent boundary  which is governed by an ordinary differential equation.
Revised:  The model variables form a coupled system of semilinear advection equation (hyperbolic), simplified stationary Stokes equation (elliptic), and linear diffusion equation (parabolic) with appropriate conditions on the time-dependent boundary which is governed by an ordinary differential equation.
Edit intent: clarity
Original:  The model variables form a coupled system of semi-linear advection equation (hyperbolic), simplified stationary Stokes equation (elliptic), and linear diffusion equation (parabolic) with appropriate conditions on the time-dependent boundary  which is governed by an ordinary differential equation.
Revised:  The model variables form a coupled system of semi-linear advection equation (hyperbolic), simplified linear Stokes equation (elliptic), and linear diffusion equation (parabolic) with appropriate conditions on the time-dependent boundary which is governed by an ordinary differential equation.
Edit intent: clarity
Original:  The model variables form a coupled system of semi-linear advection equation (hyperbolic), simplified stationary Stokes equation (elliptic), and linear diffusion equation (parabolic) with appropriate conditions on the time-dependent boundary  which is governed by an ordinary differential equation.
Revised:  The model variables form a coupled system of semi-linear advection equation (hyperbolic), simplified stationary Stokes equation (elliptic), and linear diffusion equation (parabolic) with appropriate conditions on the time-dependent boundary , which is governed by an ordinary differential equation.
Edit intent: fluency
Original:  An equivalent formulation in a fixed domain is used to overcome the difficulty associated with the time-dependent boundary in the original model.
Revised:  We employ a reformulation of the model defined in a larger, fixed time-space domain to overcome some theoretical difficulties related to the time-dependent boundary in the original model.
Edit intent: clarity
Original:  Though this reduces complexity of the model , the tight coupling between the component equationsand their non-linear nature offer challenges in proving suitablea priori estimates.
Revised:  Though this reduces complexity of the model a priori estimates.
Edit intent: clarity
Original:  We establish the existence of a time interval (0,T_{\ast}) over which the convergence of the scheme using compactness techniques is proved, thus proving the existence of a solution.
Revised:  We establish the existence of a time interval (0,T_{\ast}) over which , using compactness techniques is proved, thus proving the existence of a solution.
Edit intent: clarity
Original: Astroturfing attacks use automated accounts to artificially propel a chosen keyword to the top of Twitter trending topics.
Revised: Astroturfing attacks use automated accounts to artificially propel a chosen keywords to the top of Twitter trending topics.
Edit intent: fluency
Original:  Our results aid in understanding user manipulation on social media and more generally shed light on the type of adversarial behavior that arises to evade detection.
Revised:  Our results aid in understanding user manipulation on social media and more generally shed light on the types of adversarial behavior that arises to evade detection.
Edit intent: fluency
Original:  Our results aid in understanding user manipulation on social media and more generally shed light on the type of adversarial behavior that arises to evade detection.
Revised:  Our results aid in understanding user manipulation on social media and more generally shed light on the type of adversarial behavior that arise to evade detection.
Edit intent: fluency
Original:  Trends astroturfed by these attacks account for at least 20\% of top 10 global trends.
Revised:  Trends astroturfed by these attacks account for at least 20\% of top 10 world trends.
Edit intent: clarity
Original: We uncover and study ongoing ephemeral astroturfing attacks in which many automatically generated tweets are posted by a collection of fake and compromised accounts and then deleted immediately to artificially propel a chosen keywords to the top of Twitter trends .
Revised: We uncover and study ongoing ephemeral astroturfing attacks . In this attack, a chosen keyword or topic is artificially promoted by coordinated and inauthentic activity to appear popular, and, crucially, this activity is removed as part of the attack .
Edit intent: coherence
Original:  We observe such attacks in the wild and determine that they are not only quite successful in pushing a keyword to trends but also extremely prevalent .
Revised:  We observe such attacks in the wild and determine that they are not only successful but also pervasive .
Edit intent: clarity
Original:  Trends astroturfed by these attacks account for at least 20\% of  top 10 world trends.
Revised:  Trends astroturfed by these attacks account for at least 20\% of the top 10 world trends.
Edit intent: fluency
Original:  Trends astroturfed by these attacks account for at least 20\% of  top 10 world trends.
Revised:  Trends astroturfed by these attacks account for at least 20\% of top 10 global trends.
Edit intent: clarity
Original:  Our results aid in understanding user manipulation on social media and more generally shed light on the types of adversarial behavior that arise to evade detection .
Revised:  Our results aid in understanding user manipulation on social media platforms and by extension the integrity of the platforms .
Edit intent: clarity
Original: In two-player repeated games, Zero-Determinant (ZD) strategies are a class of strategies that can enable a player to unilaterally enforce a linear payoff relation between her own and her opponent's payoff irrespective of the opponent's strategy.
Revised: In two-player repeated games, Zero-Determinant (ZD) strategies enable a player to unilaterally enforce a linear payoff relation between her own and her opponent's payoff irrespective of the opponent's strategy.
Edit intent: clarity
Original:  Necessary and sufficient conditions are derived for a linear relation to be enforceable by a ZD strategist in n-player social dilemmas , in which the expected number of rounds can be captured by a fixed and common discount factor (0<\delta<1) .
Revised:  Necessary and sufficient conditions are derived for a payoff relation to be enforceable by a ZD strategist in n-player social dilemmas , in which the expected number of rounds can be captured by a fixed and common discount factor (0<\delta<1) .
Edit intent: clarity
Original:  Necessary and sufficient conditions are derived for a linear relation to be enforceable by a ZD strategist in n-player social dilemmas , in which the expected number of rounds can be captured by a fixed and common discount factor (0<\delta<1) .
Revised:  Necessary and sufficient conditions are derived for a linear relation to be enforceable in multiplayer social dilemmas with a finite expected number of rounds can be captured by a fixed and common discount factor (0<\delta<1) .
Edit intent: clarity
Original:  Necessary and sufficient conditions are derived for a linear relation to be enforceable by a ZD strategist in n-player social dilemmas , in which the expected number of rounds can be captured by a fixed and common discount factor (0<\delta<1) .
Revised:  Necessary and sufficient conditions are derived for a linear relation to be enforceable by a ZD strategist in n-player social dilemmas , in which the expected number of rounds that is determined by a fixed and common discount factor (0<\delta<1) .
Edit intent: clarity
Original:  Thresholds exist for such a discount factor above which generous, extortionate and equalizer payoff relations can be enforced.
Revised:  Thresholds exist for such a discount factor above which desired payoff relations can be enforced.
Edit intent: clarity
Original:  For the first time in the studies of repeated games, ZD strategies are examined in the setting of finitely repeated n-player, two-action games.
Edit intent: coherence